-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
      name:  <unnamed>
       log:  E_Logfile.log
  log type:  text
 opened on:  15 Apr 2025, 19:56:15

. 
. ********************************************************************************
. ** GENERATING VARIABLES FOR DATA ANALYSIS
. ********************************************************************************
. 
. ** RENAMING OF VARIABLES (IN RAW DATA) CONSISTENT WITH VARIABLE NAMES IN MANUSCRIPT
. rename allotreatment usetreatment

.         label var usetreatment "useTreatment"

. rename allotreatmentname usetreatmentname

.         label var usetreatmentname "useTreatmentName"

. rename proptreatment designtreatment

.         label var designtreatment "designTreatment"

. rename proptreatmentname designtreatmentname

.         label var designtreatmentname "designTreatmentName"

. 
. ** TREATMENT VARIABLES (IN ROUNDS 2 THROUGH 9 BASED ON ROUND 1)
. // Design (Self-Including = 0, Self-Excluding = 1)
.         bysort playernr (period): replace designtreatment = designtreatment[_n-1] if period>1
(1,600 real changes made)

. // Recoding of Use (Formulaic Use = 0, Discretionary Use = 1) Consistent with Description in the Manuscript
. replace usetreatment = (usetreatment - 1) * (-1)
(200 real changes made)

.         bysort playernr (period): replace usetreatment = usetreatment[_n-1] if period>1
(1,600 real changes made)

. 
. ** Sorting of data
. sort groupnr subjectnr period

. 
. ** GENERATING TREATMENT VARIABLES FOR DATA ANALYSIS
. // Experimental Manipulations 
. gen design = designtreatment                    // Corresponds to "Self-Excluding" in manuscript

. gen use = usetreatment                                  // Corresponds to "Discretionary" in manuscript 

. // Interaction Term
. gen int_design_use = design*use                 // Corresponds to "Self-Excluding x Discretionary" in manuscript

. // Conditions
. gen condition = 1

.         replace condition = 2 if use==0 & design==1
(432 real changes made)

.         replace condition = 3 if use==1 & design==0
(468 real changes made)

.         replace condition = 4 if use==1 & design==1
(468 real changes made)

. label define conditionlabels 1 "Formulaic/Self-Including" 2 "Formulaic/Self-Excluding." 3 "Discretionary/Self-Including." 4 "Discretionary/Self-Excluding"

. label values condition conditionlabels

. 
. ** GENERATING VARIABLES AT DECISION LEVEL (captured for each of the three employees in any given observation)
. local player "a b c"

. local index = 0

. // Fair Bonus: Fair Bonus for a given employee (based on contribution)
. foreach var in `player' {
  2.         gen fairbonus_`var' = . 
  3.         local `index++'
  4.         foreach playernr in 1 2 3 {
  5.                 local reference = (`index' - `playernr') * 9
  6.                 bysort groupnr (subjectnr period): replace fairbonus_`var' = 1.5 * contribution[_n+`reference'] if subjectnr==`playernr' 
  7.                 }
  8.         }
(1,800 missing values generated)
(400 real changes made)
(400 real changes made)
(400 real changes made)
(1,800 missing values generated)
(400 real changes made)
(400 real changes made)
(400 real changes made)
(1,800 missing values generated)
(400 real changes made)
(400 real changes made)
(400 real changes made)

. // Proposal: Proposed Bonus in a given employee's proposal. 
. foreach var in `player' {
  2.         gen proposal_`var' = proposal`var'
  3.         drop proposal`var'      
  4.         }
(600 missing values generated)
(600 missing values generated)
(600 missing values generated)

. // Average Proposed Bonus: Average of Proposed Bonuses for a given employee. 
. foreach var in `player' {
  2.         gen av_proposal_`var' = .
  3.         }
(1,800 missing values generated)
(1,800 missing values generated)
(1,800 missing values generated)

. // Final Bonus: Final Bonus allocated to a given employee. 
. foreach var in `player' {
  2.         gen finalbonus_`var' = finalbonus`var'
  3.         drop finalbonus`var'
  4.         }
(200 missing values generated)
(200 missing values generated)
(200 missing values generated)

.         
. ** GENERATING VARIABLES AT DECISION LEVEL (captured for the specific employee represented in a given observation)
. gen fairbonus = .               // Fair Bonus for a given employee in a given round
(1,800 missing values generated)

. gen av_proposal = .             // Average Proposed Bonus for a given employee in a given round
(1,800 missing values generated)

. gen finalbonus = .              // Final Bonus for a given employee in a given round
(1,800 missing values generated)

. local player "a b c"

. local index = 0

. foreach var in `player' {
  2.         local `index++'
  3.         replace fairbonus = fairbonus_`var' if subjectnr==`index'
  4.         local reference1 = (1 - `index') * 9
  5.         local reference2 = (2 - `index') * 9
  6.         local reference3 = (3 - `index') * 9
  7.         bysort groupnr (subjectnr period): replace av_proposal = (proposal_`var'[_n+`reference1'] + proposal_`var'[_n+`reference2'] + proposal_`var'[_n+`reference3'])/3 if subjectnr==`index'
  8.         bysort groupnr (subjectnr period): replace av_proposal_`var' = av_proposal[_n-`reference1'] if subjectnr==1
  9.         bysort groupnr (subjectnr period): replace av_proposal_`var' = av_proposal[_n-`reference2'] if subjectnr==2
 10.         bysort groupnr (subjectnr period): replace av_proposal_`var' = av_proposal[_n-`reference3'] if subjectnr==3
 11.         replace finalbonus = finalbonus_`var' if subjectnr==`index'
 12.         }
(400 real changes made)
(400 real changes made)
(400 real changes made)
(400 real changes made)
(400 real changes made)
(400 real changes made)
(400 real changes made)
(400 real changes made)
(400 real changes made)
(400 real changes made)
(400 real changes made)
(400 real changes made)
(400 real changes made)
(400 real changes made)
(400 real changes made)
(400 real changes made)
(400 real changes made)
(400 real changes made)

. gen teambonus = finalbonus_a + finalbonus_b + finalbonus_c // Team Bonus for the team of a given employee in a given round
(200 missing values generated)

.         
. ** GENERATING VARIABLES AT EMPLOYEE LEVEL (captured as average across Rounds 1 through 8 for a given employee)
. local outcome "contribution fairbonus av_proposal finalbonus teamoutput"

. foreach var in `outcome' {
  2.         foreach start in 1 3 5 7 {
  3.                 bysort playernr (period): egen `var'_`start'_8 = mean(`var') if period>=`start'
  4.                 bysort playernr (period): replace `var'_`start'_8 = . if period<9
  5.                 }
  6.         }
(450 missing values generated)
(1200 real changes made, 1200 to missing)
(750 missing values generated)
(900 real changes made, 900 to missing)
(1,050 missing values generated)
(600 real changes made, 600 to missing)
(1,350 missing values generated)
(300 real changes made, 300 to missing)
(450 missing values generated)
(1200 real changes made, 1200 to missing)
(750 missing values generated)
(900 real changes made, 900 to missing)
(1,050 missing values generated)
(600 real changes made, 600 to missing)
(1,350 missing values generated)
(300 real changes made, 300 to missing)
(450 missing values generated)
(1200 real changes made, 1200 to missing)
(750 missing values generated)
(900 real changes made, 900 to missing)
(1,050 missing values generated)
(600 real changes made, 600 to missing)
(1,350 missing values generated)
(300 real changes made, 300 to missing)
(450 missing values generated)
(1200 real changes made, 1200 to missing)
(750 missing values generated)
(900 real changes made, 900 to missing)
(1,050 missing values generated)
(600 real changes made, 600 to missing)
(1,350 missing values generated)
(300 real changes made, 300 to missing)
(1600 real changes made, 1600 to missing)
(400 missing values generated)
(1200 real changes made, 1200 to missing)
(800 missing values generated)
(800 real changes made, 800 to missing)
(1,200 missing values generated)
(400 real changes made, 400 to missing)

. ** GENERATING CONTRIBUTION AT TEAM LEVEL (captured as average across rounds and employees in a given team)
. gen contribution_1_8_team = teamoutput_1_8 *  0.75 / 1.5 / 3 
(1,600 missing values generated)

. 
. ** GENERATING PROCESS VARIABLES
. ** 'SELF-PROPOSAL' (Self-Including Design Only)
.         // Decision Level
.         gen selfproposal = .
(1,800 missing values generated)

.                 replace selfproposal = proposal_a if design==0 & subjectnr==1
(200 real changes made)

.                 replace selfproposal = proposal_b if design==0 & subjectnr==2
(200 real changes made)

.                 replace selfproposal = proposal_c if design==0 & subjectnr==3
(200 real changes made)

. ** 'DISTORTION IN SELF-PROPOSALS' (Deviation from Fair Bonus, Self-Including Design Only)
.         // Decision Level
.         gen dev_selfproposal_fair = .
(1,800 missing values generated)

.                 replace dev_selfproposal_fair = proposal_a - fairbonus_a if design==0 & subjectnr==1
(200 real changes made)

.                 replace dev_selfproposal_fair = proposal_b - fairbonus_b if design==0 & subjectnr==2
(200 real changes made)

.                 replace dev_selfproposal_fair = proposal_c - fairbonus_c if design==0 & subjectnr==3
(200 real changes made)

.         // Employee Level
.         bysort playernr (period): egen dev_selfproposal_fair_1_8 = mean(dev_selfproposal_fair) if period>=1
(1,125 missing values generated)

.                 bysort playernr (period): replace dev_selfproposal_fair_1_8 = . if period<9
(600 real changes made, 600 to missing)

.         // Team Level
.         bysort groupnr (playernr period): egen dev_selfproposal_fair_team_1_8 = mean(dev_selfproposal_fair_1_8) if subjectnr<4 & period==9 
(1,725 missing values generated)

. ** 'ABSOLUTE DEVIATION OF FINAL BONUS FROM FAIR BONUS'
.         // Decision Level
.         gen dev_finalfromfair = .
(1,800 missing values generated)

.                 replace dev_finalfromfair = abs(finalbonus - fairbonus)
(1,200 real changes made)

.         // Employee Level
.         bysort playernr (period): egen dev_finalfromfair_1_8 = mean(dev_finalfromfair) if period>=1
(450 missing values generated)

.                 bysort playernr (period): replace dev_finalfromfair_1_8 = . if period<9
(1200 real changes made, 1200 to missing)

.         // Team Level
.         bysort groupnr (playernr period): egen dev_finalfromfair_1_8_team = mean(dev_finalfromfair_1_8) if subjectnr<4 & period==9 
(1,650 missing values generated)

. ** 'PROPOSAL DISTORTION'
.         // Decision Level
.         gen proposal_dist = .
(1,800 missing values generated)

.                 // Self-including
.                 replace proposal_dist = (abs(proposal_a - fairbonus_a) + abs(proposal_b - fairbonus_b) + abs(proposal_c - fairbonus_c))/3 if design==0
(600 real changes made)

.                 // Self-excluding
.                 replace proposal_dist = (abs((proposal_b * (teambonus - fairbonus_a)/teambonus) - fairbonus_b) + abs((proposal_c * (teambonus - fairbonus_a)/teambonus) - fairbonus_c))/2 if design==
> 1 & subjectnr==1
(200 real changes made)

.                 replace proposal_dist = (abs((proposal_a * (teambonus - fairbonus_b)/teambonus) - fairbonus_a) + abs((proposal_c * (teambonus - fairbonus_b)/teambonus) - fairbonus_c))/2 if design==
> 1 & subjectnr==2
(200 real changes made)

.                 replace proposal_dist = (abs((proposal_a * (teambonus - fairbonus_c)/teambonus) - fairbonus_a) + abs((proposal_b * (teambonus - fairbonus_c)/teambonus) - fairbonus_b))/2 if design==
> 1 & subjectnr==3
(200 real changes made)

.         // Employee Level
.         bysort playernr (period): egen proposal_dist_1_8 = mean(proposal_dist) if period>=1
(450 missing values generated)

.                 bysort playernr (period): replace proposal_dist_1_8 = . if period<9
(1200 real changes made, 1200 to missing)

.         // Team Level
.         bysort groupnr (playernr period): egen proposal_dist_1_8_team = mean(proposal_dist_1_8) if subjectnr<4 & period==9      
(1,650 missing values generated)

. ** 'ADJUSTED AVERAGE PROPOSED BONUS'
.         // Decision Level
.         gen scaled_av_proposal = .
(1,800 missing values generated)

.                 // Self-Including
.                 bysort groupnr (subjectnr period): replace scaled_av_proposal = ((proposal_a[_n] + proposal_a[_n+9] + proposal_a[_n+18])/3) if design==0 & subjectnr==1
(200 real changes made)

.                 bysort groupnr (subjectnr period): replace scaled_av_proposal = ((proposal_b[_n-9] + proposal_b[_n] + proposal_b[_n+9])/3) if design==0 & subjectnr==2
(200 real changes made)

.                 bysort groupnr (subjectnr period): replace scaled_av_proposal = ((proposal_c[_n-18] + proposal_c[_n-9] + proposal_c[_n])/3) if design==0 & subjectnr==3
(200 real changes made)

.                 // Self-Excluding
.                 bysort groupnr (subjectnr period): replace scaled_av_proposal = ((proposal_a[_n+9] * ((teambonus - fairbonus_b)/teambonus) + proposal_a[_n+18] * ((teambonus - fairbonus_c)/teambonus
> ))/2) if design==1 & subjectnr==1
(200 real changes made)

.                 bysort groupnr (subjectnr period): replace scaled_av_proposal = ((proposal_b[_n-9] * ((teambonus - fairbonus_a)/teambonus) + proposal_b[_n+9] * ((teambonus - fairbonus_c)/teambonus)
> )/2) if design==1 & subjectnr==2
(200 real changes made)

.                 bysort groupnr (subjectnr period): replace scaled_av_proposal = ((proposal_c[_n-18] * ((teambonus - fairbonus_a)/teambonus) + proposal_c[_n-9] * ((teambonus - fairbonus_b)/teambonus
> ))/2) if design==1 & subjectnr==3
(200 real changes made)

.         // Employee Level
.         bysort playernr (period): egen scaled_av_proposal_1_8 = mean(scaled_av_proposal) if period>=1
(450 missing values generated)

.                 bysort playernr (period): replace scaled_av_proposal_1_8 = . if period<9
(1200 real changes made, 1200 to missing)

.         // Team Level
.         bysort groupnr (playernr period): egen scaled_av_proposal_1_8_team = mean(scaled_av_proposal_1_8) if subjectnr<4 & period==9    
(1,650 missing values generated)

. ** 'DISTORTION'
.         // Decision Level
.         gen distortion = .
(1,800 missing values generated)

.                 replace distortion = abs(scaled_av_proposal - fairbonus)
(1,200 real changes made)

.         // Employee Level
.         bysort playernr (period): egen distortion_1_8 = mean(distortion) if period>=1
(450 missing values generated)

.                 bysort playernr (period): replace distortion_1_8 = . if period<9
(1200 real changes made, 1200 to missing)

.         // Team Level
.         bysort groupnr (playernr period): egen distortion_1_8_team = mean(distortion_1_8) if subjectnr<4 & period==9 
(1,650 missing values generated)

. ** 'DISTORTION & EFFICIENCY LOSS'
.         // Decision Level
.         gen dist_efficiency = .
(1,800 missing values generated)

.                 replace dist_efficiency = abs(av_proposal - fairbonus)
(1,200 real changes made)

.         // Employee Level
.         bysort playernr (period): egen dist_efficiency_1_8 = mean(dist_efficiency) if period>=1
(450 missing values generated)

.                 bysort playernr (period): replace dist_efficiency_1_8 = . if period<9
(1200 real changes made, 1200 to missing)

.         // Team Level
.         bysort groupnr (playernr period): egen dist_efficiency_1_8_team = mean(dist_efficiency_1_8) if subjectnr<4 & period==9 
(1,650 missing values generated)

. ** 'EFFICIENCY LOSS'
.         // Decision Level
.         gen efficiency_loss = .
(1,800 missing values generated)

.                 replace efficiency_loss = dist_efficiency - distortion
(1,200 real changes made)

.         // Employee Level
.         bysort playernr (period): egen efficiency_loss_1_8 = mean(efficiency_loss) if period>=1
(450 missing values generated)

.                 bysort playernr (period): replace efficiency_loss_1_8 = . if period<9
(1200 real changes made, 1200 to missing)

.         // Team Level
.         bysort groupnr (playernr period): egen efficiency_loss_1_8_team = mean(efficiency_loss_1_8) if subjectnr<4 & period==9 
(1,650 missing values generated)

. ** 'MANAGERIAL BIAS'
.         // Decision Level
.         gen managerial_bias = .
(1,800 missing values generated)

.                 replace managerial_bias = dev_finalfromfair - dist_efficiency
(1,200 real changes made)

.         // Employee Level
.         bysort playernr (period): egen managerial_bias_1_8 = mean(managerial_bias) if period>=1
(450 missing values generated)

.                 bysort playernr (period): replace managerial_bias_1_8 = . if period<9
(1200 real changes made, 1200 to missing)

.         // Team Level
.         bysort groupnr (playernr period): egen managerial_bias_1_8_team = mean(managerial_bias_1_8) if subjectnr<4 & period==9 
(1,650 missing values generated)

. ** 'EFFICIENCY LOSS & MANAGERIAL BIAS'
.         // Decision Level
.         gen mechanism = .
(1,800 missing values generated)

.                 replace mechanism = dev_finalfromfair - distortion
(1,200 real changes made)

.         // Employee Level
.         bysort playernr (period): egen mechanism_1_8 = mean(mechanism) if period>=1
(450 missing values generated)

.                 bysort playernr (period): replace mechanism_1_8 = . if period<9
(1200 real changes made, 1200 to missing)

.         // Team Level
.         bysort groupnr (playernr period): egen mechanism_1_8_team = mean(mechanism_1_8) if subjectnr<4 & period==9 
(1,650 missing values generated)

.         
. ** GENERATING ADDITIONAL INTERACTION VARIABLES (FOR ONLINE APPENDIX)
. // Decision Level
.         gen int_contribution_use = contribution * use
(600 missing values generated)

.         gen int_contribution_design = contribution * design
(600 missing values generated)

.         gen int_contribution_design_use = contribution * design * use   
(600 missing values generated)

. // Employee Level
.         gen int_contribution_1_8_use = contribution_1_8 * use
(1,650 missing values generated)

.         gen int_contribution_1_8_design = contribution_1_8 * design
(1,650 missing values generated)

.         gen int_contribution_1_8_design_use = contribution_1_8 * design * use           
(1,650 missing values generated)

.         
. ** GENERATING PROCESS FACTOR VARIABLES FOR FAIRNESS PERCEPTIONS
. ** Procedural Fairness Factor - Employee Level
. factor peqprocedfairness1 peqprocedfairness2 peqprocedfairness3 peqprocedfairness4 if subjectnr<4
(obs=150)

Factor analysis/correlation                      Number of obs    =        150
    Method: principal factors                    Retained factors =          2
    Rotation: (unrotated)                        Number of params =          6

    --------------------------------------------------------------------------
         Factor  |   Eigenvalue   Difference        Proportion   Cumulative
    -------------+------------------------------------------------------------
        Factor1  |      1.75157      1.67470            1.1825       1.1825
        Factor2  |      0.07687      0.24197            0.0519       1.2344
        Factor3  |     -0.16511      0.01699           -0.1115       1.1229
        Factor4  |     -0.18210            .           -0.1229       1.0000
    --------------------------------------------------------------------------
    LR test: independent vs. saturated:  chi2(6)  =  166.46 Prob>chi2 = 0.0000

Factor loadings (pattern matrix) and unique variances

    -------------------------------------------------
        Variable |  Factor1   Factor2 |   Uniqueness 
    -------------+--------------------+--------------
    peqprocedf~1 |   0.4604    0.2089 |      0.7444  
    peqprocedf~2 |   0.5915   -0.1747 |      0.6196  
    peqprocedf~3 |   0.7749    0.0409 |      0.3978  
    peqprocedf~4 |   0.7676   -0.0319 |      0.4097  
    -------------------------------------------------

.         rotate

Factor analysis/correlation                      Number of obs    =        150
    Method: principal factors                    Retained factors =          2
    Rotation: orthogonal varimax (Kaiser off)    Number of params =          6

    --------------------------------------------------------------------------
         Factor  |     Variance   Difference        Proportion   Cumulative
    -------------+------------------------------------------------------------
        Factor1  |      1.68553      1.54263            1.1379       1.1379
        Factor2  |      0.14290            .            0.0965       1.2344
    --------------------------------------------------------------------------
    LR test: independent vs. saturated:  chi2(6)  =  166.46 Prob>chi2 = 0.0000

Rotated factor loadings (pattern matrix) and unique variances

    -------------------------------------------------
        Variable |  Factor1   Factor2 |   Uniqueness 
    -------------+--------------------+--------------
    peqprocedf~1 |   0.4097    0.2962 |      0.7444  
    peqprocedf~2 |   0.6144   -0.0538 |      0.6196  
    peqprocedf~3 |   0.7514    0.1939 |      0.3978  
    peqprocedf~4 |   0.7587    0.1212 |      0.4097  
    -------------------------------------------------

Factor rotation matrix

    --------------------------------
                 | Factor1  Factor2 
    -------------+------------------
         Factor1 |  0.9801   0.1986 
         Factor2 | -0.1986   0.9801 
    --------------------------------

.         predict peqprocedfairness_factor
(option regression assumed; regression scoring)

Scoring coefficients (method = regression; based on varimax rotated factors)

    ----------------------------------
        Variable |  Factor1   Factor2 
    -------------+--------------------
    peqprocedf~1 |  0.07654   0.25253 
    peqprocedf~2 |  0.23019  -0.18912 
    peqprocedf~3 |  0.36379   0.16697 
    peqprocedf~4 |  0.37706   0.01816 
    ----------------------------------


. ** Distributive Fairness Factor - Employee Level
. factor peqdistrifairness1 peqdistrifairness2 peqdistrifairness3 peqdistrifairness4 if subjectnr<4
(obs=150)

Factor analysis/correlation                      Number of obs    =        150
    Method: principal factors                    Retained factors =          1
    Rotation: (unrotated)                        Number of params =          4

    --------------------------------------------------------------------------
         Factor  |   Eigenvalue   Difference        Proportion   Cumulative
    -------------+------------------------------------------------------------
        Factor1  |      3.20984      3.23857            1.0455       1.0455
        Factor2  |     -0.02873      0.01318           -0.0094       1.0361
        Factor3  |     -0.04191      0.02704           -0.0137       1.0225
        Factor4  |     -0.06895            .           -0.0225       1.0000
    --------------------------------------------------------------------------
    LR test: independent vs. saturated:  chi2(6)  =  588.07 Prob>chi2 = 0.0000

Factor loadings (pattern matrix) and unique variances

    ---------------------------------------
        Variable |  Factor1 |   Uniqueness 
    -------------+----------+--------------
    peqdistrif~1 |   0.9109 |      0.1702  
    peqdistrif~2 |   0.8848 |      0.2171  
    peqdistrif~3 |   0.9439 |      0.1090  
    peqdistrif~4 |   0.8404 |      0.2938  
    ---------------------------------------

.         rotate

Factor analysis/correlation                      Number of obs    =        150
    Method: principal factors                    Retained factors =          1
    Rotation: orthogonal varimax (Kaiser off)    Number of params =          4

    --------------------------------------------------------------------------
         Factor  |     Variance   Difference        Proportion   Cumulative
    -------------+------------------------------------------------------------
        Factor1  |      3.20984            .            1.0455       1.0455
    --------------------------------------------------------------------------
    LR test: independent vs. saturated:  chi2(6)  =  588.07 Prob>chi2 = 0.0000

Rotated factor loadings (pattern matrix) and unique variances

    ---------------------------------------
        Variable |  Factor1 |   Uniqueness 
    -------------+----------+--------------
    peqdistrif~1 |   0.9109 |      0.1702  
    peqdistrif~2 |   0.8848 |      0.2171  
    peqdistrif~3 |   0.9439 |      0.1090  
    peqdistrif~4 |   0.8404 |      0.2938  
    ---------------------------------------

Factor rotation matrix

    -----------------------
                 | Factor1 
    -------------+---------
         Factor1 |  1.0000 
    -----------------------

.         predict peqdistrifairness_factor
(option regression assumed; regression scoring)

Scoring coefficients (method = regression; based on varimax rotated factors)

    ------------------------
        Variable |  Factor1 
    -------------+----------
    peqdistrif~1 |  0.26082 
    peqdistrif~2 |  0.19875 
    peqdistrif~3 |  0.42837 
    peqdistrif~4 |  0.14505 
    ------------------------


. 
. ********************************************************************************
. 
. 
. 
. 
. ********************************************************************************
. ** RESULTS REPORTED IN MANUSCRIPT
. ********************************************************************************
. 
. ** 3.2 PARTICIPANTS AND PROCEDURES
. 
. ** Footnote 25: Demographics and Randomization Success
. // Demographics
. quietly: sum age

. display "Average Age = "round(r(mean),1) " years"
Average Age = 20 years

. quietly: tab gender             // 0 for Women, 1 for Men, and 2 for Other

. quietly: sum gender if gender == 0

. display "Identify as Female: "round(100*r(N)/200,1) " percent"
Identify as Female: 36 percent

. quietly: tab language   // 0 for English, 1 for Spanish, 2 for Other

. quietly: sum language if language == 0

. display "Primary Language is English: "round(100*r(N)/200,1) " percent"
Primary Language is English: 89 percent

. //Randomization Success
. reg age use design int_design_use if subjectnr<=4 & period==9

      Source |       SS           df       MS      Number of obs   =       200
-------------+----------------------------------   F(3, 196)       =      1.60
       Model |  5.68833333         3  1.89611111   Prob > F        =    0.1913
    Residual |  232.666667       196  1.18707483   R-squared       =    0.0239
-------------+----------------------------------   Adj R-squared   =    0.0089
       Total |     238.355       199  1.19776382   Root MSE        =    1.0895

--------------------------------------------------------------------------------
           age | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
           use |  -.1634615   .2180805    -0.75   0.454     -.593547    .2666239
        design |   .2916667   .2223993     1.31   0.191    -.1469362    .7302695
int_design_use |  -.1955128   .3084123    -0.63   0.527    -.8037455    .4127199
         _cons |     19.875   .1572601   126.38   0.000     19.56486    20.18514
--------------------------------------------------------------------------------

. reg gender use design int_design_use if subjectnr<=4 & period==9

      Source |       SS           df       MS      Number of obs   =       200
-------------+----------------------------------   F(3, 196)       =      1.16
       Model |  .828525641         3  .276175214   Prob > F        =    0.3263
    Residual |  46.6714744       196  .238119767   R-squared       =    0.0174
-------------+----------------------------------   Adj R-squared   =    0.0024
       Total |        47.5       199  .238693467   Root MSE        =    .48798

--------------------------------------------------------------------------------
        gender | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
           use |   .1698718   .0976732     1.74   0.084    -.0227536    .3624971
        design |   .1458333   .0996075     1.46   0.145    -.0506068    .3422734
int_design_use |  -.2035256   .1381308    -1.47   0.142     -.475939    .0688877
         _cons |   .5416667   .0704331     7.69   0.000     .4027626    .6805708
--------------------------------------------------------------------------------

. reg language use design int_design_use if subjectnr<=4 & period==9

      Source |       SS           df       MS      Number of obs   =       200
-------------+----------------------------------   F(3, 196)       =      1.13
       Model |  1.16025641         3  .386752137   Prob > F        =    0.3364
    Residual |  66.8397436       196    .3410191   R-squared       =    0.0171
-------------+----------------------------------   Adj R-squared   =    0.0020
       Total |          68       199  .341708543   Root MSE        =    .58397

--------------------------------------------------------------------------------
      language | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
           use |  -.1730769   .1168872    -1.48   0.140     -.403595    .0574412
        design |  -.0416667   .1192021    -0.35   0.727    -.2767499    .1934166
int_design_use |   .2339744   .1653035     1.42   0.159    -.0920275    .5599762
         _cons |        .25   .0842886     2.97   0.003      .083771     .416229
--------------------------------------------------------------------------------

. 
. ** Average Payment per Participant
. quietly: sum earningsround

. display "Average Pay per Participant = $"round(8*0.05*r(mean),0.01)
Average Pay per Participant = $20.46

. 
. 
. ** 4. RESULTS
. 
. ** 4.1 DESCRIPTIVE RESULTS AND HYPOTHESIS TEST
. 
. ********************************************************************************
. ** TABLE 2: EFFORT CONTRIBUTIONS
. ********************************************************************************
. // Condition [1]: Formulaic Use & Self-Including Design
. sum contribution if use==0 & design==0 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
contribution |        288    19.64583    10.88295          0         40

. sum contribution_1_8 if use==0 & design==0 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
contribu~1_8 |         36    19.64583    7.673557          0       37.5

. sum contribution_1_8_team if use==0 & design==0 & period==9 & subjectnr==1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
contributi~m |         12    19.64583    7.026027        3.5   30.08333

. // Condition [2]: Formulaic Use & Self-Excluding Design
. sum contribution if use==0 & design==1 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
contribution |        288    27.44444     11.4117          0         40

. sum contribution_1_8 if use==0 & design==1 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
contribu~1_8 |         36    27.44444    7.930527       8.25         40

. sum contribution_1_8_team if use==0 & design==1 & period==9 & subjectnr==1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
contributi~m |         12    27.44444    7.549193         15   38.16667

. // Condition [3]: Discretionary Use & Self-Including Design
. sum contribution if use==1 & design==0 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
contribution |        312    19.74359    14.34928          0         40

. sum contribution_1_8 if use==1 & design==0 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
contribu~1_8 |         39    19.74359    8.644379       5.25       37.5

. sum contribution_1_8_team if use==1 & design==0 & period==9 & subjectnr==1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
contributi~m |         13    19.74359    7.863966   9.666667   34.83333

. // Condition [4]: Discretionary Use & Self-Excluding Design
. sum contribution if use==1 & design==1 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
contribution |        312    19.66667    13.72553          0         40

. sum contribution_1_8 if use==1 & design==1 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
contribu~1_8 |         39    19.66667    10.48704          1         40

. sum contribution_1_8_team if use==1 & design==1 & period==9 & subjectnr==1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
contributi~m |         13    19.66667    9.761449   4.583333   32.58333

. 
. ********************************************************************************
. ** FIGURE 1: EFFORT
. ********************************************************************************
. ** PANEL A
. preserve

. sort groupnr subjectnr period

. drop if period==9
(200 observations deleted)

. drop if subjectnr==4
(400 observations deleted)

. label define use_l 0 "Formulaic Use" 1 "Discretionary Use"

. label define design_l 0 "Self-Including Design" 1 "Self-Excluding Design"

. label values use use_l

. label values design design_l

. // Regression that is mirrored:
. reg contribution design use int_design_use if subjectnr<4 & period<9, vce(cluster groupnr)

Linear regression                               Number of obs     =      1,200
                                                F(3, 49)          =       3.32
                                                Prob > F          =     0.0274
                                                R-squared         =     0.0636
                                                Root MSE          =     12.736

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
  contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   7.798611   2.882875     2.71   0.009     2.005257    13.59196
           use |   .0977564   2.889559     0.03   0.973     -5.70903    5.904543
int_design_use |  -7.875534   4.441196    -1.77   0.082    -16.80045    1.049384
         _cons |   19.64583   1.964065    10.00   0.000      15.6989    23.59277
--------------------------------------------------------------------------------

. // Clustered SEs by condition
. gen secluster = 0

. forvalues x = 0/1 {
  2.         forvalues y = 0/1 {
  3.                 reg contribution if design == `x' & use==`y', vce(cluster groupnr)
  4.                 replace secluster = _se[_cons] if design == `x' & use==`y' & _se[_cons] !=.
  5.                 }
  6.         }

Linear regression                               Number of obs     =        288
                                                F(0, 11)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     10.883

                               (Std. err. adjusted for 12 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   19.64583   2.028239     9.69   0.000     15.18171    24.10996
------------------------------------------------------------------------------
(288 real changes made)

Linear regression                               Number of obs     =        312
                                                F(0, 12)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     14.349

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   19.74359   2.181072     9.05   0.000     14.99144    24.49574
------------------------------------------------------------------------------
(312 real changes made)

Linear regression                               Number of obs     =        288
                                                F(0, 11)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     11.412

                               (Std. err. adjusted for 12 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   27.44444   2.179264    12.59   0.000     22.64792    32.24097
------------------------------------------------------------------------------
(288 real changes made)

Linear regression                               Number of obs     =        312
                                                F(0, 12)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     13.726

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   19.66667   2.707339     7.26   0.000     13.76788    25.56545
------------------------------------------------------------------------------
(312 real changes made)

. // Settings
. set scheme s2color

. grstyle init

. grstyle color background white

. grstyle yesno draw_major_hgrid no

. graph set window fontface "Times New Roman"

. local DV "contribution"

. local Color1 "navy"

. local Color2 "maroon"

. local xsize "xsize(5)"

. local ysize "ysize(5)"

. local yticks "yticks(15(5)30)"

. local ylabels "ylabels(15(5)30, nogrid)"

. local yticks_DO "yticks(0(.05).25)"

. local ylabels_DO "ylabels(0(.1).25, nogrid)"

. local ytitle "ytitle("Effort")"

. local xticks "xticks(0(1)1)"

. local xlabels "xlabels(0 `" "Self-Including" "Design" "' 1 `" "Self-Excluding" "Design" "', nogrid)"

. local xtitle "xtitle("")"

. local mfcolor_SelfExcluding "mfcolor(white)"

. local msymbol_Formulaic "msymbol(S)"

. local msymbol_Discretionary "msymbol(T)"

. local lpattern_SelfIncluding "lpattern(solid)"

. local lpattern_SelfExcluding "lpattern(dash)"

. local graphregion "graphregion(margin(0 0 0 0))"

. local plotregion "plotregion(margin(0 0 0 0))"

. // Graph
. local Sample1 "`Condition0'"

. local Sample2 "`Condition0'" //For the legend

. local Title1 "Graph"

. local Title2 "Legend"

. local Legend1 "off"

. local Legend2 "size(small) rows(2) cols(1) position(6) region(lstyle(none) lcolor(white) fcolor(white)) symxsize(6.5)"

. local Legend2 "`Legend2' order(1 "Formulaic Use" "

. local Legend2 "`Legend2' 2 "Discretionary Use")"

. local xsize_1 "`xsize'"

. local xsize_2 "xsize(5)"

. collapse (mean) `DV' (mean) secluster, by(use design)

. gen plus = contribution + secluster

. gen minus = contribution - secluster

. replace contribution = round(contribution,0.001) 
(4 real changes made)

. // Figure (Without Legend) 
. graph twoway (connected `DV' design if use==0, mlcolor(`Color1') mfcolor(`Color1') msymbol(none) `lpattern_SelfIncluding' lcolor(`Color1')) || ////
>                          (connected `DV' design if use==0 & design==0, mlabel(`DV') mlabcolor(`Color1') mlabposition(8) mlcolor(`Color1') mfcolor(`Color1') `msymbol_Formulaic') || ////
>                          (connected `DV' design if use==0 & design==1, mlabel(`DV') mlabcolor(`Color1') mlabposition(2) mlcolor(`Color1') mfcolor(`Color1') `msymbol_Formulaic') || ////
>                          (connected `DV' design if use==1, mlcolor(`Color2') mfcolor(`Color2') msymbol(none) `lpattern_SelfIncluding' lcolor(`Color2')) || ////
>                          (connected `DV' design if use==1 & design==0, mlabel(`DV') mlabcolor(`Color2') mlabposition(10) mlcolor(`Color2') mfcolor(`Color2') `msymbol_Discretionary') || ////
>                          (connected `DV' design if use==1 & design==1, mlabel(`DV') mlabcolor(`Color2') mlabposition(4) mlcolor(`Color2') mfcolor(`Color2') `msymbol_Discretionary') ///
>                          (rcap plus minus design if use==0 & design==0, lcolor(`Color1'%50)) ///
>                          (rcap plus minus design if use==0 & design==1, lcolor(`Color1'%50)) ///
>                          (rcap plus minus design if use==1 & design==0, lcolor(`Color2'%50)) ///
>                          (rcap plus minus design if use==1 & design==1, lcolor(`Color2'%50)), ///
>                                  `ytitle' `yticks' `ylabels' `xtitle' `xticks' `xlabels' `xsize_1' `ysize' legend(`Legend1') xscale(range(-0.4 1.4))

. // Figure (With Legend)         
. graph twoway (connected `DV' design if use==0, mlcolor(`Color1') mfcolor(`Color1') `msymbol_Formulaic' `lpattern_SelfIncluding' lcolor(`Color1')) || ////
>                          (connected `DV' design if use==1, mlcolor(`Color2') mfcolor(`Color2') `msymbol_Discretionary' `lpattern_SelfIncluding' lcolor(`Color2')) ////
>                          (rcap plus minus design if use==0 & design==0, lcolor(`Color1'%50)) ///
>                          (rcap plus minus design if use==0 & design==1, lcolor(`Color1'%50)) ///
>                          (rcap plus minus design if use==1 & design==0, lcolor(`Color2'%50)) ///
>                          (rcap plus minus design if use==1 & design==1, lcolor(`Color2'%50)), ///
>                                  `ytitle' `yticks' `ylabels' `xtitle' `xticks' `xlabels' `xsize_2' `ysize' legend(`Legend2') xscale(range(-0.4 1.4))                             

. restore

. ********************************************************************************
. ** PANEL B
. preserve

. sort groupnr subjectnr period

. drop if period==9
(200 observations deleted)

. drop if subjectnr==4
(400 observations deleted)

. label define use_l 0 "Formulaic Use" 1 "Discretionary Use"

. label define design_l 0 "Self-Including Design" 1 "Self-Excluding Design"

. label values use use_l

. label values design design_l

. // Clustered Standard Errors by Condition
. gen seclusterperiod = 0

. forvalues x = 0/1 {
  2.         forvalues y = 0/1 {
  3.                 forvalues z=1/8  {
  4.                         reg contribution if design == `x' & use==`y' & period==`z', vce(cluster groupnr)
  5.                         replace seclusterperiod = _se[_cons] if design == `x' & use==`y' & period==`z' & _se[_cons] !=.
  6.                         }
  7.                 }
  8.         }

Linear regression                               Number of obs     =         36
                                                F(0, 11)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     8.0354

                               (Std. err. adjusted for 12 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   19.05556   1.164741    16.36   0.000     16.49198    21.61913
------------------------------------------------------------------------------
(36 real changes made)

Linear regression                               Number of obs     =         36
                                                F(0, 11)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     10.674

                               (Std. err. adjusted for 12 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   21.05556   2.524571     8.34   0.000     15.49901     26.6121
------------------------------------------------------------------------------
(36 real changes made)

Linear regression                               Number of obs     =         36
                                                F(0, 11)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     11.069

                               (Std. err. adjusted for 12 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   19.33333   1.945382     9.94   0.000     15.05158    23.61509
------------------------------------------------------------------------------
(36 real changes made)

Linear regression                               Number of obs     =         36
                                                F(0, 11)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     10.113

                               (Std. err. adjusted for 12 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   21.05556   2.679839     7.86   0.000     15.15727    26.95384
------------------------------------------------------------------------------
(36 real changes made)

Linear regression                               Number of obs     =         36
                                                F(0, 11)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =      9.798

                               (Std. err. adjusted for 12 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   20.66667    2.48768     8.31   0.000     15.19132    26.14201
------------------------------------------------------------------------------
(36 real changes made)

Linear regression                               Number of obs     =         36
                                                F(0, 11)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     11.342

                               (Std. err. adjusted for 12 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   20.61111   2.851497     7.23   0.000     14.33501    26.88721
------------------------------------------------------------------------------
(36 real changes made)

Linear regression                               Number of obs     =         36
                                                F(0, 11)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     12.314

                               (Std. err. adjusted for 12 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   18.88889   2.921341     6.47   0.000     12.45906    25.31872
------------------------------------------------------------------------------
(36 real changes made)

Linear regression                               Number of obs     =         36
                                                F(0, 11)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     13.201

                               (Std. err. adjusted for 12 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |       16.5   3.645139     4.53   0.001     8.477104     24.5229
------------------------------------------------------------------------------
(36 real changes made)

Linear regression                               Number of obs     =         39
                                                F(0, 12)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     11.076

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   19.48718   1.650613    11.81   0.000      15.8908    23.08356
------------------------------------------------------------------------------
(39 real changes made)

Linear regression                               Number of obs     =         39
                                                F(0, 12)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     12.811

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   21.23077   1.915369    11.08   0.000     17.05754      25.404
------------------------------------------------------------------------------
(39 real changes made)

Linear regression                               Number of obs     =         39
                                                F(0, 12)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     12.813

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   21.64103   2.202841     9.82   0.000     16.84145     26.4406
------------------------------------------------------------------------------
(39 real changes made)

Linear regression                               Number of obs     =         39
                                                F(0, 12)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     14.252

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   21.64103   2.511076     8.62   0.000     16.16986    27.11219
------------------------------------------------------------------------------
(39 real changes made)

Linear regression                               Number of obs     =         39
                                                F(0, 12)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     15.307

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |    21.4359    3.09659     6.92   0.000     14.68901    28.18279
------------------------------------------------------------------------------
(39 real changes made)

Linear regression                               Number of obs     =         39
                                                F(0, 12)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     16.495

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   19.33333   3.890964     4.97   0.000     10.85565    27.81102
------------------------------------------------------------------------------
(39 real changes made)

Linear regression                               Number of obs     =         39
                                                F(0, 12)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     15.926

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   18.87179   3.789613     4.98   0.000     10.61494    27.12865
------------------------------------------------------------------------------
(39 real changes made)

Linear regression                               Number of obs     =         39
                                                F(0, 12)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     15.069

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   14.30769   3.205778     4.46   0.001     7.322903    21.29248
------------------------------------------------------------------------------
(39 real changes made)

Linear regression                               Number of obs     =         36
                                                F(0, 11)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     10.921

                               (Std. err. adjusted for 12 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   18.38889    1.83578    10.02   0.000     14.34836    22.42941
------------------------------------------------------------------------------
(36 real changes made)

Linear regression                               Number of obs     =         36
                                                F(0, 11)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     10.388

                               (Std. err. adjusted for 12 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   24.72222   1.766616    13.99   0.000     20.83393    28.61052
------------------------------------------------------------------------------
(36 real changes made)

Linear regression                               Number of obs     =         36
                                                F(0, 11)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     9.4227

                               (Std. err. adjusted for 12 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   26.88889   2.325866    11.56   0.000     21.76969    32.00809
------------------------------------------------------------------------------
(36 real changes made)

Linear regression                               Number of obs     =         36
                                                F(0, 11)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     10.425

                               (Std. err. adjusted for 12 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |         29   2.903035     9.99   0.000     22.61046    35.38954
------------------------------------------------------------------------------
(36 real changes made)

Linear regression                               Number of obs     =         36
                                                F(0, 11)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     11.686

                               (Std. err. adjusted for 12 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   29.11111    3.33266     8.74   0.000     21.77598    36.44625
------------------------------------------------------------------------------
(36 real changes made)

Linear regression                               Number of obs     =         36
                                                F(0, 11)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     10.102

                               (Std. err. adjusted for 12 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   31.05556   2.573444    12.07   0.000     25.39144    36.71967
------------------------------------------------------------------------------
(36 real changes made)

Linear regression                               Number of obs     =         36
                                                F(0, 11)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     11.355

                               (Std. err. adjusted for 12 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   30.44444   2.688463    11.32   0.000     24.52718    36.36171
------------------------------------------------------------------------------
(36 real changes made)

Linear regression                               Number of obs     =         36
                                                F(0, 11)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     12.203

                               (Std. err. adjusted for 12 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   29.94444   3.471343     8.63   0.000     22.30407    37.58482
------------------------------------------------------------------------------
(36 real changes made)

Linear regression                               Number of obs     =         39
                                                F(0, 12)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     11.159

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   18.71795    1.89986     9.85   0.000     14.57851    22.85739
------------------------------------------------------------------------------
(39 real changes made)

Linear regression                               Number of obs     =         39
                                                F(0, 12)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     12.432

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   21.74359    2.52795     8.60   0.000     16.23566    27.25152
------------------------------------------------------------------------------
(39 real changes made)

Linear regression                               Number of obs     =         39
                                                F(0, 12)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     13.852

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   20.46154   3.443798     5.94   0.000     12.95815    27.96493
------------------------------------------------------------------------------
(39 real changes made)

Linear regression                               Number of obs     =         39
                                                F(0, 12)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     14.645

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   20.87179   3.249707     6.42   0.000     13.79129     27.9523
------------------------------------------------------------------------------
(39 real changes made)

Linear regression                               Number of obs     =         39
                                                F(0, 12)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     15.028

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   21.17949     3.7509     5.65   0.000     13.00698      29.352
------------------------------------------------------------------------------
(39 real changes made)

Linear regression                               Number of obs     =         39
                                                F(0, 12)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     14.516

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   20.10256   3.225474     6.23   0.000     13.07486    27.13027
------------------------------------------------------------------------------
(39 real changes made)

Linear regression                               Number of obs     =         39
                                                F(0, 12)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     14.841

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   17.38462   3.216288     5.41   0.000     10.37693    24.39231
------------------------------------------------------------------------------
(39 real changes made)

Linear regression                               Number of obs     =         39
                                                F(0, 12)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     13.273

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   16.87179   3.037641     5.55   0.000     10.25334    23.49025
------------------------------------------------------------------------------
(39 real changes made)

. // Settings
. set scheme s2color

. grstyle init

. grstyle color background white

. grstyle yesno draw_major_hgrid no

. graph set window fontface "Times New Roman"

. local DV "contribution"

. local Color1 "navy"

. local Color2 "maroon"

. local xsize "xsize(5)"

. local ysize "ysize(5)"

. local yticks "yticks(10(5)35)"

. local ylabels "ylabels(10(5)35, nogrid)"

. local yticks_DO "yticks(0(.05).25)"

. local ylabels_DO "ylabels(0(.1).25, nogrid)"

. local ytitle "ytitle("Effort")"

. local xticks "xticks(1(1)8)"

. local xlabels "xlabels(1(1)8, nogrid)"

. local xtitle "xtitle("Round")"

. local mfcolor_SelfExcluding "mfcolor(white)"

. local msymbol_Formulaic "msymbol(S)"

. local msymbol_Discretionary "msymbol(T)"

. local lpattern_SelfIncluding "lpattern(solid)"

. local lpattern_SelfExcluding "lpattern(dash)"

. local graphregion "graphregion(margin(0 0 0 0))"

. local plotregion "plotregion(margin(0 0 0 0))"

. // Graph
. local Condition0 "period <= 8"

. local Sample1 "`Condition0'"

. local Sample2 "`Condition0'" //For the legend

. local Title1 "Graph"

. local Title2 "Legend"

. local Legend1 "off"

. local Legend2 "size(small) rows(4) cols(1) position(6) region(lstyle(none) lcolor(white) fcolor(white)) symxsize(6.5)"

. local Legend2 "`Legend2' order(1 "[1] Formulaic Use &" "Self-Including Design" "

. local Legend2 "`Legend2' 2 "[2] Formulaic Use &" "Self-Excluding Design"" 

. local Legend2 "`Legend2' 3 "[3] Discretionary Use &" "Self-Including Design"" 

. local Legend2 "`Legend2' 4 "[4] Discretionary Use &" "Self-Excluding Design")"

. local xsize_1 "`xsize'"

. local xsize_2 "xsize(5)"

. collapse (mean) `DV' (mean) seclusterperiod, by(use design period)      

. gen plus = contribution + seclusterperiod

. gen minus = contribution - seclusterperiod

. // Figure (Without Legend)
. graph twoway (connected `DV' period if use==0 & design==0, mlcolor(`Color1') mfcolor(`Color1') `msymbol_Formulaic' `lpattern_SelfIncluding' lcolor(`Color1')) || ////
>                          (connected `DV' period if use==0 & design==1, mlcolor(`Color1') `mfcolor_SelfExcluding' `msymbol_Formulaic' `lpattern_SelfExcluding' lcolor(`Color1')) || ////
>                          (connected `DV' period if use==1 & design==0, mlcolor(`Color2') mfcolor(`Color2') `msymbol_Discretionary' `lpattern_SelfIncluding' lcolor(`Color2')) || ////
>                          (connected `DV' period if use==1 & design==1, mlcolor(`Color2') `mfcolor_SelfExcluding' `msymbol_Discretionary' `lpattern_SelfExcluding' lcolor(`Color2')) ////
>                          (rcap plus minus period if use==0 & design==0, `lpattern_SelfIncluding' lcolor(`Color1'%50)) ///
>                          (rcap plus minus period if use==0 & design==1, `lpattern_SelfExcluding' lcolor(`Color1'%50)) ///
>                          (rcap plus minus period if use==1 & design==0, `lpattern_SelfIncluding' lcolor(`Color2'%50)) ///
>                          (rcap plus minus period if use==1 & design==1, `lpattern_SelfExcluding' lcolor(`Color2'%50)), ///
>                                  `ytitle' `yticks' `ylabels' `xtitle' `xticks' `xlabels' `xsize_2' `ysize' legend(`Legend1')

. // Figure (With Legend)
. graph twoway (connected `DV' period if use==0 & design==0, mlcolor(`Color1') mfcolor(`Color1') `msymbol_Formulaic' `lpattern_SelfIncluding' lcolor(`Color1')) || ////
>                          (connected `DV' period if use==0 & design==1, mlcolor(`Color1') `mfcolor_SelfExcluding' `msymbol_Formulaic' `lpattern_SelfExcluding' lcolor(`Color1')) || ////
>                          (connected `DV' period if use==1 & design==0, mlcolor(`Color2') mfcolor(`Color2') `msymbol_Discretionary' `lpattern_SelfIncluding' lcolor(`Color2')) || ////
>                          (connected `DV' period if use==1 & design==1, mlcolor(`Color2') `mfcolor_SelfExcluding' `msymbol_Discretionary' `lpattern_SelfExcluding' lcolor(`Color2')) ///
>                          (rcap plus minus period if use==0 & design==0, `lpattern_SelfIncluding' lcolor(`Color1'%50)) ///
>                          (rcap plus minus period if use==0 & design==1, `lpattern_SelfExcluding' lcolor(`Color1'%50)) ///
>                          (rcap plus minus period if use==1 & design==0, `lpattern_SelfIncluding' lcolor(`Color2'%50)) ///
>                          (rcap plus minus period if use==1 & design==1, `lpattern_SelfExcluding' lcolor(`Color2'%50)), ////
>                                  `ytitle' `yticks' `ylabels' `xtitle' `xticks' `xlabels' `xsize_1' `ysize' legend(`Legend2')

. restore

. ********************************************************************************
. 
. ********************************************************************************
. ** TABLE 3: EFFORT - OLS REGRESSION RESULTS
. ********************************************************************************
. // Column 1: Effort - Decision Level
. reg contribution design use int_design_use if subjectnr<4 & period<9, vce(cluster groupnr)

Linear regression                               Number of obs     =      1,200
                                                F(3, 49)          =       3.32
                                                Prob > F          =     0.0274
                                                R-squared         =     0.0636
                                                Root MSE          =     12.736

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
  contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   7.798611   2.882875     2.71   0.009     2.005257    13.59196
           use |   .0977564   2.889559     0.03   0.973     -5.70903    5.904543
int_design_use |  -7.875534   4.441196    -1.77   0.082    -16.80045    1.049384
         _cons |   19.64583   1.964065    10.00   0.000      15.6989    23.59277
--------------------------------------------------------------------------------

.         // Simple Comparisons
.         display "Comparison: "round(_b[design],0.001)
Comparison: 7.799

.         quietly: test _b[design] = 0

.         display "t-stat = "round(sqrt(r(F)),0.01)       
t-stat = 2.71

.         display "Comparison: "round(- _b[use] + _b[design],0.001)
Comparison: 7.701

.         quietly: test - _b[use] + _b[design] = 0

.         display "t-stat = "round(sqrt(r(F)),0.01)
t-stat = 2.57

.         display "Comparison: "round(- _b[use] - _b[int_design_use],0.001)
Comparison: 7.778

.         quietly: test - _b[use] - _b[int_design_use] = 0

.         display "t-stat = "round(sqrt(r(F)),0.01)
t-stat = 2.31

. // Column 2a: Effort - Employee Level
. reg contribution_1_8 design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       3.26
                                                Prob > F          =     0.0293
                                                R-squared         =     0.1274
                                                Root MSE          =     8.7901

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
contributi~1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   7.798611   2.908697     2.68   0.010     1.953366    13.64386
           use |   .0977564   2.915441     0.03   0.973    -5.761042    5.956555
int_design_use |  -7.875534   4.480977    -1.76   0.085    -16.88039    1.129326
         _cons |   19.64583   1.981657     9.91   0.000     15.66354    23.62812
--------------------------------------------------------------------------------

.         // Simple Comparisons
.         display "Comparison: "round(_b[design],0.001)
Comparison: 7.799

.         quietly: test _b[design] = 0

.         display "t-stat = "round(sqrt(r(F)),0.01)       
t-stat = 2.68

.         display "Comparison: "round(- _b[use] + _b[design],0.001)
Comparison: 7.701

.         quietly: test - _b[use] + _b[design] = 0

.         display "t-stat = "round(sqrt(r(F)),0.01)
t-stat = 2.55

.         display "Comparison: "round(- _b[use] - _b[int_design_use],0.001)
Comparison: 7.778

.         quietly: test - _b[use] - _b[int_design_use] = 0

.         display "t-stat = "round(sqrt(r(F)),0.01)
t-stat = 2.29

. // Column 2b: Distributive Fairness - Employee Level
. reg peqdistrifairness_factor design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =      10.60
                                                Prob > F          =     0.0000
                                                R-squared         =     0.1602
                                                Root MSE          =     .89741

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
peqdistrifai~r | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   .7795105   .2568524     3.03   0.004     .2633463    1.295675
           use |  -.0958916   .2991021    -0.32   0.750    -.6969599    .5051766
int_design_use |  -.9022568   .3605198    -2.50   0.016    -1.626748   -.1777652
         _cons |  -.1053048   .2263614    -0.47   0.644    -.5601951    .3495855
--------------------------------------------------------------------------------

.         // Simple Comparisons
.         display "Comparison: "round(_b[design],0.001)
Comparison: .78

.         quietly: test _b[design] = 0

.         display "t-stat = "round(sqrt(r(F)),0.01)       
t-stat = 3.03

.         display "Comparison: "round(- _b[use] + _b[design],0.001)
Comparison: .875

.         quietly: test - _b[use] + _b[design] = 0

.         display "t-stat = "round(sqrt(r(F)),0.01)
t-stat = 3.8

.         display "Comparison: "round(- _b[use] - _b[int_design_use],0.001)
Comparison: .998

.         quietly: test - _b[use] - _b[int_design_use] = 0

.         display "t-stat = "round(sqrt(r(F)),0.01)
t-stat = 4.96

. // Column 2c: Effort - Employee Level (including Distributive Fairness as Regressor)
. reg contribution_1_8 design use int_design_use peqdistrifairness_factor if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(4, 49)          =      17.01
                                                Prob > F          =     0.0000
                                                R-squared         =     0.3742
                                                Root MSE          =     7.4695

                                           (Std. err. adjusted for 50 clusters in groupnr)
------------------------------------------------------------------------------------------
                         |               Robust
        contribution_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------------------+----------------------------------------------------------------
                  design |   3.737859   2.342093     1.60   0.117    -.9687525     8.44447
                     use |   .5972907   2.288143     0.26   0.795    -4.000905    5.195486
          int_design_use |  -3.175352   3.477621    -0.91   0.366    -10.16389     3.81319
peqdistrifairness_factor |   5.209362   .6973469     7.47   0.000     3.807991    6.610733
                   _cons |    20.1944   1.657767    12.18   0.000       16.863    23.52581
------------------------------------------------------------------------------------------

.         // Simple Comparisons
.         display "Comparison: "round(_b[design],0.001)
Comparison: 3.738

.         quietly: test _b[design] = 0

.         display "t-stat = "round(sqrt(r(F)),0.01)       
t-stat = 1.6

.         display "Comparison: "round(- _b[use] + _b[design],0.001)
Comparison: 3.141

.         quietly: test - _b[use] + _b[design] = 0

.         display "t-stat = "round(sqrt(r(F)),0.01)
t-stat = 1.33

.         display "Comparison: "round(- _b[use] - _b[int_design_use],0.001)
Comparison: 2.578

.         quietly: test - _b[use] - _b[int_design_use] = 0

.         display "t-stat = "round(sqrt(r(F)),0.01)
t-stat = .95

. // Column 3: Effort - Team Level
. reg contribution_1_8_team design use int_design_use if subjectnr==1 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =         50
                                                F(3, 49)          =       3.12
                                                Prob > F          =     0.0342
                                                R-squared         =     0.1523
                                                Root MSE          =       8.15

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
contribution~m | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   7.798611   2.971672     2.62   0.012     1.826812    13.77041
           use |   .0977564   2.978562     0.03   0.974    -5.887889    6.083402
int_design_use |  -7.875534   4.577993    -1.72   0.092    -17.07535    1.324287
         _cons |   19.64583   2.024562     9.70   0.000     15.57732    23.71434
--------------------------------------------------------------------------------

.         // Simple Comparisons
.         display "Comparison: "round(_b[design],0.001)
Comparison: 7.799

.         quietly: test _b[design] = 0

.         display "t-stat = "round(sqrt(r(F)),0.01)       
t-stat = 2.62

.         display "Comparison: "round(- _b[use] + _b[design],0.001)
Comparison: 7.701

.         quietly: test - _b[use] + _b[design] = 0

.         display "t-stat = "round(sqrt(r(F)),0.01)
t-stat = 2.5

.         display "Comparison: "round(- _b[use] - _b[int_design_use],0.001)
Comparison: 7.778

.         quietly: test - _b[use] - _b[int_design_use] = 0

.         display "t-stat = "round(sqrt(r(F)),0.01)
t-stat = 2.24

. 
. ** Footnote 26: Assumption of Normality
. // Effort
. swilk contribution if period<9 & subjectnr<4                    // Reject assumption of normality (p < 0.001)

                   Shapiro–Wilk W test for normal data

    Variable |        Obs       W           V         z       Prob>z
-------------+------------------------------------------------------
contribution |      1,200    0.98890      8.266     5.269    0.00000

. swilk contribution_1_8 if period==9 & subjectnr<4               // Do no reject assumption of normality (p = 0.139)

                   Shapiro–Wilk W test for normal data

    Variable |        Obs       W           V         z       Prob>z
-------------+------------------------------------------------------
contribu~1_8 |        150    0.98612      1.615     1.086    0.13872

. swilk contribution_1_8_team if period==9 & subjectnr==1         // Do no reject assumption of normality (p = 0.741)

                   Shapiro–Wilk W test for normal data

    Variable |        Obs       W           V         z       Prob>z
-------------+------------------------------------------------------
contributi~m |         50    0.98430      0.738    -0.647    0.74130

. // Error Term (Effort Residuals)
. reg contribution design use int_design_use if subjectnr<4 & period<9, vce(cluster groupnr)

Linear regression                               Number of obs     =      1,200
                                                F(3, 49)          =       3.32
                                                Prob > F          =     0.0274
                                                R-squared         =     0.0636
                                                Root MSE          =     12.736

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
  contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   7.798611   2.882875     2.71   0.009     2.005257    13.59196
           use |   .0977564   2.889559     0.03   0.973     -5.70903    5.904543
int_design_use |  -7.875534   4.441196    -1.77   0.082    -16.80045    1.049384
         _cons |   19.64583   1.964065    10.00   0.000      15.6989    23.59277
--------------------------------------------------------------------------------

.         predict contr_residual, residuals
(600 missing values generated)

.         swilk contr_residual if period<9 & subjectnr<4                          // Reject assumption of normality (p < 0.001)

                   Shapiro–Wilk W test for normal data

    Variable |        Obs       W           V         z       Prob>z
-------------+------------------------------------------------------
contr_resi~l |      1,200    0.96524     25.885     8.117    0.00000

.         drop contr_residual

. reg contribution_1_8 design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       3.26
                                                Prob > F          =     0.0293
                                                R-squared         =     0.1274
                                                Root MSE          =     8.7901

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
contributi~1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   7.798611   2.908697     2.68   0.010     1.953366    13.64386
           use |   .0977564   2.915441     0.03   0.973    -5.761042    5.956555
int_design_use |  -7.875534   4.480977    -1.76   0.085    -16.88039    1.129326
         _cons |   19.64583   1.981657     9.91   0.000     15.66354    23.62812
--------------------------------------------------------------------------------

.         predict contr_residual_1_8, residuals
(1,650 missing values generated)

.         swilk contr_residual_1_8 if period==9 & subjectnr<4             // Do no reject assumption of normality (p = 0.432)

                   Shapiro–Wilk W test for normal data

    Variable |        Obs       W           V         z       Prob>z
-------------+------------------------------------------------------
contr_resi~8 |        150    0.99073      1.079     0.172    0.43182

.         drop contr_residual_1_8

. reg contribution_1_8_team design use int_design_use if subjectnr==1 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =         50
                                                F(3, 49)          =       3.12
                                                Prob > F          =     0.0342
                                                R-squared         =     0.1523
                                                Root MSE          =       8.15

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
contribution~m | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   7.798611   2.971672     2.62   0.012     1.826812    13.77041
           use |   .0977564   2.978562     0.03   0.974    -5.887889    6.083402
int_design_use |  -7.875534   4.577993    -1.72   0.092    -17.07535    1.324287
         _cons |   19.64583   2.024562     9.70   0.000     15.57732    23.71434
--------------------------------------------------------------------------------

.         predict contr_residual_1_8_team, residuals
(1,600 missing values generated)

.         swilk contr_residual_1_8_team if subjectnr==1 & period==9       // Do no reject assumption of normality (p = 0.516)

                   Shapiro–Wilk W test for normal data

    Variable |        Obs       W           V         z       Prob>z
-------------+------------------------------------------------------
contr_resi~m |         50    0.97912      0.982    -0.039    0.51553

.         drop contr_residual_1_8_team            

.         
. ** Untabulated Tests Related to Table 3
. // Effect of Design on Effort under the Discretionary Use
. reg contribution design use int_design_use if subjectnr<4 & period<9, vce(cluster groupnr)

Linear regression                               Number of obs     =      1,200
                                                F(3, 49)          =       3.32
                                                Prob > F          =     0.0274
                                                R-squared         =     0.0636
                                                Root MSE          =     12.736

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
  contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   7.798611   2.882875     2.71   0.009     2.005257    13.59196
           use |   .0977564   2.889559     0.03   0.973     -5.70903    5.904543
int_design_use |  -7.875534   4.441196    -1.77   0.082    -16.80045    1.049384
         _cons |   19.64583   1.964065    10.00   0.000      15.6989    23.59277
--------------------------------------------------------------------------------

. display "Comparison: "round(_b[design] + _b[int_design_use],0.001)
Comparison: -.077

. test _b[design] + _b[int_design_use] = 0

 ( 1)  design + int_design_use = 0

       F(  1,    49) =    0.00
            Prob > F =    0.9819

. // Differences in Effort Among Three Other Conditions ([1], [3], and [4])
. test (_b[use] = 0) (_b[design] + _b[int_design_use] = 0) (_b[design] + _b[use] + _b[int_design_use] = 0)

 ( 1)  use = 0
 ( 2)  design + int_design_use = 0
 ( 3)  design + use + int_design_use = 0
       Constraint 3 dropped

       F(  2,    49) =    0.00
            Prob > F =    0.9994

. 
. ** Footnote 28: Factor Analysis of Perceived Distributive Fairness
. factor peqdistrifairness1 peqdistrifairness2 peqdistrifairness3 peqdistrifairness4 if subjectnr<4
(obs=150)

Factor analysis/correlation                      Number of obs    =        150
    Method: principal factors                    Retained factors =          1
    Rotation: (unrotated)                        Number of params =          4

    --------------------------------------------------------------------------
         Factor  |   Eigenvalue   Difference        Proportion   Cumulative
    -------------+------------------------------------------------------------
        Factor1  |      3.20984      3.23857            1.0455       1.0455
        Factor2  |     -0.02873      0.01318           -0.0094       1.0361
        Factor3  |     -0.04191      0.02704           -0.0137       1.0225
        Factor4  |     -0.06895            .           -0.0225       1.0000
    --------------------------------------------------------------------------
    LR test: independent vs. saturated:  chi2(6)  =  588.07 Prob>chi2 = 0.0000

Factor loadings (pattern matrix) and unique variances

    ---------------------------------------
        Variable |  Factor1 |   Uniqueness 
    -------------+----------+--------------
    peqdistrif~1 |   0.9109 |      0.1702  
    peqdistrif~2 |   0.8848 |      0.2171  
    peqdistrif~3 |   0.9439 |      0.1090  
    peqdistrif~4 |   0.8404 |      0.2938  
    ---------------------------------------

. rotate // Eigenvalue: 3.210

Factor analysis/correlation                      Number of obs    =        150
    Method: principal factors                    Retained factors =          1
    Rotation: orthogonal varimax (Kaiser off)    Number of params =          4

    --------------------------------------------------------------------------
         Factor  |     Variance   Difference        Proportion   Cumulative
    -------------+------------------------------------------------------------
        Factor1  |      3.20984            .            1.0455       1.0455
    --------------------------------------------------------------------------
    LR test: independent vs. saturated:  chi2(6)  =  588.07 Prob>chi2 = 0.0000

Rotated factor loadings (pattern matrix) and unique variances

    ---------------------------------------
        Variable |  Factor1 |   Uniqueness 
    -------------+----------+--------------
    peqdistrif~1 |   0.9109 |      0.1702  
    peqdistrif~2 |   0.8848 |      0.2171  
    peqdistrif~3 |   0.9439 |      0.1090  
    peqdistrif~4 |   0.8404 |      0.2938  
    ---------------------------------------

Factor rotation matrix

    -----------------------
                 | Factor1 
    -------------+---------
         Factor1 |  1.0000 
    -----------------------

. 
. ** Footnote 29: Procedural Fairness
. // Effect of Manipulations on Procedural Fairness
. reg peqprocedfairness_factor design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       4.03
                                                Prob > F          =     0.0122
                                                R-squared         =     0.0699
                                                Root MSE          =     .83366

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
peqprocedfai~r | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   .3582158   .1905825     1.88   0.066     -.024774    .7412056
           use |  -.2397492    .248845    -0.96   0.340     -.739822    .2603236
int_design_use |  -.2612312   .2996213    -0.87   0.388    -.8633428    .3408804
         _cons |   .0134818   .1527613     0.09   0.930    -.2935035    .3204671
--------------------------------------------------------------------------------

. // Main Effect of Use
. test _b[use] + 0.5*_b[int_design_use] = 0

 ( 1)  use + .5*int_design_use = 0

       F(  1,    49) =    6.11
            Prob > F =    0.0169

. // Procedural Fairness does not explain differences in Effort among the four conditions
. reg contribution_1_8 design use int_design_use peqprocedfairness_factor if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(4, 49)          =       7.76
                                                Prob > F          =     0.0001
                                                R-squared         =     0.2154
                                                Root MSE          =      8.364

                                           (Std. err. adjusted for 50 clusters in groupnr)
------------------------------------------------------------------------------------------
                         |               Robust
        contribution_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------------------+----------------------------------------------------------------
                  design |   6.599332   2.834504     2.33   0.024     .9031838    12.29548
                     use |   .9004183   2.730249     0.33   0.743    -4.586222    6.387059
          int_design_use |  -7.000952   4.150224    -1.69   0.098    -15.34114    1.339235
peqprocedfairness_factor |   3.347923   .8274778     4.05   0.000     1.685044    5.010802
                   _cons |    19.6007   1.928717    10.16   0.000     15.72479     23.4766
------------------------------------------------------------------------------------------

.         //reg contribution_1_8 design use int_design_use peqdistrifairness_factor peqprocedfairness_factor if subjectnr<4 & period==9, vce(cluster groupnr)
. 
. 
. 
. ** 4.2 SUPPLEMENTAL ANALYSES
. 
. ** 4.2.1 EMPLOYEES' EFFORT CONTRIBUTIONS (STAGE 1)
. 
. ** Interaction Variables
. gen period_n = period - 1

. gen int_design_period = design * period_n

. gen int_use_period = use * period_n

. gen int_design_use_period = design * use * period_n

. 
. ** Difference Among the Four Conditions in Round 1
. reg contribution design use int_design_use if subjectnr<4 & period==1, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       0.08
                                                Prob > F          =     0.9721
                                                R-squared         =     0.0016
                                                Root MSE          =     10.412

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
  contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |  -.6666667   2.124168    -0.31   0.755    -4.935343    3.602009
           use |   .4316239   1.978389     0.22   0.828    -3.544099    4.407346
int_design_use |  -.1025641   3.255882    -0.03   0.975    -6.645503    6.440375
         _cons |   19.05556   1.137991    16.74   0.000     16.76868    21.34243
--------------------------------------------------------------------------------

. test (_b[design] = _b[use] = _b[int_design_use] = 0)

 ( 1)  design - use = 0
 ( 2)  design - int_design_use = 0
 ( 3)  design = 0

       F(  3,    49) =    0.08
            Prob > F =    0.9721

. 
. reg contribution design use int_design_use period_n int_design_period int_use_period int_design_use_period if subjectnr<4 & period<9, vce(cluster groupnr)

Linear regression                               Number of obs     =      1,200
                                                F(7, 49)          =       2.00
                                                Prob > F          =     0.0744
                                                R-squared         =     0.0845
                                                Root MSE          =     12.614

                                        (Std. err. adjusted for 50 clusters in groupnr)
---------------------------------------------------------------------------------------
                      |               Robust
         contribution | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
----------------------+----------------------------------------------------------------
               design |   1.657407   2.840714     0.58   0.562    -4.051221    7.366036
                  use |   1.343661   2.640701     0.51   0.613    -3.963027    6.650349
       int_design_use |  -2.554843   3.980614    -0.64   0.524    -10.55419    5.444501
             period_n |  -.3009259   .4740288    -0.63   0.528    -1.253522    .6516706
    int_design_period |    1.75463   .7019507     2.50   0.016     .3440068    3.165252
       int_use_period |  -.3559727   .7353482    -0.48   0.630     -1.83371    1.121765
int_design_use_period |  -1.520197   .9697536    -1.57   0.123     -3.46899    .4285954
                _cons |   20.69907   2.077112     9.97   0.000     16.52496    24.87319
---------------------------------------------------------------------------------------

. // Difference Among the Four Conditions in Round 1
. test (_b[design] = _b[use] = _b[int_design_use] = 0)

 ( 1)  design - use = 0
 ( 2)  design - int_design_use = 0
 ( 3)  design = 0

       F(  3,    49) =    0.15
            Prob > F =    0.9292

. // Effect of Round
.         // Condition [2]
.         display "Increase: "round(_b[period] + _b[int_design_period], 0.001)
Increase: 1.454

.         test _b[period] + _b[int_design_period] = 0

 ( 1)  period_n + int_design_period = 0

       F(  1,    49) =    7.88
            Prob > F =    0.0071

.         // Condition [1]
.         display "Increase: "round(_b[period], 0.001)
Increase: -.301

.         test _b[period] = 0

 ( 1)  period_n = 0

       F(  1,    49) =    0.40
            Prob > F =    0.5285

.         // Condition [3]
.         display "Increase: "round(_b[period] + _b[int_use_period], 0.001)
Increase: -.657

.         test _b[period] + _b[int_use_period] = 0

 ( 1)  period_n + int_use_period = 0

       F(  1,    49) =    1.37
            Prob > F =    0.2483

.         // Condition [4]
.         display "Increase: "round(_b[period] + _b[int_design_period] + _b[int_use_period] + _b[int_design_use_period], 0.001)
Increase: -.422

.         test _b[period] + _b[int_design_period] + _b[int_use_period] + _b[int_design_use_period] = 0

 ( 1)  period_n + int_design_period + int_use_period + int_design_use_period = 0

       F(  1,    49) =    1.36
            Prob > F =    0.2499

. // Comparison of Effect of Round among Conditions
.         // Conditions [2] vs [1]
.         display "Comparison: "round(_b[int_design_period], 0.001)
Comparison: 1.755

.         test _b[int_design_period] = 0

 ( 1)  int_design_period = 0

       F(  1,    49) =    6.25
            Prob > F =    0.0158

.         // Conditions [2] vs [3]
.         display "Comparison: "round(_b[int_design_period] - _b[int_use_period], 0.001) 
Comparison: 2.111

.         test _b[int_design_period] - _b[int_use_period] = 0

 ( 1)  int_design_period - int_use_period = 0

       F(  1,    49) =    7.63
            Prob > F =    0.0081

.         // Conditions [2] vs [4]
.         display "Comparison: "round(- _b[int_use_period] - _b[int_design_use_period], 0.001)
Comparison: 1.876

.         test - _b[int_use_period] - _b[int_design_use_period] = 0

 ( 1)  - int_use_period - int_design_use_period = 0

       F(  1,    49) =    8.81
            Prob > F =    0.0046

. // Applies Also for Team (Rather than Individual)
.         /*gen contribution_team = .
>         bysort groupnr (subjectnr period): replace contribution_team = (contribution[_n] + contribution[_n+9] + contribution[_n+18])/3 if subjectnr==1 & period<9
>         reg contribution_team design use int_design_use period_n int_design_period int_use_period int_design_use_period if subjectnr==1 & period<9, vce(cluster groupnr)*/
. 
. /* Round by Round Comparison of Effort Among Conditions
> foreach round in 1 2 3 4 5 6 7 8 {
>         display "Round "`round'
>         reg contribution design use int_design_use if subjectnr<4 & period==`round', vce(cluster groupnr)
>         display "Round "`round' ": Condition [2] vs Condition [1]"
>         display _b[design]
>         test _b[design] = 0
>         display "Round "`round' ": Condition [2] vs Condition [3]"
>         display - _b[use] + _b[design]
>         test - _b[use] + _b[design] = 0
>         display "Round "`round' ": Condition [2] vs Condition [4]"
>         display - _b[use] - _b[int_design_use]
>         test - _b[use] - _b[int_design_use] = 0 
>         }
> */
. 
. ********************************************************************************
. ** FIGURE 2: EFFORT HISTOGRAMS
. ********************************************************************************
. ** Histogram of effort (by condition and round)
. label var condition "Condition"

. label var contribution "Effort"

. label var period "Round"

. set scheme s2color //plotplainblind // s1mono

. grstyle init

. grstyle color background white

. graph set window fontface "Times New Roman"

. grstyle color major_grid dimgray

. graph twoway (histogram contribution if subjectnr<4 & period<9, by(condition period, cols(8) note("")) discrete percent lcolor(dknavy) fcolor(edkblue) ytitle("") ylabel(0(10)50) xtitle("") plotregi
> on(margin(tiny)) subtitle("") )

. ********************************************************************************
. 
. /* Round by Round 
> // Average Effort
> foreach round in 1 2 3 4 5 6 7 8 {
>         display "Round "`round'
>         display "Condition [1]: Formulaic Use & Self-Including Design"
>         sum contribution if use==0 & design==0 & period==`round'
>         display "Condition [2]: Formulaic Use & Self-Excluding Design"
>         sum contribution if use==0 & design==1 & period==`round'
>         display "Condition [3]: Discretionary Use & Self-Including Design"
>         sum contribution if use==1 & design==0 & period==`round'
>         display "Condition [4]: Discretionary Use & Self-Excluding Design"
>         sum contribution if use==1 & design==1 & period==`round'
>         }
> // Frequency Table of Effort
> foreach round in 1 2 3 4 5 6 7 8 {
>         display "Round "`round'
>         display "Condition [1]: Formulaic Use & Self-Including Design"
>         tab contribution if use==0 & design==0 & period==`round'
>         display "Condition [2]: Formulaic Use & Self-Excluding Design"
>         tab contribution if use==0 & design==1 & period==`round'
>         display "Condition [3]: Discretionary Use & Self-Including Design"
>         tab contribution if use==1 & design==0 & period==`round'
>         display "Condition [4]: Discretionary Use & Self-Excluding Design"
>         tab contribution if use==1 & design==1 & period==`round'
>         }
> */
. 
. ** Footnote 31: Distribution of Effort in Round 8
. display "Condition [1]: Formulaic Use & Self-Including Design"
Condition [1]: Formulaic Use & Self-Including Design

. tab contribution if use==0 & design==0 & period==8

     Effort |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |          9       25.00       25.00
          2 |          1        2.78       27.78
          6 |          1        2.78       30.56
          8 |          1        2.78       33.33
         10 |          1        2.78       36.11
         14 |          2        5.56       41.67
         16 |          3        8.33       50.00
         18 |          2        5.56       55.56
         20 |          5       13.89       69.44
         24 |          1        2.78       72.22
         26 |          1        2.78       75.00
         28 |          2        5.56       80.56
         30 |          2        5.56       86.11
         32 |          1        2.78       88.89
         38 |          1        2.78       91.67
         40 |          3        8.33      100.00
------------+-----------------------------------
      Total |         36      100.00

. display "Condition [2]: Formulaic Use & Self-Excluding Design"
Condition [2]: Formulaic Use & Self-Excluding Design

. tab contribution if use==0 & design==1 & period==8

     Effort |      Freq.     Percent        Cum.
------------+-----------------------------------
          2 |          2        5.56        5.56
          4 |          1        2.78        8.33
         12 |          1        2.78       11.11
         16 |          2        5.56       16.67
         20 |          3        8.33       25.00
         22 |          2        5.56       30.56
         24 |          1        2.78       33.33
         26 |          1        2.78       36.11
         28 |          1        2.78       38.89
         30 |          2        5.56       44.44
         34 |          2        5.56       50.00
         36 |          1        2.78       52.78
         40 |         17       47.22      100.00
------------+-----------------------------------
      Total |         36      100.00

. display "Condition [3]: Discretionary Use & Self-Including Design"
Condition [3]: Discretionary Use & Self-Including Design

. tab contribution if use==1 & design==0 & period==8

     Effort |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |         14       35.90       35.90
          2 |          2        5.13       41.03
          4 |          1        2.56       43.59
          6 |          1        2.56       46.15
         10 |          3        7.69       53.85
         12 |          1        2.56       56.41
         16 |          1        2.56       58.97
         20 |          5       12.82       71.79
         26 |          1        2.56       74.36
         28 |          1        2.56       76.92
         30 |          2        5.13       82.05
         36 |          2        5.13       87.18
         40 |          5       12.82      100.00
------------+-----------------------------------
      Total |         39      100.00

. display "Condition [4]: Discretionary Use & Self-Excluding Design"
Condition [4]: Discretionary Use & Self-Excluding Design

. tab contribution if use==1 & design==1 & period==8

     Effort |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |          4       10.26       10.26
          2 |          3        7.69       17.95
          4 |          4       10.26       28.21
          6 |          2        5.13       33.33
          8 |          2        5.13       38.46
         10 |          1        2.56       41.03
         12 |          1        2.56       43.59
         16 |          1        2.56       46.15
         18 |          2        5.13       51.28
         20 |          7       17.95       69.23
         22 |          2        5.13       74.36
         24 |          1        2.56       76.92
         26 |          1        2.56       79.49
         30 |          1        2.56       82.05
         34 |          1        2.56       84.62
         36 |          1        2.56       87.18
         40 |          5       12.82      100.00
------------+-----------------------------------
      Total |         39      100.00

. 
. 
. 
. ** 4.2.2 EMPLOYEES' ALLOCATION PROPOSALS (STAGE 2)
. 
. ********************************************************************************
. ** TABLE 4: DEVIATION OF FINAL BONUS FROM FAIR BONUS
. ********************************************************************************
. // Condition [1]: Formulaic Use & Self-Including Design
. sum dev_finalfromfair if use==0 & design==0 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
dev_finalf~r |        288    7.513889    9.073441          0         60

. sum dev_finalfromfair_1_8 if use==0 & design==0 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
dev_finalf~8 |         36    7.513889    5.223041      1.125     20.125

. sum dev_finalfromfair_1_8_team if use==0 & design==0 & period==9 & subjectnr==1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
dev_finalf~m |         12    7.513889    5.034456   1.666667   16.58333

. // Condition [2]: Formulaic Use & Self-Excluding Design
. sum dev_finalfromfair if use==0 & design==1 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
dev_finalf~r |        288    4.673611    6.630444          0         40

. sum dev_finalfromfair_1_8 if use==0 & design==1 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
dev_finalf~8 |         36    4.673611    3.417298       .625     13.875

. sum dev_finalfromfair_1_8_team if use==0 & design==1 & period==9 & subjectnr==1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
dev_finalf~m |         12    4.673611    2.949589   1.083333   10.41667

. // Condition [3]: Discretionary Use & Self-Including Design
. sum dev_finalfromfair if use==1 & design==0 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
dev_finalf~r |        312    10.67308    12.80708          0         77

. sum dev_finalfromfair_1_8 if use==1 & design==0 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
dev_finalf~8 |         39    10.67308    7.148772      1.375     28.625

. sum dev_finalfromfair_1_8_team if use==1 & design==0 & period==9 & subjectnr==1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
dev_finalf~m |         13    10.67308    6.701425   2.083333   23.33333

. // Condition [4]: Discretionary Use & Self-Excluding Design
. sum dev_finalfromfair if use==1 & design==1 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
dev_finalf~r |        312    11.27564    16.19578          0        120

. sum dev_finalfromfair_1_8 if use==1 & design==1 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
dev_finalf~8 |         39    11.27564    9.480771       1.75      42.75

. sum dev_finalfromfair_1_8_team if use==1 & design==1 & period==9 & subjectnr==1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
dev_finalf~m |         13    11.27564    8.959424   2.583333   29.33333

. 
. ** Untabulated Tests Related to Table 4
. // Decision Level
. quietly: reg dev_finalfromfair design use int_design_use if subjectnr<4 & period<9, vce(cluster groupnr)

.         display "Comparison: "round(_b[design],0.001)
Comparison: -2.84

.         test _b[design] = 0

 ( 1)  design = 0

       F(  1,    49) =    3.03
            Prob > F =    0.0879

.         display "Comparison: "round(_b[design] - _b[use],0.001)
Comparison: -5.999

.         test _b[design] - _b[use] = 0

 ( 1)  design - use = 0

       F(  1,    49) =    9.13
            Prob > F =    0.0040

.         display "Comparison: "round(- _b[use] - _b[int_design_use],0.001)
Comparison: -6.602

.         test - _b[use] - _b[int_design_use] = 0 

 ( 1)  - use - int_design_use = 0

       F(  1,    49) =    6.69
            Prob > F =    0.0127

.         // Comparison Among Conditions [1], [3], and [4]
.         test (_b[use] = _b[design] + _b[use] + _b[int_design_use] = 0)

 ( 1)  - design - int_design_use = 0
 ( 2)  use = 0

       F(  2,    49) =    1.42
            Prob > F =    0.2518

. // Employee Level
. quietly: reg dev_finalfromfair_1_8 design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

.         display "Comparison: "round(_b[design],0.001)
Comparison: -2.84

.         test _b[design] = 0

 ( 1)  design = 0

       F(  1,    49) =    2.98
            Prob > F =    0.0907

.         display "Comparison: "round(_b[design] - _b[use],0.001)
Comparison: -5.999

.         test _b[design] - _b[use] = 0

 ( 1)  design - use = 0

       F(  1,    49) =    8.97
            Prob > F =    0.0043

.         display "Comparison: "round(- _b[use] - _b[int_design_use],0.001)
Comparison: -6.602

.         test - _b[use] - _b[int_design_use] = 0 

 ( 1)  - use - int_design_use = 0

       F(  1,    49) =    6.58
            Prob > F =    0.0134

.         // Comparison Among Conditions [1], [3], and [4]
.         test (_b[use] = _b[design] + _b[use] + _b[int_design_use] = 0)

 ( 1)  - design - int_design_use = 0
 ( 2)  use = 0

       F(  2,    49) =    1.39
            Prob > F =    0.2578

. // Team Level
. quietly: reg dev_finalfromfair_1_8_team design use int_design_use if subjectnr==1 & period==9, vce(cluster groupnr)

.         display "Comparison: "round(_b[design],0.001)
Comparison: -2.84

.         test _b[design] = 0

 ( 1)  design = 0

       F(  1,    49) =    2.85
            Prob > F =    0.0975

.         display "Comparison: "round(_b[design] - _b[use],0.001)
Comparison: -5.999

.         test _b[design] - _b[use] = 0

 ( 1)  design - use = 0

       F(  1,    49) =    8.59
            Prob > F =    0.0051

.         display "Comparison: "round(- _b[use] - _b[int_design_use],0.001)
Comparison: -6.602

.         test - _b[use] - _b[int_design_use] = 0 

 ( 1)  - use - int_design_use = 0

       F(  1,    49) =    6.30
            Prob > F =    0.0154

.         // Comparison Among Conditions [1], [3], and [4]
.         test (_b[use] = _b[design] + _b[use] + _b[int_design_use] = 0)

 ( 1)  - design - int_design_use = 0
 ( 2)  use = 0

       F(  2,    49) =    1.34
            Prob > F =    0.2725

. 
. ********************************************************************************
. ** TABLE 5: DISTORTION - DESCRIPTIVE RESULTS
. ********************************************************************************
. ** PANEL A: PROPOSAL DISTORTION
. // Condition [1]: Formulaic Use & Self-Including Design
. sum proposal_dist if use==0 & design==0 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
proposal_d~t |        288    14.20833     17.9138          0         80

. sum proposal_dist_1_8 if use==0 & design==0 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
proposal_d~8 |         36    14.20833    13.63196          0      57.75

. sum proposal_dist_1_8_team if use==0 & design==0 & period==9 & subjectnr==1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
proposal_d~m |         12    14.20833    13.27076   2.333333   49.41667

. // Condition [2]: Formulaic Use & Self-Excluding Design
. sum proposal_dist if use==0 & design==1 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
proposal_d~t |        288    4.795243    8.689977          0         60

. sum proposal_dist_1_8 if use==0 & design==1 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
proposal_d~8 |         36    4.795243    4.326802    .256579   16.39163

. sum proposal_dist_1_8_team if use==0 & design==1 & period==9 & subjectnr==1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
proposal_d~m |         12    4.795243    3.437843   1.467654   13.43104

. // Condition [3]: Discretionary Use & Self-Including Design
. sum proposal_dist if use==1 & design==0 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
proposal_d~t |        312     11.1859    13.39545          0         70

. sum proposal_dist_1_8 if use==1 & design==0 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
proposal_d~8 |         39     11.1859    9.201637          0         45

. sum proposal_dist_1_8_team if use==1 & design==0 & period==9 & subjectnr==1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
proposal_d~m |         13     11.1859     6.56398       2.25   24.83333

. // Condition [4]: Discretionary Use & Self-Excluding Design
. sum proposal_dist if use==1 & design==1 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
proposal_d~t |        312    5.823919    9.644832          0         60

. sum proposal_dist_1_8 if use==1 & design==1 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
proposal_d~8 |         39    5.823919     4.90319   .5535714   21.95519

. sum proposal_dist_1_8_team if use==1 & design==1 & period==9 & subjectnr==1     

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
proposal_d~m |         13    5.823919    3.654692    1.13631   13.31409

. ** PANEL B: DISTORTION
. // Condition [1]: Formulaic Use & Self-Including Design
. sum distortion if use==0 & design==0 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
  distortion |        288    7.513889    9.073441          0         60

. sum distortion_1_8 if use==0 & design==0 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
distortion~8 |         36    7.513889    5.223041      1.125     20.125

. sum distortion_1_8_team if use==0 & design==0 & period==9 & subjectnr==1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
distortion~m |         12    7.513889    5.034456   1.666667   16.58333

. // Condition [2]: Formulaic Use & Self-Excluding Design
. sum distortion if use==0 & design==1 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
  distortion |        288    3.889957    6.119729          0         40

. sum distortion_1_8 if use==0 & design==1 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
distortion~8 |         36    3.889957    3.226064   .4376321   12.97044

. sum distortion_1_8_team if use==0 & design==1 & period==9 & subjectnr==1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
distortion~m |         12    3.889957    2.878851   1.318743   10.64388

. // Condition [3]: Discretionary Use & Self-Including Design
. sum distortion if use==1 & design==0 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
  distortion |        312    9.147436    9.362856          0         54

. sum distortion_1_8 if use==1 & design==0 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
distortion~8 |         39    9.147436    5.341686      1.375         23

. sum distortion_1_8_team if use==1 & design==0 & period==9 & subjectnr==1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
distortion~m |         13    9.147436    4.992025       2.25   18.58333

. // Condition [4]: Discretionary Use & Self-Excluding Design
. sum distortion if use==1 & design==1 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
  distortion |        312    4.763019    6.575191          0         45

. sum distortion_1_8 if use==1 & design==1 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
distortion~8 |         39    4.763019     3.43718      .7625   16.95005

. sum distortion_1_8_team if use==1 & design==1 & period==9 & subjectnr==1                

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
distortion~m |         13    4.763019     3.03918   .9392857    11.7417

. ** PANEL C: DISTORTION & EFFICIENCY LOSS
. // Condition [1]: Formulaic Use & Self-Including Design
. sum dist_efficiency if use==0 & design==0 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
dist_effic~y |        288    7.513889    9.073441          0         60

. sum dist_efficiency_1_8 if use==0 & design==0 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
dist_effic~8 |         36    7.513889    5.223041      1.125     20.125

. sum dist_efficiency_1_8_team if use==0 & design==0 & period==9 & subjectnr==1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
dist_effic~m |         12    7.513889    5.034456   1.666667   16.58333

. // Condition [2]: Formulaic Use & Self-Excluding Design
. sum dist_efficiency if use==0 & design==1 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
dist_effic~y |        288    4.673611    6.630444          0         40

. sum dist_efficiency_1_8 if use==0 & design==1 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
dist_effic~8 |         36    4.673611    3.417298       .625     13.875

. sum dist_efficiency_1_8_team if use==0 & design==1 & period==9 & subjectnr==1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
dist_effic~m |         12    4.673611    2.949589   1.083333   10.41667

. // Condition [3]: Discretionary Use & Self-Including Design
. sum dist_efficiency if use==1 & design==0 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
dist_effic~y |        312    9.147436    9.362856          0         54

. sum dist_efficiency_1_8 if use==1 & design==0 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
dist_effic~8 |         39    9.147436    5.341686      1.375         23

. sum dist_efficiency_1_8_team if use==1 & design==0 & period==9 & subjectnr==1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
dist_effic~m |         13    9.147436    4.992025       2.25   18.58333

. // Condition [4]: Discretionary Use & Self-Excluding Design
. sum dist_efficiency if use==1 & design==1 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
dist_effic~y |        312    6.012821    6.913789          0         40

. sum dist_efficiency_1_8 if use==1 & design==1 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
dist_effic~8 |         39    6.012821    3.183892       1.25     16.375

. sum dist_efficiency_1_8_team if use==1 & design==1 & period==9 & subjectnr==1           

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
dist_effic~m |         13    6.012821    2.659897          2   11.16667

. 
. ********************************************************************************
. ** TABLE 6: DISTORTION - REGRESSION RESULTS (EMPLOYEE LEVEL)
. ********************************************************************************
. ** COLUMN 1: PROPOSAL DISTORTION
. reg proposal_dist_1_8 design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       4.86
                                                Prob > F          =     0.0049
                                                R-squared         =     0.1626
                                                Root MSE          =     8.7938

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
proposal_dis~8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   -9.41309   3.866508    -2.43   0.019    -17.18313   -1.643052
           use |  -3.022436   4.146762    -0.73   0.470    -11.35567    5.310794
int_design_use |   4.051112   4.373038     0.93   0.359    -4.736838    12.83906
         _cons |   14.20833   3.742954     3.80   0.000     6.686586    21.73008
--------------------------------------------------------------------------------

.         display "Comparison: "round(_b[design] + _b[int_design_use],0.001)
Comparison: -5.362

.         test _b[design] + _b[int_design_use] = 0

 ( 1)  design + int_design_use = 0

       F(  1,    49) =    6.89
            Prob > F =    0.0115

.         display "t-stat = "round(sqrt(r(F)),0.01)
t-stat = 2.62

.         display "Comparison: "round(_b[use] + _b[int_design_use],0.001)
Comparison: 1.029

.         test _b[use] + _b[int_design_use] = 0

 ( 1)  use + int_design_use = 0

       F(  1,    49) =    0.55
            Prob > F =    0.4623

.         display "t-stat = "round(sqrt(r(F)),0.01)
t-stat = .74

. ** COLUMN 2: DISTORTION
. reg distortion_1_8 design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       4.63
                                                Prob > F          =     0.0063
                                                R-squared         =     0.1902
                                                Root MSE          =       4.42

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
distortion_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |  -3.623932   1.635705    -2.22   0.031    -6.911005   -.3368597
           use |   1.633547    1.96442     0.83   0.410    -2.314103    5.581197
int_design_use |   -.760485   2.280619    -0.33   0.740    -5.343561    3.822591
         _cons |   7.513889   1.419944     5.29   0.000     4.660404    10.36737
--------------------------------------------------------------------------------

.         display "Comparison: "round(_b[design] + _b[int_design_use],0.001)
Comparison: -4.384

.         test _b[design] + _b[int_design_use] = 0

 ( 1)  design + int_design_use = 0

       F(  1,    49) =    7.61
            Prob > F =    0.0081

.         display "t-stat = "round(sqrt(r(F)),0.01)
t-stat = 2.76

.         display "Comparison: "round(_b[use] + _b[int_design_use],0.001)
Comparison: .873

.         test _b[use] + _b[int_design_use] = 0

 ( 1)  use + int_design_use = 0

       F(  1,    49) =    0.57
            Prob > F =    0.4547

.         display "t-stat = "round(sqrt(r(F)),0.01)
t-stat = .75

. ** COLUMN 3: DISTORTION & EFFICIENCY LOSS
. reg dist_efficiency_1_8 design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       2.99
                                                Prob > F          =     0.0397
                                                R-squared         =     0.1290
                                                Root MSE          =      4.405

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
dist_efficie~8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |  -2.840278     1.6457    -1.73   0.091    -6.147436    .4668803
           use |   1.633547    1.96442     0.83   0.410    -2.314103    5.581197
int_design_use |  -.2943376   2.252596    -0.13   0.897    -4.821099    4.232423
         _cons |   7.513889   1.419944     5.29   0.000     4.660404    10.36737
--------------------------------------------------------------------------------

.         display "Comparison: "round(_b[design] + _b[int_design_use],0.001)
Comparison: -3.135

.         test _b[design] + _b[int_design_use] = 0

 ( 1)  design + int_design_use = 0

       F(  1,    49) =    4.15
            Prob > F =    0.0470

.         display "t-stat = "round(sqrt(r(F)),0.01)
t-stat = 2.04

.         display "Comparison: "round(_b[use] + _b[int_design_use],0.001)
Comparison: 1.339

.         test _b[use] + _b[int_design_use] = 0

 ( 1)  use + int_design_use = 0

       F(  1,    49) =    1.48
            Prob > F =    0.2303

.         display "t-stat = "round(sqrt(r(F)),0.01)
t-stat = 1.21

.         
. ** Footnote 35: Table 6 Robustness
. ** Results Table
. // Decision Level: 
.         reg proposal_dist design use int_design_use if subjectnr<4 & period<9, vce(cluster groupnr)

Linear regression                               Number of obs     =      1,200
                                                F(3, 49)          =       4.95
                                                Prob > F          =     0.0044
                                                R-squared         =     0.0812
                                                Root MSE          =     12.883

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
 proposal_dist | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   -9.41309   3.832182    -2.46   0.018    -17.11415   -1.712032
           use |  -3.022436   4.109949    -0.74   0.466    -11.28169    5.236815
int_design_use |   4.051112   4.334216     0.93   0.355    -4.658822    12.76104
         _cons |   14.20833   3.709725     3.83   0.000     6.753361    21.66331
--------------------------------------------------------------------------------

.         reg distortion design use int_design_use if subjectnr<4 & period<9, vce(cluster groupnr)

Linear regression                               Number of obs     =      1,200
                                                F(3, 49)          =       4.71
                                                Prob > F          =     0.0057
                                                R-squared         =     0.0666
                                                Root MSE          =     7.9234

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
    distortion | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |  -3.623932   1.621184    -2.24   0.030    -6.881824   -.3660411
           use |   1.633547   1.946981     0.84   0.406    -2.279057    5.546151
int_design_use |   -.760485   2.260373    -0.34   0.738    -5.302875    3.781905
         _cons |   7.513889   1.407339     5.34   0.000     4.685736    10.34204
--------------------------------------------------------------------------------

.         reg dist_efficiency design use int_design_use if subjectnr<4 & period<9, vce(cluster groupnr)

Linear regression                               Number of obs     =      1,200
                                                F(3, 49)          =       3.05
                                                Prob > F          =     0.0373
                                                R-squared         =     0.0411
                                                Root MSE          =     8.0951

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
dist_efficie~y | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |  -2.840278    1.63109    -1.74   0.088    -6.118076    .4375207
           use |   1.633547   1.946981     0.84   0.406    -2.279057    5.546151
int_design_use |  -.2943376   2.232598    -0.13   0.896    -4.780912    4.192237
         _cons |   7.513889   1.407339     5.34   0.000     4.685736    10.34204
--------------------------------------------------------------------------------

. // Team Level           
.         reg proposal_dist_1_8_team design use int_design_use if subjectnr==1 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =         50
                                                F(3, 49)          =       4.66
                                                Prob > F          =     0.0061
                                                R-squared         =     0.2103
                                                Root MSE          =     7.7243

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
proposal_dis~m | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   -9.41309    3.95022    -2.38   0.021    -17.35135   -1.474826
           use |  -3.022436   4.236542    -0.71   0.479    -11.53609    5.491214
int_design_use |   4.051112   4.467717     0.91   0.369    -4.927102    13.02933
         _cons |   14.20833   3.823991     3.72   0.001     6.523735    21.89293
--------------------------------------------------------------------------------

.         reg distortion_1_8_team design use int_design_use if subjectnr==1 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =         50
                                                F(3, 49)          =       4.43
                                                Prob > F          =     0.0078
                                                R-squared         =     0.2226
                                                Root MSE          =     4.1174

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
distortion_1~m | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |  -3.623932   1.671119    -2.17   0.035    -6.982172   -.2656925
           use |   1.633547   2.006951     0.81   0.420    -2.399572    5.666666
int_design_use |  -.7604851   2.329996    -0.33   0.746    -5.442788    3.921818
         _cons |   7.513889   1.450687     5.18   0.000     4.598624    10.42915
--------------------------------------------------------------------------------

.         reg dist_efficiency_1_8_team design use int_design_use if subjectnr==1 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =         50
                                                F(3, 49)          =       2.87
                                                Prob > F          =     0.0459
                                                R-squared         =     0.1557
                                                Root MSE          =     4.0605

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
dist_efficie~m | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |  -2.840278   1.681331    -1.69   0.098    -6.219038    .5384825
           use |   1.633547   2.006951     0.81   0.420    -2.399572    5.666666
int_design_use |  -.2943376   2.301366    -0.13   0.899    -4.919106    4.330431
         _cons |   7.513889   1.450687     5.18   0.000     4.598624    10.42915
--------------------------------------------------------------------------------

. ** Assumption of Normality 
. // Decision Level
.         swilk proposal_dist if period<9 & subjectnr<4                                                           // Reject assumption of normality: p < 0.001

                   Shapiro–Wilk W test for normal data

    Variable |        Obs       W           V         z       Prob>z
-------------+------------------------------------------------------
proposal_d~t |      1,200    0.74325    191.193    13.105    0.00000

.         swilk distortion if period<9 & subjectnr<4                                                                      // Reject assumption of normality: p < 0.001

                   Shapiro–Wilk W test for normal data

    Variable |        Obs       W           V         z       Prob>z
-------------+------------------------------------------------------
  distortion |      1,200    0.77758    165.633    12.747    0.00000

.         swilk dist_efficiency if period<9 & subjectnr<4                                                         // Reject assumption of normality: p < 0.001

                   Shapiro–Wilk W test for normal data

    Variable |        Obs       W           V         z       Prob>z
-------------+------------------------------------------------------
dist_effic~y |      1,200    0.82459    130.626    12.155    0.00000

. // Employee Level
.         swilk proposal_dist_1_8 if period==9 & subjectnr<4                                                      // Reject assumption of normality: p < 0.001

                   Shapiro–Wilk W test for normal data

    Variable |        Obs       W           V         z       Prob>z
-------------+------------------------------------------------------
proposal_d~8 |        150    0.75778     28.184     7.569    0.00000

.         swilk distortion_1_8 if period==9 & subjectnr<4                                                         // Reject assumption of normality: p < 0.001

                   Shapiro–Wilk W test for normal data

    Variable |        Obs       W           V         z       Prob>z
-------------+------------------------------------------------------
distortion~8 |        150    0.87835     14.155     6.008    0.00000

.         swilk dist_efficiency_1_8 if period==9 & subjectnr<4                                            // Reject assumption of normality: p < 0.001

                   Shapiro–Wilk W test for normal data

    Variable |        Obs       W           V         z       Prob>z
-------------+------------------------------------------------------
dist_effic~8 |        150    0.89787     11.883     5.611    0.00000

. // Team Level
.         swilk proposal_dist_1_8_team if period==9 & subjectnr==1                                        // Reject assumption of normality: p < 0.001

                   Shapiro–Wilk W test for normal data

    Variable |        Obs       W           V         z       Prob>z
-------------+------------------------------------------------------
proposal_d~m |         50    0.74666     11.915     5.284    0.00000

.         swilk distortion_1_8_team if period==9 & subjectnr==1                                           // Reject assumption of normality: p < 0.001

                   Shapiro–Wilk W test for normal data

    Variable |        Obs       W           V         z       Prob>z
-------------+------------------------------------------------------
distortion~m |         50    0.88367      5.471     3.624    0.00014

.         swilk dist_efficiency_1_8_team if period==9 & subjectnr==1                                      // Reject assumption of normality: p < 0.001

                   Shapiro–Wilk W test for normal data

    Variable |        Obs       W           V         z       Prob>z
-------------+------------------------------------------------------
dist_effic~m |         50    0.90526      4.456     3.187    0.00072

. ** Robustness with Logarithmic Transformation (Employee Level)
. // Distortion in Proposal: proposal_dist
.         gen ln_proposal_dist_1_8 = ln(1+proposal_dist_1_8)                                                      
(1,650 missing values generated)

.         swilk ln_proposal_dist_1_8 if period==9 & subjectnr<4                                           // Cannot reject assumption of normality: p = 0.303

                   Shapiro–Wilk W test for normal data

    Variable |        Obs       W           V         z       Prob>z
-------------+------------------------------------------------------
ln_proposa~8 |        150    0.98921      1.256     0.517    0.30273

.         reg ln_proposal_dist_1_8 design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)             

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       5.16
                                                Prob > F          =     0.0035
                                                R-squared         =     0.1557
                                                Root MSE          =     .81179

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
ln_proposal_~8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |  -.8053186   .2931155    -2.75   0.008    -1.394356    -.216281
           use |  -.0840091   .2987846    -0.28   0.780    -.6844392     .516421
int_design_use |   .2504841   .3667826     0.68   0.498    -.4865931    .9875613
         _cons |   2.315076   .2517491     9.20   0.000     1.809167    2.820985
--------------------------------------------------------------------------------

.                 test _b[design] = 0                                                                                                             // p = 0.004 (one-tailed)

 ( 1)  design = 0

       F(  1,    49) =    7.55
            Prob > F =    0.0084

.                 test _b[design] + _b[int_design_use] = 0                                                                // p = 0.008 (one-tailed)       

 ( 1)  design + int_design_use = 0

       F(  1,    49) =    6.33
            Prob > F =    0.0152

. // Distortion
.         gen ln_distortion_1_8 = ln(1+distortion_1_8)
(1,650 missing values generated)

.         swilk ln_distortion_1_8 if period==9 & subjectnr<4                                                      // Cannot reject assumption of normality: p = 0.176

                   Shapiro–Wilk W test for normal data

    Variable |        Obs       W           V         z       Prob>z
-------------+------------------------------------------------------
ln_distort~8 |        150    0.98703      1.509     0.933    0.17553

.         reg ln_distortion_1_8 design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)                

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       5.88
                                                Prob > F          =     0.0016
                                                R-squared         =     0.2202
                                                Root MSE          =     .57546

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
ln_distortio~8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |    -.54861   .2267041    -2.42   0.019    -1.004189    -.093031
           use |   .2222873   .2207132     1.01   0.319    -.2212525    .6658271
int_design_use |  -.0363472   .2994985    -0.12   0.904    -.6382119    .5655176
         _cons |   1.960237    .172587    11.36   0.000     1.613411    2.307064
--------------------------------------------------------------------------------

.                 test _b[design] = 0                                                                                                             // p = 0.010 (one-tailed)

 ( 1)  design = 0

       F(  1,    49) =    5.86
            Prob > F =    0.0193

.                 test _b[design] + _b[int_design_use] = 0                                                                // p < 0.002 (one-tailed)

 ( 1)  design + int_design_use = 0

       F(  1,    49) =    8.93
            Prob > F =    0.0044

. // Distortion & Efficiency Loss
.         gen ln_dist_efficiency_1_8 = ln(1+dist_efficiency_1_8)
(1,650 missing values generated)

.         swilk ln_dist_efficiency_1_8 if period==9 & subjectnr<4                                         // Cannot reject assumption of normality: p = 0.623

                   Shapiro–Wilk W test for normal data

    Variable |        Obs       W           V         z       Prob>z
-------------+------------------------------------------------------
ln_dist_ef~8 |        150    0.99252      0.871    -0.314    0.62316

.         reg ln_dist_efficiency_1_8 design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)           

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       3.20
                                                Prob > F          =     0.0314
                                                R-squared         =     0.1396
                                                Root MSE          =     .54889

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
ln_dist_effi~8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |  -.3847153   .2248873    -1.71   0.093    -.8366432    .0672125
           use |   .2222873   .2207132     1.01   0.319    -.2212525    .6658271
int_design_use |   .0501605   .2852023     0.18   0.861    -.5229749    .6232959
         _cons |   1.960237    .172587    11.36   0.000     1.613411    2.307064
--------------------------------------------------------------------------------

.                 test _b[design] = 0                                                                                                             // p = 0.047 (one-tailed)

 ( 1)  design = 0

       F(  1,    49) =    2.93
            Prob > F =    0.0935

.                 test _b[design] + _b[int_design_use] = 0                                                                // p < 0.031 (one-tailed)

 ( 1)  design + int_design_use = 0

       F(  1,    49) =    3.64
            Prob > F =    0.0623

. ** Robustness with Wilcoxon Rank-Sum Test
. // Main Effect of Self-excluding Design
.         ranksum proposal_dist_1_8_team if subjectnr==1 & period==9, by(design)                          // p < 0.001 (one-tailed)

Two-sample Wilcoxon rank-sum (Mann–Whitney) test

      design |      Obs    Rank sum    Expected
-------------+---------------------------------
           0 |       25         810       637.5
           1 |       25         465       637.5
-------------+---------------------------------
    Combined |       50        1275        1275

Unadjusted variance     2656.25
Adjustment for ties        0.00
                     ----------
Adjusted variance       2656.25

H0: propos~m(design==0) = propos~m(design==1)
         z =  3.347
Prob > |z| = 0.0008
Exact prob = 0.0006

.         ranksum distortion_1_8_team if subjectnr==1 & period==9, by(design)                                     // p < 0.001 (one-tailed)

Two-sample Wilcoxon rank-sum (Mann–Whitney) test

      design |      Obs    Rank sum    Expected
-------------+---------------------------------
           0 |       25         801       637.5
           1 |       25         474       637.5
-------------+---------------------------------
    Combined |       50        1275        1275

Unadjusted variance     2656.25
Adjustment for ties       -0.26
                     ----------
Adjusted variance       2655.99

H0: distor~m(design==0) = distor~m(design==1)
         z =  3.173
Prob > |z| = 0.0015
Exact prob = 0.0012

.         ranksum dist_efficiency_1_8_team if subjectnr==1 & period==9, by(design)                        // p = 0.019 (one-tailed)

Two-sample Wilcoxon rank-sum (Mann–Whitney) test

      design |      Obs    Rank sum    Expected
-------------+---------------------------------
           0 |       25         745       637.5
           1 |       25         530       637.5
-------------+---------------------------------
    Combined |       50        1275        1275

Unadjusted variance     2656.25
Adjustment for ties       -1.02
                     ----------
Adjusted variance       2655.23

H0: dist_e~m(design==0) = dist_e~m(design==1)
         z =  2.086
Prob > |z| = 0.0370
Exact prob = 0.0366

. // Simple Effect of Self-excluding Design When Use is Formulaic
.         ranksum proposal_dist_1_8_team if use==0 & subjectnr==1 & period==9, by(design)         // p = 0.008 (one-tailed)

Two-sample Wilcoxon rank-sum (Mann–Whitney) test

      design |      Obs    Rank sum    Expected
-------------+---------------------------------
           0 |       12         192         150
           1 |       12         108         150
-------------+---------------------------------
    Combined |       24         300         300

Unadjusted variance      300.00
Adjustment for ties        0.00
                     ----------
Adjusted variance        300.00

H0: propos~m(design==0) = propos~m(design==1)
         z =  2.425
Prob > |z| = 0.0153
Exact prob = 0.0145

.         ranksum distortion_1_8_team if use==0 & subjectnr==1 & period==9, by(design)            // p = 0.019 (one-tailed)

Two-sample Wilcoxon rank-sum (Mann–Whitney) test

      design |      Obs    Rank sum    Expected
-------------+---------------------------------
           0 |       12         186         150
           1 |       12         114         150
-------------+---------------------------------
    Combined |       24         300         300

Unadjusted variance      300.00
Adjustment for ties        0.00
                     ----------
Adjusted variance        300.00

H0: distor~m(design==0) = distor~m(design==1)
         z =  2.078
Prob > |z| = 0.0377
Exact prob = 0.0387

.         ranksum dist_efficiency_1_8_team if use==0 & subjectnr==1 & period==9, by(design)       // p = 0.092 (one-tailed)

Two-sample Wilcoxon rank-sum (Mann–Whitney) test

      design |      Obs    Rank sum    Expected
-------------+---------------------------------
           0 |       12         173         150
           1 |       12         127         150
-------------+---------------------------------
    Combined |       24         300         300

Unadjusted variance      300.00
Adjustment for ties       -0.26
                     ----------
Adjusted variance        299.74

H0: dist_e~m(design==0) = dist_e~m(design==1)
         z =  1.328
Prob > |z| = 0.1840
Exact prob = 0.1926

. // Simple Effect of Self-excluding Design When Use is Discretionary
.         ranksum proposal_dist_1_8_team if use==1 & subjectnr==1 & period==9, by(design)         // p = 0.009 (one-tailed)

Two-sample Wilcoxon rank-sum (Mann–Whitney) test

      design |      Obs    Rank sum    Expected
-------------+---------------------------------
           0 |       13         222       175.5
           1 |       13         129       175.5
-------------+---------------------------------
    Combined |       26         351         351

Unadjusted variance      380.25
Adjustment for ties        0.00
                     ----------
Adjusted variance        380.25

H0: propos~m(design==0) = propos~m(design==1)
         z =  2.385
Prob > |z| = 0.0171
Exact prob = 0.0164

.         ranksum distortion_1_8_team if use==1 & subjectnr==1 & period==9, by(design)            // p = 0.007 (one-tailed)

Two-sample Wilcoxon rank-sum (Mann–Whitney) test

      design |      Obs    Rank sum    Expected
-------------+---------------------------------
           0 |       13         223       175.5
           1 |       13         128       175.5
-------------+---------------------------------
    Combined |       26         351         351

Unadjusted variance      380.25
Adjustment for ties        0.00
                     ----------
Adjusted variance        380.25

H0: distor~m(design==0) = distor~m(design==1)
         z =  2.436
Prob > |z| = 0.0149
Exact prob = 0.0140

.         ranksum dist_efficiency_1_8_team if use==1 & subjectnr==1 & period==9, by(design)       // p = 0.041 (one-tailed)                               

Two-sample Wilcoxon rank-sum (Mann–Whitney) test

      design |      Obs    Rank sum    Expected
-------------+---------------------------------
           0 |       13       209.5       175.5
           1 |       13       141.5       175.5
-------------+---------------------------------
    Combined |       26         351         351

Unadjusted variance      380.25
Adjustment for ties       -0.13
                     ----------
Adjusted variance        380.12

H0: dist_e~m(design==0) = dist_e~m(design==1)
         z =  1.744
Prob > |z| = 0.0812
Exact prob = 0.0836

. 
. ** Untabulated Tests: Percentage of Distortion<=2
. // Descriptives
. tab proposal_dist if design==0          // 34.7 percent

proposal_di |
         st |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |        154       25.67       25.67
          2 |         54        9.00       34.67
          4 |         59        9.83       44.50
          6 |         27        4.50       49.00
          8 |         32        5.33       54.33
         10 |         47        7.83       62.17
         12 |         18        3.00       65.17
         14 |         17        2.83       68.00
         16 |         15        2.50       70.50
         18 |         16        2.67       73.17
         20 |         43        7.17       80.33
         22 |         14        2.33       82.67
         24 |         11        1.83       84.50
         26 |         10        1.67       86.17
         28 |          6        1.00       87.17
         30 |         12        2.00       89.17
         32 |          3        0.50       89.67
         34 |          7        1.17       90.83
         36 |          2        0.33       91.17
         38 |          8        1.33       92.50
         40 |         16        2.67       95.17
         42 |          4        0.67       95.83
         44 |          1        0.17       96.00
         48 |          2        0.33       96.33
         50 |          4        0.67       97.00
         54 |          1        0.17       97.17
         60 |          5        0.83       98.00
         66 |          1        0.17       98.17
         70 |          1        0.17       98.33
         80 |         10        1.67      100.00
------------+-----------------------------------
      Total |        600      100.00

. tab proposal_dist if design==1          // 52.8 percent

proposal_di |
         st |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |        127       21.17       21.17
   .0545455 |          1        0.17       21.33
   .0810811 |          1        0.17       21.50
   .1363636 |          2        0.33       21.83
      .1875 |          2        0.33       22.17
   .2142857 |          1        0.17       22.33
   .2264151 |          1        0.17       22.50
   .2307692 |          1        0.17       22.67
   .2608696 |          1        0.17       22.83
   .2727273 |          1        0.17       23.00
   .2941177 |          1        0.17       23.17
         .3 |          1        0.17       23.33
   .3191489 |          1        0.17       23.50
   .3529412 |          2        0.33       23.83
    .368421 |          1        0.17       24.00
       .375 |          1        0.17       24.17
   .3870968 |          1        0.17       24.33
         .4 |          1        0.17       24.50
   .4285714 |          6        1.00       25.50
      .4375 |          1        0.17       25.67
   .4390244 |          1        0.17       25.83
        .45 |          1        0.17       26.00
   .4545455 |          2        0.33       26.33
   .4615385 |          1        0.17       26.50
     .46875 |          1        0.17       26.67
   .4821429 |          1        0.17       26.83
    .483871 |          3        0.50       27.33
   .5142857 |          1        0.17       27.50
   .5172414 |          2        0.33       27.83
       .525 |          1        0.17       28.00
   .5263158 |          1        0.17       28.17
   .5294118 |          2        0.33       28.50
   .5384616 |          1        0.17       28.67
   .5454546 |          4        0.67       29.33
   .5555556 |          3        0.50       29.83
         .6 |          4        0.67       30.50
   .6382979 |          1        0.17       30.67
   .6521739 |          2        0.33       31.00
   .6666667 |          2        0.33       31.33
   .6923077 |          1        0.17       31.50
   .7272727 |          1        0.17       31.67
        .75 |          6        1.00       32.67
   .7826087 |          1        0.17       32.83
   .8181818 |          2        0.33       33.17
   .8275862 |          1        0.17       33.33
        .84 |          1        0.17       33.50
   .8571429 |          3        0.50       34.00
   .8888889 |          1        0.17       34.17
   .9130435 |          1        0.17       34.33
   .9230769 |          1        0.17       34.50
      .9375 |          1        0.17       34.67
   .9574468 |          1        0.17       34.83
   .9677419 |          4        0.67       35.50
          1 |         10        1.67       37.17
   1.034483 |          4        0.67       37.83
   1.036364 |          1        0.17       38.00
   1.052632 |          1        0.17       38.17
   1.054054 |          1        0.17       38.33
   1.058824 |          1        0.17       38.50
   1.090909 |          4        0.67       39.17
   1.153846 |          2        0.33       39.50
        1.2 |          6        1.00       40.50
   1.216216 |          1        0.17       40.67
   1.285714 |          1        0.17       40.83
   1.304348 |          1        0.17       41.00
       1.32 |          1        0.17       41.17
   1.333333 |          2        0.33       41.50
   1.344828 |          2        0.33       41.83
   1.363636 |          1        0.17       42.00
   1.378378 |          1        0.17       42.17
   1.384615 |          1        0.17       42.33
   1.395349 |          1        0.17       42.50
    1.40625 |          1        0.17       42.67
   1.444444 |          1        0.17       42.83
   1.448276 |          1        0.17       43.00
   1.457143 |          1        0.17       43.17
        1.5 |         17        2.83       46.00
   1.528302 |          1        0.17       46.17
   1.542857 |          1        0.17       46.33
   1.551724 |          1        0.17       46.50
       1.56 |          1        0.17       46.67
   1.578947 |          2        0.33       47.00
   1.636364 |          3        0.50       47.50
   1.641509 |          3        0.50       48.00
   1.666667 |          3        0.50       48.50
       1.68 |          1        0.17       48.67
   1.714286 |          1        0.17       48.83
   1.764706 |          1        0.17       49.00
        1.8 |          2        0.33       49.33
   1.811321 |          1        0.17       49.50
   1.826087 |          1        0.17       49.67
   1.846154 |          2        0.33       50.00
   1.864865 |          2        0.33       50.33
      1.875 |          3        0.50       50.83
   1.909091 |          1        0.17       51.00
   1.914894 |          1        0.17       51.17
   1.945946 |          1        0.17       51.33
    1.96875 |          1        0.17       51.50
          2 |          8        1.33       52.83
   2.018182 |          1        0.17       53.00
   2.027027 |          1        0.17       53.17
   2.035714 |          1        0.17       53.33
   2.057143 |          2        0.33       53.67
   2.076923 |          2        0.33       54.00
        2.1 |          1        0.17       54.17
   2.142857 |          1        0.17       54.33
   2.181818 |          2        0.33       54.67
       2.25 |          3        0.50       55.17
   2.294118 |          1        0.17       55.33
   2.315789 |          1        0.17       55.50
   2.365385 |          1        0.17       55.67
   2.419355 |          1        0.17       55.83
   2.432432 |          1        0.17       56.00
   2.516129 |          2        0.33       56.33
   2.538461 |          2        0.33       56.67
   2.555556 |          1        0.17       56.83
   2.634146 |          1        0.17       57.00
   2.666667 |          2        0.33       57.33
   2.727273 |          3        0.50       57.83
    2.73913 |          1        0.17       58.00
   2.823529 |          1        0.17       58.17
   2.926829 |          1        0.17       58.33
          3 |         29        4.83       63.17
   3.136364 |          1        0.17       63.33
   3.157895 |          1        0.17       63.50
     3.1875 |          1        0.17       63.67
       3.25 |          1        0.17       63.83
   3.272727 |          1        0.17       64.00
   3.333333 |          3        0.50       64.50
   3.409091 |          1        0.17       64.67
   3.486486 |          2        0.33       65.00
   3.488372 |          1        0.17       65.17
        3.5 |          1        0.17       65.33
   3.538461 |          1        0.17       65.50
   3.642857 |          1        0.17       65.67
   3.652174 |          1        0.17       65.83
   3.697675 |          1        0.17       66.00
       3.75 |          4        0.67       66.67
   3.769231 |          1        0.17       66.83
   3.774194 |          1        0.17       67.00
   3.810811 |          1        0.17       67.17
   3.857143 |          1        0.17       67.33
        3.9 |          1        0.17       67.50
          4 |          5        0.83       68.33
   4.043478 |          1        0.17       68.50
      4.125 |          1        0.17       68.67
   4.170732 |          1        0.17       68.83
   4.173913 |          1        0.17       69.00
        4.2 |          2        0.33       69.33
   4.263158 |          1        0.17       69.50
   4.285714 |          2        0.33       69.83
   4.363636 |          1        0.17       70.00
        4.5 |          2        0.33       70.33
   4.545455 |          1        0.17       70.50
   4.548387 |          2        0.33       70.83
   4.565217 |          1        0.17       71.00
   4.588235 |          1        0.17       71.17
   4.615385 |          1        0.17       71.33
   4.621622 |          1        0.17       71.50
   4.636364 |          2        0.33       71.83
   4.744186 |          1        0.17       72.00
       4.75 |          1        0.17       72.17
   4.826087 |          1        0.17       72.33
   4.897959 |          1        0.17       72.50
   4.945946 |          1        0.17       72.67
          5 |          3        0.50       73.17
   5.142857 |          1        0.17       73.33
   5.294117 |          1        0.17       73.50
        5.4 |          1        0.17       73.67
   5.454545 |          1        0.17       73.83
        5.5 |          1        0.17       74.00
   5.590909 |          2        0.33       74.33
   5.612903 |          1        0.17       74.50
   5.647059 |          1        0.17       74.67
   5.660378 |          1        0.17       74.83
   5.744681 |          1        0.17       75.00
   5.888889 |          1        0.17       75.17
          6 |          9        1.50       76.67
   6.210526 |          1        0.17       76.83
   6.219512 |          1        0.17       77.00
      6.375 |          1        0.17       77.17
   6.405406 |          1        0.17       77.33
   6.413793 |          2        0.33       77.67
   6.666667 |          1        0.17       77.83
   6.705883 |          1        0.17       78.00
          7 |          1        0.17       78.17
   7.105263 |          1        0.17       78.33
        7.2 |          1        0.17       78.50
   7.317073 |          1        0.17       78.67
   7.333333 |          1        0.17       78.83
   7.344828 |          1        0.17       79.00
   7.378378 |          1        0.17       79.17
       7.44 |          1        0.17       79.33
        7.5 |          4        0.67       80.00
   7.565217 |          1        0.17       80.17
      7.575 |          1        0.17       80.33
   7.636364 |          1        0.17       80.50
   7.645161 |          1        0.17       80.67
   7.666667 |          1        0.17       80.83
   7.714286 |          1        0.17       81.00
   7.924528 |          1        0.17       81.17
          8 |          2        0.33       81.50
    8.04878 |          1        0.17       81.67
   8.157895 |          1        0.17       81.83
   8.235294 |          1        0.17       82.00
       8.25 |          1        0.17       82.17
   8.275862 |          1        0.17       82.33
        8.4 |          1        0.17       82.50
   8.571428 |          3        0.50       83.00
   8.594595 |          1        0.17       83.17
   8.816326 |          1        0.17       83.33
          9 |          4        0.67       84.00
   9.153846 |          1        0.17       84.17
   9.193548 |          1        0.17       84.33
   9.230769 |          1        0.17       84.50
   9.348837 |          1        0.17       84.67
      9.375 |          1        0.17       84.83
   9.446809 |          2        0.33       85.17
   9.489796 |          1        0.17       85.33
   9.529411 |          1        0.17       85.50
       9.75 |          1        0.17       85.67
     10.125 |          1        0.17       85.83
   10.21277 |          1        0.17       86.00
    10.2439 |          1        0.17       86.17
       10.5 |          1        0.17       86.33
   10.54054 |          1        0.17       86.50
   10.63636 |          1        0.17       86.67
   10.71429 |          1        0.17       86.83
   10.88889 |          1        0.17       87.00
       11.4 |          1        0.17       87.17
   11.57895 |          1        0.17       87.33
         12 |          5        0.83       88.17
   12.09091 |          1        0.17       88.33
   12.16667 |          1        0.17       88.50
   12.30769 |          1        0.17       88.67
   12.91304 |          1        0.17       88.83
         13 |          1        0.17       89.00
   13.88889 |          1        0.17       89.17
   13.90909 |          1        0.17       89.33
         14 |          1        0.17       89.50
    14.0625 |          1        0.17       89.67
   14.66667 |          1        0.17       89.83
   14.76923 |          1        0.17       90.00
         15 |          2        0.33       90.33
     15.375 |          1        0.17       90.50
   15.38461 |          1        0.17       90.67
   16.39024 |          1        0.17       90.83
   16.45161 |          1        0.17       91.00
   17.14286 |          1        0.17       91.17
   17.27273 |          1        0.17       91.33
         18 |          3        0.50       91.83
      18.75 |          1        0.17       92.00
   19.02439 |          1        0.17       92.17
   19.60976 |          1        0.17       92.33
    19.6875 |          1        0.17       92.50
         20 |          4        0.67       93.17
   20.32076 |          1        0.17       93.33
   20.75676 |          1        0.17       93.50
   22.37143 |          1        0.17       93.67
   23.10811 |          1        0.17       93.83
       23.4 |          1        0.17       94.00
   23.65385 |          1        0.17       94.17
         24 |          3        0.50       94.67
      24.75 |          1        0.17       94.83
   26.08696 |          1        0.17       95.00
   26.38461 |          1        0.17       95.17
    26.7907 |          1        0.17       95.33
   27.69231 |          1        0.17       95.50
      27.75 |          1        0.17       95.67
   28.43478 |          1        0.17       95.83
   28.62162 |          1        0.17       96.00
         30 |          8        1.33       97.33
       30.3 |          1        0.17       97.50
       31.5 |          1        0.17       97.67
         33 |          2        0.33       98.00
   35.55556 |          1        0.17       98.17
         40 |          1        0.17       98.33
   43.09091 |          1        0.17       98.50
   43.92857 |          1        0.17       98.67
         45 |          1        0.17       98.83
   45.71429 |          1        0.17       99.00
         48 |          1        0.17       99.17
         54 |          1        0.17       99.33
   57.07317 |          1        0.17       99.50
         60 |          3        0.50      100.00
------------+-----------------------------------
      Total |        600      100.00

. // Associated Test
. gen test_dummy = .
(1,800 missing values generated)

.         replace test_dummy = 0 if proposal_dist>2 & period<9 & subjectnr<4
(675 real changes made)

.         replace test_dummy = 1 if proposal_dist<=2 & period<9 & subjectnr<4
(525 real changes made)

. probit test_dummy design use int_design_use, vce(cluster groupnr)                               // Model p = 0.0134

Iteration 0:   log pseudolikelihood = -822.37705  
Iteration 1:   log pseudolikelihood =  -800.0459  
Iteration 2:   log pseudolikelihood = -800.04156  
Iteration 3:   log pseudolikelihood = -800.04156  

Probit regression                                       Number of obs =  1,200
                                                        Wald chi2(3)  =  10.72
                                                        Prob > chi2   = 0.0134
Log pseudolikelihood = -800.04156                       Pseudo R2     = 0.0272

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
    test_dummy | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   .6056872   .2417676     2.51   0.012     .1318314    1.079543
           use |   .0695257   .2445971     0.28   0.776    -.4098759    .5489272
int_design_use |  -.2685901   .3082986    -0.87   0.384    -.8728443     .335664
         _cons |  -.4307273   .2009628    -2.14   0.032    -.8246072   -.0368474
--------------------------------------------------------------------------------

.         test _b[design] + 0.5*_b[int_design_use] = 0                                                            // p = 0.002

 ( 1)  [test_dummy]design + .5*[test_dummy]int_design_use = 0

           chi2(  1) =    9.35
         Prob > chi2 =    0.0022

. drop test_dummy

. 
. ** Untabulated Tests: Self-proposals (Self-Including Design Only)
. reg dev_selfproposal_fair_1_8, vce(cluster groupnr)

Linear regression                               Number of obs     =         75
                                                F(0, 24)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     16.851

                               (Std. err. adjusted for 25 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
dev_se~r_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |      13.76   2.872825     4.79   0.000     7.830782    19.68922
------------------------------------------------------------------------------

.         display _b[_cons]
13.76

.         test _b[_cons] = 0

 ( 1)  _cons = 0

       F(  1,    24) =   22.94
            Prob > F =    0.0001

. // Does not Differ between Formulaic and Discretionary Uses     (p = 0.273)
. reg dev_selfproposal_fair_1_8 use, vce(cluster groupnr)

Linear regression                               Number of obs     =         75
                                                F(1, 24)          =       1.26
                                                Prob > F          =     0.2727
                                                R-squared         =     0.0378
                                                Root MSE          =     16.642

                               (Std. err. adjusted for 25 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
dev_se~r_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         use |  -6.511218   5.800105    -1.12   0.273    -18.48205    5.459611
       _cons |   17.14583   5.425328     3.16   0.004     5.948507    28.34316
------------------------------------------------------------------------------

. 
. ** Footnote 37: Distribution of Self-Allocations
. tab dev_selfproposal_fair

dev_selfpro |
 posal_fair |      Freq.     Percent        Cum.
------------+-----------------------------------
        -60 |          3        0.50        0.50
        -57 |          1        0.17        0.67
        -48 |          1        0.17        0.83
        -30 |          2        0.33        1.17
        -27 |          2        0.33        1.50
        -24 |          1        0.17        1.67
        -18 |          1        0.17        1.83
        -15 |          8        1.33        3.17
        -12 |          4        0.67        3.83
         -9 |          6        1.00        4.83
         -6 |          9        1.50        6.33
         -3 |         14        2.33        8.67
          0 |        196       32.67       41.33
          3 |         62       10.33       51.67
          6 |         34        5.67       57.33
          9 |         22        3.67       61.00
         12 |         22        3.67       64.67
         15 |         41        6.83       71.50
         18 |         16        2.67       74.17
         21 |          6        1.00       75.17
         24 |         13        2.17       77.33
         27 |          9        1.50       78.83
         30 |         32        5.33       84.17
         33 |         14        2.33       86.50
         36 |          8        1.33       87.83
         39 |          6        1.00       88.83
         42 |          3        0.50       89.33
         45 |          9        1.50       90.83
         48 |          2        0.33       91.17
         51 |          7        1.17       92.33
         54 |          2        0.33       92.67
         57 |          7        1.17       93.83
         60 |         10        1.67       95.50
         63 |          3        0.50       96.00
         66 |          1        0.17       96.17
         72 |          2        0.33       96.50
         75 |          4        0.67       97.17
         81 |          1        0.17       97.33
         90 |          4        0.67       98.00
         99 |          1        0.17       98.17
        105 |          1        0.17       98.33
        120 |         10        1.67      100.00
------------+-----------------------------------
      Total |        600      100.00

.         // 58.7% (352 of 600) self-allocate more than deserved.
.                 tab dev_selfproposal_fair if selfproposal==teambonus & dev_selfproposal_fair>0

dev_selfpro |
 posal_fair |      Freq.     Percent        Cum.
------------+-----------------------------------
          3 |          4        5.41        5.41
          6 |          3        4.05        9.46
         15 |          6        8.11       17.57
         18 |          3        4.05       21.62
         21 |          1        1.35       22.97
         30 |          7        9.46       32.43
         33 |          4        5.41       37.84
         36 |          1        1.35       39.19
         39 |          1        1.35       40.54
         42 |          1        1.35       41.89
         45 |          5        6.76       48.65
         51 |          3        4.05       52.70
         54 |          2        2.70       55.41
         57 |          4        5.41       60.81
         60 |          9       12.16       72.97
         63 |          1        1.35       74.32
         66 |          1        1.35       75.68
         72 |          1        1.35       77.03
         75 |          2        2.70       79.73
         81 |          1        1.35       81.08
         90 |          2        2.70       83.78
         99 |          1        1.35       85.14
        105 |          1        1.35       86.49
        120 |         10       13.51      100.00
------------+-----------------------------------
      Total |         74      100.00

.                 // 74 of those 352 over-allocations, self-allocate all to themselves            
.         //  8.7% ( 52 of 600) self-allocate less than deserved, 
.         // 32.7% (196 of 600) self-allocate what they deserved,  and
.                 // 24 of those 194 exact allocations have a team bonus of zero [**tab teambonus]
. 
. 
. ** 4.2.3 FINAL BONUS ALLOCATIONS (STAGE 3)
.                 
. ********************************************************************************
. ** TABLE 7: EFFICIENCY LOSS AND MANAGERIAL BIAS - DESCRIPTIVE RESULTS
. ********************************************************************************
. ** PANEL A: PROPOSAL DISTORTION
. // Condition [1]: Formulaic Use & Self-Including Design
. sum efficiency_loss if use==0 & design==0 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
efficiency~s |        288           0           0          0          0

. sum efficiency_loss_1_8 if use==0 & design==0 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
efficiency~8 |         36           0           0          0          0

. sum efficiency_loss_1_8_team if use==0 & design==0 & period==9 & subjectnr==1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
efficiency~m |         12           0           0          0          0

. // Condition [2]: Formulaic Use & Self-Excluding Design
. sum efficiency_loss if use==0 & design==1 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
efficiency~s |        288    .7836545    2.276363       -7.5   12.69643

. sum efficiency_loss_1_8 if use==0 & design==1 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
efficiency~8 |         36    .7836545    .9576807  -1.200739   2.957106

. sum efficiency_loss_1_8_team if use==0 & design==1 & period==9 & subjectnr==1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
efficiency~m |         12    .7836546    .7983997  -.2354097   2.136748

. // Condition [3]: Discretionary Use & Self-Including Design
. sum efficiency_loss if use==1 & design==0 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
efficiency~s |        312           0           0          0          0

. sum efficiency_loss_1_8 if use==1 & design==0 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
efficiency~8 |         39           0           0          0          0

. sum efficiency_loss_1_8_team if use==1 & design==0 & period==9 & subjectnr==1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
efficiency~m |         13           0           0          0          0

. // Condition [4]: Discretionary Use & Self-Excluding Design
. sum efficiency_loss if use==1 & design==1 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
efficiency~s |        312    1.249802    3.324549  -10.42683   17.27273

. sum efficiency_loss_1_8 if use==1 & design==1 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
efficiency~8 |         39    1.249802    1.769555  -2.030113    7.71129

. sum efficiency_loss_1_8_team if use==1 & design==1 & period==9 & subjectnr==1   

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
efficiency~m |         13    1.249802    1.545371  -.9386959    5.21836

. ** PANEL B: DISTORTION
. // Condition [1]: Formulaic Use & Self-Including Design
. sum managerial_bias if use==0 & design==0 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
managerial~s |        288           0           0          0          0

. sum managerial_bias_1_8 if use==0 & design==0 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
managerial~8 |         36           0           0          0          0

. sum managerial_bias_1_8_team if use==0 & design==0 & period==9 & subjectnr==1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
managerial~m |         12           0           0          0          0

. // Condition [2]: Formulaic Use & Self-Excluding Design
. sum managerial_bias if use==0 & design==1 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
managerial~s |        288           0           0          0          0

. sum managerial_bias_1_8 if use==0 & design==1 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
managerial~8 |         36           0           0          0          0

. sum managerial_bias_1_8_team if use==0 & design==1 & period==9 & subjectnr==1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
managerial~m |         12           0           0          0          0

. // Condition [3]: Discretionary Use & Self-Including Design
. sum managerial_bias if use==1 & design==0 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
managerial~s |        312    1.525641    11.74348        -35         60

. sum managerial_bias_1_8 if use==1 & design==0 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
managerial~8 |         39    1.525641    5.615502     -7.875      16.25

. sum managerial_bias_1_8_team if use==1 & design==0 & period==9 & subjectnr==1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
managerial~m |         13    1.525641    4.369558  -5.416667   9.333333

. // Condition [4]: Discretionary Use & Self-Excluding Design
. sum managerial_bias if use==1 & design==1 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
managerial~s |        312    5.262821    13.14041        -21         90

. sum managerial_bias_1_8 if use==1 & design==1 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
managerial~8 |         39    5.262821    7.190362      -.875     26.375

. sum managerial_bias_1_8_team if use==1 & design==1 & period==9 & subjectnr==1           

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
managerial~m |         13    5.262821    6.705343  -.4166667   18.16667

. ** PANEL C: DISTORTION & EFFICIENCY LOSS
. // Condition [1]: Formulaic Use & Self-Including Design
. sum mechanism if use==0 & design==0 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
   mechanism |        288           0           0          0          0

. sum mechanism_1_8 if use==0 & design==0 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
mechanism_~8 |         36           0           0          0          0

. sum mechanism_1_8_team if use==0 & design==0 & period==9 & subjectnr==1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
mechanism_~m |         12           0           0          0          0

. // Condition [2]: Formulaic Use & Self-Excluding Design
. sum mechanism if use==0 & design==1 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
   mechanism |        288    .7836545    2.276363       -7.5   12.69643

. sum mechanism_1_8 if use==0 & design==1 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
mechanism_~8 |         36    .7836545    .9576807  -1.200739   2.957106

. sum mechanism_1_8_team if use==0 & design==1 & period==9 & subjectnr==1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
mechanism_~m |         12    .7836546    .7983997  -.2354097   2.136748

. // Condition [3]: Discretionary Use & Self-Including Design
. sum mechanism if use==1 & design==0 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
   mechanism |        312    1.525641    11.74348        -35         60

. sum mechanism_1_8 if use==1 & design==0 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
mechanism_~8 |         39    1.525641    5.615502     -7.875      16.25

. sum mechanism_1_8_team if use==1 & design==0 & period==9 & subjectnr==1

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
mechanism_~m |         13    1.525641    4.369558  -5.416667   9.333333

. // Condition [4]: Discretionary Use & Self-Excluding Design
. sum mechanism if use==1 & design==1 & period<9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
   mechanism |        312    6.512622    13.63382     -15.75         90

. sum mechanism_1_8 if use==1 & design==1 & period==9

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
mechanism_~8 |         39    6.512623    7.298465  -2.030113   25.79995

. sum mechanism_1_8_team if use==1 & design==1 & period==9 & subjectnr==1         

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
mechanism_~m |         13    6.512623    6.819324  -.9386959   19.08364

.                 
. ********************************************************************************
. ** TABLE 8: EFFICIENCY LOSS AND MANAGERIAL BIAS - REGRESSION RESULTS (EMPLOYEE LEVEL)
. ********************************************************************************
. ** COLUMN 1: EFFICIENCY LOSS
. reg efficiency_loss_1_8 design int_design_use if design==1 & subjectnr<4 & period==9, noconstant vce(cluster groupnr)

Linear regression                               Number of obs     =         75
                                                F(2, 24)          =      10.33
                                                Prob > F          =     0.0006
                                                R-squared         =     0.3546
                                                Root MSE          =     1.4387

                                 (Std. err. adjusted for 25 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
efficiency_l~8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   .7836545   .2267537     3.46   0.002      .315658    1.251651
int_design_use |   .4661474   .4800801     0.97   0.341    -.5246892    1.456984
--------------------------------------------------------------------------------

.         display "Comparison: "round(_b[design] + _b[int_design_use],0.001)
Comparison: 1.25

.         test _b[design] + _b[int_design_use] = 0

 ( 1)  design + int_design_use = 0

       F(  1,    24) =    8.72
            Prob > F =    0.0069

.         display "t-stat = "round(sqrt(r(F)),0.01)
t-stat = 2.95

. ** COLUMN 2: MANAGERIAL BIAS
. reg managerial_bias_1_8 use int_design_use if use==1 & subjectnr<4 & period==9, noconstant vce(cluster groupnr)

Linear regression                               Number of obs     =         78
                                                F(2, 25)          =       4.93
                                                Prob > F          =     0.0157
                                                R-squared         =     0.2702
                                                Root MSE          =     6.4512

                                 (Std. err. adjusted for 26 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
managerial_b~8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
           use |   1.525641   1.195198     1.28   0.214    -.9359163    3.987198
int_design_use |   3.737179   2.189162     1.71   0.100    -.7714839    8.245843
--------------------------------------------------------------------------------

.         display "Comparison: "round(_b[use] + _b[int_design_use],0.001)
Comparison: 5.263

.         test _b[use] + _b[int_design_use] = 0

 ( 1)  use + int_design_use = 0

       F(  1,    25) =    8.23
            Prob > F =    0.0082

.         display "t-stat = "round(sqrt(r(F)),0.01)
t-stat = 2.87

. ** COLUMN 3: EFFICIENCY LOSS & MANAGERIAL BIAS
. reg mechanism_1_8 design use int_design_use if subjectnr<4 & period==9 & condition>1, noconstant vce(cluster groupnr)

Linear regression                               Number of obs     =        114
                                                F(3, 37)          =       8.66
                                                Prob > F          =     0.0002
                                                R-squared         =     0.3519
                                                Root MSE          =     5.4148

                                 (Std. err. adjusted for 38 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
 mechanism_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   .7836545   .2256338     3.47   0.001     .3264771    1.240832
           use |   1.525641   1.190566     1.28   0.208    -.8866747    3.937957
int_design_use |   4.203327   2.218266     1.89   0.066    -.2913075    8.697961
--------------------------------------------------------------------------------

.         display "Comparison: "round(_b[design] + _b[int_design_use],0.001)
Comparison: 4.987

.         test _b[design] + _b[int_design_use] = 0

 ( 1)  design + int_design_use = 0

       F(  1,    37) =    5.11
            Prob > F =    0.0298

.         display "t-stat = "round(sqrt(r(F)),0.01)
t-stat = 2.26

.         display "Comparison: "round(_b[use] + _b[int_design_use],0.001)
Comparison: 5.729

.         test _b[use] + _b[int_design_use] = 0

 ( 1)  use + int_design_use = 0

       F(  1,    37) =    9.37
            Prob > F =    0.0041

.         display "t-stat = "round(sqrt(r(F)),0.01)               
t-stat = 3.06

.                 
. ** Footnote 35: Table 8 Robustness with Wilcoxon Rank-Sum Test
. // Efficiency Loss:
.         ranksum efficiency_loss_1_8_team if use==0 & subjectnr==1 & period==9, by(design)       // p = 0.002 (one-tailed)

Two-sample Wilcoxon rank-sum (Mann–Whitney) test

      design |      Obs    Rank sum    Expected
-------------+---------------------------------
           0 |       12         102         150
           1 |       12         198         150
-------------+---------------------------------
    Combined |       24         300         300

Unadjusted variance      300.00
Adjustment for ties      -37.30
                     ----------
Adjusted variance        262.70

H0: effici~m(design==0) = effici~m(design==1)
         z = -2.962
Prob > |z| = 0.0031
Exact prob = 0.0019

.         ranksum efficiency_loss_1_8_team if use==1 & subjectnr==1 & period==9, by(design)       // p = 0.001 (one-tailed)       

Two-sample Wilcoxon rank-sum (Mann–Whitney) test

      design |      Obs    Rank sum    Expected
-------------+---------------------------------
           0 |       13         117       175.5
           1 |       13         234       175.5
-------------+---------------------------------
    Combined |       26         351         351

Unadjusted variance      380.25
Adjustment for ties      -47.32
                     ----------
Adjusted variance        332.93

H0: effici~m(design==0) = effici~m(design==1)
         z = -3.206
Prob > |z| = 0.0013
Exact prob = 0.0007

. // Managerial Bias: managerial_bias
.         ranksum managerial_bias_1_8_team if use==1 & subjectnr==1 & period==9, by(design)       // p = 0.065 (one-tailed)

Two-sample Wilcoxon rank-sum (Mann–Whitney) test

      design |      Obs    Rank sum    Expected
-------------+---------------------------------
           0 |       13         146       175.5
           1 |       13         205       175.5
-------------+---------------------------------
    Combined |       26         351         351

Unadjusted variance      380.25
Adjustment for ties       -0.13
                     ----------
Adjusted variance        380.12

H0: manage~m(design==0) = manage~m(design==1)
         z = -1.513
Prob > |z| = 0.1303
Exact prob = 0.1353

. // Efficiency Loss & Managerial Bias: managerial_bias
.         ranksum mechanism_1_8_team if use==1 & subjectnr==1 & period==9, by(design)                     // p = 0.044 (one-tailed)

Two-sample Wilcoxon rank-sum (Mann–Whitney) test

      design |      Obs    Rank sum    Expected
-------------+---------------------------------
           0 |       13         142       175.5
           1 |       13         209       175.5
-------------+---------------------------------
    Combined |       26         351         351

Unadjusted variance      380.25
Adjustment for ties        0.00
                     ----------
Adjusted variance        380.25

H0: mecha~am(design==0) = mecha~am(design==1)
         z = -1.718
Prob > |z| = 0.0858
Exact prob = 0.0908

.                                 
. ** Footnote 42: 
. tab managerial_bias if use==1 & subjectnr<4 & period<9

managerial_ |
       bias |      Freq.     Percent        Cum.
------------+-----------------------------------
        -35 |          1        0.16        0.16
        -27 |          2        0.32        0.48
        -25 |          3        0.48        0.96
        -22 |          1        0.16        1.12
        -21 |          3        0.48        1.60
        -19 |          1        0.16        1.76
        -18 |          2        0.32        2.08
        -17 |          1        0.16        2.24
        -16 |          1        0.16        2.40
        -15 |          8        1.28        3.69
        -13 |          4        0.64        4.33
        -12 |          3        0.48        4.81
        -11 |          2        0.32        5.13
        -10 |          9        1.44        6.57
         -9 |          2        0.32        6.89
         -8 |         11        1.76        8.65
         -7 |          6        0.96        9.62
         -6 |          7        1.12       10.74
         -5 |         24        3.85       14.58
         -4 |         13        2.08       16.67
         -3 |         16        2.56       19.23
         -2 |         26        4.17       23.40
         -1 |         36        5.77       29.17
          0 |        154       24.68       53.85
          1 |         39        6.25       60.10
          2 |         28        4.49       64.58
          3 |         20        3.21       67.79
          4 |         19        3.04       70.83
          5 |         26        4.17       75.00
          6 |         16        2.56       77.56
          7 |         13        2.08       79.65
          8 |         16        2.56       82.21
          9 |          8        1.28       83.49
         10 |         11        1.76       85.26
         11 |          6        0.96       86.22
         12 |          9        1.44       87.66
         13 |          3        0.48       88.14
         14 |          7        1.12       89.26
         15 |          5        0.80       90.06
         16 |          5        0.80       90.87
         18 |          2        0.32       91.19
         19 |          1        0.16       91.35
         20 |          4        0.64       91.99
         21 |          2        0.32       92.31
         22 |          2        0.32       92.63
         23 |          3        0.48       93.11
         24 |          2        0.32       93.43
         25 |          2        0.32       93.75
         26 |          3        0.48       94.23
         27 |          3        0.48       94.71
         28 |          2        0.32       95.03
         29 |          1        0.16       95.19
         30 |          6        0.96       96.15
         31 |          2        0.32       96.47
         33 |          1        0.16       96.63
         35 |          2        0.32       96.96
         37 |          2        0.32       97.28
         38 |          1        0.16       97.44
         40 |          1        0.16       97.60
         41 |          3        0.48       98.08
         43 |          1        0.16       98.24
         44 |          1        0.16       98.40
         45 |          3        0.48       98.88
         51 |          1        0.16       99.04
         58 |          1        0.16       99.20
         60 |          1        0.16       99.36
         68 |          1        0.16       99.52
         69 |          1        0.16       99.68
         79 |          1        0.16       99.84
         90 |          1        0.16      100.00
------------+-----------------------------------
      Total |        624      100.00

.         // 154 (24.7 percent) have a managerial bias of zero 
.                 // Of those, 9 are zero due to a bonus pool of zero
. // Self-Including Design
. tab managerial_bias if design==0 & use==1 & subjectnr<4 & period<9

managerial_ |
       bias |      Freq.     Percent        Cum.
------------+-----------------------------------
        -35 |          1        0.32        0.32
        -27 |          2        0.64        0.96
        -25 |          3        0.96        1.92
        -22 |          1        0.32        2.24
        -21 |          2        0.64        2.88
        -19 |          1        0.32        3.21
        -18 |          1        0.32        3.53
        -17 |          1        0.32        3.85
        -15 |          7        2.24        6.09
        -13 |          3        0.96        7.05
        -12 |          3        0.96        8.01
        -11 |          2        0.64        8.65
        -10 |          9        2.88       11.54
         -9 |          2        0.64       12.18
         -8 |          8        2.56       14.74
         -7 |          4        1.28       16.03
         -6 |          6        1.92       17.95
         -5 |         22        7.05       25.00
         -4 |          8        2.56       27.56
         -3 |          9        2.88       30.45
         -2 |         11        3.53       33.97
         -1 |         21        6.73       40.71
          0 |         47       15.06       55.77
          1 |         12        3.85       59.62
          2 |         15        4.81       64.42
          3 |         12        3.85       68.27
          4 |         11        3.53       71.79
          5 |         15        4.81       76.60
          6 |          7        2.24       78.85
          7 |          8        2.56       81.41
          8 |          7        2.24       83.65
          9 |          1        0.32       83.97
         10 |          8        2.56       86.54
         11 |          6        1.92       88.46
         12 |          3        0.96       89.42
         14 |          3        0.96       90.38
         15 |          4        1.28       91.67
         16 |          2        0.64       92.31
         19 |          1        0.32       92.63
         20 |          3        0.96       93.59
         21 |          1        0.32       93.91
         22 |          2        0.64       94.55
         23 |          1        0.32       94.87
         25 |          2        0.64       95.51
         26 |          1        0.32       95.83
         27 |          2        0.64       96.47
         30 |          4        1.28       97.76
         33 |          1        0.32       98.08
         37 |          1        0.32       98.40
         40 |          1        0.32       98.72
         43 |          1        0.32       99.04
         44 |          1        0.32       99.36
         58 |          1        0.32       99.68
         60 |          1        0.32      100.00
------------+-----------------------------------
      Total |        312      100.00

.         //  47 (15.1 percent) have a managerial bias of zero
.         // 127 (40.7 percent) have a negative managerial bias (i.e., the manager makes the bonus allocation fairer)
.         // 138 (44.2 percent) have a positive managerial bias (i.e., the manager makes the bonus allocation less fair). 
. // Self-Excluding Design
. tab managerial_bias if design==1 & use==1 & teambonus!=0 & subjectnr<4 & period<9

managerial_ |
       bias |      Freq.     Percent        Cum.
------------+-----------------------------------
        -21 |          1        0.32        0.32
        -18 |          1        0.32        0.64
        -16 |          1        0.32        0.96
        -15 |          1        0.32        1.28
        -13 |          1        0.32        1.60
         -8 |          3        0.96        2.56
         -7 |          2        0.64        3.21
         -6 |          1        0.32        3.53
         -5 |          2        0.64        4.17
         -4 |          5        1.60        5.77
         -3 |          7        2.24        8.01
         -2 |         15        4.81       12.82
         -1 |         15        4.81       17.63
          0 |        107       34.29       51.92
          1 |         27        8.65       60.58
          2 |         13        4.17       64.74
          3 |          8        2.56       67.31
          4 |          8        2.56       69.87
          5 |         11        3.53       73.40
          6 |          9        2.88       76.28
          7 |          5        1.60       77.88
          8 |          9        2.88       80.77
          9 |          7        2.24       83.01
         10 |          3        0.96       83.97
         12 |          6        1.92       85.90
         13 |          3        0.96       86.86
         14 |          4        1.28       88.14
         15 |          1        0.32       88.46
         16 |          3        0.96       89.42
         18 |          2        0.64       90.06
         20 |          1        0.32       90.38
         21 |          1        0.32       90.71
         23 |          2        0.64       91.35
         24 |          2        0.64       91.99
         26 |          2        0.64       92.63
         27 |          1        0.32       92.95
         28 |          2        0.64       93.59
         29 |          1        0.32       93.91
         30 |          2        0.64       94.55
         31 |          2        0.64       95.19
         35 |          2        0.64       95.83
         37 |          1        0.32       96.15
         38 |          1        0.32       96.47
         41 |          3        0.96       97.44
         45 |          3        0.96       98.40
         51 |          1        0.32       98.72
         68 |          1        0.32       99.04
         69 |          1        0.32       99.36
         79 |          1        0.32       99.68
         90 |          1        0.32      100.00
------------+-----------------------------------
      Total |        312      100.00

.         // 107 (34.3 percent) have a managerial bias of zero
.         //  55 (17.6 percent) have a negative managerial bias (i.e., the manager makes the bonus allocation fairer)
.         // 150 (48.1 percent) have a positive managerial bias (i.e., the manager makes the bonus allocation less fair). 
. 
. ** Untabulated Results: Cross-subsidization                                                             
. gen dev_final_avprop = finalbonus - av_proposal
(600 missing values generated)

. // Self-Including Design
. reg dev_final_avprop if use==1 & design==0 & contribution<20, vce(cluster groupnr)

Linear regression                               Number of obs     =        140
                                                F(0, 12)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =      13.13

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
dev_final_~p | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |  -.4285714   1.187265    -0.36   0.724      -3.0154    2.158257
------------------------------------------------------------------------------

. reg dev_final_avprop if use==1 & design==0 & contribution>=20, vce(cluster groupnr)

Linear regression                               Number of obs     =        172
                                                F(0, 12)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     15.821

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
dev_final_~p | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   .3488372   .9272085     0.38   0.713    -1.671377    2.369051
------------------------------------------------------------------------------

. // Self-Excluding Design
. reg dev_final_avprop if use==1 & design==1 & contribution<20, vce(cluster groupnr)

Linear regression                               Number of obs     =        136
                                                F(0, 12)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =     11.629

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
dev_final_~p | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   2.558824   1.366439     1.87   0.086    -.4183906    5.536038
------------------------------------------------------------------------------

. reg dev_final_avprop if use==1 & design==1 & contribution>=20, vce(cluster groupnr)

Linear regression                               Number of obs     =        176
                                                F(0, 12)          =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.0000
                                                Root MSE          =      22.69

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
dev_final_~p | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |  -1.977273   1.060049    -1.87   0.087    -4.286922    .3323764
------------------------------------------------------------------------------

.         
. 
.         
.         
. ********************************************************************************
. ** ONLINE APPENDIX, SECTION A
. ********************************************************************************
. 
. factor peqprocedfairness1 peqprocedfairness2 peqprocedfairness3 peqprocedfairness4 if subjectnr<4
(obs=150)

Factor analysis/correlation                      Number of obs    =        150
    Method: principal factors                    Retained factors =          2
    Rotation: (unrotated)                        Number of params =          6

    --------------------------------------------------------------------------
         Factor  |   Eigenvalue   Difference        Proportion   Cumulative
    -------------+------------------------------------------------------------
        Factor1  |      1.75157      1.67470            1.1825       1.1825
        Factor2  |      0.07687      0.24197            0.0519       1.2344
        Factor3  |     -0.16511      0.01699           -0.1115       1.1229
        Factor4  |     -0.18210            .           -0.1229       1.0000
    --------------------------------------------------------------------------
    LR test: independent vs. saturated:  chi2(6)  =  166.46 Prob>chi2 = 0.0000

Factor loadings (pattern matrix) and unique variances

    -------------------------------------------------
        Variable |  Factor1   Factor2 |   Uniqueness 
    -------------+--------------------+--------------
    peqprocedf~1 |   0.4604    0.2089 |      0.7444  
    peqprocedf~2 |   0.5915   -0.1747 |      0.6196  
    peqprocedf~3 |   0.7749    0.0409 |      0.3978  
    peqprocedf~4 |   0.7676   -0.0319 |      0.4097  
    -------------------------------------------------

. rotate

Factor analysis/correlation                      Number of obs    =        150
    Method: principal factors                    Retained factors =          2
    Rotation: orthogonal varimax (Kaiser off)    Number of params =          6

    --------------------------------------------------------------------------
         Factor  |     Variance   Difference        Proportion   Cumulative
    -------------+------------------------------------------------------------
        Factor1  |      1.68553      1.54263            1.1379       1.1379
        Factor2  |      0.14290            .            0.0965       1.2344
    --------------------------------------------------------------------------
    LR test: independent vs. saturated:  chi2(6)  =  166.46 Prob>chi2 = 0.0000

Rotated factor loadings (pattern matrix) and unique variances

    -------------------------------------------------
        Variable |  Factor1   Factor2 |   Uniqueness 
    -------------+--------------------+--------------
    peqprocedf~1 |   0.4097    0.2962 |      0.7444  
    peqprocedf~2 |   0.6144   -0.0538 |      0.6196  
    peqprocedf~3 |   0.7514    0.1939 |      0.3978  
    peqprocedf~4 |   0.7587    0.1212 |      0.4097  
    -------------------------------------------------

Factor rotation matrix

    --------------------------------
                 | Factor1  Factor2 
    -------------+------------------
         Factor1 |  0.9801   0.1986 
         Factor2 | -0.1986   0.9801 
    --------------------------------

. 
. ********************************************************************************
. ** TABLE A.2
. ********************************************************************************
. // Column 1: Effort
. reg contribution_1_8 design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       3.26
                                                Prob > F          =     0.0293
                                                R-squared         =     0.1274
                                                Root MSE          =     8.7901

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
contributi~1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   7.798611   2.908697     2.68   0.010     1.953366    13.64386
           use |   .0977564   2.915441     0.03   0.973    -5.761042    5.956555
int_design_use |  -7.875534   4.480977    -1.76   0.085    -16.88039    1.129326
         _cons |   19.64583   1.981657     9.91   0.000     15.66354    23.62812
--------------------------------------------------------------------------------

. // Column 2: Distributive Fairness
. reg peqdistrifairness_factor design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =      10.60
                                                Prob > F          =     0.0000
                                                R-squared         =     0.1602
                                                Root MSE          =     .89741

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
peqdistrifai~r | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   .7795105   .2568524     3.03   0.004     .2633463    1.295675
           use |  -.0958916   .2991021    -0.32   0.750    -.6969599    .5051766
int_design_use |  -.9022568   .3605198    -2.50   0.016    -1.626748   -.1777652
         _cons |  -.1053048   .2263614    -0.47   0.644    -.5601951    .3495855
--------------------------------------------------------------------------------

. // Column 3: Effort
. reg contribution_1_8 design use int_design_use peqdistrifairness_factor if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(4, 49)          =      17.01
                                                Prob > F          =     0.0000
                                                R-squared         =     0.3742
                                                Root MSE          =     7.4695

                                           (Std. err. adjusted for 50 clusters in groupnr)
------------------------------------------------------------------------------------------
                         |               Robust
        contribution_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------------------+----------------------------------------------------------------
                  design |   3.737859   2.342093     1.60   0.117    -.9687525     8.44447
                     use |   .5972907   2.288143     0.26   0.795    -4.000905    5.195486
          int_design_use |  -3.175352   3.477621    -0.91   0.366    -10.16389     3.81319
peqdistrifairness_factor |   5.209362   .6973469     7.47   0.000     3.807991    6.610733
                   _cons |    20.1944   1.657767    12.18   0.000       16.863    23.52581
------------------------------------------------------------------------------------------

. // Column 4: Procedural Fairness
. reg peqprocedfairness_factor design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       4.03
                                                Prob > F          =     0.0122
                                                R-squared         =     0.0699
                                                Root MSE          =     .83366

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
peqprocedfai~r | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   .3582158   .1905825     1.88   0.066     -.024774    .7412056
           use |  -.2397492    .248845    -0.96   0.340     -.739822    .2603236
int_design_use |  -.2612312   .2996213    -0.87   0.388    -.8633428    .3408804
         _cons |   .0134818   .1527613     0.09   0.930    -.2935035    .3204671
--------------------------------------------------------------------------------

.         // Test reported in text
.         display _b[use] + 0.5*_b[int_design_use]
-.3703648

.         test _b[use] + 0.5*_b[int_design_use] = 0

 ( 1)  use + .5*int_design_use = 0

       F(  1,    49) =    6.11
            Prob > F =    0.0169

.         display "t-stat = "sqrt(r(F))
t-stat = 2.4722191

.         display _b[design] + 0.5*_b[int_design_use]
.22760021

.         test _b[design] + 0.5*_b[int_design_use] = 0

 ( 1)  design + .5*int_design_use = 0

       F(  1,    49) =    2.31
            Prob > F =    0.1351

.         display "t-stat = "sqrt(r(F))   
t-stat = 1.5192523

. // Column 5: Effort
. reg contribution_1_8 design use int_design_use peqprocedfairness_factor if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(4, 49)          =       7.76
                                                Prob > F          =     0.0001
                                                R-squared         =     0.2154
                                                Root MSE          =      8.364

                                           (Std. err. adjusted for 50 clusters in groupnr)
------------------------------------------------------------------------------------------
                         |               Robust
        contribution_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------------------+----------------------------------------------------------------
                  design |   6.599332   2.834504     2.33   0.024     .9031838    12.29548
                     use |   .9004183   2.730249     0.33   0.743    -4.586222    6.387059
          int_design_use |  -7.000952   4.150224    -1.69   0.098    -15.34114    1.339235
peqprocedfairness_factor |   3.347923   .8274778     4.05   0.000     1.685044    5.010802
                   _cons |    19.6007   1.928717    10.16   0.000     15.72479     23.4766
------------------------------------------------------------------------------------------

. // Column 6: Effort
. reg contribution_1_8 design use int_design_use peqdistrifairness_factor peqprocedfairness_factor if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(5, 49)          =      13.88
                                                Prob > F          =     0.0000
                                                R-squared         =     0.3800
                                                Root MSE          =     7.4604

                                           (Std. err. adjusted for 50 clusters in groupnr)
------------------------------------------------------------------------------------------
                         |               Robust
        contribution_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------------------+----------------------------------------------------------------
                  design |    3.71383   2.353854     1.58   0.121    -1.016417    8.444077
                     use |   .7903573   2.315457     0.34   0.734    -3.862728    5.443442
          int_design_use |  -3.296563   3.511925    -0.94   0.353    -10.35404    3.760915
peqdistrifairness_factor |   4.793735   .8106876     5.91   0.000     3.164597    6.422872
peqprocedfairness_factor |   .9715227   .8171319     1.19   0.240    -.6705653    2.613611
                   _cons |   20.13754   1.673172    12.04   0.000     16.77517     23.4999
------------------------------------------------------------------------------------------

. 
. ********************************************************************************
. ** TABLE A.3
. ********************************************************************************
. // Column 1: PEQ_Contribution-1
. reg peqcontribution1 design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       0.62
                                                Prob > F          =     0.6023
                                                R-squared         =     0.0132
                                                Root MSE          =     1.8859

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
peqcontribut~1 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |  -.5833333   .4821008    -1.21   0.232    -1.552151    .3854845
           use |  -.4679487   .4015568    -1.17   0.250    -1.274907    .3390098
int_design_use |   .6602564   .6125788     1.08   0.286    -.5707669     1.89128
         _cons |   5.083333   .3159726    16.09   0.000     4.448363    5.718304
--------------------------------------------------------------------------------

. // Column 2: PEQ_Contribution-2
. reg peqcontribution2 design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       4.86
                                                Prob > F          =     0.0049
                                                R-squared         =     0.1207
                                                Root MSE          =     1.7449

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
peqcontribut~2 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |          1   .5895141     1.70   0.096     -.184673    2.184673
           use |  -.2884615   .5115853    -0.56   0.575    -1.316531    .7396076
int_design_use |  -1.461538   .6926182    -2.11   0.040    -2.853407   -.0696701
         _cons |   4.083333   .4244899     9.62   0.000     3.230289    4.936378
--------------------------------------------------------------------------------

. // Column 3: Effort
. reg contribution_1_8 design use int_design_use peqcontribution1 if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(4, 49)          =       6.76
                                                Prob > F          =     0.0002
                                                R-squared         =     0.2141
                                                Root MSE          =     8.3709

                                   (Std. err. adjusted for 50 clusters in groupnr)
----------------------------------------------------------------------------------
                 |               Robust
contribution_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
          design |   6.941752   2.773374     2.50   0.016     1.368449    12.51505
             use |  -.5896142   2.862943    -0.21   0.838    -6.342914    5.163685
  int_design_use |  -6.905682   4.279682    -1.61   0.113    -15.50603     1.69466
peqcontribution1 |  -1.468902   .3758907    -3.91   0.000    -2.224282   -.7135211
           _cons |   27.11275   2.271007    11.94   0.000     22.54899    31.67651
----------------------------------------------------------------------------------

. // Column 4: Effort
. reg contribution_1_8 design use int_design_use peqcontribution2 if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(4, 49)          =       5.40
                                                Prob > F          =     0.0011
                                                R-squared         =     0.1828
                                                Root MSE          =     8.5355

                                   (Std. err. adjusted for 50 clusters in groupnr)
----------------------------------------------------------------------------------
                 |               Robust
contribution_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
          design |   6.528693   2.473242     2.64   0.011     1.558526    11.49886
             use |    .464079   2.644367     0.18   0.861    -4.849976    5.778134
  int_design_use |    -6.0195   3.978351    -1.51   0.137     -14.0143    1.975296
peqcontribution2 |   1.269918   .3973559     3.20   0.002     .4714017    2.068435
           _cons |   14.46033   2.740795     5.28   0.000     8.952501    19.96817
----------------------------------------------------------------------------------

. // Column 5: Effort
. reg contribution_1_8 design use int_design_use peqcontribution1 peqcontribution2 if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(5, 49)          =       7.72
                                                Prob > F          =     0.0000
                                                R-squared         =     0.2684
                                                Root MSE          =     8.1042

                                   (Std. err. adjusted for 50 clusters in groupnr)
----------------------------------------------------------------------------------
                 |               Robust
contribution_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
          design |   5.689805   2.471341     2.30   0.026     .7234583    10.65615
             use |  -.2225804   2.606709    -0.09   0.932    -5.460958    5.015797
  int_design_use |  -5.074132   3.877069    -1.31   0.197    -12.86539     2.71713
peqcontribution1 |  -1.459635   .3876147    -3.77   0.000    -2.238576   -.6806946
peqcontribution2 |   1.257352   .3551271     3.54   0.001     .5436976    1.971007
           _cons |   21.93146   2.578405     8.51   0.000     16.74996    27.11296
----------------------------------------------------------------------------------

. // Column 6: Effort
. reg contribution_1_8 design use int_design_use peqdistrifairness_factor peqcontribution1 peqcontribution2 if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(6, 49)          =      14.91
                                                Prob > F          =     0.0000
                                                R-squared         =     0.4260
                                                Root MSE          =     7.2033

                                           (Std. err. adjusted for 50 clusters in groupnr)
------------------------------------------------------------------------------------------
                         |               Robust
        contribution_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------------------+----------------------------------------------------------------
                  design |   3.230616   2.171475     1.49   0.143    -1.133126    7.594358
                     use |   .1036962   2.237385     0.05   0.963    -4.392498    4.599891
          int_design_use |   -2.50524   3.243984    -0.77   0.444     -9.02427    4.013791
peqdistrifairness_factor |   4.592419   .7674399     5.98   0.000     3.050191    6.134647
        peqcontribution1 |   -1.13087   .3536513    -3.20   0.002    -1.841559   -.4201812
        peqcontribution2 |   .3284821   .3804967     0.86   0.392    -.4361547    1.093119
                   _cons |   24.53673   2.566375     9.56   0.000      19.3794    29.69405
------------------------------------------------------------------------------------------

. 
. ********************************************************************************
. ** TABLE A.4
. ********************************************************************************
. // Column 1: PEQ_Proposal-1
. reg peqproposal1 design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       1.17
                                                Prob > F          =     0.3309
                                                R-squared         =     0.0259
                                                Root MSE          =     1.6975

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
  peqproposal1 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |  -.7222222   .4402099    -1.64   0.107    -1.606857    .1624127
           use |  -.4209402   .4518581    -0.93   0.356    -1.328983    .4871026
int_design_use |    .517094   .6023656     0.86   0.395     -.693405    1.727593
         _cons |   4.138889   .3012175    13.74   0.000      3.53357    4.744208
--------------------------------------------------------------------------------

. // Column 2: PEQ_Proposal-2
. reg peqproposal2 design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       5.31
                                                Prob > F          =     0.0030
                                                R-squared         =     0.0812
                                                Root MSE          =     1.4318

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
  peqproposal2 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |  -1.194444   .3214353    -3.72   0.001    -1.840393   -.5484961
           use |  -.6709402   .2979197    -2.25   0.029    -1.269632   -.0722481
int_design_use |    1.09188   .4285904     2.55   0.014     .2305956    1.953165
         _cons |   6.055556    .195708    30.94   0.000     5.662266    6.448845
--------------------------------------------------------------------------------

. // Column 3: PEQ_Proposal-3
. reg peqproposal3 design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       2.97
                                                Prob > F          =     0.0410
                                                R-squared         =     0.0874
                                                Root MSE          =     1.6424

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
  peqproposal3 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |       1.25   .5174713     2.42   0.019     .2101025    2.289897
           use |   .0833333   .4201329     0.20   0.844    -.7609553    .9276219
int_design_use |  -1.173077   .6166622    -1.90   0.063    -2.412306    .0661521
         _cons |   3.583333   .3698663     9.69   0.000     2.840059    4.326607
--------------------------------------------------------------------------------

. // Column 4: PEQ_Proposal-4
. reg peqproposal4 design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       2.88
                                                Prob > F          =     0.0455
                                                R-squared         =     0.0665
                                                Root MSE          =     1.4544

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
  peqproposal4 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |  -1.083333   .3777481    -2.87   0.006    -1.842447   -.3242201
           use |  -.4017094   .3249755    -1.24   0.222    -1.054772    .2513534
int_design_use |   .8782051   .5015004     1.75   0.086    -.1295977    1.886008
         _cons |   5.555556   .2577308    21.56   0.000     5.037626    6.073485
--------------------------------------------------------------------------------

. // Column 5: PEQ_Proposal-5
. reg peqproposal5 design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       6.36
                                                Prob > F          =     0.0010
                                                R-squared         =     0.1339
                                                Root MSE          =     1.5886

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
  peqproposal5 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |  -1.45e-15   .3198691    -0.00   1.000    -.6428009    .6428009
           use |  -1.316239   .3560427    -3.70   0.001    -2.031734   -.6007447
int_design_use |   .1794872   .6054725     0.30   0.768    -1.037255     1.39623
         _cons |   5.444444   .1851593    29.40   0.000     5.072353    5.816536
--------------------------------------------------------------------------------

.         // Test reported in text
.         display _b[use] + 0.5*_b[int_design_use]
-1.2264957

.         test _b[use] + 0.5*_b[int_design_use] = 0

 ( 1)  use + .5*int_design_use = 0

       F(  1,    49) =   16.41
            Prob > F =    0.0002

.         display "t-stat = "sqrt(r(F))
t-stat = 4.0513675

. // Column 6: Effort
. reg contribution_1_8 design use int_design_use peqproposal1 peqproposal2 peqproposal3 peqproposal4 peqproposal5 if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(8, 49)          =       3.73
                                                Prob > F          =     0.0018
                                                R-squared         =     0.1902
                                                Root MSE          =     8.6168

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
contributi~1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   6.668144   2.781805     2.40   0.020     1.077896    12.25839
           use |   .5358669   2.861856     0.19   0.852    -5.215249    6.286983
int_design_use |   -7.15575   4.191008    -1.71   0.094     -15.5779    1.266396
  peqproposal1 |   -.944167   .4469758    -2.11   0.040    -1.842398   -.0459355
  peqproposal2 |   .3848619   .4489151     0.86   0.395    -.5172669    1.286991
  peqproposal3 |   .1897439   .5369055     0.35   0.725     -.889208    1.268696
  peqproposal4 |  -.6194634   .5323273    -1.16   0.250    -1.689215    .4502884
  peqproposal5 |   .6396901   .5846142     1.09   0.279    -.5351362    1.814516
         _cons |   20.50187   5.753424     3.56   0.001     8.939935    32.06381
--------------------------------------------------------------------------------

. // Column 7: Effort
. reg contribution_1_8 design use int_design_use peqdistrifairness_factor peqproposal1 peqproposal2 peqproposal3 peqproposal4 peqproposal5 if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(9, 49)          =       8.41
                                                Prob > F          =     0.0000
                                                R-squared         =     0.4075
                                                Root MSE          =     7.3966

                                           (Std. err. adjusted for 50 clusters in groupnr)
------------------------------------------------------------------------------------------
                         |               Robust
        contribution_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------------------+----------------------------------------------------------------
                  design |   2.988708    2.30601     1.30   0.201    -1.645393    7.622809
                     use |  -.0471555   2.170963    -0.02   0.983    -4.409868    4.315557
          int_design_use |  -2.626658   3.297619    -0.80   0.430    -9.253471    4.000155
peqdistrifairness_factor |   5.377522   .7378327     7.29   0.000     3.894792    6.860253
            peqproposal1 |  -.6180861   .3571614    -1.73   0.090    -1.335829    .0996566
            peqproposal2 |   .0718643   .3826601     0.19   0.852    -.6971201    .8408486
            peqproposal3 |   -.477659   .4815231    -0.99   0.326    -1.445316    .4899978
            peqproposal4 |  -.7888468   .5079563    -1.55   0.127    -1.809623    .2319295
            peqproposal5 |  -.1303171   .4799578    -0.27   0.787    -1.094828    .8341942
                   _cons |   29.13872   4.750586     6.13   0.000     19.59206    38.68538
------------------------------------------------------------------------------------------

. 
. 
. // PEQ_Factor_Procedure
. factor peqfinalallocation1 peqfinalallocation2 peqfinalallocation3 if subjectnr<4
(obs=150)

Factor analysis/correlation                      Number of obs    =        150
    Method: principal factors                    Retained factors =          1
    Rotation: (unrotated)                        Number of params =          3

    --------------------------------------------------------------------------
         Factor  |   Eigenvalue   Difference        Proportion   Cumulative
    -------------+------------------------------------------------------------
        Factor1  |      1.60724      1.72668            1.2255       1.2255
        Factor2  |     -0.11944      0.05689           -0.0911       1.1344
        Factor3  |     -0.17633            .           -0.1344       1.0000
    --------------------------------------------------------------------------
    LR test: independent vs. saturated:  chi2(3)  =  147.91 Prob>chi2 = 0.0000

Factor loadings (pattern matrix) and unique variances

    ---------------------------------------
        Variable |  Factor1 |   Uniqueness 
    -------------+----------+--------------
    peqfinalal~1 |   0.7707 |      0.4060  
    peqfinalal~2 |   0.6864 |      0.5289  
    peqfinalal~3 |   0.7363 |      0.4578  
    ---------------------------------------

. rotate

Factor analysis/correlation                      Number of obs    =        150
    Method: principal factors                    Retained factors =          1
    Rotation: orthogonal varimax (Kaiser off)    Number of params =          3

    --------------------------------------------------------------------------
         Factor  |     Variance   Difference        Proportion   Cumulative
    -------------+------------------------------------------------------------
        Factor1  |      1.60724            .            1.2255       1.2255
    --------------------------------------------------------------------------
    LR test: independent vs. saturated:  chi2(3)  =  147.91 Prob>chi2 = 0.0000

Rotated factor loadings (pattern matrix) and unique variances

    ---------------------------------------
        Variable |  Factor1 |   Uniqueness 
    -------------+----------+--------------
    peqfinalal~1 |   0.7707 |      0.4060  
    peqfinalal~2 |   0.6864 |      0.5289  
    peqfinalal~3 |   0.7363 |      0.4578  
    ---------------------------------------

Factor rotation matrix

    -----------------------
                 | Factor1 
    -------------+---------
         Factor1 |  1.0000 
    -----------------------

. predict peqfinalallocation_factor
(option regression assumed; regression scoring)

Scoring coefficients (method = regression; based on varimax rotated factors)

    ------------------------
        Variable |  Factor1 
    -------------+----------
    peqfinalal~1 |  0.39655 
    peqfinalal~2 |  0.27631 
    peqfinalal~3 |  0.33692 
    ------------------------


. // Team-Liking
. factor peqteamliking1 peqteamliking2 peqteamliking3 peqteamliking4 peqteamliking5 peqteamliking6 peqteamliking7 peqteamliking8 peqteamliking9 if subjectnr<4
(obs=150)

Factor analysis/correlation                      Number of obs    =        150
    Method: principal factors                    Retained factors =          4
    Rotation: (unrotated)                        Number of params =         30

    --------------------------------------------------------------------------
         Factor  |   Eigenvalue   Difference        Proportion   Cumulative
    -------------+------------------------------------------------------------
        Factor1  |      5.59247      4.38550            0.8310       0.8310
        Factor2  |      1.20698      1.04456            0.1793       1.0103
        Factor3  |      0.16241      0.05777            0.0241       1.0344
        Factor4  |      0.10465      0.11727            0.0155       1.0500
        Factor5  |     -0.01263      0.01796           -0.0019       1.0481
        Factor6  |     -0.03058      0.04589           -0.0045       1.0436
        Factor7  |     -0.07647      0.01970           -0.0114       1.0322
        Factor8  |     -0.09616      0.02440           -0.0143       1.0179
        Factor9  |     -0.12056            .           -0.0179       1.0000
    --------------------------------------------------------------------------
    LR test: independent vs. saturated:  chi2(36) = 1275.67 Prob>chi2 = 0.0000

Factor loadings (pattern matrix) and unique variances

    ---------------------------------------------------------------------
        Variable |  Factor1   Factor2   Factor3   Factor4 |   Uniqueness 
    -------------+----------------------------------------+--------------
    peqteamlik~1 |   0.8159   -0.2870   -0.1587    0.1511 |      0.2040  
    peqteamlik~2 |   0.7862   -0.2979   -0.1706    0.0579 |      0.2608  
    peqteamlik~3 |   0.8318   -0.2462    0.1025   -0.1723 |      0.2073  
    peqteamlik~4 |   0.8882   -0.2347   -0.0459   -0.1452 |      0.1328  
    peqteamlik~5 |   0.7583   -0.0711    0.2185    0.1488 |      0.3500  
    peqteamlik~6 |   0.8886   -0.2062    0.1394    0.0085 |      0.1484  
    peqteamlik~7 |   0.5989    0.5444    0.1083    0.0489 |      0.3308  
    peqteamlik~8 |   0.7290    0.5854   -0.0847   -0.0058 |      0.1187  
    peqteamlik~9 |   0.7571    0.4833   -0.0972   -0.0553 |      0.1808  
    ---------------------------------------------------------------------

. rotate

Factor analysis/correlation                      Number of obs    =        150
    Method: principal factors                    Retained factors =          4
    Rotation: orthogonal varimax (Kaiser off)    Number of params =         30

    --------------------------------------------------------------------------
         Factor  |     Variance   Difference        Proportion   Cumulative
    -------------+------------------------------------------------------------
        Factor1  |      4.14444      1.55467            0.6158       0.6158
        Factor2  |      2.58977      2.38379            0.3848       1.0006
        Factor3  |      0.20598      0.07966            0.0306       1.0312
        Factor4  |      0.12632            .            0.0188       1.0500
    --------------------------------------------------------------------------
    LR test: independent vs. saturated:  chi2(36) = 1275.67 Prob>chi2 = 0.0000

Rotated factor loadings (pattern matrix) and unique variances

    ---------------------------------------------------------------------
        Variable |  Factor1   Factor2   Factor3   Factor4 |   Uniqueness 
    -------------+----------------------------------------+--------------
    peqteamlik~1 |   0.8271    0.2320    0.0354    0.2383 |      0.2040  
    peqteamlik~2 |   0.8161    0.2097   -0.0303    0.1684 |      0.2608  
    peqteamlik~3 |   0.8293    0.2622    0.0692   -0.1773 |      0.2073  
    peqteamlik~4 |   0.8732    0.3144   -0.0307   -0.0703 |      0.1328  
    peqteamlik~5 |   0.6422    0.3474    0.3417    0.0127 |      0.3500  
    peqteamlik~6 |   0.8388    0.3195    0.2084   -0.0503 |      0.1484  
    peqteamlik~7 |   0.1741    0.7750    0.1928   -0.0337 |      0.3308  
    peqteamlik~8 |   0.2692    0.8986    0.0188    0.0314 |      0.1187  
    peqteamlik~9 |   0.3541    0.8327   -0.0188    0.0023 |      0.1808  
    ---------------------------------------------------------------------

Factor rotation matrix

    --------------------------------------------------
                 | Factor1  Factor2  Factor3  Factor4 
    -------------+------------------------------------
         Factor1 |  0.8194   0.5630   0.1063   0.0154 
         Factor2 | -0.5673   0.8222   0.0238  -0.0396 
         Factor3 | -0.0410  -0.0793   0.8182  -0.5680 
         Factor4 | -0.0710  -0.0258   0.5646   0.8219 
    --------------------------------------------------

. // PEQ_Factor_Team-I
. factor peqteamliking1 peqteamliking2 peqteamliking3 peqteamliking4 peqteamliking5 peqteamliking6 if subjectnr<4
(obs=150)

Factor analysis/correlation                      Number of obs    =        150
    Method: principal factors                    Retained factors =          3
    Rotation: (unrotated)                        Number of params =         15

    --------------------------------------------------------------------------
         Factor  |   Eigenvalue   Difference        Proportion   Cumulative
    -------------+------------------------------------------------------------
        Factor1  |      4.42743      4.28587            1.0007       1.0007
        Factor2  |      0.14156      0.05765            0.0320       1.0327
        Factor3  |      0.08391      0.11601            0.0190       1.0517
        Factor4  |     -0.03209      0.04788           -0.0073       1.0444
        Factor5  |     -0.07997      0.03655           -0.0181       1.0263
        Factor6  |     -0.11652            .           -0.0263       1.0000
    --------------------------------------------------------------------------
    LR test: independent vs. saturated:  chi2(15) =  850.37 Prob>chi2 = 0.0000

Factor loadings (pattern matrix) and unique variances

    -----------------------------------------------------------
        Variable |  Factor1   Factor2   Factor3 |   Uniqueness 
    -------------+------------------------------+--------------
    peqteamlik~1 |   0.8611   -0.2058    0.0875 |      0.2085  
    peqteamlik~2 |   0.8350   -0.2024   -0.0094 |      0.2617  
    peqteamlik~3 |   0.8690    0.1372   -0.1391 |      0.2066  
    peqteamlik~4 |   0.9167   -0.0044   -0.1480 |      0.1378  
    peqteamlik~5 |   0.7488    0.1497    0.1760 |      0.3859  
    peqteamlik~6 |   0.9124    0.1304    0.0628 |      0.1466  
    -----------------------------------------------------------

. rotate

Factor analysis/correlation                      Number of obs    =        150
    Method: principal factors                    Retained factors =          3
    Rotation: orthogonal varimax (Kaiser off)    Number of params =         15

    --------------------------------------------------------------------------
         Factor  |     Variance   Difference        Proportion   Cumulative
    -------------+------------------------------------------------------------
        Factor1  |      1.99472      0.24265            0.4509       0.4509
        Factor2  |      1.75207      0.84595            0.3960       0.8469
        Factor3  |      0.90612            .            0.2048       1.0517
    --------------------------------------------------------------------------
    LR test: independent vs. saturated:  chi2(15) =  850.37 Prob>chi2 = 0.0000

Rotated factor loadings (pattern matrix) and unique variances

    -----------------------------------------------------------
        Variable |  Factor1   Factor2   Factor3 |   Uniqueness 
    -------------+------------------------------+--------------
    peqteamlik~1 |   0.4297    0.6999    0.3422 |      0.2085  
    peqteamlik~2 |   0.4743    0.6684    0.2580 |      0.2617  
    peqteamlik~3 |   0.7187    0.4077    0.3327 |      0.2066  
    peqteamlik~4 |   0.6971    0.5460    0.2798 |      0.1378  
    peqteamlik~5 |   0.4475    0.3659    0.5291 |      0.3859  
    peqteamlik~6 |   0.6184    0.4662    0.5036 |      0.1466  
    -----------------------------------------------------------

Factor rotation matrix

    -----------------------------------------
                 | Factor1  Factor2  Factor3 
    -------------+---------------------------
         Factor1 |  0.6615   0.6132   0.4317 
         Factor2 |  0.4147  -0.7788   0.4707 
         Factor3 | -0.6248   0.1324   0.7694 
    -----------------------------------------

. predict peqteamliking_factor_A
(option regression assumed; regression scoring)

Scoring coefficients (method = regression; based on varimax rotated factors)

    --------------------------------------------
        Variable |  Factor1   Factor2   Factor3 
    -------------+------------------------------
    peqteamlik~1 | -0.31839   0.57686   0.09056 
    peqteamlik~2 | -0.08640   0.42741  -0.15625 
    peqteamlik~3 |  0.46481  -0.22374  -0.00491 
    peqteamlik~4 |  0.55347   0.14359  -0.47236 
    peqteamlik~5 | -0.03909  -0.06550   0.35377 
    peqteamlik~6 |  0.11293  -0.17974   0.68578 
    --------------------------------------------


. // PEQ_Factor_Team-II
. factor peqteamliking7 peqteamliking8 peqteamliking9 if subjectnr<4
(obs=150)

Factor analysis/correlation                      Number of obs    =        150
    Method: principal factors                    Retained factors =          1
    Rotation: (unrotated)                        Number of params =          3

    --------------------------------------------------------------------------
         Factor  |   Eigenvalue   Difference        Proportion   Cumulative
    -------------+------------------------------------------------------------
        Factor1  |      2.30812      2.32245            1.0525       1.0525
        Factor2  |     -0.01433      0.08652           -0.0065       1.0460
        Factor3  |     -0.10085            .           -0.0460       1.0000
    --------------------------------------------------------------------------
    LR test: independent vs. saturated:  chi2(3)  =  352.78 Prob>chi2 = 0.0000

Factor loadings (pattern matrix) and unique variances

    ---------------------------------------
        Variable |  Factor1 |   Uniqueness 
    -------------+----------+--------------
    peqteamlik~7 |   0.7945 |      0.3688  
    peqteamlik~8 |   0.9396 |      0.1171  
    peqteamlik~9 |   0.8911 |      0.2060  
    ---------------------------------------

. rotate

Factor analysis/correlation                      Number of obs    =        150
    Method: principal factors                    Retained factors =          1
    Rotation: orthogonal varimax (Kaiser off)    Number of params =          3

    --------------------------------------------------------------------------
         Factor  |     Variance   Difference        Proportion   Cumulative
    -------------+------------------------------------------------------------
        Factor1  |      2.30812            .            1.0525       1.0525
    --------------------------------------------------------------------------
    LR test: independent vs. saturated:  chi2(3)  =  352.78 Prob>chi2 = 0.0000

Rotated factor loadings (pattern matrix) and unique variances

    ---------------------------------------
        Variable |  Factor1 |   Uniqueness 
    -------------+----------+--------------
    peqteamlik~7 |   0.7945 |      0.3688  
    peqteamlik~8 |   0.9396 |      0.1171  
    peqteamlik~9 |   0.8911 |      0.2060  
    ---------------------------------------

Factor rotation matrix

    -----------------------
                 | Factor1 
    -------------+---------
         Factor1 |  1.0000 
    -----------------------

. predict peqteamliking_factor_B
(option regression assumed; regression scoring)

Scoring coefficients (method = regression; based on varimax rotated factors)

    ------------------------
        Variable |  Factor1 
    -------------+----------
    peqteamlik~7 |  0.14896 
    peqteamlik~8 |  0.57438 
    peqteamlik~9 |  0.28509 
    ------------------------


. 
. ********************************************************************************
. ** TABLE A.5
. ********************************************************************************
. // Column 1: PEQ_Factor_Procedure-1
. reg peqfinalallocation_factor design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       7.59
                                                Prob > F          =     0.0003
                                                R-squared         =     0.1409
                                                Root MSE          =     .80729

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
peqfinalallo~r | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   .3958458   .1951868     2.03   0.048     .0036032    .7880884
           use |  -.3679866    .183315    -2.01   0.050    -.7363718    .0003986
int_design_use |  -.4317801   .2603238    -1.66   0.104    -.9549203      .09136
         _cons |   .1056929   .1225319     0.86   0.393    -.1405441    .3519299
--------------------------------------------------------------------------------

.         // Test reported in text
.         display _b[use] + 0.5*_b[int_design_use]
-.58387663

.         test _b[use] + 0.5*_b[int_design_use] = 0

 ( 1)  use + .5*int_design_use = 0

       F(  1,    49) =   20.12
            Prob > F =    0.0000

.         display "t-stat = "sqrt(r(F))
t-stat = 4.485773

.         display _b[design] + 0.5*_b[int_design_use]
.17995577

.         test _b[design] + 0.5*_b[int_design_use] = 0

 ( 1)  design + .5*int_design_use = 0

       F(  1,    49) =    1.91
            Prob > F =    0.1731

.         display "t-stat = "sqrt(r(F))   
t-stat = 1.3825536

. // Column 2: PEQ_Factor-Team-I
. reg peqteamliking_factor_A design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       4.02
                                                Prob > F          =     0.0123
                                                R-squared         =     0.0905
                                                Root MSE          =     .74278

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
peqteamlikin~A | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   .3256053   .2127337     1.53   0.132    -.1018992    .7531097
           use |  -.2445583   .2010469    -1.22   0.230    -.6485772    .1594607
int_design_use |   -.318716   .2718548    -1.17   0.247    -.8650287    .2275968
         _cons |   .0472338   .1585817     0.30   0.767    -.2714481    .3659158
--------------------------------------------------------------------------------

.         // Test reported in text
.         display _b[use] + 0.5*_b[int_design_use]
-.40391625

.         test _b[use] + 0.5*_b[int_design_use] = 0

 ( 1)  use + .5*int_design_use = 0

       F(  1,    49) =    8.83
            Prob > F =    0.0046

.         display "t-stat = "sqrt(r(F))
t-stat = 2.9715584

. // Column 3: PEQ_Factor-Team-II
. reg peqteamliking_factor_B design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       0.66
                                                Prob > F          =     0.5812
                                                R-squared         =     0.0108
                                                Root MSE          =     .95956

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
peqteamlikin~B | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   .2247884   .1904358     1.18   0.244    -.1579066    .6074833
           use |   .1822212   .2414101     0.75   0.454    -.3029106     .667353
int_design_use |  -.3935159   .3099037    -1.27   0.210    -1.016291     .229259
         _cons |   -.104835   .1410146    -0.74   0.461    -.3882145    .1785444
--------------------------------------------------------------------------------

. // Column 4: Effort
. reg contribution_1_8 design use int_design_use peqfinalallocation_factor peqteamliking_factor_A peqteamliking_factor_B if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(6, 49)          =       3.71
                                                Prob > F          =     0.0040
                                                R-squared         =     0.2075
                                                Root MSE          =     8.4645

                                            (Std. err. adjusted for 50 clusters in groupnr)
-------------------------------------------------------------------------------------------
                          |               Robust
         contribution_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
--------------------------+----------------------------------------------------------------
                   design |   6.940513   2.587283     2.68   0.010     1.741174    12.13985
                      use |   .2374391   2.579665     0.09   0.927    -4.946593    5.421471
           int_design_use |    -6.8535    4.05429    -1.69   0.097     -15.0009    1.293901
peqfinalallocation_factor |  -.8503898   .9158471    -0.93   0.358    -2.690854     .990074
   peqteamliking_factor_A |   2.794656   1.021411     2.74   0.009     .7420535    4.847258
   peqteamliking_factor_B |    1.26682   .7814194     1.62   0.111     -.303501    2.837141
                    _cons |   19.73652   1.799497    10.97   0.000     16.12029    23.35274
-------------------------------------------------------------------------------------------

. // Column 5: Effort
. reg contribution_1_8 design use int_design_use peqdistrifairness_factor peqfinalallocation_factor peqteamliking_factor_A peqteamliking_factor_B if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(7, 49)          =      12.26
                                                Prob > F          =     0.0000
                                                R-squared         =     0.3962
                                                Root MSE          =     7.4142

                                            (Std. err. adjusted for 50 clusters in groupnr)
-------------------------------------------------------------------------------------------
                          |               Robust
         contribution_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
--------------------------+----------------------------------------------------------------
                   design |   3.856382   2.310659     1.67   0.102    -.7870604    8.499824
                      use |    .444666   2.166641     0.21   0.838    -3.909361    4.798693
           int_design_use |  -3.343931   3.444264    -0.97   0.336    -10.26544    3.577577
 peqdistrifairness_factor |   4.960417   .8437322     5.88   0.000     3.264873     6.65596
peqfinalallocation_factor |  -1.382774   .7764224    -1.78   0.081    -2.943053    .1775052
   peqteamliking_factor_A |   1.740458   .9681127     1.80   0.078    -.2050378    3.685953
   peqteamliking_factor_B |   .2499927   .7845694     0.32   0.751    -1.326658    1.826644
                    _cons |   20.25834     1.5746    12.87   0.000     17.09406    23.42262
-------------------------------------------------------------------------------------------

. 
. ********************************************************************************
. ** TABLE A.6
. ********************************************************************************
. // Column 1: PEQ_General-1
. reg peqpreferencemodel1 design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       0.25
                                                Prob > F          =     0.8633
                                                R-squared         =     0.0054
                                                Root MSE          =     1.3762

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
peqpreferenc~1 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |  -.0555556    .305083    -0.18   0.856    -.6686427    .5575316
           use |  -.2457265   .3528829    -0.70   0.490    -.9548712    .4634182
int_design_use |   .1068376   .4514207     0.24   0.814    -.8003263    1.014002
         _cons |   5.527778   .2283912    24.20   0.000     5.068809    5.986747
--------------------------------------------------------------------------------

. // Column 2: PEQ_General-2
. reg peqpreferencemodel2 design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       1.09
                                                Prob > F          =     0.3636
                                                R-squared         =     0.0148
                                                Root MSE          =     1.2276

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
peqpreferenc~2 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   .3055556   .2469845     1.24   0.222    -.1907784    .8018895
           use |   .0299145   .2600625     0.12   0.909    -.4927006    .5525296
int_design_use |  -.4337607   .3444104    -1.26   0.214    -1.125879     .258358
         _cons |   5.611111   .1692904    33.14   0.000     5.270909    5.951313
--------------------------------------------------------------------------------

. // Column 3: PEQ_General-3
. reg peqpreferencemodel3 design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       2.56
                                                Prob > F          =     0.0655
                                                R-squared         =     0.0399
                                                Root MSE          =     1.6721

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
peqpreferenc~3 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |        .25   .3798693     0.66   0.514    -.5133759    1.013376
           use |   .3247863   .4291529     0.76   0.453    -.5376287    1.187201
int_design_use |  -1.096154   .5361421    -2.04   0.046    -2.173572    -.018736
         _cons |   3.444444   .3008839    11.45   0.000     2.839796    4.049093
--------------------------------------------------------------------------------

. // Column 4: PEQ_General-4
. reg peqpreferencemodel4 design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       7.55
                                                Prob > F          =     0.0003
                                                R-squared         =     0.1084
                                                Root MSE          =     1.5244

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
peqpreferenc~4 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   .8611111   .3091167     2.79   0.008     .2399178    1.482304
           use |    .707265   .3525158     2.01   0.050    -.0011421    1.415672
int_design_use |  -1.989316    .461062    -4.31   0.000    -2.915855   -1.062777
         _cons |   4.138889   .2486059    16.65   0.000     3.639297    4.638481
--------------------------------------------------------------------------------

. // Column 5: PEQ_General-5
. reg peqpreferencemodel5 design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       2.84
                                                Prob > F          =     0.0476
                                                R-squared         =     0.0339
                                                Root MSE          =     1.0697

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
peqpreferenc~5 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   .4722222   .1813223     2.60   0.012     .1078414    .8366031
           use |   .3782051   .1828682     2.07   0.044     .0107177    .7456926
int_design_use |  -.7799145   .3055143    -2.55   0.014    -1.393868   -.1659606
         _cons |       5.75   .1275598    45.08   0.000     5.493659    6.006341
--------------------------------------------------------------------------------

. // Column 6: PEQ_General-6
. reg peqpreferencemodel6 design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       3.61
                                                Prob > F          =     0.0196
                                                R-squared         =     0.0337
                                                Root MSE          =     1.7469

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
peqpreferenc~6 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |  -.3611111   .2958342    -1.22   0.228    -.9556121    .2333899
           use |   .4679487   .3332681     1.40   0.167    -.2017785    1.137676
int_design_use |  -.3568376   .4482874    -0.80   0.430    -1.257705    .5440296
         _cons |   4.583333   .2570805    17.83   0.000     4.066711    5.099956
--------------------------------------------------------------------------------

. // Column 7: PEQ_General-7
. reg peqpreferencemodel7 design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =       3.48
                                                Prob > F          =     0.0228
                                                R-squared         =     0.0312
                                                Root MSE          =     1.6268

                                 (Std. err. adjusted for 50 clusters in groupnr)
--------------------------------------------------------------------------------
               |               Robust
peqpreferenc~7 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        design |   .0555556   .2646527     0.21   0.835     -.476284    .5873951
           use |   .6901709   .2270307     3.04   0.004     .2339356    1.146406
int_design_use |  -.6965812   .4668284    -1.49   0.142    -1.634708    .2415455
         _cons |   4.361111   .1470658    29.65   0.000     4.065571    4.656651
--------------------------------------------------------------------------------

. // Column 8: Effort
. reg contribution_1_8 design use int_design_use peqpreferencemodel1 peqpreferencemodel2 peqpreferencemodel3 peqpreferencemodel4 peqpreferencemodel5 peqpreferencemodel6 peqpreferencemodel7 if subject
> nr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(10, 49)         =       2.95
                                                Prob > F          =     0.0056
                                                R-squared         =     0.1845
                                                Root MSE          =     8.7088

                                      (Std. err. adjusted for 50 clusters in groupnr)
-------------------------------------------------------------------------------------
                    |               Robust
   contribution_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
--------------------+----------------------------------------------------------------
             design |   7.444121   2.877605     2.59   0.013     1.661357    13.22688
                use |   -.212528   3.009661    -0.07   0.944    -6.260669    5.835613
     int_design_use |  -7.120213   4.381495    -1.63   0.111    -15.92516    1.684731
peqpreferencemodel1 |  -.6251936   .5181909    -1.21   0.233    -1.666537    .4161501
peqpreferencemodel2 |   1.894745   .6198028     3.06   0.004      .649205    3.140286
peqpreferencemodel3 |  -.3895563   .4289999    -0.91   0.368    -1.251664    .4725514
peqpreferencemodel4 |   .2851063   .5457295     0.52   0.604    -.8115782    1.381791
peqpreferencemodel5 |  -.6662098   .7457213    -0.89   0.376    -2.164793    .8323733
peqpreferencemodel6 |   .2883693   .3601164     0.80   0.427    -.4353117     1.01205
peqpreferencemodel7 |   .2055667   .4152798     0.50   0.623    -.6289693    1.040103
              _cons |   14.24443   5.848083     2.44   0.019     2.492272     25.9966
-------------------------------------------------------------------------------------

. // Column 9: Effort
. reg contribution_1_8 design use int_design_use peqdistrifairness_factor peqpreferencemodel1 peqpreferencemodel2 peqpreferencemodel3 peqpreferencemodel4 peqpreferencemodel5 peqpreferencemodel6 peqpr
> eferencemodel7 if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(11, 49)         =       7.28
                                                Prob > F          =     0.0000
                                                R-squared         =     0.4124
                                                Root MSE          =     7.4193

                                           (Std. err. adjusted for 50 clusters in groupnr)
------------------------------------------------------------------------------------------
                         |               Robust
        contribution_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------------------+----------------------------------------------------------------
                  design |   3.675548   2.305831     1.59   0.117    -.9581921    8.309289
                     use |   .4474861   2.351065     0.19   0.850    -4.277156    5.172128
          int_design_use |  -3.211583   3.458619    -0.93   0.358    -10.16194    3.738772
peqdistrifairness_factor |   5.156923   .7811425     6.60   0.000     3.587158    6.726687
     peqpreferencemodel1 |  -.1915176   .4793668    -0.40   0.691    -1.154841    .7718061
     peqpreferencemodel2 |   1.215732   .6475812     1.88   0.066    -.0856308    2.517095
     peqpreferencemodel3 |  -.5375256   .3365521    -1.60   0.117    -1.213852    .1388012
     peqpreferencemodel4 |  -.0095302   .5082211    -0.02   0.985    -1.030839    1.011778
     peqpreferencemodel5 |  -.4748183   .7431299    -0.64   0.526    -1.968194    1.018557
     peqpreferencemodel6 |  -.1351444    .365867    -0.37   0.713    -.8703817    .6000929
     peqpreferencemodel7 |   .7034312   .4093682     1.72   0.092    -.1192249    1.526087
                   _cons |   16.59874   5.108474     3.25   0.002     6.332874     26.8646
------------------------------------------------------------------------------------------

. 
. 
. ********************************************************************************
. ** TABLE A.7
. ********************************************************************************
. pwcorr contribution_1_8 peqdistrifairness_factor peqprocedfairness_factor peqcontribution1 peqcontribution2 peqproposal1 peqproposal2 peqproposal3 peqproposal4 peqproposal5 peqfinalallocation_facto
> r peqteamliking_factor_A peqteamliking_factor_B peqpreferencemodel1 peqpreferencemodel2 peqpreferencemodel3 peqpreferencemodel4 peqpreferencemodel5 peqpreferencemodel6 peqpreferencemodel7 if subjec
> tnr<4, sig

             | cont~1_8 peqdis~r peqpro~r peqcon~1 peqcon~2 peqp~al1 peqp~al2
-------------+---------------------------------------------------------------
contribu~1_8 |   1.0000 
             |
             |
peqdistrif~r |   0.5952   1.0000 
             |   0.0000
             |
peqprocedf~r |   0.3731   0.5072   1.0000 
             |   0.0000   0.0000
             |
peqcontrib~1 |  -0.3163  -0.1602  -0.2369   1.0000 
             |   0.0001   0.0501   0.0035
             |
peqcontrib~2 |   0.3333   0.4743   0.3176  -0.0189   1.0000 
             |   0.0000   0.0000   0.0001   0.8182
             |
peqproposal1 |  -0.2056  -0.0888  -0.1398   0.1030  -0.0996   1.0000 
             |   0.0116   0.2799   0.0880   0.2096   0.2252
             |
peqproposal2 |  -0.0333   0.0339  -0.0654   0.1631  -0.0151   0.0989   1.0000 
             |   0.6858   0.6808   0.4265   0.0462   0.8541   0.2286
             |
peqproposal3 |   0.2139   0.3859   0.3499  -0.0844   0.6860  -0.0242  -0.1143 
             |   0.0086   0.0000   0.0000   0.3043   0.0000   0.7687   0.1638
             |
peqproposal4 |  -0.2151  -0.1344  -0.0501   0.2191  -0.4212   0.2369   0.2468 
             |   0.0082   0.1011   0.5423   0.0071   0.0000   0.0035   0.0023
             |
peqproposal5 |   0.1872   0.3965   0.1993   0.0653   0.3850   0.1146   0.1166 
             |   0.0218   0.0000   0.0145   0.4275   0.0000   0.1627   0.1553
             |
peqfinalal~r |   0.1727   0.3524   0.3458   0.0312   0.5148   0.1171  -0.0172 
             |   0.0346   0.0000   0.0000   0.7051   0.0000   0.1537   0.8345
             |
peqteamlik~A |   0.3437   0.3976   0.3753  -0.2094   0.6405  -0.0395  -0.1432 
             |   0.0000   0.0000   0.0000   0.0101   0.0000   0.6310   0.0804
             |
peqteamlik~B |   0.2368   0.3435   0.3079  -0.1558   0.3737  -0.0840  -0.0498 
             |   0.0035   0.0000   0.0001   0.0570   0.0000   0.3068   0.5452
             |
peqprefere~1 |   0.0359  -0.0240  -0.0055   0.1197   0.0528  -0.0623   0.0379 
             |   0.6625   0.7705   0.9471   0.1444   0.5210   0.4486   0.6454
             |
peqprefere~2 |   0.2336   0.1576   0.1216  -0.0758  -0.0010  -0.0687   0.2323 
             |   0.0040   0.0541   0.1383   0.3563   0.9904   0.4036   0.0042
             |
peqprefere~3 |  -0.0236   0.0934   0.1323  -0.1775   0.1194   0.1093  -0.1095 
             |   0.7745   0.2556   0.1065   0.0298   0.1455   0.1829   0.1823
             |
peqprefere~4 |   0.1366   0.1733   0.3539  -0.2488   0.2522  -0.1398  -0.0363 
             |   0.0956   0.0339   0.0000   0.0021   0.0018   0.0879   0.6592
             |
peqprefere~5 |   0.0723   0.0577   0.1038  -0.2647  -0.0333  -0.1131   0.0850 
             |   0.3791   0.4834   0.2060   0.0011   0.6860   0.1681   0.3010
             |
peqprefere~6 |   0.0392   0.0019  -0.1139  -0.0218  -0.1127   0.0503   0.1635 
             |   0.6338   0.9812   0.1653   0.7908   0.1696   0.5409   0.0456
             |
peqprefere~7 |   0.0552  -0.0799  -0.0060  -0.1598  -0.0613   0.0869   0.0820 
             |   0.5021   0.3309   0.9423   0.0508   0.4560   0.2903   0.3184
             |

             | peqp~al3 peqp~al4 peqpro~5 peqfin~r peqtea~A peqtea~B peqpre~1
-------------+---------------------------------------------------------------
peqproposal3 |   1.0000 
             |
             |
peqproposal4 |  -0.4333   1.0000 
             |   0.0000
             |
peqproposal5 |   0.4445  -0.0961   1.0000 
             |   0.0000   0.2423
             |
peqfinalal~r |   0.6279  -0.1591   0.4700   1.0000 
             |   0.0000   0.0519   0.0000
             |
peqteamlik~A |   0.5778  -0.3481   0.2790   0.4440   1.0000 
             |   0.0000   0.0000   0.0005   0.0000
             |
peqteamlik~B |   0.4355  -0.2159   0.3105   0.3785   0.4945   1.0000 
             |   0.0000   0.0080   0.0001   0.0000   0.0000
             |
peqprefere~1 |  -0.0456   0.0956   0.1181   0.1018  -0.0106  -0.1150   1.0000 
             |   0.5794   0.2444   0.1502   0.2153   0.8971   0.1610
             |
peqprefere~2 |   0.0365   0.0724   0.1211   0.1405   0.0286  -0.0207   0.4575 
             |   0.6574   0.3789   0.1398   0.0864   0.7286   0.8018   0.0000
             |
peqprefere~3 |   0.2022  -0.0727   0.0826   0.1965   0.2962   0.1609   0.0401 
             |   0.0131   0.3766   0.3147   0.0159   0.0002   0.0492   0.6258
             |
peqprefere~4 |   0.2822  -0.2680   0.0676   0.1907   0.3157   0.1862   0.0301 
             |   0.0005   0.0009   0.4114   0.0194   0.0001   0.0225   0.7144
             |
peqprefere~5 |   0.1275  -0.1292   0.0458   0.1125   0.0217  -0.0065   0.0328 
             |   0.1199   0.1151   0.5779   0.1705   0.7917   0.9373   0.6900
             |
peqprefere~6 |  -0.1335   0.1491  -0.0405  -0.0689  -0.1443  -0.1665   0.0804 
             |   0.1033   0.0686   0.6223   0.4019   0.0780   0.0417   0.3278
             |
peqprefere~7 |   0.0278   0.0197  -0.0961  -0.0580  -0.1149  -0.1977   0.0721 
             |   0.7356   0.8106   0.2423   0.4809   0.1614   0.0153   0.3808
             |

             | peqpre~2 peqpre~3 peqpre~4 peqpre~5 peqpre~6 peqpre~7
-------------+------------------------------------------------------
peqprefere~2 |   1.0000 
             |
             |
peqprefere~3 |   0.0379   1.0000 
             |   0.6455
             |
peqprefere~4 |   0.2847   0.3168   1.0000 
             |   0.0004   0.0001
             |
peqprefere~5 |   0.3664  -0.0097   0.3440   1.0000 
             |   0.0000   0.9059   0.0000
             |
peqprefere~6 |   0.0208  -0.0579  -0.0904  -0.0649   1.0000 
             |   0.8008   0.4817   0.2713   0.4297
             |
peqprefere~7 |   0.0882   0.0764   0.1728   0.1397   0.5736   1.0000 
             |   0.2830   0.3527   0.0345   0.0881   0.0000
             |

. 
. 
.         
. ********************************************************************************
. ** ONLINE APPENDIX, SECTION B
. ********************************************************************************
. 
. ********************************************************************************
. ** TABLE B.1: FINAL BONUS
. ********************************************************************************
. ** PANEL A: DECISION LEVEL
. // Column 1: Formulaic Use & Self-Including Design
. reg finalbonus contribution if subjectnr<4 & period<9 & use==0 & design==0, vce(cluster groupnr)

Linear regression                               Number of obs     =        288
                                                F(1, 11)          =     112.87
                                                Prob > F          =     0.0000
                                                R-squared         =     0.5356
                                                Root MSE          =     10.819

                               (Std. err. adjusted for 12 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
  finalbonus | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
contribution |   1.065779    .100319    10.62   0.000      .844978    1.286579
       _cons |   8.530642   2.457175     3.47   0.005     3.122436    13.93885
------------------------------------------------------------------------------

. // Column 2: Formulaic Use & Self-Including Design
. reg finalbonus contribution if subjectnr<4 & period<9 & use==0 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =        288
                                                F(1, 11)          =     967.83
                                                Prob > F          =     0.0000
                                                R-squared         =     0.7891
                                                Root MSE          =     7.9244

                               (Std. err. adjusted for 12 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
  finalbonus | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
contribution |   1.340696   .0430954    31.11   0.000     1.245844    1.435548
       _cons |   4.372006   .9769525     4.48   0.001     2.221748    6.522264
------------------------------------------------------------------------------

. // Column 3: Discretionary Use & Self-Including Design
. reg finalbonus contribution if subjectnr<4 & period<9 & use==1 & design==0, vce(cluster groupnr)

Linear regression                               Number of obs     =        312
                                                F(1, 12)          =      76.90
                                                Prob > F          =     0.0000
                                                R-squared         =     0.4731
                                                Root MSE          =     15.016

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
  finalbonus | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
contribution |   .9900952   .1129018     8.77   0.000     .7441033    1.236087
       _cons |   10.06735   1.884282     5.34   0.000     5.961852    14.17285
------------------------------------------------------------------------------

. // Column 4: Discretionary Use & Self-Excluding Design
. reg finalbonus contribution if subjectnr<4 & period<9 & use==1 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =        312
                                                F(1, 12)          =      97.28
                                                Prob > F          =     0.0000
                                                R-squared         =     0.3630
                                                Root MSE          =     18.667

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
  finalbonus | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
contribution |   1.024965   .1039189     9.86   0.000     .7985449    1.251385
       _cons |    9.34236   2.512958     3.72   0.003     3.867094    14.81763
------------------------------------------------------------------------------

. // Column 5: All Conditions
. reg finalbonus contribution int_contribution_design int_contribution_use int_contribution_design_use design use int_design_use if subjectnr<4 & period<9, vce(cluster groupnr)

Linear regression                               Number of obs     =      1,200
                                                F(7, 49)          =     205.48
                                                Prob > F          =     0.0000
                                                R-squared         =     0.5311
                                                Root MSE          =     13.872

                                              (Std. err. adjusted for 50 clusters in groupnr)
---------------------------------------------------------------------------------------------
                            |               Robust
                 finalbonus | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
----------------------------+----------------------------------------------------------------
               contribution |   1.065779    .097138    10.97   0.000     .8705724    1.260985
    int_contribution_design |   .2749175   .1057218     2.60   0.012     .0624616    .4873735
       int_contribution_use |  -.0756834   .1465398    -0.52   0.608     -.370166    .2187993
int_contribution_design_use |   -.240048   .1827947    -1.31   0.195    -.6073878    .1272917
                     design |  -4.158635   2.560421    -1.62   0.111    -9.303994    .9867235
                        use |   1.536709   3.002332     0.51   0.611    -4.496704    7.570121
             int_design_use |   3.433645   3.984058     0.86   0.393    -4.572619    11.43991
                      _cons |   8.530642   2.379262     3.59   0.001     3.749336    13.31195
---------------------------------------------------------------------------------------------

.         display _b[int_contribution_design]
.27491754

.         test _b[int_contribution_design] = 0

 ( 1)  int_contribution_design = 0

       F(  1,    49) =    6.76
            Prob > F =    0.0123

.         display "t-stat = "sqrt(r(F))   
t-stat = 2.6003859

.         display _b[int_contribution_design] - _b[int_contribution_use]
.35060089

.         test _b[int_contribution_design] - _b[int_contribution_use] = 0

 ( 1)  int_contribution_design - int_contribution_use = 0

       F(  1,    49) =    8.92
            Prob > F =    0.0044

.         display "t-stat = "sqrt(r(F))   
t-stat = 2.9867423

.         display - _b[int_contribution_use] - _b[int_contribution_design_use]
.3157314

.         test - _b[int_contribution_use] - _b[int_contribution_design_use] = 0

 ( 1)  - int_contribution_use - int_contribution_design_use = 0

       F(  1,    49) =    8.35
            Prob > F =    0.0057

.         display "t-stat = "sqrt(r(F))
t-stat = 2.8894517

. **PANEL B: EMPLOYEE LEVEL       
. // Column 1: Formulaic Use & Self-Including Design
. reg finalbonus_1_8 contribution_1_8 if subjectnr<4 & period==9 & use==0 & design==0, vce(cluster groupnr)

Linear regression                               Number of obs     =         36
                                                F(1, 11)          =      42.30
                                                Prob > F          =     0.0000
                                                R-squared         =     0.7151
                                                Root MSE          =     6.0104

                                   (Std. err. adjusted for 12 clusters in groupnr)
----------------------------------------------------------------------------------
                 |               Robust
  finalbonus_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
contribution_1_8 |   1.223076   .1880647     6.50   0.000     .8091483    1.637004
           _cons |   5.440403   3.948384     1.38   0.196    -3.249931    14.13074
----------------------------------------------------------------------------------

. // Column 2: Formulaic Use & Self-Including Design
. reg finalbonus_1_8 contribution_1_8 if subjectnr<4 & period==9 & use==0 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =         36
                                                F(1, 11)          =    3001.85
                                                Prob > F          =     0.0000
                                                R-squared         =     0.9689
                                                Root MSE          =     2.1323

                                   (Std. err. adjusted for 12 clusters in groupnr)
----------------------------------------------------------------------------------
                 |               Robust
  finalbonus_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
contribution_1_8 |   1.478904   .0269927    54.79   0.000     1.419494    1.538315
           _cons |   .5789635   .7175483     0.81   0.437     -1.00035    2.158277
----------------------------------------------------------------------------------

. // Column 3: Discretionary Use & Self-Including Design
. reg finalbonus_1_8 contribution_1_8 if subjectnr<4 & period==9 & use==1 & design==0, vce(cluster groupnr)

Linear regression                               Number of obs     =         39
                                                F(1, 12)          =     436.75
                                                Prob > F          =     0.0000
                                                R-squared         =     0.8981
                                                Root MSE          =     3.9733

                                   (Std. err. adjusted for 13 clusters in groupnr)
----------------------------------------------------------------------------------
                 |               Robust
  finalbonus_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
contribution_1_8 |   1.346147   .0644135    20.90   0.000     1.205802    1.486492
           _cons |   3.037611   1.121052     2.71   0.019     .5950489    5.480173
----------------------------------------------------------------------------------

. // Column 4: Discretionary Use & Self-Excluding Design
. reg finalbonus_1_8 contribution_1_8 if subjectnr<4 & period==9 & use==1 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =         39
                                                F(1, 12)          =     272.93
                                                Prob > F          =     0.0000
                                                R-squared         =     0.7835
                                                Root MSE          =       7.35

                                   (Std. err. adjusted for 13 clusters in groupnr)
----------------------------------------------------------------------------------
                 |               Robust
  finalbonus_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
contribution_1_8 |   1.315506   .0796281    16.52   0.000     1.142011    1.489001
           _cons |   3.628382   1.680057     2.16   0.052    -.0321483    7.288913
----------------------------------------------------------------------------------

. // Column 5: All Conditions
. reg finalbonus_1_8 contribution_1_8 int_contribution_1_8_design int_contribution_1_8_use int_contribution_1_8_design_use design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(7, 49)          =    1013.98
                                                Prob > F          =     0.0000
                                                R-squared         =     0.8581
                                                Root MSE          =     5.2847

                                                  (Std. err. adjusted for 50 clusters in groupnr)
-------------------------------------------------------------------------------------------------
                                |               Robust
                 finalbonus_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
--------------------------------+----------------------------------------------------------------
               contribution_1_8 |   1.223076   .1836346     6.66   0.000     .8540485    1.592103
    int_contribution_1_8_design |   .2558282   .1855164     1.38   0.174     -.116981    .6286373
       int_contribution_1_8_use |    .123071   .1942022     0.63   0.529    -.2671929    .5133349
int_contribution_1_8_design_use |  -.2864692   .2109763    -1.36   0.181     -.710442    .1375036
                         design |  -4.861439   3.918521    -1.24   0.221      -12.736    3.013124
                            use |  -2.402792   4.009156    -0.60   0.552    -10.45949    5.653908
                 int_design_use |   5.452211   4.390959     1.24   0.220    -3.371752    14.27617
                          _cons |   5.440403   3.855373     1.41   0.165     -2.30726    13.18807
-------------------------------------------------------------------------------------------------

.         display _b[int_contribution_1_8_design]
.25582817

.         test _b[int_contribution_1_8_design] = 0

 ( 1)  int_contribution_1_8_design = 0

       F(  1,    49) =    1.90
            Prob > F =    0.1742

.         display "t-stat = "sqrt(r(F))   
t-stat = 1.3790058

.         display _b[int_contribution_1_8_design] - _b[int_contribution_1_8_use]
.13275718

.         test _b[int_contribution_1_8_design] - _b[int_contribution_1_8_use] = 0

 ( 1)  int_contribution_1_8_design - int_contribution_1_8_use = 0

       F(  1,    49) =    3.76
            Prob > F =    0.0583

.         display "t-stat = "sqrt(r(F))   
t-stat = 1.9390387

.         display - _b[int_contribution_1_8_use] - _b[int_contribution_1_8_design_use]
.16339818

.         test - _b[int_contribution_1_8_use] - _b[int_contribution_1_8_design_use] = 0

 ( 1)  - int_contribution_1_8_use - int_contribution_1_8_design_use = 0

       F(  1,    49) =    3.93
            Prob > F =    0.0531

.         display "t-stat = "sqrt(r(F))
t-stat = 1.9820015

. 
. ********************************************************************************        
. ** TABLE B.2: ADJUSTED AVERAGE PROPOSED BONUS
. ********************************************************************************
. ** PANEL A: DECISION LEVEL
. // Column 1: Formulaic Use & Self-Including Design
. reg scaled_av_proposal contribution if subjectnr<4 & period<9 & use==0 & design==0, vce(cluster groupnr)

Linear regression                               Number of obs     =        288
                                                F(1, 11)          =     112.87
                                                Prob > F          =     0.0000
                                                R-squared         =     0.5356
                                                Root MSE          =     10.819

                               (Std. err. adjusted for 12 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
scaled_av_~l | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
contribution |   1.065779    .100319    10.62   0.000      .844978    1.286579
       _cons |   8.530642   2.457175     3.47   0.005     3.122436    13.93885
------------------------------------------------------------------------------

. // Column 2: Formulaic Use & Self-Including Design
. reg scaled_av_proposal contribution if subjectnr<4 & period<9 & use==0 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =        288
                                                F(1, 11)          =    1378.92
                                                Prob > F          =     0.0000
                                                R-squared         =     0.8363
                                                Root MSE          =     7.2202

                               (Std. err. adjusted for 12 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
scaled_av_~l | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
contribution |   1.427403   .0384395    37.13   0.000     1.342798    1.512008
       _cons |   1.992381   .9459169     2.11   0.059     -.089568     4.07433
------------------------------------------------------------------------------

. // Column 3: Discretionary Use & Self-Including Design
. reg scaled_av_proposal contribution if subjectnr<4 & period<9 & use==1 & design==0, vce(cluster groupnr)

Linear regression                               Number of obs     =        312
                                                F(1, 12)          =     143.11
                                                Prob > F          =     0.0000
                                                R-squared         =     0.6316
                                                Root MSE          =      10.99

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
scaled_av_~l | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
contribution |   1.001308   .0837009    11.96   0.000     .8189393    1.183676
       _cons |   9.845975   1.586591     6.21   0.000      6.38909    13.30286
------------------------------------------------------------------------------

. // Column 4: Discretionary Use & Self-Excluding Design
. reg scaled_av_proposal contribution if subjectnr<4 & period<9 & use==1 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =        312
                                                F(1, 12)          =    1926.34
                                                Prob > F          =     0.0000
                                                R-squared         =     0.8555
                                                Root MSE          =     8.0798

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
scaled_av_~l | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
contribution |   1.430132   .0325844    43.89   0.000     1.359137    1.501128
       _cons |   1.374064    .603939     2.28   0.042     .0581943    2.689934
------------------------------------------------------------------------------

. // Column 5: All Conditions
. // Column 5a: Full Model
. reg scaled_av_proposal contribution int_contribution_design int_contribution_use int_contribution_design_use design use int_design_use if subjectnr<4 & period<9, vce(cluster groupnr)

Linear regression                               Number of obs     =      1,200
                                                F(7, 49)          =     914.59
                                                Prob > F          =     0.0000
                                                R-squared         =     0.7559
                                                Root MSE          =     9.4332

                                              (Std. err. adjusted for 50 clusters in groupnr)
---------------------------------------------------------------------------------------------
                            |               Robust
         scaled_av_proposal | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
----------------------------+----------------------------------------------------------------
               contribution |   1.065779    .097138    10.97   0.000     .8705724    1.260985
    int_contribution_design |   .3616245   .1040249     3.48   0.001     .1525787    .5706704
       int_contribution_use |  -.0644708   .1266969    -0.51   0.613    -.3190778    .1901362
int_contribution_design_use |      .0672   .1357947     0.49   0.623    -.2056896    .3400897
                     design |   -6.53826   2.549471    -2.56   0.013    -11.66161   -1.414906
                        use |   1.315333   2.835172     0.46   0.645    -4.382157    7.012824
             int_design_use |   -1.93365   3.036705    -0.64   0.527    -8.036137    4.168837
                      _cons |   8.530642   2.379262     3.59   0.001     3.749336    13.31195
---------------------------------------------------------------------------------------------

.         display _b[int_contribution_design]
.36162453

.         test _b[int_contribution_design] = 0

 ( 1)  int_contribution_design = 0

       F(  1,    49) =   12.08
            Prob > F =    0.0011

.         display "t-stat = "sqrt(r(F))   
t-stat = 3.4763273

.         display _b[int_contribution_design] + _b[int_contribution_design_use]
.42882456

.         test _b[int_contribution_design] + _b[int_contribution_design_use] = 0

 ( 1)  int_contribution_design + int_contribution_design_use = 0

       F(  1,    49) =   24.14
            Prob > F =    0.0000

.         display "t-stat = "sqrt(r(F))   
t-stat = 4.9128106

. // Column 5b: Reduced Model
. reg scaled_av_proposal contribution int_contribution_design design if subjectnr<4 & period<9, vce(cluster groupnr)

Linear regression                               Number of obs     =      1,200
                                                F(3, 49)          =    1408.93
                                                Prob > F          =     0.0000
                                                R-squared         =     0.7556
                                                Root MSE          =     9.4234

                                          (Std. err. adjusted for 50 clusters in groupnr)
-----------------------------------------------------------------------------------------
                        |               Robust
     scaled_av_proposal | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
------------------------+----------------------------------------------------------------
           contribution |   1.023671   .0642287    15.94   0.000     .8945982    1.152743
int_contribution_design |   .4115174   .0681759     6.04   0.000     .2745129     .548522
                 design |  -7.865501   1.462982    -5.38   0.000    -10.80547   -4.925528
                  _cons |   9.382102   1.373957     6.83   0.000     6.621031    12.14317
-----------------------------------------------------------------------------------------

. **PANEL B: EMPLOYEE LEVEL       
. // Column 1: Formulaic Use & Self-Including Design
. reg scaled_av_proposal_1_8 contribution_1_8 if subjectnr<4 & period==9 & use==0 & design==0, vce(cluster groupnr)

Linear regression                               Number of obs     =         36
                                                F(1, 11)          =      42.30
                                                Prob > F          =     0.0000
                                                R-squared         =     0.7151
                                                Root MSE          =     6.0104

                                   (Std. err. adjusted for 12 clusters in groupnr)
----------------------------------------------------------------------------------
                 |               Robust
scaled_av_prop~8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
contribution_1_8 |   1.223076   .1880647     6.50   0.000     .8091483    1.637004
           _cons |   5.440403   3.948384     1.38   0.196    -3.249931    14.13074
----------------------------------------------------------------------------------

. // Column 2: Formulaic Use & Self-Including Design
. reg scaled_av_proposal_1_8 contribution_1_8 if subjectnr<4 & period==9 & use==0 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =         36
                                                F(1, 11)          =    2689.33
                                                Prob > F          =     0.0000
                                                R-squared         =     0.9674
                                                Root MSE          =     2.2471

                                   (Std. err. adjusted for 12 clusters in groupnr)
----------------------------------------------------------------------------------
                 |               Robust
scaled_av_prop~8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
contribution_1_8 |   1.520304   .0293162    51.86   0.000     1.455779    1.584828
           _cons |  -.5572213   .8310918    -0.67   0.516    -2.386442    1.271999
----------------------------------------------------------------------------------

. // Column 3: Discretionary Use & Self-Including Design
. reg scaled_av_proposal_1_8 contribution_1_8 if subjectnr<4 & period==9 & use==1 & design==0, vce(cluster groupnr)

Linear regression                               Number of obs     =         39
                                                F(1, 12)          =     206.83
                                                Prob > F          =     0.0000
                                                R-squared         =     0.7895
                                                Root MSE          =      5.695

                                   (Std. err. adjusted for 13 clusters in groupnr)
----------------------------------------------------------------------------------
                 |               Robust
scaled_av_prop~8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
contribution_1_8 |   1.259107   .0875494    14.38   0.000     1.068353     1.44986
           _cons |   4.756099   1.515115     3.14   0.009     1.454947    8.057251
----------------------------------------------------------------------------------

. // Column 4: Discretionary Use & Self-Excluding Design
. reg scaled_av_proposal_1_8 contribution_1_8 if subjectnr<4 & period==9 & use==1 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =         39
                                                F(1, 12)          =     591.25
                                                Prob > F          =     0.0000
                                                R-squared         =     0.9436
                                                Root MSE          =     4.0535

                                   (Std. err. adjusted for 13 clusters in groupnr)
----------------------------------------------------------------------------------
                 |               Robust
scaled_av_prop~8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
contribution_1_8 |    1.56009   .0641602    24.32   0.000     1.420297    1.699883
           _cons |  -1.181767   1.347248    -0.88   0.398    -4.117168    1.753633
----------------------------------------------------------------------------------

. // Column 5: All Conditions
. // Column 5a: Full Model
. reg scaled_av_proposal_1_8 contribution_1_8 int_contribution_1_8_design int_contribution_1_8_use int_contribution_1_8_design_use design use int_design_use if subjectnr<4 & period==9, vce(cluster gr
> oupnr)

Linear regression                               Number of obs     =        150
                                                F(7, 49)          =    1597.63
                                                Prob > F          =     0.0000
                                                R-squared         =     0.8922
                                                Root MSE          =      4.753

                                                  (Std. err. adjusted for 50 clusters in groupnr)
-------------------------------------------------------------------------------------------------
                                |               Robust
         scaled_av_proposal_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
--------------------------------+----------------------------------------------------------------
               contribution_1_8 |   1.223076   .1836346     6.66   0.000     .8540485    1.592103
    int_contribution_1_8_design |   .2972276   .1858523     1.60   0.116    -.0762566    .6707118
       int_contribution_1_8_use |   .0360307   .2027261     0.18   0.860    -.3713627    .4434241
int_contribution_1_8_design_use |   .0037556   .2141934     0.02   0.986    -.4266822    .4341933
                         design |  -5.997624   3.939855    -1.52   0.134    -13.91506    1.919811
                            use |  -.6843041   4.131951    -0.17   0.869    -8.987771    7.619163
                 int_design_use |   .0597582   4.413422     0.01   0.989    -8.809346    8.928862
                          _cons |   5.440403   3.855373     1.41   0.165     -2.30726    13.18807
-------------------------------------------------------------------------------------------------

.         display _b[int_contribution_1_8_design]
.29722763

.         test _b[int_contribution_1_8_design] = 0

 ( 1)  int_contribution_1_8_design = 0

       F(  1,    49) =    2.56
            Prob > F =    0.1162

.         display "t-stat = "sqrt(r(F))   
t-stat = 1.5992679

.         display _b[int_contribution_1_8_design] + _b[int_contribution_1_8_design_use]
.30098318

.         test _b[int_contribution_1_8_design] + _b[int_contribution_1_8_design_use] = 0

 ( 1)  int_contribution_1_8_design + int_contribution_1_8_design_use = 0

       F(  1,    49) =    7.99
            Prob > F =    0.0068

.         display "t-stat = "sqrt(r(F))   
t-stat = 2.8266967

. // Column 5b: Reduced Model
. reg scaled_av_proposal_1_8 contribution_1_8 int_contribution_1_8_design design if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =     715.80
                                                Prob > F          =     0.0000
                                                R-squared         =     0.8920
                                                Root MSE          =     4.6918

                                              (Std. err. adjusted for 50 clusters in groupnr)
---------------------------------------------------------------------------------------------
                            |               Robust
     scaled_av_proposal_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
----------------------------+----------------------------------------------------------------
           contribution_1_8 |   1.243963   .0909237    13.68   0.000     1.061245    1.426681
int_contribution_1_8_design |   .2954118   .0985414     3.00   0.004     .0973855    .4934382
                     design |  -5.964447   2.038509    -2.93   0.005    -10.06098   -1.867908
                      _cons |   5.043073   1.819705     2.77   0.008     1.386239    8.699906
---------------------------------------------------------------------------------------------

.         
. ********************************************************************************        
. ** TABLE B.3: AVERAGE PROPOSED BONUS
. ********************************************************************************
. ** PANEL A: DECISION LEVEL
. // Column 1: Formulaic Use & Self-Including Design
. reg av_proposal contribution if subjectnr<4 & period<9 & use==0 & design==0, vce(cluster groupnr)

Linear regression                               Number of obs     =        288
                                                F(1, 11)          =     112.87
                                                Prob > F          =     0.0000
                                                R-squared         =     0.5356
                                                Root MSE          =     10.819

                               (Std. err. adjusted for 12 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
 av_proposal | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
contribution |   1.065779    .100319    10.62   0.000      .844978    1.286579
       _cons |   8.530642   2.457175     3.47   0.005     3.122436    13.93885
------------------------------------------------------------------------------

. // Column 2: Formulaic Use & Self-Including Design
. reg av_proposal contribution if subjectnr<4 & period<9 & use==0 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =        288
                                                F(1, 11)          =     967.83
                                                Prob > F          =     0.0000
                                                R-squared         =     0.7891
                                                Root MSE          =     7.9244

                               (Std. err. adjusted for 12 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
 av_proposal | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
contribution |   1.340696   .0430954    31.11   0.000     1.245844    1.435548
       _cons |   4.372006   .9769525     4.48   0.001     2.221748    6.522264
------------------------------------------------------------------------------

. // Column 3: Discretionary Use & Self-Including Design
. reg av_proposal contribution if subjectnr<4 & period<9 & use==1 & design==0, vce(cluster groupnr)

Linear regression                               Number of obs     =        312
                                                F(1, 12)          =     143.11
                                                Prob > F          =     0.0000
                                                R-squared         =     0.6316
                                                Root MSE          =      10.99

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
 av_proposal | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
contribution |   1.001308   .0837009    11.96   0.000     .8189393    1.183676
       _cons |   9.845975   1.586591     6.21   0.000      6.38909    13.30286
------------------------------------------------------------------------------

. // Column 4: Discretionary Use & Self-Excluding Design
. reg av_proposal contribution if subjectnr<4 & period<9 & use==1 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =        312
                                                F(1, 12)          =     606.63
                                                Prob > F          =     0.0000
                                                R-squared         =     0.8074
                                                Root MSE          =     8.8169

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
 av_proposal | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
contribution |   1.313072   .0533121    24.63   0.000     1.196915    1.429229
       _cons |   3.676255   .9736559     3.78   0.003     1.554841    5.797669
------------------------------------------------------------------------------

. // Column 5: All Conditions
. // Column 5a: Full Model
. reg av_proposal contribution int_contribution_design int_contribution_use int_contribution_design_use design use int_design_use if subjectnr<4 & period<9, vce(cluster groupnr)

Linear regression                               Number of obs     =      1,200
                                                F(7, 49)          =     329.76
                                                Prob > F          =     0.0000
                                                R-squared         =     0.7269
                                                Root MSE          =     9.7357

                                              (Std. err. adjusted for 50 clusters in groupnr)
---------------------------------------------------------------------------------------------
                            |               Robust
                av_proposal | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
----------------------------+----------------------------------------------------------------
               contribution |   1.065779    .097138    10.97   0.000     .8705724    1.260985
    int_contribution_design |   .2749175   .1057218     2.60   0.012     .0624616    .4873735
       int_contribution_use |  -.0644708   .1266969    -0.51   0.613    -.3190778    .1901362
int_contribution_design_use |   .0368465   .1430999     0.26   0.798    -.2507235    .3244164
                     design |  -4.158635   2.560421    -1.62   0.111    -9.303994    .9867235
                        use |   1.315333   2.835172     0.46   0.645    -4.382157    7.012824
             int_design_use |  -2.011085   3.135022    -0.64   0.524    -8.311147    4.288978
                      _cons |   8.530642   2.379262     3.59   0.001     3.749336    13.31195
---------------------------------------------------------------------------------------------

.         display _b[int_contribution_design] + _b[int_contribution_design_use]
.31176401

.         test _b[int_contribution_design] + _b[int_contribution_design_use] = 0

 ( 1)  int_contribution_design + int_contribution_design_use = 0

       F(  1,    49) =   10.45
            Prob > F =    0.0022

.         display _b[int_contribution_design] + 0.5 * _b[int_contribution_design_use]
.29334077

.         test _b[int_contribution_design] + 0.5 * _b[int_contribution_design_use] = 0

 ( 1)  int_contribution_design + .5*int_contribution_design_use = 0

       F(  1,    49) =   16.81
            Prob > F =    0.0002

. // Column 5b: Reduced Model
. reg av_proposal contribution int_contribution_design design if subjectnr<4 & period<9, vce(cluster groupnr)

Linear regression                               Number of obs     =      1,200
                                                F(3, 49)          =     624.44
                                                Prob > F          =     0.0000
                                                R-squared         =     0.7260
                                                Root MSE          =     9.7352

                                          (Std. err. adjusted for 50 clusters in groupnr)
-----------------------------------------------------------------------------------------
                        |               Robust
            av_proposal | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
------------------------+----------------------------------------------------------------
           contribution |   1.023671   .0642287    15.94   0.000     .8945982    1.152743
int_contribution_design |   .3153567   .0723826     4.36   0.000     .1698984    .4608151
                 design |   -5.61534   1.554302    -3.61   0.001    -8.738827   -2.491854
                  _cons |   9.382102   1.373957     6.83   0.000     6.621031    12.14317
-----------------------------------------------------------------------------------------

. **PANEL B: EMPLOYEE LEVEL       
. // Column 1: Formulaic Use & Self-Including Design
. reg av_proposal_1_8 contribution_1_8 if subjectnr<4 & period==9 & use==0 & design==0, vce(cluster groupnr)

Linear regression                               Number of obs     =         36
                                                F(1, 11)          =      42.30
                                                Prob > F          =     0.0000
                                                R-squared         =     0.7151
                                                Root MSE          =     6.0104

                                   (Std. err. adjusted for 12 clusters in groupnr)
----------------------------------------------------------------------------------
                 |               Robust
 av_proposal_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
contribution_1_8 |   1.223076   .1880647     6.50   0.000     .8091483    1.637004
           _cons |   5.440403   3.948384     1.38   0.196    -3.249931    14.13074
----------------------------------------------------------------------------------

. // Column 2: Formulaic Use & Self-Including Design
. reg av_proposal_1_8 contribution_1_8 if subjectnr<4 & period==9 & use==0 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =         36
                                                F(1, 11)          =    3001.85
                                                Prob > F          =     0.0000
                                                R-squared         =     0.9689
                                                Root MSE          =     2.1323

                                   (Std. err. adjusted for 12 clusters in groupnr)
----------------------------------------------------------------------------------
                 |               Robust
 av_proposal_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
contribution_1_8 |   1.478904   .0269927    54.79   0.000     1.419494    1.538315
           _cons |   .5789635   .7175483     0.81   0.437     -1.00035    2.158277
----------------------------------------------------------------------------------

. // Column 3: Discretionary Use & Self-Including Design
. reg av_proposal_1_8 contribution_1_8 if subjectnr<4 & period==9 & use==1 & design==0, vce(cluster groupnr)

Linear regression                               Number of obs     =         39
                                                F(1, 12)          =     206.83
                                                Prob > F          =     0.0000
                                                R-squared         =     0.7895
                                                Root MSE          =      5.695

                                   (Std. err. adjusted for 13 clusters in groupnr)
----------------------------------------------------------------------------------
                 |               Robust
 av_proposal_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
contribution_1_8 |   1.259107   .0875494    14.38   0.000     1.068353     1.44986
           _cons |   4.756099   1.515115     3.14   0.009     1.454947    8.057251
----------------------------------------------------------------------------------

. // Column 4: Discretionary Use & Self-Excluding Design
. reg av_proposal_1_8 contribution_1_8 if subjectnr<4 & period==9 & use==1 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =         39
                                                F(1, 12)          =     370.98
                                                Prob > F          =     0.0000
                                                R-squared         =     0.9191
                                                Root MSE          =     4.6978

                                   (Std. err. adjusted for 13 clusters in groupnr)
----------------------------------------------------------------------------------
                 |               Robust
 av_proposal_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
contribution_1_8 |   1.490376   .0773786    19.26   0.000     1.321783     1.65897
           _cons |   .1892647    1.51187     0.13   0.902    -3.104817    3.483347
----------------------------------------------------------------------------------

. // Column 5: All Conditions
. // Column 5a: Full Model
. reg av_proposal_1_8 contribution_1_8 int_contribution_1_8_design int_contribution_1_8_use int_contribution_1_8_design_use design use int_design_use if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(7, 49)          =    8180.24
                                                Prob > F          =     0.0000
                                                R-squared         =     0.8819
                                                Root MSE          =     4.8928

                                                  (Std. err. adjusted for 50 clusters in groupnr)
-------------------------------------------------------------------------------------------------
                                |               Robust
                av_proposal_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
--------------------------------+----------------------------------------------------------------
               contribution_1_8 |   1.223076   .1836346     6.66   0.000     .8540485    1.592103
    int_contribution_1_8_design |   .2558282   .1855164     1.38   0.174     -.116981    .6286373
       int_contribution_1_8_use |   .0360307   .2027261     0.18   0.860    -.3713627    .4434241
int_contribution_1_8_design_use |  -.0245585     .21807    -0.11   0.911    -.4627865    .4136695
                         design |  -4.861439   3.918521    -1.24   0.221      -12.736    3.013124
                            use |  -.6843041   4.131951    -0.17   0.869    -8.987771    7.619163
                 int_design_use |   .2946053   4.445626     0.07   0.947    -8.639215    9.228426
                          _cons |   5.440403   3.855373     1.41   0.165     -2.30726    13.18807
-------------------------------------------------------------------------------------------------

.         display _b[int_contribution_1_8_design]
.25582817

.         test _b[int_contribution_1_8_design] = 0

 ( 1)  int_contribution_1_8_design = 0

       F(  1,    49) =    1.90
            Prob > F =    0.1742

.         display "t-stat = "sqrt(r(F))   
t-stat = 1.3790058

.         display _b[int_contribution_1_8_design] + _b[int_contribution_1_8_design_use]
.23126969

.         test _b[int_contribution_1_8_design] + _b[int_contribution_1_8_design_use] = 0

 ( 1)  int_contribution_1_8_design + int_contribution_1_8_design_use = 0

       F(  1,    49) =    4.07
            Prob > F =    0.0491

.         display "t-stat = "sqrt(r(F))   
t-stat = 2.0176746

. // Column 5b: Reduced Model
. reg av_proposal_1_8 contribution_1_8 int_contribution_1_8_design design if subjectnr<4 & period==9, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(3, 49)          =     549.73
                                                Prob > F          =     0.0000
                                                R-squared         =     0.8818
                                                Root MSE          =     4.8267

                                              (Std. err. adjusted for 50 clusters in groupnr)
---------------------------------------------------------------------------------------------
                            |               Robust
            av_proposal_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
----------------------------+----------------------------------------------------------------
           contribution_1_8 |   1.243963   .0909237    13.68   0.000     1.061245    1.426681
int_contribution_1_8_design |   .2445025   .1001927     2.44   0.018     .0431577    .4458473
                     design |  -4.773168      2.066    -2.31   0.025    -8.924951   -.6213862
                      _cons |   5.043073   1.819705     2.77   0.008     1.386239    8.699906
---------------------------------------------------------------------------------------------

. 
. ********************************************************************************        
. ** TABLE B.4: ADJUSTED AVERAGE and AVERAGE PROPOSED BONUS
. ********************************************************************************
. ** PANEL A: DECISION LEVEL
. // Column 1: Formulaic Use & Self-Including Design
. reg scaled_av_proposal contribution if subjectnr<4 & period<9 & use==0 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =        288
                                                F(1, 11)          =    1378.92
                                                Prob > F          =     0.0000
                                                R-squared         =     0.8363
                                                Root MSE          =     7.2202

                               (Std. err. adjusted for 12 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
scaled_av_~l | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
contribution |   1.427403   .0384395    37.13   0.000     1.342798    1.512008
       _cons |   1.992381   .9459169     2.11   0.059     -.089568     4.07433
------------------------------------------------------------------------------

. // Column 2: Formulaic Use & Self-Including Design
. reg av_proposal contribution if subjectnr<4 & period<9 & use==0 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =        288
                                                F(1, 11)          =     967.83
                                                Prob > F          =     0.0000
                                                R-squared         =     0.7891
                                                Root MSE          =     7.9244

                               (Std. err. adjusted for 12 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
 av_proposal | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
contribution |   1.340696   .0430954    31.11   0.000     1.245844    1.435548
       _cons |   4.372006   .9769525     4.48   0.001     2.221748    6.522264
------------------------------------------------------------------------------

. // Column 3: Discretionary Use & Self-Including Design
. reg scaled_av_proposal contribution if subjectnr<4 & period<9 & use==1 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =        312
                                                F(1, 12)          =    1926.34
                                                Prob > F          =     0.0000
                                                R-squared         =     0.8555
                                                Root MSE          =     8.0798

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
scaled_av_~l | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
contribution |   1.430132   .0325844    43.89   0.000     1.359137    1.501128
       _cons |   1.374064    .603939     2.28   0.042     .0581943    2.689934
------------------------------------------------------------------------------

. // Column 4: Discretionary Use & Self-Excluding Design
. reg av_proposal contribution if subjectnr<4 & period<9 & use==1 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =        312
                                                F(1, 12)          =     606.63
                                                Prob > F          =     0.0000
                                                R-squared         =     0.8074
                                                Root MSE          =     8.8169

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
 av_proposal | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
contribution |   1.313072   .0533121    24.63   0.000     1.196915    1.429229
       _cons |   3.676255   .9736559     3.78   0.003     1.554841    5.797669
------------------------------------------------------------------------------

. // Column 5: Within Comparison
. // Column 5a: Full Model
. ********************************************************************************
. preserve

. gen outcome1 = scaled_av_proposal
(600 missing values generated)

. gen outcome2 = av_proposal
(600 missing values generated)

. gen identifier = 10*playernr + period

. reshape long outcome, i(identifier) j(dv)
(j = 1 2)

Data                               Wide   ->   Long
-----------------------------------------------------------------------------
Number of observations            1,800   ->   3,600       
Number of variables                 167   ->   167         
j variable (2 values)                     ->   dv
xij variables:
                      outcome1 outcome2   ->   outcome
-----------------------------------------------------------------------------

. replace dv = dv - 1
(3,600 real changes made)

. gen int_dv_use = dv * use

. gen int_contr_dv = contribution * dv
(1,200 missing values generated)

. gen int_contr_use = contribution * use
(1,200 missing values generated)

. gen int_contr_dv_use = contribution * dv * use
(1,200 missing values generated)

. // Column 5a: Full Model
. reg outcome contribution int_contr_dv int_contr_use int_contr_dv_use dv use int_dv_use if subjectnr<4 & period<9 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =      1,200
                                                F(5, 24)          =          .
                                                Prob > F          =          .
                                                R-squared         =     0.8399
                                                Root MSE          =      8.048

                                   (Std. err. adjusted for 25 clusters in groupnr)
----------------------------------------------------------------------------------
                 |               Robust
         outcome | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
    contribution |   1.427403   .0376063    37.96   0.000     1.349787    1.505019
    int_contr_dv |   -.086707    .019637    -4.42   0.000    -.1272358   -.0461781
   int_contr_use |   .0027292   .0493745     0.06   0.956    -.0991747    .1046331
int_contr_dv_use |  -.0303536   .0381427    -0.80   0.434    -.1090762    .0483691
              dv |   2.379625   .5552629     4.29   0.000     1.233619    3.525632
             use |  -.6183168   1.099105    -0.56   0.579    -2.886758    1.650125
      int_dv_use |  -.0774345   .8394706    -0.09   0.927    -1.810017    1.655148
           _cons |   1.992381   .9254152     2.15   0.042      .082418    3.902344
----------------------------------------------------------------------------------

.         display _b[int_contr_dv]
-.08670699

.         test _b[int_contr_dv] = 0

 ( 1)  int_contr_dv = 0

       F(  1,    24) =   19.50
            Prob > F =    0.0002

.         display "t-stat = "sqrt(r(F))   
t-stat = 4.4154825

.         display _b[int_contr_dv] + _b[int_contr_dv_use]
-.11706055

.         test _b[int_contr_dv] + _b[int_contr_dv_use] = 0

 ( 1)  int_contr_dv + int_contr_dv_use = 0

       F(  1,    24) =   12.82
            Prob > F =    0.0015

.         display "t-stat = "sqrt(r(F))   
t-stat = 3.5798971

. // Column 5b: Reduced Model
. reg outcome contribution int_contr_dv dv if subjectnr<4 & period<9 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =      1,200
                                                F(2, 24)          =          .
                                                Prob > F          =          .
                                                R-squared         =     0.8392
                                                Root MSE          =     8.0509

                               (Std. err. adjusted for 25 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
     outcome | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
contribution |   1.435188    .023098    62.13   0.000     1.387516     1.48286
int_contr_dv |  -.0961607   .0196804    -4.89   0.000     -.136779   -.0555424
          dv |   2.250161   .4616034     4.87   0.000     1.297458    3.202863
       _cons |   1.516601   .5077594     2.99   0.006     .4686373    2.564565
------------------------------------------------------------------------------

. restore

. ********************************************************************************
. **PANEL B: EMPLOYEE LEVEL       
. // Column 1: Formulaic Use & Self-Including Design
. reg scaled_av_proposal_1_8 contribution_1_8 if subjectnr<4 & period==9 & use==0 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =         36
                                                F(1, 11)          =    2689.33
                                                Prob > F          =     0.0000
                                                R-squared         =     0.9674
                                                Root MSE          =     2.2471

                                   (Std. err. adjusted for 12 clusters in groupnr)
----------------------------------------------------------------------------------
                 |               Robust
scaled_av_prop~8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
contribution_1_8 |   1.520304   .0293162    51.86   0.000     1.455779    1.584828
           _cons |  -.5572213   .8310918    -0.67   0.516    -2.386442    1.271999
----------------------------------------------------------------------------------

. // Column 2: Formulaic Use & Self-Including Design
. reg av_proposal_1_8 contribution_1_8 if subjectnr<4 & period==9 & use==0 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =         36
                                                F(1, 11)          =    3001.85
                                                Prob > F          =     0.0000
                                                R-squared         =     0.9689
                                                Root MSE          =     2.1323

                                   (Std. err. adjusted for 12 clusters in groupnr)
----------------------------------------------------------------------------------
                 |               Robust
 av_proposal_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
contribution_1_8 |   1.478904   .0269927    54.79   0.000     1.419494    1.538315
           _cons |   .5789635   .7175483     0.81   0.437     -1.00035    2.158277
----------------------------------------------------------------------------------

. // Column 3: Discretionary Use & Self-Including Design
. reg scaled_av_proposal_1_8 contribution_1_8 if subjectnr<4 & period==9 & use==1 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =         39
                                                F(1, 12)          =     591.25
                                                Prob > F          =     0.0000
                                                R-squared         =     0.9436
                                                Root MSE          =     4.0535

                                   (Std. err. adjusted for 13 clusters in groupnr)
----------------------------------------------------------------------------------
                 |               Robust
scaled_av_prop~8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
contribution_1_8 |    1.56009   .0641602    24.32   0.000     1.420297    1.699883
           _cons |  -1.181767   1.347248    -0.88   0.398    -4.117168    1.753633
----------------------------------------------------------------------------------

. // Column 4: Discretionary Use & Self-Excluding Design
. reg av_proposal_1_8 contribution_1_8 if subjectnr<4 & period==9 & use==1 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =         39
                                                F(1, 12)          =     370.98
                                                Prob > F          =     0.0000
                                                R-squared         =     0.9191
                                                Root MSE          =     4.6978

                                   (Std. err. adjusted for 13 clusters in groupnr)
----------------------------------------------------------------------------------
                 |               Robust
 av_proposal_1_8 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
contribution_1_8 |   1.490376   .0773786    19.26   0.000     1.321783     1.65897
           _cons |   .1892647    1.51187     0.13   0.902    -3.104817    3.483347
----------------------------------------------------------------------------------

. // Column 5: All Conditions
. ********************************************************************************
. preserve

. gen outcome1 = scaled_av_proposal_1_8
(1,650 missing values generated)

. gen outcome2 = av_proposal_1_8
(1,650 missing values generated)

. gen identifier = 10*playernr + period

. reshape long outcome, i(identifier) j(dv)
(j = 1 2)

Data                               Wide   ->   Long
-----------------------------------------------------------------------------
Number of observations            1,800   ->   3,600       
Number of variables                 167   ->   167         
j variable (2 values)                     ->   dv
xij variables:
                      outcome1 outcome2   ->   outcome
-----------------------------------------------------------------------------

. replace dv = dv - 1
(3,600 real changes made)

. gen int_dv_use = dv * use

. gen int_contr_1_8_dv = contribution_1_8 * dv
(3,300 missing values generated)

. gen int_contr_1_8_use = contribution_1_8 * use
(3,300 missing values generated)

. gen int_contr_1_8_dv_use = contribution_1_8 * dv * use
(3,300 missing values generated)

. // Column 5a: Full Model
. reg outcome contribution_1_8 int_contr_1_8_dv int_contr_1_8_use int_contr_1_8_dv_use dv use int_dv_use if subjectnr<4 & period==9 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(5, 24)          =          .
                                                Prob > F          =          .
                                                R-squared         =     0.9516
                                                Root MSE          =     3.5113

                                       (Std. err. adjusted for 25 clusters in groupnr)
--------------------------------------------------------------------------------------
                     |               Robust
             outcome | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------------+----------------------------------------------------------------
    contribution_1_8 |   1.520304   .0289223    52.57   0.000     1.460611    1.579996
    int_contr_1_8_dv |  -.0413995   .0184584    -2.24   0.034    -.0794957   -.0033032
   int_contr_1_8_use |   .0397862   .0698608     0.57   0.574    -.1043993    .1839718
int_contr_1_8_dv_use |   -.028314    .035559    -0.80   0.434    -.1017042    .0450761
                  dv |   1.136185   .5272171     2.16   0.041     .0480621    2.224307
                 use |  -.6245459   1.566966    -0.40   0.694    -3.858605    2.609513
          int_dv_use |   .2348471   .8218011     0.29   0.778    -1.461267    1.930961
               _cons |  -.5572213   .8199238    -0.68   0.503    -2.249461    1.135018
--------------------------------------------------------------------------------------

.         display _b[int_contr_1_8_dv]
-.04139945

.         test _b[int_contr_1_8_dv] = 0

 ( 1)  int_contr_1_8_dv = 0

       F(  1,    24) =    5.03
            Prob > F =    0.0344

.         display "t-stat = "sqrt(r(F))   
t-stat = 2.2428549

.         display _b[int_contr_1_8_dv] + _b[int_contr_1_8_dv_use]
-.06971349

.         test _b[int_contr_1_8_dv] + _b[int_contr_1_8_dv_use] = 0

 ( 1)  int_contr_1_8_dv + int_contr_1_8_dv_use = 0

       F(  1,    24) =    5.26
            Prob > F =    0.0309

.         display "t-stat = "sqrt(r(F))   
t-stat = 2.2937394

. // Column 5b: Reduced Model
. reg outcome contribution_1_8 int_contr_1_8_dv dv if subjectnr<4 & period==9 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =        150
                                                F(2, 24)          =          .
                                                Prob > F          =          .
                                                R-squared         =     0.9515
                                                Root MSE          =     3.4676

                                   (Std. err. adjusted for 25 clusters in groupnr)
----------------------------------------------------------------------------------
                 |               Robust
         outcome | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
contribution_1_8 |   1.539375   .0383843    40.10   0.000     1.460154    1.618596
int_contr_1_8_dv |  -.0509093   .0185431    -2.75   0.011    -.0891804   -.0126383
              dv |   1.191278   .4484413     2.66   0.014     .2657408    2.116816
           _cons |   -.921374   .9283226    -0.99   0.331    -2.837338    .9945896
----------------------------------------------------------------------------------

. restore

. ********************************************************************************
. 
. ********************************************************************************        
. ** TABLE B.5: AVERAGE PROPOSED BONUS and FINAL BONUS
. ********************************************************************************        
. ** PANEL A: OLS REGRESSION ON AVERAGE PROPOSAL / FINAL BONUS - DICRETIONARY USE ONLY
. *************
. preserve

. gen outcome1 = av_proposal
(600 missing values generated)

. gen outcome2 = finalbonus
(600 missing values generated)

. gen identifier = 10*playernr + period

. reshape long outcome, i(identifier) j(dv)
(j = 1 2)

Data                               Wide   ->   Long
-----------------------------------------------------------------------------
Number of observations            1,800   ->   3,600       
Number of variables                 167   ->   167         
j variable (2 values)                     ->   dv
xij variables:
                      outcome1 outcome2   ->   outcome
-----------------------------------------------------------------------------

. replace dv = dv - 1
(3,600 real changes made)

. gen int_dv_design = dv * design

. gen int_contr_dv = contribution * dv
(1,200 missing values generated)

. gen int_contr_design = contribution * design
(1,200 missing values generated)

. gen int_contr_dv_design = contribution * dv * design
(1,200 missing values generated)

. **Column 1
. reg outcome contribution if subjectnr<4 & period<9 & dv==0 & use==1 & design==0, vce(cluster groupnr)

Linear regression                               Number of obs     =        312
                                                F(1, 12)          =     143.11
                                                Prob > F          =     0.0000
                                                R-squared         =     0.6316
                                                Root MSE          =      10.99

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
     outcome | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
contribution |   1.001308   .0837009    11.96   0.000     .8189393    1.183676
       _cons |   9.845975   1.586591     6.21   0.000      6.38909    13.30286
------------------------------------------------------------------------------

. **Column 2
. reg outcome contribution if subjectnr<4 & period<9 & dv==1 & use==1 & design==0, vce(cluster groupnr)

Linear regression                               Number of obs     =        312
                                                F(1, 12)          =      76.90
                                                Prob > F          =     0.0000
                                                R-squared         =     0.4731
                                                Root MSE          =     15.016

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
     outcome | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
contribution |   .9900952   .1129018     8.77   0.000     .7441033    1.236087
       _cons |   10.06735   1.884282     5.34   0.000     5.961852    14.17285
------------------------------------------------------------------------------

. **Column 3
. reg outcome contribution if subjectnr<4 & period<9 & dv==0 & use==1 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =        312
                                                F(1, 12)          =     606.63
                                                Prob > F          =     0.0000
                                                R-squared         =     0.8074
                                                Root MSE          =     8.8169

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
     outcome | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
contribution |   1.313072   .0533121    24.63   0.000     1.196915    1.429229
       _cons |   3.676255   .9736559     3.78   0.003     1.554841    5.797669
------------------------------------------------------------------------------

. **Column 4
. reg outcome contribution if subjectnr<4 & period<9 & dv==1 & use==1 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =        312
                                                F(1, 12)          =      97.28
                                                Prob > F          =     0.0000
                                                R-squared         =     0.3630
                                                Root MSE          =     18.667

                               (Std. err. adjusted for 13 clusters in groupnr)
------------------------------------------------------------------------------
             |               Robust
     outcome | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
contribution |   1.024965   .1039189     9.86   0.000     .7985449    1.251385
       _cons |    9.34236   2.512958     3.72   0.003     3.867094    14.81763
------------------------------------------------------------------------------

. **Column 5
. reg outcome contribution int_contr_dv int_contr_design int_contr_dv_design dv design int_dv_design if subjectnr<4 & period<9 & use==1, vce(cluster groupnr)

Linear regression                               Number of obs     =      1,248
                                                F(5, 25)          =          .
                                                Prob > F          =          .
                                                R-squared         =     0.5473
                                                Root MSE          =     13.897

                                      (Std. err. adjusted for 26 clusters in groupnr)
-------------------------------------------------------------------------------------
                    |               Robust
            outcome | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
--------------------+----------------------------------------------------------------
       contribution |   1.001308   .0821086    12.19   0.000      .832202    1.170414
       int_contr_dv |  -.0112125    .076684    -0.15   0.885    -.1691463    .1467212
   int_contr_design |    .311764   .0973493     3.20   0.004     .1112693    .5122587
int_contr_dv_design |  -.2768945   .1142927    -2.42   0.023    -.5122847   -.0415044
                 dv |   .2213756    1.50561     0.15   0.884    -2.879486    3.322238
             design |   -6.16972   1.826113    -3.38   0.002     -9.93067    -2.40877
      int_dv_design |    5.44473   2.552863     2.13   0.043       .18701    10.70245
              _cons |   9.845975   1.556409     6.33   0.000     6.640491    13.05146
-------------------------------------------------------------------------------------

.         display _b[int_contr_dv]
-.01121253

.         test _b[int_contr_dv] = 0

 ( 1)  int_contr_dv = 0

       F(  1,    25) =    0.02
            Prob > F =    0.8849

.         display "t-stat = "sqrt(r(F))   
t-stat = .14621729

.         display _b[int_contr_dv] + _b[int_contr_dv_design]
-.28810705

.         test _b[int_contr_dv] + _b[int_contr_dv_design] = 0

 ( 1)  int_contr_dv + int_contr_dv_design = 0

       F(  1,    25) =   11.56
            Prob > F =    0.0023

.         display "t-stat = "sqrt(r(F))   
t-stat = 3.3995389

.         display _b[int_contr_design] + _b[int_contr_dv_design]
.03486949

.         test _b[int_contr_design] + _b[int_contr_dv_design] = 0

 ( 1)  int_contr_design + int_contr_dv_design = 0

       F(  1,    25) =    0.05
            Prob > F =    0.8187

.         display "t-stat = "sqrt(r(F))   
t-stat = .2316481

. restore

. *************
. ** PANEL B
. *************
. preserve

. gen outcome1 = av_proposal_1_8
(1,650 missing values generated)

. gen outcome2 = finalbonus_1_8
(1,650 missing values generated)

. gen identifier = 10*playernr + period

. reshape long outcome, i(identifier) j(dv)
(j = 1 2)

Data                               Wide   ->   Long
-----------------------------------------------------------------------------
Number of observations            1,800   ->   3,600       
Number of variables                 167   ->   167         
j variable (2 values)                     ->   dv
xij variables:
                      outcome1 outcome2   ->   outcome
-----------------------------------------------------------------------------

. replace dv = dv - 1
(3,600 real changes made)

. gen int_dv_design = dv * design

. gen int_contr_1_8_dv = contribution_1_8 * dv
(3,300 missing values generated)

. gen int_contr_1_8_design = contribution_1_8 * design
(3,300 missing values generated)

. gen int_contr_1_8_dv_design = contribution_1_8 * dv * design
(3,300 missing values generated)

. **Column 1
. reg outcome contribution_1_8 if subjectnr<4 & period==9 & dv==0 & use==1 & design==0, vce(cluster groupnr)

Linear regression                               Number of obs     =         39
                                                F(1, 12)          =     206.83
                                                Prob > F          =     0.0000
                                                R-squared         =     0.7895
                                                Root MSE          =      5.695

                                   (Std. err. adjusted for 13 clusters in groupnr)
----------------------------------------------------------------------------------
                 |               Robust
         outcome | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
contribution_1_8 |   1.259107   .0875494    14.38   0.000     1.068353     1.44986
           _cons |   4.756099   1.515115     3.14   0.009     1.454947    8.057251
----------------------------------------------------------------------------------

. **Column 2
. reg outcome contribution_1_8 if subjectnr<4 & period==9 & dv==1 & use==1 & design==0, vce(cluster groupnr)

Linear regression                               Number of obs     =         39
                                                F(1, 12)          =     436.75
                                                Prob > F          =     0.0000
                                                R-squared         =     0.8981
                                                Root MSE          =     3.9733

                                   (Std. err. adjusted for 13 clusters in groupnr)
----------------------------------------------------------------------------------
                 |               Robust
         outcome | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
contribution_1_8 |   1.346147   .0644135    20.90   0.000     1.205802    1.486492
           _cons |   3.037611   1.121052     2.71   0.019     .5950489    5.480173
----------------------------------------------------------------------------------

. **Column 3
. reg outcome contribution_1_8 if subjectnr<4 & period==9 & dv==0 & use==1 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =         39
                                                F(1, 12)          =     370.98
                                                Prob > F          =     0.0000
                                                R-squared         =     0.9191
                                                Root MSE          =     4.6978

                                   (Std. err. adjusted for 13 clusters in groupnr)
----------------------------------------------------------------------------------
                 |               Robust
         outcome | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
contribution_1_8 |   1.490376   .0773786    19.26   0.000     1.321783     1.65897
           _cons |   .1892647    1.51187     0.13   0.902    -3.104817    3.483347
----------------------------------------------------------------------------------

. **Column 4
. reg outcome contribution_1_8 if subjectnr<4 & period==9 & dv==1 & use==1 & design==1, vce(cluster groupnr)

Linear regression                               Number of obs     =         39
                                                F(1, 12)          =     272.93
                                                Prob > F          =     0.0000
                                                R-squared         =     0.7835
                                                Root MSE          =       7.35

                                   (Std. err. adjusted for 13 clusters in groupnr)
----------------------------------------------------------------------------------
                 |               Robust
         outcome | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
contribution_1_8 |   1.315506   .0796281    16.52   0.000     1.142011    1.489001
           _cons |   3.628382   1.680057     2.16   0.052    -.0321483    7.288913
----------------------------------------------------------------------------------

. **Column 5
. reg outcome contribution_1_8 int_contr_1_8_dv int_contr_1_8_design int_contr_1_8_dv_design dv design int_dv_design if subjectnr<4 & period==9 & use==1, vce(cluster groupnr)

Linear regression                               Number of obs     =        156
                                                F(5, 25)          =          .
                                                Prob > F          =          .
                                                R-squared         =     0.8505
                                                Root MSE          =     5.5748

                                          (Std. err. adjusted for 26 clusters in groupnr)
-----------------------------------------------------------------------------------------
                        |               Robust
                outcome | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
------------------------+----------------------------------------------------------------
       contribution_1_8 |   1.259107   .0866229    14.54   0.000     1.080703     1.43751
       int_contr_1_8_dv |   .0870403   .0502315     1.73   0.095    -.0164133     .190494
   int_contr_1_8_design |   .2312697   .1156068     2.00   0.056    -.0068269    .4693663
int_contr_1_8_dv_design |  -.2619107   .1091118    -2.40   0.024    -.4866306   -.0371908
                     dv |  -1.718488   .9687145    -1.77   0.088    -3.713593    .2766168
                 design |  -4.566834   2.117753    -2.16   0.041    -8.928427    -.205241
          int_dv_design |   5.157606   2.333541     2.21   0.036     .3515875    9.963624
                  _cons |   4.756099   1.499082     3.17   0.004     1.668682    7.843515
-----------------------------------------------------------------------------------------

.         display _b[int_contr_1_8_dv]
.08704031

.         test _b[int_contr_1_8_dv] = 0

 ( 1)  int_contr_1_8_dv = 0

       F(  1,    25) =    3.00
            Prob > F =    0.0955

.         display "t-stat = "sqrt(r(F))
t-stat = 1.7327844

.         display _b[int_contr_1_8_dv] + _b[int_contr_1_8_dv_design]
-.17487039

.         test _b[int_contr_1_8_dv] + _b[int_contr_1_8_dv_design] = 0

 ( 1)  int_contr_1_8_dv + int_contr_1_8_dv_design = 0

       F(  1,    25) =    3.26
            Prob > F =    0.0831

.         display "t-stat = "sqrt(r(F))   
t-stat = 1.8053628

.         display _b[int_contr_1_8_design] + _b[int_contr_1_8_dv_design]
-.030641

.         test _b[int_contr_1_8_design] + _b[int_contr_1_8_dv_design] = 0

 ( 1)  int_contr_1_8_design + int_contr_1_8_dv_design = 0

       F(  1,    25) =    0.09
            Prob > F =    0.7649

.         display "t-stat = "sqrt(r(F))   
t-stat = .30237167

. restore

. *************
. 
. log close
      name:  <unnamed>
       log:  C:\Users\2148\Dropbox\Projects\PeerEvaluations_JAR\FinalSubmission\E_Logfile.log
  log type:  text
 closed on:  15 Apr 2025, 19:56:34
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
