New: Inference on Treatment Effects after Selection Amongst High-Dimensional Controls
We propose robust methods for inference on the effect of a treatment variable on a scalar outcome in the presence of very many controls. Our setting is a partially linear model with possibly non-Gaussian and heteroscedastic disturbances where the number of controls may be much larger than the sample size. To make informative inference feasible, we require the model to be approximately sparse; that is, we require that the effect of confounding factors can be controlled for up to a small ...
New: Sparse Models and Methods for Optimal Instruments with an Application to Eminent Domain
We develop results for the use of LASSO and Post-LASSO methods to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments, p, that apply even when p is much larger than the sample size, n. We rigorously develop asymptotic distribution and inference theory for the resulting IV estimators and provide conditions under which these estimators are asymptotically oracle-efficient. In simulation experiments, the LASSO-based IV ...
New: Lasso Methods for Gaussian Instrumental Variables Models
In this note, we propose the use of sparse methods (e.g. LASSO, Post-LASSO, p LASSO, and Post-p LASSO) to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments in the canonical Gaussian case. The methods apply even when the number of instruments is much larger than the sample size. We derive asymptotic distributions for the resulting IV estimators and provide conditions under which these sparsity-based IV estimators are ...
New: Grouped Effects Estimators in Fixed Effects Models
We consider estimation of nonlinear panel data models with common and individual specific parameters. Fixed effects estimators are known to suffer from the incidental parameters problem, which can lead to large biases in estimates of common parameters. Pooled estimators, which ignore heterogeneity across individuals, are also generally inconsistent. We assume that individuals in our data are grouped on multiple levels. These groups may be based on some external classification (for ...
New: Inference with Dependent Data Using Cluster Covariance Estimators
This paper presents an inference approach for dependent data in time series, spatial, and panel data applications. The method involves constructing and Wald statistics using a cluster covariance matrix estimator (CCE). We use an approximation that takes the number of clusters/groups as fixed and the number of observations per group to be large. The resulting limiting distributions of the t and Wald statistics are standard t and F distributions where the number of groups plays the role of ...
REVISION: Plausibly Exogenous
Instrumental variables (IVs) are widely used to identify effects in models with potentially endogenous explanatory variables. In many cases, the instrument exclusion restriction that underlies the validity of the usual IV inference holds only approximately; that is, the instruments are 'plausibly exogenous.' We introduce a method of relaxing the exclusion restriction and performing sensitivity analysis with respect to the degree of violation. This provides a practical tool for applied ...
New: Identification of Marginal Effects in a Nonparametric Correlated Random Effects Model
In this paper, we consider identification and estimation of average marginal effects in a correlated random coefficients model without imposing strong functional form assumptions on the structural likelihood or the mixing distribution. Identification is achieved through imposing that the mixing distribution depends on observed covariates only through an index function and the assumption that at least three time periods are available for each cross sectional unit. We leave the functional form ...
REVISION: A Semi-Parametric Bayesian Approach to the Instrumental Variable Problem
We develop a Bayesian semi-parametric approach to the instrumental variable problem. We assume linear structural and reduced form equations, but model the error distributions non-parametrically. A Dirichlet process prior is used for the joint distribution of structural and instrumental variable equations errors. Our implementation of the Dirichlet process prior uses a normal distribution as a base model. It can therefore be interpreted as modeling the unknown joint distribution with a ...
New: Admissible Invariant Similar Tests for Instrumental Variables Regression
This paper studies a model widely used in the weak instruments literature and establishes admissibility of the weighted average power likelihood ratio tests recently derived by Andrews, Moreira, and Stock (2004). The class of tests covered by this admissibility result contains the Anderson and Rubin (1949) test. Thus, there is no conventional statistical sense in which the Anderson and Rubin (1949) test "wastes degrees of freedom". In addition, it is shown that the test proposed by Moreira ...
New: Bias Reduction for Bayesian and Frequentist Estimators
We show that in parametric likelihood models the first order bias in the posterior mode and the posterior mean can be removed using objective Bayesian priors. These bias-reducing priors are defined as the solution to a set of differential equations which may not be available in closed form. We provide a simple and tractable data dependent prior that solves the differential equations asymptotically and removes the first order bias. When we consider the posterior mode, this approach can be ...
New: The Reduced Form: A Simple Approach to Inference with Weak Instruments
In this paper, we consider simple methods for performing robust inference in linear instrumental variables models with weak instruments. We focus on inference based on the reduced form and show that conventional inference procedures about the relevance of the instruments excluded from the structural equation lead to tests of the structural parameters which are valid even if the instruments are weakly correlated to the endogenous variables. The use of standard heteroskedasticity and ...
New: Instrumental Variable Quantile Regression
The paper develops estimation and inference methods for econometric models with partial identification, focusing on models defined by moment inequalities and equalities. Main applications of this framework include analysis of game-theoretic models, regression with missing and mismeasured data, bounds in structural quantile models, and bounds in asset pricing, among others.
Finite Sample Inference for Quantile Regression Models
Under minimal assumptions finite sample confidence bands for quantile regression models can be constructed. These confidence bands are based on the "conditional pivotal property" of estimating equations that quantile regression methods aim to solve and will provide valid finite sample inference for both linear and nonlinear quantile models regardless of whether the covariates are endogenous or exogenous. The confidence regions can be computed using MCMC, and confidence bounds for single ...
A Penalty Function Approach to Bias Reduction in Non-linear Panel Models with Fixed Effects
In this paper, we consider estimation of nonlinear panel data models that include individual specific fixed effects. Estimation of these models is complicated by the incidental parameters problem; that is, noise in the estimation of the fixed effects when the time dimension is short generally results in inconsistent estimates of the common parameters due to the nonlinearity of the problem. We present a penalty for the objective function that reduces the bias in the resulting point estimates.
Inference for Distributional Effects using Instrumental Quantile Regression
In this paper we describe how quantile regression can be used to evaluate the impact of treatment on the entire distribution of outcomes, when the treatment is endogenous or selected in relation to potential outcomes. We describe an instrumental variable quantile regression process and the set of inferences derived from it, focusing on tests of distributional equality, non-constant treatment effects, conditional dominance, and exogeneity. The inference, which is subject to the Durbin problem, ...