Central banks are starting to raise interest rates. The US Federal Reserve has raised rates six times and a total of 3.75 percentage points in 2022, with one more meeting of its Federal Open Market Committee still scheduled before year-end. Those rate hikes may do a lot of things—slow the economy, depress asset prices—but what will they mean for the issue animating the Fed’s actions, inflation?

The Fed expects higher interest rates to lower inflation. Higher interest rates may lower investment demand, especially in housing, and cool the economy; cooling the economy may bring down the rise in wages and prices. But the Fed will run in to headwinds. Cooling the economy will not be popular with Congress, the Biden administration, businesses, or regular people. Higher interest rates will raise debt-service costs, worsening the deficit that is behind inflation to begin with. And, as the United Kingdom is discovering, higher interest rates may reveal financial fragility that the army of financial regulators overlooked, again.

Today, however, I want to consider one particular headwind. These are all short-run effects. Higher interest rates should, in the long run, raise inflation. This long-run force will increasingly battle against whatever short-run forces push in the opposite direction.

How does this strange-sounding proposition work? It follows from two simple core principles of economics. First, the real interest rate equals the nominal interest rate (how many dollars you get next year per dollar invested this year) minus the expected rate of inflation. Second, the real interest rate is, in the long run, determined by real factors—the productivity of capital, people’s desire to save versus consume—not by the Fed. This is the principle of “long-run neutrality.” It follows that if the Fed raises the nominal interest rate, once the real rate settles back to its long-run value, the inflation rate must be higher. This proposition is similar to the monetarist proposition that a higher rate of money growth eventually just raises inflation by the same amount.

Still, the proposition is hard to believe, and that intuition is the point of this essay. In one direction this is easy: if people expect a lot of inflation, they demand higher nominal interest rates to compensate for the declining value of the dollar, so that the real return is unchanged. Higher steady inflation must come with higher interest rates. And it does: countries with 100 percent inflation have, order of magnitude, 105 percent interest rates, not 5 percent interest rates.

The other direction is harder to understand. How might the Fed setting higher nominal interest rates eventually cause higher inflation? Eventually, when the real rate recovers to reflect real things, just what force makes expected inflation rise? Standard intuition says overwhelmingly that higher interest rates cause people to spend less, which lowers inflation.

This is a lovely case in which individual causality goes in the opposite direction of equilibrium causality. That happens a lot in macroeconomics and can cause a lot of confusion. It also is an interesting case of mistaking expected inflation for unexpected inflation. It’s easy to do.

For any individual, the interest rate and expected inflation are given, or exogenous. A consumer observes inflation and interest rates, and then chooses how much to consume or save. If the Fed raises interest rates and prices do not yet adjust, the real return to saving is larger. The consumer wishes to buy less today, save more, and buy even more in the future, with the higher interest.

Now, a desire to lower consumption today pushes down the price level today, and consuming more in the future pushes up the future price level. As the price level falls today and rises in the future—as inflation increases—the real return to saving falls. This process continues until the consumer’s demand equals supply. Expected inflation rises to meet the nominal interest rate—as promised, and by exactly the conventional mechanism in which higher interest rates induce saving.

To the individual, the price levels and expected inflation are given, exogenous, and the decision of how much to consume follows, is endogenous. In equilibrium, the amount that can be consumed, supply, is exogenous, and the price levels and expected inflation follow in order to clear markets.

In sum, a higher interest rate produces higher future inflation over a sufficiently long horizon that (1) prices, sticky in the short run, can move, (2) output runs into supply constraints, and (3) the real interest rate is consequently set by real factors.

Pick your path

A rate hike can produce higher inflation through either a lower price level today or a higher price level in the future, or a combination of both.

But you can get higher inflation by a lower initial price (as represented by the blue line in the graph above) or from a higher later price (the red line). The graph also shows an intermediate possibility (in green).

So the original intuition can be right: higher interest rates might well depress current demand and lower initial prices. (See the blue line in the chart.) That produces lower ex post inflation today and higher expected inflation from today to the future. The intervention can well “lower inflation” in this sense. This is how standard (New Keynesian) models work.

If we stop here, the confusion between whether higher interest rates raise or lower inflation is just semantic. As often in life, you can resolve a lot of seemingly intractable arguments just by defining terms more carefully. Higher interest rates can lower current inflation. Sticky prices and other frictions can draw out this period of decline. As for the price recovery, and higher future inflation from a lower price level, we often do see that—inflation comes back, as it did in the 1970s—or maybe the Fed doesn’t leave interest rates alone long enough to see it. The long run is a long time.

But there is another possibility. Maybe the higher expected inflation—the larger slope of the line when interest rates rise—all comes from a higher future price level, not a lower current price level. Maybe the price level follows the red line in the chart, not the blue line.

Which is it? It comes down to fiscal policy. To have an unexpected decline in inflation, Congress must raise tax revenue or cut spending to pay off bondholders in more valuable money. If Congress refuses, we get the red line: more future inflation, no inflation reduction today. If Congress goes along, we can get the blue line. Fiscal and monetary policies always work in tandem.

In sum, there is a natural and intuitive force by which higher nominal interest rates raise inflation in the long run. That force can push down the price level, so it can rise again in the future. That price-level decline corresponds to the intuition that higher interest rates lower inflation in the short run. But for the US to see that, fiscal policy must tighten. Without fiscal help, we have only a force for higher inflation, starting immediately. Headwinds indeed for the Fed’s efforts to temporarily lower inflation by pushing us toward recession.

John H. Cochrane is a senior fellow of the Hoover Institution at Stanford University and was previously a professor of finance at Chicago Booth. This essay is adapted from a post on his blog, The Grumpy Economist.

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