It is a truth universally acknowledged – well, anyway, a truth acknowledged by everyone I know who thinks about the subject – that a hot economy leads to higher wages and prices. When demand for labor is strong, workers can and do demand wage hikes; when demand for goods and services is strong, businesses have "pricing power," or the ability to raise prices without losing customers.

But does a hot economy lead to a higher level of prices? Or does it lead to a higher rate of change in prices, i.e., ongoing inflation? Or maybe even to accelerating inflation, a higher rate of change in the rate of change?

These may sound like abstruse questions, but they aren't. On the contrary, they have frequently been at the heart of debates over economic policy; they are, in fact, central to current debate. Yet I'm not sure everyone writing on economics right now understands these distinctions. Nor am I even sure that all academic macroeconomists are fully aware either of the history or the importance of these questions: Much modern academic macroeconomics (as opposed to policy analysis) is wrapped up in the study of dynamic stochastic general equilibrium models (don't ask), which in a way assume away the whole issue.

So I thought I'd use today's newsletter to talk about what a hot economy does to inflation – in particular, about how both the evidence and widely held views about that relationship have changed over time. It's a story that is, frankly, not very encouraging for those who want to think of economics as a science.

A note to professional colleagues: This newsletter is not intended as a research paper. I present some data, but only for illustrative purposes, not as part of a serious empirical analysis. If you want a state-of-the-art look at the empirical evidence, I recommend you start with this highly influential paper by Emi Nakamura, Jón Steinsson and associates. Or if you want detailed analysis of what the current inflation data seem to be saying, you might want to read Matthew Klein and this Brookings discussion.

But if you want a quick and dirty look at what the real issues seem to be, read on.

In the beginning was the aggregate supply curve – a putative upward-sloping relationship between output and the overall price level, or more or less equivalently a downward-sloping relationship between unemployment and prices. And I do mean in the beginning: It's right there in John Maynard Keynes. It's also clearly visible in Depression-era data. Overall prices slumped when the U.S. economy plunged into depression, rose back up as the economy recovered, then fell again as the economy relapsed in 1937. Here's what the scatterplot for those years looks like:

The way it used to be.
Credit... Historical Statistics of the United States, Millennial Edition

In 1958, however, the economist A.W. Phillips pointed out that there had historically been a relationship between unemployment and the rate of change in wages (as opposed to their level). This was soon reinterpreted more generally as what we now call the Phillips curve, a relationship between unemployment and inflation, which seemed to work pretty well in the 1960s:

Ye good old Phillips curve.
Credit... FRED

So, how do you get from "a hot economy causes high prices" to "a hot economy causes ongoing inflation"? It's actually a bit awkward, something that becomes especially apparent when you co-write an economics textbook. There is, however, an insightful discussion of that transition in a classic 1968 paper by Edmund S. Phelps, which I wish I could recommend to readers. Unfortunately, I can't, at least not in good conscience: It's amazingly hard to decipher, even for professional economists. And that's a shame, because Phelps's analysis of inflation was, I'd argue, considerably more realistic than that of Milton Friedman, who simultaneously and independently arrived at more or less the same conclusion: that the Phillips curve wouldn't prove to be a stable relationship.

What both economists argued was that sustained inflation would get "built in" to wage- and price-setting, so that trying to keep unemployment low would require not just high but ever-accelerating inflation. And this claim, made at a time when the traditional Phillips curve still seemed to be working pretty well, appeared to be vindicated by the era of stagflation. From 1970 until sometime in the 1980s, it looked as if unemployment determined not the rate of inflation but the rate of change in the inflation rate, a relationship sometimes described as an "accelerationist" Phillips curve.

The idea of an accelerationist Phillips curve is what underlies the concept of the nonaccelerating inflation rate of unemployment, or NAIRU – that is, the unemployment rate at which inflation will be stable, neither rising nor falling. This concept is a staple of practical policy analysis, so much so that the Congressional Budget Office regularly publishes estimates of the NAIRU, although these days it calls it the noncyclical rate of unemployment.

The NAIRU straitjacket.
Credit... FRED

But a funny thing happened to the Phillips curve after inflation receded in the 1980s: It stopped looking accelerationist. In fact, in the two decades before the pandemic the U.S. economy exhibited something that looked like a (weak) version of the old Phillips curve, with a correlation between unemployment and the inflation rate, not the change in the inflation rate:

Back to the future?
Credit... FRED

What happened? The most common explanation out there is that after a long period of low inflation, expectations became "anchored": People setting wages and prices did so in the belief that future inflation would run at around 2 percent, and didn't update that belief in the face of the latest inflation numbers.

Which brings us to current policy debate. Pessimists who insist that we're doomed to years of high unemployment are basically asserting that we're back to the inflation environment of the 1970s and early 1980s, that expectations have gotten unanchored and that to reduce inflation we'll need to go through an extended period of unemployment well above the NAIRU.

I don't agree; when I look at various measures of medium-term inflation expectations, they still look pretty anchored to me. But I could of course be wrong – the brief history of inflation theorizing I've just recounted doesn't inspire much confidence that any of us has a really solid grip on the relationship between economic hotness (or coldness) and prices.

The point I want to make, however, is that you do need a theory. The evidence is fairly overwhelming that the U.S. economy is currently running too hot and needs to cool off. But how much cooling it needs isn't a question that can be settled without deciding what kind of inflation process you think is currently operating.

Paul Krugman has been an Opinion columnist since 2000 and is also a distinguished professor at the City University of New York Graduate Center. He won the 2008 Nobel Memorial Prize in Economic Sciences for his work on international trade and economic geography. @PaulKrugman