Several colleagues at Stanford got together to talk about inflation, which prompted me to summarize recent work as concisely as possible. Thanks everyone for the great discussion.

**big question**

That’s 9% inflation. Yes, I think it was due to the crash of a large fiscal helicopter. Others have other theories.

Don’t confuse inflation with relative prices. An oil price shock can make oil more expensive than other commodities. But he does not determine whether oil will rise in price by 10% and wages by 5%, or the price of oil will fall by 5% and wages by 10%. The central phenomenon is the depreciation of the value of money when prices and wages rise at the same time. The most obvious sign of this phenomenon is wage growth. Of course, people and politicians care most about prices in relation to wages. But let this not confuse us in the economic question.

Slide courtesy of Arvind Krishnamurti |

The big question now is, will the Fed’s slow response lead to higher inflation? Conventional economic wisdom says that reducing inflation requires that interest rates exceed inflation. As long as interest rates are below the rate of inflation, inflation will rise. It requires 10% or more interest rates, now. But the Fed believes that interest rates are already “neutral,” meaning that the 2.25-2.5% interest rate and 9% inflation are no longer pushing inflation higher. How can they believe it?

Markets also believe that inflation will largely disappear on its own, without a period of interest rates substantially higher than inflation:

Right now (right side of the chart), the markets think that inflation in 5 years (lower blue line) will be 2.5%, and the average inflation over the next 5 years will be around 3.4%. And these numbers have recently decreased! Of course, markets like the Fed completely missed the emergence of inflation: both were at 2.5% in January 2021, the day inflation broke out. But this is their current forecast.

And here is the market forecast for interest rates. Markets expect rates to briefly rise to 3.5% but then quickly drop to 2.5%. Inflation goes away on its own. How can it be?

**So much for the real world, how does it work in theory?**

This slide minimizes 50 years of macroeconomics. i is the interest rate, pi is inflation, x is output, the rest are parameters. There are two main ingredients. First, in IS, higher real interest rates—the nominal interest rate i minus the expected inflation—reduce output x. (In the correct equation, the term is greyed out, but that doesn’t matter at these points.) Second, inflation is higher at Phillips if people expect more inflation in the future—in which case raise prices. now — and if the economy is booming.

Now add these ingredients together and we get the dynamic relationship between interest rates and inflation shown in the third equation.

But what is the expected inflation rate? Starting with Milton Friedman in 1968 and continuing the Keynesian tradition ever since, conventional wisdom holds that expected inflation is determined by what happened last year, “adaptive” expectations. Substitute this and you have the dynamics right above the left graph.

Inflation = (number greater than one) x last year’s inflation minus (number) times the interest rate.

(A number greater than one) means that inflation *unstable. *If the Fed leaves interest rates alone, any small amount of inflation will get bigger and bigger over time. It’s a commonly held belief that until the Fed raises rates above existing inflation, inflation will get worse and worse.

What if people are smarter than this? What if their expectations for the next year are “rational”, including all information, or at least “consistent”, the model should write that people *in* model has the same expectations as those* or* model, we economists are not so much smarter than everyone else. Now we have the right group, and inflationary dynamics is like that.

Expected inflation next year = (number less than one) x inflation this year plus (number) times the interest rate.

Now inflation *stable. *Even if the Fed does *nothing* Inflation will eventually — let us emphasize, in the end, a lot can happen along the way — will fall again.

Rational (or at least consistent) expectations, the idea of what people think about the future when making decisions today, has been a cornerstone of macroeconomics since about 1972. This is part of the “New Keynesian” tradition, designated by N.K. There, too, inflation is stable. The NK models cannot tell you which of the dotted paths will occur, so they predict that inflation will fluctuate between them. But they are all stable. The fiscal theory of the price level chooses one of the dotted paths. Inflation is now stable and certain.

Now you see the central economic issue. In other words, we are talking about the release sign on the Phillips curve. Does higher output and lower real interest rates cause inflation to rise or fall, i.e., higher inflation today than future inflation?

The Fed and the markets take the standpoint of stability that the model creates based on rational expectations. It’s not exactly crazy.

**Data**

What does history tell us about this important issue? Well, it depends.

The traditional stylized history of inflation dates back to the 1970s, top graph. The Federal Reserve didn’t do as bad a job as most people say. In each of the four waves of inflation, interest rates rose rapidly at least one to one, and usually more so with inflation. The Fed has never waited a whole year to do something. Yet this was not enough, as inflation steadily increased until, in 1980, the Fed finally set interest rates well above inflation and kept them at that level for years to come, despite a tumultuous recession.

With this standard interpretation of history and the adaptive unstable model in mind, conventional economists are absolutely right to shout from the rooftops that the Fed needs to raise interest rates right now.

But now another story. In the era of zero frontier, lower chart, the threat of deflation. (I drew the core CPI. The actual CPI got a 2% deflation.) The same unstable/spiral view said we were going. The Fed can no longer cut interest rates, so we will have a deflationary spiral. *It never happened.* Inflation was quieter at zero bound than before when the Fed changed interest rates!

The zero border of Europe has lasted longer, until now. And Japan is even longer, starting in the early 1990s. You cannot demand a clearer test that inflation can be stable (and quiet) while central banks do nothing with interest rates. Theoretically, this requires a lot of preconditions, in particular, that no other “shocks” occur – we just saw a big one, more are coming. But there is at least one episode in the “stable” theory that contradicts the standard story of the 1970s.

In short, you who say that inflation will spiral unless the Federal Reserve raises interest rates to 10% or more tomorrow, haven’t you also said that inflation will spiral down at the zero boundary?

It’s not exactly crazy.

**A more complete simple model**

My last slide shows a simulation of a real but still very simple model. It has tight prices, a full IS curve, rational expectations, and long-term debt. The top panel shows a 1% fiscal shock – the government is allocating 1% more debt and people don’t think it will be repaid – and the Fed is doing nothing. Again, in my opinion, we have just done this about 30 times. The graph shows a lot of interesting things. The first, *a one-time fiscal shock leads to sustained inflation. *Over several years of inflation above interest rates, inflation eats away at the value of government bonds. This does not lead to a one-time jump in the price level. We live in that period. But *the inflation of a one-time fiscal shock eventually disappears on its own*. (Don’t take steadily declining inflation too seriously. It’s fairly easy to modify the model to a hump-like response that rises smoothly for a while before turning around.)

Monetary policy is not helpless. What happens if the Fed raises rates, as it is starting to do, but there is no unexpected change in fiscal policy (i.e. continues to spend like a drunken sailor, like before covid). In this simple model *The Fed may reduce inflation in the short term. *Notice the drop in performance. Yes, the Fed’s tool is to induce a small recession (IS) and that will bring inflation down (Phillips). The Fed is looking to add enough of the lower curve to the upper curve to keep inflation moderate. But *The Fed cannot eliminate inflation. *Note that inflation rises in the long run. The Fed bought lower initial inflation by extending the inflationary period. After all, in this model, inflation goes where the Fed sets interest rates. I’ve drawn interest rates that are always high so you can see how it works, but if the Fed ends up lowering those rates, then inflation will come down too.

The ideal end to inflation would be if the Fed does a little bit of it, and then Congress wakes up and gets fiscal policy in order – goes through the negative part of the top chart.

The bottom line is that both fiscal and monetary policy matter for inflation. Add two graphs if you like to think about scenarios.

It’s not that crazy.

Is this how the world works? I have no confidence that I can hit the table with my fist. I’ve spent so much of my life thinking that the Fed should raise interest rates quickly to avoid inflation, and so many economists think this is true, it’s hard to fully digest the rational expectations view. However, the theory, the Fed, the markets, and the zero-bound experience speak loudly.

In any case, if nothing terrible happens (these simulations do not suggest additional shocks), we will soon have another big test of macroeconomic theories, complementing the Zero Boundary episode. Inflation will either decline back to Fed interest rates, or inflation will continue to spiral upward until the Fed raises rates sharply.

Yes, the economy does not fully know the answer to the most basic question: is inflation stable or unstable around its interest rate target, and does the Fed need to raise interest rates more than observed inflation to bring inflation under control. Now you know as much as anyone else.

IS and Phillips curves (especially the latter) are also very weak building blocks.