# The Term-Structure of Inflation Expectations

### Are long-term expectations on the rise?

Some interesting pushback from folks on econ twitter. People seem convinced that the current bout of inflation is broad-based. That result can hardly be argued with:

But people seem to be less convinced that the current bout of inflation is not transitory but persistent. I am not a fan of the transitory vs permanent team sport. The issue is not inflation at all but inflation *expectations* — the forcing variable of US monetary policy. And we’re seen that, by a variety of measures, inflation expectations are on the rise.

More serious analysts have questioned whether the movement in expectations is restricted to the short-term horizon. The issue is whether long-term expectations (expectations *sensu stricto*) are getting de-anchored. More precisely, at issue is the term-structure of inflation expectations. For, if long-term inflation expectations are really and truly anchored on target, then the Fed need not worry so much. On the other hand, if medium-term and long-term expectations are rising rapidly, then the Fed should be very worried about squandering its hard-earned credibility. In that case, it has no choice but to tighten — perhaps considerably more than current market pricing suggests.

Fortunately, the Cleveland Fed publishes their estimates of the term-structure of inflation expectations. The calculation requires estimating the term-structure of inflation and duration risk premia (that compensate investors for bearing inflation and interest rate risk). These estimates must be taken with a pinch of salt because these risk premia are actually much more volatile that their model estimates suggest. Put another way, their estimates of risk premia are implausibly stable (see below). That being said, their estimates of expected inflation do contain a good signal of expected inflation. We’re going to use this signal to obtain our own estimates from the detailed CPI series.

The Cleveland term-structure of inflation expectations suggest that expectations are on the move but remain anchored. As we shall see, this sanguine conclusion is not warranted once we dig into the price series.

Here’s the term-structure as of the past three Decembers. Expectations have risen considerably more at the short end of the curve than at the long end. And they have done so much more dramatically since December 2020. The expected inflation curve as a whole was pushed down by the end of 2020, but has since risen dramatically, particularly at the short end.

In order to estimate the expected inflation component of our price series we use partial least squares (PLS). The PLS procedure allows us to obtain linear combinations of a set of predictors that best explain the joint variation of a set of response variables. We take the response variables to be the term-structure of expected inflation estimated by the Cleveland Fed (out to 10 years). We take the predictors to be the 179 price series reported by the BEA. We compute monthly returns for the price series to obtain monthly inflation series. We detrend the term-structure of expected inflation by taking their first-difference. We admit 3 components (essentially, the level, slope and curvature of the term structure). Note that, increasing the number of components to 5 or 10 (the maximum possible, since we have 10 LHS variables), does not alter the result. (In fact, there is not enough cross-sectional variation to justify even 3 components for the Cleveland term-structure estimates.) We rescale the fitted values to have the same location and scale as mean inflation.

The following graph presents our main result. It displays the estimated expected inflation 5 years out, as well as our preferred measure of expected inflation, the lowest volatility quintile of the 179 series reported by the BEA. We can see that expected inflation over the next five years is almost as high as its previous peak in May 2004. In fact, that was the only month when this estimate was higher than its current level. We also find that our preferred proxy of underlying inflation expectations, the lowest volatility quintile, is much more stable, suggesting that the signal-to-noise ratio of this measure is much higher — this increases our confidence in our preferred measure of expectations. This is what we should expect given our interpretation that the lowest volatility quintile reflects the expectations of the slowest moving price-setters in the economy, who must pay careful attention to expected inflation when setting their prices. Note that working at the 10 year horizon yields nearly identical results.

As a robustness check, we also compute OLS estimates as follows. We regress each of our series on the 2-year forward and 5-year forward inflation expectations. We then compute a weighted average inflation of the 179 inflation series, with the weights given by the t-statistics truncated at *t *= 1.64 (the standard 90 percent significance level). The idea is to restrict the computation to series that contain information on expected inflation. Because we’re controlling for short-term expectations (at the 2 year horizon), this procedure yields a more reliable estimate than PLS. It again shows that inflation expectations are now higher than they have been in twenty years.

Here’s a graph of our OLS estimate of expected inflation 5 years out, all by itself. It shows that expected inflation 5 years out, as measured by the price series most sensitive to long-term inflation, is now higher than it has been since 1999.

The bottomline is this: By a variety of measures, long-term inflation expectations are getting de-anchored. The Fed will not allow that to happen. It will hike much faster and much more than current pricing suggests, at least until inflation expectations are forced back down to target again.

A number of observers have taken my position to imply that I don’t care about people’s welfare; that I’m some sort of inflation hawk. That’s nonsense. I opposed Yellen’s hiking cycle. Back then, the Fed was hiking in anticipation of inflation because labor markets were running hot, not because inflation had returned. I support the present tightening cycle because *it really is important* to keep inflation expectations anchored. The Fed has no choice but to hike. In fact, if the Fed remains sanguine for too long, it may have to tighten faster and much more, with the attendant risk of pushing of the economy into recession. Now, recessions are extremely costly. It is true what they said in *The Big Short* — each additional percentage point of unemployment means thousands of avoidable deaths. So, the prudent thing to do, the safe thing to do, is to seek a soft landing. The Fed must hike to temper inflation expectations. And it must do so soon.

I attended the US inflation session at the ASSA. There was no disagreement among serious economists that the Fed must depart on a hiking cycle. The only question is how fast. I am of the position that the Fed must signal multiple hikes in 2022 and 2023, while making it clear that it will respond appropriately to the situation as it develops. I am perhaps more confident that the Powell Fed will be able to get ahead of this than a lot of economists, who are much more concerned that the Fed is really behind the curve. Let’s hope I’m right. Oh, and, ignore the ideologues. They don’t know what they’re talking about.

How we have come to equate inflation with “people’s welfare” is mind boggling. Maybe take a look at countries with inflation problems - it’s not great. Even if you believe in the power of inflation to add jobs, the underlying theory is that wages are sticky thus real wages fall. That may be desirable at certain times in an economic cycle, but it’s hardly some obvious boost to welfare.

Nominal tools have only nominal effects in the long run. Presumably we want real gains. To do that we need be more productive, which oddly gets very little attention. It’s as though we’ve given up on real solutions and are hoping the money illusion has some magical powers to create welfare. Economic discourse is going backwards.