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Nick Rowe on Forecasting Price Inflation

[2nd UPDATE in text.]

[UPDATE below.]

Nick Rowe has an intriguing post that pushed me over the edge to mention something that’s been bothering me for a few weeks now. (No, I’m not talking about the rash.) Here’s Rowe:

You can’t test whether core inflation is a useful indicator for a central bank to look at just by seeing whether core inflation forecasts future total inflation (or whatever the bank is targeting). You can’t test whether anything is a useful indicator for central banks to look at that way. Everything ought to look useless by that test, if the bank is doing it right. What you are testing is whether the bank is doing it right.

If a central bank is targeting (say) 2% total inflation at a (say) 2-year horizon, and if it’s doing it right, then deviations of total inflation from 2% ought to be uncorrelated with anything that the bank knew 2 years ago. This means that nothing (i.e. nothing in the bank’s information set) should forecast 2-year ahead total inflation, if the bank is reacting correctly to those indicators. Core should fail to forecast future total inflation. Total inflation should fail to forecast future total inflation. Trimmed mean inflation should fail to forecast future total inflation. Unemployment should fail to forecast future inflation. Everything should fail to forecast future total inflation.

This is an immediate implication of rational expectations (on the part of the central bank). The bank sets monetary policy, looking at the indicators in its information set, so that the bank’s forecast of 2-year ahead total inflation is equal to the 2% target. Deviations of actual inflation from 2% are therefore forecast errors. Under rational expectations (on the part of the bank) forecast errors should be unforecastable from anything in the bank’s information set. They wouldn’t be rational if you could forecast errors.

When you look at correlations between core inflation and future total inflation, you are not testing whether core inflation is a useful indicator of future headline inflation that the bank should pay attention to. You are doing something quite different.

Now I’m not fully on-board with the rational expectations stuff, but Rowe’s basic point is totally right. (In the comments, he’s goes toe-to-toe with some critics and neither side is bluffing. So if you want to get your econometrics game on with a debate involving terms like “orthogonal” and “serial correlation” then jump right in.)

In the context of my favorite living economist, Krugman has repeatedly been mocking people who want the Fed to tighten, by showing charts of core inflation versus headline inflation. Krugman’s point is that in the past, just because headline inflation rose by (say) 4 percent in a 12-month period, while core only rose by (say) 2 percent, that wouldn’t lead us to think headline inflation would be unusually high in the near future. In other words, Krugman was saying that core inflation seemed to predict headline inflation better than headline inflation predicted itself. Ergo, Krugman concludes, people who are freaking out right now about headline inflation–driven by rising commodity prices–are looking at a bad indicator. Instead they should look at core CPI, which is still rising at a reasonable pace.

Yet this proves nothing, for the reasons Rowe gives. What if the Fed in the past jacked up rates whenever headline inflation started to pick up, in order to maintain the target of stable core inflation?! Then history would look just like what Krugman is now pointing to, as proof that the Fed should ignore headline inflation. Except, this time, if the Fed ignores the strategy that (in principle) it may have been following to generate the charts up till today, we will now see a breakdown of the pattern.

Note that my story isn’t necessarily what’s going on; maybe Krugman’s version is right, and the Fed has always been (correctly) ignoring headline inflation and looked at core CPI for the last 30 years. My point is simply that Krugman thinks he is demonstrating his interpretation by pointing at charts of core versus headline inflation rates, and that by itself tells us just about nothing.

For example, back in the early 1980s Arthur Laffer met with Paul Volcker, who apparently literally pointed to a chart of a commodity index, and told Laffer that when commodity prices went above a certain range, Volcker would tighten. When they dropped below a certain point, he would loosen. That led Laffer to write a WSJ piece at the time, titled something like, “Does Volcker Have a Commodity-Price Rule?” (I can’t find it on google, but I saw it with my own eyes and heard Laffer tell the story several times. UPDATE: Aristos sends me an excerpt from Laffer’s book, talking about this episode.)

So assuming that anecdote is true, and Volcker really were explicitly following a commodity price rule, Krugman’s method would lead you to conclude that commodity prices had little to do with future CPI. I mean, every time commodity prices shot up, they would soon come back down, and next year’s CPI wouldn’t be much above the prior year’s. So today, if commodity prices shoot up, the Fed can safely ignore it and keep monetary policy nice and loose, since “history shows” that commodity prices are just wacky and volatile, they’ll come down on their own. CPI has little to do with commodity price spikes, right…?

I’m trying to think of an analogy to do this justice. Maybe something like: “We don’t need to turn on the air conditioner this summer even when the temperature goes up outside. We looked at a history of outside versus inside temperatures over the last 20 years, and there’s surprisingly little correlation between the two. So let’s save a bunch of money this year by turning off the AC and heat.”

UPDATE: In the comments, “NickRoweFan” points us to an earlier Rowe post that spells out the thermostat analogy much better than I did.