Bachmann, Berg and Sims on inflation as stimulus

Rüdiger Bachmann, Tim Berg, and Eric Sims have an interesting article, "Inflation Expectations and Readiness to Spend: Cross-Sectional Evidence" in the American Economic Journal: Economic Policy.

Many macroeconomists have advocated deliberate, expected inflation to "stimulate" the economy while interest rates are stuck at the lower bound. The idea is that higher expected inflation amounts to a lower real interest rate. This lower rate encourages people to spend today rather than to save, which, the story goes, will raise today's level of output and employment.

As usual in macroeconomics, measuring this effect is hard. There are few zero-bound observations, fewer still with substantial variation in expected inflation.  And as always in macro it's hard to tell causation from correlation, supply from demand, because from despite of any small inflation-output correlation we see.

This paper is an interesting part of the movement that uses microeconomic observations to illuminate such macroeconomic questions, and also a very interesting use of survey data. Bachman, Berg, and Sims look at survey data from the University of Michigan. This survey asks about spending plans and inflation expectations. Thus, looking across people at a given moment in time, Bachman, Berg, and Sims ask whether people who think there is going to be a lot more inflation are also people who are planning to spend a lot more. (Whether more "spending" causes more GDP is separate question.)

The answer is... No. Not at all. There is just no correlation between people's expectations of inflation and their plans to spend money.

In a sense that's not too surprising. The intertemporal substitution relation -- expected consumption growth = elasticity times expected real interest rate -- has been very unreliable in macro and micro data for decades. That hasn't stopped it from being the center of much macroeconomics and the article of faith in policy prescriptions for stimulus. But fresh reminders of its instability are welcome.

At first blush, this just seems great. Finally, micro data are illuminating macro questions.


It's cleaner than the  Hagedorn, Manovskii and Mitman paper I blogged last week, because many of the aggregation issues are absent. There, I complained that employment in one state might be  gained by business moving from another, which would not be an available channel for the whole economy. Here, if we know that people who expect more inflation spend more, it's an easier jump that if we all expect more inflation we all want to spend more. This aggregation problem is usually one of the biggest stumbling blocks for the project to measure macro effects from micro data.

Now, for a little whining. This isn't really criticism as I don't know how to do any better. But it does make for a very well-done example in which to ponder the limitations of the micro evidence on macro questions methodology.

Here are Table 1 and 2, the "baseline specification."

It's a probit regression. The left hand variable is whether a person answered yes or no to the question,

Q1: “About the big things people buy for their homes—such as furniture, a refrigerator, stove, television, and things like that. Generally speaking, do you think now is a good or a bad time for people to buy major household items?” 

The main right hand variable, ("Inflation expectations (1Y)") is the answer to the question,

Q2: “By about what percent do you expect future prices to go (up/down) on the average, during the next 12 months?”

The main fact is that the top row of numbers are all essentially zero, decently well measured, and nonetheless statistically insignificant. Where it is significant, in the zero-bound years, it's negative -- higher inflation expectations are associated with plans to spend less, not more!

So far, so good. But what are all those other numbers in the table? Well, these are "controls," extra right hand variables in the regression.

What in the world are they doing there? The fact is not "people with higher inflation expectations don't plan to spend any less." The fact is that "people with higher inflation expectations, holding constant their expected financial situation and income, their expected change in nominal interest rate and aggregate business conditions, ..., a long vector of aggregate variables, and then the whole Table 2 of demographic variables, don't plan to spend any less." Hmm.

The long list of "controls" brings back memories of all the regression horror stories I was taught in graduate school (thank you Tom Rothenberg).

Left shoe sales = a + b price + c right shoe sales + error. 

Wage = a + b education + c industry + error. 

(In case the latter isn't obvious: including industry helps a lot to "explain" wages and raise R2. But the point of education is to let you change industries from fast food to computers, so you absolutely do not want to "control" for industry!)

What are all the controls doing here? Could we not at least start with OLS, a clean digestible fact, or a graph so that poor bloggers have something to brighten up posts?

I asked the correspondent who sent me the paper (thanks) who opined that the referees probably made the authors do it, and out of a reasonable concern. Maybe the correlation between inflation expectations and spending plans across people does not measure the causal effect, what if we change inflation and leave other things constant?  It could well be that the correlation of expectations across people is zero, reflecting other forces at work, but if we raise everyone's inflation expectations, then we would raise everyone's spending.

Most simply, just because we put inflation expectations on the right hand side of a regression and spending on the left, does not mean that changes in inflation expectations across people cause their spending plans to change.

Demographic controls seem reasonable. Suppose the fact was that women all expected higher inflation and planned to spend a lot, while men expected low inflation and did not plan to spend a lot. One would not want to use that correlation to measure how increasing expected inflation for all of us would affect our spending. Such a demographic correlation is much more likely a result of other causes affecting both variables (inflation expectations and spending). This really remains the deep issue of micro to macro implications: Does a correlation across people tell us what happens if something affects all of us?

But if demographic controls changed the result a lot over OLS, one would be very suspicious. A correlation that survives controls is a lot more persuasive than a correlation that only emerges with controls. It's much nicer to say there is a raw correlation, and verify that it is not the result of differences between demographic groups, than to say the correlation is only measured after demographic controls. Because no set of controls is perfect. (The implicit assumption "my controls perfectly capture all the reverse causation or all third variable influences" pervades regression analysis.)

Many of the controls are macro variables. There are almost as many controls here as time data points. Year dummies would have removed all the time-series variation and left us the pure cross section a lot more simply.

The first set of controls for other expectations strikes me as the most fishy. Why would we measure the effect of a change in expected inflation holding constant expected unemployment? The whole point of the macro experiment is to raise both expected inflation and to lower expected unemployment.

This is the hard nut of all regression analysis: why does the right hand variable vary? People spend a lot of effort on the left hand variable, but that's actually less important. What caused the variation in your data? We don't have randomized experiments. Why is it that households have such widely (insanely!) varying expectations of inflation? Until we know that, it's really going to be hard to tell whether their similarly widely varying spending plans are because of higher inflation expectations, or because inflation and spending plans are both results of some third cause.

The paper isn't much help on this issue. At least I wish they (or much of any regression work) at least asked the question. They don't even really discuss the "controls" in this way; why expected inflation varies, and then control for determinants of expected inflation that are correlated with determinants of spending.

The discussion of the control variables sounds a lot like the habit of assuming everything on the right is a "cause," and fishing for R2, like left shoes in the right shoe equation, and industry in the wage equations.

With respect to the coefficients on the economic control variables, we obtain for the most part plausible and significant estimates,... the expected financial situation of the household and its real income, the expected business conditions (idiosyncratic and aggregate), the current financial situation, and the current real household income all have significantly positive effects on the reported spending readiness. In addition, a positive judgement of US economic policy also affects spending dispositions positively. Moreover, an expected increase in future nominal interest rates makes people want to spend more today,  while higher economic uncertainty in the form of stock market volatility, inflation volatility and higher unemployment rates (both current and expected) decrease the probability that people find buying conditions favorable ...

But enough whining. My point is that micro, regression-based analysis has its limitations too. This seemed like a good example on which to remind graduate student readers of common regression pitfalls: Always ask what caused the variation in the right hand variable. Use minimal controls, not the kitchen sink. Make sure the partial effects of your regression (move x holding z constant) make sense. And so on.

But I don't think I could have done better, as making sense of why people's expectations are as widely dispersed as they are seems a big challenge.

It's still a powerful observation, and I trust it's there in the OLS with minimal controls. People who expect more inflation do not plan to spend more. If you think raising all our expected inflation will make us all spend more, you have some creative explaining to do.

Update: Eric responds:

On your point about all the control variables . . . we did (more or less) what you suggest in the blog post. If you look at Table 3, we drop all of the idiosyncratic control variables in one specification and get essentially the same results; also in Table 3 we do the version with time fixed effects instead of aggregate controls. If you go to the online appendix, in Table 8 we show raw correlations between expected inflation and buying attitudes. We also split the raw correlation by a large number of different demographics. In Figure 7 we show plots of time-varying raw correlations between expected inflation and spending attitudes -- it is the analog of Figure 6 in the main paper which plots a time-varying marginal effect based on the probit estimation. Basically this all shows exactly what you ask for in the blog post -- the correlation/coefficient between expected inflation and buying attitudes does not depend on the controls.

I admit not reading all the way through or the online appendix. They also confirm that the early drafts started with raw correlations. There is an interesting writing (and editing and refereeing) conundrum, should a paper start with the "main" result, or should one start with suggestive robust facts and correlations and then address objections with a more sophisticated model. It's not an easy question -- Most papers drag you through 10 tables of motivation and summary statistics and suggestive correlations before getting to the point, and I really admire that this paper had the main result on Table 1.  OTOH, by going the other way around busy bloggers miss the interesting correlations in online appendix Table 8!