Blair Fix caused a bit of a stir last week on economics Twitter with a cleaned up version of the above chart taken from his article on interest rates and inflation. My chart is a scatter plot of the U.S. annual CPI inflation rate versus the effective funds rate, from 1954-2022. The blue line is the best linear fit of the two variables. The “linear model” suggests that inflation is an increasing function of the nominal interest rate.

Blair was met with a predictable howl of indignation on Twitter. Why predictable? The belief that higher interest rates reduce inflation (with a technical twist I note below) is pretty much enshrined as an assumption in neoclassical economics.* (I use “neoclassical” as a fancy-pants word to describe “mainstream academic economics,” as “mainstream” is somewhat ambiguous if we are not referring to academia.)*

Although the firestorm of indignation the article created was fun and if I had any commercial sense I would pile into it (and I did in the past). However, I have gotten more boring as I have aged. The real answer is that “things are complicated.”

## Initial Complication: Real Rates

The first source of well-deserved indignation is that the above chart is a misleading representation of neoclassical theory. The driving variable in neoclassical models are real interest rates, where the “real” interest rate is the nominal interest rate minus inflation. To add to the complexity, the inflation rate is supposed to be the expected inflation rate, not the historical rate of inflation.

It is entirely correct to describe neoclassical economics as assuming that the real interest rate drives inflation. These models have at their core dynamics that are driven by households optimising their expected consumption over time, where they are trading off current consumption versus future consumption. By definition, the expected increase in nominal goods prices is expected inflation, and the pay-off for not consuming now is that households can buy “bonds” that pay the nominal interest rate. Quick math tells us that the trade-off between spot and future consumption is linked by the real interest rate. These dynamics are assumed to be true in a neoclassical model — since the presence of those dynamics is the defining characteristic of “neoclassical” models. *(A mainstream academic could invent a model not of this structure, but it would not qualify as a “neoclassical model” as I define the term. This is the sort of problem that labels like “mainstream” contend with.) *On paper, the model could have wacky dynamics that a real rate increase could cause higher inflation (that model would probably never be taken seriously, as it is the “wrong” answer), but the key point is that real rates are an* assumed *driver of economic dynamics.

From a scientific point of view, if you assume something is true and build your methodology around that assumption, your assumption is not falsifiable. (See Kalman filter discussion below if you object to that assertion.)

I generated the chart above by subtracting the annual CPI inflation rate from the (overnight) Fed Funds rate. That is, it is comparing measured inflation data on a backwards-looking basis over the past year versus the nominal return looking one day forward. Given the low quality and short time availability of expected inflation rates, I will not attempt to create a long history of real rates. For the purposes of my article, I will largely use “real rates” and “nominal rates” somewhat interchangeably, on the argument that the central bank hiking rates will tend to raise both the nominal and real policy rate, and what we are interested in in is the effect of policy rate changes on inflation.

## What Do We Need To Do?

The problem with the “effect of interest rates on inflation” debate is that it is so poorly framed. Inflation is normally thought of as an “outcome” of the trends in the real economy. If interest rates have any effect on the economy, they presumably have *some* effect on inflation. The real question is: is there a predictable effect on inflation that allows central banks to micro-manage the inflation rate (which is what inflation targetters and their theoretical offspring insist is possible)?

In other words, we need to test particular models of the relationship between interest rates and inflation, and see whether they allow for micromanagement of the economy. Given that there is an infinite number of models that could allow for such micromanagement, it is going to be extremely hard to reject all of them. We would effectively need to find and validate a model that shows such micromanagement is impossible. That is a difficult task, with the difficulty increased by the reality that not a lot of people are looking for such models.

## The Empirical Problem

I have repeatedly noted the following, but will repeat for new readers. The following observations appears to cover a lot of the observed data — call them “stylised facts.”

Inflation tends to rise during expansions, and will spike in response to shortages. (E.g., periodic oil price spikes, the post-pandemic price hikes.)

Recessions generally result in lower inflation, for the straightforward reason that a collapse in production and employment will reduce the intensity of shortages. Once the shortages are cleared out, deflationary tendencies reverse.

A rapid increase in nominal rates will cause stress on private sector balance sheets, and can trigger a crisis that results in a recession.

This allows monetary policy to have limited control over inflation — central banks can trigger recessions, reducing high inflation rates. This certainly does not qualify as “micromanagement of inflation rates” as claimed by neoclassical boosters of inflation-targeting central banks.

Meanwhile, empirical testing is confounded by the known ideological biases of central banks. Central bankers believe that raising real interest rates cools inflation, and cut rates rapidly in response to recessions. As such, they will increase real rates during an expansion in response to the inflation rise in point #1 above. Survivorship bias implies that real rates will peak before recessions — and plunge once the central bank is aware of the recession.

## About that “Overwhelming” Empirical Literature

Neoclassicals continuously claim that they have an “overwhelming” empirical literature that demonstrates that interest rates work the way they do.

A lot of the tests are model-agnostic (I discuss the model-based ones next). Unfortunately, if we accept the stylised facts as true, they can explain almost all of the test not tied to particular models in the literature that I have seen. I cannot claim to have read every single article published in the literature, but 100% of the ones I have read were terrible. Neoclassical economists get mad when I write things like this, but if I have a 0% success rate reading a literature, I see little point in keeping reading.

As an aside, the worst part of the literature was the idea that we can read internal policy deliberations of policymakers to “prove” that interest rates work the way that neoclassicals insist. Even a slight knowledge of intellectual history tells us that closed groups believe that their shared beliefs are true, and will use those beliefs to explain events around them. By that standard, we could have elite universities handing out doctorates in haruspicy (“100,000 Romans cannot be wrong!”).

## Model Based — Why Hello *r**!

If we move away from model-agnostic test methods, we end up with the “neutral” interest rate — now rebranded *r** — literature. Since all the standard neoclassical models predict that something like* r** exists, we should see it in the observed data.

The problem is that we can reject *r** being a constant, or a known simple function of other observed economic variables. So, neoclassicals assume that* r** is time-varying, and estimate *r* *based on procedures like the Kalman Filter.

Once we strip the mathematical goobledy-gook away from the procedure, the Kalman Filter works as follows.

*Assume the dynamic model is true.*- Use the observed data (real interest rates, inflation, GDP growth, whatever) into a statistical procedure to estimate the “internal variables” of the model — r*, y* (“potential GDP”), etc. — so that observed data is in line with the estimated model.
- Update the “star variables” as data comes in.

However, the issue here is that if inflation and real interest rates are autocorrelated variables (move slowly over time), we can force *r** to move rapidly enough to get the model to fit the recent history. As long as the autocorrelation continues, the model will have roughly correct predictions.

And this is exactly what we saw in practice. The estimate for *r** in the United States plunged after 2008 once the negative real interest rates did not result in the predicted acceleration in growth/inflation. (Yay! Secular stagnation!) The models roughly matched the sclerotic pace of economic variables during the 2010s. And one the 2020 pandemic disruptions hit, people stopped estimating the variables since the models blew up. (In technical applied mathematics terms, “lol, lmao.”)

In other words, it is very hard to falsify a model using a statistical procedure that assumes that the model is true.

## Concluding Remarks

The correct answer to the “inflation-interest rate debate” is that most the “answers” being pushed are incorrect. Like other areas of heterodox-neoclassical controversy, my prediction is that pretty much the exact same points will be raised a decade from now.

Great title; I took the heterodox solution years ago and I still feel great!

ReplyDeleteDo they use a vanilla Kalman filter? Because that doesn't just assume the dynamic model is true, is assumes the dynamic model is _linear_ and also that the measurement model is linear. Fancier variants of the Kalman filter relax those assumptions somewhat, but there is still plenty of scope for creating garbage.

ReplyDeleteIt's also worth noting (in defence of using Kalman filters), that both observations and model can be noisy (as in, with additional Gaussian noise of some covariance), which makes the "dynamic model is true" a little fuzzier.

DeleteWith a sensibly designed system, the data will dominate eventually, even if your dynamics model is wrong - more rapidly if sufficient noise is included (effectively, a wrong model can be considered as "noise"). It's often the case that you might have a constant model (because you don't really know the dynamics) but sufficient noise that the state tracks the data with some smoothness. It's poor, but potentially useful.

Of course, your observation model might be garbage too!

Kalman filters (and its non-linear variants, notably the UKF) work really well if the dynamics model is well defined but noisy and the observation process is well defined but noisy (say an aeroplane with some uncaptured atmospheric effects being tracked by a radar which has some noise on it).

(This is Brian.) Not a technique that I looked at, but throwing in parameter errors as another thing to be estimated still implies that you have the correct model - it just includes known parameter errors.

DeleteIt has been years since I looked at that work. They have a few dozen quarterly observations to try and pin down multiple time-varying hidden state variables. They do not have enough extra information to also try to estimate a model out of a huge class of models.

How do you defined 'tracking the data'? Models are not noisy - they may be correct, approximately correct or just plain wrong. If the model used in the KF is wrong, but produces some kind of smooth result which 'looks as if' it tracks the data, you would be as well using other forms of smoothing.

DeletePerhaps it would be better to talk about a 'good model', one that represents the most important characteristics of the underlying reality. In the most successful applications of the KF (and its extensions), a good model is *derived* from the underlying reality - where do you find that in economics?

(This is Brian. Problems with logging in from mobile. Sigh.) Not sure who this comment is directed at. The obvious definition of “tracking the data” would be be how well it predicts inflation. In the 1990s era of flatflation, it might be that such models would have decently low errors. The problem is when variables change radically (e.g. post-2020), or forecasts fail (“whoops, r* fell” in the 2010s).

DeleteApologies, my comment was intended as a response to heng's comment at 7:09am. I agree with his final paragraph. My point, badly expressed by me in the above, is that the noise in a model is often an attempt to compensate for the dynamics model being approximate or wrong. If you don't have a "good model" based on an underlying reality, which seems to be rare in economics, you may as well use non-KF estimating techniques. I don't think forcing a poor model to follow the data will add very much.

DeleteThe only encounter I have had with an alternative to the neoclassical claim about the relationship between interest rates and inflation is Mosler, and he appears to be convinced not only that they are wrong, but that they have it precisely backwards.

ReplyDeleteIs Mosler's own claim falsifiable or not empirically?

1) Mosler's assertions have the same falsifiability hurdles: need to propose a mechanism that can be tested versus data.

Delete2) Obviously, it is possible that Mosler and the neoclassicals can be both wrong.