Why Inflation Expectations Matter A Lot For Theory

The fallout from the Rudd article on inflation expectations (that I described here) is still percolating around the internet. Duncan Weldon just wrote “We Have No Theory of Inflation” which discusses the issues from the empirical side. In this article, I am re-writing and expanding on some points that I noted in my previous article. If inflation expectations do not behave as predicted by neoclassical models, that is a critical problem that cannot be easily dealt with by adding epicycles to the models.

A Theory Cannot Test Assumptions

I constantly harp on the assumptions made by neoclassical economics. The reason for this is that a theory cannot test its underlying assumptions, so they need to be rock solid.

To illustrate this, I will use an example that should be familiar to readers who took (and remember) high school physics: the Newtonian (or pre-Relativity) inverse square law of gravity.

If we take a textbook that covers Newtonian mechanics, it will state as an assumption that gravity is an attractive force between two bodies that is proportional to the product of the two bodies’ masses, divided by the square of the distance between them. (The formal version of the law would need to be expressed with vector notation, which I will skip.)

If we use the terminology of applied mathematics, the inverse square law is an assumption. (It is perhaps more likely to see the inverse square law described as a “hypothesis” — which can be re-phrased as a “working assumption.”) We can use the inverse square law to make predictions about other things, such as the properties of planetary orbits, and that “normal-sized” bodies will all accelerate at the same rate towards the earth in a vacuum. However, we cannot say that the inverse square law is a “prediction” of Newtonian mechanics.

All we can do with the inverse square law is to validate whether its implications are observed in nature. Until General Relativity rolled up, nobody was able to find anything that convincingly contradicted it.

There is nothing wrong with making assumptions: any applied mathematical model has to make some. In the case of gravity, newer theories (e.g., General Relativity) started with different assumptions, and one of the implications of those assumptions was that the inverse square law was approximately correct.

Back to Macro

We can now look at neoclassical dynamic stochastic general equilibrium (DSGE) models with this in mind. What do we see?

The first thing to note that in order to qualify as DSGE model, it has to have all of the properties listed below. The second observation is that the neoclassical establishment blocked any macro theory paper from their journals unless it qualified (whether that policy has changed is unclear, since I don’t waste my time looking at neoclassical articles any more).

• Dynamic. The model must be specified in terms of agents that are forward looking, with decisions based on optimisations using forward values of economic variables. (There is the issue of whether we should conflate forward pricing with realised outcomes over calendar time.)

• Stochastic. The model must include random variables (although deterministic models can pop up as a special case). In practice, decision rules are based on the mathematical expectation operator of forward variables.

• General Equilibrium. All decisions are based on optimisations based on spot/forward pricing that are market-clearing levels.

I will skip the stochastic part, on the basis that it is really only of interest for formal discussions of the empirical testing of the models.

Market Clearing Requirements

It is a safe generalisation that the DSGE literature in practice spends as little text as possible in discussing equilibrium. I will not offer a suggestion as to why this is case, although I have strong opinions on the matter. Instead, I will discuss a point that I have never seen discussed: what are the requirements for market clearing of “expectations”?

We have a straightforward example of such a market: the rates market (e.g., fixed income not including products with credit risk). We can either trade or infer forward rates, which are the “risk neutral” expected values of the underlying spot rate. (E.g., the 5-year rate 5 years forward is the expected value of the random variable that is the 5-year spot rate starting 5 years in the future, using the risk-neutral probability distribution.) I apologise for dropping “risk neutral probability distribution” into my text, but it can be easily interpreted as the probability distribution implied by taking mid-market fixed income option prices.

So long as the reader understands how the rates market trades, they know exactly how any market based on “expected values” would trade.

We can then ask: what do we need for a market to function in the way posited by DSGE models? We need market participants to make binding orders that at the minimum specify a quantity and price. The exact mechanism by which the market is then “cleared” depends upon market structure, which can vary.

Why are these necessary?

• If orders are not binding, then participants can input whatever orders they want with no repercussions, and so they can go nuts. “I will buy one kajillion widgets at eleventy-billion dollars a piece!”

• If the orders do not specify a price or quantity, they are useless. (“I will pay four score nine-ten million dollars per widget!” — and buy zero widgets.)

Forecasts Cannot Be Cleared!

When mainstream economists talk about “inflation expectations,” they either refer to surveys, or possibly inflation pricing inferred (somehow) from inflation-linked markets. Putting aside the linker market, we immediately see that they do not meet the above requirements.

Returning to the rates market, we can immediately see the problem. The 1-year forward of the 10-year rate is an extremely useful figure, in that it gives us an economic breakeven for a directional position in that rate. Conversely, the consensus opinion of street economists for the forecast 10-year rate one year from now is a worthless piece of information (other than for providing entertainment).

DSGE models assume market clearing of forward values of prices like wages and the aggregate price level. You cannot clear opinions, you can only clear orders. The models assume that it is possible to trade wages and the aggregate consumer good forward.

Note that inflation-linked breakevens do not qualify: they represent pricing on a derivative instrument, and do not allow purchases of the underlying good. Furthermore, they at best cover the CPI basket, and not wages — which also have to be traded forward to match the models.

Inflation Expectations Are Simple in the Model World

Within the mathematical model, expected prices are very easy to deal with: you just look up the price quote in the market.

This means that there is no reason for agents to disagree about expected inflation and so forth: they can all see the market.

The only way that agents can disagree is that if they incorporate the equivalent of a term premium: the observed forward pricing is a risk-neutral measure, but they believe future realised values are somehow biased versus the risk neutral measure.

Such a variant poses problems for other parts of the model structure. Things like budget constraints use the risk-neutral expectation for future variables. After all, if every agent (including the government) can plant the expected values of future values wherever they want because of “risk premia,” those future values do not practically constrain the agent.

What Are The Testable Predictions?

What are the predictions made by DSGE models about inflation expectations?

• Everyone trades goods and wage contracts in the spot and forward markets.

• Everyone is aware of the market pricing for forward goods and wages.

• They make plans for the future based on that market pricing.

Well, it is clear that this is not the case, given the absence of forward markets for most goods, services, and wages.

My belief is that the standard defence against that observation is that neoclassical economists are mainly aware of the lack of required forward markets, yet observed behaviour is supposed to result from real world agents acting “as if” the forward markets exist.

The problem with this is straightforward: in the absence of forward markets, there is no reason for forecasts to clear, and so actual behaviour is invariably incoherent. Given the importance of large firms in the economy, we cannot pretend that there is an infinite number of agents whose errors cancel out — a few CEOs going nuts can cause a major disruption.

Agent-Based Models to the Rescue

I would argue that only an agent-based model of some sort could handle the issues raised by the incoherence of internal inflation forecasts. The model structure is sufficiently complex to allow for agents following complex decision rules while at the same time interacting in “simple” markets.

So?

Although mainstream economists enjoy making textual assertions about their models that are not backed by the mathematics, it is clear that DSGE models fit very uneasily with the types of “inflation expectations” we work with in the real world (mainly surveys). You need to have models in which agents have forecasts about the future, but without a market mechanism to enforce coherence of expectations. Such a model structure would not qualify as a DSGE model.

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(c) Brian Romanchuk 2021