The Fed’s macroeconomic model

There has been some comment on the decision of the US central bank (the Fed) to publish its main econometric model in full. In terms of openness I agree with Tony Yates that this is a great move, and that the Bank of England should follow. The Bank publishes some details of its model (somewhat belatedly, as I noted here), but as Tony argues this falls some way short of what is now provided by the Fed.

However I think Noah Smith makes the most interesting point: unlike the Bank's model, the model published by the Fed is not a DSGE model. Instead, it is what is often called a Structural Econometric Model (SEM): a pretty ad hoc mixture of theory and econometric estimation that would not please either a macro theorist or a time series econometrician. As Noah notes, they use this model for forecasting and policy analysis. Noah speculates that the Fed’s move to publish a model of this kind indicates that they are perhaps less embarrassed about using a SEM than they once were. I’ve no idea if this is true, but for most academic macroeconomists it raises a puzzling question - why are they still using this type of model? If the Bank of England can use a DSGE model as their core model, why doesn’t the Fed?

I have discussed the question of what type of model a central bank should use before. In addition, I have written many posts (most recently here) advocating the advantages of augmenting DSGE models and VARs with this kind of middle way approach. For various reasons, this middle way approach will be particularly attractive to a policy making organisation like a central bank, but I also think that a SEM can play a role in academic analysis. For the moment, though, let me just focus on policy analysis by policy makers.

Consider a particular question: what is the impact of a temporary cut in income taxes? What kind of methods should an economist employ to answer this question? We could estimate reduced forms/VARs relating variables of interest (output, inflation etc) to changes in income taxes in the past. However there are serious problems with this approach. The most obvious is that the impact of past changes in taxes will depend on the reaction of monetary policy at the time, and whether monetary policy will act in a similar way today. Results will also depend on how permanent past changes in taxes were expected to be. I would not want to suggest that these issues make reduced form estimation a waste of time, but they do indicate how difficult it will be to get a good answer using this approach. Similar problems arise if we relate growth to debt, money to prices (a personal reflection here) and so on. Macro reduced form analysis relating policy variables to outcomes is very fragile.

An alternative would be for the economist to build a DSGE model, and simulate that. This has a number of advantages over the reduced form estimation approach. The nature of the experiment can be precisely controlled: the fact that the tax cut is temporary, how it is financed, what monetary policy is doing etc. But any answer is only going to be as good as the model used to obtain it. A prerequisite for a DSGE model is that all relationships have to be microfounded in an internally consistent way, and there should be nothing ad hoc in the model. In practice that can preclude including things that we suspect are important, but that we do not know exactly how to model in a microfounded manner. We model what we can microfound, not what we can see.

A specific example that is likely to be critical to the impact of a temporary income tax cut is how the consumption function treats income discounting. If future income is discounted at the rate of interest, we get Ricardian Equivalence. Yet this same theory tells us that the marginal propensity to consume (mpc) out of windfall gains in income is very small, and yet there is a great deal of evidence to suggest the mpc lies somewhere around a third or more. (Here is a post discussing one study from today’s Mark Thoma links.) DSGE models can try and capture this by assuming a proportion of ‘income constrained’ consumers, but is that all that is going on? Another explanation is that unconstrained consumers discount future labour income at a much greater rate than the rate of interest. This could be because of income uncertainty and precautionary savings, but these are difficult to microfound, so DSGE models typically ignore this.

The Fed model does not. To quote: “future labor and transfer income is discounted at a rate substantially higher than the discount rate on future income from non-human wealth, reflecting uninsurable individual income risk.” My own SEM that I built 20+ years ago, Compact, did something similar. My colleague, John Muellbauer, has persistently pursued estimating consumption functions that use an eclectic mix of data and theory, and as a result has been incorporating the impact of financial frictions in his work long before it became fashionable.

So I suspect the Fed uses a SEM rather than a DSGE model not because they are old fashioned and out of date, but because they find it more useful. (Actually this is a little more than a suspicion.) Now that does not mean that academics should be using models of this type, but it should at least give pause to those academics who continue to suggest that SEMs are a thing of the past.