Microfounded Social Welfare Functions

More on Beauty and Truth for economists

I have just been rereading Ricardo Caballero’s Journal of Economic Perspectives paper entitled “Macroeconomics after the Crisis: Time to Deal with the Pretense-of-Knowledge Syndrome”. I particularly like this quote:

The dynamic stochastic general equilibrium strategy is so attractive, and even plain addictive, because it allows one to generate impulse responses that can be fully described in terms of seemingly scientific statements. The model is an irresistible snake-charmer.

I thought of this when describing here (footnote [5]) Woodford’s derivation of social welfare functions from representative agent’s utility. Although it has now become a standard part of the DSGE toolkit, I remember when I had to really work through the maths for this paper. I recall how exciting it was, first to be able to say something about policy objectives that was more than ad hoc, and secondly to see how terms in second order Taylor expansions nicely cancelled out when first order conditions describing optimal individual behaviour were added.

This kind of exercise can tell us some things that are interesting. But can it provide us with a realistic (as opposed to model consistent) social welfare function that should guide many monetary and fiscal policy decisions? Absolutely not. As I noted in that recent post, these derived social welfare functions typically tell you that deviations of inflation from target are much more important than output gaps - ten or twenty times more important. If this was really the case, and given the uncertainties surrounding measurement of the output gap, it would be tempting to make central banks pure (not flexible) inflation targeters - what Mervyn King calls inflation nutters.

Where does this result come from? The inflation term in Woodford’s derivation of social welfare comes from relative price distortions when prices are sticky due to Calvo contracts. Let’s assume for the sake of argument that these costs are captured correctly. The output gap term comes from sticky prices leading to fluctuations in consumption and fluctuations in labour supply. Lucas famously argued [1] that the former are small. Again, for the sake of argument lets focus on fluctuations in labour supply.

Many DSGE models use sticky prices and not sticky wages, so labour markets clear. They tend, partly as a result, to assume labour supply is elastic. Gaps between the marginal product of labor and the marginal rate of substitution between consumption and leisure become small. Canzoneri and coauthors show here how sticky wages and more inelastic labour supply will increase the cost of output fluctuations: agents are now working more or less as a result of fluctuations in labour demand, and inelasticity means that these fluctuations are more costly in terms of utility. Canzoneri et al argue that labour supply inelasticity is more consistent with micro evidence.

Just as important, I would suggest, is heterogeneity. The labour supply of many agents is largely unaffected by recessions, while others lose their jobs and become unemployed. Now this will matter in ways that models in principle can quantify. Large losses for a few are more costly than the same aggregate loss equally spread. Yet I believe even this would not come near to describing the unhappiness the unemployed actually feel (see Chris Dillow here). For many there is a psychological/social cost to unemployment that our standard models just do not capture. Other evidence tends to corroborate this happiness data.

So there are two general points here. First, simplifications made to ensure DSGE analysis remains tractable tend to diminish the importance of output gap fluctuations. Second, the simple microfoundations we use are not very good at capturing how people feel about being unemployed. What this implies is that conclusions about inflation/output trade-offs, or the cost of business cycles, derived from microfounded social welfare functions in DSGE models will be highly suspect, and almost certainly biased.

Now I do not want to use this as a stick to beat up DSGE models, because often there is a simple and straightforward solution. Just recalculate any results using an alternative social welfare function where the cost of output gaps is equal to the cost of inflation. For many questions addressed by these models results will be robust, which is worth knowing. If they are not, that is worth knowing too. So its a virtually costless thing to do, with clear benefits.

Yet it is rarely done. I suspect the reason why is that a referee would say ‘but that ad hoc (aka more realistic) social welfare function is inconsistent with the rest of your model. Your complete model becomes internally inconsistent, and therefore no longer properly microfounded.’ This is so wrong. It is modelling what we can microfound, rather than modelling what we can see. Let me quote Caballero again

“[This suggests a discipline that] has become so mesmerized with its own internal logic that it has begun to confuse the precision it has achieved about its own world with the precision that it has about the real one.”

As I have argued before (post here, article here), those using microfoundations should be pragmatic about the need to sometimes depart from those microfoundations when there are clear reasons for doing so. (For an example of this pragmatic approach to social welfare functions in the context of US monetary policy, see this paper by Chen, Kirsanova and Leith.) The microfoundation purist position is a snake charmer, and has to be faced down.

[1] Lucas, R. E., 2003, Macroeconomic Priorities, American Economic Review 93(1): 1-14.