Winner of the New Statesman SPERI Prize in Political Economy 2016

Saturday 4 May 2013

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.


  1. The problem is that when you do micro-found things properly, the results may not always line up with your prior intuition. Thijs van Rens has a new paper in which he looks at costs of business cycles in a world of permanent differences in "training costs". When fluctuations are large, in booms even people who are very difficult to train get hired, and since once they're trained, they're as good as anyone else, they may remain employed for many cycles. As a result, van Rens shows that in this heterogeneous world, large business cycles are actually good for aggregate welfare, since they permit these "difficult-to-train" people occasional spells of employment. Now of course, one can quibble with the model (if heterogeneity is in productivity, not in training costs, then the "bad" workers would be fired in the first bust following the boom in which they were hired), but one needs the model there in the first place to discuss the merits of these quibbles.

    (None of this lessens your arguments in favour of demonstrating robustness of results to different welfare functions though, which seems universally desirable.)

    1. Tom - I entirely agree with your first point. I learnt a great deal from writing the paper I mentioned, and it repeatedly showed me that my intuition was not well thought through. As I tried to make clear in the post, I am not attacking the usefulness of deriving social welfare from utility, but the unwillingness to depart from a microfoundations purist position. I'm glad to see from your last sentence that you agree.

  2. If something is costly, why cannot it be modelled as a part of DSGE?

    1. One of the characteristics of the microfoundations behind DSGE models is that they are very simple, and very conventional. Perhaps it does not have to be this way, but it is interesting to ask why DSGE models tend to be very conservative in the micro that gets used.

  3. Please help.... Textbook microeconomics tells us that individual utility functions can only be aggregated into a social welfare function if they are of the Gorman Polar form. Is this result lost on DSGE macro?

    1. The Gorman form is about the aggregation of different individuals into one representative individual. It simplifies your welfare analysis, but is by no means necessary.

    2. Not so sure.... social welfare function and representative consumer are very specific concepts in micro theory. See section 4.D of MWG

  4. Simon: in your paper, you show that when departing from Gali and Monacelli's strict assumptions (e.g. about intertemporal elasticity) in the small open economy, the loss function's *relative* weight on inflation falls. This is because a relaxation of the standard assumptions introduces a bunch of new arguments to the loss function (e.g. the terms of trade, and some other covariance terms), and these gain importance while inflation loses importance.

    In that paper, you do not take into account the costs of unemployment, but you do open up welfare analysis to consider losses accruing to a wider set of economic frictions than had previously been considered. What is your take on the fact that that exercise lowers the importance of the costs of inflation, but without increasing the importance of the costs of unemployment? Does that count as an improvement in loss-function analysis, or is it still in the wrong ballpark?

  5. "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."

    That's not in itself enough to make the output gap important, as long as you assume that policy only changes the variance and not the mean of output/employment, which IMHO (and Larry Summers') is the real elephant in the room.

    IIRC there is an example in Romer's textbook showing that, under these assumptions, there is no gain at all from reducing the variance of the output gap/unemployment - you are just spreading the same amount of pain out more smoothly in the aggregate, which is of no comfort to the individuals concerned.

  6. It is remarkable how ad hoc all the arguments and assumptions are in the article above and the thread: 'in principle', 'the microfoundations we use are not very good', 'as long as you assume', 'optimal individual behaviour (Help. Do we still believe in this neo classical nonsense?)' 'Utility' lacks, as Samuelson rightly stated, proper definition and measurement and Samuelson's revealed preference has not saved it either - as preferences are neither transitive nor stable. Please tell me if you now anything which even vaguely resembles the precision and consistency of the SNA, when it comes to the definition and measurement of social welfare functions. I strongly advise to read a book about actual consumer behaviour, these scientists left the neo-classical consumer many, many decades ago as it does not help them at all to sell stuff. We can do so much better.

    Merijn Knibbe


Unfortunately because of spam with embedded links (which then flag up warnings about the whole site on some browsers), I have to personally moderate all comments. As a result, your comment may not appear for some time. In addition, I cannot publish comments with links to websites because it takes too much time to check whether these sites are legitimate.