In a recent post, Paul Krugman used a well known Tobin quote: it takes a lot of Harberger triangles to fill an Okun gap. For non-economists, this means that the social welfare costs of resource misallocations because prices are ‘wrong’ (because of monopoly, taxation etc) are small compared to the costs of recessions. Stephen Williamson takes issue with this idea. His argument can be roughly summarised as follows:
1) Keynesian recessions arise because prices are sticky, and therefore 'wrong', so their costs are not fundamentally different from resource misallocation costs.
2) Models of price stickiness exaggerate these costs, because their microfoundations are dubious.
3) If the welfare costs of price stickiness were significant, why are they not arbitraged away?
I’ve heard these arguments, or variations on them, many times before. So lets see why they are mistaken, taking the points in roughly reverse order.
Keynesian recessions arise because of deficient demand. If you want to think of this as being because some price is wrong, in my view that price is the real interest rate. Now flexible wages and prices might get you the right real interest rate, either because they encourage monetary policy to do the right thing (by changing inflation), or because a particular monetary policy combines with inflation expectations to generate the appropriate real interest rate. However when nominal interest rates hit zero and there are inflation targets, flexible prices may not be enough (as argued here), so there may be no flexible price solution that gets rid of the costs of recession. At the very least, that suggests that recessions are a bit different from, say, the costs of monopoly or distortionary taxation. It also tells you why they cannot be arbitraged away by the actions of individuals.(See also Nick Rowe on this.)
What we have in a recession is a coordination problem. If everyone were to spend more, the additional output would generate incomes that matched the spending. If monetary policy cannot induce that coordination, then individuals could try and persuade someone with a great deal of spending power who could borrow freely and very cheaply to embark on additional spending. The obvious someone is the government, and the real puzzle is why governments have been so reluctant to arbitrage away recessions in this way.
The second point is horribly wrong, and it explains the title of this post. The problem with modelling price rigidity is that there are too many plausible reasons for this rigidity - too many microfoundations. (Alan Blinder’s work is a classic reference here.) Microfounded models typically choose one for tractability. It is generally possible to pick holes in any particular tractable story behind price rigidity (like Calvo contracts). But it does not follow that these models of Keynesian business cycles exaggerate the size of recessions. It seems much more plausible to argue completely the opposite: because microfounded models typically only look at one source of nominal rigidity, they underestimate its extent and costs.
I could make the same point in a slightly different way. Lets suppose that we do not fully understand what causes recessions. What we do understand, in the simple models we use, accounts for small recessions, but not large ones. Therefore, large recessions cannot exist. The logic is obviously faulty, but too many economists argue this way. There appears to be a danger in only ‘modelling what we understand’ that modellers can go on to confuse models with reality.
Lets move from wage and price stickiness to the major cost of recessions: unemployment. The way that this is modelled in most New Keynesian set-ups based on representative agents is that workers cannot supply as many hours as they want. In that case, workers suffer the cost of lower incomes, but at least they get the benefit of more leisure. Here is a triangle maybe (see Nick Rowe again.) Now this grossly underestimates the cost of recessions. One reason is heterogeneity: many workers carry on working the same number of hours in a recession, but some become unemployed. Standard consumer theory tells us this generates larger aggregate costs, and with more complicated models this can be quantified. However the more important reason, which follows from heterogeneity, is that the long term unemployed typically do not think that at least they have more leisure time, so they are not so badly off. Instead they feel rejected, inadequate, despairing, and it scars them for life. Now that may not be in the microfounded models, but that does not make these feelings disappear, and certainly does not mean they should be ignored.
It is for this reason that I have always had mixed feelings about representative agent models that measure the costs of recessions and inflation in terms of the agent’s utility. In terms of modelling it has allowed business cycle costs to be measured using the same metric as the costs of distortionary taxation and under/over provision of public goods, which has been great for examining issues involving fiscal policy, for example. Much of my own research over the last decade has used this device. But it does ignore the more important reasons why we should care about recessions. Which is perhaps OK, as long as we remember this. The moment we actually think we are capturing the costs of recessions using our models in this way, we once again confuse models with reality.
 A classic example comes from Robert Lucas. This includes the rather unfortunate statement that the “central problem of depression prevention has been solved”, but I don’t think that should be used as evidence against the more substantive claim of the paper, which is that the gains from stabilising the business cycle are relatively small. This assertion has been criticised even if we stick with New Keynesian representative agent models (see this paper by Canzoneri, Cumby and Diba), but the problems I outline below are more fundamental.
 For non-economists: twenty years ago most Keynesian analysis measured the success of policy (social welfare) by how well it stabilised inflation and the output gap, and the relative importance of inflation compared to output was a ‘choice for policy makers’. Since work by Michael Woodford, a similar measure of social welfare can be derived from the utility of individual agents, often using pages of maths, but the importance of output compared to inflation is then a function of this utility and the model’s structure and parameters.