What’s the significance of Arrow & Debreu’s canonical article, “Existence of an Equilibrium for a Competitive Economy” (1951)? According to one school of thought, which is well summarized by Kartik Athreya in Big Ideas in Macroeconomics (2013), Arrow-Debreu (and McKenzie) is the “bedrock” on which mainstream macroeconomics has been constructed. The implicit premise of this body of work, which, on Athreya’s view, includes the best of both New Classical and New Keynesian Economics, is that real-world economies can be usefully modeled within a general equilibrium framework in which all markets clear.
According to a different school of thought, however, Arrow-Debreu is more profitably understood as a compendium of the stringent conditions that must be satisfied if, as Arrow’s collaborator, Frank Hahn put it, there are to be no “Keynesian problems.” Although this latter scheme of thought seems to have petered out (Hahn isn’t even mentioned in Athreya’s book), it’s nevertheless an avenue worth exploring.
Kenneth Arrow, himself, has been asked on several occasions about the scheme of thought described in Athreya’s book. In 1995, in an interview conducted at the Federal Reserve Bank of Minnesota, Arrow was asked whether he was surprised by the advances made by New Classical economists who were “greatly influenced by your [i.e., Arrow’s] work in the 1950s in general equilibrium.” Arrow replied,
“The vision I had that wasn't articulated in my articles exactly was that the macroeconomy was the disequilibrium phenomenon. The idea that we could interpret economic fluctuations as an equilibrium phenomenon was something that did not cross my mind. And I'm still not sure that the disequilibrium interpretation isn't more appropriate, although much more has been gotten out of this equilibrium theory than I would have ever dreamt.”
More than a decade later, in an interview published in MPRA (2005), Arrow was asked about a forthcoming article in the Journal of Political Economy, "New Deal Policies and the Persistence of the Great Depression: A General Equilibrium Analysis," by Harold Cole and Lee Ohanian, which argues that large fluctuations, like the Great Depression, may be the result of poor policy in a general equilibrium framework. Arrow’s response,
“Do you know their explanation for depression? That the total factor productivity in 1932 was 24% lower, so they say, than it was in 1929. That's what explains the depression, as they see it. In their model, that drop in productivity is exogenous. In my book that's not an explanation.”
Ohanian applied the same general equilibrium model to explain the Great Recession in the U.S., though in this case the culprit isn’t a decline in total productivity, but a decline in hours worked, which Ohanian attributes to a sudden increase in the marginal value of leisure relative to the marginal product of labor, leading to a voluntary reduction in hours worked. Perhaps Arrow would now find this “equilibrium” approach more congenial, but in 1995, he said,
“I do think the interpretation of unemployment specifically is not well represented in the equilibrium models. I don't believe that unemployment is all voluntary, by anticipation of future wage movements or this sort of thing. I know you can modify the models by taking into account the indivisibilities, but I don't really think that people are voluntarily unemployed. When a job is offered, not so much today but say a few years ago, you would have had many applicants for it--people who do not seem to be conspicuously differently qualified than those who are now working.”