Reigns of Error

The death of Kenneth Arrow has led lots of people to swap stories about their interactions with him. Larry Blume has posted several of these on facebook, including the following response to my own contribution (quoted with permission):

This story is not at all surprising; Ken read everything. I think I mentioned elsewhere that my last conversation with Ken, this past June, concerned The Theory of Moral Sentiments. He and Amartya Sen were taking turns quoting from it, from memory... I could recognize the quotes, but not respond in kind. Once in a conversation about Nash equilibrium and rational expectations, Ken wondered if I had read Merton on expectations - not Robert Jr.: https://www.jstor.org/stable/4609267. He also had a good stock of Shakespeare to call on.

The link is to a 1948 paper by the great sociologist Robert K. Merton (father of the Nobel-winning economist). Reading anything at all by Merton is an excellent use of one's time, so I went through this paper. It's extraordinary. Not only does Merton provide a very clear account of equilibrium beliefs, but goes on to point out that even when these beliefs are correct in a narrow sense, they can hold in place an incorrect understanding of the social world. To translate this into the contemporary language of economics, Merton points out that the play of equilibrium strategies can go hand in hand with a deeply erroneous understanding of the game.

Merton begins with an account of a Depression-era bank run that perfectly captures the multiple equilibrium logic he has in mind:

It is the year 1932. The Last National Bank is a flourishing institution. A large part of its resources is liquid without being watered. Cartwright Millingville has ample reason to be proud of the banking institution over which he presides. Until Black Wednesday. As he enters his bank, he notices that business is unusually brisk. A little odd, that, since the men at the A.M.O.K. steel plant and the K.O.M.A. mattress factory are not usually paid until Saturday. Yet here are two dozen men, obviously from the factories, queued up in front of the tellers' cages. As he turns into his private office, the president muses rather compassionately: "Hope they haven't been laid off in midweek. They should be in the shop at this hour."

But speculations of this sort have never made for a thriving bank, and Millingville turns to the pile of documents upon his desk. His precise signature is affixed to fewer than a score of papers when he is disturbed by the absence of something familiar and the intrusion of something alien. The low discreet hum of bank business has given way to a strange and annoying stridency of many voices. A situation has been defined as real. And that is the beginning of what ends as Black Wednesday -- the last Wednesday, it might be noted, of the Last National Bank.

You can see why Arrow saw in this a precursor to the concept of Nash equilibrium, the existence of which would be established just two years later. There are also echoes here of the Diamond and Dybvig model of bank runs, in which the multiple equilibrium nature of the problem finds formal expression.

But Merton doesn't stop there, he considers how the people expressing the described behavior interpret the situation they are in. And here he observes an important disparity between the manner in which the situation is viewed by the the participants themselves, as compared with its interpretation from the analytical viewpoint of the social scientist:

The self-fulfilling prophecy is, in the beginning, a false definition of the situation evoking a new behavior which makes the originally false conception come true. The specious validity of the self-fulfilling prophecy perpetuates a reign of error. For the prophet will cite the actual course of events as proof that he was right from the very beginning. (Yet we know that Millingville's bank was solvent, that it would have survived for many years had not the misleading rumor created the very conditions of its own fulfillment.) Such are the perversities of social logic.

So beliefs are correct in one sense, but at sharp variance with reality in another. Such "reigns of error" are not something we economists pay much attention to, with one very notable exception.

In his book The Anatomy of Racial Inequality Glenn Loury discusses the manner in which negative stereotypes about a group can become self-fulfilling through the incentive effects that the stereotypes themselves create. This is the phenomenon of statistical discrimination, introduced into the economics literature by none other than Kenneth Arrow. Like Merton, however, Loury is not content to simply identify the kinds of behaviors consistent with equilibrium beliefs. He wants to know how people with these beliefs will interpret the behaviors. And here he deploys the idea of biased social cognition, which can give rise to essentialist causal misattributions.

That is, behavior arising in equilibrium through the operation of incentives can be interpreted by casual observers as being a consequence of deep differences in character. And this has enormous consequences, since biased social cognitions can "cause some situations to appear anomalous, disquieting, contrary to expectation, worthy of further investigation, inconsistent with the natural order of things---while other situations appear normal, about right, in keeping with what one might expect, consistent with the social world as we know it."

Loury has argued elsewhere that the level of mass incarceration currently prevailing in the United States could not possibly be sustained were it not for its racial character. As long as essentialist interpretations of incentive-driven actions continue to be widespread, such high levels of confinement will not be seen as anomalous or disquieting, and will not give rise to urgent calls for action.

The economic method, for all its flaws, has one very important virtue: it shines a bright light on interests and incentives, and in doing so can challenge essentialist interpretations of social reality. But if this potential is to be realized, it is important to focus not just on the characterization of equilibrium behavior, but also on the reigns of error that distort our mental models of the underlying game.