A Nobel for Planning?

This is from Arindrajit Dube:

A Nobel for Planning?: “The combination of Shapley’s basic theory and Roth’s empirical investigations, experiments and practical design has generated a flourishing field of research and improved the performance of many markets,” said the committee awarding the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel.

The use of the word "market" in describing exchanges of every sort has become ubiquitous, even in cases where there is no actual price that helps clear the market or channel information. Perhaps due to this slippage, an interesting fact about the work receiving the award has been largely ignored. The concrete applications that are discussed as ways of "improving the performance of many markets"--such as matching residents to hospitals, matching donors to organs, and students to schools--are not really "markets." At least not if we think of markets as institutions where prices help clear supply and demand. Instead, they involve non-market interactions, where the matches are actually formed by centralized exchanges. In these situations, decentralized and uncoordinated matching can produce unstable and inefficient matches, and gains are possible from centralization of some sort. Sometimes the price may not exist because of legal restrictions, but in other cases the participants may voluntarily forego using prices, as it might conflict with other objectives. This is exactly where the Gale-Shapley algorithm can be useful in implementing a "stable" allocation: an allocation where no pair-wise trades exist which can make both parties better off, which is one notion of optimality. In other words, this and similar algorithms can help implement … gasp! … economic planning.

I know the word "planning" makes most of us feel uncomfortable--it surely produces many more whispers and giggles in economics seminars than terms like "aggregate demand" and "Keynes." But the reality is that the technologies involved in designing exchanges for matching parties without using actual prices is at the heart of planning. In fact, this should not be a particularly controversial view, even though I think it's largely a neglected one. (To my knowledge, the only person who has alluded to this is David Henderson, who bemoaned that this would all be irrelevant if we could just have prices for kidneys--and presumably college admissions; and suggested that next year's award go to "the free market.") Mathematically speaking, the Gale-Shapley algorithm is part of a class of optimal matching algorithms which is equivalent to the Monge-Kantorovich optimal transport solution (see here, here), a signature accomplishment of Soviet mathematics. Oh, and it also implements the hedonic price equilibrium--you know, the same one if kidneys really did have a price.

A final note. A popular view today is that it is not possible to implement an efficient allocation using planning because people don't have the incentives to reveal their true preferences to begin with, which makes this whole exercise rather pointless. A variant of this position was originally articulated by Austrian economists, including Ludwig von Mises, during the so called "socialist calculation" debate of the early 20th century. And in many cases this criticism rings true. However, it does not follow that the truthful revelation problem is ubiquitous. For example, it is interesting to note that Alvin Roth and Elliott Peranson show (both theoretically and empirically) that when implementing optimal matching, this problem may be smaller than one might imagine: when each applicant only interviews a small number of positions overall, the gains from strategic manipulation of preferences are small. This, too, has important implications for the "socialist calculation" debate, as it suggests that for a range of cases, a centralized exchange implementing planning without using prices can (and indeed does) implement relatively efficient allocations. And it can do so without having distributional effects such as rationing kidneys out of the reach of the 99 percent by using prices to allocate organs.

So when asked by our students and friends "what was the 'Nobel' all about?" we could do a lot worse than by answering "economic planning."

PS: For those who may not know, Leonid Kantorovich was a Soviet mathematician and economist who, among other things, helped invent the technique of linear programming while trying to fix the Soviet plywood sector. Let's say that he was not entirely successful in the latter venture, but was the only Soviet economist to win the "Nobel" in economics. For much more on the promises and failures of Soviet planning, use of shadow prices in planning, and other fun stuff, read Red Plenty. You could do a lot worse.