A landmark market design paper, on school choice in NYC, by Abdulkadiroglu, Agarwal, and Pathak

When market design was young, it was a game played by game theorists.  As it matured, and we wanted market designs be adopted, implemented, and maintained, it became a kind of economic engineering. But for market design to become a fully mature part of economics, not only must designs move into practice, and be monitored and maintained, they must also be evaluated.*

So I find myself thinking again about this paper from the December AER that I already blogged about:

Abdulkadiroglu, Atila, Nikhil Agarwal, and Parag A. Pathak, “The WelfareEffects of Coordinated Assignment: Evidence from the New York City High SchoolMatch,”American Economic Review, 107(12), December 2017, 3635–3689.

I think of it as the third of three papers: the first two were about the engineering aspects of the NYC high school match, the first school choice design of its kind:

Abdulkadiroglu, Atila , Parag A. Pathak, and Alvin E. Roth, "The New York City High School Match," American Economic Review, Papers and Proceedings, 95,2, May, 2005, 364-367.

and

Abdulkadiroglu, Atila , Parag A. Pathak, and Alvin E. Roth, "Strategy-proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match,'' American Economic Review, 99, 5, Dec. 2009, pp1954-1978. 

Now, in this third paper, two of the original designers (Abdulkadiroglu and Pathak) together with one of the new generation of market design investigators  (Agarwal) evaluate the impact on students of the current centralized school choice system (it uses a deferred acceptance algorithm) in comparison to the decentralized ("uncoordinated") system it replaced.  

The new system produces a stable matching, which good evidence suggests is helpful in keeping the system healthy in the long term in a school system like NYC, in which the school principals are also strategic players.  But aside from being long lasting, how good is the system for students?

Using the (ordinal) rank order lists submitted by students in the new system, the paper measures welfare by estimating a cardinal random  utility model, with (cardinal) tradeoffs among school attributes being measured in terms of the additional distance a student is willing to travel to be at a more preferred school.

The uncoordinated system suffered from congestion, with many students having to be placed administratively in a school for which they had expressed no preference.  They find that these schools were by and large significantly less desirable.

They find that the new system improves welfare over the old by 80% of the gains that could be achieved by a utility-maximizing allocation made independent of other constraints. They further find that changes in the algorithm (e.g. choosing a different stable matching, among the multiple that arise from random tie-breaking) would have very little effect on welfare.

The biggest difference is that under the old system, only about half the students were placed in the "main round" (now occupied by the deferred acceptance algorithm), whereas in the new system this number immediately climbed to over 80% (with some additional subsequent gains). So students who used to be administratively assigned are now largely assigned instead to a school over which they have expressed a preference. That turns out to be very good for them.

Market design is coming of age...
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* Of course, not all steps in the market design process have to be accomplished by the same individuals, but in this case that's an extra plus.  And of course other  school choice markets have been investigated by these and other investigators, but in most cases those markets were not designed by economists, so that's another extra bonus here too, especially since features of the design (which encourage truthful reporting of preferences) add to the ability to estimate welfare gains.