Demand Analysis for Matching Markets

The assignment of students to various schools in their district can have important implications for student achievement and student welfare. A large body of theoretical work in Economics studies the design of matching markets. Several school districts including New York, Chicago, Boston, Cambridge, Denver and New Orleans employ mechanisms in which students rank schooling options and a computerized algorithm matches students to schools. A similar mechanism is used to assign medical residents to residency training positions. The design and their implementation is based on theoretical insights for which Alvin E. Roth and Loyd Shapley were awarded the Nobel Prize in 2012. However, the empirical study of these markets is lagging. An important barrier to progress is methodological since most mechanisms still in use today do not make it safe for agents to report their true preferences. This fact may have important implications on student welfare, and fairness. The primary goal of the proposed research is to develop new methods for estimating preference models using data from matching markets, and apply them to analyze policy relevant questions that have been thus far theoretically and empirically intractable.

The proposed research will develop a new method for estimating a discrete choice model using reported preferences from an assignment mechanism where participants do not have the incentive to report their preferences truthfully. Previous research estimating preferences has largely been limited to settings where particular institutional/theoretical features support treating reported preferences as truthful or specific details of the mechanism provide partial information on preferences. Our baseline approach analyzes information that is revealed by assuming that the observed reports are optimal. We then analyze relaxations of this strong form of rationality to study what can be learned under weaker assumptions on agents' sophistication. The methodological analysis involves studying large sample properties of a two-step estimator, extending techniques from the literature on demand models to study non-parametric identification of the model, and comparing computational methods for implementing the estimator. As an application, the proposed research will study the elementary school admissions system in Cambridge, MA that uses a variant of the (old) Boston mechanism, which is susceptible to manipulation. Subsequently, we plan to compare preference estimates under varying assumptions on the sophistication to assess their sensitivity to economic assumptions.