Abstract
This paper considers two-sided matching models with nontransferable utilities, with one side having homogeneous preferences over the other side. When one observes only one or several large matchings, despite the large number of agents involved, asymptotic inference is difficult because the observed matching involves the preferences of all the agents on both sides in a complex way, and creates a complicated form of cross-sectional dependence across observed matches. When we assume that the observed matching is a consequence of a stable matching mechanism with homogeneous preferences on one side, and the preferences are drawn from a parametric distribution conditional on observables, the large observed matching follows a parametric distribution. This paper shows in such a situation how the method of Monte Carlo inference can be a viable option. Being a finite sample inference method, it does not require independence or local dependence among the observations which are often used to obtain asymptotic validity. Results from a Monte Carlo simulation study are presented and discussed.
Highlights
Two-sided matching models have been widely used to study various interactions among people and firms
When a college and a group of students prefer to be matched more than their alternatives, this match limits the set of students available to other colleges and the set of colleges available to other students. This strategic interdependence potentially creates a nonstandard pattern of stochastic dependence among matches and makes asymptotic inference difficult, because the stochastic dependence is not in the form of weak spatial dependence or conditional independence much studied in the literature of asymptotic inference with cross-sectionally dependent data
This paper proposes Monte Carlo inference for a large matching model
Summary
Two-sided matching models have been widely used to study various interactions among people and firms. The assumption of one-sided homogeneity of preferences in this paper is made mainly to ensure an explicit form of a unique stable matching mechanism that underlies the matching data. Monte Carlo inference approach of this paper without assuming one-sided homogeneity of preferences. The major limitation of this paper’s approach is the assumption that we observe the entire set of players in the large matching game This assumption is frequently used in many game-theoretic models, and hard to remove, because without this assumption, the payoff specification involves actions or characteristics of players that are not observed by the econometrician and one needs to assume a particular way the players are sampled in each game.. It would be good to relax this requirement so that multiple stable matchings are potentially allowed in the model This assumption of homogeneity in preferences of one side is certainly restrictive, and yet this asymmetry of preference heterogeneity between the two sides reflects various many-to-one matching markets in practice. In Appendix A, we provide a simple algorithm that generates a matching based on a serial dictatorship mechanism
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