Monte Carlo Inference on Two-Sided Matching Models

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.

Schooling Choice, Labour Market Matching, and Wages

“…In particular, the additive structure of AKM implies that wages are monotone in firm type -an implication that is difficult to reconcile with equilibrium models of sorting with and without frictions (Eeckhout and Kircher (2011), Lopes de Melo ( 2018)). 6 For example, in Eeckhout and Kircher (2011), a lowtype worker can receive a lower wage at a high-type firm since the worker must implicitly 5 This idea of using a structural model to characterize the joint distribution of a discrete matching model that can then be used for inference on the model parameters builds from Kim, Schwartz, Song and Whang (2019). Although computationally intractable when the dimension of the parameter is large, this approach is attractive for inference on the matching technology parameter in the second stage of our approach.…”

“…This means that asymptotic inference approaches that appeal to the the law of large numbers and central limit theorems will not work. The approach we pursue builds on Kim, Schwartz, Song and Whang (2019) which discusses how inference in structural matching models are possible when knowledge of the matching process can be used to characterize the joint distribution of the observed matching. This paper shows how such a simulation-based inference approach, cumbersome when the dimension of the parameter space is high dimensional or complex, is useful for estimating a subset of the parameters in structural models with cross-sectional dependence.…”

“…This test statistic is similar to the one used inKim, Schwartz, Song and Whang (2019). See alsoDiamond and Agarwal (2017).29 In this example, we are implicitly assuming that the distribution of K is discrete and has M support points.…”