Latent indices in assortative matching models

Abstract

A large class of two-sided matching models that include both transferable and non-transferable utility result in positive assortative matching along a latent index. Data from matching markets, however, may not exhibit perfect assortativity due to the presence of unobserved characteristics. This paper studies the identification and estimation of such models. We show that the distribution of the latent index is not identified when data from one-to-one matches are observed. Remarkably, the model is nonparametrically identified using data in a single large market when each agent on one side has at least two matched partners. The additional empirical content in many-to-one matches is demonstrated using simulations and stylized examples. We then derive asymptotic properties of a minimum distance estimator as the size of the market increases, allowing estimation using dependent data from a single large matching market. The nature of the dependence requires modification of existing empirical process techniques to obtain a limit theorem.

Demand Analysis Using Strategic Reports: An Application to a School Choice Mechanism

“…A growing literature is interested in methods of analyzing preferences in matching markets, usually using pairwise stability (Choo and Siow, 2006;Fox, 2010Fox, , 2017Chiappori et al, 2017;Agarwal, 2015;Diamond and Agarwal, 2016). In some cases, estimates are based on the strategic decision to engage in costly courting decisions (Hitsch et al, 2010).…”

Monte Carlo Inference on Two-Sided Matching Models

“…HereP(x s , x c ; Y, X) measures the proportion of students with characteristic x s which are matched with colleges with characteristic x c through matching Y. (See Diamond and Agarwal (2017) and Schwartz (2018) for the use of similar test statistics.) One may use some other features of the matchings.…”

“…One may use some other features of the matchings. For example, following Diamond and Agarwal (2017), we may consider…”

“…It is important to note that it is not a priori ensured that using the two criteria instead of one improves the power properties of the inference. However, Diamond and Agarwal (2017) demonstrated through simulations that using a combination of criteria such as in (7) can sharpen the accuracy of inference.…”

“…A recent body of literature develops empirical models of nontransferable utility. (See Menzel (2015) and Diamond and Agarwal (2017). ) This paper proposes a new approach of analyzing data from a large matching market.…”