Partial Identification in Matching Models for the Marriage Market

Abstract

We study partial identification of the preference parameters in the one-to-one matching model with perfectly transferable utilities. We do so without imposing parametric distributional assumptions on the unobserved heterogeneity and with data on one large market. We provide a tractable characterisation of the identified set under various classes of nonparametric distributional assumptions on the unobserved heterogeneity. Using our methodology, we re-examine some of the relevant questions in the empirical literature on the marriage market, which have been previously studied under the Logit assumption. Our results reveal that many findings in the aforementioned literature are primarily driven by such parametric restrictions.

Counterfactual Sensitivity and Robustness

“…Overall, our findings are complementary to Gualdani and Sinha (2022) who performed a nonparametric reanalysis of CSW using the PIES methodology of Torgovitsky (2019b). Although they did not derive nonparametric bounds on the marital education premium itself, only terms that contribute to it, they found no evidence of an increase in premiums across cohorts.…”

“…There is also a literature deriving nonparametric bounds in specific latent variable models. Examples include Manski (2007, 2014), Allen and Rehbeck (2019), Tebaldi, Torgovitsky, and Yang (2022), Lafférs (2019), Torgovitsky (2019a), and Gualdani and Sinha (2022). Most closely related is Norets and Tang (2014), who constructed identified sets of counterfactual conditional choice probabilities (CCPs) in dynamic binary choice models.…”

Identification and Estimation in Many‐to‐One Two‐Sided Matching Without Transfers

“…There is also a close relationship between the one-to-one TU matching model (Choo and Siow (2006), Diamond and Agarwal (2017), Fox (2010), Galichon and Salanie (2022), Gualdani and Sinha (2023), Sinha (2015)) and the many-to-one NTU matching model considered here. Market-clearing college cutoffs in our setting play the role of marketclearing shadow prices, although the endogenous cutoffs do not determine how the surplus is split among the agents.…”

Semi-nonparametric models of multidimensional matching: an optimal transport approach

“…Dupuy and Galichon (2014) extend this framework to continuous types. Galichon and Salanié (2022) allow for non-logit parametric distributions of unobserved heterogeneity and Gualdani and Sinha (2023) show partial identification of the systemic surplus under nonparametric assumptions. These papers rely on the separability assumption that unobserved heterogeneity does not have interactions in generating the surplus.…”