We investigate the testable implications of the theory of stable matchings. We provide a characterization of the matchings that are rationalizable as stable matchings when agents' preferences are unobserved. The characterization is a simple nonparametric test for stability, in the tradition of revealed preference tests. We also characterize the observed stable matchings when monetary transfers are allowed and the stable matchings that are best for one side of the market: extremal stable matchings. We find that the theory of extremal stable matchings is observationally equivalent to requiring that there be a unique stable matching or that the matching be consistent with unrestricted monetary transfers.

We consider the identification of counterfactual distributions and treatment effects when the outcome variables and conditioning covariates are observed in separate datasets. Under the standard selection on observables assumption, the counterfactual distributions and treatment effect parameters are no longer point identified. However, applying the classical monotone re-arrangement inequality, we derive sharp bounds on the counterfactual distributions and policy parameters of interest.

Exploiting a rich panel data set on anti-ulcer drug prescriptions, we measure the effects of uncertainty and learning in the demand for pharmaceutical drugs. We estimate a dynamic matching model of demand under uncertainty in which patients learn from prescription experience about the effectiveness of alternative drugs. Unlike previous models, we allow drugs to have distinct symptomatic and curative effects, and endogenize treatment length by allowing drug choices to affect patients' underlying probability of recovery. We find that drugs' rankings along these dimensions differ, with high symptomatic effects for drugs with the highest market shares and high curative effects for drugs with the greatest medical efficacy. Our results also indicate that while there is substantial heterogeneity in drug efficacy across patients, learning enables patients and their doctors to dramatically reduce the costs of uncertainty in pharmaceutical markets.

This paper proposes a new semi‐parametric identification and estimation approach to multinomial choice models in a panel data setting with individual fixed effects. Our approach is based on cyclic monotonicity, which is a defining convex‐analytic feature of the random utility framework underlying multinomial choice models. From the cyclic monotonicity property, we derive identifying inequalities without requiring any shape restrictions for the distribution of the random utility shocks. These inequalities point identify model parameters under straightforward assumptions on the covariates. We propose a consistent estimator based on these inequalities.