Duality in dynamic discrete-choice models

Abstract

Using results from Convex Analysis, we investigate a novel approach to identification and estimation of discrete‐choice models that we call the mass transport approach. We show that the conditional choice probabilities and the choice‐specific payoffs in these models are related in the sense of conjugate duality, and that the identification problem is a mass transport problem. Based on this, we propose a new two‐step estimator for these models; interestingly, the first step of our estimator involves solving a linear program that is identical to the classic assignment (two‐sided matching) game of Shapley and Shubik (1971). The application of convex‐analytic tools to dynamic discrete‐choice models and the connection with two‐sided matching models is new in the literature. Monte Carlo results demonstrate the good performance of this estimator, and we provide an empirical application based on Rust's (1987) bus engine replacement model.

Identification With Additively Separable Heterogeneity

“…A closely related result has previously been exploited for identification in matching games (Galichon and Salanié ()) and dynamic discrete choice (Chiong, Galichon, and Shum ()) when is known. A related technique has been used for identification in a class of games (Kline (), Larsen and Zhang ()).…”

Partial Identification and Inference for Dynamic Models and Counterfactuals

“…is again derived only from G. When εit follows the type I extreme value distribution, φaj(p (x)) = log pa (x) − log pj (x). Chiong, Galichon, and Shum (2016) propose a novel approach that can calculate ψa and φaj for a broad set of distributions G (see also Dearing, 2019).…”

Linear IV Regression Estimators for Structural Dynamic Discrete Choice Models

“…13 The Arcidiacono-Miller Lemma can be derived from the Hotz-Miller inversion (Proposition 1 of . Chiong, Galichon, and Shum (2016) propose a novel approach that can calculate ψ a for a broad set of distributions F ε (see also Dearing, 2019).…”