CLOSED-FORM IDENTIFICATION OF DYNAMIC DISCRETE CHOICE MODELS WITH PROXIES FOR UNOBSERVED STATE VARIABLES

Abstract

Proxies for unobserved skills and technologies are increasingly available in empirical data. For dynamic discrete choice models of forward-looking agents where a continuous state variable is unobserved but its proxy is available, we derive closed-form identification of the structure by explicitly solving integral equations. In the first step, we derive closed-form identification of Markov components, including the conditional choice probabilities and the law of state transition. In the second step, we plug in these first-step identifying formulas to obtain primitive structural parameters of dynamically optimizing agents.