Identification and Estimation of a Dynamic Discrete Choice Model with an Endogenous Time-Varying Unobservable State Using Proxies

Abstract

This paper studies a dynamic discrete choice model including an unobservable state, which evolves by a hidden action of agents. First, this paper shows new nonparametric identification results for observable and unobservable conditional choice probabilities (CCPs) and an initial type probability in both stationary and nonstationary model. The new identification results show two periods of data (T = 2) is sufficient and invertibility assumption on model dynamics is not necessary when there are proxies for the unobservable state variable which satisfies certain conditions. The result contrasts with Hu and Shum (2012) which required at least four periods of data (T >= 4) and required the invertibility assumption. The subjective measures of attitudes and expectations can be examples of such proxy variables. If proxy variables are missing due to rotating module design, which is the common cause of missing attitude and expectation variables in Panel data, the identification can be obtained under stronger assumptions on the model dynamics. Second, this paper proposes a two-step estimator using proxy variables, which generalizes Arcidiacono and Miller (2011) to endogenize the dynamics of the unobservable state variable. The proposed estimator is root-n consistent and asymptotically normal, conditional on that the first stage EM algorithm is initialized not too far from the global optimum of the objective function. The Monte Carlo experiment shows that the estimator performs well even when proxy variables are missing due to rotating module design.