Closed-Form Estimation of Dynamic Discrete Choice Models with Unobserved State Variables

Abstract

Suppose that individuals make forward-looking decisions based on endogenously evolving states, where econometricians do not observe the state variable, but instead observe noisy signals or proxies of them. Under this setting, we derive closed-form identification of the conditional choice probability (CCP) and the Markov law of state transition by explicitly solving relevant integral equations. Using the sample counterparts of these explicitly identified components of the Markov kernel, we develop a closed-form estimator of structural dynamic discrete choice models with unobserved state variables. Because of its closed form like the OLS, our estimator does not rely on high-dimensional numerical optimization, and therefore is readily applicable without any solution ambiguity. Monte Carlo simulations show that the estimator works well even with a small sample.