Non-Parametric identification of stationary dynamic discrete choice models
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We provide new non-parametric identification results for stationary dynamic discrete choice models, where both the flow utilities and the distribution of unobserved shocks are fully non-parametric. Our main identification result establishes that a multinomial choice model is non-parametrically identified when there is a special regressor that (i) has a known derivative in the utility function (e.g., enters utility quasi-linearly); (ii) only affects the evolution of the other variables indirectly through the policy function; and (iii) exhibits a type of bounded persistence. To our knowledge, this is the first non-parametric identification result for stationary models that does not require any state variable to exhibit a form of serial independence. Our identification arguments map conditional choice probabilities and the state transition process into structural primitives, and they can be applied to models with persistent unobserved heterogeneity. Our identification results have broad applicability in practice, since candidate variables for the special regressor are already common in the empirical literature.