Local Identification in Markov Decision Models

Abstract

We provide necessary and sufficient conditions for the local identification of the finite dimensional parameters in a semiparametric dynamic discrete choice model under additive separability and conditional independence assumption (Rust (1987)). We show that the policy value approach commonly used in the two-step estimation methodologies has convenient features so that the conditional version of Rothenberg's (1971) parametric identification results can be readily applied. We provide results for both the single agent problems and a class of games of incomplete information. These conditions are easy to check under the extreme value distributional assumption and when the payoff function has a linear-in-parameter specification. Our approach does not depend on the discreteness of the control variable and can be used to derive analogous conditions in other Markov decision models. Our approach can also be used when the value of the discounting factor not known.