Inference in dynamic discrete choice problems under local misspecification

Single‐agent dynamic discrete choice models are typically estimated using heavily parametrized econometric frameworks, making them susceptible to model misspecification. This paper investigates how misspecification affects the results of inference in these models. Specifically, we consider a local misspecification framework in which specification errors are assumed to vanish at an arbitrary and unknown rate with the sample size. Relative to global misspecification, the local misspecification analysis has two important advantages. First, it yields tractable and general results. Second, it allows us to focus on parameters with structural interpretation, instead of “pseudo‐true” parameters. We consider a general class of two‐step estimators based on the K‐stage sequential policy function iteration algorithm, where K denotes the number of iterations employed in the estimation. This class includes Hotz and Miller ()'s conditional choice probability estimator, Aguirregabiria and Mira ()'s pseudo‐likelihood estimator, and Pesendorfer and Schmidt‐Dengler ()'s asymptotic least squares estimator. We show that local misspecification can affect the asymptotic distribution and even the rate of convergence of these estimators. In principle, one might expect that the effect of the local misspecification could change with the number of iterations K. One of our main findings is that this is not the case, that is, the effect of local misspecification is invariant to K. In practice, this means that researchers cannot eliminate or even alleviate problems of model misspecification by choosing K.