  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
(1993)'s conditional choice probability estimator, Aguirregabiria and Mira
(2002)'s pseudo-likelihood estimator, and Pesendorfer and Schmidt-Dengler
(2008)'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,
i.e., 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 changing K.
