Inference in Dynamic Discrete Choice Problems under Local Misspecification

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Dynamic discrete choice models are typically estimated using heavily parametrized econometric frameworks, making them susceptible to model misspecification. This paper investigates how misspecification can affect the results of inference in these models. For tractability reasons, we consider a local misspecification framework in which specification errors are assumed to vanish with the sample size. However, we impose no restrictions on the rate at which these errors vanish. We consider a general class of two-stage estimators based on the K-step sequential policy function iteration algorithm, where K denotes the number of iterations employed in the estimation. This class includes Rust (1987)'s nested fixed point estimator, 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 asymptotic bias, asymptotic variance, and even the rate of convergence of these estimators. However, our main finding is that the effect of the local misspecification is invariant to the number of iterations K. In practice, this means that the choice of the number of iterations K should not be guided by concerns of model misspecification.

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  • Bugni, FA; Ura, T