In this paper we consider the estimation of a dynamic panel autoregressive (AR) process of possibly infinite order in the presence of individual effects. We employ double asymptotics under which both the cross-sectional sample size and the length of time series tend to infinity and utilize the sieve AR approximation with its lag order increasing with the sample size. We establish the consistency and asymptotic normality of the fixed effects estimator and propose bias-corrected fixed effects estimator based on theoretical asymptotic bias term. The properties of the generalized method of moments estimator and Hayakawa’s instrumental variables estimator are also examined. Monte Carlo simulations demonstrate the usefulness of bias correction. As an illustration, proposed methods are applied to dynamic panel estimation of the law of one price deviations among US cities.