Bias Correction in Dynamic Panels under Time Series Misspecification

Abstract

This paper considers higher-order autoregressive (AR(p)) panel models with fixed effects, where the lag order p is unknown and possibly misspecified. A pooled least squares estimator is considered and its asymptotic biases are studied. Specifically, we first extend the N-asymptotic bias formula in Nickell (1981) to the case where the dynamics follow a general autoregressive form. Second, √(NT)-normalized limit distribution for the pooled estimators is developed that allows for lag order misspecification, when both N and T are large. Third, a higher order approximation for the bias up to order N^(-1)T^(-2) is explored. Besides the well-known endogeneity bias incurred by the within-transformation in dynamic fixed-effects models, additional bias under misspecification is analytically derived, which argues that model specification should precede any bias correction in dynamic panel modeling. We suggest a general form for bias correction, which specifically incorporates the lag order selection. A consistent lag order selection criterion is also proposed, which is more suitable for large panel system with fixed effects. Some extensions of the bias correction are also considered under exogenous variable, and the bias corrected short-run and long-run coefficients are discussed. Lastly, as an empirical application, a study on habit formation in consumption preferences is presented using U.S. state-level data.