Estimation of Time-invariant Effects in Static Panel Data Models

This paper proposes the Fixed Effects Filtered (FEF) and Fixed Effects Filtered instrumental variable (FEF-IV) estimators for estimation and inference in the case of time-invariant effects in static panel data models when N is large and T is fixed. It is shown that the FEF and FEF-IV estimators are √N-consistent, and asymptotically normally distributed. The FEF estimator is compared with the Fixed Effects Vector Decomposition (FEVD) estimator proposed by Plumper and Troeger (2007) and conditions under which the two estimators are equivalent are established. It is also shown that the variance estimator proposed for FEVD estimator is inconsistent and its use could lead to misleading inference. Alternative variance estimators are proposed for both FEF and FEF-IV estimators which are shown to be consistent under fairly general conditions. The small sample properties of the FEF and FEF-IV estimators are investigated by Monte Carlo experiments, and it is shown that FEF has smaller bias and RMSE, unless an intercept is included in the second stage of the FEVD procedure which renders the FEF and FEVD estimators identical. The FEVD procedure, however, results in substantial size distortions since it uses incorrect standard errors. We also compare the FEF-IV estimator with the estimator proposed by Hausman and Taylor (1981), when one of the time-invariant regressors is correlated with the fixed effects. Both FEF and FEF-IV estimators are shown to be robust to error variance heteroskedasticity and residual serial correlation.