Dynamic Linear Panel Regression Models with Interactive Fixed Effects

TL;DR

This paper develops asymptotic theory and bias correction methods for linear panel regression models with interactive fixed effects and predetermined regressors, applicable when both cross-sectional units and time periods are large.

Contribution

It introduces bias correction techniques for the LS estimator and classical tests in dynamic linear panel models with interactive fixed effects.

Findings

Bias correction improves estimator accuracy in large samples.

Corrected test statistics follow chi-squared distribution asymptotically.

Monte Carlo simulations confirm finite-sample effectiveness of bias corrections.

Abstract

We analyze linear panel regression models with interactive fixed effects and predetermined regressors, for example lagged-dependent variables. The first-order asymptotic theory of the least squares (LS) estimator of the regression coefficients is worked out in the limit where both the cross-sectional dimension and the number of time periods become large. We find two sources of asymptotic bias of the LS estimator: bias due to correlation or heteroscedasticity of the idiosyncratic error term, and bias due to predetermined (as opposed to strictly exogenous) regressors. We provide a bias-corrected LS estimator. We also present bias-corrected versions of the three classical test statistics (Wald, LR, and LM test) and show their asymptotic distribution is a chi-squared distribution. Monte Carlo simulations show the bias correction of the LS estimator and of the test statistics also work well for finite sample sizes.