Dynamic Linear Panel Regression Models with Interactive Fixed Effects

2026-05-01

AI Summary

This study addresses dynamic linear panel models featuring interactive fixed effects and predetermined regressors, such as lagged dependent variables. Within a high-dimensional asymptotic framework where both cross-sectional and temporal dimensions diverge to infinity, the authors identify two distinct sources of asymptotic bias in the least squares estimator and develop corresponding bias-corrected estimators. They further construct corrected Wald, likelihood ratio (LR), and Lagrange multiplier (LM) test statistics and establish their asymptotic chi-squared distributions. Monte Carlo simulations demonstrate that the proposed approach substantially improves estimation accuracy and inference reliability in finite samples, effectively mitigating the bias inherent in conventional estimators.

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.

Problem

• dynamic panel data
• interactive fixed effects
• predetermined regressors
• asymptotic bias
• least squares estimator

Innovation

• interactive fixed effects
• predetermined regressors
• bias correction
• asymptotic theory
• panel regression