Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure

TLDR

The paper introduces a new method for estimation and inference in panel data models with a general multifactor error structure. The method filters individual regressors with cross‑section averages to remove common factor effects, then estimates parameters by least squares on auxiliary regressions augmented with these averages, yielding common correlated effects (CCE) estimators whose asymptotic distributions are derived. Monte Carlo experiments show that the CCE estimators perform well in small samples, maintaining satisfactory properties even with substantial heterogeneity, dynamics, and modest N and T.

Abstract

This paper presents a new approach to estimation and inference in panel data models with a general multifactor error structure. The unobserved factors and the individual-specific errors are allowed to follow arbitrary stationary processes, and the number of unobserved factors need not be estimated. The basic idea is to filter the individual-specific regressors by means of cross-section averages such that asymptotically as the cross-section dimension (N) tends to infinity, the differential effects of unobserved common factors are eliminated. The estimation procedure has the advantage that it can be computed by least squares applied to auxiliary regressions where the observed regressors are augmented with cross-sectional averages of the dependent variable and the individual-specific regressors. A number of estimators (referred to as common correlated effects (CCE) estimators) are proposed and their asymptotic distributions are derived. The small sample properties of mean group and pooled CCE estimators are investigated by Monte Carlo experiments, showing that the CCE estimators have satisfactory small sample properties even under a substantial degree of heterogeneity and dynamics, and for relatively small values of N and T.