Handling Endogenous Regressors Using Copulas: A Generalization to Linear Panel Models with Fixed Effects and Correlated Regressors

Abstract

This article proposes a panel data generalization for a recently suggested instrumental variable‐free estimation method that builds on joint estimation. The author shows how the method can be extended to linear panel models by combining fixed-effects transformations with the common generalized least squares transformation to allow for heterogeneous intercepts. To account for between-regressor dependence, the author proposes determining the joint distribution of the error term and all explanatory variables using a Gaussian copula function, with the distinction that some variables are endogenous and the others are exogenous. The identification does not require any instrumental variables if the regressor–error relation is nonlinear. With a normally distributed error, nonnormally distributed endogenous regressors are therefore required. Monte Carlo simulations assess the finite sample performance of the proposed estimator and demonstrate its superiority to conventional instrumental variable estimation. A specific advantage of the proposed method is that the estimator is unbiased in dynamic panel models with small time dimensions and serially correlated errors; therefore, it is a useful alternative to generalized-method-of-moments-style instrumentation. The practical applicability of the proposed method is demonstrated via an empirical example.