Assessing the Consistency of the Fixed-Effects Estimator: A Regression-Based Wald Test

Under large-n and fixed-T panel data asymptotics, we develop a method to test a sufficient condition for the FE estimator’s consistency using a stacked regression framework. The resulting test exploits a previously unnoted relation between the fixed-effects estimator and the short- and long-differences estimators. It takes the familiar form of a panel-robust Wald test, but is also shown to be asymptotically equivalent to a GMM test. We provide a theoretical comparison between our test and two existing ones from the literature, which are shown to focus on generic strict exogeneity conditions instead of being specifically related to the FE estimator’s moment conditions. We investigate our test’s finite-sample properties in a simulation study, where we continue the comparison with the other tests. We show that our test has good finite-sample properties, especially if the estimator of the covariance matrix is based on a panel bootstrap. The practical use of our test is illustrated in two applications to existing data from the literature.