Fixed-Effects Panel Data Models: To Cluster or Not to Cluster

Abstract

Fixed effects panel data models are not immune to problems caused by nonstationarity. Using Monte Carlo experiments, we find that OLS standard errors invariably fail to generate significance tests with correct size when either or both of the regressors are I(1). Clustered standard errors generate correct standard errors if the number of groups is 50 or more and the number of time series observations are 25 or more. With respect to unbalanced models in which an I(1) variable is regressed on an I(0) variable or vice-versa, clustering the standard errors will generate correct standard errors, but not for small values of N and T. We find that neither OLS nor clustered standard errors generate reliably sized significance tests in the case of heterogeneous panels in which the dependent variable, the independent variable, or both are mixes of stationary and nonstationary groups. This could be important given the well-known weakness of unit root tests and the fact that rejecting the null hypothesis in a panel unit root test implies only that one or more of the groups are stationary. First differencing is a simple solution, in which case OLS standard errors are preferred. However, first differences generate a short run model. For estimation in levels, clustered standard errors for relatively large N and T and a simulation or bootstrap approach for smaller samples appears to be the best method for significance tests in fixed effects models in the presence of nonstationary time series.