Testing whether group-level fixed effects are sufficient in panel data models

This presentation introduces a new command, xtfelevel, which implements a Hausman-type test to assess whether controlling for fixed effects at a more aggregate (group) level is sufficient for consistently estimating the coeacients on unit-specific, time-varying variables in linear panel-data models where units are nested within groups. The command builds on Papke and Wooldridge (2023), who develop a test of the null hypothesis that the probability limits of the fixed-effects estimators for a coefficient of interest are the same whether heterogeneity is controlled at the unit or group level. Rejection of the null suggests that unit-level fixed-effects estimation is required. xtfelevel extends this framework by comparing the unit-level fixed effects estimator with an IV estimator that allows the time-varying controls to be correlated with unit-level heterogeneity, while accounting for correlation between the variable of interest and group- level effects. This estimator yields results analogous to pooled OLS estimation of the Mundlak regression, where the time average of the variable of interest is first partialed out from the time averages of the controls. Under the null, the estimator can often be more efficient than the unit-level fixed effects estimator, especially when the variable of interest exhibits limited within-unit variation. This extension addresses a limitation in applying the usual Mundlak device to obtain more efficient estimates, as discussed by Wooldridge (2019). When the variable of interest is uncorrelated with the unit-level heterogeneity but is correlated with the time-varying controls that are themselves correlated with those effects, excluding its time mean to improve efficiency can lead to omitted variable bias.