The two-way Mundlak estimator

Abstract

Mundlak shows that the fixed effects estimator is equivalent to the random effects estimator in the one-way error component model once the random individual effects are modeled as a linear function of all the averaged regressors over time. In the spirit of Mundlak, this paper shows that this result also holds for the two-way error component model once the individual and time effects are modeled as linear functions of all the averaged regressors across time and across individuals. Wooldridge also shows that the two-way fixed effects estimator can be obtained as a pooled OLS with the regressors augmented by the time and individual averages and calls it the two-way Mundlak estimator. While Mundlak used GLS rather than OLS on this augmented regression, we show that both estimators are equivalent for this augmented regression. This extends Baltagi’s results from the one-way to the two-way error component model. The F test suggested by Mundlak to test for this correlation between the random effects and the regressors generate a Hausman type test that is easily generalizable to the two-way Mundlak regression. In fact, the resulting F-tests for the two-way error component regression are related to the Hausman type tests proposed by Kang for the two-way error component model.