The Equivalence of Panel Data Estimators under Orthogonal Experimental Design

This paper demonstrates the equivalence between pooled OLS, Fixed Effects, and Random Effects estimates when applied to data generated from an orthogonal experimental design under certain conditions. We show that the point estimates of the treatment effects are identical between these three panel data estimators but that the estimated standard errors differ. Specifically, the estimated variance covariance matrices are identical between FE and RE but differ from that of OLS. Despite the equivalence it is meaningful to test for OLS vs FE/RE because the error distributional assumptions are different.