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This paper specifies the panel data experimental design condition under which ordinary least squares, fixed effects, and random effects estimators yield identical estimates of treatment effects. This condition is relevant to the large body of laboratory experimental research that generates panel data. Although the point estimates and the true standard errors of the estimated average treatment effects are identical across the three estimators, the estimated standard errors differ. A standard F test as well as asymptotic reasoning guide the choice of which estimated standard errors are the appropriate ones to use for statistical inference.

Symmetric experimental designs: conditions for equivalence of panel data estimators