Fixed Effects Vector Decomposition: A Magical Solution to the Problem of Time Invariant Variables in Fixed Effects Models?

In “Efficient Estimation of Time Invariant and Rarely Changing Variables in Finite Sample Panel Analyses with Unit Fixed Effects,” Plümper and Troeger (2007), propose a three step procedure for the estimation of fixed effects models that, it is claimed, “provides the most reliable estimates under a wide variety of specifications common to real world data.” Their FEVD estimator is startlingly simple, involving three trivial steps, each requiring nothing more than ordinary least squares. Large gains in efficiency are claimed for cases of time invariant and slowly time varying regressors. A subsequent literature has compared the estimator to other estimators of fixed effects models, including Hausman and Taylor’s (1981) estimator, also (apparently) with impressive gains in efficiency. The article also claims to provide an efficient estimator for parameters on time invariant variables in the fixed effects model. None of the claims are correct. The FEVD estimator simply reproduces (identically) the linear fixed effects (dummy variable) estimator then substitutes an inappropriate covariance matrix for the correct one. The consistency result follows from the fact that OLS in the FE model is consistent. The “efficiency” gains are illusory. The claim that the estimator provides an estimator for the coefficients on time invariant variables in a fixed effects model is also incorrect. That part of the parameter vector remains unidentified. The “estimator” relies upon turning the fixed effects model into a random effects model, in which case simple GLS estimation of all (now identified) parameters would be efficient among all estimators. *Helpful discussions of this paper with Neal Beck are gratefully acknowledged. Any remaining errors are, of course, my own.