Fixed-Effects Vector Decomposition

Warning! Avoid the so-called "Fixed-Effects Vector Decomposition" (FEVD) estimator, introduced by Plümper and Troeger in a 2007 issue of Political Analysis.

A recent "Symposium on Fixed-Effects Vector Decomposition" in the 2011 volume of that journal, which included critiques by William Greene and by Trevor Breusch et al.,  reveals just what this estimator is.... and isn't!

Greene (2011, p.135) hits the nail on the head:

"The FEVD estimator is so simple it seems like magic. Like magic, the estimator is illusory."

Ouch!

A few points from Breusch et al. (2011b) in their reply to Plümper and Troeger's rejoinder to their critique (confused?):

• The FEVD estimator is just the familiar Hausman-Taylor (HT) instrumental variables (IV) estimator when all of the time-varying regressors are possibly endogenous; and all of the time-invariant regressors are exogenous.
• "The difference between HT and FEVD, as estimation strategies, is that HT would employ the FEVD instruments under an explicit exogeneity assumption, whereas FEVD would use a predetermined set of instruments as a 'canned' solution, without regard to any such reasoning."
• The 'third stage' of the FEVD estimator has no effect on the coefficient estimates, but is used to generate the standard errors. The latter are in fact incorrect! Worse still, they grossly under-state the correct (IV) standard errors, leading the researcher to conclude that the results are more 'significant' than they really are.

The Breusch et al. bottom line? 

"Thus, there is no need for ‘‘vector decomposition’’ and no distinct estimator to call FEVD.With appropriate justification for the instruments, FEVD is just IV. Without that justification, FEVD is just mistaken."

To which I'd add: Beware of 'canned solutions'.

References

Breusch, T., M. B. Ward, H. T. M. Nguyen, and T Kompas, 2011a. On the fixed-effects vector decompostion. Political Analysis, 19, 123-134.

Breusch, T., M. B. Ward, H. T. M. Nguyen, and T Kompas, 2011b. FEVD: Just IV or just mistaken? Political Analysis, 19, 165-169.

Greene, W. H., 2011. Fixed effects vector decomposition: A magical solution to the problem of time invariant variables in fixed effects models? Political Analysis, 19,135–46.

Plümper, T., and V. Troeger, 2007. Efficient estimation of time-invariant and rarely changing variables in finite sample panel analyses with unit fixed effects. Political Analysis, 15,124–39.

Plümper, T., and V. Troeger, 2011. Fixed effects vector decomposition: properties, reliability and instruments. Political Analysis, 19, 147–64.

© 2012, David E. Giles