Sensitivity of GLS estimators in random effects models

This paper studies the sensitivity of random effects estimators in the one-way error component regression model. Maddala and Mount (1973) give simulation evidence that in random effects models the properties of the feasible GLS estimator β̂ are not affected by the choice of the first-step estimator θ̄ used for the covariance matrix. Taylor (1980) gives a theoretical example of this effect. This paper provides a reason for this in terms of sensitivity. The properties of θ̄ are transferred via an uncorrelated (and independent under normality) link, called sensitivity. The sensitivity statistic counteracts the improvement in θ̄. A Monte Carlo experiment illustrates the theoretical findings.