The Covariance Transformation and the Instrumental Variables Estimator of the Fixed Effects Model

The covariance transformation is a useful and often necessary procedure to estimate the fixed effects model. When some explanatory variables are contemporaneously correlated with the disturbance term, the covariance transformation can be used in conjunction with an instrumental variables procedure to obtain a consistent estimator. This paper describes how to correctly compute the IV estimator as a two stage least squares estimator. In addition, I show that if the IV estimator is incorrectly computed using a two stage least squares approach where the covariance transformation is not applied until the second stage, the resulting estimator is not in general consistent.