A property of partitioned generalized regression

In this paper we consider the standard partitioned linear regression model where the model matrix is X = (X1: X2) the corresponding vector of unknown parameters being . In particular, we are interested in the best linear unbiased estimator (BLUE) of β2. Inspired by the article of Aigner and Balestra (1988), we consider a specific reduced model and show that the BLUE of β2 under the reduced model equals the corresponding BLUE under the original full model.M.