(Projection) Reconsider the panel data model in (24.42) and (24.44) with the additional moment restrictions in Section 24.8. Bhargava and Sargan (1983) and Breusch et al. (1989) suggest assuming also that Cov[X3] is a constant vector of covariances.

(a) Show that this implies that (7-1) K additional variables are uncorrelated with a,, and that one may take these variables to be AX21 = X2 X2, 1 for 1 = 2..... T.

(b) How do these additional moment restrictions alter the estimation methods described in Section 24.8.2?

(c) Show that we may just as well take the additional instruments to be AX2 = [x2x2] and use E'[2 X. Z, AX21.