Consider the seemingly unrelated regression (SUR) model (1): y=XiBi + ei for i = 1, ..., M where y, X, and B, are of sizes T x 1, T x K, and K x 1, respectively. The error term vector e is of size T x 1, with E(e) = 0, for i = 1, ..., M and cov(e; e) = alt for i, j = 1, ..., M. The stacked form of the model above is (2): y = x + e, where y. X are are respectively of sizes MT x 1, MT XK and K 1. Precisely: (3): y = (4): e X = The MT x 1 error term vector e is such that 011/T OIMIT *** = E 0 1 XMJ Page 2 of 4 1 IT and B = -w). = W, where = = 011 *** 01M 1 LOMILT UMMIT OMI (a) (6 points) Under the assumption that the individual regressions have the same set of regressors, say X = X (hence K= K) for all i = 1, ..., M, show that running GLS or FGLS estimation technique on the whole regression system (2) would be equivalent to running LS on the whole system or the individual regression models (1). MM. (b) (6 points) Show that the result above holds under the assumption that the errors driving the different regression models are contemporaneously uncorrelated regardless of whether the X's are the same. That is, oj = 0 when i # j for i, j = 1, ..., M. Otherwise said, the covariance matrix of e is diagonal, namely, = diag{011,...,OMM}.