Consider the system y1 = 1 + x + 1, y2 = 2 + 2. The disturbances are freely correlated.
Consider the system y1 = α1 + βx + ε1, y2 = α2 + ε2. The disturbances are freely correlated. Prove that GLS applied to the system leads to the OLS estimates of α1 and α2 but to a mixture of the least squares slopes in the regressions of y1 and y2 on x as the estimator of β. What is the mixture? To simplify the algebra, assume (with no loss of generality) that x = 0.
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