Consider the partitioned regression:
y = X1B1 + X2B2 + u
where y and u are a N X 1 vectors, X1 a N X k1 matrix, X2 a N X k2 matrix, B1 a k1 X 1vector, B2 a k2 X 1 vector, and k1 + k2 = k. Assume X1 and X2 are matrices of fixed regressors.
Assume that E(u) = X1gamma,Var(u) = sigma^2 I
Suppose we run an OLS regression of y on X1 and
X2 to derive the OLS estimator of b = (b1,b2). Derive the expectations of b1and b2. Are they
unbiased estimators for B1 and B2? Explain why
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