Consider the linear model yi = xiB + e = B1 + B2xi2 + ... + Bkxik + ei, i = 1, ..., n, or in matrix notation Y =XB + e.

Consider the linear model X = Z pie + u where Z is a matrix n * m, X is a matrix n * k and pie is a matrix m * k. Assume that

1. E (x'ixi) has full column rank;

2. E (ei/xi) = g (xi), , i =1, ..., n;

3. E (ei4) < infinity and E (xij/4) < infinity, i =1, ..., n; j =1, ..., k;

4. E (ui/zi) = 0, i = 1, ..., n;

A.) Let m = k and assume that rank pie = k. Derive a consistent estimator for B. Derive the asymptotic distribution of the estimator.

B.) Let m > k find a consistent estimator of B and his distribution.

C.) What happen if m = k and E (X'Z) has rank j < k?