Consider the multivariate regression y = X +

(y is a vector of length n) where we have an estimator for = (₁,...,_K), that is n-asymptotically normal with asymptotic variance ,

n (B - ) d N(0, ).

Assume furthermore that a consistent estimator * for is available.

QUESTION:

1. You want to test the joint hypothesis ₁ = 2, 1+2+3 = 0, and 4 = 0.Write the hypothesis in matrix form R = r and show R and r explicitly.

2. Show that under the hypothesis n (RB - r) d N(0, R R').

3. Dene the Wald test as W = n(RB-r)'(R*R')^-1(RB - r). Show that W d X_L² where L is the length of the vector r.

4. For which values of W do you reject the hypothesis in question 1 if you test at the 95% level?