Temple University
Department of Economics
Econometrics I
Fall 2010 Midterm Key
Question 1 

a. Find the inverse of A

or 
b. Find the eigen values

As a bonus the characteristic vectors are

C. Positive definite?

Yes, A is positive definite since the roots are all positive.

Question 2
a. Test the hypothesis that the mean growth rate of GDP is zero 

Reject the null.
b. Test the hypothesis that the mean growth rate of M1 is one. 

The relevant t-score is 2.6, so do not reject the null.
c. Test the null that the mean growth rate of m1 and GDP are the same.

Reject the null.
Question 3

a. Compute the regression coefficients. This was done above, but the answer is:

b. Compute the coefficient covariance matrix.

4. M1 and RS effects are offsetting.

Do not reject the null.

5 Test the joint hypothesis.
There are two ways to do this. One relies on using the two residual sums of squares.  The other is the more general F-test representation from which the differences in residual sums of squares is derived. 
Method 1 Recall that the unrestricted model has an intercept and two regressors.  The restricted model has an intercept only.

Reject the null.
Method 2 This is based on restricted least squares.