Introduction to Econometrics 3rd Edition by James Stock, Mark Watson

تمرين 2

( Y i X 1i X 2i ) satisfy the assumptions in Key Concept 6.4; in addition, var(u i | X 1i X 2i )= 4 and var( X 1i ) = 6. A random sample of size n = 400 is drawn from the population.
a. Assume that X 1 and X 2 are uncorrelated. Compute the variance of
1.
b. Assume that cor (Y 1 , X 2 )= 0.5. Compute the variance of ß 1.
c. Comment on the following statements: "When X 1 and X 2 are correlated, the variance of
1 is larger than it would be if X 1 and X 2 were uncorrelated. Thus, if you are interested in, it is best to leave out of the regression if it is correlated with X 1."