Week 4

Question 1

Formula for b

Answer 1

Question 2

Elaborate what each part of this regression constitutes?

Answer 2

• e is regression residual
• b1 captures the linear relation between Yi and X1i net of the influence of X2i
• b2 captures the linear relation between Yi and X2i net of the influence of X1i

Question 3

How to remove influence of X2i on X1i

Answer 3

• We run a regression of X1i on a constant and X2i

Question 4

Elaborate the parts of the regression of X1i on X2i

Answer 4

• (c1 + d1 + X2i) is part of X1i explained by X2i or you can say is correlated with X2i
• X1i(tilde) is part of X1i that is uncorrelated with X2i Cov(X1i(tilde), X2i) = 0

Question 5

After you have removed the influence of X2i on X1i What do you do to get b1

Answer 5

Run another regression of Yi on a constant and X1i(tilde)

Question 6

Under what 2 assumptions for econometric model below, is b1 = beta 1 and b2 = beta 2

Answer 6

• (No perfect multicolinearlity) X1i and X2i must not be linearly and deterministically related. If they provide same information it is impossible to net out the influence of the other
• Zero conditional mean E(ui | X1i, X2i) = 0

Question 7

Assuming the 2 assumptions for b1 and b2 = beta 1 and beta 2 hold show the derivation of b1 = beta1 for the econometric model

Answer 7

Question 8

Given multiple regression with a sample give the formula for b1(hat)

Answer 8

Question 9

Under what 3 assumptions is b1(hat) and b2(hat) desirable estimators of b1 and b2 in that they are consistent and normally distributed.

Answer 9

• Large random sample
• Large outliers in X1i, X2i and Yi are unlikely
• No perfect collinearity

Question 10

Given econometric model what 4 assumptions allow for estimators b1(hat) and b2(hat) to be consistent estimators of Beta 1 and Beta 2?

Answer 10

• Large random sample
• Large outliers in X1i, X2i and Yi are unlikely
• No perfect colienarity
• Zero conditional mean

Question 11

Assuming assumptions 1 to 4 hold and if we run a regression omitting X2i. Derive and show that Beta1 has omitted variable bias.

Answer 11

Question 12

How will the bias for OVB be if both dropped variable and Covariance dropped variable and NOT dropped variable have same sign

Answer 12

Positive

Question 13

How will the bias for OVB be if both dropped variable and Covariance dropped variable and NOT dropped variable have different sign

Answer 13

Negative

Question 14

How will the bias for OVB be if both dropped variable and Covariance dropped variable and NOT dropped variable is zero

Answer 14

Zero

Question 15

For econometric model what can the zero conditional mean be replaced with.

Answer 15

Conditional mean independence

Question 16

What does being a consistent estimator mean?

Answer 16

• b(hat) becomes closer to b as sample size increases to infinity
• b(hat) is normally distributed as sample size increases to infinity

Question 17

How to test if multiple regressors are significantly different from zero

Answer 17

F-test