Lecture 1

Question 1

What is exogeneity?

Answer 1

If cov(x_ij, u_i) = 0.

Question 2

What is endogeneity?

Answer 2

Question 3

Derive that the OLS estimator is not unbiased in case of endogeneity.

Answer 3

Question 4

Derive that the OLS estimator is inconsistant in case of endogeneity

Answer 4

Question 5

What are six possible reasons for endogeneity? What are the solutions to these problems?

Answer 5

Question 6

What are the assumptions behind the Instrumental Variable?

Answer 6

Question 7

How is the IV estimator derived?

Answer 7

Question 8

What is the formula of the IV estimator?

Answer 8

Question 9

What does instrument exogeneity mean?

Answer 9

Question 10

Derive that the IV estimator is usually not unbiased.

Answer 10

Question 11

Derive that the IV estimator is consistant

Answer 11

Question 12

Derive the asymptotic distribution of the IV estimator β_1,IV^hat

Answer 12

Question 13

Answer 13

Question 14

What is the formula for the Homoskedacity-only standard errorof the IV estimator?

Answer 14

Question 15

Answer 15

Question 16

Answer 16

We cannot test if cov(x_i1, u_i) = 0, since cov^hat(z_i1, u_i^hat) = 0 by definition of IV estimator.

Question 17

Answer 17

If they overlap, then the Durbin-Wu-Hausman test would accept exogenity. If they do not it would reject.