Exam Questions

Question 1

Answer 1

Question 2

Answer 2

Question 3

What is the distribution of the Jarque-Bera test? What is the critical value for 95% confidence?

Answer 3

χ²(2), 5.9(91)

Question 4

Answer 4

Question 5

Answer 5

Question 6

Answer 6

Question 7

Answer 7

Question 8

Answer 8

Question 9

Answer 9

Question 10

Answer 10

Question 11

Answer 11

Question 12

Answer 12

Question 13

Answer 13

Question 14

How do we test if an instrument is relevant?

Answer 14

We can simply run OLS on x₁ = β₀ + β₁z₁ + e, then if we look at the t-value of β₁, this should be larger then sqrt(10) = 3.16

Question 15

What does it mean if two 95% confidence intervals of OLS and 2SLS do not overlap?

Answer 15

It means that at least one of x₁ and z₁ is endogeneous. If both are then OLS and 2SLS are unreliable, if x₁ is, then OLS is unreliable, if z₁ is then 2SLS is unreliable.

Question 16

When is an instrument strong enough?

Answer 16

If the standard error of the variable (x₁ of which z₁ is an instrument) is small enough that the errors are not large (s.t. e.g., β₁ takes very positive and negative values).

Question 17

Answer 17

Question 18

Answer 18

Question 19

Why is the variance of the 2SLS estimator higher then the OLS estimator?

Answer 19

Since it needs to estimate twice, thus this is more difficult, and thus you have a higher variance.

Question 20

If we use the OLS estimator to estimate an variable that is endogeneous, what happens with the OLS estimator?

Answer 20

It would be biased. The 2SLS estimator would not be.

Question 21

What happens when we allow for a direct effect of an instrument to the 2SLS estimator?

Answer 21

It becomes inconsitant and biased (because it does not follow one of the assumptions, instrument exogeneity).

Question 22

How to

Answer 22

Question 23

Does the distribution of instrument z_t, or serial correlation between multiple z_t impact the OLS estimation?

Answer 23

No, it does not matter how z_t is distributed, nor any correlation between it

Question 25

Do the Newey-West standard errors work for small samples?

Answer 25

No

Question 26

Answer 26

Question 27

In case of contemporaneous exogenity is OLS still unbiased and consistant?

Answer 27

It is not unbiased, but it is consistant.

Question 28

If we do not have contemporaneous exogenity, can we test H₀: β₁ = 0?

Answer 28

Question 29

Answer 29

Question 30

Answer 30

Question 31

Answer 31

Question 32

Model: y_t = β₀ + β₁y_t-1 + u_t

Answer 32

Question 33

Model: y_t = β₀ + β₁y_t-1 + u_t

Answer 33

Question 34

Model: y_t = β₀ + β₁y_t-1 + u_t

Answer 34

Question 35

Model: y_t = β₀ + β₁y_t-1 + u_t

Answer 35

Question 36

Answer 36

Question 37

We have that the model is y_t = β₀ + β₁z_t + u_t, where u_t = u_t-1 + e_t, and e_t ~ N(0,1).

Answer 37

Question 38

How to calculate OLS using variance and covariance?

Answer 38

Question 39

When is the OLS estimator biased towards 0?

Answer 39

If there are measurement errors in the regressor.

Question 40

What is the Pearson ch-square tset?

Answer 40

Question 41

When is an instrument weak? What are the distadvantages of a weak instrument?

Answer 41

If it has a low sample correlation between z_i and x_i.

Disadvantages:

(1) Large asymptotic bias if the instruments would not exactly satisfy the

exogeneity restriction.
(2) Large standard errors

Question 42

What are the following tests for?

Breusch-Godfrey, Sargan-Hansen, Durbin-Wu-Hausman, Jarque-Bera, Chow test, Ramsey RESET test

Answer 42

Breusch-Godfrey: serial correlation

Sargan-Hansen: exogeneity of instruments

Durbin-Wu-Hausman: exogeneity of regressor

Jarque-Bera: normality

Chow test: different coefficients for different groups

Ramsey RESET: non-linearity