L2

Question 1

What is Bias?

Answer 1

Difference between expected value of an estimator and the population parameter that it is estimating

Question 2

Difference between B1 and ^B1:

Answer 2

B1 is a constant

^B1 is a random variable with sampling distribution: E(^B1) and Var(^B1)

Question 3

What makes an estimator unbiased?

Answer 3

E(^B) = B

Question 4

Draw the bias table

Answer 4

Corr
Bias

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Question 5

What is the Kitchen Sink Regression problem?

Answer 5

Temptation to include all available variables.

Question 6

Irrelevant Variables

Answer 6

Have no effect on unbiasdeness, can affect variance of OLS estimators

Most important when selecting variables is theorectical relevance

Question 7

Consider the model:

wage = B0 + B1 female + u

What is B0?

Answer 7

Avg wage in the sample for men

Question 8

Consider the model:

wage = B0 + B1 female + u

What is B1?

Answer 8

Difference in avg wages in sample between men and women

Question 9

Consider the model:

wage = B0 + B1 female + u

What is B0 + B1?

Answer 9

Avg wage in sample for women

Question 10

Consider the model:

wage = 0.62 - 2.27 female + 0.51 educ

Why is B1 negative?

Answer 10

We can believe there are ommited variables, makes no sense if evertyhing else is 0 for a women to have a negative wage

Question 11

Collinearity in dummies

Answer 11

Cannot include dummies for all model groups (so choose base group)

Question 12

Consider the model:

log(wage) = B0 + B1 married + B2 female + B3 (married x female)

What is B0?

Answer 12

Intercept for base group, in this case -> single male

Question 13

Consider the model:

log(wage) = B0 + B1 married + B2 female + B3 (married x female)

What is B0 + B1?

Answer 13

Intercept for married men

Question 14

Consider the model:

log(wage) = B0 + B1 married + B2 female + B3 (married x female)

What is B0 + B2?

Answer 14

Intercept for single women

Question 15

Consider the model:

log(wage) = B0 + B1 married + B2 female + B3 (married x female)

What is B0 + B1 + B2 + B3?

Answer 15

Intercept for married women

Question 16

Consider the model:

log(wage) = B0 + B1 married + B2 female + B3 (married x female)

What is B3?

Answer 16

Difference in marriage premium between men and women

Question 17

Larger u variance -> larger ^B1 variance

Answer 17

More variation in u -> harder to estimate B1

Question 18

Sum ( xi - avg(x) ) increases as N increases

Answer 18

Larger samples -> better estimations

Question 19

Sum ( xi - avg(x) ) reflects x variance

Answer 19

Larger x variance is good

Question 20

T-statistic tells us what?

Answer 20

How far the estimated parameter is from the true value

Question 21

Normality of the errors

Answer 21

Assume u ~ iid (0, sigma^2)

Large samples

Question 22

If H0: B1 - B2

Show t

Answer 22

t= Ô - O / se(Ô)

Ô = B1 - B2

se(B1-B2) != se(B1) - se(B2)

Question 23

What is the F-test for?

Answer 23

Understand how much worse does the restricted model fit the data, when compared to the unrestricted

Question 24

What does the F-test measure?

Answer 24

Change in SSR between models

Question 25

F-test formula

Answer 25

F = SSR (R) - SSR (UR) / SSR (UR)

cheat sheet

Question 26

Is F always larger than 0?

Answer 26

Yes

Question 27

F-stat for parameter exclusion is equal to square of t-stat in what case

Answer 27

1- parameter exclusion (2-sided H)

Question 28

3 types of Functional Form Misspecification

Answer 28

1 - Omitting higher powers of variables
2 - Omit variable interactions
3 - Using levels instead of logs

Question 29

What does FFM lead to?

Answer 29

Biased OLS coefficients ( can be tested )

Question 30

What does RESET test consist of?

Answer 30

Estimate model
Compute predicted values
See if predicted values in different powers have significance

Question 31

What does Davidson and Mckinnon test consist of?

Answer 31

Compare two models, e.g.:

y = B0 + B1 x + u
y = B0 + B1 log(x) + u

Use fitted values of other in each:

y = B0 + B1 x + B2 (^y)
y = B0 + B1 log(x) + B2 (^y)

Where the fitted are not significant in the other model, we reject

Question 32

If after Davidson and Mckinnon we cannot decide between models, what is the tie-breaker?

Answer 32

R-squared