BL12

Question 1

How are Y variables treated when they are dummy variables?

Answer 1

Bernoulli random variables tf:
E(z)=p
V(z)=pq

Question 2

What is the binary response model and what does it tell us?

Answer 2

E(y=1|x)=β0+β1x1+…+βkxk

Tells us that the probability of success, p(x)=P(y=1|x), is a linear function of the x(j)

Question 3

What is the response probability? What do we know from this?

Answer 3

P(y=1|x)
since prob must add to 1:
P(y=0|x)=1-P(y=1|x)

Question 4

What is a linear probability model (LPM)?

Answer 4

A MLRM with a binary dependent variable is a linear probability model because the response probability is linear in the parameters β(j)

Question 5

What does β(j) measure in a LPM?

Answer 5

The change in probability of success when x(j) changes, ceteris paribus. The slope coefficient measures the change when x(j) increases by one unit

Question 6

What will y(hat) be if we estimate it in the LPM?

Answer 6

The predicted probability of success

Question 7

What assumption does the LPM violate? Why? How does this affect the analysis?

Answer 7

Homoskedasticity because:
When y is a binary variable, its variance, conditional on x, is V(y|x)=p(x)[1-p(x)] where p(x)is shorthand for probability of success.
This means that there must be heteroskedasticity in a linear probability model except in the case where the probability does not depend on any of the independent variables

Can still prove unbiasedness but t and F stats are invalid

Question 8

3 drawbacks and 2 EV points on them of LPM?

Answer 8

1) Can lead to predicted prob. below 0 or greater than 1
2) LPM implies constant marginal effect of each explanatory variable.
3) Contains heteroskedasticity
EV:
1 and 2 aren’t big issues if estimating the middle range of the data
3 is fixed easily if samples are large enough using appropriate methods

Question 9

Explain the difference between economic and statistical significance?

Answer 9

Statistical significance of a variable x(j) is determined by the size of the statistic entirely.

Economic/practical significance of a variables is related to the size AND sign of the statistic

Question 10

For large samples, using a smaller significance means…

Answer 10

…economic and statistical significance will be more likely to coincide

Question 11

In large samples, what can a large standard error indicate?

Answer 11

Multicollinearity

Question 12

SEE

Answer 12

slides 27-30 stat and econ significance