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Flashcards in BL12 Deck (12)
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1
Q

How are Y variables treated when they are dummy variables?

A

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

2
Q

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

A

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)

3
Q

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

A

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

4
Q

What is a linear probability model (LPM)?

A

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

5
Q

What does β(j) measure in a LPM?

A

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

6
Q

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

A

The predicted probability of success

7
Q

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

A

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

8
Q

3 drawbacks and 2 EV points on them of LPM?

A

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

9
Q

Explain the difference between economic and statistical significance?

A

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

10
Q

For large samples, using a smaller significance means…

A

…economic and statistical significance will be more likely to coincide

11
Q

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

A

Multicollinearity

12
Q

SEE

A

slides 27-30 stat and econ significance