13.) Dummy Dependent Variable Techniques

Question 1

A linear probability model is…

Answer 1

a linear-in-the-coefficients equations used to explain a dummy dependent variable

Question 2

The term linear probability model comes from..

Answer 2

the fact that the right side of the equation is linear while the expected value of the left side measures the probability that Di = zero

Question 3

What are the two problems with a linear probability model?

Answer 3

1. ) r squared bar is not an accurate measure of overall fit.
2. ) d estimated ith observation is not bounded by 0 and 1

Question 4

For most researchers, the major difficulty with the linear probability model is…

Answer 4

the unboundedness of d estimated ith observation

Question 5

The binomial logit is..

Answer 5

an estimation technique for equations with dummy dependent variables that avoids the unboundedness problem of the linear probability model by using a variant of the cumulative logistic function

Question 6

In a binomial logit model are the d estimated ith observation now limited by 0 and 1?

Answer 6

Yes

Question 7

The maximum likelihood (ML) is used in logits because?

Answer 7

It is an iterative estimation technique that is especially useful for equations that are nonlinear in the coefficients.

Question 8

ML estimation is inherently different from least squares in that…

Answer 8

it choose coefficient estimates that maximize the likelihood of the sample data set being observed.

Question 9

ML has a number of desirable large sample properties

Answer 9

1. ) ML is consistent and asymptomatically efficient (unbiased and minimum variance for large samples)
2. ) With very large samples, ML has the added advantage of producing normally distributed coefficients, allowing the use of typical, allowing the use of typical hypothesis testing techniques.
   a. ) So sample sizes for logits should be substantially larger than for liner regressions, some researchers seek samples of 500 or more.

Question 10

What are some of the key differences btw an equation estimated using linear probability and logit?

Answer 10

1. ) The dependent variable in a logit equation isn’t the same as the dependent variable in a linear probability model
2. ) the slope of the graph of the logit changes as Di moves from 0 to 1. Thus the change in the probability ath Di = 1 caused by a one-unit increase in an independent variable (holding the other independent variables constant) will vary as we move from Di = 0 to Di =1.

Question 11

How can we interpret estimated logit coefficients? What are the three reasonable ways to interpret them?

Answer 11

1. ) Change an average observation.
2. ) Use a partial derivative.
3. ) Use a rough estimate

Question 12

Which approach do the authors suggest to interpret estimated logit coefficients?

Answer 12

They suggest that to get a rough approximation of the economic meaning of a logit coefficient, multiply by 0.25 (or, equivalently, divide by 4).

Question 13

How do the estimations of linear probability and logit estimation differ?

Answer 13

They differ mainly in that logit does not produce Dis outside the range of 0 and 1.

Question 14

The logit coefficients need to be…

Answer 14

divided by 4 to get meaningful estimates of the impact of the independent variables on the probability of passing the test.

Question 15

The binomial probit model is…

Answer 15

an estimation technique for equations with dummy dependent variables that avoids the unboundedness problem of the linear probability model by using a variant of the cumulative normal distribution.

Question 16

From a researcher’s point of view, the probit is theoretically appealing…

Answer 16

because many economic variables are normally distributed. With extremely large samples, this advantage falls away, since maximum likelihood procedures can be shown to be asymptotically normal under fairly general conditions.

Question 17

A multinomial logit model is…

Answer 17

an extension of the binomial logit technique that allows several discrete alternatives to be considered at the same time.

Question 18

A linear probability model is a…

Answer 18

linear in the coefficients equation used to explain a dummy dependent to explain dependent variable (Di). The expected value of Di is the probability that Di equals.

Question 19

The estimation of a linear probability model with OLS encounters two major problems.

Answer 19

1. ) r squared bar is not an accurate measure of overall fit.
2. ) The expected value of Di is not limited by 0 by 1.

Question 20

The binomial logit is an estimation technique for equations with..

Answer 20

dummy dependent variables that avoids the unboundedness problem of the linear probability model by using a variant of the cumulative logistic function.

Question 21

The binomial probit model is an estimation technique for …

Answer 21

equations with dummy dependent variables that uses the cumulative normal distribution function. The binomial probit has properties quite similar to the binomial logit.

Question 22

The multimonial logit model is an extension of the …

Answer 22

binomial logit that allows more than two discrete alternatives to be considered simultaneously.