Question

Suppose the following linear probability model 0.708 0.201M, Y = n 1,989, R2 = .049. (0.018) (0.020) Where y 1 if mortgage approved, M 1 if men, etc.,. a. What is the probability of mortgage approval for a typical male applicant? b. What is the probability of mortgage approval for a typical female applicant? Is the discrimination based on gender significant? c. d. What are the problems of this model? e. What other variables do you think should be added in the model? And if the variables were to be added, what happens to the coefficient of M?

Answer 1

a.

The estimated model is,

Y = 0.708 + 0.201M

For male applicant, M = 1,

Probability of mortgage approval = 0.708 + 0.201 * 1 = 0.909

b.

For female applicant, M = 0,

Probability of mortgage approval = 0.708 + 0.201 * 0 = 0.708

c.

The difference between the probabilities of male and female applicants is the slope coefficient 0.201 with standard error of 0.020

Null Hypothesis H0: Slope Coefficient of M is 0.

Alternative Hypothesis Ha: Slope Coefficient of M is not 0.

Test Statistic, t = 0.201 / 0.020 = 10.05

Degree of freedom = n - 2 = 1989 - 2 = 1987

Critical value of t at 0.05 significance level and df = 1987 is 1.96

Since the test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is significant evidence that Slope Coefficient of M is not 0 and thus, there is significant differences in the probabilities of male and female applicants. Thus we conclude that there is significant discrimination based on gender.

d.

The problems with the model is that there is only one predictor variable M, which explains only 4.9% of the variation of the probability of mortgage approval. R-square of the model is very low.

e.

The other variables which can be included in the model are - Amount of mortgage, Credit Score, Economic Status or Earnings.

On adding the other variables, the dependence of probability on gender variable M will decrease and hence the coefficient of M will decrease.