Question 11.6 If you have question plea
Meme TER 11 Regression with a Binary Dependent Variable 11.5 Using the results in column (7): a. Akira is a man with 10 years of driving experience. What is the prob. ability that he will pass the test? b. Jane is a woman with 2 years of driving experience. What is the prob- ability that she will pass the test? c. Does the effect of experience on test performance depend on gender? Explain. 11.6 Use the estimated probit model in Equation (11.8) to answer the following questions: a. A black mortgage applicant has a P/I ratio of 0.35. What is the prob- ability that his application will be denied? b. Suppose that the applicant reduced this ratio to 0.30. What effect ould this have on his probability of being denied a mortgage? c. Repeat (a) and (b) for a white applicant. d. Does the marginal effect of the P/I ratio on the probability of mortgage denial depend on race? Explain. Repeat Exercise 11.6 using the logit model in Equation (11.10). Are the logit and probit results similar? Explain. Consider the linear probability model Y; = Bo + BIX; + up, where Pr(Yi = 1| Xi) = Bo + BIXi. a. Show that E(uil Xi) = 0. b. Show that varful v oooaction is nonlinear , the effect of a change in * depends on the starting value of X . For example , it Pit ratio = 0.5 . The esti mated denial probab al probability based on Equation ( 1 1.7 ) is ( - 219 + 2.97 * 0 .5 ) $ 1 - 171 0.239 . Thus the change in the predicted probability who P/ ratio increases from O .4 10 0.5 is 0.239 - 0. 159 or 8 0 percentage points , larger than the increase of 6 . 2 percentage points when P / ratio increases from 0 . 3 10 0.4 What is the effect of race on the probability of mortgage denial holding holding can tant the payment to - income ratio To estimate this effect , we estimate a probi pratt regression with both P / I ratio and black as regressors Predeny 1 P /1 ratio , black ) = dic - 2.26 + 274P / 1 ratio + 071 black ) . ( 21.8 ) ( 1 16 ) ( 1 .41 ) (0.083 ) Again . The values of the coefficients are difficult to interpret bu erpret but the sign and status - Wall significance are not . The coefficient on black is positive , indicating that an rican American applicant has a higher probability of denial than a white app cant , holding constant their payment to - income ratio . This coefficient is statistical Munificant at the I Do level ( the I - statistic on the coefficient multiplying black is 8 55 ) For a while applicant with Pil ratio = 03 , the predicted denial probability is 7 .5 % while for a black applicant with Pil ratio = 0 . 3 it is 23 3% the difference in tical applicants is 158 percentage points
