Regression with a Binary Dependent Variable (SW Ch. 9)

1. Regression with a Binary Dependent Variable(SW Ch. 9)

2. data:hmda_aer

3. keep or drop

4. Data set reduction • drop if (s51==3) *multifamily* • drop if (s7==4)|(s7==5) *application withdrawn or file incomplete* • keep if (s4==1) *purpose of loan is home purchase* • keep if (s13==3)|(s13==5)

5. gen deny = (s7==3) • gen pi_rat = s46/100 • gen black = (s13==3)

6. sort black

7. summarize deny if (black==1) • summarize deny if (black==0)

8. regress deny pi_rat, r

9. regress deny pi_rat black, r

10. probit deny pi_rat, r

12. probit deny pi_rat black, r

13. logit deny pi_rat black, r

15. gen hse_inc = s45/100 • gen loan_val = s6/s50 • gen ccred = s43 • gen mcred = s42 • gen pubrec = (s44>0) • gen denpmi = (s53==1) • gen selfemp = (s27a==1) • gen married = (s23a=="M")

16. gen single = (married==0) • gen hischl = (school>=12) • gen probunmp = uria • gen condo = (s51 == 1)

17. sum pi_rat hse_inc loan_val ccred mcred pubrec denpmi selfemp single hischl probunmp condo black deny

18. gen ltv_med = (loan_val>=0.80)*(loan_val<=.95) • gen ltv_high = (loan_val>0.95) • gen blk_pi = black*pi_rat • gen blk_hse = black*hse_inc • gen ccred3 = (ccred==3) • gen ccred4 = (ccred==4) • gen ccred5 = (ccred==5) • gen ccred6 = (ccred==6) • gen mcred3 = (mcred==3) • gen mcred4 = (mcred==4)

19. Preliminary Analysis ... compute means of all variables • sum deny black pi_rat hse_inc ltv_med ltv_high ccred mcred pubrec denpmi selfemp single hischl probunmp mcred3 mcred4 ccred3 ccred4 ccred5 ccred6 condo

20. regress deny black pi_rathse_incltv_medltv_highccredmcredpubrecdenpmiselfemp, r

21. logit deny black pi_rathse_incltv_medltv_highccredmcredpubrecdenpmiselfemp

22. logit deny black pi_rathse_incltv_medltv_highccredmcredpubrecdenpmiselfemp, r

23. scalar w0 = _b[black]*0 + _b[ pi_rat]* .3308136 + _b[ hse_inc]* .2553461 + _b[ ltv_med]* .3743697 + _b[ltv_high]* .0323529 + _b[ ccred]* 2.116387 + _b[ mcred]* 1.721008 + _b[ pubrec]* .0735294 + _b[ denpmi]* .0201681 + _b[ selfemp]* .1163866 + _b[ _cons]* 1

24. scalar w1 = w0 + _b[black]*1 • dis "Prob for white at means = " 1/(1+exp(-w0)) • dis "Prob for black at means = " 1/(1+exp(-w1)) • dis "Difference in probs = " (1/(1+exp(-w1))) - (1/(1+exp(-w0)))

25. probit deny black pi_rathse_incltv_medltv_highccredmcredpubrecdenpmiselfemp

26. probit deny black pi_rat hse_inc ltv_med ltv_high ccred mcred pubrec denpmi selfemp, r

27. scalar z0 = _b[black]*0 + _b[ pi_rat]* .3308136 + _b[ hse_inc]* .2553461 + _b[ ltv_med]* .3743697 + _b[ltv_high]* .0323529 + _b[ ccred]* 2.116387 + _b[ mcred]* 1.721008 + _b[ pubrec]* .0735294 + _b[ denpmi]* .0201681 + _b[ selfemp]* .1163866 + _b[ _cons]* 1

28. scalar z1 = z0 + _b[black]*1 • dis "Prob for white at means = " normprob(z0) • dis "Prob for black at means = " normprob(z1) • dis "Difference in probs = " normprob(z1)-normprob(z0)

29. probit deny black pi_rathse_incltv_medltv_highccredmcredpubrecdenpmiselfemp single hischlprobunmp

30. test single hischlprobunmp

31. probit deny black pi_rathse_incltv_medltv_highccredmcredpubrecdenpmiselfemp single hischlprobunmp, r

32. scalar z0 = _b[black]*0+ _b[ pi_rat]* .3308136 + _b[ hse_inc]* .2553461 + _b[ ltv_med]* .3743697 + _b[ltv_high]* .0323529 + _b[ ccred]* 2.116387 + _b[ mcred]* 1.721008 + _b[ pubrec]* .0735294 + _b[ denpmi]* .0201681 + _b[ selfemp]* .1163866 + _b[ single]* .3932773 + _b[ hischl]* .9836134 + _b[probunmp]* 3.774496 + _b[ _cons]* 1

33. scalar z1 = z0 + _b[black]*1 • dis "Prob for white at means = " normprob(z0) • dis "Prob for black at means = " normprob(z1) • dis "Difference in probs = " normprob(z1)-normprob(z0) • test single hischl probunmp

34. probit deny black pi_rat hse_inc ltv_med ltv_high ccred mcred pubrec denpmi selfemp single hischl probunmp mcred3 mcred4 ccred3 ccred4 ccred5 ccred6 condo

35. test single hischl probunmp • test mcred3 mcred4 ccred3 ccred4 ccred5 ccred6 • test condo

36. probit deny black pi_rat hse_inc ltv_med ltv_high ccred mcred pubrec denpmi selfemp single hischl probunmp mcred3 mcred4 ccred3 ccred4 ccred5 ccred6 condo, r

37. scalar z0 = _b[black]*0 + _b[ pi_rat]* .3308136 + _b[ hse_inc]* .2553461 + _b[ ltv_med]* .3743697 + _b[ltv_high]* .0323529 + _b[ ccred]* 2.116387 + _b[ mcred]* 1.721008 + _b[ pubrec]* .0735294 + _b[ denpmi]* .0201681 + _b[ selfemp]* .1163866 + _b[ single]* .3932773 + _b[ hischl]* .9836134 + _b[probunmp]* 3.774496 + _b[ mcred3]* .0172269 + _b[ mcred4]* .0088235 + _b[ ccred3]* .0529412 + _b[ ccred4]* .0323529 + _b[ ccred5]* .0764706 + _b[ ccred6]* .0844538 + _b[ condo]* .2882353 + _b[ _cons]* 1

38. scalar z1 = z0 + _b[black]*1 • dis "Prob for white at means = " normprob(z0) • dis "Prob for black at means = " normprob(z1) • dis "Difference in probs = " normprob(z1)-normprob(z0)

39. test single hischlprobunmp • test mcred3 mcred4 ccred3 ccred4 ccred5 ccred6 • test condo

40. probit deny black pi_rathse_incltv_medltv_highccredmcredpubrecdenpmiselfemp single hischlprobunmpblk_piblk_hse

41. test single hischlprobunmp • test black blk_piblk_hse • test blk_piblk_hse

42. probit deny black pi_rathse_incltv_medltv_highccredmcredpubrecdenpmiselfemp single hischlprobunmpblk_piblk_hse, r

43. scalar z0 = _b[black]*0 + _b[ pi_rat]* .3308136 + _b[ hse_inc]* .2553461 + _b[ ltv_med]* .3743697 + _b[ltv_high]* .0323529 + _b[ ccred]* 2.116387 + _b[ mcred]* 1.721008 + _b[ pubrec]* .0735294 + _b[ selfemp]* .1163866 + _b[ denpmi]* .0201681 + _b[ single]* .3932773 + _b[ hischl]* .9836134 + _b[probunmp]* 3.774496 + _b[ _cons]* 1;

44. scalar z1 = z0 + _b[black]*1 + _b[blk_pi]*1* .3308136 + _b[blk_hse]*1* .2553461 • dis "Prob for white at means = " normprob(z0) • dis "Prob for black at means = " normprob(z1) • dis "Difference in probs = " normprob(z1)-normprob(z0)

45. test single hischl probunmp • test black blk_pi blk_hse • test blk_pi blk_hse