Regression with a Binary Dependent Variable

(SW Ch. 9)

data:hmda_aer

keep or drop

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*application withdrawn or file incomplete* keep if (s4==1)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)

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

sort black

summarize deny if (black==1) summarize deny if (black==0)

regress deny pi_rat, r

regress deny pi_rat black, r

probit deny pi_rat, r

probit deny pi_rat black, r

logit deny pi_rat black, r

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")

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

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

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)

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

regress deny black pi_rat hse_inc ltv_med ltv_high ccred mcred pubrec denpmi selfemp, r

logit deny black pi_rat hse_inc ltv_med ltv_high ccred mcred pubrec denpmi selfemp

logit deny black pi_rat hse_inc ltv_med ltv_high ccred mcred pubrec denpmi selfemp, r

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

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)))

probit deny black pi_rat hse_inc ltv_med ltv_high ccred mcred pubrec denpmi selfemp

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

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

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)

probit deny black pi_rat hse_inc ltv_med ltv_high ccred mcred pubrec denpmi selfemp single hischl probunmp

test single hischl probunmp

probit deny black pi_rat hse_inc ltv_med ltv_high ccred mcred pubrec denpmi selfemp single hischl probunmp, r

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

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

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

test single hischl probunmp test mcred3 mcred4 ccred3 ccred4 ccred5

ccred6 test condo

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

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

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 test mcred3 mcred4 ccred3 ccred4 ccred5

ccred6 test condo

probit deny black pi_rat hse_inc ltv_med ltv_high ccred mcred pubrec denpmi selfemp single hischl probunmp blk_pi blk_hse

test single hischl probunmp test black blk_pi blk_hse test blk_pi blk_hse

probit deny black pi_rat hse_inc ltv_med ltv_high ccred mcred pubrec denpmi selfemp single hischl probunmp blk_pi blk_hse, r

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;

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)

test single hischl probunmp test black blk_pi blk_hse test blk_pi blk_hse