TABLE 11.2 Mortgage Denlal Regresslons Using the Boston HMDA Data Dapandant varlable: deny = 1ifmortgage application is danled, = Oifaccepted; 2380 observations. (Table 11.2 continued) Regression Model F-Statistics and p-Values Testing Exclusion of Groups of Variables LPM Logit Probit Probit Probit Probit Ragressor (1) (2) (3) (4) (5) (6) (1) (2) (3) (4) (5) (6) 0.371 (0.099) 0.363 (0.100) black 0.084* 0.688** 0.389** 0.246 (0.023) (0.182) (0.098) (0.448) 2.57 (0.66) applicant single; high school diploma; industry unemployment rate 5.85 (< 0.001) 5.22 5.79 246 (0.60) 2.62 (0.61) P/A ratio 0.449** 4.76* 2.44 (0.001) (< 0.001) (0.114) (1.33) (0.61) houring expense-to income patio -0.048 -0.11 (1.29) -0.18 -0.30 -0.50 (0.70) -0.54 (0.110) (0.74) 0.22 (0.08) (0.68) (0.68) additional credit rating indicator variables 0,031 1.22 0.21** (0.08) 0.79 (0.18) medium loan-to-value ratio 0.46** 0.22* 0.22* (0.80 s loan-value ratio s 0.95) (0.013) (0.16) (0.08) (0.08) (0.291) high loan-to-value ratio (loan-value ratio > 0.95) 0.79 (0.18) 0.189** 1.49** 0.84** 0.79* (0.050) (0.32) (0.18) (0.18) race interactions and black 4.96 (0.002) COMLSumer credit score 0.031** 0.29** (0.04) 0 29 0.15** (0.02) 0.16** 0.34** 0.16* (0.005) (0.02) (0.11) (0.02) mortgage credit score 0.021 0.28 0.15 0.11 0.16 0.11 race interactions only 0.27 (0.011) (0.14) (0.07) (О.ок) (0.08) (0.10) 0.72 0.72* (0.12) (0.08) (0.766) a.197* (0.035) public bad credit record 0.70* (0.12) 1.23** 0.70 0.70* (0.20) (0.12) (0.12) difference in predicted probability of denial, white vs. black (percentage points) 0,702 (0.045) 2.56 (0.30) 2.59 (0.29) denied mortgage insurance 4.55** 2.59** 2.59 (0.57) (0.30) (0.29) 0.060 (0.021) 035* (0.11) 0.15 (0.11) 6.0% 6,6% 6.3% 6.5% self-employed 0.34** 8.4% 7.1% 0.67** 0.36** (0.21) (0.11) (0.11) 0.23* (0.08) 0.23 (0.08) 0.23 (0.08) single These regressions were estimated using the n = 2380 observations in the Boston HMDA data set described in Appendix 11.1. The linear probability model was estimated by OLS, and probit and logit regressions were estimated by maximum likelihood. Standard errors are given in parentheses under the coefficients, and p-values are given in parentheses under the F-statistics. The change in pre- dicted probability in the final row was computed for a hypothetical applicant whose values of the regressors, other than race, equal the sample mean. Individual coefficients are statistically significant at the *5% or **1% level. high school diploma -0.61** -0,60 -0.62 (0.23) (0.24) (0.23) unemployment rate 0.03 (0.02) 0.03 (0.02) 0.03 (0.02) condominium -0.05 (0.09) black x PI ratio -0.58 (1.47) black x houving expense- do-income ratio 1.23 (1.69) additional credit rating indicator variables no по ves по -5,71 (0.48) -3.04 (0.23) -2.90 (0.39) -2.54** (0.35) COMstant -0.183** -2.57* (0.028) (0.34)

TABLE 11.2 Mortgage Denlal Regresslons Using the Boston HMDA Data Dapandant varlable: deny = 1ifmortgage application is danled, = Oifaccepted; 2380 observations. (Table 11.2 continued) Regression Model F-Statistics and p-Values Testing Exclusion of Groups of Variables LPM Logit Probit Probit Probit Probit Ragressor (1) (2) (3) (4) (5) (6) (1) (2) (3) (4) (5) (6) 0.371 (0.099) 0.363 (0.100) black 0.084* 0.688 0.389 0.246 (0.023) (0.182) (0.098) (0.448) 2.57 (0.66) applicant single; high school diploma; industry unemployment rate 5.85 (< 0.001) 5.22 5.79 246 (0.60) 2.62 (0.61) P/A ratio 0.449** 4.76* 2.44 (0.001) (< 0.001) (0.114) (1.33) (0.61) houring expense-to income patio -0.048 -0.11 (1.29) -0.18 -0.30 -0.50 (0.70) -0.54 (0.110) (0.74) 0.22 (0.08) (0.68) (0.68) additional credit rating indicator variables 0,031 1.22 0.21 (0.08) 0.79 (0.18) medium loan-to-value ratio 0.46 0.22* 0.22* (0.80 s loan-value ratio s 0.95) (0.013) (0.16) (0.08) (0.08) (0.291) high loan-to-value ratio (loan-value ratio > 0.95) 0.79 (0.18) 0.189 1.49 0.84** 0.79* (0.050) (0.32) (0.18) (0.18) race interactions and black 4.96 (0.002) COMLSumer credit score 0.031 0.29 (0.04) 0 29 0.15 (0.02) 0.16 0.34** 0.16* (0.005) (0.02) (0.11) (0.02) mortgage credit score 0.021 0.28 0.15 0.11 0.16 0.11 race interactions only 0.27 (0.011) (0.14) (0.07) (О.ок) (0.08) (0.10) 0.72 0.72* (0.12) (0.08) (0.766) a.197* (0.035) public bad credit record 0.70* (0.12) 1.23** 0.70 0.70* (0.20) (0.12) (0.12) difference in predicted probability of denial, white vs. black (percentage points) 0,702 (0.045) 2.56 (0.30) 2.59 (0.29) denied mortgage insurance 4.55 2.59 2.59 (0.57) (0.30) (0.29) 0.060 (0.021) 035* (0.11) 0.15 (0.11) 6.0% 6,6% 6.3% 6.5% self-employed 0.34 8.4% 7.1% 0.67 0.36** (0.21) (0.11) (0.11) 0.23* (0.08) 0.23 (0.08) 0.23 (0.08) single These regressions were estimated using the n = 2380 observations in the Boston HMDA data set described in Appendix 11.1. The linear probability model was estimated by OLS, and probit and logit regressions were estimated by maximum likelihood. Standard errors are given in parentheses under the coefficients, and p-values are given in parentheses under the F-statistics. The change in pre- dicted probability in the final row was computed for a hypothetical applicant whose values of the regressors, other than race, equal the sample mean. Individual coefficients are statistically significant at the 5% or 1% level. high school diploma -0.61 -0,60 -0.62 (0.23) (0.24) (0.23) unemployment rate 0.03 (0.02) 0.03 (0.02) 0.03 (0.02) condominium -0.05 (0.09) black x PI ratio -0.58 (1.47) black x houving expense- do-income ratio 1.23 (1.69) additional credit rating indicator variables no по ves по -5,71 (0.48) -3.04 (0.23) -2.90 (0.39) -2.54 (0.35) COMstant -0.183 -2.57 (0.028) (0.34)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Question

In Table 11.2 the estimated coefficient on black is 0.084 in column (1),
0.688 in column (2), and 0.389 in column (3). In spite of these large differences, all three models yield similar estimates of the marginal effect of race on the probability of mortgage denial. How can this be?

TABLE 11.2 Mortgage Denlal Regresslons Using the Boston HMDA Data
Dapandant varlable: deny = 1ifmortgage application is danled, = Oifaccepted; 2380 observations.
(Table 11.2 continued)
Regression Model
F-Statistics and p-Values Testing Exclusion of Groups of Variables
LPM
Logit
Probit
Probit
Probit
Probit
Ragressor
(1)
(2)
(3)
(4)
(5)
(6)
(1)
(2)
(3)
(4)
(5)
(6)
0.371
(0.099)
0.363
(0.100)
black
0.084*
0.688**
0.389**
0.246
(0.023)
(0.182)
(0.098)
(0.448)
2.57
(0.66)
applicant single;
high school diploma; industry
unemployment rate
5.85
(< 0.001)
5.22
5.79
246
(0.60)
2.62
(0.61)
P/A ratio
0.449**
4.76*
2.44
(0.001)
(< 0.001)
(0.114)
(1.33)
(0.61)
houring expense-to
income patio
-0.048
-0.11
(1.29)
-0.18
-0.30
-0.50
(0.70)
-0.54
(0.110)
(0.74)
0.22
(0.08)
(0.68)
(0.68)
additional credit rating
indicator variables
0,031
1.22
0.21**
(0.08)
0.79
(0.18)
medium loan-to-value ratio
0.46**
0.22*
0.22*
(0.80 s loan-value ratio s 0.95)
(0.013)
(0.16)
(0.08)
(0.08)
(0.291)
high loan-to-value ratio
(loan-value ratio > 0.95)
0.79
(0.18)
0.189**
1.49**
0.84**
0.79*
(0.050)
(0.32)
(0.18)
(0.18)
race interactions and black
4.96
(0.002)
COMLSumer credit score
0.031**
0.29**
(0.04)
0 29
0.15**
(0.02)
0.16**
0.34**
0.16*
(0.005)
(0.02)
(0.11)
(0.02)
mortgage credit score
0.021
0.28
0.15
0.11
0.16
0.11
race interactions only
0.27
(0.011)
(0.14)
(0.07)
(О.ок)
(0.08)
(0.10)
0.72
0.72*
(0.12)
(0.08)
(0.766)
a.197*
(0.035)
public bad credit record
0.70*
(0.12)
1.23**
0.70
0.70*
(0.20)
(0.12)
(0.12)
difference in predicted
probability of denial, white
vs. black (percentage points)
0,702
(0.045)
2.56
(0.30)
2.59
(0.29)
denied mortgage insurance
4.55**
2.59**
2.59
(0.57)
(0.30)
(0.29)
0.060
(0.021)
035*
(0.11)
0.15
(0.11)
6.0%
6,6%
6.3%
6.5%
self-employed
0.34**
8.4%
7.1%
0.67**
0.36**
(0.21)
(0.11)
(0.11)
0.23*
(0.08)
0.23
(0.08)
0.23
(0.08)
single
These regressions were estimated using the n = 2380 observations in the Boston HMDA data set described in Appendix 11.1. The
linear probability model was estimated by OLS, and probit and logit regressions were estimated by maximum likelihood. Standard
errors are given in parentheses under the coefficients, and p-values are given in parentheses under the F-statistics. The change in pre-
dicted probability in the final row was computed for a hypothetical applicant whose values of the regressors, other than race, equal the
sample mean. Individual coefficients are statistically significant at the *5% or **1% level.
high school diploma
-0.61**
-0,60
-0.62
(0.23)
(0.24)
(0.23)
unemployment rate
0.03
(0.02)
0.03
(0.02)
0.03
(0.02)
condominium
-0.05
(0.09)
black x PI ratio
-0.58
(1.47)
black x houving expense-
do-income ratio
1.23
(1.69)
additional credit rating
indicator variables
no
по
ves
по
-5,71
(0.48)
-3.04
(0.23)
-2.90
(0.39)
-2.54**
(0.35)
COMstant
-0.183**
-2.57*
(0.028)
(0.34)

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