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
Problem 1P
Related questions
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?

Transcribed Image Text: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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