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

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TABLE 11.2 Mortgage Denial Regressions Using the Boston HMDA Data Dependent variable: deny = 1 if mortgage application is denied, = 0 if accepted; 2380 observations. Regression Model Regressor black LPM Logit Probit Probit Probit Probit (1) (2) (3) (4) (5) (6) 0.084** 0.688** 0.389** 0.371** 0.363** (0.023) (0.182) (0.098) (0.099) (0.100) 0.246 (0.448) P/I ratio 0.449** 4.76** 2.44** 2.46** 2.62** 2.57** (0.114) (133) (0.61) (0.60) (0.61) (0.66) housing expense-to-income ratio -0.048 -0.11 -0.18 -0.30 -0.50 -0.54 (0.110) (1.29) (0.68) (0.68) (0.70) (0.74) medium loan-to-value ratio 0.031* 0.46** 0.21** 0.22** 0.22** 0.22** (0.80 loan-value ratio 0.95) (0.013) (0.16) (0.08) (0.08) (0.08) (0.08) high loan-to-value ratio (loan-value 0.189** 1.49** 0.79** 0.79** 0.84** 0.79** ratio > 0.95) (0.050) (0.32) (0.18) (0.18) (0.18) (0.18) consumer credit score 0.031** 0.29** 0.15** 0.16** 0.34** 0.16** (0.005) (0.04) (0.02) (0.02) (0.11) (0.02) mortgage credit score 0.021 0.28* 0.15* 0.11 0.16 0.11 (0.011) (0.14) (0.07) (0.08) (0.10) (0.08) public bad credit record 0.197** 1.23** 0.70** 0.70** 0.72** 0.70** (0.035) (0.20) (0.12) (0.12) (0.12) (0.12) denied mortgage insurance 0.702** 4.55** 2.56** 2.59** 2.59** 2.59** (0.045) (0.57) (0.30) (0.29) (0.30) (0.29) self-employed 0.060** 0.67** 0.36** 0.35** 0.34** 0.35** (0.021) (0.21) (0.11) (0.11) (0.11) (0.11) single 0.23** 0.23** 0.23** (0.08) (0.08) (0.08) high school diploma unemployment rate condominium -0.61** -0.60* -0.62** (0.23) (0.24) (0.23) 0.03 0.03 0.03 (0.02) (0.02) (0.02) -0.05 (0.09) black XP/I ratio -0.58 (1.47) black x housing expense-to-income ratio additional credit rating indicator variables 1.23 (1.69) constant applicant single; high school diploma, industry unemployment rate additional credit rating indicator variables no no no no yes no -0.183** (0.028) -5.71** (0.48) -3.04** (0.23) -2.57** (0.34) -2.90** (0.39) -2.54** (0.35) 5.85 ( <0.001) 5.22 5.79 (0.001) ( <0.001) 1.22 (0.291) race interactions and black 4.96 (0.002) race interactions only 0.27 (0.766) difference in predicted probability of denial, white vs. black (percent- age points) 8.4% 6.0% 7.1% 6.6% 6.3% 6.5% 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 predicted 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.