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Update 11-ch11.Rmd
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@Ocalak
Ocalak authored Jan 10, 2024
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Expand Up @@ -605,32 +605,32 @@ Next we reproduce the estimation results presented in Table 11.2 of the book.

```{r}
# estimate all 6 models for the denial probability
l_HMDA <- lm(deny ~ black + pirat + hirat + lvrat + chist + mhist + phist
lpm_HMDA <- lm(deny ~ black + pirat + hirat + lvrat + chist + mhist + phist
+ insurance + selfemp, data = HMDA)
logit_HMDA <- glm(deny ~ black + pirat + hirat + lvrat + chist + mhist + phist
+ insurance + selfemp,
family = binomial(link = "logit"),
data = HMDA)
p_HMDA1 <- glm(deny ~ black + pirat + hirat + lvrat + chist + mhist + phist
probit_HMDA1 <- glm(deny ~ black + pirat + hirat + lvrat + chist + mhist + phist
+ insurance + selfemp,
family = binomial(link = "probit"),
data = HMDA)
p_HMDA2 <- glm(deny ~ black + pirat + hirat + lvrat + chist + mhist + phist
probit_HMDA2 <- glm(deny ~ black + pirat + hirat + lvrat + chist + mhist + phist
+ insurance + selfemp + single + hschool + unemp,
family = binomial(link = "probit"),
data = HMDA)
p_HMDA3 <- glm(deny ~ black + pirat + hirat + lvrat + chist + mhist
probit_HMDA3 <- glm(deny ~ black + pirat + hirat + lvrat + chist + mhist
+ phist + insurance + selfemp + single + hschool + unemp
+condomin + I(mhist==3) + I(mhist==4) + I(chist==3)
+ I(chist==4) + I(chist==5)+ I(chist==6),
family = binomial(link = "probit"),
data = HMDA)
p_HMDA4 <- glm(deny ~ black * (pirat + hirat) + lvrat + chist + mhist + phist
probit_HMDA4 <- glm(deny ~ black * (pirat + hirat) + lvrat + chist + mhist + phist
+ insurance + selfemp + single + hschool + unemp,
family = binomial(link = "probit"),
data = HMDA)
Expand All @@ -639,15 +639,15 @@ p_HMDA4 <- glm(deny ~ black * (pirat + hirat) + lvrat + chist + mhist + phist
Just as in previous chapters, we store heteroskedasticity-robust standard errors of the coefficient estimators in a `r ttcode("list")` which is then used as the argument `r ttcode("se")` in `r ttcode("stargazer()")`.

```{r, eval=FALSE}
rob_se <- list(sqrt(diag(vcovHC(l_HMDA, type = "HC1"))),
rob_se <- list(sqrt(diag(vcovHC(lpm_HMDA, type = "HC1"))),
sqrt(diag(vcovHC(logit_HMDA, type = "HC1"))),
sqrt(diag(vcovHC(p_HMDA1, type = "HC1"))),
sqrt(diag(vcovHC(p_HMDA2, type = "HC1"))),
sqrt(diag(vcovHC(p_HMDA3, type = "HC1"))),
sqrt(diag(vcovHC(p_HMDA4, type = "HC1"))))
sqrt(diag(vcovHC(probit_HMDA1, type = "HC1"))),
sqrt(diag(vcovHC(probit_HMDA2, type = "HC1"))),
sqrt(diag(vcovHC(probit_HMDA3, type = "HC1"))),
sqrt(diag(vcovHC(probit_HMDA4, type = "HC1"))))
stargazer(l_HMDA, logit_HMDA, p_HMDA1,
p_HMDA2, p_HMDA3, p_HMDA4,
stargazer(lpm_HMDA, logit_HMDA, probit_HMDA1,
probit_HMDA2, probit_HMDA3, probit_HMDA4,
digits = 3,
type = "latex",
header = FALSE,
Expand All @@ -662,15 +662,15 @@ stargazer(l_HMDA, logit_HMDA, p_HMDA1,
library(stargazer)
rob_se <- list(
sqrt(diag(vcovHC(l_HMDA, type = "HC1"))),
sqrt(diag(vcovHC(lpm_HMDA, type = "HC1"))),
sqrt(diag(vcovHC(logit_HMDA, type = "HC1"))),
sqrt(diag(vcovHC(p_HMDA1, type = "HC1"))),
sqrt(diag(vcovHC(p_HMDA2, type = "HC1"))),
sqrt(diag(vcovHC(p_HMDA3, type = "HC1"))),
sqrt(diag(vcovHC(p_HMDA4, type = "HC1")))
sqrt(diag(vcovHC(probit_HMDA1, type = "HC1"))),
sqrt(diag(vcovHC(probit_HMDA2, type = "HC1"))),
sqrt(diag(vcovHC(probit_HMDA3, type = "HC1"))),
sqrt(diag(vcovHC(probit_HMDA4, type = "HC1")))
)
stargazer(l_HMDA, logit_HMDA, p_HMDA1, p_HMDA2, p_HMDA3, p_HMDA4,
stargazer(lpm_HMDA, logit_HMDA, probit_HMDA1, probit_HMDA2, probit_HMDA3, probit_HMDA4,
digits = 3,
type = "html",
se = rob_se,
Expand All @@ -689,15 +689,15 @@ stargazer_html_title("HMDA Data: LPM, Probit and Logit Models", "hmdad")
library(stargazer)
rob_se <- list(
sqrt(diag(vcovHC(l_HMDA, type = "HC1"))),
sqrt(diag(vcovHC(lpm_HMDA, type = "HC1"))),
sqrt(diag(vcovHC(logit_HMDA, type = "HC1"))),
sqrt(diag(vcovHC(p_HMDA1, type = "HC1"))),
sqrt(diag(vcovHC(p_HMDA2, type = "HC1"))),
sqrt(diag(vcovHC(p_HMDA3, type = "HC1"))),
sqrt(diag(vcovHC(p_HMDA4, type = "HC1")))
sqrt(diag(vcovHC(probit_HMDA1, type = "HC1"))),
sqrt(diag(vcovHC(probit_HMDA2, type = "HC1"))),
sqrt(diag(vcovHC(probit_HMDA3, type = "HC1"))),
sqrt(diag(vcovHC(probit_HMDA4, type = "HC1")))
)
stargazer(l_HMDA, logit_HMDA, p_HMDA1, p_HMDA2, p_HMDA3, p_HMDA4,
stargazer(lpm_HMDA, logit_HMDA, probit_HMDA1, probit_HMDA2, probit_HMDA3, probit_HMDA4,
title = "\\label{tab:hmdad} HMDA Data: LPM, Probit and Logit Models",
digits = 3,
type = "latex",
Expand Down Expand Up @@ -736,27 +736,27 @@ new <- data.frame(
"condomin" = "no")
# differnce predicted by the LPM
predictions <- predict(l_HMDA, newdata = new)
predictions <- predict(lpm_HMDA, newdata = new)
diff(predictions)
# differnce predicted by the logit model
predictions <- predict(logit_HMDA, newdata = new, type = "response")
diff(predictions)
# difference predicted by probit model (3)
predictions <- predict(p_HMDA1, newdata = new, type = "response")
predictions <- predict(probit_HMDA1, newdata = new, type = "response")
diff(predictions)
# difference predicted by probit model (4)
predictions <- predict(p_HMDA2, newdata = new, type = "response")
predictions <- predict(probit_HMDA2, newdata = new, type = "response")
diff(predictions)
# difference predicted by probit model (5)
predictions <- predict(p_HMDA3, newdata = new, type = "response")
predictions <- predict(probit_HMDA3, newdata = new, type = "response")
diff(predictions)
# difference predicted by probit model (6)
predictions <- predict(p_HMDA4, newdata = new, type = "response")
predictions <- predict(probit_HMDA4, newdata = new, type = "response")
diff(predictions)
```

Expand All @@ -767,7 +767,7 @@ Regressions (4) to (6) use regression specifications that include different appl
An interesting question related to racial discrimination can be investigated using the Probit model (6) where the interactions `r ttcode("blackyes:pirat")` and `r ttcode("blackyes:hirat")` are added to model (4). If the coefficient on `r ttcode("blackyes:pirat")` was different from zero, the effect of the payment-to-income ratio on the denial probability would be different for black and white applicants. Similarly, a non-zero coefficient on `r ttcode("blackyes:hirat")` would indicate that loan officers weight the risk of bankruptcy associated with a high loan-to-value ratio differently for black and white mortgage applicants. We can test whether these coefficients are jointly significant at the $5\%$ level using an $F$-Test.

```{r}
linearHypothesis(p_HMDA4,
linearHypothesis(probit_HMDA4,
test = "F",
c("blackyes:pirat=0", "blackyes:hirat=0"),
vcov = vcovHC, type = "HC1")
Expand All @@ -776,7 +776,7 @@ linearHypothesis(p_HMDA4,
Since $p\text{-value} \approx 0.77$ for this test, the null cannot be rejected. Nonetheless, we can reject the hypothesis that there is no racial discrimination at all since the corresponding $F$-test has a $p\text{-value}$ of about $0.002$.

```{r}
linearHypothesis(p_HMDA4,
linearHypothesis(probit_HMDA4,
test = "F",
c("blackyes=0", "blackyes:pirat=0", "blackyes:hirat=0"),
vcov = vcovHC, type = "HC1")
Expand Down

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