Redlining refers to the practice of refusing to issue insurance to certain types of people or within some geographic area. In the 1970s, the US Commission on Civil Rights examined charges by Chicago community organizations that insurance companies were redlining their neighborhoods. A FAIR plan (Fair Access to Insurance Requirements) was offered by the city of Chicago as a default policy to homeowners rejected by the voluntary market. This serves as a measure of insurance availability. Of interest is the extent to which racial composition of a community affects underwriting practices after controlling for factors that legitimately affect underwriting such as theft and fire damage.
Data was collected for 47 zip codes.
Variable definitions:
Row names are zip codes.
chicago <- readRDS("chicago.rds")
head(chicago) race fire theft age involact income
60626 10.0 6.2 29 60.4 0.0 11744
60640 22.2 9.5 44 76.5 0.1 9323
60613 19.6 10.5 36 73.5 1.2 9948
60657 17.3 7.7 37 66.9 0.5 10656
60614 24.5 8.6 53 81.4 0.7 9730
60610 54.0 34.1 68 52.6 0.3 8231Numerical summaries of data.
summary(chicago) race fire theft age
Min. : 1.00 Min. : 2.00 Min. : 3.00 Min. : 2.00
1st Qu.: 3.75 1st Qu.: 5.65 1st Qu.: 22.00 1st Qu.:48.60
Median :24.50 Median :10.40 Median : 29.00 Median :65.00
Mean :34.99 Mean :12.28 Mean : 32.36 Mean :60.33
3rd Qu.:57.65 3rd Qu.:16.05 3rd Qu.: 38.00 3rd Qu.:77.30
Max. :99.70 Max. :39.70 Max. :147.00 Max. :90.10
involact income
Min. :0.0000 Min. : 5583
1st Qu.:0.0000 1st Qu.: 8447
Median :0.4000 Median :10694
Mean :0.6149 Mean :10696
3rd Qu.:0.9000 3rd Qu.:11989
Max. :2.2000 Max. :21480 What proportion are zeroes?
sum(chicago$involact == 0)[1] 15mean(chicago$involact == 0)[1] 0.3191489Pairwise correlations
round(cor(chicago), 2) race fire theft age involact income
race 1.00 0.59 0.26 0.25 0.71 -0.70
fire 0.59 1.00 0.56 0.41 0.70 -0.61
theft 0.26 0.56 1.00 0.32 0.15 -0.17
age 0.25 0.41 0.32 1.00 0.48 -0.53
involact 0.71 0.70 0.15 0.48 1.00 -0.66
income -0.70 -0.61 -0.17 -0.53 -0.66 1.00Some pairwise scatter plots. We see some outliers and possibly influential points.
library(ggplot2)
ggplot(chicago) +
aes(x = race, y = involact) +
geom_point() +
stat_smooth()
ggplot(chicago) +
aes(x = fire, y = involact) +
geom_point() +
stat_smooth()
ggplot(chicago) +
aes(x = theft, y = involact) +
geom_point() +
stat_smooth()
ggplot(chicago) +
aes(x = income, y = involact) +
geom_point() +
stat_smooth()
Comparing race with fire.
ggplot(chicago) +
aes(x = race, y = fire) +
geom_point() +
stat_smooth()
Comparing race and theft.
ggplot(chicago) +
aes(x = race, y = theft) +
geom_point() +
stat_smooth()
Model involact (new and renewed FAIR plans per 100 housing units) as function of race controlling for fire, theft, age of home, and median family income. Log transform income since it’s better to consider it on a multiplicative scale instead of an additive scale.
m1 <- lm(involact ~ race + fire + theft + age + log(income),
data = chicago)
summary(m1)
Call:
lm(formula = involact ~ race + fire + theft + age + log(income),
data = chicago)
Residuals:
Min 1Q Median 3Q Max
-0.85393 -0.16922 -0.03088 0.17890 0.81228
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -3.573976 3.857292 -0.927 0.359582
race 0.009502 0.002490 3.817 0.000449 ***
fire 0.039856 0.008766 4.547 4.76e-05 ***
theft -0.010295 0.002818 -3.653 0.000728 ***
age 0.008336 0.002744 3.038 0.004134 **
log(income) 0.345762 0.400123 0.864 0.392540
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.3345 on 41 degrees of freedom
Multiple R-squared: 0.7517, Adjusted R-squared: 0.7214
F-statistic: 24.83 on 5 and 41 DF, p-value: 2.009e-11How robust is our conclusion to the choice of covariates?
listcombo <- unlist(sapply(0:4, function(x)combn(1:4, x, simplify = FALSE)),
recursive = FALSE)
predterms <- lapply(listcombo, function(x)
paste(c("race", c("fire", "theft", "age", "log(income)")[x]),
collapse = " + "))
coefm <- matrix(NA, 16, 2)
for(i in 1:16){
lmi <- lm(as.formula(paste("involact ~ ", predterms[[i]])),
data = chicago)
# extract race coefficient and p-value
coefm[i,] <- summary(lmi)$coef[2, c(1, 4)]
}
rownames(coefm) <- predterms
colnames(coefm) <- c("race", "pvalue")
round(coefm, 4) race pvalue
race 0.0139 0.0000
race + fire 0.0089 0.0002
race + theft 0.0141 0.0000
race + age 0.0123 0.0000
race + log(income) 0.0082 0.0087
race + fire + theft 0.0082 0.0002
race + fire + age 0.0089 0.0001
race + fire + log(income) 0.0070 0.0160
race + theft + age 0.0128 0.0000
race + theft + log(income) 0.0084 0.0083
race + age + log(income) 0.0099 0.0017
race + fire + theft + age 0.0081 0.0001
race + fire + theft + log(income) 0.0073 0.0078
race + fire + age + log(income) 0.0085 0.0041
race + theft + age + log(income) 0.0106 0.0010
race + fire + theft + age + log(income) 0.0095 0.0004Pretty robust. It doesn’t matter what combination of covariates we control for, the race coefficient is positive.
Does our conclusion depend on a few cases? Do we have influential observations?
plot(m1, which = 5)
High theft and fire zip codes.
chicago["60607",] race fire theft age involact income
60607 50.2 39.7 147 83 0.9 7459Fit a model without this observation.
i <- which(rownames(chicago) == "60607")
m2 <- lm(involact ~ race + fire + theft + age + log(income),
data = chicago, subset = -i)
summary(m2)
Call:
lm(formula = involact ~ race + fire + theft + age + log(income),
data = chicago, subset = -i)
Residuals:
Min 1Q Median 3Q Max
-0.72943 -0.19062 -0.04279 0.18546 0.79648
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -4.658229 4.103618 -1.135 0.263068
race 0.010416 0.002748 3.790 0.000497 ***
fire 0.039506 0.008815 4.481 6.08e-05 ***
theft -0.012856 0.004269 -3.012 0.004488 **
age 0.009073 0.002906 3.123 0.003326 **
log(income) 0.463082 0.427708 1.083 0.285423
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.336 on 40 degrees of freedom
Multiple R-squared: 0.7545, Adjusted R-squared: 0.7239
F-statistic: 24.59 on 5 and 40 DF, p-value: 3.117e-11Compare models.
car::compareCoefs(m1, m2)Calls:
1: lm(formula = involact ~ race + fire + theft + age + log(income), data =
chicago)
2: lm(formula = involact ~ race + fire + theft + age + log(income), data =
chicago, subset = -i)
Model 1 Model 2
(Intercept) -3.57 -4.66
SE 3.86 4.10
race 0.00950 0.01042
SE 0.00249 0.00275
fire 0.03986 0.03951
SE 0.00877 0.00882
theft -0.01029 -0.01286
SE 0.00282 0.00427
age 0.00834 0.00907
SE 0.00274 0.00291
log(income) 0.346 0.463
SE 0.400 0.428
Conclusion seems robust to the exclusion of one data point.
Race coefficient is statistically significant but small. Every 10 percent increase in the minority composition leads to about a 0.09 increase in FAIR plan policies and renewals per 100 housing units
The predicted difference between 0% and 100% minority is about 1.
library(emmeans)
emmeans(m1, specs = "race", at = list(race = c(0, 100))) race emmean SE df lower.CL upper.CL
0 0.293 0.0935 41 0.104 0.482
100 1.243 0.1770 41 0.886 1.600
Confidence level used: 0.95 We can visualize this association with an effect plot.
library(ggeffects)
ggpredict(m1, terms = "race") |>
plot(show_data = TRUE)
The analysis is also at the aggregate level. The results may not hold at the individual level.
The analysis was done using the R Statistical language (v4.5.2; R Core Team, 2025) on Windows 11 x64, using the packages emmeans (v1.11.2.8), ggeffects (v2.3.1) and ggplot2 (v4.0.0).