Traditional Model vs. Upstart model
10/27/2020
fundedloans <- read_fst(path = paste0(path,"fundedloans_trad_vs_upstart.fst"),as.data.table = T)1 APR
This section compares the difference between the APR the borrower would have received under the traditional underwriting model to the actual APR. The sample consists of funded loans in the second half of 2019 (CFPB model outputs are only available for applications in the second half of 2019)
1.1 Univariate evidence
aprsummary <- fundedloans[ficobin %in% 620:800,.(estapr=mean(estimated_apr,na.rm=T),estaprsd=sd(estimated_apr,na.rm=T),actapr=mean(apr,na.rm=T),actaprsd=sd(apr,na.rm=T)),by=ficobin]
aprsummary <- melt(aprsummary,id.vars = "ficobin")
aprsummary[,variable:=as.character(variable)]
aprsummary[,variable:=ifelse(variable=="estapr","APR based on traditional variables",ifelse(variable=="actapr","APR based on Upstart model",variable))]
ggplot()+
geom_line(data=aprsummary[nchar(variable)>20],aes(x=ficobin,y=value,color=variable),size=1)+
geom_point(data=aprsummary[nchar(variable)>20],aes(x=ficobin,y=value,color=variable,shape=variable),size=3)+
theme_minimal()+labs(x="",y="APR (%)")+
scale_color_manual(values=c("dodgerblue4","dodgerblue2"))+
theme(legend.position = "bottom",legend.title = element_blank())+
scale_x_continuous(breaks = unique(aprsummary$ficobin))
1.2 Regression
Dependent variable: (Traditional APR - Actual APR)*100
Fixed effects: zip code
Standard errors: clustered at zip code
Results suggest younger, higher-educated, debt consolidating, and computer using applicants would have received a higher APR under the traditional model compared to the actual rate, when the FICO is lower.
r <- felm(aprdiff~one_over_fico100*incomelt50+one_over_fico100*agebelow30+one_over_fico100*factor(education)+one_over_fico100*chlt10yr+one_over_fico100*debtconsolidation+one_over_fico100*computer+one_over_fico100*loanaggrigator|zip.x|0|zip.x,data=fundedloans)
.printtable(r,column.labels = c("Traditional APR - Actual APR"))##
## ================================================================
## Dependent variable:
## ----------------------------
## Traditional APR - Actual APR
## ----------------------------------------------------------------
## one_over_fico100 421.255***
## (13.158)
## incomelt50 7.585***
## (1.248)
## agebelow30 -12.400***
## (1.553)
## factor(education)1 -9.028***
## (1.285)
## factor(education)2 -22.525***
## (1.969)
## chlt10yr 3.340**
## (1.501)
## debtconsolidation -6.217***
## (1.370)
## computer -9.677***
## (1.238)
## loanaggrigator 12.139***
## (1.213)
## one_over_fico100:incomelt50 -92.797***
## (8.648)
## one_over_fico100:agebelow30 92.954***
## (10.736)
## one_over_fico100:factor(education)1 78.421***
## (8.915)
## one_over_fico100:factor(education)2 188.293***
## (13.640)
## one_over_fico100:chlt10yr -25.442**
## (10.358)
## one_over_fico100:debtconsolidation 64.451***
## (9.588)
## one_over_fico100:computer 72.812***
## (8.584)
## one_over_fico100:loanaggrigator -99.150***
## (8.411)
## ----------------------------------------------------------------
##
## Observations 86,999
## Adjusted R2 0.324
## ================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01
## 1.3 Univariate evidence splits
1.3.1 By income
aprsummary <- fundedloans[ficobin %in% 620:800,.(value=mean(estimated_apr,na.rm=T)-mean(apr,na.rm=T)),by=.(ficobin,incomelt50)]
aprsummary[,variable:=ifelse(incomelt50==1,"Income less than $50,000","Income greater than $50,000")]
ggplot()+
geom_line(data=aprsummary,aes(x=ficobin,y=value,color=variable),size=1)+
geom_point(data=aprsummary,aes(x=ficobin,y=value,color=variable,shape=variable),size=3)+
theme_minimal()+labs(x="",y="Traditional APR - Actual APR (%)")+
scale_color_manual(values=c("dodgerblue4","dodgerblue2"))+
theme(legend.position = "bottom",legend.title = element_blank())+
scale_x_continuous(breaks = unique(aprsummary$ficobin))
1.3.2 By education
aprsummary <- fundedloans[ficobin %in% 620:800,.(value=mean(estimated_apr,na.rm=T)-mean(apr,na.rm=T)),by=.(ficobin,education)]
aprsummary[,variable:=ifelse(education==2,"Advanced degree",ifelse(education==1,"College degree","No college degree"))]
ggplot()+
geom_line(data=aprsummary,aes(x=ficobin,y=value,color=variable),size=1)+
geom_point(data=aprsummary,aes(x=ficobin,y=value,color=variable,shape=variable),size=3)+
theme_minimal()+labs(x="",y="Traditional APR - Actual APR (%)")+
scale_color_manual(values=c("dodgerblue4","dodgerblue2","skyblue"))+
theme(legend.position = "bottom",legend.title = element_blank())+
scale_x_continuous(breaks = unique(aprsummary$ficobin))
1.3.3 By age
aprsummary <- fundedloans[ficobin %in% 620:800,.(value=mean(estimated_apr,na.rm=T)-mean(apr,na.rm=T)),by=.(ficobin,agebelow30)]
aprsummary[,variable:=ifelse(agebelow30==1,"Age less than 30","Age greater than 30")]
ggplot()+
geom_line(data=aprsummary,aes(x=ficobin,y=value,color=variable),size=1)+
geom_point(data=aprsummary,aes(x=ficobin,y=value,color=variable,shape=variable),size=3)+
theme_minimal()+labs(x="",y="Traditional APR - Actual APR (%)")+
scale_color_manual(values=c("dodgerblue4","dodgerblue2"))+
theme(legend.position = "bottom",legend.title = element_blank())+
scale_x_continuous(breaks = unique(aprsummary$ficobin))
1.3.4 By credit history
aprsummary <- fundedloans[ficobin %in% 620:800,.(value=mean(estimated_apr,na.rm=T)-mean(apr,na.rm=T)),by=.(ficobin,chlt10yr)]
aprsummary[,variable:=ifelse(chlt10yr==1,"Credit history less than 10 years","Credit history greater than 10 years")]
ggplot()+
geom_line(data=aprsummary,aes(x=ficobin,y=value,color=variable),size=1)+
geom_point(data=aprsummary,aes(x=ficobin,y=value,color=variable,shape=variable),size=3)+
theme_minimal()+labs(x="",y="Traditional APR - Actual APR (%)")+
scale_color_manual(values=c("dodgerblue4","dodgerblue2"))+
theme(legend.position = "bottom",legend.title = element_blank())+
scale_x_continuous(breaks = unique(aprsummary$ficobin))
1.3.5 By employment type
aprsummary <- fundedloans[ficobin %in% 620:800,.(value=mean(estimated_apr,na.rm=T)-mean(apr,na.rm=T)),by=.(ficobin,employed_hourly)]
aprsummary[,variable:=ifelse(employed_hourly==1,"Hourly worker","Non-hourly worker")]
ggplot()+
geom_line(data=aprsummary,aes(x=ficobin,y=value,color=variable),size=1)+
geom_point(data=aprsummary,aes(x=ficobin,y=value,color=variable,shape=variable),size=3)+
theme_minimal()+labs(x="",y="Traditional APR - Actual APR (%)")+
scale_color_manual(values=c("dodgerblue4","dodgerblue2"))+
theme(legend.position = "bottom",legend.title = element_blank())+
scale_x_continuous(breaks = unique(aprsummary$ficobin))
1.3.6 By device type
aprsummary <- fundedloans[ficobin %in% 620:800,.(value=mean(estimated_apr,na.rm=T)-mean(apr,na.rm=T)),by=.(ficobin,computer)]
aprsummary[,variable:=ifelse(computer==1,"Computer","Smartphone")]
ggplot()+
geom_line(data=aprsummary,aes(x=ficobin,y=value,color=variable),size=1)+
geom_point(data=aprsummary,aes(x=ficobin,y=value,color=variable,shape=variable),size=3)+
theme_minimal()+labs(x="",y="Traditional APR - Actual APR (%)")+
scale_color_manual(values=c("dodgerblue4","dodgerblue2"))+
theme(legend.position = "bottom",legend.title = element_blank())+
scale_x_continuous(breaks = unique(aprsummary$ficobin))
1.3.7 By channel
aprsummary <- fundedloans[ficobin %in% 620:800,.(value=mean(estimated_apr,na.rm=T)-mean(apr,na.rm=T)),by=.(ficobin,loanaggrigator)]
aprsummary[,variable:=ifelse(loanaggrigator==1,"Loan aggregator","Other")]
ggplot()+
geom_line(data=aprsummary,aes(x=ficobin,y=value,color=variable),size=1)+
geom_point(data=aprsummary,aes(x=ficobin,y=value,color=variable,shape=variable),size=3)+
theme_minimal()+labs(x="",y="Traditional APR - Actual APR (%)")+
scale_color_manual(values=c("dodgerblue4","dodgerblue2"))+
theme(legend.position = "bottom",legend.title = element_blank())+
scale_x_continuous(breaks = unique(aprsummary$ficobin))
2 Rejection rate
This section analyses the rejection rate by the traditional model for the loans funded by Upstart. The sample consists of funded loans in the second half of 2019 (CFPB model outputs are only available for applications in the second half of 2019)
2.1 Univariate evidence
rejecsummary <- fundedloans[ficobin %in% 620:800,.(rejecttrad=mean(rejecttrad,na.rm=T)*100),by=ficobin]
ggplot(rejecsummary,aes(x=ficobin,y=rejecttrad))+geom_line(size=1,color="dodgerblue4")+geom_point(size=3,color="dodgerblue4")+theme_minimal()+labs(x="",y="Pct of funded loans rejected by traditional model")+scale_x_continuous(breaks = unique(rejecsummary$ficobin))
2.2 Regression
Dependent variable: Rejected by the traditional model
Fixed effects: zip code
Standard errors: clustered at zip code
r <- felm(rejecttrad~one_over_fico100*incomelt50+one_over_fico100*agebelow30+one_over_fico100*factor(education)+one_over_fico100*chlt10yr+one_over_fico100*debtconsolidation+one_over_fico100*computer+one_over_fico100*loanaggrigator|zip.x|0|zip.x,data=fundedloans)
.printtable(r,column.labels = c("Rejected by traditional model"))##
## =================================================================
## Dependent variable:
## -----------------------------
## Rejected by traditional model
## -----------------------------------------------------------------
## one_over_fico100 20.174***
## (0.580)
## incomelt50 0.169***
## (0.056)
## agebelow30 -0.720***
## (0.071)
## factor(education)1 -0.486***
## (0.057)
## factor(education)2 -0.753***
## (0.083)
## chlt10yr -0.118*
## (0.069)
## debtconsolidation -0.597***
## (0.060)
## computer -0.217***
## (0.054)
## loanaggrigator 0.600***
## (0.053)
## one_over_fico100:incomelt50 -2.047***
## (0.387)
## one_over_fico100:agebelow30 5.045***
## (0.485)
## one_over_fico100:factor(education)1 3.614***
## (0.393)
## one_over_fico100:factor(education)2 5.827***
## (0.565)
## one_over_fico100:chlt10yr 0.866*
## (0.470)
## one_over_fico100:debtconsolidation 4.489***
## (0.421)
## one_over_fico100:computer 1.542***
## (0.369)
## one_over_fico100:loanaggrigator -4.435***
## (0.366)
## -----------------------------------------------------------------
##
## Observations 86,999
## Adjusted R2 0.219
## =================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01
## 2.3 Univariate splits
2.3.1 By income
aprsummary <- fundedloans[ficobin %in% 620:800,.(value=mean(rejecttrad,na.rm=T)*100),by=.(ficobin,incomelt50)]
aprsummary[,variable:=ifelse(incomelt50==1,"Income less than $50,000","Income greater than $50,000")]
ggplot()+
geom_line(data=aprsummary,aes(x=ficobin,y=value,color=variable),size=1)+
geom_point(data=aprsummary,aes(x=ficobin,y=value,color=variable,shape=variable),size=3)+
theme_minimal()+labs(x="",y="Pct of funded loans rejected by traditional model")+
scale_color_manual(values=c("dodgerblue4","dodgerblue2"))+
theme(legend.position = "bottom",legend.title = element_blank())+
scale_x_continuous(breaks = unique(aprsummary$ficobin))
2.3.2 By education
aprsummary <- fundedloans[ficobin %in% 620:800,.(value=mean(rejecttrad,na.rm=T)*100),by=.(ficobin,college)]
aprsummary[,variable:=ifelse(college==1,"With college degree","Without college degree")]
ggplot()+
geom_line(data=aprsummary,aes(x=ficobin,y=value,color=variable),size=1)+
geom_point(data=aprsummary,aes(x=ficobin,y=value,color=variable,shape=variable),size=3)+
theme_minimal()+labs(x="",y="Pct of funded loans rejected by traditional model")+
scale_color_manual(values=c("dodgerblue4","dodgerblue2"))+
theme(legend.position = "bottom",legend.title = element_blank())+
scale_x_continuous(breaks = unique(aprsummary$ficobin))
2.3.3 By age
aprsummary <- fundedloans[ficobin %in% 620:800,.(value=mean(rejecttrad,na.rm=T)*100),by=.(ficobin,agebelow30)]
aprsummary[,variable:=ifelse(agebelow30==1,"Age less than 30","Age greater than 30")]
ggplot()+
geom_line(data=aprsummary,aes(x=ficobin,y=value,color=variable),size=1)+
geom_point(data=aprsummary,aes(x=ficobin,y=value,color=variable,shape=variable),size=3)+
theme_minimal()+labs(x="",y="Pct of funded loans rejected by traditional model")+
scale_color_manual(values=c("dodgerblue4","dodgerblue2"))+
theme(legend.position = "bottom",legend.title = element_blank())+
scale_x_continuous(breaks = unique(aprsummary$ficobin))
2.3.4 By credit history
aprsummary <- fundedloans[ficobin %in% 620:800,.(value=mean(rejecttrad,na.rm=T)*100),by=.(ficobin,chlt10yr)]
aprsummary[,variable:=ifelse(chlt10yr==1,"Credit history less than 10 years","Credit history greater than 10 years")]
ggplot()+
geom_line(data=aprsummary,aes(x=ficobin,y=value,color=variable),size=1)+
geom_point(data=aprsummary,aes(x=ficobin,y=value,color=variable,shape=variable),size=3)+
theme_minimal()+labs(x="",y="Pct of funded loans rejected by traditional model")+
scale_color_manual(values=c("dodgerblue4","dodgerblue2"))+
theme(legend.position = "bottom",legend.title = element_blank())+
scale_x_continuous(breaks = unique(aprsummary$ficobin))
2.3.5 By employment type
aprsummary <- fundedloans[ficobin %in% 620:800,.(value=mean(rejecttrad,na.rm=T)*100),by=.(ficobin,hourly)]
aprsummary[,variable:=ifelse(hourly==1,"Hourly worker","Non-hourly worker")]
ggplot()+
geom_line(data=aprsummary,aes(x=ficobin,y=value,color=variable),size=1)+
geom_point(data=aprsummary,aes(x=ficobin,y=value,color=variable,shape=variable),size=3)+
theme_minimal()+labs(x="",y="Pct of funded loans rejected by traditional model")+
scale_color_manual(values=c("dodgerblue4","dodgerblue2"))+
theme(legend.position = "bottom",legend.title = element_blank())+
scale_x_continuous(breaks = unique(aprsummary$ficobin))