| Literature DB >> 35024285 |
Serena Gallo1,2.
Abstract
Can peer-to-peer lending platforms mitigate fraudulent behaviors? Or have lending players been acting similar to free-riders? This paper constructs a new proxy to investigate lending platform misconduct and compares the FICO score and the LendingClub credit grade. To examine whether the lack of verification by the Fintech platform affects lenders' collection performance, I explore the recovery rate (RR) of non-performing loans through a mixed-continuous model. The regression results show that the degree of prudence taken by the lending platform in the pre-screening activity negatively affects the detection of some misreporting borrowers. I also find that the Fintech platform's missing verification information (e.g., annual income and employment length) affects the RR of non-performing loans, thereby hampering lenders' collection performance.Entities:
Keywords: Credit grade; Misconduct; Misreporting; Peer to peer lending; Recovery rate
Year: 2021 PMID: 35024285 PMCID: PMC8276212 DOI: 10.1186/s40854-021-00272-y
Source DB: PubMed Journal: Financ Innov ISSN: 2199-4730
Endogeneity check
| (1) | (2) | (3) | |
|---|---|---|---|
| Verification process | 0.0352*** (0.00493) | 0.0554*** (0.00703) | 0.0554*** (0.00703) |
| Rating grade | 0.178*** (0.00541) | 0.198*** (0.00783) | 0.198*** (0.00783) |
| Term | 0.485*** (0.00526) | 0.545*** (0.00754) | 0.545*** (0.00754) |
| Interest rate | 6.503*** (0.144) | 4.642*** (0.205) | 4.642*** (0.205) |
| Revolving utilisation | − 0.111*** (0.0139) | − 0.111*** (0.0139) | |
| Months since last delinquent | − 0.00138*** (0.000146) | − 0.00138*** (0.000146) | |
| Total account | 0.000630** (0.000294) | 0.000630** (0.000294) | |
| Debt to income ratio (DTI) | 0.0163*** (0.000400) | 0.0163*** (0.000400) | |
| Mortgage account | − 0.109*** (0.00184) | − 0.109*** (0.00184) | |
| ln(annual income) | − 0.238*** (0.00453) | ||
| Constant | − 0.859*** (0.0504) | − 3.389*** (0.0170) | − 3.389*** (0.0170) |
| Observations | 1,366,684 | 668,633 | 668,633 |
This table reports the results of logistic regression. The dependent variable is the probability of default in all columns. Standard errors in parentheses
*, ** and *** denote 1%, 5% and 10% levels of significant, respectively
Endogeneity check: regressions for the three risk classes
| (1) A-B | (2) C-D | (3) E-F-G | |
|---|---|---|---|
| Verification process | 0.0408*** (0.0123) | 0.0353** (0.0141) | 0.0394*** (0.00796) |
| Term | 0.601*** (0.0148) | 0.549*** (0.0167) | 0.532*** (0.00814) |
| Interest rate | 18.60*** (0.271) | 3.236*** (0.269) | 7.754*** (0.166) |
| ln (annual income) | − 0.140*** (0.0103) | − 0.240*** (0.0147) | − 0.164*** (0.00776) |
| Loan purpose: debt consolidation | 0.0391** (0.0175) | 0.120*** (0.0204) | 0.108*** (0.0116) |
| Loan purpose: credit card | 0.0493*** (0.0188) | 0.0514* (0.0286) | 0.102*** (0.0139) |
| Loan purpose: home improvement | 0.0822*** (0.0255) | 0.0596* (0.0347) | 0.118*** (0.0190) |
| Loan purpose: small business | 0.662*** (0.0524) | 0.283*** (0.0452) | 0.370*** (0.0333) |
| Home mortaged | − 0.340*** (0.0113) | − 0.349*** (0.0155) | − 0.345*** (0.00839) |
| Home owned | − 0.127*** (0.0173) | − 0.215*** (0.0241) | − 0.197*** (0.0129) |
| year | 0.350*** (0.0103) | 0.193*** (0.0190) | 0.272*** (0.00762) |
| 3-digit zip | Yes | Yes | Yes |
| Constant | − 3.078*** (0.120) | 0.579*** (0.167) | − 1.276*** (0.0887) |
| Observations | 429,448 | 87,932 | 394,827 |
This table reports the results of logistic regression for all risk-classes. The dependent variable is the probability of default in all columns. In the first column the regression results for the lowest risk-class (A-B), in the second column the medium risk-class (C-D) and in the third column the highest risk-class (E-F-G) are shown. Standard errors in parentheses
*, ** and *** denote 1%, 5% and 10% levels of significant, respectively
Fig. 1Theoretical framework
Variable description and descriptive statistics
| Variable | Description | Obs | Median | Average | SD | Plst | P99th |
|---|---|---|---|---|---|---|---|
| Loan amount | Loan amount chosen by borrower | 1,959,405 | 13,000 | 15,109 | 9,161 | 1,600 | 40,000 |
| Loan amount2 | Squared term of loan amount | 1,959,405 | 89.73 | 89.10 | 12.79 | 54.43 | 112.28 |
| Annual income | Borrower’s stated annual income | 1,959,332 | 69,959 | 79,563 | 116,697 | 20,000 | 275,000 |
| DTI | Debt to income ratio of loan applicant | 1,954,693 | 17.69 | 18.50 | 11.46 | 1.76 | 39.89 |
| Delinquencies 2 years | The number of 30 + days past-due delinquency in the last 2 years | 1,954,784 | 0 | 0.31 | 0.88 | 0 | 4 |
| Account open | Number of trades open | 1,954,784 | 11 | 11.69 | 5.63 | 3 | 30 |
| Total account | Number of total account | 1,954,784 | 23 | 24.34 | 11.99 | 5 | 60 |
| Employment length | Employment length in years at listing of loan request | 1,959,332 | 3 | 4.56 | 3.17 | 1 | 11 |
| Inquires last 6 mths | The number of borrower’s inquires in the last 6 months | 1,954,783 | 0 | 0.58 | 0.88 | 0 | 4 |
| LendingClub grade | Internal rating assigned by the platform. The grade can take values from A = 7 (the lowest-risk class) to G = 1 (the highest-risk class) | 1,959,405 | 5 | 5.33 | 1.26 | 2 | 7 |
| Fico score | External rating assigned by Credit Agency Bureau. The rating takes different classes from the lowest to highest risk: 1) < 660; 2)660–679; 3) 680–699; 4) 700–739; 5) 740–759; 6)760–779; 7) 780 + | 1,954,784 | 692 | 700 | 32.62 | 662 | 802 |
| Not verified | Dummy variable. It takes value 1 if borrower’s stated information is not verified, 0 otherwise | 1,959,332 | 0 | 0.32 | 0.47 | 0 | 1 |
| Default | Dummy variable. It takes value 1 if loan is defaulted or charged-off within 12–24 months post-duration, 0 otherwise | 1,494,741 | 0.19 | 0.39 | 0 | 0 | 1 |
| Interest rate | The loan interest rate sets by LendingClub | 1,959,405 | 0.12 | 0.13 | 0.04 | 0.05 | 0.27 |
| Term 5 years | Dummy taking the value 1 if the loan’ term is 5 years, 0 otherwise | 1,959,405 | 1 | 1.27 | 0.44 | 1 | 0 |
| Income divisible by 5000 | Dummy taking the value 1 if the borrower'reported income is divisible by 5,000, 0 otherwise | 1,959,332 | 0 | 0.49 | 0.5 | 0 | 1 |
| Income divisible by 10,000 | Dummy taking the value 1 if the borrower’reported income is divisible by 10,000, 0 otherwise | 1,959,332 | 0 | 0.29 | 0.45 | 0 | 1 |
| Loan amount divisible by 5000 | Dummy taking the value 1 if the loan amount is divisible by 5,000, 0 otherwise | 1,959,405 | 0 | 0.33 | 0.47 | 0 | 1 |
| Loan amount divisible by 10,000 | Dummy taking the value 1 if the loan amount is divisible by 10,000, 0 otherwise | 1,959,405 | 0 | 0.17 | 0.38 | 0 | 1 |
| Revolving utilitation | The revolving credit utilitation of the borrower | 1,953,322 | 0.50 | 0.50 | 0.24 | 0.01 | 0.98 |
| Home owned | Dummy taking the value 1 if the Homeownership status provide by borrower is “own”, 0 otherwise | 1,959,322 | 0 | 0.10 | 0.30 | 0 | 1 |
| Home mortgaged | Dummy taking the value 1 if the mortgaged status provide by borrower is “mortgage”, 0 otherwise | 1,959,322 | 0 | 0.49 | 0.5 | 0 | 1 |
| Prudence grade | Prudence of the screening system. It is calculated as the difference between LendingClub grade and Fico score. It takes value 1 (Low Prudence), 2 (Medium) or 3 (High Prudence) | 1,959,405 | 1 | 1.18 | 0.48 | 1 | 3 |
| Recovery rate | Recoveries amount on defaulted loans | 291,665 | 0.088 | 0.098 | 0.11 | 0 | 0.45 |
| Year | Dummy taking the value 1 if the loan is issued between 2016 and 2018, 0 otherwise | 1,325,744 | 1 | 0.57 | 0.49 | 0 | 1 |
| Suspect employment length | Dummy taking the value 1 if the length of employment is equal at 10 years, zero if it is less 10 | 1,959,440 | 0 | 0.40 | 0.49 | 0 | 1 |
| Length of title | Number of words provided by borrower in the title of loan | 1,959,440 | 2 | 2.147 | 0.69 | 0 | 18 |
| Amount to income | Amount of the loan issued to the annual income provided by borrower | 1,959,250 | 0.2 | 0.31 | 51.09 | 0.02 | 0 |
This table reports the description and the main descriptive statistics the variables involved in the empirical analysis. The sample covers all loans issued from LendingClub between July 2007 and September 2018. The point and comma are used as decimal and thousand separators. The construction of the variables Prudence grade and Recovery rate is presented in the following sections
Fig. 2Consumer loans by the stated purpose. Notes. This graph shows loan distribution by a self-reported goal by borrowers. As highlighted, a large part is specified to be used for consolidating borrowers’ liabilities
Loan status by each year
| Number of loans by Status | |||||||
|---|---|---|---|---|---|---|---|
| Charged off | Current | Default | Fully paid | In grace period | Late (16–30) | Late (31–120) | |
| 2007 | 38 | 175 | |||||
| 2008 | 124 | 689 | |||||
| 2009 | 406 | 2882 | |||||
| 2010 | 1131 | 7092 | |||||
| 2011 | 2351 | 12,826 | |||||
| 2012 | 6,254 | 32,025 | |||||
| 2013 | 14,895 | 79,938 | |||||
| 2014 | 28,471 | 2685 | 128,360 | 48 | 23 | 110 | |
| 2015 | 55,321 | 3 | 217,810 | ||||
| 2016 | 44,662 | 41,497 | 2 | 172,906 | 681 | 294 | 1804 |
| 2017 | 39,797 | 128,248 | 98 | 131,319 | 2169 | 867 | 4025 |
| 2018 | 19,813 | 159,716 | 152 | 64,961 | 2581 | 825 | 4093 |
| Total | 213,263 | 332,146 | 255 | 850,983 | 5479 | 2009 | 10,032 |
This table provides summary statistics on the data set used for the empirical analysis. The data covers all loans issued from LendingClub between July 2007 and September 2018. The status of loan by each year is reported in the table. According to LendingClub, a loan becomes "Default" when borrowers miss payments for an extended period. Charged off is a loan for which is no longer a reasonable expectation of further payments, and it occurs when borrowers are 120 days or more past due
Fig. 3Correlation between FICO score and the LC rating grade. Notes. This graph displays the association between two rating systems on the whole data set, involving also current loans. As can be seen, their relationship has been changing over time, confirming a declining trend. Nevertheless, the relation in 2016 seems to improve slightly once again
Fig. 4Fico and LC grade distribution by Verification status. Notes. These graphs show the relationship between FICO and LC grade by loans’ verification status. The empirical analysis is being performed on the whole data set, including loans issued between 2007 and Q3 2018
Fig. 5ROC curve of Lending Club grades. Notes. This Figure plots the ROC curve, which plots the positive true rate, also called Sensitivity versus true false rate (1-Specificity), obtained by using the LC rating grade as a predictor of defaulted loans. The analysis is performed each year separately on loans issued between 2016 and 2018. The larger the AUC, the better the model is
Summary statistics of misreporting variables
| Variables | Obs | Mean | SD | Min | Max | p25 | p50 | p75 |
|---|---|---|---|---|---|---|---|---|
| Prudence grade | 1,959,405 | 1.182 | 0.485 | 1 | 3 | 1 | 1 | 1 |
| Income divisible by 5000 | 1,959,332 | 0.296 | 0.457 | 0 | 1 | 0 | 0 | 1 |
| Income divisible by 10,000 | 1,959,332 | 0.497 | 0.5 | 0 | 1 | 0 | 0 | 1 |
| Loan amount divisible by 5000 | 1,959,405 | 0.337 | 0.473 | 0 | 1 | 0 | 0 | 1 |
| Loan amount divisible by 10,000 | 1,959,405 | 0.179 | 0.383 | 0 | 1 | 0 | 0 | 0 |
| Length of title | 1,959,440 | 2.148 | 0.691 | 0 | 18 | 2 | 2 | 2 |
| Suspect employment length | 1,959,440 | 0.403 | 0.491 | 0 | 1 | 0 | 0 | 1 |
This table provides summary statistics on the variables used for the empirical analysis of the LendingClub' Prudence grade. The data covers all the transactions between June 2007 and September 2018. Mean, Standard deviations, key percentiles and minimum and maximum values are displayed
Fig. 6Employment length by delinquency rate. Notes. This graph shows the employment length by the average delinquency rate. The empirical analysis is performed on the loan-level dataset issued from LendingClub between June 2007 and September 2018. Both current and matured loans are included. The maximum level of the working year is associated with the highest rate of delinquency
Regressions results
| (1) | (2) | (3) | ||||
|---|---|---|---|---|---|---|
| Low-prudence | Medium | Low-prudence | Medium | Low-prudence | Medium | |
| Not verified | 0.769*** (0.00433) | 0.598*** (0.00626) | 0.637*** (0.00349) | 0.468*** (0.00479) | ||
| Income div. 5000 | 0.915*** (0.00591) | 0.898*** (0.00966) | ||||
| Income div.10,000 | 0.989*** (0.00702) | 0.960*** (0.0114) | ||||
| Loan amount div. 5000 | 1.089*** (0.00717) | 1.133*** (0.0124) | ||||
| Loan amount div. 10,000 | 0.791*** (0.00652) | 0.718*** (0.0100) | ||||
| Length of title | 0.975*** (0.00657) | 0.924*** (0.0101) | ||||
| Suspect empl. length | 1.046*** (0.00634) | 1.024*** (0.0103) | ||||
| ln(Loan amount) | 0.00408*** (0.000296) | 0.00361*** (0.000461) | 0.0053*** (0.000476) | 0.00446*** (0.000686) | ||
| Loan amount2 | 1.390*** (0.00542) | 1.410*** (0.00960) | 1.379*** (0.00655) | 1.408*** (0.0115) | ||
| Debt to income ratio^α | 1.036*** (0.000300) | 1.039*** (0.000483) | 1.037*** (0.000309) | 1.039*** (0.000501) | 1.038*** (0.000372) | 1.042*** (0.000601) |
| Months since recent inquires | 0.981*** (0.000432) | 0.964*** (0.000736) | 0.982*** (0.000429) | 0.966*** (0.000733) | 0.981*** (0.000528) | 0.965*** (0.000891) |
| Revolving utilitation | 0.0753*** (0.000850) | 0.0674*** (0.00115) | 0.0867*** (0.000963) | 0.0798*** (0.00134) | 0.0935*** (0.00130) | 0.0990*** (0.00208) |
| Account open | 0.975*** (0.000771) | 0.983*** (0.00120) | 0.970*** (0.000768) | 0.980*** (0.00120) | 0.983*** (0.000947) | 0.997* (0.00146) |
| Delinquencies in last 2 years | 0.710*** (0.00305) | 0.701*** (0.00477) | 0.694*** (0.00298) | 0.687** (0.00465) | 0.707*** (0.00366) | 0.704*** (0.00564) |
| Home mortgaged | 0.983** (0.00665) | 0.858*** (0.00955) | ||||
| Home owned^α | 1.084*** (0.0110) | 1.077*** (0.0175) | ||||
| Employment length^α | 1.015*** (0.000743) | 1.014*** (0.00124) | ||||
| Loan purpose: vacation^α | 0.901*** (0.0308) | 0.892*** (0.0495) | ||||
| Loan purpose: credit card | 0.289*** (0.00423) | 0.205*** (0.00516) | ||||
| Loan purpose: debt consolidation | 0.525*** (0.00493) | 0.449*** (0.00651) | ||||
| Loan purpose: small business | 1.426*** (0.0334) | 1.481*** (0.0458) | ||||
| Loan purpose: Home improvement | 0.662*** (0.00882) | 0.569*** (0.0120) | ||||
| Year | 0.899*** (0.00163) | 0.895*** (0.00268) | ||||
| 3-digit zip code | Yes | Yes | ||||
| Observations | 1,558,546 | 1,558,546 | 1,558,546 | 1,558,546 | 1,053,512 | 1,053,512 |
This table displays odds ratios from Gologit regressions that m-1 models, where m is the number of clusters. The dependent variable is an indicator of Prudence'screening by platforms, and the highest Prudence is the reference category. Imprudent models are displayed in columns 1, 3 and 5, and neutral groups in Columns 2,4 and 6. The variables with superscript α meet the odds assumptions and are the same in all categories (e.g. debt-to-income ratio, home mortgaged, home owned). For variables violating proportional odds assumptions, refer to coefficients for responses of 2,3 vs 1 group (Low Prudence models) and category 3 vs 1, 2 in Neutral models
Regression results with the dependent variable Prudence grade
| (1) | (2) | (3) | ||||
|---|---|---|---|---|---|---|
| Low-Prundence | Medium | Low-Prundence | Medium | Low-Prundence | Medium | |
| Not verified | 0.875*** | 0.663*** | 0.719*** | 0.523*** | ||
| (0.00441) | (0.00578) | (0.00352) | (0.00444) | |||
| Income div. 5000 | 0.929*** | 0.908*** | ||||
| (0.00550) | (0.00852) | |||||
| Income div. 10,000 | 0.998 | 0.974** | ||||
| (0.00648) | (0.0101) | |||||
| Amount div. 5000 | 1.128*** | 1.162*** | ||||
| (0.00681) | (0.0110) | |||||
| Amount div. 10,000 | 0.814*** | 0.745*** | ||||
| (0.00609) | (0.00892) | |||||
| Length of title | 0.999 | 0.934*** | ||||
| (0.00622) | (0.00904) | |||||
| Suspect empl | 1.052*** | 1.020** | ||||
| (0.00586) | (0.00895) | |||||
| ln(Loan amount) | 0.00168*** | 0.00166*** | 0.00309*** | 0.00248*** | ||
| (0.000111) | (0.000179) | (0.000248) | (0.000321) | |||
| ln(Loan amount)2 | 1.460*** | 1.468*** | 1.420*** | 1.449*** | ||
| (0.00519) | (0.00847) | (0.00614) | (0.0100) | |||
| Debt to income ratio | 1.039*** | 1.044*** | 1.042*** | 1.044*** | 1.041*** | 1.046*** |
| (0.000279) | (0.000426) | (0.000287) | (0.000439) | (0.000345) | (0.000530) | |
| Months since recent inq | 0.988*** | 0.972*** | 0.990*** | 0.974*** | 0.989*** | 0.973*** |
| (0.000392) | (0.000631) | (0.000388) | (0.000626) | (0.000480) | (0.000767) | |
| Revolving utilitation | 0.0422*** | 0.0440*** | 0.0491*** | 0.0523*** | 0.0496*** | 0.0592*** |
| (0.000449) | (0.000676) | (0.000511) | (0.000794) | (0.000652) | (0.00112) | |
| Account open | 0.954*** | 0.967*** | 0.948*** | 0.963*** | 0.959*** | 0.977*** |
| (0.000712) | (0.00106) | (0.000707) | (0.00104) | (0.000872) | (0.00127) | |
| Delinquencies in last 2y | 0.622*** | 0.625*** | 0.607*** | 0.610*** | 0.616*** | 0.620*** |
| (0.00268) | (0.00403) | (0.00261) | (0.00389) | (0.00321) | (0.00479) | |
| Purpose: credit card | 0.328*** | 0.245*** | ||||
| (0.00438) | (0.00533) | |||||
| Purpose: debt consol | 0.555*** | 0.485*** | ||||
| (0.00488) | (0.00626) | |||||
| Purpose: home | 0.671*** | 0.585*** | ||||
| (0.00835) | (0.0109) | |||||
| Purpose: vacation | 0.947* | 0.950 | ||||
| (0.0297) | (0.0451) | |||||
| Purpose: small business | 1.388*** | 1.464*** | ||||
| (0.0319) | (0.0422) | |||||
| Home mortgaged | 1.221*** | 1.085*** | 1.085*** | 0.908*** | ||
| (0.00609) | (0.00859) | (0.00675) | (0.00886) | |||
| Home owned | 1.175*** | 1.164*** | 1.113*** | 1.094*** | ||
| (0.00886) | (0.0135) | (0.0105) | (0.0157) | |||
| Year | 0.794*** | 0.745*** | ||||
| (0.00454) | (0.00672) | |||||
| 3-digit zip code | Yes | Yes | ||||
| Observations | 1,558,546 | 1,558,546 | 1,558,546 | 1,558,546 | 1,053,512 | 1,053,512 |
The dependent variable is created by comparing the LC grade and the new classification of FICO scores based on the percentiles. This table displays odds ratios from Gologit regressions that m-1 models, where m is the number of clusters. The dependent variable is an indicator of Prudence'screening by platforms, and the highest Prudence is the reference category. Prudence degree takes value 1 (Low Prudence) if LC rating grade has been underestimating borrowers'credit risk; Prudence degree takes value 2 (Medium) if the assessing of the borrower riskiness is the same in LC rating grade and FICO score; Prudence degree takes value 3 (High Prudence) if LC rating grade has been overestimating borrowers'credit risk.Imprudent models are displayed in columns 1, 3 and 5, and neutral groups in Columns 2,4 and 6. The variables with superscript α meet the odds assumptions and are the same in all categories (e.g. debt-to-income ratio, home mortgaged, home owned). For variables violating proportional odds assumptions refer to coefficients for responses of 2,3 vs 1 group (Low Prudence models) and category 3 vs 1, 2 in Neutral models
Descriptive statistics of RR and LGD
| Variable of interest | Number sample | Mean value | Median value | Standard deviation | Minimum value | Maximum value |
|---|---|---|---|---|---|---|
| Loss given default | 291,664 | 0.902 | 0.867 | 0.109 | 0 | 1 |
| Recovery rate | 291,664 | 0.098 | 0.089 | 0.109 | 0 | 1 |
Notes: In this table, the chief summary statistics of RR and LGD are listed. Following literature in mortgage loans, the RR and LGD have truncated within the interval [0, 1]
Fig. 7Kernel density of recovery rates in the sample. Notes. This graph shows the density distributions of the recovery rates on defaulted loans in the sample. The stack of 0 s shows the frequency of RR = 0, resulting in a not unimodal distribution
Fig. 8Mean-recovery rate by country. Notes. This graph shows the average distribution of the Recovery Rate of the loans issued on the LendingClub platform by each country. The US is classified in 10 zones based on the borrower’s first three digits of the ZIP code
Models’ comparison
| Model | RMSE | MAE |
|---|---|---|
| Standard beta regression | 0.123 | 0.0050 |
| Zero–one inflated beta regression | 0.003 | 0.0003 |
| Beta with logistic regression | 0.005 | 0.0091 |
| Fractional regression with logit estimator | 0.129 | 0.0048 |
This table lists the predictive results of different approaches applied in the empirical analysis. The dependent variable is the recovery rate on defaulted loans issued from LendingClub between July 2007 and September 2018
Regression results recovery rate in the overall sample
| (1) | (2) | (3) | ||||
|---|---|---|---|---|---|---|
| Beta | Zero-inflate | Beta | Zero-inflate | Beta | Zero-inflate | |
| Not verified | − 0.042*** (0.0043) | 0.1169*** (0.0100) | − 0.0054*** (0.0058) | 0.138*** (0.0146) | − 0.0412*** (0.0055) | 0.0896*** (0.0130) |
| ln(Loan Amount) | 0.0003 (0.0030) | 0.0445*** (0.0738) | − 0.0049 (0.0057) | − 0.0531*** (0.0110) | 0.0088 (0.0099) | − 0.0183 (0.0230) |
| Term | 0.028*** (0.0042) | 0.172*** (0.0102) | − 0.0061*** (0.0005) | 0.171*** (0.0149) | − 0.00407*** (0.0055) | 0.259*** (0.0135) |
| Interest rate | − 0.0006 (0.0004) | − 0.026 (0.0009 | − 0.024*** (0.0042) | − 0.0225*** (0.0014) | − 0.00126*** (0.0005) | − 0.0334*** (0.0012) |
| Revolving utilitation | − 0.0539*** (0.0139) | − 0.338*** (0.0364) | ||||
| Months since last delinquent | 0.0006*** (0.0001) | 0.00215*** (0.0003) | ||||
| Total account | 0.00137*** (0.0002) | − 0.0015*** (0.0005) | ||||
| Bankcard balance > 75% | 6.94e−05 (9.06e−05) | 0.0009*** (0.00024) | ||||
| Debt to income ratio | 0.00182*** (0.0002) | 0.00850*** (0.0006) | ||||
| Mortgage account | − 0.0053*** (0.0013) | − 0.0070** (0.0035) | ||||
| ln(Annual Income) | 0.0282*** (0.0106) | − 0.0423* (0.0245) | ||||
| Employment length | 0.00100 (0.0007) | 0.00764*** (0.00165) | ||||
| Loan to annual income | − 0.263*** (0.0482) | 1.008*** (0.105) | ||||
| Loan purpose: credit card | 0.0264*** (0.0098) | 0.135*** (0.0242) | ||||
| Loan purpose: debt consolidation | 0.0243*** (0.00870) | 0.0775*** (0.0217) | ||||
| Loan purpose: small business | − 0.146*** (0.0190) | − 0.0550 (0.0492) | ||||
| Home mortgaged | − 0.00809 (0.103) | − 0.0492** (0.299) | ||||
| Home owned | 0.0432 (0.103) | − 0.0950* (0.299) | ||||
| 3-digit zip | Yes | Yes | ||||
| Year | 0.191*** (0.00458) | 0.716*** (0.0112) | ||||
| Observations | 291,664 | 145,646 | 177,963 | |||
| AIC | − 105,632 | − 62,897 | − 73,825 | |||
| BIC | − 105,516 | − 62,630 | − 73,381 | |||
The table reports results from beta regression and the logit model on RR with indicators and continuous explanatory variables. Both in the beta models and zero-inflated are reported the coefficients. The standards errors are in parentheses. All models are estimated with intercepts. The primary independent variable is associated with the verification process. Other control variables are inserted, like loan contract information and borrower’ characteristics. For brevity, only the loan’s significance is exposed. The borrowers’ state is based on the first three-digit ZIP code, captured into ten dummy variables building on the classification of the United States. The estimated goodness of fit is shown
***, ** and * denotes significance at levels 1%, 5%, and 10% levels, respectively
Average marginal effects
| (1) | (2) | (3) | ||||
|---|---|---|---|---|---|---|
| AME | SE | AME | SE | AME | SE | |
| Not verified | − 0.00681*** | 0.000457 | − 0.00403*** | 0.000645 | − 0.00591*** | 0.000590 |
| ln(Loan Amount) | 0.00120*** | 0.000326 | − 0.000854* | 0.000482 | 0.00524*** | 0.00105 |
| Term | − 0.00692*** | 0.000454 | − 0.00505*** | 0.000650 | − 0.00678*** | 0.000593 |
| Interest rate | 0.000653*** | 4.25e−05 | 0.000017 | 6.33e−05 | 0.000734*** | 5.57e−05 |
| Revolving utilitation | 0.00845*** | 0.001201 | ||||
| Months since last delinquent | − 0.00009*** | 0.00001 | ||||
| Debt to income ratio | − 0.00004* | 0.00003 | ||||
| Mortgage account | − 0.000302** | 0.00001 | ||||
| Bankcard Balance > 75% | − 0.000186*** | 0.00003 | ||||
| Total account | 0.00019*** | 0.00002 | ||||
| ln(Annual Income) | 0.00304*** | 0.00112 | ||||
| Loan to annual income | − 0.0495*** | 0.00501 | ||||
| Home mortgaged | − 0.0144 | 0.0118 | ||||
| Home owned | − 0.0142 | 0.0118 | ||||
| Home rented | − 0.00849 | 0.0118 | ||||
| Loan purpose: credit card | − 0.00149 | 0.00106 | ||||
| Loan purpose: debt consolidation | − 0.000265 | 0.000943 | ||||
| Loan purpose: small business | − 0.0111*** | 0.00209 | ||||
| Employment length | 0.000146** | 7.31e−05 | ||||
| Year | − 0.00107** | 0.000493 | ||||
| Observations | ||||||
| 291,664 | 146,246 | 177,963 | ||||
The table report results from beta regression and logit model on RR with indicators and continuous explanatory variables. Both in the beta models and zero-inflated are reported the average marginal effects. The standards errors are in paratheses. All models are estimated with intercepts. For brevity, only the loan purpose' significant are exposed. The estimated goodness of fit is shown
***, ** and * denotes significative at levels 1%, 5% and 10% levels, respectively
Regression results within each risk-class
| (1) Low-risk class | (2) Medium-risk class | (3) High-risk class | ||||
|---|---|---|---|---|---|---|
| Beta | Zero-inflate | Beta | Zero-inflate | Beta | Zero-inflate | |
| Not verified | − 0.0415*** (0.0116) | 0.0762*** (0.0264) | − 0.0298*** (0.0061) | 0.128*** (0.0151) | − 0.0137*** (0.0106) | 0.136*** (0.0273) |
| ln(Loan Amount) | 0.0369 (0.0242) | − 0.170*** (0.0533) | 0.00493 (0.0109) | − 0.185*** (0.0269) | − 0.00356 (0.0176) | − 0.223*** (0.0455) |
| Term | − 0.0144 (0.0181) | 0.462*** (0.0383) | − 0.0225*** (0.0060) | 0.140*** (0.0155) | − 0.0146* (0.0086) | 0.0212 (0.0234) |
| Interest rate | − 0.0529*** (0.00314) | − 0.122*** (0.00733) | 0.0033*** (0.0006) | 0.0233*** (0.0015) | 0.00233* (0.0012) | 0.0251*** (0.0031) |
| Revolving utilitation | 0.0098 (0.0245) | − 0.589*** (0.0572) | − 0.0829*** (0.0109) | − 0.449*** (0.0281) | − 0.108*** (0.0164) | − 0.310*** (0.0444) |
| Months since last delinquent | 0.0008*** (0.0002) | 0.0024*** (0.0005) | 0.0005*** (0.0001) | 0.0019*** (0.00029) | − 0.00026 (0.0002) | 0.00150*** (0.0004) |
| Debt to income ratio | 0.00629*** (0.0007) | 0.0096*** (0.0016) | 0.00502*** (0.0003) | 0.0079*** (0.0007) | 0.0051*** (0.0004) | 0.0071*** (0.0011) |
| ln(Annual Income) | 0.00741 (0.0251) | 0.0871 (0.0561) | 0.0399*** (0.0115) | 0.0778*** (0.0288) | 0.0121 (0.0187) | 0.0105 (0.0488) |
| Employment length | 0.00286* (0.00160) | 0.00256 (0.00372) | 0.0033*** (0.0007) | 0.0029 (0.0019) | 0.003*** (0.0011) | 0.00212 (0.00303) |
| Loan to annual income | − 0.660*** (0.142) | 1.362*** (0.295) | − 0.250*** (0.0543) | 1.039*** (0.130) | − 0.204** (0.0799) | 0.945*** (0.201) |
| Loan purpose: credit card | 0.0601*** (0.0230) | − 0.0692 (0.0514) | 0.00690 (0.0103) | 0.0758*** (0.0263) | − 0.00121 (0.0162) | 0.142*** (0.0436) |
| Loan purpose: debt consolidation | 0.0370* (0.0215) | − 0.104** (0.0477) | 0.00038 (0.00868) | 0.0267 (0.0225) | 0.00493 (0.0124) | 0.116*** (0.0338) |
| Loan purpose: small business | − 0.170*** (0.0575) | − 0.427*** (0.142) | − 0.106*** (0.0201) | − 0.105* (0.0545) | 0.069*** (0.0261) | − 0.187** (0.0769) |
| Home mortgaged | − 0.506* (0.282) | − 0.579 (0.635) | 0.0352 (0.136) | 0.142 (0.363) | 0.387* (0.198) | 0.397 (0.559) |
| Home owned | − 0.427 (0.283) | − 0.610 (0.636) | 0.0682 (0.136) | 0.0772 (0.363) | 0.420** (0.198) | 0.293 (0.560) |
| 3-digit zip | ||||||
| Yes | Yes | Yes | Yes | Yes | Yes | |
| Constant | − 1.159*** (0.323) | 0.494 (0.731) | − 2.281*** (0.751) | − 0.774* (0.406) | − 2.394*** (0.2271) | − 0.757 (0.635) |
| Observations | 32,906 | 136,791 | 56,652 | |||
The dependent variable is RR within each risk class. In both models, estimated coefficients are reported. Standard errors are in parentheses
*, ** and *** denotes 1%, 5% and 10% significative levels, respective
Average marginal effects
| (1) Low-risk class | (2) Medium-risk class | (3) High-risk class | ||||
|---|---|---|---|---|---|---|
| AME | SE | AME | SE | AME | SE | |
| Not verified | − 0.00600*** | 0.00129 | − 0.00597*** | 0.000671 | − 0.00449*** | 0.00115 |
| ln(Loan Amount) | 0.00923*** | 0.00189 | 0.00853*** | 0.000843 | 0.00622*** | 0.00133 |
| Term | − 0.0155*** | 0.00197 | − 0.00572*** | 0.000672 | − 0.00188** | 0.000958 |
| Interest rate | − 0.00107*** | 0.000354 | 0.000282*** | 6.63e−05 | − 0.000415*** | 0.000132 |
| Revolving utilitation | 0.0195*** | 0.00276 | 0.00509*** | 0.00121 | − 0.00165 | 0.00181 |
| Months since last delinquent | − 0.00016*** | 2.77e−05 | − 0.000105*** | 1.26e−05 | − 6.75e−05*** | 1.90e−05 |
| Debt to income ratio | 0.000307*** | 7.78e−05 | 0.000267*** | 3.24e−05 | 0.000304*** | 4.70e−05 |
| ln(Annual Income) | − 0.00217 | 0.00166 | − 0.00174** | 0.000737 | − 5.18e−05 | 0.00117 |
| Employment length | 0.000236 | 0.000181 | 0.000258*** | 8.24e−05 | 0.000253** | 0.000125 |
| Loan to annual income | − 0.101*** | 0.0108 | − 0.0633*** | 0.00420 | − 0.0447*** | 0.00604 |
| Loan purpose: credit card | 0.00879*** | 0.00249 | − 0.00129 | 0.00112 | − 0.00381** | 0.00178 |
| Loan purpose: debt consolidation | 0.00775*** | 0.00232 | − 0.000549 | 0.000952 | − 0.00260* | 0.00136 |
| Loan purpose: small business | − 0.00140 | 0.00663 | − 0.00683*** | 0.00227 | − 0.00226 | 0.00297 |
| Home mortgaged | − 0.0277 | 0.0314 | 0.00167 | 0.0153 | 0.0272 | 0.0222 |
| Home owned | − 0.0198 | 0.0315 | 0.00626 | 0.0153 | 0.0327 | 0.0222 |
| Observations | 32,906 | 136,791 | 56,652 | |||
This table reports the average marginal effects of the models presented in Panel A. The dependent variable is RR within each risk class. Standard errors in parentheses
*, ** and *** denote 1%, 5% and 10% levels of significance, respectively