Social Influence and Defaults in Peer-to-Peer Lending Networks

Thirty Third International Conference on Information Systems, Orlando 2012 1

SOCIAL INFLUENCE AND DEFAULTS IN PEER-TO-PEER LENDING NETWORKS

Completed Research Paper

Yong Lu

Pennsylvania State University 76 University Drive Hazleton, PA 18202

[email protected]

Bin Gu Arizona State University

P O Box 874606 Tempe, AZ 85287 [email protected]

Qiang Ye

Harbin Institute of Technology 13 Court Street

Harbin, Heilongjian China, 150001

[email protected]

Zhexiang Sheng University of Illinois at Urbana-

Champaign 801 South Wright Street Champaign, IL 61820 [email protected]

Abstract

We assess social influence on borrowers’ default decisions in a peer-to-peer lending market. Our analysis suggests that online borrowers are significantly influenced by defaults in their social networks. A friend’s default decision more than doubles a user’s default rate. We also find that not all friends have equal influences. The social influence is highly significant among online friends made through the peer-to-peer lending site. Social influence is much weaker in magnitude among offline friendships that were carried over to the peer-to-peer lending site.

Keywords: peer-to-peer lending, social influence, empirical analysis

Digital and Social Networks

2 Thirty Third International Conference on Information Systems, Orlando 2012

Introduction

Online social influence has substantial impact on human behaviors, ranging from product choices to life style decisions (Oestreicher-Singer and Sundararajan. 2012, Christakis and Fowler 2007). In this study, we analyze online social influence in individual financial decisions, in particular, borrowers’ default decisions. Individual financial decisions form the cornerstone of financial markets. While financial markets expect some borrower defaults, an unexpected wave of borrower defaults could trigger financial crisis with far reaching consequences. Therefore, understanding the process of online social influence in borrowers’ default decisions provides the foundation to a better understanding of the functioning of financial markets.

We conduct our research in the context of online peer-to-peer lending markets. Online peer-to-peer lending is a new form of financial markets where private borrowers and lenders interact directly without financial institutions as an intermediary. These markets primarily provide micro credits to budding entrepreneurs and small businesses that often have difficulties in accessing traditional financial markets due to their small scale and/or low credit rating.

Loans are typically not collateralized in the P2P lending market, and thus lenders face the inherent risk of defaults. Everett (2008) found that the overall default rate was 7.5% for online lending. Greiner and Wang (2009) noticed that 35% of peer-to-peer loans were in some kind of delinquency. These numbers suggest that investing in P2P lending can be risky and that lenders need to choose the loans they want to invest in carefully. Without financial intermediaries, a key characteristic of the online peer-to-peer lending market is information asymmetry between lenders and borrowers. While steps have been taken by peer-to-peer lending sites to validate borrowers and assess their credit worthiness, default risk is inherent by nature and Lenders bear the full risk in the case of default.

In this study, we focus on how events in a borrower’s social networks shape their default decisions. In particular, we consider the following two research questions: 1) How others’ default decisions in a borrower’s social networks affect his/her default propensity; and 2) What factors moderate the social influence in borrowers’ default decision.

A key challenge in assessing online social influence is to distinguish social influence from unobserved common factors (Aral 2012; Aral, Muchnik, and Sundararajan 2009) that affect both the focal member and his online social network. This is of particular concern in online lending market where economic factors change dynamically. We take a two-prone approach to address the identification issue. First, we use a panel data setting that allows us to control for individual heterogeneity and identifies social influence by comparing a focal member’s behavior before and after his/her friends’ default event. This approach removes time-invariant common factors. Second, a unique characteristic of our data is that it distinguishes online and offline friends in a focal member’s social network. Under the assumption that offline friends are more closely related to the focal member and thus more likely to share common factors, the difference between the effects of online friends and offline friends provide a lower bound on the magnitude of online social influence. This approach allows us to remove time-varying common factors that influence both the focal member and his friends in the network.

Using detailed transaction level data from a large peer-to-peer lending site, we analyze individual borrowers’ default propensity before and after their friends’ default event. Our analysis suggests that online borrowers are significantly influenced by default events in their social networks. A friend’s default more than doubles a user’s default rate. Further, the effect is highly significant among online friends made through the peer-to-peer lending site. The effect is much weaker among offline friendship that was carried over to peer-to-peer lending sites. The contract indicates the presence of significant online social influence in borrower’s default decision. Our analysis also reveals that social influence varies with borrower characteristics. In particular, borrowers with low credit ratings are most susceptible to social influence.

Literature Review

The emergency of P2P lending platforms along with the wealth of publicly available data has led to a large number of studies on information asymmetry in the market and its implications.

Lu et al. / Social Influence and Defaults in Peer-to-peer Lending


Information asymmetry is particularly severe in online P2P lending markets because it is difficult and costly for individual lenders to obtain comprehensive information about borrowers (Lin, et al. 2012). Freedman and Jin (2010) studied information asymmetry in P2P lending markets and found that the lack of information of borrowers’ credit history could lead to adverse selections even though lenders knew the credit grades of the borrowers. Given the importance of information asymmetry in P2P lending markets, several studies focused on factors that could potentially mitigate information asymmetry between borrowers and lenders in the lending process. Two categories of factors have been examined in the prior literature: hard credit information and soft credit information.

“Hard credit information” refers to the information that are provided and displayed by the P2P platforms, including credit profile, demographic information, loan purpose, and so on. Credit scores were identified as a major factor for loans to be funded (Iyer, et al. 2009, Lin, et al. 2012). Borrowers’ demographic information (e.g. gender, age, and race) also affects lending outcomes (Berger and Gleisner 2007, Kumar 2007). In addition, previous studies showed that information in the loan listing (e.g. loan purpose, auction format, and maximum interest rate) affected lending outcomes as well (Lin, et al. 2012, Puro, et al. 2010).

“Soft information” refers to the information that is fuzzy, hard-to-quantify about borrowers beyond “hard credit information” (Lin, et al. 2009). Such information could be generated from social networks between borrowers and lenders (Collier and Hampshire. 2010, Iyer, et al. 2009). Freedman and Jin (2008; 2010) examined the impacts of social networks on mitigating information asymmetry. Lin (2009, 2012) found that the relational aspects of social networks were consistently significant predictors of lending outcomes, while the structural aspects had no significant relationships with lending outcomes.

Information asymmetry also leads to herding behavior among lenders as it is cost effective for lenders to free ride on others’ lending decisions. Studies have focused on whether such herding behavior is irrational or rational in P2P markets. Rational herding means “happens as a result of observational learning among lenders” (p. 1, Zhang and Liu 2012). Two studies found evidence of rational herding among lenders based on data from Prosper.com. Herzenstern et al. (2011) found that listings with a larger number of lenders that were more likely to receive further funding. Zhang and Liu (2012) observed that well-funded borrower listings tended to attract more funding and rational herding beat irrational herding in predicting loan performance.

Prior studies on P2P loan default

In addition to information asymmetry, social networks, and herding, prior studies have investigated extensively factors that influence P2P loan default (Appendix 1). Everett (2008) listed three categories of determinants of default risk: loan characteristics, borrower characteristics, and instrumental variables. He found a positive relationship between interest rate and default risk. He also discovered that credit score and home ownership were both negatively related to default rate, with credit score being the most significant determinant. Freeman and Jin (2010) observed that the credit score was an important measure for borrowers’ default propensity. Krumme and Herrero-Lopez (2009) found that nearly half of borrowers with credit score E had defaults.

Several studies investigated the effects of friendship on default risk. Lin et al. (2009) discovered that having friends registered as lenders decreased default risk by 9%. They also found that the probabilities of default were significantly lower when lender-friends bid on the borrower's listing. These results are consistent with Everett (2010), who found that loan default rate was significantly reduced when a borrower is a member of a group that had personal relationships. On the contrary, from Greiner and Wang (2009) found little support that social capital helped to reduce delinquencies.

Despite the extensive researches on the role of social networks in online P2P lending process, current studies have several limitations. For example, prior studies have shown association between borrowers’ social networks and his/her credit worthiness. Such association could be due to either homophily or social influence. Our study takes a step further to delineate the influence of social networks. By leveraging the panel data nature of our data set and the difference between online and offline friends, we show that events happened within a borrower’s social network could have a profound impact on their later financial decisions. In particular, when an individual borrower defaults, the event not only affects his lenders, but also affects individuals in the borrower’s social network. Second, prior studies often face the challenge of



removing the influence of unobserved time-varying common factors such as economic fluctuation. The uniqueness of our data set enables us to assess the difference between online and offline friends which helps remove such common factors.

Data

Overview of PPDai

We conduct our study using data from PPDai.com, the largest peer-to-peer lending marketplace in China. PPDai has over 500,000 registered members and 100 million RMB in funded loans since its official launch in 2007. As in Prosper, borrowers create loan requests, called listings, indicating the amount they seek, the maximum interest rate they are willing to pay, and a short description of loan usage. Lenders “bid” on a listing in terms of the amount to fund and the interesting rate. The amount funded by each lender is typically a fraction of listing amount and a listing becomes a loan only if it is 100% funded.

The design of PPDai’s lending platform is very similar to other online peer-to-peer lending sites such as Prosper, Lending Club, Zopa, and Easycredit. Given the lack of a nationwide credit rating system in China, PPDai develops a proprietary credit rating system for its peer-to-peer lending market. PPDai requires potential borrowers to provide personal information, including national ID card, cell phone number, online video footage, diploma and degrees, professional certificates, and others. This information is verified subsequently by PPDai and a credit score is calculated based on the information each user provides. The credit score has two components: subjective credit points and objective credit points. Subjective points are calculated by PPDai based on the demographic information that the user provides to PPDai, including age, occupation, income, and others. A user could improve his/her subjective points further by providing other information such as marriage certificate, student’s ID, salary stub, etc. Objective points are based on specific verifications or actions taken by the borrower. Each completed action earns the borrower a pre-determined amount of credit points. Table 1 shows the list of verifications and actions and their corresponding credit points. PPDai then converts a borrower’s credit score to a seven-level scale credit rating, ranging from AA, A, B, C, D, E to HR (“high risk”). Based on each borrower’s credit rating, he/she can create loan requests ranging from RMB 3000 to 200000.

Table 1: Objective Credit Points

Items Credit Points

National ID Verification (Required) 10 Cell Phone Verification 10 Video Verification 10 Diploma Verification 5 Pay On-time 1 Late Payment (15-60 day) -2 Late Payment (61-120 days) -5 Late Payment (more than 120 days) -10

To request a loan, a borrower must create a listing, which specifies the amount they would like to borrow, the maximum interest rate they will pay, the duration, and other optional details, such as images or other descriptions. A lender then decides whether to fund the listing, how much and the interesting rate. Like most P2P lending marketplaces, an individual lender doesn’t have to finance the entire loan request on PPDai. Typically, a lender bids a small portion of the loan request and the minimum bidding amount on PPDai is 50 RMB.

Once the bidding process ends, the listing is closed and submitted to the staff of PPDai for further review. Once the review process is completed, funds are directly transferred from winning bidder’s accounts to the borrower’s account. Repayments are deducted directly from the borrower’s account and distributed to the lenders’ accounts based on the loan terms.



Default Policy on PPDai

Since the loans are usually not collateralized for P2P lending, there is a great risk for delinquency. PPDai takes several steps to punish the borrowers who are delinquent. Starting from sending reminder emails and text messages, PPDai gradually escalates its actions to publicly exposing the name of borrowers, turning over copies of borrowers’ identification information (including national ID card, credit card statements, deeds, insurance policies) to lenders to facilitate legal actions. PPDai also provides legal counseling to lenders if requested. Table 2 lists the detailed PPDai actions given the length of late payment. For our analysis, we define default as not making the required payment for over 60 days, at which point PPDai publishes the borrower name and personal information to the public.

Table 2: Late Payment and PPDai Actions

Late Payment PPDai Actions

After 1 to 5 days 1. PPDai will send reminder emails and short messages to the borrower.

2. PPDai will start to place the borrower’s information on the blacklist. (Only the lenders can access the information on the blacklist.)

After 6 to 15 days 1. PPDai will give phone calls to the borrower. 2. The lenders can contact the borrower self.

After 16 to 60 days 1. A formal legal attorney letter will be sent to the borrower. 2. PPDai will charge 50 RMB or 1% of the due payment.

After 60 days 1. PPDai will place all the borrower’s information on the blacklist After 90 days 1. PPDai will give all the borrowers’ information to the lenders.

2. Lenders can turn the loan over to a collection agency or pursue legal actions.

Data Description

With the help of managers of PPDai, we obtain a panel data set from its inception June 18, 2007 to June 15, 2011. The data set includes: 1) user information table, (2) friendship information table, (3) listing information table, and (4) repayment information table.

User information table contains the personal information of a user. In particular, it provides a user’s credit rating and demographic information such as location, gender, age, education status, marriage status and number of children. After removing users who never lent or borrowed, we obtain information on 26,434 valid users, who have successfully lent or borrowed, from 324,293 registered members.

Friendships are self-reported by users but require confirmations from the counter-parties. PPDai distinguishes six types of offline friendships (colleagues, friends, close friends, classmates, acquaintances, and relatives) and two types of online relationships (PPDai friends and others). Colleagues refer to both existing and former colleagues of a user. Friends and close friends refer to individuals who a user shares a bond of mutual affection, while acquaintances refer to individuals who a user knows in person but does not necessarily shares a bond. PPDai friends refer to individuals that a user befriends through the PPDai website while other online friends refer to individuals that a user befriends through other online venues. We omit relatives and other online friends for analysis due to their rarity. Our final data shows 107,563 valid records of friendship are collected.

Listing information table contains information on each loan request initiated by the borrower. In particular, it records whether a loan is successfully funded and the payment term. Besides, listing information table includes list borrowers’ credit score, maximum interest rate the borrower is willing to pay and the current interest rate of the micro-loan market. Our original data set has 52,906 valid listings. The summary statistics shows that the average loan size is about 9000RMB with a monthly repayment of 2000RMB. The average interest rating for all listings is 7.55%.



Repayment information table contains information on borrowers’ repayment of loans. In particular, it contains borrower default information that we use for our analysis. We obtain repayment information of all 52,906 listings. We also note that the default rate is relatively low at 2.1%. However, due to the presence of friendship networks, a much higher percentage of users know someone who had defaulted (34.36%). Table 3 shows the summary statistics of key measures used in our analysis.

Table 3: Summary Statistics

Variable Name Mean Std Dev

User Information Gender (1=Male) 0.79 0.40 Age 28.02 9.23 Number of Children 0.90 0.79 Credit as Lender 65.11 430.51 Credit as Borrower 29.23 15.06 Marriage (Dummy: 1=Married) 0.36 0.48

Education (Dummy: 1=PhD, Master, Undergraduate)

0.23 0.42

Listing information Loan Principal 9318.56 11588.27 Monthly Payment 2080.87 4212.67 Interest Rate_prime 16.22 4.40 Interest Rate_current 16.34 4.26

List Borrower’s Credit Level (AA=0, A=1, B=2, C=3, D=4, E=5, HR=6)

3.77 0.62

Friend Information Friends 0.55 2.75 Close Friends 0.06 3.22 Colleagues 0.03 3.82 Classmates 0.02 3.69 Online Friends 3.32 3.48 Repayment information Default (Dummy: 1=default) 0.021 0.14 Friend Default (Dummy: 1=default) 0.34 0.47 Repayment times 8.40 3.35

Empirical Modeling

P2P Default Network

Figure 1 displays the setting of our model. Consider the ith borrower in the peer-to-peer lending market with J listings. Given the rules of PPDai, many loans are paid on installments. At each due date t of ith borrower’s jth listing, the borrower can make a decision to default or not. We also note that, at each due date t, the friend network of ith borrower could be different. For example, borrower i may make a new online friend through PPDai between t1 and t2. This friend’s decision has no impact on the borrower’s decision at t1, but may influence borrower’s decision at t2. Therefore, the change in friendship network over time allows us to identify the influence of friendship.

Figure 1: P2P Default Network



Based on the framework in Figure 1, the unit of our analysis is whether borrower i makes a default decision on his/her listing j at due date t, which is expressed as Dijt. The measurement of network effect is divided into three steps. At the first step, we focus on whether there has been default behavior in a borrower’s friend network by time t (dijt=1, default; dijt =0, no default), and the ratio of default in his/her friend network by time t (𝑅�𝑖𝑡). The second step is to discriminate different level of default network effect from different types of friends (𝑅�𝑖𝑡

(𝑛)). The third step is to add friend network’s attributes and evaluate their influence. Besides the effect from friends, it is also necessary to consider individual effect of borrowers themselves. Thus, we add both time-variant individual effects and non-time-variant individual effect in our model. Table 4 lists all the variables used in our analysis.

Table 4: Notation Variable Description Equation

Dependent Variable

Dijt or Dijtk Default or not for borrower i at due time t for listing j

Dijt or Dijtk =1 (default) =0 (no default)

Independent Variable

Friend Network

dit Default behavior in ith borrower’s friend network by time t or not

dit =1 (default) =0 (no default)

𝑁𝑖𝑡 Number of friends for ith borrower by time t -

𝑁𝑖𝑡(𝑛)

Number of nth type of friends for ith borrower by time t -

𝑅�𝑖𝑡 Ratio of defaulted friends in ith borrower’s friend network by time t

𝑅�𝑖𝑡 =1𝑁𝑖𝑡

�𝑑𝑖𝑗𝑡𝑘𝑘

𝑅�𝑖𝑡(𝑛)

Ratio of nth type of defaulted friends in ith borrower’s friend network by time t

𝑅�𝑖𝑡(𝑛) =

1

𝑁𝑖𝑡(𝑛) �𝑑𝑖𝑗𝑡𝑘

(𝑛)

𝑘

Borrower i

Listing 1 Listing 2 Listing j ……

Due Date t1 ……

…… ……

i

j

t

Due Date t2 Due Date tt

Friend 1

Friend 2

……

Friend kt1

Friend 1

Friend 2

……

Friend kt2

……

Friend 1

Friend 2

……

Friend ktt

k



Network Attributes

𝑍𝑖𝑗𝑡𝑘

Default network attributes matrix: defaulters’ lender credit rating, defaulters’ borrower credit rating, defaulters’ gender and defaulters’ marriage statues

Female=1, Male=0 Married=1, Single=0

Borrower Attributes

𝑋𝑖𝑗𝑡 Time-variant individual effects (e.g. prime market IR < lending rate)

Prime IR < Lending Rate=1 Prime IR ≥ Lending Rate=0

𝜃𝑖 Non-time-variant individual effect (e.g. individual credit worthiness) -

𝑣𝑖𝑗 Non-time-variant individual loan effect (e.g. loan usage) -

It is useful to provide an illustration of our identification strategy. Suppose there is only one borrower, Adam (i=1). He has two listings, Listing 1 (j=1) and Listing 2 (j=2). The due dates of Listing 1 are 12/31/2011 and 12/31/2012, respectively; while the due dates of Listing 2 are 06/30/2012 and 06/30/2013. That is, Adam will make two decisions for each listing. Let Dijt be the decision variable of Adam, and we assign the value of Dijt as Table 5. Suppose that Adam has only one friend Beth on PPDai.com before 12/31/2011. On 03/31/2012, he makes a new friend, Catherine, who defaulted once on 12/01/2011. No other new friends are made until 06/30/2013. We now calculate the Column 6 and Column 7 in Table 5. Although her default behavior is early than Adam’s first due date, 12/31/2011, however, at this due date, they had not become friends. Therefore, Catherine’s default will have no effect on Adam’s first decision, but will certainly influence his following decisions. Further, we suppose Beth also defaulted only once on 01/01/2013. Then this default will only influence the decision made after 06/30/2012.

Table 5: Example of Notation Variable Description

i j T k Dijt / Dijtk dijt rijt 1 1 12/31/2011 Beth 0 0 0 12/31/2012 Beth, Catherine 0 1 0.5 Catherine has defaulted 2 06/30/2012 Beth, Catherine 0 1 0.5 Catherine has defaulted 06/30/2013 Beth, Catherine 1 1 1 Both Beth and Catherine

have defaulted

Expanded Fixed Effects Model

We use an expanded fixed effect probit model to assess the social network influence among borrowers. Our unit of analysis is a borrower’s decision at each due date on whether to default on a particular loan. The effect of social influence of the friends network is captured by two variables, presence of default and ratio of default, respectively. The initial model expressed as follows:

𝑃�𝐷𝑖𝑗𝑡� = 𝛾1𝑑𝑖𝑡 + 𝛾2 𝑅�𝑖𝑡 + 𝜀𝑖𝑗𝑡 (Model I)

Where dit is a dummy variable indicating the presence of default among a user’s friend network at time t. 𝑅�𝑖𝑡 is the ratio of default among a user’s friend network at time t.

We recognize that many unobserved factors could influence a borrower’s default decision on a given loan. These factors are potentially related characteristics unique to the borrower (i), listing (j), or time (t). To control for such influence, a standard approach is to add borrower, listing and time fixed effects to the regression model. However, given the large number of fixed effects involved, it is necessary to identify key



factors that could potentially confound our analysis. For diagnostic purpose, we add each group of fixed effects at a time into the original model, as Model II, Model III and Model IV:

𝑃�𝐷𝑖𝑗𝑡� = 𝛾1𝑑𝑖𝑡 + 𝛾2 𝑅�𝑖𝑡 + 𝜏𝑡 + 𝜀𝑖𝑗𝑡 (Model II)

𝑃�𝐷𝑖𝑗𝑡� = 𝛾1𝑑𝑖𝑡 + 𝛾2 𝑅�𝑖𝑡 + 𝜏𝑖 + 𝜀𝑖𝑗𝑡 (Model III)

𝑃�𝐷𝑖𝑗𝑡� = 𝛾1𝑑𝑖𝑡 + 𝛾2 𝑅�𝑖𝑡 + 𝜏𝑗 + 𝜀𝑖𝑗𝑡 (Model IV)

We compare the result of Model I with Model II, III and IV. If there is a significance change in the coefficients, it indicates the corresponding fixed effects generate a confounding effect.

It is also necessary to distinguish different effects from various types of friends. As mentioned earlier, PPDai identifies eight types of friendship relationships and we omit relatives, acquaintances and others online friends from our analysis due to their rarity. Thus, we have five types of friendship: colleagues, friends, close friends, classmates, and PPDai online friends and we incorporate them into Model V:

𝑃�𝐷𝑖𝑗𝑡� = 𝒅𝒊𝒕(𝒏)𝚪𝟏 + 𝑹�𝒊𝒕

(𝒏)𝚪𝟐 + 𝜀𝑖𝑗𝑡 (Model V)

Where 𝒅𝒊𝒕(𝒏) and 𝑹�𝒊𝒕

(𝒏) are the matrices for default status and default ratio of different relation types.

Model I to Model V mainly consider the soft information of social network. Next, we consider hard information of the friendship network since hard information provides us with more quantitative and objective data (Lin, 2009; Mayer et al. 1995). Model VI divide friend network’s hard information into four factors, namely defaulters’ lender credit rating, defaulters’ borrower credit rating, defaulters’ gender and defaulters’ marriage statues. The model of this step can be described as follows:


(𝒏)𝚪𝟐 + 𝒁𝒊𝒋𝒕𝒌𝚩 + 𝜀𝑖𝑗𝑡 (Model VI)

Where 𝚩 is the coefficient vector of the defaulter effect matrix 𝒁𝒊𝒋𝒕𝒌 . The definition and relevant description of the defaulter effects matrix can be found in Table 4.

In addition, whether a borrower decide to default also depends on the borrower individual factors, which contains both time-variant individual factors, such as interest-rate spread between the market rate and listing rate, and non-time-variant individual and loan factors, such as marriage, gender, loan guarantee, and credit level. Consequently, the model of the final step can be expressed as follows:


(𝒏)𝚪𝟐 + 𝒁𝒊𝒋𝒕𝒌𝚩𝟏 + 𝑿𝒊𝒋𝒕𝚩𝟐 + 𝑣𝑖𝑗 + 𝜀𝑖𝑗𝑡 (Model VI)

Where 𝑿𝒊𝒋𝒕 captures time-variant individual effects, while 𝑣𝑖𝑗 captures non-time-variant individual and loan fixed effects.

Estimation and Empirical Results

Estimation Correction

The original data set has 52,906 lists. After removing loans initiated by borrowers with incomplete demographic information, our sample size has 28,858 lists. The statistical result shows that default events are relatively rare in our data. The average default rate in our data is close to 2 percent. The traditional estimation method of binary variable requires approximately equal probability of events and nonevents. Otherwise, rare events will be largely underestimated by probit/logit model (King and Zeng, 2001). Three adjusted estimation can be used to correct the tradition method, prior correction, weighted correction, and finite sample MCN correction (including two estimators). According to King and Zeng (2001), Bayesian estimator of MCN correction is relatively better to for rare events.

The correction method can be briefly described as follows. King and Zeng (2003) identify the bias of the coefficient as: 𝑏𝑖𝑎𝑠��̂�� = (𝑋′𝑊𝑋)−1𝑋′𝑊𝜉, where 𝑊 = 𝑑𝑖𝑎𝑔{𝜋�𝑖(1 − 𝜋�𝑖)𝑤𝑖}, 𝜉𝑖 = 0.5𝑄𝑖𝑖[(1 + 𝑤𝑖)𝜋�𝑖 − 𝑤𝑖], Qii are the diagonal elements of 𝑄 = (𝑋′𝑊𝑋)−1𝑋′. The probability of event given independent variables can be expressed as𝑃(𝑌𝑖 = 1|𝑋 = 𝑥) = 𝐸𝛽�(𝜋�𝑖) ≈ 𝜋�𝑖 + 𝐶𝑖 where the correction factor 𝐶𝑖 = (0.5 − 𝜋�𝑖)𝜋�𝑖(1 −𝜋�𝑖)𝑥0𝑉�𝛽��𝑥0′ .



Empirical Results

Table 5 shows the empirical results of MCN correction estimation for Model I to Model VII. The estimation result of Model I is shown in Column 2. Both multiplier effects of friend default and its ratio in borrowers’ network are significant (p<0.0001), which means a 1% increase in friend default ratio leads to a 0.946% increase of odds ratio of borrowers’ default probability. The presence of a defaulted friend in borrower’s network leads to a 3.5% increase of the odds ratio of borrower’s default propensity. This result illustrates that a borrower is significantly influenced by default events in his/her friendship network.

The results of Model II, Model III and Model IV are presented in Column 3 to Column 5 respectively. All three groups of fixed effects are significant, suggesting that unobserved heterogeneities in borrowers, listings, and time have a significant effect on borrowers’ default decisions. Moreover, we find the significance decreases in the magnitude of key coefficients from Model I, Model III, to Model IV, indicating that these fixed effects are confounding factors. These results are similar with findings of Lin (2009), Iyer er al. (2009), and Collier et al. (2010). They stated that these confounding reasons are caused by borrower’s attributes, such as gender, marriage, statues, and credit rating.

The result of Model V is presented in Column 6. In this model, we consider the effect of different types of friends. The analysis shows that the influence of online friends is significantly different from offline friends. A default among a borrower’s online friends increases the odds ratio of borrower’s default propensity by 4.491, much larger than the sum of the influence of all offline friends combined. This result contradicts findings from prior studies that suggest social influence from strong ties (typically offline relationship) is stronger than weak ties (typically online relationship) (Brown and Reingen 1987). One potential explanation of the finding is the lack of detailed information in online relationship which lead to herding behavior (Bikhchandani et al. 1992).

The results of Model VI are shown in Column 7. Given the finding that a borrower’s default behavior is mainly influenced by online friend’s network, we focus on attributes of online friends who have defaulted. The results indicate that the effects of all attributes of online friends who have defaulted are significant. The number of female online friends who defaulted has a positive effect while the number of married friends who have defaulted has a negative effect. This result is similar to the finding in Barasinska (2009), which shows that female lenders often require higher lending rate, thus they are more likely to meet high risk borrowers while married lenders tend to choose less risky borrowers.

In Model VII, we add borrowers’ own attributes and non-time varying individual and listing fixed effects. Our analysis suggests that higher lending interest rate is associated with higher default probability. A similar finding is also reported by Freedman (2009). Longer loan age reduces the probability of default, since it reduces the burden of repayment. Each additional month in the age of a loan leads to a 5.7% decrease in the odds ratio of default. Our analysis also show that having guarantee from PPdai also reduce the risk of default. An interesting phenomenon is that the coefficient of the dummy variable for prime market interest rate lower than lending rate is negative. We traced these listings, and found that most of them are urgent, short-term loans. It means people are not inclined to default on emergent loan, although its lending rate is relatively higher than prime market interest rate. The above discussion focuses on the attributes of listings and markets. We next discuss the attributes of borrowers. Our analysis shows that an increase in a borrower’s credit rating reduces his default propensity. The effect of a borrower’s marriage status is opposite to the effect of friends’ marriage status. Collier et al. (2010) explained such phenomenon from the perspective of signal theory. He suggests that the borrowers who are in a dire situation are more willing to reveal more affirmative personal information, like he/she has married, to give potential lenders a more creditable signal. Such borrowers, not surprisingly, carry high risks.

Table 5: Empirical Results of Probit Fixed Effect Model with MCN Correction Variable Name Model

I Model II Model

III Model

IV Model

V Model

VI Model

VII Intercept - - - - -3.219***

(0.0462) -3.227*** (0.0462)

-6.571*** (0.4241)

Total Friend Default (Dummy)

0.035*** (0.0030)

-0.021*** (0.0035)

0.006* (0.0024)

-0.001 (0.0030) - - -



Offline Friend Default Status

Close Friend Default 0.345 (0.3244)

Classmate Default 0.000*** (0.0001) - -

Colleague Default 0.000*** (0.0084) - -

Regular Friend Default 0.000*** (0.0898) - -

Online Friend Default Status Online Friend Default 4.491***

(0.4644) 5.197*** (0.5095)

4.480*** (0.5047)

Total Ratio of Friend Default

0.666*** (0.0378)

0.422*** (0.0353)

0.204*** (0.0553)

0.353*** (0.0737) - - -

Offline Friend Default Ratio Close Friends Default Ratio -1.415

(1.552)

Classmates Default Ratio - - - - 0.000***

(0.0023) - -

Colleagues Default Ratio - - - - 0.000***

(0.0017) - -

Regular Friends Default Ratio - - - - 0.000***

(0.0244) - -

Online Friend Default Ratio Online Friends Default Ratio 0.734***

(0.1029) 0.642*

(0.3871) 0.078

(0.1191) Online Friend Attributes Online (P2P) Relation Defaulter LenderCredit Rating

- - - - - -0.000* (0.0002)

-0.000* (0.0002)

Online (P2P) Relation Defaulter BorrowerCredit Rating

- - - - - 0.004 (0.0055)

-0.002 (0.0023)

Online (P2P) Relation Defaulter Female - - - - - 1.327***

(0.2932) 1.124*** (0.2654)

Online (P2P) Relation Defaulter Marriage - - - - -

-0.856*** (0.2497)

-0.729*** (0.2190)

Listing Attributes Loan Amount - - - - - - 0.000

(0.0000) Interest Rate - - - - - - 0.130***

(0.0163) Loan Age

- - - - - - -

0.056*** (0.0130)

Guarantee - - - - - - -0.600* (0.2626)

Prime market IR < Lending Rate - - - - - - -1.291*

(0.5931) Borrower Individual Attributes Borrower Gender - - - - - - 0.072

(0.1064)



Borrower Marriage - - - - - - 0.342*** (0.0841)

Borrower credit level - - - - - - 0.333*** (0.0772)

Group Fixed Effect - Yes Yes Yes - - - Individual Fixed Effect - - - - - - Yes Exogenesis Factors Fixed Effect - - - - - - Yes

Notes. The result of Table 5 is estimated by weighted correction on R-2.9.2 with package ‘zelig’. Authors also used ordinary probit estimation, and find correction method significantly improves the results. * p<0.1; ** p<0.05; *** p<0.001. Standard Errors are in parentheses.

Robustness Tests

In this section, we verify the robustness of our results with respect to alternative specifications. Since our objective is to measure the influences on borrower default, we use Model VII as our main model.

Multicollinearity

Although what we use is a set of general linear models, there are still some independent variables may be correlated, which might decrease the efficiency of estimation. Table A1 reports the variance inflation factors (VIFs) of independent variables in our main model. All VIFs are below the conventional cutoff of 10, and the highest VIF is merely 2.108 on Guarantee. This results shows that there is no severe multicollinearity for independent variables in our main model. Namely, the default behavior of borrower does not seem to be driven by multicollinearity.

Additional Covariates

Table 6, column 2 and column 3 permit a closer look at the separate effects of friend type. Column 2 investigates the interaction of specified friend type default status and its credit level. The result illustrates that all interactions, except p2p friends, are significant positive. Namely, borrower will take friends’ credit grade into account when he/she makes a default decision. Moreover, the coefficient of interaction for offline friend is larger than online friend. This pattern means the closer friendship is, the larger effect of credit level will influence borrowers. Zhang and Liu (2012) pointed this phenomenon as herding behavior. Namely, people are likely to make friends with others having similar credit level.

Table 6, column 3, investigates the interaction of specified friend type default ratio and its credit level. The results are similar with column 2. This pattern reinforces our conclusion. And all other variable estimates in column 2 and column 3 remain close to their counterparts in our main model.

Alternative Models

First, due to incidental parameters problem, sometimes the assumption of a fixed effect logit model may be not satisfied. In particular, the effect of interest rate may change at different time, given the supply and demand status of microloan market. Besides, guarantee from PPdai could also have different impact on a borrower’s default decision in different situations. Thus, instead of using a fixed effect model, we use a mixed effect logit model by modeling guarantee and difference between prime interest and lending rate as random effects. Column 4 of Table 6 shows the estimation of mixed model. Compared with our main model, we find that both fixed and mixed effect specifications yield highly consistent results.

Verification

A priori, it is not clear whether a borrower’s verification status should carry any additional information as they are included in PPDai’s calculation of credit score. There are four kinds of verifications in the PPDai.com, ID authentication, mobile verification, diploma verification and video verification, respectively. ID authentication is obligatory before a borrower is allowed to submit a borrowing request, while the other three types are optional and self-reported by borrowers but verified by PPDai. The use of



these three types of verification could act as a signal by borrower for his credit worthiness. For instance, a borrower with defaulted propensity is unwilling to provide much verification information to lenders, because more information will engender higher delinquency cost.

Table 6, column 6 investigates that signaling effect of the three verifications. The results are negative and significant, confirming the presence of signaling effect that a borrower with a willing to offer more information will be less inclined to default, due to the higher delinquency cost and each type of verification decrease default probability by approximately 29%.

Table 6: Robustness Tests Variable Name Friend type

default * Credit grade

Friend type default ratio * Credit grade

Logit Model with Mixed

Effect

Probit Model with Fixed

Effect

Verification Influence

Intercept -6.411*** (0.4186)

-6.486*** (0.4237)

-6.843*** (0.4072)

-3.434*** (0.1666)

- 5.382*** (0.5239)

Offline Friend Default Close Friend Default×Credit

0.442*** (0.1139)

- - -

Classmate Default ×Credit

0.780*** (0.1183)

- - -

Colleague Default ×Credit

0.343*** (0.7844)

- - -

Regular Friend Default ×Credit

0.786*** (0.1217) - - -

Online Friend Default Online Friend Default ×credit

0.000 (0.0008)

- - -

Online Friend Default - - 4.563*** (0. 5025)

2.190*** (0.1170)

4.380*** (0.5020)

Offline Friend Default Ratio

Close Relation Default Ratio×Credit

- 0.217*** (0.0636)

- -

Classmate Default Ratio ×Credit

- 0.584*** (0.0262)

- -

Colleague Default Ratio × Credit

- 0.235*** (0.0164)

- -

Regular Friend Default Ratio ×Credit -

0.145*** (0.0019) - -

Online Friend Default Ratio

Online Friend Default Ratio ×Credit

- 0.015*** (0.0024)

- -

Online Friend Default Ratio - -

0.066 (0.1189)

-0.035 (0.0467)

0.092 (0.1197)

Online Friend Attributes Online (P2P) Relation Defaulter Lender Credit Rating

-0.000 (0.0008)

-0.002*** (0.0004)

-0.000* (0.0002)

-0.000 (0.0001)

-0.000* (0.0002)

Online (P2P) Relation Defaulter

0.000 (0.0022)

0.003 (0.0022)

-0.002 (0.0023)

0.004** (0.0015)

-0.002 (0.0023)



BorrowerCredit Rating

Online Friend Defaulter Female

0.747** (0.2590)

0.937*** (0.2581)

1.128*** (0.2667)

0.567*** (0.0999)

-1.142*** (0.2633)

Online Friend Defaulter Marriage

-0.310 (0.2033)

-0.421* (0.2156)

-0.721** (0.2202)

-0.079 (0.0839)

-0.732*** (0.2183)

Listing Attributes

Loan Amount 0.000

(0.0000) 0.000

(0.0000) -0.000

(0.0000) -0.000

(0.0000) 0.000

(0.0000) Interest Rate 0.128***

(0.0162) 0.133*** (0.0163)

0.153*** (0.0138)

0.064*** (0.0065)

0.129*** (0.0164)

Loan Age -0.064*** (0.0129)

-0.062*** (0.0129)

-0.005*** (0.0127)

-0.030*** (0.0050)

-0.054*** (0.0130)

Guarantee -0.684** (0.2653)

-0.574* (0.2645)

- -0.050 (0.1112)

-0.713** (0.2641)

Prime market IR < Lending Rate

-1.292 * (0.5910)

-1.253* (0.5912)

- -0.897* (0.5284)

-1.423* (0.5984)

Borrower Individual Attributes

Borrower Gender

0.032

(0.1061)

0.052

(0.1061)

0.081

(0.1063)

0.008

(0.0429)

0.074

(0.1069) Borrower Marriage 0.321***

(0.0835) 0.314*** (0.0838)

0.339*** (0.0841)

0.097** (0.0324)

0.447*** (0.0873)

Borrower credit level 0.329*** (0.0762)

0.315*** (0.0077)

0.278*** (0.0753)

0.139*** (0.0298)

0.231** (0.0788)

Verification

mobile verification - - - -

-0.373* (0.2163)

diploma verification - - - -

-0.363*** (0.0890)

video verification - - - -

-0.343** (0.1484)

Group Fixed Effect Yes Yes Yes Yes Yes Individual Fixed Effect Yes Yes Yes Yes Yes Exogenesis Factors Fixed Effect Yes Yes Yes Yes Yes

Conclusions

In sum, the data we gathered from a large peer-to-peer lending site indicates that online social influence is an important driver of borrowers’ default decisions. Borrowers who observe their online friends default are twice as likely to default in the future. This type of social influence introduces significant network externality into the peer-to-peer market that could destabilize the market. It also raises a dilemma for market operators – many market operators use the publication of delinquent list as a way to alert lenders and impose social pressure on the delinquent borrowers. Our analysis indicates that such action could backfire as other borrowers may follow suit.

While our study identifies the presence of social influence, future research is needed to understand what causes the online social influence. One possible explanation is that borrowers may find that default is quite a common event and thus become more willing to default if needed. However, this explanation



cannot fully explain the difference between online and offline influence. Future research will also be valuable in understanding how default influences lender behavior and to what degree default reduces the supply of easy credit in the market.

Appendix 1: Summary of Prior Studies on P2P Loan Default

Authors Data Set Model Major Findings

Lin et al. (2012)

Prosper, Jan 2007 to May 2008

Cox proportional hazards model

1. The total number of friends is insignificant as a predictor of default.

2. Having more unverified friends increases the odds of default, while friends with verified identity decrease the odds of default. However, neither variable is significant.

3. It shows statistically significant effects for Prosper.com verified friends who are lenders in a borrower's social network. Having friends registered as lenders decreases default risk by 9% on average.

4. Having real lender-friends decreases the odds of default.

5. When considering lender-friends who bid on the borrower's listing. Both coefficients are significant at 1%.

6. The odds of default are significantly lower when lender-friends bid and win on the borrower's listing.

Everett, 2008

Prosper, 2006-05-31 to 2007-11-06

Two-stage probability model Default rate is estimated using a simple two-stage probability model, where DI is the dummy default indicator, X is a vector of independent variables representing borrower characteristics, W represents the loan characteristics, and Z represents the group and investor characteristics.

1. Surprisingly, group membership in itself actually has a positive and significant effect on default rate.

2. The positive relationship between membership and default rate disappears once the regression controls for the type relationships in the group. In every regression in which relationships are included, membership in those groups has a negative impact on default rate.

3. All regressions in Table V show a positive relationship between interest rate and default risk.

4. As expected, credit score and home ownership are both negatively related to default rate, with credit score being the most significant determinant.

5. When a borrower is a member of a group that has personal relationships, loan default rate is significantly reduced.

Freedman and Jin 2010

Prosper, 2006-06-01 to 2008-07-31

1. The probability of being default or late increases by credit grade, and in response, interest rate increases and the funding probability decreases. This suggests that credit grade is an important measure of borrower risk and lenders understand their ordinal differences.

2. Similarly, lenders understand that the more



a borrower requests to borrow, the higher the risk of mis-performance, and therefore deserves a lower funding probability and a higher interest rate.

3. Lenders also foresee the higher risk of auto funded loans and adjust funding rate and interest rate accordingly.

Greiner and Wang 2009

Prosper, 2006-02/13 to 2008-10-12

- 1. It is striking to note that around 35% of the loans are in some kind of delinquency.

2. It was hypothesized that social capital helps to reduce delinquencies. However, the empirical results provide very limited support for that.

3. The number of loans per group member (a proxy of the experience of the group) is significant but has a negative influence on loan payment.

Kumar 2007

Prosper, July to December 2007.

1. Higher loan amount leads to higher probability of loan default and also higher interest rates charged and both of these effects are statistically significant. This shows that lenders recognize the risks of a loan with higher loan amount and appropriately charge higher risk premiums.

2. Group membership actually leads to lower bidding and higher interest rates as it increases the risk of defaults.

3. Further, we observed that even though group leader endorsements provide lenders with enhanced trust and they ask for lower interest rates for such loans, the endorsements in fact have no significant impact on the default risk.

Krumme and Herrero-Lopez 2009

Prosper, consisting of 36 months of data through Nov 2008

1. The expected payoff of investment in a lender with a credit score of AA is higher than that of an investment in a lender with score E, as nearly half of borrowers with score E default

References

Aral, S. 2012. “Identifying Social Influence: A Comment on Opinion Leadership and Social Contagion in New Product Diffusion,” Marketing Science, (30:2) pp. 217-223.

Aral, S., Muchnik, L., and Sundararajan, A. 2009. “Distinguishing Influence Based Contagion from Homophily Driven Diffusion in Dynamic Networks,” Proceedings of the National Academy of Sciences, (106:51), pp. 21544-21549.

Aral, S. and D. Walker. 2012. “Creating Social Contagion through Viral Product Design: A Randomized Trial of Peer Influence in Networks,” Management Science. forthcoming

Bacharach, M., and Gambetti, D. 2001. “Trust in Signs,” in Trust in Society, K. Cook (ed.), New York: Russell Sage Foundation, pp. 148-184.

Berger, S. C., and Gleisner, F. 2007. “Electronic Marketplaces and Intermediation: An Empirical Investigation of An Online P2P Lending Marketplace,” Working Paper, University of Frankfurt.

Bikhchandani, S., Hirshleifer, D., and Welch, I. 1992. “A Theory of Fads, Fashion, Custom, and Cultural Change as Informational Cascades,” Journal of Political Economy, (100:5), pp. 992-1026.



Brown, J. J., and P. H. Reingen. 1987. “Social Ties and Word-of-Mouth Referral Behavior,” Journal of Consumer Research (14:3) pp. 350-362

Christakis, N. A., and Fowler, J. H. 2007. “The Spread of Obesity in a Large Social Network over 32 Years,” New England Journal of Medicine 357, pp. 370-379.

Collier, B., and Hampshire, R. 2010. “Sending Mixed Signals: Multilevel Reputation Effects in Peer-to-Peer Lending Markets,” Proceedings of the 2010 ACM Conference on Computer Supported Cooperative Work, Savannah, Georgia, USA, pp. 197-206.

Everett, C. R., 2010. “Group Membership, Relationship Banking and Loan Default Risk: The Case of Online Social Lending,” Pepperdine University Working Paper. Available at SSRN: http://ssrn.com/abstract=1114428.

Freedman, S., and Jin, G. Z. 2008. “Do Social Networks Solve Information Problems for Peer-to-Peer Lending? Evidence from Prosper.com,” NET Institute Working Paper No. 08-43. Available at SSRN: http://ssrn.com/abstract=1304138 .

Freedman, S. and Jin, G. Z. 2011. “Learning by Doing with Asymmetric Information: Evidence from Prosper.com,” NBER Working Paper No. 16855.

Galloway, I. J. 2009. “Peer-to-peer Lending and Community Development Finance,” Federal Reserve Bank of San Francisco Working Paper 2009-06.

Garman, S., Hampshire, R., and Krishnan, R. 2008. “Person-to-person Lending: The Pursuit of (More) Competitive Credit Markets,” Proceedings of the 2008 International Conference on Information Systems, Paper 160.

Greiner, M. E., and Wang, H. 2009. “The Role of Social Capital in People-to-People Lending Marketplaces,” Proceedings of the 2009 International Conference on Information Systems, Paper 29.

Herzenstein, M., Dholakia, U. M., and Andrews, R. L. 2011. “Strategic Herding Behavior in Peer-to-peer Loan Auctions,” Journal of Interactive Marketing, (25:1) pp. 27-36.

Iyer, R., Khwajaand A. I., Luttmer, E. F. P., and Shue K. 2009. "Screening in New Credit Markets: Can Individual Lenders Infer Borrower Creditworthiness in Peer-to-peer Lending?" NBER Working Paper No. 15242.

Karlan, D. S. 2007. Social Connections and Group Banking. The Economic Journal, (117:517), pp. 52-84. King, G and Zheng, L. 2001. "Logistic Regression in Rare Events Data," Political Analysis, 9, pp. 137-163. Krumme, K. and Herrero-Lopez, S. 2009. “Do Lenders Make Optimal Decisions in a Peer-to-Peer

Network?” Proceedings of the IEEE/WIC/ACM International Joint Conference on Web Intelligence and Intelligent Agent Technology, pp. 124–127.

Kumar, S. 2007. "Bank of One: Empirical Analysis of Peer-to-peer Financial Marketplaces," Proceedings of the 2007 Americas Conference on Information Systems Paper 305.

Lin, M. F. 2009. “Peer-to-peer Lending: An Empirical Study,” 2009 Americas Conference on Information Systems Doctoral Consortium Paper 17.

Lin, M. F., Prabhala, N. R., and Viswanathan, S. 2009. “Judging Borrowers by the Company They Keep: Friendship Networks and Information Asymmetry in Online Peer-to-peer Lending,” Management Science, forthcoming

Ma, L., R. Krishnan, and A. Montgomery. 2010. “Homophily or Influence? An Empirical Analysis of Purchase within a Social Network,” Carnegie Mellon University Working Paper

Manski, C. F. 1993. “Identification of Endogenous Social Effects: The Reflection Problem,” Review of Economic Studies (60:3) pp. 531-542.

Oestreicher-Singer, G., A. Sundararajan. 2012. “The Visible Hand? Demand Effects of Recommendation Networks in Electronic Markets,” Management Science, forthcoming

Puro, L., Teich, J. E., Wallenius, H., and Wallenius, J. 2010. “Borrower Decision Aid for People-to-people Lending,” Decision Support System, (49:1), pp. 52-60.

Spence, M. 1973. “Job Market Signaling,” Quarterly Journal of Economics, (87:3), pp. 355-374. Wang, H., Greiner, M., and Aronson, J. E. 2009. “People-to-people Lending: The emerging E-commerce

Transformation of a Financial Market,” Value Creation in E-Business Management, (36:3), pp. 182-195.

Zhang, J. and Liu, P. 2012. "Rational Herding in Microloan Markets," Management Science, (58:5) pp. 892-912.

Documents

Social Influence and Defaults in Peer-to-Peer Lending Networks