influencing factors of online p2p lending success rate in...
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Influencing Factors of Online P2P Lending Success Rate in China
Yanmei Zhang
School of Information, Central University of Finance and Economics
No.39 South Xueyuan Road, Beijing, China, 100081
Zhuopei Yang
School of Information, Central University of Finance and Economics
No.39 South Xueyuan Road, Beijing, China, 100081
Huating Pan
School of Information, Central University of Finance and Economics
No.39 South Xueyuan Road, Beijing, China, 100081
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Influencing Factors of Online P2P Lending Success Rate in China
ABSTRACT
Currently, online Chinese P2P lending platform is stuck with low success rate caused by information
asymmetry. Bidding record, acting as a social capital, has been ignored in previous studies despite its important
role in reducing information asymmetry. Therefore, in combination with relevant social capital theories, we
build a multiple linear regression model with social network analytical method to study the influencing factors
of online Chinese P2P lending platform, especially the bidding record. Using the largest Chinese P2P lending
platform Ppdai as the object of study, data analysis shows that bidding record has a greater influence on online
Chinese P2P lending compared to other factors, and that Chinese users rely heavily on social capital. Bidding
record reduces the information asymmetry effectively, thus helps improve the success rate of online P2P
lending.
Keywords: Bidding record; online P2P lending; influencing factors; success rate;
1. Introduction
In the last few years, the wide use of mobile phones has provided the Internet Finance with more growth
opportunities. With the prosperity of mobile payment, social network and cloud computing, a new financial
model guided by information technology is witnessed-the Internet Finance model, which currently springs up in
forms of mobile banking service and P2P finance. Originating from petty loan and serving especially for those
unqualified to borrow from the bank, online P2P (peer-to-peer) lending has gained its fame and popularity
through the years. In China, the development of online P2P lending is generally on the primary level, with
successful examples as Ppdai, RenRendai and CreditEase. In contrast, that in most of the developed countries
has undergone longer history, and still wider range and faster growth.
In comparison to those in developed countries like the US, online Chinese P2P lending platforms appear to
be lack in social capital information. Most of the previous researches have ignored the bidding record, a
transaction-based social capital which acts as “soft” credit information to exert great influence on the success
rate. Through digging, we found that, apart from “hard” credit information e.g. basic personal information and
credit evaluation by the platform, other clues the lenders on the platform have access to include bidding record.
This is a network database that describes the complex social relationship between the bidders and the lenders,
and to some extent reflects the lending behavior under the Chinese mode.
We believe that transaction information can reduce the information asymmetry effectively, therefore
improve the lending success rate. Under this hypothesis, we build the theoretical model as below (Picture 1).
This model, based on real transaction data, is built with “hard” credit information (the borrower credit, success
numbers other demographic information) and “soft” credit information (indexes extracted from bidding record
to measure social capital). Among them, bidding record is the main focus of this essay.
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Information asymmetry
Borrower credit Lender credit
Life of loan
Loan amountPrevious success
Previous failure
“soft” credit information
Bidding record
Degree centrality
Closeness centrality
Betweenness centrality
“hard” credit information
Lending success rate
Figure 1: Theoretical model
2. Comparison Between Chinese and American Online P2P Lending
Most of the online Chinese lending platforms imitate foreign pioneers in their operation style, and thus bear
a great similarity in registration, identification, listing, bidding, limitation of amount and the source of profit.
However, due to the great differentiation in financial background, legal and national credit system, their
emergence and development vary a lot. Table 1 compares their similarities and differences in operation mode,
information reliance and risk control process.
Table 1: Comparison between Chinese and American online P2P lending
Platform
Aspect U.S. China
Operation
mode
Threshold Credit evaluation by
authentication Almost none
Credit evaluation Third party evaluation Previous credit accumulation
Identity check Online Online and offline
Charge of fees On borrower, relatively low;
Based on amount, life and credit
On borrower & lender, relatively high;
Based on life;
Extra charge (prepay & withdraw)
Social network Create or join group freely;
Medium social networks
Forum only, no “friendship”;
Weak social networks
Risk control Scattered risk Before, during and after lending Afterward penalty
Lasting period Lifelong Temporary
“Hard” and “soft” credit information Both have influence Rely more on “soft” credit information
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From the table above, there are three aspects of difference between Chinese and American online P2P
lending platforms.
1) Credit evaluation system. There is a lack of solid credit evaluation system in China, making it
difficult for the platform to verify and assess the users.
2) Risk control process. Unlike in the US, where the credit risks as well as the risk control methods are
dispersed before, during and after the lending, the credit control method in China is merely aftermath
punishment, which has limited impact on regulating adverse behaviors.
3) Effect of social capital. American platforms allow users to make friends and create groups freely,
while this function is blank in China. In contrast, due to the poor exposure of personal information,
Chinese lenders tend to rely greater on “soft” credit information, which is actually much weaker
compared to American platforms.
Problems hindering current online Chinese P2P lending platforms from further development are: few
participants, lack of friendship, weak social capital, information asymmetry and trust crisis. All of these
contribute to a low success rate in China. According to Bandura [Bandura 1982], people won’t act hastily
without enough information to support reasonable judgment. As a high success rate guarantees the platform’s
sustainable growth, how to take full advantage of the users’ social capital in order to reduce information
asymmetry thus improve lending success rate is a problem in desperate need to be solved.
3. Literature Review
Scholars all over the world have carried out a lot of researches on P2P online lending including the
influence of “hard” credit information (identity information) and “soft” credit information (mostly social
capital). They have made some achievements, mainly based on the data from Prosper.com. According to the
findings of Herzenstein’s research [Herzenstein et al. 2008], demographic characteristics such as race and gentle
have but little impact on the success rate of online lending, in comparison with the borrower economic power
and lending history. H. Wang [Wang et al. 2009] discussed different P2P lending marketplace models and how
information systems support the creation and management of these new marketplaces, and how they support the
individuals involved. In a literature review focusing on how decisive factors influence the lending success rate,
Bachmann [Bachmann et al. 2011] distinguishes financial characters and individual ones the same as we
distinguish friendship and team relationship in analyzing social characteristics. Most Chinese scholars study
online P2P lending using statistics from Ppdai, the biggest platform in China. Xu [Xu et al. 2010] compared the
influence of social capital in different communities and different cultures based on the archival data of Prosper
and Ppdai. Using a funding probability model, Li [Li et al. 2011] empirically prove that borrower two critical
decisions have significant impacts on auction results of listings, especially the requested amount of loan. Later,
using data collected from Ppdai, Chen [Chen et al. 2013] found that, female borrowers, whose default rates are
lower though, are less likely to be funded than male borrowers. They thought it suggested that there was
significant gender discrimination in P2P lending market in China, but such discrimination was out of prejudice
rather than rational reasoning.
In study of factors influencing the success rate of online P2P lending, social capital, which acts as a
borrower “soft” credit information, has caught many scholars’ attention. Scholars in western countries carry out
researches based on data collected on Prosper, and most of the Chinese ones, owing to a lack of data access, also
use public statistics on Prosper (and some of the others: Ppdai.com). M. Lin [Lin et al. 2009] analyzed a large
sample of data on Prosper and found that stronger and more verifiable relational network measures are
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associated with a higher likelihood of a loan being funded, a lower risk of default, and lower interest rates. They
tested whether social networks lead to better lending outcomes, focusing on the distinction between the
structural and relational aspects of networks. While the structural aspects have limited to no significance, the
relational aspects are consistently significant predictors of lending outcomes, with a striking gradation based on
the verifiability and visibility of a borrower social capital. When examining whether marketplace members
(lenders, borrowers) are able to capitalize on borrowers' accumulated social capital, Greiner found that social
capital does not provide equal benefits to all members and that borrowers especially high-risk borrowers benefit
most from social capital. Therefore, social capital is not a good predictor of loan payment and does not
necessarily help lenders in making better investment decisions [Greiner & Wang 2009]. They also proved the
importance of economic status as the major driver for bidding behavior and of social capital and listing quality
as trust-building mechanisms that influence trust behavior [Greiner & Wang 2010]. It was mentioned that a
more thorough social network provides a higher possibility of a successful outcome and lower interest rates.
And influence of social capital becomes greater when the borrower has a lower credit rate.
Sven C. Berger [Berger & Gleisner 2011] believed that a middleman really helps to get a loan by raising
the borrower credit. S. Li [Li et al. 2011] found that friendship plays a significant part in successful online
lending. Based on the archival data of Prosper and Ppdai, Xu [Xu et al. 2011] compared the influence of social
capital in different communities and different cultures. The empirical results show that social capital is not
equally important in different cultures. It seems to be more influential for likelihood of getting funded in China
than in the U.S. In contrast, social capital has influence on interest rate in the U.S. only. Chen [Chen & Han
2012] conducted a comparative study of online P2P lending practices in the US and China, and found that two
categories of credit information, “hard” and “soft” credit information, may have profound influences on lending
outcomes in both countries, but lenders in China is more reliable on “soft” credit information. Seth Freedman
[Freedman & Jin 2014] examined whether social networks facilitate online markets and verified that borrowers
with social ties are consistently more likely to have their loans funded and receive lower interest rates.
Information asymmetry on P2P lending platform occurs when a lender cannot have a full knowledge of the
borrower’s other information (such as his ability and willingness to repay, and the authenticity of his
demographic information) except for what is provided. Scholars believe that information asymmetry is likely to
influence lending success rate, which makes it a focus how to reduce information asymmetry effectively. Lin
[Lin 2009] believes social network is capable of reducing information asymmetry. The methodology of Iyer
[Iyer et al. 2009] shows that lenders in peer-to-peer markets are able to partly infer borrower credit worthiness
using the rich information set that these markets provide. While lenders in these markets mostly rely on standard
banking variables to draw inferences on credit worthiness, they also use non-standard or soft sources of
information in their screening process, especially in the lower credit categories. In Yang’s study [Yang et al.
2014], 1000 lenders and borrowers chosen randomly are sent questionnaires to solicit their opinions after
getting their agreement to take part in the survey. Their ideas help in building a model evaluating how
performance-individual and group can be used as signals to reduce information asymmetry.
In summary, there are a lot of factors affecting P2P online finance, including demographic characteristics,
financial condition, previous successful deals and social capital. Scholars all over the world have carried out
plenty of research on these factors and have come to a few conclusions, which resemble to each other despite
the various different methodologies. Moreover, it’s easy to see that social capital plays an important part on the
success rate of P2P online lending.
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American P2P lending platforms have imposed feasible regulation on user information exposure and
identification, while the Chinese ones have fewer and less strict requirements on a borrower’s credit and
information exposure owing to the scarce personal information and a lack of thorough credit evaluation system.
Although many scholars have discussed various issues regarding online P2P lending, most of them base their
studies on second-hand data from Prosper.com, which apparently cannot fully represent the Chinese mode,
given its specialty in economics, policy and cultural background. Finding it difficult getting access to public
data on P2P lending platform except those revealed by prosper.com, many Chinese scholars turn to collect
questionnaire data from surveys. However, resulting from the narrow sphere and poor randomness,
questionnaire data have its limitation to illustrate current transaction situation without distortion. Although the
UK is the cradle of P2P lending, the differences in background, environment and policy has made the prospects
vary from China to the western world. It’s difficult to explain the phenomena and behaviors in China with
foreign data or questionnaire data. Therefore, we retrieve information about social capital from users’
transaction history and use a social network analytical method to study the influence it has on the success rate of
online P2P lending.
4. Empirical Analysis
4.1. Object of Study
Transaction data on Ppdai.com is used as the object of study, by collecting and analyzing which the factors
especially bidding record that influence online Chinese P2P lending success rate are dug. Ppdai (Shanghai Ppdai
Financial Information Service Co. Ltd.), founded in June 2007, is the first P2P online finance platform in China.
Ppdai hands out loans in the following procedure: the platform tests and verifies borrower information and
rates him before he launches a loan demand including amount of loan, life of loan, highest annual interest rate
affordable, etc., and actually gets a loan; potential lenders bid with full or part of their capital for interest
income. He who offers the lowest interest will win the bid. It calls a deal if a set of loan of varied interest rate
meets the borrower requirement. After that, the borrower needs to deposit amount payable monthly into his
Ppdai account until the final payoff.
To help lenders make better investment, both demographic information (such as gentle and occupation) and
previous lending record (such as borrower credit and previous success and failure) are required to be exposed in
public. With reference to personal information and bidding records, we use real transaction data as the object to
study the influence of social capital based on transaction on lending success rate.
4.2. Variable Analysis
In our research, we use LocoySpider to collect data from Ppdai.com from May 2013 to May 2014. To
improve accuracy, all the data used are from closed bids and have gone through laundry, selection, omission,
integration and matching. The sample generated from a random 5% selection, that is: 16,005 loan applies,
212,404 corresponding bid records, covering 26,315 register users, 6,641 borrowers included. Based on that, we
built a multiple linear regression model to conduct the empirical analysis.
We use social network analytical method to measure and assess social capital since the majority of scholars
have acknowledged the method. With the assistance of Pajek, a social network analysis tool, indexes reflecting
borrower’s social capital are measured in detail. It is advisable to use degree centrality, betweenness centrality
and closeness centrality as indexes measuring social capital to study the influence it has on P2P online lending
success rate.
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Taking relevant findings from previous studies and circumstances on Ppdai into consideration, the factors
as follows are chosen to study their influence on P2P online lending success rate. The explanatory variables are:
borrower credit, lender credit, previous success, previous failure, loan amount, life of loan, degree centrality,
betweenness centrality and closeness centrality. The explained variable is the success rate of lending. We cast a
spotlight on bidding record and its influence on the P2P lending success rate. Brief introduction to the
explanatory variables are as follows:
1) Borrower credit. The lending platform rates the users according to their identification and transaction
records,thorough information bringing high score. In addition, a good transaction adds bonus score
to borrow-in credit while a poor one results in a deduction.
2) Lender credit. This is a property of the lender, giving us information about his investment history,
experience and judgment. Generally, a high lend-out credit score indicates more investment
experience as well as better judgment and analytical capability, which guarantee capital safety and
steady profit.
3) Previous success. Only if the borrower gets 100% of the loan he has demanded, the deal is successful.
More successful deals, more active the borrower is, and possibly higher his credit score. The number
of previous successful deals is defined here as previous success.
4) Previous failure. A loan bid launched by a certain borrower that goes no-reply in due time is called
pass of bid. The number of previous passes of bid is defined as previous failure.
5) Life of loan. It describes the time engaged to use the loan. The borrower is not allowed for
prepayment or delayed repayment.
6) Loan amount. Currently the maximum amount of loan allowed on Ppdai.com is ¥500, 000.
7) Degree centrality. It is defined as the number of links incident upon a node (i.e., the number of ties
that a node has). The degree can be interpreted in terms of the nodes linked to a borrower.
8) Closeness centrality. The closeness centrality of a vertex is the number of other vertices divided by
the sum of all distances between the vertex and all others. [Nooy et al. 2011] In connected graphs
there is a natural distance metric between all pairs of nodes, defined by the length of their shortest
paths. The farness of a node S is defined as the sum of its distances to all other nodes, and its
closeness is defined as the reciprocal of the farness. Thus, the more central a node is the lower its
total distance to all other nodes. Closeness can be regarded as a measure of how long it will take to
spread information from S to all other nodes sequentially.
9) Betweenness centrality. Betweenness is a centrality measure of a vertex within a graph. [Nooy et al.
2011] Betweenness centrality quantifies the number of times a node acts as a bridge along the
shortest path between two other nodes. It measures the frequency that a member is on the shortest
paths between any two other members on the friendship network. It was introduced as a measure for
quantifying the control of a human on the communication between other humans in a social network.
Individuals that cart greater influence on communication or intermediation have a high betweenness.
4.3. Regression Results and Discussions
In order to study factors influencing the lending success rate, we import the data collected from Ppdai.com
into SPSS 19.0 to conduct multiple linear regression (Enter). Initial results using explanatory parameters enter
method are as follows:
Table 2: MLR Test Results Summary (Enter)
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Model R Adjusted Standard Error of Estimate
1 0.782 0.612 0.612 0.159260253810
Numbers of independent variables: 9
Coefficient of determination ( ): 0.612
Adjusted : 0.612
Standard error of the estimate: 0.159
The adjusted equals to 0.612, which means 61.2% of the variance is accounted for by this regression
model. The goodness of fit is relatively high.
Table 3: MLR Test Results Anovab (Enter)
Model Sum of square Degree of freedom Mean square F Sig.
1
Regression 211.913 9 23.546 928.325 0.000
Error 134.225 5292 0.025
Total 346.138 5301
Sum of squares, regression (SSR): 211.913
Sum of squares, error (SSE): 134.225
Sum of squares, total (SST): 346.138
Mean square regression: 23.546
F-ratio: 928.325
P-value: 0.000<0.050
According to the results in table 3, the significance of F-ratio approximately equals to 0.000<0.05. There’s
significant linear correlation between the dependent variable and independent variables. We are allowed to do
the significance test.
Table 4: Significant Test of Regression Coefficient (Enter)
Model Unstandardized coefficient
Standardized
coefficient t Sig. Linearity
B Standard error Beta Tolerance VIF
1
(Constant) 0.622 0.038 16.167 0.000
Borrower credit 0.002 0.000 0.183 18.494 0.000 0.748 1.337
Lender credit
-2.970
0.000 -0.013 -0.766 0.444 0.268 3.732
Loan amount
-1.394
0.000 -0.013 -0.976 0.329 0.418 2.391
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Previous failure -0.099 0.001 -0.809 -83.878 0.000 0.787 1.270
Previous success 0.000 0.000 0.061 3.144 0.002 0.196 5.103
Life of loan 0.000 0.001 -0.004 -0.498 0.618 0.965 1.036
Closeness centrality 0.648 0.126 0.068 5.144 0.000 0.415 2.410
Degree centrality 0.000 0.000 0.125 3.270 0.001 0.050 19.809
Betweenness centrality -9.606 2.351 -0.130 -4.086 0.000 0.072 13.896
Table 4 illustrates the result of significance test of coefficients. Under the significance level of 0.05,
p-values suggest there’s no significant linear correlation between lender credit, loan amount, life of loan and the
dependent variable. These variables should be left out when deducting the equation. There is significant linear
correlation between other independent variables and the dependent variable. The coefficients before previous
success, life of loan and degree centrality are 0.00, which indicates their lack of relevance to the success rate.
These three variables should also be eliminated from the model. Taking the tolerance of explanatory variable
and variance inflation factor (VIF) into consideration, degree centrality as well as betweenness centrality may be
eliminated because of high multicolinearity with other explanatory variables.
From the analysis above, the original regression model is supposed to be redone to modify a series of
inaccuracy. The explanatory parameters backwards method is employed in the new model.
Table 5: MLR Test Results Summary (Backwards)
Model R
Adjusted
Standard Error of
Estimate
Statistics Change Durbin
Watson Change F Change df1 df2 Sig. F
Change
1 0.782a 0.611 0.610 0.159499630303 0.611 1385.166 6 5295 0.000
2 0.782b 0.611 0.610 0.159487724329 0.000 0.209 1 5295 0.647
3 0.782c 0.611 0.610 0.159482695078 0.000 0.666 1 5296 0.415 1.982
a. Predictor variable: (constant), betweenness centrality, borrower credit, loan amount, previous failure, closeness centrality
and lender credit.
b. Predictor variable: (constant), betweenness centrality, borrower credit, previous failure, closeness centrality and lender credit.
c. Predictor variable: (constant), borrower credit, previous failure, closeness centrality and lender credit.
d. Dependent variable: success rate
Table 6: Significant Test of Regression Coefficient (Backwards)
Model Unstandardized coefficient
Standardized
coefficient t Sig. Linearity
B Standard error Tolerance VIF
1
(Constant) 0.555 0.034 16.409 0.000
Borrower credit 0.002 0.000 0.186 18.876 0.000 0.757 1.322
Lender credit
6.769
0.000 0.029 2.217 0.027 0.433 2.308
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Loan amount
-4.941
0.000 -0.005 -0.458 0.647 0.734 1.362
Previous failure -0.099 0.001 -0.811 -84.092 0.000 0.790 1.266
Closeness centrality 0.872 0.112 0.092 7.793 0.000 0.528 1.895
Betweenness centrality -0.553 0.943 -0.008 -0.586 0.558 0.449 2.228
2
(Constant) 0.559 0.033 16.907 0.000
Borrower credit 0.002 0.000 0.185 19.081 0.000 0.779 1.283
Lender credit
7.315
0.000 0.031 2.603 0.009 0.511 1.956
Previous failure -0.099 0.001 -0.811 -84.982 0.000 0.808 1.238
Closeness centrality 0.861 0.109 0.091 7.881 0.000 0.554 1.807
Betweenness centrality -0.714 0.875 -0.010 -0.816 0.415 0.521 1.918
3
(Constant) 0.567 0.031 18.170 0.000
Borrower credit 0.002 0.000 0.186 19.260 0.000 0.787 1.270
Lender credit
6.286
0.000 0.027 2.503 0.012 0.640 1.563
Previous failure -0.099 0.001 -0.811 -84.985 0.000 0.808 1.238
Closeness centrality 0.831 0.103 0.088 8.089 0.000 0.627 1.596
From table 5, goodness of fit of the regression models built with backwards method remains unchanged.
Table 6 illustrates the results of biased regression coefficients of explanatory variables as well as their
significance test. Under the significance level of 0.05, p-values in model 1(for loan amount and betweenness
centrality) and model 2 (for betweenness centrality) denies their validation. Model 3, with all the p-values less
than 0.05, verifies a significant linear relationship between explanatory variables and the explained variable, and
is used to generate the final equation.
Regression equation:
Yi=-0.567+0.002X1+6.286E-7
X2-0.099X3+0.831X4
: Borrower credit; : Lender credit; : Previous failure; : Closeness centrality.
From the regression we can see, there’s positive correlation between borrower credit and the success rate,
which means a higher borrower credit will improve success rate, so does lender credit, though referring to the
coefficient, lender credit has only minor impact. Previous failure has negative correlation with the success rate,
that is, more passes of bid or a higher degree centrality contribute to a lower success rate. Among the variables
connecting to social capital, merely closeness centrality shows positive correlation to the success rate, proving it
more likely to get a loan when there’s easier access to information. Neither the traditional variables amount of
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loan and life of loan nor the social capital indexes degree centrality and betweenness centrality have significant
relationship with the lending success rate.
According to the proportion of the coefficients, although both borrower credit and lender credit have
positive influence on the success rate, the lenders tend to rely more on borrower credit. Previous failure has
relatively greater influence on the success rate, in comparison to previous success, making it a receivable
reference. Despite the insignificance of degree centrality and betweenness centrality, closeness centrality does
have a great impact on the success rate, indicating an easier access to information reduces information
asymmetry, thus lubricates the lending process. Transaction information plays an irreplaceable role in releasing
information asymmetry and improving lending success rate.
5. Conclusion
Factors influencing online Chinese P2P lending success rate are analyzed in this essay. Apart from
variables measuring “hard” credit information: borrower credit, lender credit, previous success, previous failure,
loan amount, life of loan, the variable measuring a borrower’s “soft” credit information i.e. bidding record is
innovatively added to the study. A social network analytical method is used to quantify bidding record as degree
centrality, closeness centrality and betweenness centrality. After that, we built a multiple linear regression
model to study the relationship between these variables and the success rate. The findings show that, compared
with other factors, an index describing social capital-closeness centrality-has greater influence on the success
rate. Higher closeness centrality means smaller distance between users, making it easier for information
transition, thus releases the asymmetry and improves the lending success rate. Hence, bidding record, which acts
as social capital based on real transaction, plays an important part in reducing information asymmetry.
Moreover, bidding record has an influence excessive to demographic information on the success rate, indicating
the online Chinese P2P finance users tend to be more dependent on social capital, which is likely to result from
a credit evaluation system poor and unable to guarantee the transparency and authenticity of the borrower’s
personal information. Users in the P2P market do not attach much significance to “hard” credit information,
whereas they refer to “soft” credit information when it comes to judgment.
Through analysis into real data on online Chinese P2P lending platform Ppdai.com, the influence of social
capital based on transaction on lending success rate is discussed. On one hand, attributing to the realness and
wideness of the data, the findings help grasp a better understanding of the lending behaviors of Chinese P2P
users, further completing the studies concerning the influence of social capital on online Chinese P2P lending,
and offers useful reference for relevant studies to follow. On the other, the findings also assist lenders to find
suitable invest opportunities as well as borrowers to raise money more promptly. The platform will benefit from
the study in undoing the negative effect of points system (which measures credit in points), therefore improve
the credit evaluation system and reduce information asymmetry, accelerating the sustainable development of
online Chinese P2P lending market with higher success rate and healthier borrowing/lending procedure.
The objects of study are users with at least one successful record. For fresh users with blank transaction
record, their initial credit shall be set according to a similarity to previous users so as to help them get first loan
more quickly. Details of this approach will be discussed in further studies.
6. Acknowledgments
This study was supported by the National Natural Science Foundation of China (No.61309029, 61273293)
and Ministry of Education Humanities Social Sciences Research Project(No.11YJC880163)and Discipline
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Construction Foundation of Central University of Finance and Economics. We would like to thank professor
Ning Zhang for her valuable comment and suggestions.
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