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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

jlzym0309@sina.com

Zhuopei Yang

School of Information, Central University of Finance and Economics

No.39 South Xueyuan Road, Beijing, China, 100081

yangtian0723@sina.com

Huating Pan

School of Information, Central University of Finance and Economics

No.39 South Xueyuan Road, Beijing, China, 100081

Panhuating333@163.com

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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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