Can investors’ collective decision-making evolve? Evidence from peer-to-peer lending markets

This study tries to identify the accuracy of individual investors’ capability to predict a borrower’s creditworthiness in peer-to-peer lending markets and examine whether their ability is likely to evolve over time. The results of this study show that there is no significant difference between the predictive power of investors’ ex-ante funding decision model and that of the ex-post repayment model over a borrower’s repayment performance. Furthermore, the predictive power of investors’ ex-ante funding decision over a borrower’s repayment performance is shown to improve over time. It is also found that the main reason why investors’ predictive power improves over time is because investors can assess more accurately the information provided by the platform operator and describe the borrower's characteristics. The results of this study are important as they confirm the possibility of optimizing and streamlining the P2P lending market, through the evolution of investors’ decision making.


Introduction
Peer-to-peer (P2P) lending is one of the newly emerging e-commerce businesses in which investors and borrowers make loan transactions through an online platform [4,60]. Emerging in the mid-2000s, P2P lending is seen as an alternative to traditional financing in the lending market. Unlike traditional financing, P2P lending can provide higher welfare for individual market participants by eliminating the intermediary function of financial institutions. In other words, a borrower and an investor can make direct money transactions without the intervention of an intermediary; instead of eliminating the transaction margin held by the intermediary in traditional 1 3 financing, the borrower can take out loans at lower interest rates, and the investors can pursue higher returns.
However, there are important prerequisites. In order for the eliminated brokerage margin of existing financing methods to be linked to minimizing the borrowers' costs and maximizing investors' profits, the P2P lending system must have similar or higher efficiency than traditional financial systems. For this to be possible, the most important factor is the investors' credit assessment capability on the borrower. If the accuracy and efficiency of individual investors' credit assessments are significantly inferior to those of existing financial systems, the credit risk that could be resolved in existing financial institutions could lead to new costs, offsetting the possibility of greater savings from eliminating brokerage margins. In this case, the increase in the welfare of individual participants, which is the advantage of P2P lending over traditional finance, will no longer be valid. Thus, upgrading individual investors' credit assessment capabilities in P2P lending is an important factor that should be secured, in order for P2P lending to grow as a competitive or alternative means to traditional financing.
In particular, the efficiency of P2P lending should be secured at a high level to make it a competitive alternative financing method, given that traditional financing has long pursued cost optimization based on accumulated data, expertise, and experience. However, unlike traditional financing with a professional credit rating system, it is difficult for P2P lending to maximize the accuracy of credit evaluations, given that most investors are regular individuals relatively lacking experience and expertise.
At present, individual investors' decision-making in P2P lending markets and the assessment of their quality has been a matter of both practical and theoretical interest. The investors' decision-making is not that of individual investors, but an aggregated outcome of investor groups. That is, it means collective decision-making. In the P2P lending market, each individual makes a bidding decision, but the actual availability of the loan is determined by the collective results of these individual decisions [17,66]. Therefore, it is important to focus on the collective decisionmaking of investor groups, not individual investors' decision-making, when evaluating funding decisions in P2P lending. Meanwhile, several studies have shown that individual investors in the P2P lending markets still lack the ability to evaluate [55,67]. The lack of collective credit evaluation capabilities of investors can be a serious obstacle for P2P lending to grow as an alternative means of financing. However, its potential as an alternative financial instrument could be high if the collective decision-making of investors were to improve as the market gradually matures in the future. Therefore, it is a practical and academically important issue to ensure that investors' collective decisions have room for improvement as market structures evolve over time. In this respect, the study is the first to our knowledge to study this issue.
To do this, it is necessary to first identify the level of collective decision-making by investors. However, so far, while studies related to P2P lending have raised the issue of individual investors' lack of credit evaluation capabilities, there has been no further study on by how much they fall short. Identifying the skill level of a group of inexperienced, non-professional investors to assess a borrower's creditworthiness is important in assessing whether the P2P lending can serve as a competitive alternative market. In this respect, the study seeks to compare the exante actual credit evaluation capabilities of investors compared to ex-post optimal capabilities. Therefore, this study first presents the following research question.
Research question 1 How different is the predictive power on a borrower's default of the individual investors' ex-ante funding decision model from that of the ex-post repayment model?
After identifying suboptimal levels of investors' ability to make collective funding decisions, this study's primary research purpose is to determine whether the quality of the decision can be improved as the market structure evolves over time. Therefore, we present a second research question as follows.
Research question 2 Do investors' predictive powers improve as market structures evolve over time?
In addition, it will also be important to identify what the specific improvement factors are if investors' collective decision-making evolves. To this end, the study also seeks to further clarify what investor information is improving the judgment among the borrowers' various information. The study also presents the following research questions in relation to it.

Research question 3 If investors' predictive power evolves, what is the reason for it?
While the investors' ex-ante funding decision primarily determines whether the funding is approved or not, the fundamental criterion for investors' decisionmaking is whether or not the borrower will repay the money loaned on time [15,18,30,64]. That is, the borrower's creditworthiness plays a decisive role in the investor's ex-ante funding decision-making. Although the borrower's ex-post repayment performance may not necessarily be consistent with his/her creditworthiness as it is determined by a combination of various factors, it could still be the best proxy. Therefore, the closer the proximity of the borrower's creditworthiness, evaluated in advance by investors at the funding stage, to the borrower's ex-post repayment result, the higher the predictive power over the borrower's creditworthiness. From this perspective, the better the investors' ex-ante decision-making, which predicts the borrower's ex-post repayment performance, the more the investors' credit assessment capabilities evolve. Therefore, it would be important to investigate how well investors' ex-ante funding decisions predict the resultant ex-post repayment performance. In that respect, the study first seeks to identify the difference between the predictive power of investors' ex-ante funding decision model and that of the ex-post repayment model on a borrower's actual repayment result. Additionally, as mentioned earlier, in order for P2P lending to firmly establish itself as an alternative financing method that can compete with traditional financing, the investors' credit assessment capabilities need to be enhanced. To this end, this study tries to confirm the potential for the evolution of investors' credit assessment capability, and identify the cause of such evolution, if it is confirmed.
This study theoretically contributes to prior studies by identifying the evolution of investors' ex-ante collective decision-making and its detailed rationale for the first time. In a practical perspective, this study emphasizes the platform operators' role in developing the market through providing accurate information and maintaining dynamic communication with investors.

Review of related literature
In Fig. 1, I have schematized and classified existing studies on lending markets into subtopics to identify factors affecting a borrower's repayment performance or investors' funding decision-making and developing predictive models on repayment performance. Traditionally, identifying factors (i.e., ex-post determinants) affecting the borrower's repayment performance in the loan market is an important research topic. First, studies on repayment performance determinants have been conducted mainly on the traditional loan markets such as banks and credit cards. These studies have identified various factors affecting a borrower's loan default, including demographic information such as gender, age, education, credit-related information such as debtincome ratio, annual income, credit score, and loan-related characteristics such as loan amount, interest rate, loan duration [9,11,49,53]. Recently, this research has also been actively performed on P2P lending. Some studies have identified factors on repayment performance in the post-loan process and discovered new information through comparative analysis with the ex-ante determinants on investors' decisionmaking. Among these, several have compared and analyzed the effects of the diverse characteristics of the borrower [24,55], others highlighted particular features including gender [5,8], historical loan performance [14], appearance [15], social network [17], university reputation [37], residential district [27], friendship [39], race [48], platform guarantee mechanism [52,67], lender-borrower communication [63], and loan pricing structure [61].
Some studies further identify ex-post determinants and suggest predictive models of repayment performance for conventional loan markets. These studies use traditional loan market data to test the predictive accuracy of existing credit rating models [12,34], to create loan assessment models [35,44], or to develop new models that predict the credit risk of individual borrowers [47]. Recently, published studies

Topics of previous studies
Extended topics of this study Fig. 1 Theoretical contributions of this study 1 3 Can investors' collective decision-making evolve? Evidence… have also presented models that predict repayment performance with ex-post determinants on P2P lending [19,26,28,38,42,43,50]. Few studies have been conducted on factors that affect investors' decision-making at the loan funding stage for conventional loan markets. The investors are generally single financial institutions, such as banks and credit card companies, not crowds. The practical need for such research was not significant because financial institutions could make their loan decision-making using the credit rating model based on their accumulated loan transaction data. However, unlike the conventional loan market, the emerging P2P loan market has resulted in many investors participating. The platform operator retains the borrower's information, weakening the investor's access to it. In this regard, studies on factors affecting loan funding have been actively carried out in recent years.
Previous studies related to predictions in P2P lending markets have focused on presenting an ex-post model that can be called an optimal decision model. This is important because it could serve an optimal decision model for ordinary individual investors who lack experience and expertise in credit evaluation, presenting an instruction that can be referenced in future funding decisions. However, it is no less important to assess how accurately the ex-ante model, which is a realistic suboptimal decision model for investor groups, predicts the actual ex-post repayment results. This is because it can give the investors an opportunity to access to what degree their collective decision-making capability is inferior to the optimal case. This study includes all three aforementioned topics, and further attempts to present a predictive model based on ex-ante determinants, and compare and analyze how much this predictive model predicts repayment performance over ex-post predictive models. This study is intended to contribute to existing studies as it attempts to determine whether investors' ex-ante funding decision model evolves over time and, if so, identify the reasons why.

Bounded rationality
According to the findings of the previous studies, there is a gap between the factors investors consider in their funding decision-making and those that affect actual repayment results of borrowers to some extent. X. Chen et al. [8] revealed that while Cultural and geographical differences D. Chen et al. [4], Wan et al. [59] Trust in borrowers or intermediaries X. Chen et al. [7] Punctuation used in loan descriptions Jin et al. [29] Appearance Han et al. [20], Michels [46] Voluntary information Liu et al. [40] Friendship Herzenstein et al. [22,23], Y. Jiang et al. [26,28], Kim [31], Luo and Lin [41], Yu et al. [65] Herding behavior female borrowers outperform male borrowers in repayment performance in the Chinese P2P lending market, investors hardly reflect this difference in their funding decisions. Additionally, Freedman and Jin [17] argued that investors do not fully understand the relationship between the borrower's social ties and his/her creditworthiness and found that although the repayment performance of the borrower with social ties is inferior to that of the borrower without ties, investors tend to prefer them more in their funding decisions. These differences can be explained by the theory of bounded rationality. In P2P lending, as the platform operator has the authority to determine the scope of the information disclosed, investors must make funding decisions with limited accessibility to borrowers' information. Therefore, although they try to make decisions with the best sense of rationality, the decisions are likely to be inferior to the predictive power of the model based on the ex-post repayment performance. Based on such logical development, this study presents the following hypothesis to answer research question 1.

Hypothesis 1
The predictive power of the ex-ante funding model for the borrower's actual repayment performance will be inferior to that of the ex-post repayment model.

Law of effect
Bounded rationality-based investors' funding decisions can be improved through the process of cumulative trial and error experience. Particularly, psychologist Thorndike has presented the law of effect, one of the most representative principles of learning [56]. According to the law, people engage in behaviors that have desirable consequences and avoid behaviors that result in undesirable consequences. Therefore, the important outcome of a behavior is the information it provides about behavioral consequences. That is, if specific decision-making produces a satisfying result in a particular situation, and it becomes more likely to recur in the future, decision-makings that result in unpleasant outcomes are less likely to recur. Based on the law of effect to P2P lending, investors' funding decisions can be changed to increase the predictive power on borrowers' repayment performance by using consistent repayment results to modify each predictor's judgment. Based on this logical flow, this study suggests the hypothesis of research question 2 as follows.

Hypothesis 2
The predictive power of investors' funding decision-making on the borrower's repayment performance will improve over time.
Borrower information available to investors on the P2P lending platform can be classified into three types: platform-generated, loan-describing, and borrowerattributed. In previous studies, borrower information was divided into two types of loan-describing and borrower-attributed [21]. However, unlike other platforms, in Moneyauction and Popfunding, the credit factors, which were classified as borrower-attributed information in previous studies, are generated internally and not by being provided from external credit agencies. In this regard, they are classified separately as the platform-generated information in this study. Among them, for the platform-generated information, which are the internally-evaluated credit factors, and the loan-describing information covering loan amount, interest rate, duration, and others, investors' judgment can be straightforward. This is because the information's empirical or logical relationships with a borrower's repayment performance are relatively well established. The higher the credit score, the smaller the loan amount, the lower the loan interest rate, and the shorter the loan duration, the better the borrower's repayment performance. However, investors' judgment of borrower-attributed information is unclear compared to the two types of information discussed. In other words, the relationship between the borrower-attributed information, such as gender, age, marital status, region, and occupation with his/her repayment performance is often not statistically significant or varies depending on the circumstances. Given the nature of this information, part of the greater influence of the law of effect on investors' decision-making may be borrower-attributed information rather than platform-generated or loan-describing information. The cumulative trial and error experience is likely to show more tangibly decisional improvement on the borrower-attributed information, which is relatively unclear in the tendency of judgment. Therefore, this study presents the following hypothesis regarding research question 3.

Hypothesis 3.2
The predictive power based on borrower-attributed information improves more than the predictive power based on platform-generated or loan describing information.

Data
The data used in the study is extracted from Korea's oldest market-leading platforms, Moneyauction and Popfunding, through web-scrapping methods. Since the two platforms dominated the Korean P2P lending market for a considerable period of time, the transactions on these platforms represent the market situation and is also superior in terms of data availability compared to other platforms. Therefore, the study uses data from the two platforms for the analysis. Depending on the type of analysis, dependent variables include dichotomous variables such as funding and repayment results. The dependent variable Funding, which represents funding status, is set to 1 if 100% of the funding has been achieved and 0 otherwise. Similarly, the dependent variable Repayment, which represents repayment status, is 1 when the borrower has repaid 100% of the principal and interest due, and 0 otherwise. Explanatory variables include platform-generated information (credit score, credit rating, repayment quality), loan-describing information (amount, interest rate, period, and etc.), and borrower-attributed information (gender, age, marital status and etc.). As different types and numbers of available information vary by platform, we try to clarify the structure of research datasets. For each platform, the variables used for analysis and their descriptions are listed in Table 2.
Moneyauction data used in the analysis consists of 34,961 funding data and 4384 repayment data as of the end of November 2016. For each analysis, the above funding data were reclassified into three categories: full period, former period, and latter period. The reason for subsetting the full period into the former and latter periods is to compare the change in predictive power over time and to investigate whether the collective decision-making of investors improves with changes in market structure. According to the primary objective of this study, the analysis using the full period data was named Model I. The full period data was divided into two subsequent datasets: before and after 2011, which was roughly the median year based on the dataset. This is because 2011 was a time when there was a big change in the Korean P2P lending market. Previously, Moneyauction had a monopoly in the market, but it later changed to the more competitive structure of an oligopolistic system with the entry of a second player, namely Popfunding. This market change created a more diverse pool of investors than before. Therefore, this is likely to be an appropriate reference point to investigate whether collective decision-making by investor groups evolves over time. The related analyses were named Models I-1 and I-2. Accordingly, there are 34,961 data used in Model I, and 16,178 and 18,783 data used in Model I-1 and Model I-2, respectively. For the repayment data, the number of data used in Model II, which is the analysis of the full period, is 4384. For each analysis, the descriptive statistics of the data are shown in Table 3 below.
Popfunding data used in the analysis was taken from January 2011 until the end of December 2019, with 10,794 funding cases and 1186 repayment cases. The timeframe for analysis based on time changes was around 2014. In 2014, the Korean P2P lending market began to change significantly once again as a number of new second-generation platforms entered the market following the entry of Moneyauction and Popfunding. As platform diversity increased and the market grew, the pool of investors began to expand in earnest. Thus, similar to 2011, it is considered an appropriate reference point to determine whether collective decisions by investor groups evolve over time by comparing the time points before and after 2011. Similar to Moneyauction, the funding data was classified into three types: full period, former period, and latter period. Model III, the analysis using full period data, contains 10,794 cases. Model III-1 containing the former data, and Model III-2 containing the latter data, divided according to the year 2014, contain 7671 and 3123 cases, respectively. Model IV, the analysis of repayment, used a total of 1186 cases. For each analysis, the descriptive statistics of the data are described in Table 4.

Methodology
This study first adopts a logit equation using stepwise logistic regressions to establish the optimal model for each analysis described. The structure of the empirical equation is as follows:

3
Can investors' collective decision-making evolve? Evidence… Table 2 Variables Can investors' collective decision-making evolve? Evidence… Can investors' collective decision-making evolve? Evidence…  Here the dependent variable Y i is a binary variable equal to 1 if the loans are successfully funded (in case of funding) or the loans are successfully repaid (in case of repayment) and 0 otherwise. The explanatory variables are represented as X i , with their details described in Table 2. The time intervals of the data used in this study are just under 10 years: from 2007 to 2016 for Moneyauction and from 2011 to 2019 for Popfunding. Therefore, the dependent variables, funding and repayment results, are likely to be affected by macro factors in addition to the explanatory variables. In addition, consideration of the time element is important because the primary purpose of this study is to investigate whether the collective decision-making of investors improves as the market structure evolves over time. Therefore, it should not be excluded from the possibility that macro factors as well as the characteristic elements of a borrower will affect the change in collective decision-making over time.
To this end, as in several prior studies [17,64], macro factors such as the unemployment rate, banks' average interest rate for unsecured loan, stock market index, and exchange rate were added as control variables. ε i is the random disturbance term. Equation (1) is estimated using logistic regression, widely employed to predict binary dependent variables and constructed via the logit transformation [25]. For each model applied to this study, the composition of the variables is as shown in Table 5.
Stepwise selection with backward elimination of predictors from the full predictor model was applied to find each model's most suitable specification. That is, from a full model including all explanatory variables (i.e., 18 variables for Moneyauction and 21 variables for Popfunding), every variable with a p-value higher than 0.1 was excluded starting with the variable with the highest p-value. The stepwise selection method effectively develops predictive functions because when other independent variables exist in the regression equation, only variables that influence the dependent variables are included in the equation [36]. The model with the lowest AIC (Akaike Information Criterion) value was selected [10]. Next, we adopted relative weight analyses to determine the relative importance of explanatory variables for each model [57,58]. A cross validation method was then used to determine how much the predictability for a borrower's actual . For the ex-ante models, the predictive model was developed using the funding data, and the consequent prediction was made using the repayment data. For each model, the resulting estimates were classified into one of the dichotomous predicted results of normal or default, based on a cut-off value of 0.5, creating a confusion matrix comparing actual and predicted repayment results. The prediction accuracy was then calculated in average proportion of corrected predictions of all estimates using the values in the confusion matrix. A total of ten predictions were made for each model, with first the funding data divided into five, then each subgroup again divided into two groups, one being used as a training data to set the model, and the other being used to validate the optimal cut-off value of the prediction. The actual repayment data was then used to make predictions to obtain the results. The above process was repeated once more for each subgroup by switching the training data and the validation data to make an alternative prediction. This created two predictions for each of the five subgroups, and ten were made overall. This is a variant of the 5 × 2 cross validation presented by Dietterich [13]. For the ex-post model, the prediction was made by applying the original Dieterich's 5 × 2 cross validation method. After dividing the repayment data into five subgroups, one subgroup was designated as test data for actual prediction and the other four subgroups were each divided into two again. Of the two further subgroups, one was used as training data for model setup and the other as a validation data for finding the optimal cut-off value for the prediction. Then, the training and validation data were switched to make another prediction for the same test data. These five changes resulted in two predictions for each dataset, resulting in ten predictions. The above cross validation method is schematic in Fig. 2.
To ensure that the resulting predictions from the ex-ante predictive models and ex-post models for each platform showed significant differences, a paired t-test and a Wilcoxon signed rank test [62] were performed. For both tests, we set the same null hypothesis (H 0 ) as the mean of the two sample groups. In addition, a Shapiro-Wilk normality test (H 0 : normality exists) was performed to verify the normality of the distribution of prediction accuracy values [51].

Ex-ante prediction model
Ex-post prediction model Modified method of the Dietterich's 5x2 cross validation Dietterich's 5x2 cross validation method

Fig. 2 Cross validation methods for measuring prediction accuracy of models
Next, in the analyses comparing the prediction accuracies with time changes, to determine whether investors' funding decision is evolving for each platform, the predictive accuracies of the ex-ante model divided on a time basis (i.e., Models I-1, I-2 for Moneyauciton and Models III-1, III-2 for Popfunding) were calculated and compared using the modified Dieterich 5 × 2 cross validation method.
Finally, to find the causes of possible differences in the prediction accuracies of ex-ante models in each platform, this study compared the differences in prediction accuracy and which type of explanatory variables is considered or not. For this, the types of explanatory variables are divided into three: platform-generated, loandescribing, and borrower-attributed. The platform-generated variables refer to information that the platform operator has evaluated in order to assess the borrower's creditworthiness on his own, including the Score variable for Moneyauction, and the Rating and Quality variables for Popfunding. The loan-describing variables refer to the information provided by the borrower during the load application process, including the Amount, Rate, Duration, Purpose, and Text. Other details about the borrower are grouped into the borrower-attributed variables.
In the case of Moneyauction, models without the platform-generated variables are Models I-1-1 and I-2-1, depending on time changes, and models without the loan-describing variables are Models I-1-2 and I-2-2. Models without the borrowerattributed variables are Models I-1-3 and I-2-3. Similarly, for Popfunding, models without the platform-generating variables are Models III-1-1 and III-2-1, and models without the loan-describing variables are Models III-1-2 and III-2-2. Models without the borrower-attributed variables are Models III-1-3 and III-2-3. All analyses were performed using the statistical package R (version 3.6.3). Table 6 shows the optimal ex-ante and ex-post models for each platform, selected through the stepwise logistic regression method. First, the AUC (Area Under the Curve) values, which proxy in-sample classification accuracies for Models I and II, are 0.837 and 0.713, respectively. This can be generally assessed as moderate and good classification power, respectively [45,54]. Model I distinguishes investors' funding decisions well with the AUC value of 0.837, and Model II distinguishes the borrower's repayment results to a moderate level with the AUC value of 0.713. However, a closer look at each predictor shows a difference in its effect between the investors' funding decision and the borrower's repayment performance. For the Score variable, the result of the self-assessment of the borrowers' creditworthiness by the Moneyauction operator and its effect on the investors' ex-ante funding decision is found to be statistically significant, and has high relative importance of 27.5%. However, it has not had a significant impact on the ex-post repayment result. While the collective relative importance of loan-describing variables (Amount, Rate, Duration, Purpose, and Text) is 56.1% for the investors' ex-ante funding decision, it is just 34.5% for ex-post repayment performance. In particular, rate is the variable found to affect the ex-ante funding decision and ex-post repayment performance in opposite ways. This means that while investors prefer higher-interest loans in funding decision, lower-interest loans actually show better repayment performance. In addition, among the borrower-attributed variables, the Residence and Failure, also have opposite effects on the ex-ante funding decision and ex-post repayment performance.

How different is the individual investors' predictive power on a borrower's default ex-ante funding decision model from that of the ex-post repayment model?
Next, as seen in Models III and IV, for Popfunding, the classification accuracy of each model is higher than Moneyauction. The AUC value for Model III is 0.945, rated excellently by general criteria, and the AUC value for Model IV is also good at 0.863. However, in the case of Popfunding, there is also a difference in the explanatory variables that make up the ex-ante model and ex-post model, as in Moneyauction. Especially, for the borrower-attributed variables, far fewer factors affect the ex-post repayment performance than the investors' ex-ante decision-making. Given that there have been similar findings in several existing studies [24,27], this study confirms again that there are differences between factors considered by investors at the ex-ante funding decision stage and factors affecting the actual ex-post repayment results.
The differences between the ex-ante and ex-post models make it possible to speculate that investors may not be able to properly predict the borrower's repayment performance at the funding decision stage. To confirm this, the results of an outof-sample prediction with cross-verification of the method described in Fig. 2 are provided in Table 7.
The Shapiro-Wilk test confirms that the distribution of both sample groups is normal. Accordingly, a pair of t-tests is conducted to check if the difference in the mean between the two groups is significant, resulting in the prediction accuracy of Models I and II being different at a 95% confidence level. However, Wilcoxon signed rank test results show no difference at the 95% confidence level. Even Models III and IV are found to have no difference in prediction accuracy at a 95% confidence level. Therefore, the out-of-sample predictive power of the ex-ante and ex-post models for each platform is found to have minimal differences. This is a rather surprising result considering that the previous analyses show the differences in the composition of the explanatory variables and their relative importance to each model. In conclusion, although the two models differ in the composition of the explanatory variables and their relative importance, their accuracy of predicting repayment performance is found not to have significant differences. Hypothesis 1 is therefore partially supported as summarized in Table 8. Table 9 shows the changes seen in the ex-ante model with over time for each platform. The in-sample classification accuracies for Moneyacution are considered good for Models I-1 and I-2, with AUC values of 0.803 and 0.861, respectively; in contrast, Popfunding's is considered excellent, at AUC values at 0.961 and 0.918, for Models III-1 and III-2, respectively. When comparing Models I-1 and I-2, there are variables in which the relative importance or the directional orientation affecting the investor's decision making has changed significantly. In addition, the composition of the variables that have a significant impact on the investors' decision-making is also different. Specifically, the relative importance of Amount increases significantly over time, while that of Score, Rate, Text, Success, and Insurance decrease. The variables Purpose, Residence, and Work years have changed the direction of the impact on funding success. For Purpose, the probability of funding success for repayment purposes is higher than other purposes as seen in Model I-1, but loan applications for the purpose of repayment have a rather lower probability of funding success as seen in Model I-2. For Residence, the funding success probability of the borrower of one's own house is higher in Model I-1, while in Model I-2, the funding success probability of the borrower of a rental house is higher. In the case of the Work years, the shorter the working period, the higher the probability of funding success a borrower has as shown in Model I-1; in contrast to the results in Model I-2, which shows that the longer the working period, the higher the probability of funding success. In addition, the composition of the explanatory variables that are significant to the models has also changed. In Model I-1, while the Cohabitants variable is significant, and the Marriage variable is not, the exact opposite is found in Model I-2. Similar changes are identified in Popfunding. In Model III-2, compared to Model III-1, the relative importance of the variables Quality and Past loans increase, while that of Rate and Income decrease. For Quality, even the direction of the effect on the dependent variable, goes opposite ways in the two models. It is found in Model III-1 that borrowers with poorer past repayment performance have a higher funding probability, while in Model III-2, borrowers with better Can investors' collective decision-making evolve? Evidence… Table 9 Comparisons of ex-ante logistic models over time β and RW stands for the regression coefficient and relative weight, respectively ** and *indicate statistical significance at the 1% and 5% levels, respectively   past repayment performance have a higher funding probability instead. In the case of Income, the funding probability is higher for those with lower incomes in Model III-1; however, it is the opposite in Model III-2. There is also a difference in the composition of significant explanatory variables. In Model III-1, Region, Resistance, and Office are significant variables, but in Model III-2, these variables become less significant and instead the Gender, Cohabitants, Home, and Credit events are the more significant variables. As time goes by, this study identifies differences in the relative importance and directional effect of variables, and the type of variables that make up the ex-ante models for each platform. If that is the case, will these change in a way that increases the out-of-sample predictive power of the model? To answer this, the results of the comparative analyses of predictive power are given in Table 10.

Does the investors' predictive power evolve over time?
Since the Shapiro-Wilk test confirms that all sample groups exhibit normal distribution, the difference in prediction accuracy between each group is determined by through a paired t-test. Even if the normal distribution assumption is not satisfied, the Wilcoxon signed rank test also shows similar results to the paired t-test. The prediction accuracies of Models I-1 and I-2 are different at a 99.9% confidence level, although both are likely to be poor levels. Thus, the prediction accuracy of Model I-2 is shown to be 1.2%p higher than that of Model I-1. The prediction accuracies of Models III-1 and III-2 are moderate and good levels, and it they are also different at a 99.9% confidence level. The predictive accuracy of Model III-2 is found to be 6.2%p higher than that of Model III-1. These confirm that, as outlined in Table 11, the predictive power of investors' ex-ante funding decision model for both platforms evolves over time. In conclusion, Hypothesis 2 has been verified.  Table 12 shows the differences in predictive power when explanatory variables by type (platform-generated, loan-describing, and, borrower-attributed) are included and excluded from the Moneyauction model. Model I-1 and its derivatives (Models I-1-1, I-1-2, and I-1-3) are for the ex-ante model in former period, and Model I-2 and its derivatives (Models I-2-1, I-2-2, and I-2-3) are for the ex-ante model in the latter period. First, results show that in the former period, the predictive power is significantly lower when the platform-generated variables are included (i.e., Model I-1), than when they are excluded (i.e., Model I-1-1). On the other hand, for the latter period, the predictive power of the model when the platform-generated variables are included (i.e., Model I-2) is significantly higher compared to when they are included (i.e., Model I-2-1). This means that in the early days, the Score, a platformgenerated variable, contributed to improving the investors' ex-ante predictive power, but over time, it is undermining it. Next, it is shown in both the former and latter periods that even though loan-describing variables are relatively the most important to the investors' ex-ante model, the predictive accuracy of the ex-ante model is relatively intact whether that type of variable exists or not, compared to the cases of other types of variables. However, both periods show that the predictive accuracy drops by 3.3p% and 4.2%p, for the former period and the latter period, respectively, when borrower-attributed variables are omitted from the model, resulting in a relatively significant decrease in investors' ex-ante predictive power. Therefore, the borrower-attributed variables have the greatest impact on the investors' ex-ante predictive power over the other two types of variables, particularly in latter period. In conclusion, it is possible that the reason why the investors' prediction accuracy has improved over time on Moneyauction is due to more accurate judgments made about the information. Table 13 shows the effects of the variables by type on the investors' ex-ante predictive power in Popfunding. For platform-generated and borrower-attributed variables in the former period, the predictive power increases by 1.5%p and 2.3%p respectively, when the variables are excluded (as shown on Models III-1-1 and III-1-3 respectively), compared to when they are included (Model III-1). This means that in the former period, investors are inaccurately assessing the effects of the platform-generated and borrower-attributed variables. On the other hand, in the latter period, when the variables are excluded, as shown on Models III-2-1 and III-2-3, the predictive power is lower by 6.8%p and 0.8%p, respectively, compared to when they are not excluded (Model III-2). Thus, over time, it can be seen that investors are more accurately considering the platform-generated and borrower-attributed information in making ex-ante funding decisions.

If the investors' predictive power does evolve, what is the reason for it?
In the latter period, the prediction accuracies are found not to have significant differences when the loan-describing variables are considered (Model III-2) and when they are not (Model III-2-2). Therefore, it can be said that the loan-describing information do not significantly contribute to improving the investors' ex-ante predictive power. In conclusion, it is possible that the reason why the investors' exante decision-making increases the predictability of repayment performance over time in Popfunding, is due to the investors being able to more accurately evaluate Table 12 The effects of types of variables on prediction accuracy on Moneyauction ** and * indicate statistical significance at the 1% and 5% levels, respectively  the platform-generated and borrower-attributed information. The investors' proper understanding of the impact of the information provided by the platform operator about a borrower's creditworthiness, highly contributes to the improved prediction accuracy. Therefore, Hypothesis 3.1 is supported in both cases of Moneyauction and Popfunding. In Hypothesis 3.2, it is supported in Moneyauction, but not in Popfunding. This is because in Popfunding, the improvement of the predictive power by platform-generated information is greater than that by borrower-attributed information. Table 14 summarizes the detailed rationale that improves the predictive power of investors' ex-ante decision on a borrower's repayment performance over time in Moneyauction and Popfunding.

Discussion
In summary, the results show that there is no significant difference between the predictive power of the investors' ex-ante funding decision over a borrower's repayment performance, and that of the ex-post repayment model. Second, the results show that the predictive power of investors' ex-ante funding decision over a borrower's repayment performance improves over time. Finally, although the detailed rationales may vary between platforms, the results show that the reason why investors' predictive power improves over time is mainly the investors accessing more accurately the borrower's information and characteristics provided by the platform operator. It also shows that the effect of loan-describing information on improving investors' predictive power is likely to be relatively limited.
Based on these results, there are several issues to be considered. First, the information provided by the platform operator plays a very important role in the investors' ex-ante prediction over the actual repayment results. Moneyauction investors have relatively lower ex-ante prediction accuracy than Popfunding investors, most likely because of the accuracy of the information provided by the platform operator. Table 6 shows in detail how investors consider the Score variable that is provided by the Moneyauction operator. It has an average relative importance of 27.5% in their ex-ante funding decision, even though it does not play a significant role in the ex-post model. This means that while the Score variable does not significantly affect a borrower's actual repayment performance, investors are likely miscalculating its  Table 6, the Rating and Quality variables which are information provided by the Popfunding operator, are proven to play an important role in the ex-post model, with a relative importance of 61.8%. Investors are found to consider this with a relative importance of 42.2% in their ex-ante funding decision. This difference is estimated to have significantly affected the investors' ex-ante predictive power on both platforms. In Tables 6 and 7, Moneyauction investors have an ex-ante predictive power of only 62.0%, a poor level of accuracy, while Popfunding investors are at 76.5%, a relatively good level of accuracy. Therefore, to increase the predictability of investors' ex-ante funding decision in a P2P loan market, it very important for platform operators to make accurate credit assessments of borrowers. Consequently, the role of the platform operator's information analysis and delivery needs to be more emphasized in P2P lending. In addition, the platform operator needs to continuously update its own credit rating system as the empirical loan transaction data gradually accumulates. We can reference Table 12, which shows the results of the Moneyauction analysis. Initially, when considering the information provided by the platform operator, the predictive power of the investors' ex-ante funding decision improves. However, when it comes to the latter period, it rather has an adverse effect of worsening the predictive power. It has been argued in previous papers that there may be problems with the accuracy of the platform's self-assessed credit rating model [55,67]. On the other hand, Table 13 shows that the case of Popfunding is the opposite of Moneyauction. In the beginning, information provided by the platform operator undermined the investors' ex-ante predictive power, but over time it has contributed to significantly improving the investors' predictive power. As such, it has been proven that the effectiveness of the platform's credit rating system will change over time, and it is important for the platform operator to continuously update the initial credit rating model based on accumulated empirical data.
This study confirms the possibility that the prediction accuracy of investors' exante funding decision over a borrower's repayment performance can be improved over time. For example, in Table 9, the Moneyauction investors have made adjustments to lower the relative importance of the Score variables, information that is provided by the platform, over time. This may be because they gradually realized the inaccuracy of the Score variables. In the case of Popfunding, investors initially considered the Quality variable, information that is generated by the platform, as opposed to the actual directional effect it had on actual repayment performance. They also considered it being less important. However, they are observed to have improved judgement, identifying the proper direction and recognizing its importance gradually. In the introduction, the researcher pointed out that cost-effectiveness must be achieved for the P2P lending system to be firmly established as an alternative for traditional financing. Thus, to this end, it is most important to improve the investors' accuracy of judgement. From this point of view, as investors' judgment is actually improving, the P2P lending system can gradually become an alternative to traditional financing by further strengthening its theoretical advantages in the near future.
On the contrary, it is also partially observed that the investors' ex-ante decision-making is inaccurate for certain types of information. In Table 9, Moneyauction investors tend to prefer rental borrowers over self-owned borrowers over time in ex-ante funding decision. This reflects the opposite effect of the Residence variable on actual repayment performance. This phenomenon is also seen in the Purpose variable. Investors gradually prefer borrowers who apply for loans for other purposes than for repayment of existing loans, but in reality, borrowers with the purpose of repaying existing loans are found to have better repayment performance. It is not much different in Popfunding either. At the borrower's income level, it has been proven that the repayment performance of low-income borrowers is actually better, but over time, investors have shifted their ex-ante funding decision to favor high-income borrowers. As such, investors' decisions may change over time to improve the accuracy of their predictions for certain information, while on the contrary, the accuracy of their decisions for other information may deteriorate. In this respect, to improve the quality of the investors' decision making, it will be important for platform operators make a constant effort to analyze their accumulated empirical data and give feedback and communicate with investors.

Implication
This study theoretically contributes to existing studies by examining the predictive power of investors' ex-ante decision-making model over the borrower's expost repayment performance model, which has not been covered by P2P lending related studies yet. It is also meaningful in that the evolution of investors' exante decision-making and its detailed rationale are first identified in this paper. This study confirms the possibility of optimizing and streamlining the P2P lending market through the evolution of investors' decision making, thus giving hope to the sustainable development of the market as an alternative financing method in the near future. In addition, this study has gone a step further from simply confirming that the investors' ex-ante decision-making model differs from the actual ex-post repayment model. It also presents a rather unexpected result of finding no significant difference between the two models in terms of predictive performance, despite the differences in each of their predictor composition.
In a practical perspective, this study reaffirms the results of several previous studies that show how the platform's credit assessment capabilities may be inaccurate. Through this, the need for platform operators to continually refine and update their information analysis and its delivery to investors is highlighted. It empirically confirms for the first time that if the platform provides inaccurate information, the predictive power of investors' ex-ante decision-making could deteriorate significantly. Another contribution of this study is that, based on empirical evidence, it emphasizes the platform operators' role in developing the market through providing accurate information and maintaining dynamic communication with investors.

Limitations
This study analyzes how investors' decision-making evolves by classifying the explanatory variables by type of information (platform-generated, loan-describing, and borrower-attributed information). However, as there may certain limitations in analyzing the detailed cause of the evolutionary change, this topic deserves to the subject of future research.
In addition, it seems necessary to consider not only the micro factors covered in this study but also the macro factors that cause the overall P2P lending market change. In Korea, the P2P lending market first emerged in 2007, not too late compared to the UK, where the market was first developed. Since then, it had plateaued for some time, but market conditions have changed rapidly with the emergence of many platforms around 2014. In fact, the two platforms, Moneyauction and Popfunding, which are the subjects of this study, also showed significant changes in transaction volume and number of loan listings around that time. In this regard, macro factors may have also affected the evolution of investors' exante funding decision. There is a need for further research on these factors to gain a more thorough understanding on the evolutionary change of investors' decisionmaking over time.
This study proves that investors' decision-making evolves. However, the results of this study alone may not indicate whether this evolution is only attributed to the improved capabilities of existing investors, or because investors with inferior capabilities are kicked out of the platform and replaced with new investors with superior capabilities. Therefore, further studies that take into account the characteristics of investors, such as their investment experience, could make the outcomes of this study more valuable.
Additionally, all cases except 100%-funded listings were uniformly regarded as unfunded, even if the bidding rates varied from 0 to 100%. Although we treated the dependent variables as two-dimensional categorical variables owing to the data limitation, we would have had more detailed results by identifying them as continuous variables.