This article was downloaded by: [98.223.229.188] On: 15 June 2017, At: 09:05Publisher: Institute for Operations Research and the Management Sciences (INFORMS)INFORMS is located in Maryland, USA

Management Science

Publication details, including instructions for authors and subscription information:http://pubsonline.informs.org

Market Mechanisms in Online Peer-to-Peer LendingZaiyan Wei, Mingfeng Lin

To cite this article:Zaiyan Wei, Mingfeng Lin (2016) Market Mechanisms in Online Peer-to-Peer Lending. Management Science

Published online in Articles in Advance 07 Sep 2016

. https://doi.org/10.1287/mnsc.2016.2531

Full terms and conditions of use: http://pubsonline.informs.org/page/terms-and-conditions

This article may be used only for the purposes of research, teaching, and/or private study. Commercial useor systematic downloading (by robots or other automatic processes) is prohibited without explicit Publisherapproval, unless otherwise noted. For more information, contact permissions@informs.org.

The Publisher does not warrant or guarantee the article’s accuracy, completeness, merchantability, fitnessfor a particular purpose, or non-infringement. Descriptions of, or references to, products or publications, orinclusion of an advertisement in this article, neither constitutes nor implies a guarantee, endorsement, orsupport of claims made of that product, publication, or service.

Copyright © 2016, INFORMS

Please scroll down for article—it is on subsequent pages

INFORMS is the largest professional society in the world for professionals in the fields of operations research, managementscience, and analytics.For more information on INFORMS, its publications, membership, or meetings visit http://www.informs.org

MANAGEMENT SCIENCEArticles in Advance, pp. 1–22ISSN 0025-1909 (print) � ISSN 1526-5501 (online) http://dx.doi.org/10.1287/mnsc.2016.2531

© 2016 INFORMS

Market Mechanisms in Online Peer-to-Peer Lending

Zaiyan WeiKrannert School of Management, Purdue University, West Lafayette, Indiana 47907, zaiyan@purdue.edu

Mingfeng LinEller College of Management, University of Arizona, Tucson, Arizona 85721, mingfeng@eller.arizona.edu

Online peer-to-peer lending (P2P lending) has emerged as an appealing new channel of financing in recentyears. A fundamental but largely unanswered question in this nascent industry is the choice of market

mechanisms, i.e., how the supply and demand of funds are matched, and the terms (price) at which transactionswill occur. Two of the most popular mechanisms are auctions (where the “crowd” determines the price of thetransaction through an auction process) and posted prices (where the platform determines the price). WhileP2P lending platforms typically use one or the other, there is little systematic research on the implicationsof such choices for market participants, transaction outcomes, and social welfare. We address this questionboth theoretically and empirically. We first develop a game-theoretic model that yields empirically testablehypotheses, taking into account the incentive of the platform. We then test these hypotheses by exploiting aregime change from auctions to posted prices on one of the largest P2P lending platforms. Consistent with ourhypotheses, we find that under platform-mandated posted prices, loans are funded with higher probability, butthe preset interest rates are higher than borrowers’ starting interest rates and contract interest rates in auctions.More important, all else equal, loans funded under posted prices are more likely to default, thereby undermininglenders’ returns on investment and their surplus. Although platform-mandated posted prices may be faster inoriginating loans, auctions that rely on the crowd to discover prices are not necessarily inferior in terms ofoverall social welfare.

Keywords : peer-to-peer lending; market mechanisms; auctions; posted prices; debt crowdfundingHistory : Received May 29, 2014; accepted April 8, 2016, by Chris Forman, information systems. Published

online in Articles in Advance September 7, 2016.

1. IntroductionIn recent years, online peer-to-peer lending (P2P lend-ing, also known as marketplace lending) has emergedas an appealing new channel of financing (Zhangand Liu 2012, Lin et al. 2013, Rigbi 2013, Iyer et al.2016, Lin and Viswanathan 2016). Online P2P lend-ing platforms allow individual lenders to aggregatetheir funds to finance loan requests from individualsand businesses. It is essentially a debt form of crowd-funding. By one estimate, in the year 2014 alone inthe United States, P2P lending generated more than$8.9 billion in loans and received more than $1.32 bil-lion in venture capital investments.1 Investors, busi-nesses, and regulators are all increasingly interestedin this new business model. It is a prime example ofhow information and Internet technologies are trans-forming the finance industry.

P2P lending platforms are essentially online mar-kets that match the supply and demand of funds.A fundamental question in any market—be it

1 http://cdn.crowdfundinsider.com/wp-content/uploads/2015/04/P2P-Lending-Infographic-RealtyShares-2014.jpg (last accessedAugust 24, 2016).

online or offline, for physical products or financialproducts—is how to match demand and supply, anduncover the “correct” price for transactions to occur,namely, what the market mechanism should be. Twoof the most common market mechanisms, both ofwhich have seen implementations in P2P lending, areauctions and posted prices. As their names suggest,auctions typically rely on the relative strength of themarket participants (i.e., supply versus demand) touncover the price, through an auction process; postedprices start with a predetermined price instead. P2Plending platforms mostly choose one or the other,and this important choice lays the foundations forinvestors and fundraisers to match with each other inthese markets. Market mechanisms have the poten-tial to affect the behavior of both sides of the mar-ket, the platform, and overall social welfare, and aretherefore an important research topic (Wang 1993,Biais et al. 2002, Hortaçsu and McAdams 2010). How-ever, there is little systematic research on the compar-ison of these mechanisms in the context of P2P lend-ing, despite its potential impact on this nascent butburgeoning industry. The research question that weaddress in this paper, therefore, is the following: How

1

Dow

nloa

ded

from

info

rms.

org

by [

98.2

23.2

29.1

88]

on 1

5 Ju

ne 2

017,

at 0

9:05

. Fo

r pe

rson

al u

se o

nly,

all

righ

ts r

eser

ved.

Wei and Lin: Market Mechanisms in Peer-to-Peer Lending2 Management Science, Articles in Advance, pp. 1–22, © 2016 INFORMS

do these mechanisms compare in terms of their influenceon market participant behaviors, transaction outcomes, andsocial welfare?

P2P lending is an ideal context to study the impactof market mechanisms. First, both types of mech-anisms are used in P2P lending in different plat-forms across the globe. Despite some small variations,the primary features of these mechanisms are highlyconsistent on different platforms. Second, P2P lend-ing features an unequivocal and universal metric for“price,” i.e., interest rate of loans. Third, the quality, orex post resolution of uncertainty associated with eachloan, can be objectively measured when loans reachtheir maturity. Last but not least, we observe a uniqueregime change on an online P2P lending platform.Therefore, even though the impact of market mecha-nisms can be studied in different contexts, includingproduct markets or other types of crowdfunding, P2Plending provides many unique advantages to investi-gate this research question.

We study the impact of the market mechanisms onloan transactional outcomes and also social welfare.To this end, we first propose an analytical model com-paring a multiunit uniform-price auction against theposted-price mechanism in P2P lending. Our modelpredicts that the P2P lending platform, the pricingagent in the posted-price regime, will assign higherinterest rates compared to what the borrowers wouldhave chosen as their reserve interest rates in auc-tions. Loans will be funded with higher probabilityunder the posted-price mechanism. The contract inter-est rates for loans funded in the posted-price regimewill be higher as well, since in auctions the final inter-est rates cannot be higher than borrowers’ reservationinterest rates. Further, since loans with higher inter-est rates are more likely to default (all else equal)(Stiglitz and Weiss 1981, Bester 1985), loans fundedunder posted prices should be more likely to defaultas well.

Our empirical analysis employs detailed transac-tions data from Prosper.com, one of the leading P2Plending platforms in the United States. Prosper.comis an online market for unsecured personal loans.Since its inception in 2005, Prosper.com had used auc-tions as its market mechanism, and because of thatit was aptly called the “eBay for personal loans.”But on December 20, 2010, Prosper.com unexpect-edly abandoned its well-known auctions model andswitched the entire website to a posted-price mech-anism (Renton 2010).2 This regime change was effec-tive immediately on the whole site, and unanticipated

2 Renton (2010) provides evidence that this change was largelyunexpected. Prosper.com’s corporate blog about the regime changecan be found at https://web.archive.org/web/20110312134825/http://blog.prosper.com/2010/12/30/exciting-new-enhancements-at-prosper/ (last accessed August 24, 2016). In addition to the

by market participants. It therefore provides anideal opportunity to investigate how different marketmechanisms impact participant behaviors and marketefficiency, especially considering the incentives of theplatform itself.3 More specifically we focus on listingsinitiated during a short time period before and afterthe regime change, from August 20, 2010, to April 19,2011. We compare the pricing (the initial interest rateof a listing), funding probabilities (the listings’ prob-ability of full funding), the contract interest rates, aswell as default probabilities of funded loans. Con-sistent with our theoretical predictions, under postedprices, listings are much more likely to be funded andthey are also funded faster. These results are consis-tent with our analyses of lender behavior after theregime change: They submit larger bids and submittheir bids sooner, and rely less on the actions of otherlenders (i.e., less herding). In addition, we find thatthe initial and contract interest rates under the posted-price mechanism are higher than those in auctions. Inother words, while the regime change indeed led to ahigher funding probability, it came at a cost of higherinterest rates. More important, we find evidence thatloans funded under the posted-price regime are morelikely to default, and the hazard rate of default ishigher for loans initiated after the regime change.These long-term results have important implicationsbut have not been previously documented.

To better understand the consequences of marketmechanisms, we further examine the welfare impli-cations of the regime change. We first show analyti-cally that under certain conditions, social welfare can,in fact, be higher under auctions than posted prices.In particular, the increase in platform profits (feesfrom higher probability of successful funding) is nogreater than the decrease in borrower surplus. For thetotal surplus, the ambiguity lies with lender surplus,since the contract interest rate and default rate bothincrease. To ascertain the change in lender surplus, wefirst calculate lenders’ return-on-investment on loansoriginated, then further numerically calibrate lender’s

change in market mechanism Prosper.com also changed thestandard duration of auctions. We rule out the duration change asan alternative explanation to our findings later in the paper; seeSection 5.3.2.3 As is common in the literature, data generated from such naturalexperiments provides clean identification opportunities in a naturalsetting; its strength lies in the internal validity. Meanwhile for ourstudy, even though this was an exogenous event, the website today(as of the time of writing) is not dramatically different from whatit was in 2010. In addition, our analysis is based on our hypothe-ses developed from a game theoretic model that captures incen-tive structures of all stakeholders; and these incentives are still thesame today. The use of data from this natural experiment, there-fore, does not diminish the general relevance and applicability ofour findings. We discuss more along these lines toward the end ofthe paper.

Dow

nloa

ded

from

info

rms.

org

by [

98.2

23.2

29.1

88]

on 1

5 Ju

ne 2

017,

at 0

9:05

. Fo

r pe

rson

al u

se o

nly,

all

righ

ts r

eser

ved.

Wei and Lin: Market Mechanisms in Peer-to-Peer LendingManagement Science, Articles in Advance, pp. 1–22, © 2016 INFORMS 3

supply curve to derive lender surplus. Comparisonsof these results across market mechanisms show thatlender surplus is strictly lower under posted prices.Hence, the total social welfare is, in fact, lower afterthe regime change.

Our study is among the first to compare twopopular market mechanisms both theoretically andempirically to understand their impact on partic-ipant behaviors, transaction outcomes, and socialwelfare. Our paper, therefore, contributes to the grow-ing literature on peer-to-peer lending as well as thebroader literature on crowdfunding. Recent inves-tigations include Zhang and Liu (2012), Burtch etal. (2013), Hahn and Lee (2013), Lin et al. (2013),Rigbi (2013), Kawai et al. (2014), Kim and Hann(2015), Iyer et al. (2016), and Lin and Viswanathan(2016). Given the global expansion of this industry,our study has important and timely implications notonly for researchers and practitioners, but for pol-icy makers as well. Since crowdfunding is essen-tially sourcing funds from the crowd, our study alsocontributes to the growing literature on crowdsourc-ing, such as Dellarocas et al. (2010), Hosanagar etal. (2010), Chen et al. (2014), and Liu et al. (2014).Furthermore, our work also contributes to a long lit-erature on the optimal sales mechanism, and auc-tions in particular. For instance, Bulow and Klemperer(1996) compare auctions against negotiations, whereasWang (1993) provides theoretical comparison betweensingle object auctions and posted-price mechanisms.More recent comparisons of these market mechanismscan be found in treasury auctions (Ausubel et al.2014, Hortaçsu and McAdams 2010), initial publicofferings (IPO) (Biais et al. 2002, Zhang 2009), andonline product markets (Chen et al. 2007) such aseBay.com (Wang et al. 2008; Hammond 2010, 2013;Einav et al. 2016).4

2. Research ContextSince the inception of Zopa.com in 2005 in theUnited Kingdom, online peer-to-peer lending has wit-nessed rapid growth around the globe. In the UnitedStates, Prosper.com and LendingClub.com are the twolargest platforms. As of 2014, there were over twomillion registered members (either as a borrower, alender, or both) on Prosper.com. More than 100,000personal loans, valued over USD 204 billion in total,had been funded.

4 Einav et al. (2016), notably, document a trend by eBay.com sellersto gradually switching from auctions to posted prices. However,it is important to note that on eBay.com, market mechanism is anendogenous choice of sellers. In P2P lending, market mechanismsare imposed by the platform. There are many other important dif-ferences between these contexts, and between our study and theirs,which we will discuss at the end of this paper.

A brief outline of the funding process on Pros-per.com is as follows.5 A potential borrower first reg-isters on Prosper.com and verifies identity. After that,the borrower creates a listing Web page, describingthe purpose, requested amount, and duration of theloan (typically three years). The request also specifiesthe initial interest rate, which has different meaningsunder different market mechanisms. Before December20, 2010, under auctions, this is the borrower’s reser-vation or maximum interest rate that they are will-ing to accept. After the regime change, Prosper.compresets an interest rate for the loan based on the bor-rower’s creditworthiness.

Before December 20, 2010, once the listing is postedwith a specified expiration date (typically in sevendays), a multiunit uniform-price auction will be con-ducted until the listing is either fully funded orexpired. Any verified Prosper.com lender can bid inthe auction. In their bids, lenders specify the amountof funds that they would like to invest, and theminimum interest rate at which they are willing tolend. Typically many lenders fund a loan. Lenderscan observe previous lenders’ identities and their bid-ding amount. Lender’s priority in participating in theloan is ranked by the interest rate that they specifiedin their bids, where those with lowest interest ratesare most likely to participate. During the auction, theongoing interest rate is either the starting interest ratethat the borrower sets at the beginning, if the loan isnot 100% funded, or the lowest interest rate amongall lenders that are outbid (excluded from funding theloan) once funds from lenders exceed the requestedamount. At the end, if the loan receives full funding,the winners will be all lenders who specified the low-est interest rates among all those who bid; the contractinterest rate will be the ongoing interest rate at theend, which will apply to all lenders in that loan. Inother words, the borrower sets the initial interest rate,and the auction “discovers” the contract interest rate.

On December 20, 2010, Prosper.com unexpectedlyeliminated this auctions model. Since then, the inter-est rate is preset by Prosper.com based on the web-site’s evaluation of the borrower’s creditworthiness.The borrower can no longer use the auction for-mat. Lenders now only specify a dollar amount fortheir investment, implicitly accepting the preset inter-est rate. Multiple lenders are still allowed to fund aloan. Listings will not be converted into loans unlessthe full amount requested by the borrower is fundedbefore listing expiration; and the contract interest rate

5 Our descriptions are accurate for the period of time that we study.We emphasize website features that are most relevant to our inves-tigation but may not cover all institutional details. Interested read-ers can refer to other studies using data from Prosper.com, such asZhang and Liu (2012), Lin et al. (2013), Freedman and Jin (2011),and Lin and Viswanathan (2016), for further details.

Dow

nloa

ded

from

info

rms.

org

by [

98.2

23.2

29.1

88]

on 1

5 Ju

ne 2

017,

at 0

9:05

. Fo

r pe

rson

al u

se o

nly,

all

righ

ts r

eser

ved.

Wei and Lin: Market Mechanisms in Peer-to-Peer Lending4 Management Science, Articles in Advance, pp. 1–22, © 2016 INFORMS

Table 1 A Comparison of Auctions vs. Price Posting—The Regime Change

Auctions Posted prices

Initial Interest Rate: Chosen by the borrower Preset by Prosper.comContract Interest Rate: Prevailing interest rate at the end of auction Initial interest rate

is the rate preset at the beginning. Table 1 summarizesthe key difference between these two regimes.

When announcing the regime change, Prosper.comargued that the new market mechanism wouldallow “a quicker deployment of funds” for investors,and borrowers would “get their loan listing fundedsooner.” “Quicker deployment” refers to the fact thatinvestors’ funds can only generate returns wheninvested in a loan that is successfully funded. Tounderstand whether the regime change indeed hadthese effects, and more important whether there areother consequences of this change, we develop a styl-ized model to generate several empirically testablehypotheses. We then test these hypotheses using datafrom Prosper.com around the time of the regimechange. After that, we examine the social welfareimplications of this regime change.

Before we dive into the analytical model, it isworth noting that intuitions behind our hypothesesare straightforward and will be described in detail.The model in the next section provides a more generaland formal treatment of the hypothesis development.

3. A Model of Market MechanismsWe now propose a model to compare the multiu-nit uniform-price auctions against platform-mandatedposted prices. The benefit of the game theoretic modelis that it not only captures primary features of the twomarket mechanisms but also mathematically modelsthe incentives of key stakeholders including borrow-ers, lenders, and the platform. It allows a more formalprocess of hypothesis development and ensures thatour hypotheses are based on general features of themarket and stakeholder incentives, not peculiarities ofthe natural experiment that we exploit for empiricaltesting. For these reasons, this approach (using ana-lytical models to derive hypotheses then empiricallytest them) has been used in many empirical studiesin information systems and economics, such as Aroraet al. (2010), Sun (2012), and Lemmon and Ni (2014).

Our model is based on the share auction modelproposed by Wilson (1979) and further developedin Back and Zender (1993) and Wang and Zender(2002). We develop the following model to highlightthe key difference between auctions and posted-pricemechanisms (Chen et al. 2014). Consider a borrowerrequesting a personal loan on the platform. In an auc-tion, either the lowest losing interest rate or the bor-rower’s initial interest rate sets the contract interest

rate for all winning lenders if the loan is funded.Under posted prices, Prosper.com presets the inter-est rate for the loan, and the borrower either acceptsor rejects it. Once the borrower accepts and the list-ing is created, any lender can “purchase” a portionof the loan at the preset interest rate. All lenders willfund the personal loan at this rate. We denote p as thecontract rate of a loan funded from either an auctionor a posted-price sale. A highly consistent finding inthe finance literature (Stiglitz and Weiss 1981, Bester1985) is that higher contract interest rates cause higherdefault rates. Hence, let �4p5 be the default rate giventhe contract interest rate is p, where �′4 · 5≥ 0.

For the borrower, there is a variable cost c for eachdollar he or she borrows from the site. If the loanis successfully funded, this cost (cf. Prosper.com fees)will be deducted before the borrower receives thefunds. The borrower may also incur other explicit orimplicit costs, such as their time and efforts in creatingthe request. For simplicity, we assume that the bor-rower is requesting a loan with Q units, and the dis-count rate is � . This can be interpreted as the lowestinterest rate from his or her outside options or otherchannels. The maximum interest rate that the bor-rower is willing to pay for this loan on Prosper.comwill then be � − c.

On the other side of the market, suppose thereare N potential lenders for this particular loan. Weassume N � Q, i.e., there are always enough lendersto fund the loan if the price is right. This assumptionis reasonable considering the large pool of lenders onProsper.com. We assume that each lender supplies atmost one unit of the loan and has an independentprivate willingness to lend (WTL). A lender’s WTLis the lowest rate at which they are willing to lendto the borrower. They will never fund the listing atany interest rate below this WTL. This is equivalentto the lender’s true valuation of the loan, or the max-imum risk-free interest rate from the lender’s outsideoptions. The private value assumption is not restric-tive given the fact that there were no resale opportu-nities for loans during the time we study, so a lender’sWTL is independent of others’ valuations. Let Wn

denote lender n’s WTL, n= 1121 0 0 0 1N . Let wn denoteits realization. We assume that Wn is IID (indepen-dent and identically distributed) with CDF FW 4 · 5, andPDF fW 4 · 5. We let WN2k denote the kth lowest valueamong N IID willingness-to-lend, and k = 1121 0 0 0 1N .Let wN2k denote its realization. We denote the distri-bution of WN2k by Gk4 · 5 (or PDF gk4 · 5).

Dow

nloa

ded

from

info

rms.

org

by [

98.2

23.2

29.1

88]

on 1

5 Ju

ne 2

017,

at 0

9:05

. Fo

r pe

rson

al u

se o

nly,

all

righ

ts r

eser

ved.

Wei and Lin: Market Mechanisms in Peer-to-Peer LendingManagement Science, Articles in Advance, pp. 1–22, © 2016 INFORMS 5

3.1. AuctionsWe model a multiunit uniform-price auction withsingle-unit demand. In such an auction, the mar-ket clearing interest rate is set by the lowest los-ing bid or the borrower’s reserve rate. The lendersincur a nonnegative transaction cost, �. It reflectsthe lenders’ efforts to overcome uncertainties associ-ated with the auction process, such as evaluating theborrower’s creditworthiness, deciding whether theongoing interest rate reflects borrower quality, observ-ing the behavior of other investors (Zhang and Liu2012), and accepting the risk that the loan may notbe fully funded at the end. This cost �, therefore,increases the lenders’ minimum acceptable interestrate to Wn + �. In other words, lenders will requirehigher interest rates than their true values to com-pensate for the transaction costs associated with theauction mechanism. We normalize � to zero underposted prices, reflecting the idea that lenders in auc-tions incur strictly higher transaction costs than inposted prices.

In the private value paradigm, auction theory(Krishna 2009) suggests that the weakly dominantstrategy for a lender is to submit their true valueWn +�. Compared to models in the auction literature,our context presents two complications. First, lenders’bids are bounded above by the borrower’s reserveinterest rate. Second, lenders will take into accountthe loan’s potential likelihood of default, which isclosely related to the contract interest rate. However,it is straightforward to show that these two factors donot affect lenders’ equilibrium bidding strategy, andtheir weakly dominant strategy is still to bid their truevaluation. Thus, the winners will be the Q lenderswith the lowest true WTL, and each of them winsone unit of the loan. Knowing the lenders’ biddingstrategy, the borrower will choose a reserve interestrate, r∗, to maximize their expected payoff. Before theregime change, this reserve interest rate correspondsto the initial interest rate set at the very beginning ofthe auction process.6

To derive the borrower’s payoff function, we noticethat this is a personal loan market with borrowingand repayment obligations in a future date. If theloan is funded, the borrower receives Q units fromthe lenders immediately but is also committed to payback the principal and interest within a certain timeperiod. Without loss of generality, we assume that thisis a one-period loan. The total repayment amount willbe Q · 41 + pA4r5+ c5, where pA4r5 is the market clear-ing interest rate if the loan is funded. The subscript

6 Recall that we assume the borrower’s discount rate to be � . Wecan interpret this as the interest rate of the borrower’s best outsideoption, i.e., the lowest rate he or she is offered from other financialinstitutions. Hence, the borrower’s reserve interest rate must satisfyr < � . Our results later confirm this observation.

indicates that the listing is funded from an auction,and this interest rate is a function of the borrower’sreserve interest rate. If the borrower is risk neutral,then their payoff in terms of present value will be�A = Q − Q · 41 + pA4r5 + c5/41 + �5, or as a functionof r :

�A =Q · 4� − pA4r5− c5

1 + �0

It is clear that the market clearing interest rate willvary across listings:

{

wN2Q+1 +�1 if wN2Q+1 +�≤ r3

r1 if wN2Q +�≤ r <wN2Q+1 +�0

The first case corresponds to the scenario where thelowest losing interest rate is less than the borrower’sreserve rate, thus setting the price of the loan. Thesecond case is where the reserve rate sets the price,since no losing lender is willing to bid lower thanthat rate. Note that the probability of being funded isPr4WN2Q+1 +�≤ r5 and Pr4WN2Q+�≤ r <WN2Q+1 +�5,respectively. Then the expected market clearing ratepA4r5 conditional on the reserve interest rate r willbe E6WN2Q+1 + � � WN2Q+1 + � ≤ r7 and r , respectively.Therefore, we can write the borrower’s expected pay-off as

E�A =Q · 6� −E6WN2Q+1 +� �WN2Q+1 +�≤ r7− c7

1 + �

· Pr4WN2Q+1+�≤ r5+

Q · 4� − r − c5

1 + �

· Pr4WN2Q+�≥ r >WN2Q+1

+�50

The borrower maximizes expected payoff by choos-ing the initial reserve interest rate r . It is straightfor-ward to show that the optimal reserve interest rate r∗

is defined by the implicit function as in Equation (1).We can interpret the ratio as the normalized premiumdeducted to rule out the possibility that the lowestlosing bid is less than the reserve interest rate:

r∗= � − c−

FW 4r∗ −�5

Q · fW 4r∗ −�50 (1)

An important implication of this result is that theoptimal reserve interest rate is strictly lower thanthe borrower’s underlying maximum acceptable rate,� − c. This allows the borrower to secure a posi-tive expected profit. Also recall that FW 4 · 5 and fW 4 · 5are the distribution functions of lenders’ values. Theresult implies that the optimal reserve price is inde-pendent of the number of lenders. If Wn has alog-concave distribution, r∗ is increasing with thequantity Q.

Dow

nloa

ded

from

info

rms.

org

by [

98.2

23.2

29.1

88]

on 1

5 Ju

ne 2

017,

at 0

9:05

. Fo

r pe

rson

al u

se o

nly,

all

righ

ts r

eser

ved.

Wei and Lin: Market Mechanisms in Peer-to-Peer Lending6 Management Science, Articles in Advance, pp. 1–22, © 2016 INFORMS

3.2. (Platform-Mandated) Posted PricesWe now model the dynamics among borrowers,lenders, and the platform under the posted-pricemechanism. Importantly, since Prosper.com sets theinitial interest rate (p∗) under this new mechanism,rather than borrowers, we specifically consider theplatform’s incentive in pricing borrower loans to max-imize its own expected profit. The borrower eitheraccepts or rejects the interest rate that Prosper.comsets for their loan. If they accept, the interest rate willbe fixed at that level.

Before we model Prosper.com’s decision, we firstconsider a hypothetical setting where the borrower isable to choose the interest rate under posted prices.Note that this is, in fact, not possible on Prosper.comeven after the regime change, but it merely provides auseful starting point for our analysis. This hypothet-ical setting is analogous to the model in Einav et al.(2016). More specifically, if the borrower could choosethe fixed interest rate, his expected payoff can be writ-ten as

E�B =Q · 4� − p− c5

1 + �· Pr4WN2Q

≤ p− �4p541 + p551

where �4 · 5 is the default rate function. The B sub-script indicates that it is (for now) the borrower’schoice. To see the inequality in the equation, noticethat a lender will find the loan profitable if and onlyif 1 + wn ≤ 41 + p541 − �4p55, which can be simplifiedto wn ≤ p− �4p541 + p5. Let �4p5 = p− �4p541 + p5; thisis the loan’s expected rate of return.

The borrower would maximize their revenue bychoosing p. The following equation characterizes thisoptimal price level implicitly,

p∗

B = � − c−GQ4�4p

∗B55

gQ4�4p∗B55 ·�

′4p∗B50 (2)

It can be shown that the relationship between p∗B and

the reserve interest rate r∗ in auctions depends onthe return function, �4 · 5, as well as the distributionof lenders’ valuations. Under mild conditions, p∗

B isstrictly less than r∗. This result in our hypotheticalsetting is an extension to Einav et al. (2016). Underthe usual commodity economy interpretation, there-fore, the seller assigns higher “price”—analogous tolower interest rate in our context—in the posted-pricesetting, given the common value setup.

In reality however, it is Prosper.com that deter-mines the posted interest rates. The platform presetsthe interest rate p for a particular loan. The borrower’sstrategy is to pick a threshold or cutoff rate p̃. If p islower than this cutoff, the borrower will accept theoffer. If it is higher, they will reject it and leave themarket. In other words, the borrower accepts p if p ≤ p̃and rejects it otherwise. Note that the probability of

full funding is Pr4WN2Q ≤ �4p55. Similar to our anal-ysis of the auctions, the borrower’s expected payofffor accepting Prosper.com’s preset interest rate can beshown to be 4Q · 4� − p− c5/41 + �55 · Pr4WN2Q ≤ �4p55,while rejecting the offer generates zero payoff. At thethreshold, the borrower is indifferent between accept-ing and rejecting. That is, 4Q · 4� − p − c5/41 + �55 ·

Pr4WN2Q ≤ �4p55= 0. It is easy to show that the cutoffprice is p̃ = � − c.

Suppose now that the platform knows the bor-rower’s true cost c and discount rate � , and thus� − c.7 Prosper.com’s profit comes from the fees thatit charges on funded loans. We let � denote this fixedfee, i.e., Prosper.com does not change it in the shortrun (consistent with what we observe for our studyperiod). Then Prosper.com’s expected profit is

E�P = � ·Q · Pr4WN2Q≤ �4p550

Prosper.com chooses an interest rate to maximizethis profit given p ≤ � − c and p ≥ 0. It can be shownthat the following assumption is a sufficient conditionunder which Prosper.com assigns the highest possibleinterest rate, i.e., � − c.

Assumption 1. The hazard rate for the default rate func-tion, �′4p5/41 − �4p55, is bounded above by 1/41 + � − c5,i.e., for all p ∈ 601 � − c7,

�′4p5

1 − �4p5≤

11 + � − c

0

Assumption 1 adds some functional form restric-tions but remains fairly reasonable and intuitive.Under this assumption, we can show that Pr4WN2Q ≤

�4p55 is a nondecreasing function of p.8 This impliesthat Prosper.com will choose an interest rate as highas possible to maximize its expected profit. To sum-marize, in a posted-price setting Prosper.com presetsan interest rate,

p∗= � − c0 (3)

3.3. Comparisons and PredictionsAn immediate observation is that p∗ > r∗. In otherwords, Prosper.com will preset an interest rate higherthan what the borrower would have chosen in auc-tions. Also note that the probability of being fundedin auctions, Pr4WN2Q + � ≤ r∗5, is strictly lower than

7 This is a reasonable assumption since we interpret � as the bor-rower’s lowest interest rate from outside options. As a professionalfinancial organization, Prosper.com has the credit information nec-essary to derive the interest rate that the borrower is able to obtainfrom other channels.8 Note that Assumption 1 is a sufficient condition for the returnfunction, �4 · 5, to be nondecreasing on 601 � − c7.

Dow

nloa

ded

from

info

rms.

org

by [

98.2

23.2

29.1

88]

on 1

5 Ju

ne 2

017,

at 0

9:05

. Fo

r pe

rson

al u

se o

nly,

all

righ

ts r

eser

ved.

Wei and Lin: Market Mechanisms in Peer-to-Peer LendingManagement Science, Articles in Advance, pp. 1–22, © 2016 INFORMS 7

that with posted prices, Pr4WN2Q ≤ �4p∗55.9 Condi-tional on the loan being funded, since the initial inter-est rate in the posted-price regime is higher thanthat in the auctions, and the contract rate is identi-cal to the initial rate under posted prices, the con-tract rate is also strictly higher than the contract ratein auctions. In turn, the loan default rate, whichthe finance literature has shown to be increasing incontract interest rates, should also be higher in theposted-price regime. Therefore, we summarize the fol-lowing hypotheses from the model:

Hypothesis 1. All else equal, the initial interest ratesassigned by Prosper.com under the posted-price mechanismare higher than the initial interest rates chosen by borrow-ers in auctions.

Hypothesis 2. Conditional on loans being funded, thecontract interest rates under the posted-price mechanismare higher than those under the auction regime.

Hypothesis 3. The fundingprobabilityunder the posted-price mechanism is higher than in auctions.

Hypothesis 4. For funded loans, the probability ofdefault under the posted-price mechanism is higher thanin auctions.

In addition to these predictions, for the higher ini-tial interest rate to induce higher funding probabili-ties, we should observe that lenders are more likely tobid under posted prices. Hence, an auxiliary hypothe-sis is that lenders should be likely to place bids earlierin auctions, and place larger bids, in the new regime.And because the price information (interest rate) fromProsper.com should carry more weight than the ask-ing rate of borrowers, lenders should be able to relyless on the behaviors of others to judge borrowerquality. Therefore, the herding behavior documentedin Zhang and Liu (2012) should be reduced, if noteliminated, under posted prices. However, our focusremains on the four hypotheses above.

3.4. Intuitions for the Stylized ModelAlthough we derived the hypotheses from a styl-ized model, the intuitions behind them are straight-forward. Under both regimes, the borrower movesbefore the lenders, as the borrower needs to commit toan initial interest rate before lenders decide whetheror not to invest. The website’s profit comes from origi-nated loans. In addition, there are two key features forthe posted-price mechanism. First, the pricing powerlies with Prosper.com. Second, by serving as the pric-ing agent, Prosper.com reduces the uncertainty asso-ciated with ongoing interest rates in auctions.

9 A necessary condition is �4� − c5≤ 4� − c5/41 + � − c5, which sug-gests that unless the default rate is too high, the funding probabilityunder the posted-price regime is strictly higher.

Under auctions, the borrower is faced with a trade-off between the initial (asking) interest rate and prob-ability of funding. The borrower will favor a lowerstarting interest rate because they cannot revise thatrate once the auction starts, and if the rate is unnec-essarily high, that rate will be effective for the life ofthe loan (cf. “winner’s curse”). In fact, if the lowerrate does not attract sufficient funding, it is virtuallycostless to post another request with a higher ask-ing rate. Under posted prices, Prosper.com implicitlysignals that the interest rate reflects borrower qual-ity. In other words, at the same starting interest rate,lenders will be more likely to place bids under postedprices than in auctions. Prosper.com is, therefore, ableto extract surplus from the borrower because the bor-rower has to move first, and by setting the interestrate higher, Prosper.com will entice potential lendersto participate and fund loans—after which the web-site is able to charge fees. This is the intuition behindHypothesis 1, and the other hypotheses follow.

We now turn to transactions data from Prosper.comto empirically test these hypotheses.

4. DataWe obtained data from Prosper.com on January 14,2013. The data set contains all transactions since thewebsite’s inception in 2006, including both fundedand failed listings. For each listing, we obtain anextensive set of variables including the requestedamount, initial interest rate, loan term, starting andending time, result, and repayment status as of ourdata collection date (if funded). The borrower’s creditinformation includes their Prosper rating (a lettergrade indicating the borrower’s creditworthiness),debt to income ratio, as well as extended credit infor-mation such as the number of credit lines, delin-quency history, and bank card utilization. We alsoobtain detailed information for each bid, includingthe identity of the lender, bid amount, bid time, andoutcome (winning or losing). Finally, for successfullyfunded loans, we have the loan origination date, con-tract interest rate, repayment status each month, andso on.

Prosper.com eliminated auctions on December 20,2010. We, therefore, construct our main sample toinclude all listings that were posted between August20, 2010, and April 19, 2011, except those suspectedof borrower identity theft and repurchased by Pros-per.com.10 During this period, the regime change

10 Prior to August 2010, Prosper.com allowed borrowers to use“automatic funding” for their auctions, where the borrower sets areserve interest rate and the auction process would end as soon as100% funding was reached. This funding option was discontinuedby the website, and during the time that we study, no such auctionsexisted.

Dow

nloa

ded

from

info

rms.

org

by [

98.2

23.2

29.1

88]

on 1

5 Ju

ne 2

017,

at 0

9:05

. Fo

r pe

rson

al u

se o

nly,

all

righ

ts r

eser

ved.

Wei and Lin: Market Mechanisms in Peer-to-Peer Lending8 Management Science, Articles in Advance, pp. 1–22, © 2016 INFORMS

Table 2 Summary Statistics: All Listings

All listings Auctions Posted prices

Variable Mean SD Mean SD Mean SD t-stat. p-value

Listing characteristics# of Bids 70084 93088 58024 94039 94032 88027 −21070 <00011(Loan Funded) 0034 0047 0023 0042 0055 0050 −37076 <00011(Electronic Transfer) 0099 0008 0099 0010 1 0 −8099 <00011(With Description) 0010 0005 0010 0004 0010 0005 1019 00881(Group Member) 0005 0021 0005 0022 0004 0019 3047 11(With Images) 0016 0037 0024 0043 00002 0005 51007 1Amount Requested 61589045 41368021 61105062 31953051 71490071 41926006 −16034 <0001Estimated Loss (%) 13066 8058 15086 9029 9055 4089 50074 1Initial Interest Rate (%) 24032 9027 25058 9035 21098 8064 22004 1Listing Effective Days 7083 6046 7005 5026 9029 8005 −16093 <0001Loan Term in Months 36074 6011 36020 2079 37074 9053 −10062 <00011(With Friends Bidding) 0002 0013 0002 0014 0001 0012 2027 0099Length of Description 130089 80078 144091 87063 104078 57071 31034 1

Credit profiles1(Verified Bank Account) 1 0 1 0 1 0 — —Debt/Income (DTIR) (%) 21029 44072 22007 46013 19082 41094 2082 00991(Top Coded DTIR) 00001 0004 00001 0004 00001 0004 — —1(Missing DTIR) 0017 0038 0019 0040 0013 0034 — —1(Homeowner) 0049 0050 0050 0050 0047 0050 2078 1Amount Delinquent 11012045 61724071 996073 51719038 11041074 81278070 −0033 0037Bankcard Utilization (%) 50053 33093 53012 34056 45070 32015 12023 1Current Credit Lines 9006 5029 9008 5031 9004 5026 0036 0064Current Delinquencies 0042 1022 0046 1028 0034 1010 5066 1Delinquencies Last 7 Years 3011 8025 30121 8021 3010 8031 0013 0055Inquiries Last 6 Months 1035 1092 1054 2012 0099 1040 17080 1Length Credit History 51939049 21964023 51843095 21915002 61117046 31046012 −4096 <0001Open CreditLines 8000 4077 8000 4078 8000 4075 −0011 0046Pub Rec Last 12 Months 0001 0014 0001 0013 0002 0015 −1070 0005Pub Rec Last 10 Years 0024 0067 0024 0067 0025 0066 −0013 0045Revolving Credit Balance 171200092 371234034 171794058 381372088 161095008 341992020 2055 0099Stated Monthly Income 51010090 131875029 41571000 121482046 51830032 161122023 −4058 <0001Total Credit Lines 24095 13099 25007 14019 24074 13059 1033 0091Total Open Accounts 6016 4030 6010 4030 6027 4031 31034 1

Macroeconomic environmentUnemployment Rate 9044 1089 9062 1088 9011 1086 14096 11(Miss Unemployment) 0001 0008 0001 0007 0001 0009 −1074 0004Zillow Home Value Index 1871424010 821477059 1891662010 831724063 1831255020 791945008 4029 11(Miss Zillow Index) 0002 0013 0002 0013 0002 0014 −1021 0011

Number of observations 13,017 8,470 4,547

Notes. This table presents the summary statistics of the corresponding variables from all listings. We conduct two-sided t-test for each variable. The alternativeis that the mean of the corresponding variable in the auction regime is less than that in the posted-price regime. Zillow.com calculates and publishes the dataon a monthly basis. The data are available at http://www.zillow.com/research/data/ (last accessed August 24, 2016).

under investigation was the only major policy changeon the platform.11

Tables 2 and 3 summarize the main sample. Therewere 131017 listings posted during the period; 81470of them began before December 20, 2010, and 41547listings were initiated in the posted-price regime. Outof these listings, 41446 were funded and becameloans. Among them, 11925 were funded using auc-tions, and 21521 were funded under posted prices.

11 Prosper.com also extended listing durations from 7 to 14 days.As we will show later in Section 5.3.2, this is highly unlikely to bedriving our findings.

We also include summary statistics of some additionalvariables about macroeconomic conditions, which wewill discuss in detail later. We further depict thedaily average quantities of the four outcome vari-ables in Figure 1. We observe that the daily ratioof funded and defaulted loans both increased afterthe regime change, and that the average asking inter-est rates and contract interest rates for funded loansboth declined under posted prices, when we do notcontrol for any covariates. We also find that half ofthe funded loans under posted-prices received fullfunding within 80 hours, compared to more than160 hours in the auction regime; this is consistent with

Dow

nloa

ded

from

info

rms.

org

by [

98.2

23.2

29.1

88]

on 1

5 Ju

ne 2

017,

at 0

9:05

. Fo

r pe

rson

al u

se o

nly,

all

righ

ts r

eser

ved.

Wei and Lin: Market Mechanisms in Peer-to-Peer LendingManagement Science, Articles in Advance, pp. 1–22, © 2016 INFORMS 9

Table 3 Summary Statistics: Funded Loans

All listings Auctions Posted prices

Variable Mean SD Mean SD Mean SD t-stat. p-value

Listing characteristics# of Bids 123020 97055 140051 108045 109097 86003 10015 11(Electronic Transfer) 1000 0005 1000 0007 1000 0000 −3001 <00011(With Description) 1000 0004 1000 0002 1000 0005 1093 00971(Group Member) 0006 0023 0007 0026 0004 0021 3054 11(Images) 0012 0032 0027 0044 00001 0003 26021 1Amount Requested 61108074 41321044 51234043 41057003 61776035 41398017 −12011 <0001Contract Interest Rate (%) 22079 9008 24025 9032 21068 8073 9036 1Estimated Loss (%) 10037 6009 11061 7022 9042 4085 11047 1Initial Interest Rate (%) 23030 9024 25044 9046 21068 8073 13058 1Listing Effective Days 7069 5093 6032 3018 8074 7019 −15007 <0001Loan Term in Months 36048 7003 36025 3036 36066 8086 −2012 00021(With Friends Bidding) 0003 0017 0004 0020 0002 0014 4023 1Length of Description 127082 76075 150056 90071 110046 58041 16090 1Closing Fees 210082 140018 180055 125032 233092 146041 −13007 <00011(Defaulted by 540 Days) 0009 0028 0008 0026 0009 0029 −2012 0002

Credit profiles1(Verified Bank Account) 1000 0000 1000 0000 1000 0000 — —Debt/Income (DTIR) (%) 19077 33048 19068 31032 19084 35005 −0016 00441(Top Coded DTIR) 6.75e−04 0003 5.20e−04 0002 7.93e−04 0003 — —1(Missing DTIR) 0010 0031 0011 0032 0010 0030 — —1(Homeowner) 0051 0050 0052 0050 0050 0050 1049 0093Amount Delinquent 765044 61035019 661071 41283006 844065 71087008 −1007 0014Bankcard Utilization (%) 50073 32059 52088 33007 49009 32013 3083 1Current Credit Lines 9024 5018 9020 5012 9027 5023 −0045 0033Current Delinquencies 0034 1013 0035 1016 0033 1012 0077 0078Delinquencies Last 7 Years 2091 7066 2067 6089 3009 8020 −1089 0003Inquiries Last 6 Months 0094 1038 0099 1047 0091 1030 1087 0097Length Credit History 51997056 21821095 51945018 21843014 61037056 21805056 −1008 0014Open Credit Lines 8015 4067 8010 4064 8019 4070 −0065 0026Pub Rec Last 12 Months 0001 00120 0001 0010 0002 0013 −1038 0008Pub Rec Last 10 Years 0026 0065 0026 0064 0027 0067 −0042 0034Revolving Credit Balance 161409010 341784077 161615013 331808010 161251077 351518038 0035 0064Stated Monthly Income 51533068 121454072 51040051 41108085 51910026 161136082 −2060 <0001Total Credit Lines 25043 13056 25021 13061 25060 13053 −0095 00232Total Open Accounts 6026 4019 6021 4013 6030 4023 −0073 0023

Macroeconomic environmentUnemployment Rate 9032 1087 9059 1085 9011 1086 8054 11(Miss Unemployment) 0001 0008 0001 0008 0001 0009 −0090 0018Zillow Home Value Index 1851355000 801456074 1871407040 821348041 1831787080 781962031 1048 00931(Miss Zillow Index) 0002 0014 0002 0014 0002 0014 −0008 0047

Number of observations 4,446 1,925 2,521

the website’s claim for “quicker deployment of funds”as a rationale for the regime change. To more formallytest the hypotheses derived in Section 3, we estimatehow funding probabilities, interest rates and defaultrate change as a result of the regime change, holdinglistings characteristics constant.

5. Empirical Analysis: Impact ofMarket Mechanism onFunding and Repayment

We now turn to the empirical tests. Our empiricaltests consist of two major tasks. In this section weexamine the impact of market mechanisms on trans-actional outcomes by testing the hypotheses discussed

above, and on lenders’ behaviors such as the amountand timing of bids as well as their herding behavior(Zhang and Liu 2012). In the next section we examinethe impact of the market mechanism change on socialwelfare.

5.1. Empirical StrategyOur analytical model predicts that Prosper.com, inthe posted-price regime, will assign higher interestrates compared to what the borrower would havechosen as the reserve interest rates in auctions, ceterisparibus. Further, the contract interest rates (for fundedloans), funding probability, and default rate should allbe higher under posted prices. Before we test thesehypotheses, we notice that borrowers under posted

Dow

nloa

ded

from

info

rms.

org

by [

98.2

23.2

29.1

88]

on 1

5 Ju

ne 2

017,

at 0

9:05

. Fo

r pe

rson

al u

se o

nly,

all

righ

ts r

eser

ved.

Wei and Lin: Market Mechanisms in Peer-to-Peer Lending10 Management Science, Articles in Advance, pp. 1–22, © 2016 INFORMS

Figure 1 Daily Transaction Outcomes Before and After the Regime Change

15

20

25

Inte

rest

rat

e (%

)

Daily average of contract interest rate (funded loans only)

Dec

embe

r 20

,20

10

10

15

20

25

30

35

2010-10-01 2010-12-01 2011-02-01 2011-04-01

Date

2010-10-01 2010-12-01 2011-02-01 2011-04-01

Date

2010-10-01 2010-12-01 2011-02-01 2011-04-01

Date

2010-10-01 2010-12-01 2011-02-01 2011-04-01

Date

Inte

rest

rat

e (%

)

Daily average initial interest rate

0

0.05

0.10

0.15

0.20

0.25

Per

cent

age

Daily percentage of defaulted loans by 12-month maturity

0

0.25

0.50

0.75

Per

cent

age

Daily percentage of funded loans

Dec

embe

r 20

,20

10D

ecem

ber

20,

2010

Dec

embe

r 20

,20

10

Regime: Auctions Posted prices

prices have better credit (see Tables 2 and 3 and Fig-ure 2): The fraction of borrowers with better credits issignificantly higher than before. We further notice thatthe drop in the number of posted listings (Table 2)is mainly due to the decrease in the number of highrisk borrowers. Our empirical strategy, therefore, hasto account for such changes by controlling for bor-rowers’ credit profile, loan and listing characteristics,and other covariates.

The key variables we control for in our estima-tions are summarized in Tables 2 and 3. We further

Figure 2 Distributions of Loans Across Credit Grades Before andAfter Regime Change

Prosper ratings

Per

cent

age

0

0.1

0.2

0.3

0.4

0.5

AA A B C D E HR

Regime:

AuctionsPosted prices

control for the creditworthiness categories of borrow-ers as specified by Prosper.com. Prosper.com sets theinterest rate for different borrowers based on theircredit rating, the term of their loans, and the numberof previous Prosper loans. For example, on Septem-ber 26, 2011, borrowers at the “A” credit grade couldhave four possible interest rates. If they had one ormore Prosper loans previously, their loans’ interestrate would be 9.29% if they were requesting a one-year loan, or 11.29% if they were requesting a three-year loan. In contrast, if they had no prior Prosperloans, their interest rate would be 10.70% if they wererequesting a one-year loan, versus 13.90% if they wererequesting a three-year loan. There are 24 such cate-gories as of that day across all credit grades.12 We con-trol for borrower creditworthiness categories in thismanner as well.

Our main empirical strategy is propensity scorematching. Specifically, we consider the posted-pricemechanism as the “treatment.” Therefore, listings andloans under posted prices are in the treatment group,whereas those under auctions are in the control group.We estimate the treatment effect associated with the

12 Screenshots of this pricing table can be viewed on Archive.org at https://web.archive.org/web/20110926231350/http://www.prosper.com/loans/rates-and-fees/.

Dow

nloa

ded

from

info

rms.

org

by [

98.2

23.2

29.1

88]

on 1

5 Ju

ne 2

017,

at 0

9:05

. Fo

r pe

rson

al u

se o

nly,

all

righ

ts r

eser

ved.

Wei and Lin: Market Mechanisms in Peer-to-Peer LendingManagement Science, Articles in Advance, pp. 1–22, © 2016 INFORMS 11

Table 4 Matching Estimates of the Regime Change Effects on Main Transaction Outcomes

Matching estimates (M = 4)

Initial ContractDep. var.: Interest Rate a 1(Loan Funded) Interest Rate 1(Defaulted)b

(1) (2) (3) (4)

1(Posted Prices) −10036∗∗∗ 10076∗∗∗ 00325∗∗∗ 00308∗∗∗ 00078 00726∗∗ 00018∗ 00025∗∗

4001555 4001145 4000105 4000125 4007145 4003295 4000105 4000105Covariates

Personal loan characteristics Yes Yes Yes Yes Yes Yes Yes YesBorrower’s credit profile Yes Yes Yes Yes Yes Yes Yes YesMacroeconomic environment Yes Yes Yes Yes Yes Yes Yes YesInterest rate categories Yes Yes Yes Yes

Number of observations 13,017 13,017 13,017 13,017 4,446 4,446 4,443c 4,443

Notes. This table presents the nearest-neighbor propensity score matching estimates of the regime change effect on transaction outcomes. M is the numberof matches to be searched. The rule of thumb for M is 3 or 4. The standard errors are calculated by the method suggested in Abadie and Imbens (2006). Allmatching estimations are performed in R (Sekhon 2011).

aIn auctions, borrowers set the initial interest rates. These are borrowers’ reservation rates. In posted prices, Prosper.com presets the initial rate. It is fixedover the whole funding process.

bWe examine the payment results by the 18th cycle (or month) since loan origination. Results are highly similar if we use 6th- or 12th-cycle maturity.cThree observations are dropped because of incomplete records.∗p < 001; ∗∗p < 0005; ∗∗∗p < 0001.

market mechanism change using nearest-neighborpropensity score matching. First, we estimate the fol-lowing probability of being in the posted-price regime(the treatment) given the set of covariates discussedabove, using a logit regression,

�4xi5= Pr4Di = 1 �X= xi51 (4)

where Di is a dummy variable equal to 1 if the list-ing is posted after the regime change, and X includesall the covariates. Then we estimate the average treat-ment effects (ATE) with bias adjusted and robust stan-dard errors. In other words, in matching we firstfind the nearest “neighbors” in the auction regime(untreated) for each listing under the posted-pricemechanism (treated) in terms of propensity score,and vice versa. We then estimate the sample ATEwith replacement. We follow Abadie and Imbens(2006) to calculate the standard errors of the match-ing estimates. All estimations are performed in R(Sekhon 2011).

5.2. Results and Discussions

5.2.1. Funding Probability and Interest Rates.We report the results of our matching estimations inTable 4. Panel (1) in Table 4 reports the estimates forthe comparison of initial interest rates. Estimates forthe comparison of funding probability are reportedin panel (2). Panel (3) in Table 4 presents the resultsfor the comparison of contract interest rates for thesubsample of funded loans. In addition to the match-ing method, we also estimate linear regressions usingordinary least squares (OLS) for all outcomes (exceptcontract interest rate where a Heckman model is

required since only funded loans report contract inter-est rates), and logit regressions for funding probabil-ity and default rate. Results (shown in Table 7) arehighly consistent with our matching estimates.

Our empirical results lend support to our hypothe-ses about the comparisons of initial interest rates,funding probability, as well as the contract interestrates if funded. The matching estimate for the ATE ofthe regime change in Table 4 shows that in the posted-price regime, the initial interest rate is around 1%,or 100 basis points, higher than what the borrowerwould have set in auctions. This is a nontrivial differ-ence for interest rates (cf. Saunders 1993). Notice thathad we not controlled for the interest rate categories,the results would have been the opposite.

Table 4 shows that all else equal, the funding prob-ability under posted prices is on average more than30% higher than under auctions. The top right panelin Figure 1 also displays this apparent trend in fund-ing probability. Notice that there is a kink at theregime change date, and this turns out to be signifi-cant even if we control for multiple covariates.13

Furthermore, estimates in panel (3) of Table 4 showthat after the regime change, the contract interest ratesfor funded loans are around 007% higher than theloans funded in auctions. These results lend supportto our theoretical prediction that the contract inter-est rates should be higher in the posted-price regime.They show that while loans were more likely to be

13 One may argue that the kink could be driven by seasonalityeffect since the regime change was made right before the Christmasholiday. We check that possibility by examining the daily ratio offunded loans one year prior to our study period (when there wasno regime change), and do not find evidence of such seasonality.

Dow

nloa

ded

from

info

rms.

org

by [

98.2

23.2

29.1

88]

on 1

5 Ju

ne 2

017,

at 0

9:05

. Fo

r pe

rson

al u

se o

nly,

all

righ

ts r

eser

ved.

Wei and Lin: Market Mechanisms in Peer-to-Peer Lending12 Management Science, Articles in Advance, pp. 1–22, © 2016 INFORMS

funded under posted prices, it came at a nontrivialcost for borrowers in the form of higher interest rates.All results above are robust to the choice of differentmatching estimators. Similar results hold when weestimate the average treatment effect on the treated(ATT) for all three outcome variables.

5.2.2. Loan Repayment. Prosper.com focuses onfaster “fund deployment” as a motivation for theregime change. In the long run, however, it is therepayment of the loans that matters most for investorsas uncertainties resolve and returns materialize. Iflenders’ choices turn out to be wrong, that could hurttheir incentive to continuously participate in the mar-ket. Our Hypothesis 4 is that the default rate will behigher under posted prices, and we test it next.

Since some loans originated in this period havenot yet matured as of the time of writing, we com-pare the repayment of loans in two ways. First, werecord loan repayment status as of the 18th pay-ment cycle (month) since their origination date. Thisensures that we are comparing loans at a similar stageof “maturity.” The base rate of default at the 18thcycle for the whole sample is 9092%. We find that8062% of loans originated in auction stage default atthe 18-month maturity, whereas this ratio is 10091%for posted prices.

We then estimate whether the regime change isassociated with a higher or lower default rate, andwe present the estimation results in panel (4) ofTable 4. Our results are robust to the choice of dif-ferent repayment dates. Consistent with Hypothe-sis 4, we find that loans originated after the regimechange have higher default rates: roughly 205% higherthan in auctions. This is a subtle but important con-sequence of the regime change.14 It suggests thateven though lenders see a higher interest rate atthe time of loan origination, their overall return is

14 One may be concerned that after the regime change the lendersrace to secure a fraction of the loan before full funding, andthis competition effect may encourage risk-taking behavior amonglenders, which in turn causes the higher default rate. However,this is unlikely to be driving our results. First, we observe that themedian credit grade of lenders’ investment was actually higher afterthe regime change, meaning more funds were invested in less riskyloans. Second, this scenario is akin to herding. Our results later inthe paper actually show that herding is in fact lower under postedprices. In particular, even if we look at listings at the lowest creditgrade, herding is still lower than under auctions. Last but not least,we also conduct another analysis (regression and matching yieldsimilar results) with the outcome being whether the loan defaults atthe end, and the independent variable is how much time (in hours)it took the loan to reach full funding; we control for all other vari-ables as before. If the “frenzy” suggested by this scenario leads toirrational behavior, then loans that were funded faster (more eagerinvestors) should be more likely to default. The result contradictsthis: the time variable is not significant at any level. For brevity wedo not report these results here.

not necessarily higher, due to the increase in ex postdefault probabilities.

The second method that we use to compare loanperformance is a survival analysis of a loan’s time-to-default (Lin et al. 2013). We study the effects upto various maturity dates as the previous method,and results are highly consistent. Results are shownin Table 5. Estimates in the table are the exponenti-ated estimates from a Cox proportional hazard regres-sion. Results from the main specification (Spec 5 in thetable) suggest that after the regime change, the hazardrate of default15 increases by 5004%. Taken together,our findings indicate that loans funded under postedprices are indeed more likely to default, consistentwith our hypothesis.

5.2.3. Lenders’ Bidding Behaviors. While thefocus of our paper is the effect of regime changeon loan outcomes, our understanding of the marketmechanism’s impact will not be complete withoutcharacterizing how investors respond to the regimechange. The goal of this section is to investigate if theimpact on investor behavior is consistent with—andtherefore further lends support to—our findings onloan-level outcomes.

We study the change in lender’s bidding behav-iors from two aspects. The first one uses each bid asthe unit of analysis to compare the timing of lenders’bids as well as the amount of their bids. The secondone draws on published studies of herding in the con-text of Prosper.com (Zhang and Liu 2012) and testswhether the regime change affects lender’s tendencyto follow each other.

Figure 3 compares the dollar amount in each bid.It shows that under posted prices, lenders tend toinvest more in each bid than they do under auctions.As a result, the median number of days to reach fullfunding is 80 hours under posted prices, comparedto more than 160 hours for auctions. Both resultsare consistent with our prior finding that loans arefunded faster under posted prices.

Another important characterization of lenderbehavior is herding. Since lenders are more likely totrust the starting price assigned by the platform thanby borrowers, lenders will have lower needs to waitand observe the behaviors of others. Therefore, herd-ing should be less likely to occur under posted prices.To test this, we draw on prior empirical work byZhang and Liu (2012) who also used data from Pros-per.com, and we estimate their models using listingsfrom both regimes. Estimation results (Table 6) show

15 In the main specification, we define a loan being defaulted ifthe status shows “more than four months late,” “defaulted,” or“charge-off.” For robustness, we tried changing the definition ofdefault to being late and beyond, one month late and beyond, twomonths late and beyond, or three months late and beyond. Coxestimates from all these extensions are qualitatively similar.

Dow

nloa

ded

from

info

rms.

org

by [

98.2

23.2

29.1

88]

on 1

5 Ju

ne 2

017,

at 0

9:05

. Fo

r pe

rson

al u

se o

nly,

all

righ

ts r

eser

ved.

Wei and Lin: Market Mechanisms in Peer-to-Peer LendingManagement Science, Articles in Advance, pp. 1–22, © 2016 INFORMS 13

Table 5 Cox Estimates of a Competing Risks Model for Loan Repayment

Cox proportional hazard estimates

Spec 1 Spec 2 Spec 3 Spec 4 Spec 5

exp(Coef. of 1(Posted Prices)) 1�250∗∗ 1�371∗∗∗ 1�396∗∗∗ 1�417∗∗∗ 1�504∗∗∗

�0�102� �0�108� �0�110� �0�110� �0�111�Covariates

Personal loan characteristics Yes Yes Yes YesBorrower’ s credit profile Yes Yes YesMacroeconomic environment Yes YesInterest rate categories Yes

Number of observations 4,446 4,446 4,446 4,446 4,446

Notes. This table presents Cox proportional hazard estimates of a competing risks model for the duration of the funded loans’ repay-ment on Prosper.com. Specifically, we model the length of time until a loan being defaulted, and define a loan as defaulted if thestatus shows either over four months late, defaulted, or charge-off. We treat early payoff as a competing “risk” of terminating the loanrepayment process. We compare loans’ repayment up to 540 days since their origination dates, thus loans still in payoff progress areright-censored. Estimations are performed in R (Scrucca et al. 2007).

∗∗p < 0�05; ∗∗∗p < 0�01.

Figure 3 Distribution of Average Bid Amount Across Listings Beforeand After Regime Change

0

0.01

0.02

0.03

0.04

0.05

20 40 60 80 100

Average amount (per bid)

Den

sity

Regime:

Auctions

Posted prices

an interesting reversal in lenders’ herding behavior.In auctions, a listing with USD 100 more funding atthe start of a day will receive on average USD 2�7more funds during the day; while this number underposted prices is negative (−USD 17�2), confirming ourexpectation. This again is consistent with our find-ing that loans are funded faster under posted prices:Lenders do not need to wait to observe peer actions,so they bid sooner and bid more.

5.3. RobustnessWe conduct a large number of tests to ensure thatour main results are robust and not due to alter-native explanations. We explore sensitivity of ourmatching estimator; linear regression estimator ratherthan matching; potential confounding effect of list-ing duration change; composition of lenders and theirbehaviors; as well as alternative samples. Our resultsremain highly consistent.

Table 6 Comparison of Herding Behavior

Within estimates

Dep. var.: Daily Fund Received Auctions Posted prices

Lag Cum Amount 0�027∗ −0�172∗∗∗

�0�014� �0�018�Lag Percent Needed −0�005∗∗∗ −0�003∗∗∗

�0�000� �0�001�Lag Min Rate −0�098∗∗∗

�0�022�Lag Bids −0�001 0�015∗∗∗

�0�001� �0�001�Lag Cum Amount× Lag Percent Needed 0�001∗∗∗ 0�008∗∗∗

�0�000� �0�000�Listing fixed effects Yes YesDay of listing fixed effects Yes YesWeekday fixed effects Yes YesAdjusted R2 0.090 0.252Number of observations 24,773 21,366

Notes. This table presents the within estimates of a panel model that exploresthe correlation between the funds received in a day and the total fundsreceived by the end of previous day. Full descriptions and justifications canbe found in Zhang and Liu (2012). Note that the listings sampled in this tableinclude only those with at least one bid.

∗p < 0�1; ∗∗∗p < 0�01.

5.3.1. Empirical Model Robustness.Propensity Score Matching Sensitivity� The propen-

sity score matching method that we use assumesselection on observables, so a common concern is thatunobservables may be driving the difference betweentreatment and comparison groups. To investigate howsensitive our matching estimates are to the possiblepresence of an unobserved confounding variable, weconduct sensitivity analysis (Rosenbaum 2002). Wefind that for the regime change effect to disappear,the unobserved confounder has to change the odds ofselection into the treatment by at least 30% for all out-comes. This is, therefore, unlikely a first order concernin our analysis.

Dow

nloa

ded

from

info

rms.

org

by [

98.2

23.2

29.1

88]

on 1

5 Ju

ne 2

017,

at 0

9:05

. Fo

r pe

rson

al u

se o

nly,

all

righ

ts r

eser

ved.

Wei and Lin: Market Mechanisms in Peer-to-Peer Lending14 Management Science, Articles in Advance, pp. 1–22, © 2016 INFORMS

Alternative Specifications0 As an alternative tomatching, we reestimate the regime change effects oninterest rates, funding probability, and default ratesusing linear models. The specific equation we esti-mate is

yir = �r +�114Posted Prices5ir +�′

2Xir + �ir1 (5)

where yir are the transaction outcomes of initial inter-est rates, indicator of full funding, contract interestrates if funded, or the indicator of default for fundedloans; �r are the interest rate category fixed effects;Xir are the control variables in Equation (4). The coef-ficient of interest is �1, which captures the regimechange effects.

We report estimation results using our main sam-ple in the first, second, fourth, and sixth columnsof Table 7. The estimates are qualitatively consistentwith our findings in matching except for contractinterest rates. However, the linear model for inter-est rate is biased due to a selection process, sinceonly funded loans have data on interest rates. Inauctions, given an interest rate category, loans withhigher interest rates are more likely to be funded. Inaddition, the variation of interest rates within eachcategory is larger under auctions. We, therefore, esti-mate a Heckman selection model using the two-stepmethod (Lin et al. 2013). Results are reported in thefifth column of Table 7. The estimate of the regimechange effect, �1, is again positive and consistent withthe matching estimate. For comparisons of fundingprobability and default rate, we also estimate logitmodels in view of the dichotomous dependent vari-ables. Results are reported in the third and seventhcolumns of Table 7. Estimates of the regime effects arein the same direction as our matching estimates.

Table 7 Comparisons of Transaction Outcomes Using Linear Regressions

Transaction outcomes

Initial ContractDep. var.: Interest Rate 1(Loan Funded) Interest Rate 1(Defaulted)

OLS OLS Logit OLS Heckmana OLS Logit

1(Posted Prices) 10181∗ 00255∗∗∗ 00210∗∗∗ −00414∗ 00701∗∗ 00032∗ 00029∗

4005925 4000145 4000155 4002375 4003415 4000185 4000175Covariates

Personal loan characteristics Yes Yes Yes Yes Yes Yes YesBorrower’s credit profile Yes Yes Yes Yes Yes Yes YesMacroeconomic environment Yes Yes Yes Yes Yes Yes YesInterest rate categories Yes Yes Yes Yes Yes Yes Yes

R2 0.735 0.242 — 0.953 — 0.086 —Pseudo R2 — — 0.211 — — — 0.144Number of observations 13,017 13,017 13,017 4,446 13,017 4,443 4,443

Notes. This table displays estimation results of linear models for all transaction outcomes. For comparisons of funding probability and default rate at 18th-cyclematurity, we also estimate logit models. Similar results show up for probit models. Robust standard errors (in all models) are present in the table.

aFor the comparison of contract rates, there is a selection issue that in auctions the loans with higher reserve rates are more likely to be funded, even if wecontrol for all observed characteristics. Thus we also estimate a Heckman selection model using the two-step method.

∗p < 001, ∗∗p < 0005, ∗∗∗p < 0001.

5.3.2. Alternative Explanation: Funding Dura-tion? Along with the regime change, Prosper.comalso extended the funding duration for all listingsafter December 20, 2010, to 14 days (it was 7 daysbefore that). It appears plausible that longer dura-tions may explain some of our findings, especially theincreased funding probability. To examine this possi-bility, we take several different approaches: summarystatistics; a survival analysis; and evidence from aprevious exogenous event (unrelated to the marketmechanism change) on duration that also occurred onProsper.com.

We first examine whether the extended durationwas indeed a binding constraint on the funding pro-cess, or the extent to which the longer duration actu-ally helped more loans receive full funding. We findthat after the regime change, about 70% of loans werestill funded within seven days. Further, as we showin Section 5.2.3, more than half of posted-price loanswere funded within 80 hours, which is significantlyless than seven days.

Second, to better take into account that the fund-ing duration can be different under the two regimes,we model the funding process using a survival anal-ysis. Specifically, we estimate a Cox competing risksmodel where t0 is the start of a listing, and the depen-dent variable is the length of time to full funding.The main censoring event of interest is full fund-ing. Table 8 reports the exponentiated estimates fromthe Cox regressions. The main specification, Spec 5in the table, suggests that after the regime change,the hazard rate of being funded increased by a fac-tor of 20422, or, by 14202%. This significant changein funding rate is consistent with our main findingsof higher funding probability, and further impliesthat the posted-price loans were indeed quicker to

Dow

nloa

ded

from

info

rms.

org

by [

98.2

23.2

29.1

88]

on 1

5 Ju

ne 2

017,

at 0

9:05

. Fo

r pe

rson

al u

se o

nly,

all

righ

ts r

eser

ved.

Wei and Lin: Market Mechanisms in Peer-to-Peer LendingManagement Science, Articles in Advance, pp. 1–22, © 2016 INFORMS 15

Table 8 Cox Estimates of a Competing Risks Model for the Duration of Prosper Loans’ Funding Processes

Cox proportional hazard estimates

Spec 1 Spec 2 Spec 3 Spec 4 Spec 5

exp(Coef. of 1(Posted Prices)) 20380∗∗∗ 20796∗∗∗ 20627∗∗∗ 20632∗∗∗ 20422∗∗∗

4000305 4000355 4000365 4000365 4000375Covariates

Personal loan characteristics Yes Yes Yes YesBorrower’s credit profile Yes Yes YesMacroeconomic environment Yes YesInterest rate categories Yes

Number of observations 13,017 13,017 13,017 13,017 13,017

Notes. This table presents Cox proportional hazard estimates of a competing risks model for the duration of fundingprocess. Specifically, we model the length of time until a loan is fully funded, and we treat listing expiration orwithdrawn by the borrowers as competing risks.

∗∗∗p < 0001.

fund even if we account for the funding durationdifference.

Third, to more directly investigate how dura-tion changes could affect our outcome variables, weexploit an exogenous event related to funding dura-tion (but unrelated to regime change that we focuson) to better tease out the causal impact of dura-tion, if any. Prosper.com implemented another policychange on listing durations on April 15, 2008; beforethat date, borrowers could choose 3, 5, 7, or 10 daysas the funding duration. Starting on April 15, 2008,the platform standardized durations for all listingsto seven days. This provides an ideal opportunity toevaluate the effects of funding durations. In particularsince the confounding factor to our main analysis isan increase in funding duration, we focus on listingswith three- or five-day durations prior to April 15,2008, which were increased to seven days due to thepolicy change. Our results16 show that the variable onduration change is not statistically significant for anyof the outcome variables. Therefore, the increase induration is unlikely to be driving our main findingsduring the regime change. In fact, when we exam-ine listings with 10-day duration (which would repre-sent a decrease in funding duration), the result is alsoinsignificant.

5.3.3. Alternative Explanation: Changes in LenderCompositions? Another concern is that our resultsmay be driven by changes in the composition oflenders. We address this both conceptually (the firsttwo points below) and empirically (the other threepoints). First, this would have been a plausible expla-nation if our data came from temporally or spatiallydisjoint samples, but we focus on data immediatelyaround the regime change. Second, since we study

16 Because of space constraints, we do not report the results here,but they are available from the authors upon request.

the effect of market mechanisms, lender composi-tion is more appropriately an outcome than an inde-pendent variable: Lenders arrive at listings after themarket mechanism is public knowledge, and afterthe borrower’s listing (including borrower informa-tion and loan characteristics) is revealed to all poten-tial investors. To include lender composition into theright-hand side of our models will introduce endo-geneity and bias our results.

Third, despite the previous points, nonetheless weinvestigate whether considering the lender compo-sition alters our findings. Specifically, we considerthe composition using the proportion of participatinglenders who had invested in at least one listing beforethe regime change. We repeat our matching estima-tions by including loan requests with at least 90% ofthese “old” lenders. Results are presented in Table 9and are highly consistent with our main findings.

Fourth, there is no evidence that there is an influxof new (and potentially different) lenders after theregime change. The time series of the daily number ofnewly registered lenders shows no structural changebefore and after. Alternatively, when we compare thedaily number of newly registered lenders before andafter, a two-sample T -test rejects the null that themeans of these two groups are different at any com-mon significance levels. Figure 4 shows that the plat-form had a steady but relatively low level of growthon the supply side (of funds), with on average 18 newlenders joining per day.

Last but not least, and also consistent with the pre-vious point, the “old” lenders are still dominant infunding loans during our study period. In more than90% of posted-price listings (with at least one invest-ment), at least 80% of lenders were actually regis-tered before the regime change. In other words, theproportion of funds from lenders that register afterthe regime change was largely negligible. This ratio iseven higher for funded loans, with almost all funded

Dow

nloa

ded

from

info

rms.

org

by [

98.2

23.2

29.1

88]

on 1

5 Ju

ne 2

017,

at 0

9:05

. Fo

r pe

rson

al u

se o

nly,

all

righ

ts r

eser

ved.

Wei and Lin: Market Mechanisms in Peer-to-Peer Lending16 Management Science, Articles in Advance, pp. 1–22, © 2016 INFORMS

Table 9 Matching Estimates of Regime Change Effect Considering Lender Compositions

Matching estimates (M = 4)

Initial ContractDep. var.: Interest Rate 1(Loan Funded) Interest Rate 1(Defaulted)

1(Posted Prices) 1�011∗∗∗ 0�319∗∗∗ 0�468∗ 0�018∗

�0�119� �0�013� �0�265� �0�011�Covariates

Personal loan characteristics Yes Yes Yes YesBorrower’ s credit profile Yes Yes Yes YesMacroeconomic environment Yes Yes Yes YesInterest rate categories Yes Yes Yes Yes

Number of observations 12,047 12,047 3,943 3,940

Notes. Only loan requests with at least 90% of lenders that participated before the regime change are included.Similar results appear for other thresholds such as 70% and 80%.

∗p < 0�1; ∗∗∗p < 0�01.

Figure 4 Daily Number of Newly Registered Lenders Before and Afterthe Regime Change

2010-10-01

0

20

40

Cou

nt

60

2010-12-01

Date

2011-02-01 2011-04-01

Regime: Auctions Posted prices

Dec

embe

r 20

,20

10

posted-price loans (98�69%) having at least 80% “old”lenders.

All the above evidence suggests that change inlender compositions is unlikely to be a plausible alter-native explanation to our findings.

5.3.4. Alternative Explanation: Role of Soft In-formation? Research has shown that soft informa-tion or nonstandard information about borrowers, notavailable to traditional banks, can influence lenderdecisions in P2P lending (Iyer et al. 2016). If low qual-ity borrowers are more likely to use soft informa-tion, and soft information is more likely to positivelyimpact investor behavior under posted prices, thenwe will observe that borrowers are more likely todefault under the posted-price regime, because badborrowers are more likely to be funded but will notbe able to repay.17

This, however, did not turn out to be a valid alter-native explanation for our findings, because (1) after

17 We thank an anonymous reviewer for pointing us to the role ofsoft information.

the regime change, among borrowers who use softor nonstandard information, the proportion of highquality borrowers is, in fact, higher; and (2) we didnot find evidence that the impact of soft or non-standard information changes in a statistically sig-nificant way after the regime change. Evidence forthe first point is presented in Figure 5, which showsthat among borrowers with soft information, the pro-portion of higher credit grade borrowers is in facthigher after the regime change, regardless of whichsoft information variable we look at. Evidence forthe second point comes from a formal statistical test,where we interact these soft or nonstandard infor-mation variables with the regime change dummy.The coefficient for the interaction term is positive forsome variables and negative for others, but none isstatistically significant, as shown in Figure 6, whichillustrates the point estimates and 95% confidenceintervals of these coefficients.18

5.3.5. Alternative Samples.Extended Sample� Another potential concern is the

sample used in our estimations. Our main samplecontains all listings posted four months immediatelybefore and after the regime change. As an alternative,we compare loans that were generated four monthsbefore the regime change and those posted betweenApril 20, 2011, and August 19, 2011—a larger win-dow than our main sample. Matching estimates arereported in Table 10 and are highly similar to ourmain results.

“Interim” Loans� The regime change we study is anovernight change, where all new listings that appearafter midnight on December 20, 2010, use postedprices. Listings that were created prior to the changeand were still open were included in our main anal-ysis. However, our main results are virtually identi-cal when we exclude them. There were only 144 such

18 These coefficients are also not statistically significant when weuse default likelihood as dependent variable.

Dow

nloa

ded

from

info

rms.

org

by [

98.2

23.2

29.1

88]

on 1

5 Ju

ne 2

017,

at 0

9:05

. Fo

r pe

rson

al u

se o

nly,

all

righ

ts r

eser

ved.

Wei and Lin: Market Mechanisms in Peer-to-Peer LendingManagement Science, Articles in Advance, pp. 1–22, © 2016 INFORMS 17

Figure 5 Distributions of Personal Loans (Funded or In Request) with “Soft Information”

Funded loans (description) Funded loans (friends) Funded loans (group member)

Loan requests (description) Loan requests (friends) Loan requests (group member)

0

0.25

0.50

0.75

1.00

0

0.25

0.50

0.75

1.00

Auctions Posted prices Auctions Posted prices Auctions Posted prices

Regime

Fra

ctio

n

Quality: High Low

listings, and 40 of them were successfully funded.The interest rates of these loans were frozen at thetime of the change, and the funding processes contin-ued under the prevailing rates using the posted-pricemechanism; they would be originated immediatelywhen they receive 100% funding. In all previous

Table 10 Matching Estimates of the Regime Change Effects Using an Extended Sample

Matching estimates (M = 4)

Initial ContractDep. var.: Interest Rate 1(Loan Funded) Interest Rate 1(Defaulted)

1(Posted Prices) 3�007∗∗∗ 0�207∗∗∗ 2�511∗∗∗ 0�042∗∗∗

�0�270� �0�045� �0�612� �0�007�Covariates

Personal loan characteristics Yes Yes Yes YesBorrower’ s credit profile Yes Yes Yes YesMacroeconomic environment Yes Yes Yes YesInterest rate categories Yes Yes Yes Yes

Number of observations 16,459 16,459 5,438 5,438

Note. In this table we compare loans that were generated four months before the regime change and those postedbetween April 20, 2011, and August 19, 2011.

∗∗∗p < 0�01.

empirical investigations, we include these loans as ifthey were under the auction regime (since their ini-tial interest rates were not set by Prosper.com). Totest whether our results are driven by these loans,we conduct a robustness check by excluding them. AsTable 11 shows, results are highly consistent.

Dow

nloa

ded

from

info

rms.

org

by [

98.2

23.2

29.1

88]

on 1

5 Ju

ne 2

017,

at 0

9:05

. Fo

r pe

rson

al u

se o

nly,

all

righ

ts r

eser

ved.

Wei and Lin: Market Mechanisms in Peer-to-Peer Lending18 Management Science, Articles in Advance, pp. 1–22, © 2016 INFORMS

Figure 6 (Color online) Changes in the Effectiveness of Soft/Nonstandard Information on Funding Success

Zillow Home Value Index

Unemployment Rate

1(With Description)

1(Group Member)

With Images

Length of Description

Friends

With Friends

Borrower Max. Rate

Notes. Each square represents the point estimate of the coefficient for the interaction term between that variable and a dummy for posted prices. Each greyline represents the 95% confidence interval of that estimate. If that line covers 0, it is not statistically significant.

Table 11 Matching Estimates of Regime Change Effect Excluding “Interim” Loans

Matching estimates (M = 4)

Initial ContractDep. var.: Interest Rate 1(Loan Funded) Interest Rate 1(Defaulted)

1(Posted Prices) 1�107∗∗∗ 0�308∗∗∗ 0�888∗∗∗ 0�026∗∗∗

�0�115� �0�011� �0�304� �0�010�Covariates

Personal loan characteristics Yes Yes Yes YesBorrower’ s credit profile Yes Yes Yes YesMacroeconomic environment Yes Yes Yes YesInterest rate categories Yes Yes Yes Yes

Number of observations 12,873 12,873 4,406 4,403

Note. We exclude “interim” loans that were still being funded at the time of the regime change.∗∗∗p < 0�01.

6. Empirical Analysis: Impact ofMarket Mechanism onSocial Welfare

Our results so far show that funding probability, inter-est rates, and default probability are all higher underposted prices. A natural and important follow-upquestion is whether the regime change is “better”for various stakeholders in this market. This questionhas important policy implications because it concernssocial welfare, and we investigate it next. Our goalis to understand which market mechanism generateshigher overall social welfare.

Although the posted-price mechanism brings higherfunding probability, the higher contract interest rateswill increase ex post default rates (Stiglitz and Weiss1981). The total social surplus depends not only onhow often the loans are being funded but also on howoften the funded loans are repaid. A welfare compar-ison should take both into account. We present a for-mal treatment of this analysis in the online appendix(available as supplemental material at http://dx.doi.org/10.1287/mnsc.2016.2531). Since the platform cap-tures all borrowers surplus, borrowers’ surplus shouldbe decreasing, and the platform’s surplus should be

Dow

nloa

ded

from

info

rms.

org

by [

98.2

23.2

29.1

88]

on 1

5 Ju

ne 2

017,

at 0

9:05

. Fo

r pe

rson

al u

se o

nly,

all

righ

ts r

eser

ved.

Wei and Lin: Market Mechanisms in Peer-to-Peer LendingManagement Science, Articles in Advance, pp. 1–22, © 2016 INFORMS 19

Table 12 Matching Estimates for the Comparison of Lender Returns and Surplus

Matching estimates (M = 4)

Dep. var.: ROI (%)a Lender Surplus

(1) (2)

1(Posted Prices) −00031∗∗∗ −00029∗∗∗ −460637∗∗∗ −430676∗∗∗

4000105 4000105 4507215 4501935Covariates

Personal loan characteristics Yes Yes Yes YesBorrower’s credit profile Yes Yes Yes YesMacroeconomic environment Yes Yes Yes YesInterest rate categories Yes Yes

Number of observations 4,443 4,443 4,446 4,446

Note. This table presents the nearest-neighbor propensity score matching estimates of the regime change effectson lender ROI and surplus.

aWe examine the ROI by the 18th billing cycle (or month) since origination. Similar results hold for 6th or12th billing cycle.

∗∗∗p < 0001.

increasing.19 In addition, the increase in platform sur-plus is no greater than the decrease in borrowersurplus, otherwise the borrower would not find itprofitable to borrow from the platform. However, thelender’s surplus change is ambiguous because thereis a tradeoff between higher nominal contract inter-est rates and higher default likelihood. Our analysisin the online appendix illustrates conditions underwhich auctions can generate higher social welfare thanposted prices.

To further determine the net total surplus changedue to the regime change, we need to empiricallyascertain whether lenders’ surplus is higher or lowerunder posted prices. We conduct two different analy-ses. First, we calculate the lenders’ return on investment(ROI) using the loan performance data, thereby takinginto account the influence of both the higher contractinterest rate and higher likelihood of default. Lenders’ROI on a loan is calculated as (Cumulative payment −

Loan amount requested)/Loan amount requested, whichfactors in the loan’s repayment status. We can, hence,calculate each loan’s ROI up to a certain billing cycle.We repeat our matching estimations and report theresults in panel (1) of Table 12. We find that after theregime change, the lenders’ returns are significantlylower by about 3% by the 18th cycle. Therefore, thehigher probability of default dominates the positiveeffects of higher contract interest rates. This findingindicates that all else equal, lender surplus decreasedafter the switch to posted prices.

Second, we use a numerical approach to moredirectly and structurally calculate the change of

19 We calculated and compared the platform’s revenue under auc-tions and posted prices, and we found that platform surplus isindeed higher after the regime change. Detailed results are avail-able from the authors.

lender surplus. To this end, we first recover a rep-resentative lender’s supply function. Such a functionspecifies a relationship between the lender’s valuationof a loan (measured by the lender’s lowest acceptableinterest rate) and loan amount. We use S4 · 5 to denotethe supply function with W = S4Q5. We assume asimple functional form20 of the supply function, W =

� ·Q� . We take a log-transformation to obtain

logW = log�+� · logQ0 (6)

With the supply function, the lender’s surplus will besimply the area above this supply function but belowthe market transaction interest rate, factoring in theprobability of default. We next empirically estimatethe parameters of the supply function.

We use bids submitted to listings that are postedone year before our main sample (Section 4), betweenAugust 20, 2009, and August 19, 2010, to calibrate thesupply function. We focus on open requests wherethe funding process continues after full funding. Inopen auctions, if and only if a bid is outbid willwe observe its actual bid interest rate. We use thesefailed bids to uncover our parameters for the sup-ply function. The identification of the supply func-tion assumes that lenders are truthfully bidding bysubmitting their lowest acceptable interest rates. Sincethe auction on Prosper.com is essentially a second-price proxy auction, this assumption is reasonable. Wefurther allow the representative lender to have dif-ferent supply functions for loans in different creditgrades. Therefore, we estimate one supply functionfor loans in each credit grade, ranging from AA (thebest) to HR (the most risky). To estimate the expected

20 In our robustness checks, we allow for flexible functional formsincluding linear and higher-order terms. Results are highly similar.

Dow

nloa

ded

from

info

rms.

org

by [

98.2

23.2

29.1

88]

on 1

5 Ju

ne 2

017,

at 0

9:05

. Fo

r pe

rson

al u

se o

nly,

all

righ

ts r

eser

ved.

Wei and Lin: Market Mechanisms in Peer-to-Peer Lending20 Management Science, Articles in Advance, pp. 1–22, © 2016 INFORMS

probability of default, we run logit regressions withthe dependent variable being the dummy for loandefault. We then use the predicted value from thelogit regressions as the proxy for the default rate. Itis straightforward to calculate the lender surplus foreach funded loan after estimating the supply func-tions. We find that the average lender surplus forloans under auctions is $35.95, while the averagesurplus for posted-price loans is −$29.49. We repeatmatching estimations using the calculated lender sur-plus on a loan as the dependent variable. Results arereported in panel (2) in Table 12. Not surprisinglyand consistent with our findings based on ROI, wefind that the regime change lowers lender surplus.Therefore, as a result of the regime change, borrowersurplus is lower, platform surplus is higher (but notgreater than the decrease in borrower surplus), andlender surplus is lower. The overall social welfare is,therefore, lower under posted prices.

7. Discussions and Conclusions7.1. Summary of ResultsThe choice of market mechanisms is one of the mostfundamental questions in any marketplace. For anascent industry such as online peer-to-peer lending,this choice is especially critical but not well under-stood. For market designers, platform owners, andpolicy makers, there are delicate short-term and long-term consequences that should be carefully weighed.Although currently the two major peer-to-peer lend-ing platforms in the United States both use postedprices, many peer-to-peer lending platforms in othercountries still use auctions. More important, there islittle systematic empirical evidence in favor of a par-ticular mechanism, and the popularity of posted-pricemechanisms per se does not guarantee its efficiencyor superiority.

We first develop a stylized game theoretic model tocompare uniform-price auctions against posted-pricesales, taking into account the incentive of the platformto maximize its own expected payoff. Then we test themodel’s predictions using detailed transactions datafrom Prosper.com, around the time of a unique regimechange from auctions to posted prices. Our empiricalresults support our hypotheses. Specifically, we findevidence of short-term improvements for both bor-rowers and lenders. Lenders benefit from a quicker“deployment” of funds because loans are more likelyto be funded and are funded faster under postedprices. Borrowers also seem to benefit from the newregime, since their requests are funded sooner. Both ofthese short-term benefits were noted by Prosper.comwhen they announced the regime change, and rightlyso. The quicker deployment of funds into loans fur-ther translates into higher revenue for Prosper.com,

and the platform’s short-term surplus is unequivo-cally higher as a result.

On the other hand, however, as our theoreticalmodel predicts and our empirical analysis shows,Prosper.com assigns higher initial interest rates underposted prices than borrowers would have in auctions.Hence, while lenders enjoy a higher nominal return onloans, it comes at a cost to borrowers. Most impor-tant, this change has long-term implications for therepayment of loans. As the finance literature has longdocumented (Stiglitz and Weiss 1981), the interest rateis one of the most critical factors in determining expost loan default. Our analysis of loans originatedaround the time of the regime change is consistentwith this prediction: All else equal, loans are morelikely to default under posted prices. Furthermore,welfare reduction due to increases in default actuallydominates welfare increase from higher nominal inter-est rates, since lenders’ overall return on investment(ROI) and surplus are lower under posted prices thanauctions in our data. These findings suggest that theregime change actually resulted in a net loss in totalsocial welfare. While the traditional “crowd”-basedauctions may be slower to fund loans, its long-termwelfare impact is not necessarily worse than postedprices set by experts. Since peer-to-peer lending plat-forms deduct service fees at the time of the loanorigination rather than repayment, it is in their bestinterest to ensure a higher funding probability in theshort term. However, borrowers, lenders, platforms,and regulators will all be well advised to take intoaccount the impact on long-term repayment, whichmay not receive as much attention as short-term ben-efits such as funding speed.

7.2. Contributions to LiteratureOur paper contributes to the growing literature inonline peer-to-peer lending by systematically doc-umenting intended and unintended (and previ-ously unknown) consequences of market mechanismchanges. We exploit an exogenously imposed regimechange to study the impact of market mechanismson transactional outcomes such as funding probabil-ities and repayment likelihood, and on overall socialwelfare. Furthermore, by comparing the impact ofauctions against posted prices, our paper also con-tributes to the long-standing broader literature onmarket mechanisms. A notable paper in that literatureis Einav et al. (2016), which documents an interestingtrend that eBay.com sellers increasingly prefer postedprices to auctions. However, as shown in Table 13,our paper is different from Einav et al. (2016) not justin the context that we study, but also in terms of thegoal, method and findings.

Dow

nloa

ded

from

info

rms.

org

by [

98.2

23.2

29.1

88]

on 1

5 Ju

ne 2

017,

at 0

9:05

. Fo

r pe

rson

al u

se o

nly,

all

righ

ts r

eser

ved.

Wei and Lin: Market Mechanisms in Peer-to-Peer LendingManagement Science, Articles in Advance, pp. 1–22, © 2016 INFORMS 21

Table 13 A Comparison of This Study vs. Einav et al. (2016)

Current study Einav et al. (2016)

Context differenceWho decides on which

mechanism to use?The platform; borrowers cannot opt out Each individual seller; sellers are not obliged to use

posted pricesWho sets the price

under posted prices?The platform Each individual seller

How did themechanism changetake place?

Instantaneous (overnight) and exogenous toborrowers and lenders

Gradual and endogenously chosen by each seller

Nature of the market A market for personal loans A market for physical products

Paper differenceResearch goal What impact market mechanisms have on

individual behaviors, transactionaloutcomes, and social welfare

What drives sellers to increasingly prefer fixed pricesto auctions

Identification The overnight switch in mechanisms “Seller experiments,” i.e., many sellers sell the sameitems using different mechanisms

Opposite findings Under posted prices, interest rate is higher,and probability of funding is higher

Under posted prices, price is higher (correspondingto lower interest rate in loan settings), andprobability of sale is lower

7.3. Generality of FindingsWhile our main analysis is based on data from Pros-per.com around the time of a natural experiment thatoccurred in 2010, the findings nonetheless should stillbe relevant today and should generalize well to otherpeer-to-peer lending platforms. First, from a tem-poral point of view, Prosper.com is still similar towhat it was around the time of the regime change.When we examine data from 2013 (the most recenttime when Prosper.com makes its detailed data pub-licly available), the most popular three categories ofloan requests have always been debt consolidation,home improvement, and businesses. In addition, therelative forces between the demand and supply offunds are highly comparable as well: We find that theratio between borrower requested funds and investorinvestments, and the ratio between number of lendersand the number of loan requests, are both statisti-cally indistinguishable between the time of the natu-ral experiment and 2013. Second, the incentives of allmajor stakeholders (platform, borrower, and lender)that we formally modeled are consistent with most,if not all, peer-to-peer lending platforms that we areaware of. In addition, the posted-price mechanismon Prosper.com is essentially the same as that imple-mented on its main rival, LendingClub.com, andother platforms outside the United States. The auctionmechanism that Prosper.com previously used is stillwidely seen in many peer-to-peer lending platformsaround the globe. For these reasons, our findings stillhave important relevance today and for other peer-to-peer lending platforms.

7.4. Future ResearchOur study is situated in the context of P2P lend-ing, a debt form of crowdfunding. Yet, the issue of

market mechanism is a fundamental one in othertypes of crowdfunding as well, and this can bea fertile direction for future research. Even thoughthe concept of initial interest rates may manifestitself differently in other crowdfunding formats, aslong as the payoff function of platforms is short-term driven—i.e., deduction of transaction fees attime of funding, be it debt-, equity- or reward-basedcrowdfunding—platforms will not surprisingly pro-mote short-term success over long-term prospects. Fora nascent industry, this is perhaps a “necessary evil”because platforms have to demonstrate their prof-itability to potential investors; the promise of crowd-funding to transform traditional finance and broadenaccess to capital will not materialize if platformscannot even sustain themselves. But as the marketmatures and leading platforms become public com-panies, a longer-term orientation will serve the bestinterest of all stakeholders. One may argue that inthe long run, investors will learn, and platforms ulti-mately will pay for the long-term lower performance.That, however, crucially depends on a sufficient levelof competition within the industry, which will bechallenging due to the fact that these platforms aretwo-sided markets with strong network effects. Link-ing market mechanisms to interplatform competitions,therefore, is also an interesting area of future empir-ical research. While the choice of market mechanismwill most likely always lie with the platforms, indus-try self-regulations or government oversight may benecessary in terms of either a more transparent pricingprocess (i.e., the initial interest rate or firm valuation),a revenue model that takes into account long-termperformance (e.g., linking platform revenue to debtrepayment, rewards shipment, or venture success), orfurther innovations (e.g., other market mechanisms).

Dow

nloa

ded

from

info

rms.

org

by [

98.2

23.2

29.1

88]

on 1

5 Ju

ne 2

017,

at 0

9:05

. Fo

r pe

rson

al u

se o

nly,

all

righ

ts r

eser

ved.

Wei and Lin: Market Mechanisms in Peer-to-Peer Lending22 Management Science, Articles in Advance, pp. 1–22, © 2016 INFORMS

Supplemental MaterialSupplemental material to this paper is available at http://dx.doi.org/10.1287/mnsc.2016.2531.

AcknowledgmentsThe authors contributed equally to this research. Theythank Keisuke Hirano, Tanjim Hossain, Karthik Kannan,Christopher Lamoureux, Adair Morse, Chris Parker, JeffPrince, Stanley Reynolds, Siva Viswanathan, John Wooders,and Mo Xiao, as well as seminar participants at the Univer-sity of Arizona, Purdue University, the 2013 Conference onInformation Systems and Technology, the 2013 Workshopon Information Systems and Economics, the 12th Interna-tional Industrial Organization Conference, the Conferenceon Internet Search and Innovation at Northwestern Uni-versity, the Academic Symposium on Crowdfunding at theUniversity of California, Berkeley, and the Platform StrategyResearch Symposium at Boston University for helpful com-ments and suggestions. All errors remain the authors’ own.

ReferencesAbadie A, Imbens G (2006) Large sample properties of match-

ing estimators for average treatment effects. Econometrica 74(1):235–267.

Arora A, Krishnan R, Telang R, Yang Y (2010) An empirical analysisof software vendors patch release behavior: Impact of vulner-ability disclosure. Inform. Systems Res. 21(1):115–132.

Ausubel LM, Cramton P, Pycia M, Rostek M, Weretka M (2014)Demand reduction and inefficiency in multi-unit auctions. Rev.Econom. Stud. 81(4):1366–1400.

Back K, Zender JF (1993) Auctions of divisible goods: on therationale for the treasury experiment. Rev. Financial Stud. 6(4):733–764.

Bester H (1985) Screening vs. rationing in credit markets withimperfect information. Amer. Econom. Rev. 75(4):850–855.

Biais B, Bossaerts P, Rochet J-C (2002) An optimal IPO mechanism.Rev. Econom. Stud. 69(1):117–146.

Bulow J, Klemperer P (1996) Auctions versus negotiations. Amer.Econom. Rev. 86(1):180–194.

Burtch G, Ghose A, Wattal S (2013) An empirical examination ofthe antecedents and consequences of contribution patterns incrowd-funded markets. Inform. Systems Res. 24(3):499–519.

Chen H, De P, Hu J, Hwang B (2014) Wisdom of crowds: The valueof stock opinions transmitted through social media. Rev. Finan-cial Stud. 27(5):1367–1403.

Chen J, Chen X, Song X (2007) Comparison of the group-buyingauction and the fixed pricing mechanism. Decision Support Sys-tems 43(2):445–459.

Chen N, Ghosh A, Lambert NS (2014) Auctions for social lending:A theoretical analysis. Games Econom. Behav. 86:367–391.

Dellarocas C, Malone TW, Laubacher R (2010) Harnessing crowds:Mapping the genome of collective intelligence. Sloan Manage-ment Rev. 51(3):21–31.

Einav L, Farronato C, Levin J, Sundaresan N (2016) Auctions ver-sus posted prices in online markets. Working paper, StanfordUniversity, Stanford, CA.

Freedman S, Jin GZ (2011) Learning by doing with asymmet-ric information: Evidence from Prosper.com. NBER WorkingPaper 16855, National Bureau of Economic Research, Cam-bridge, MA.

Hahn J, Lee G (2013) Archetypes of crowdfunders backing behav-iors and the outcome of crowdfunding efforts: An exploratory

analysis of kickstarter. Working paper, National University ofSingapore, Singapore.

Hammond RG (2010) Comparing revenue from auctions andposted prices. Internat. J. Indust. Organ. 28(1):1–9.

Hammond RG (2013) A structural model of competing sellers: Auc-tions and posted prices. Eur. Econom. Rev. 60(1):52–68.

Hortaçsu A, McAdams D (2010) Mechanism choice and strategicbidding in divisible good auctions: An empirical analysis ofthe turkish treasury auction market. J. Political Econom. 118(5):833–865.

Hosanagar K, Han P, Tan Y (2010) Diffusion models for peer-to-peer (P2P) media distribution: On the impact of decentralized,constrained supply. Inform. Systems Res. 21(2):271–287.

Iyer R, Khwaja AI, Luttmer EFP, Shue K (2016) Screening peerssoftly: Inferring the quality of small borrowers. ManagementSci. 62(6):1554–1577.

Kawai K, Onishi K, Uetake K (2014) Signaling in online creditmarkets. Working paper, University of California, Berkeley,Berkeley.

Kim K, Hann I-H (2015) Does crowdfunding democratize access tofinance? A geographical analysis of technology projects. Work-ing paper, City University of Hong Kong, Kowloon.

Krishna V (2009) Auction Theory (Academic Press, San Diego).Lemmon M, Ni SX (2014) Differences in trading and pricing

between stock and index options. Management Sci. 60(8):1985–2001.

Lin M, Viswanathan S (2016) Home bias in online investments: Anempirical study of an online crowdfunding market. Manage-ment Sci. 62(5):1393–1414.

Lin M, Prabhala NR, Viswanathan S (2013) Judging borrowers bythe company they keep: Friendship networks and informa-tion asymmetry in online peer-to-peer lending. Management Sci.59(1):17–35.

Liu TX, Yang J, Adamic L, Chen Y (2014) Crowdsourcing with all-pay auctions: A field experiment on taskcn. Management Sci.60(8):2020–2037.

Renton P (2010) Prosper.com ending their auction process Dec19th. Lend Academy (December 16), http://www.lendacademy.com/prosper-com-ending-their-auction-process-dec-19th/.

Rigbi O (2013) The effects of usury laws: Evidence from the onlineloan market. Rev. Econom. Statist. 95(4):1238–1248.

Rosenbaum PR (2002) Observational Studies (Springer, New York).Saunders EM Jr (1993) Stock prices and wall street weather. Amer.

Econom. Rev. 83(5):1337–1345.Scrucca L, Santucci A, Aversa F (2007) Competing risk analysis

using R: An easy guide for clinicians. Bone Marrow Transplan-tation 40(4):381–387.

Sekhon JS (2011) Multivariate and propensity score matching soft-ware with automated balance optimization: The matchingpackage for R. J. Statist. Software 42(7):1–52.

Stiglitz JE, Weiss A (1981) Credit rationing in markets with imper-fect information. Amer. Econom. Rev. 71(3):393–410.

Sun M (2012) How does the variance of product ratings matter?Management Sci. 58(4):696–707.

Wang JJD, Zender JF (2002) Auctioning divisible goods. Econom.Theory 19(4):673–705.

Wang R (1993) Auctions versus posted-price selling. Amer. Econom.Rev. 83(4):838–851.

Wang X, Montgomery A, and Srinivasan K (2008) When auctionmeets fixed price: A theoretical and empirical examination ofbuy-it-now auctions. Quant. Marketing Econom. 6(4):339–370.

Wilson R (1979) Auctions of shares. Quart. J. Econom. 93(4):675–689.Zhang J, Liu P (2012) Rational herding in microloan markets. Man-

agement Sci. 58(5):892–912.Zhang P (2009) Uniform price auctions and fixed price offerings

in IPOs: An experimental comparison. Experiment. Econom.12(2):202–219.

Dow

nloa

ded

from

info

rms.

org

by [

98.2

23.2

29.1

88]

on 1

5 Ju

ne 2

017,

at 0

9:05

. Fo

r pe

rson

al u

se o

nly,

all

righ

ts r

eser

ved.