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The Threat of Exclusion and Implicit ContractingMartin Brown, Marta Serra-Garcia

To cite this article:Martin Brown, Marta Serra-Garcia (2017) The Threat of Exclusion and Implicit Contracting. Management Science63(12):4081-4100. https://doi.org/10.1287/mnsc.2016.2572

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MANAGEMENT SCIENCEVol. 63, No. 12, December 2017, pp. 4081–4100

http://pubsonline.informs.org/journal/mnsc/ ISSN 0025-1909 (print), ISSN 1526-5501 (online)

The Threat of Exclusion and Implicit ContractingMartin Brown,a Marta Serra-Garciab

a Swiss Institute of Banking and Finance, University of St. Gallen, CH-9000 St. Gallen, Switzerland; bRady School of Management,University of California, San Diego, La Jolla, California 92093Contact: [email protected] (MB); [email protected] (MS-G)

Received: May 18, 2015Revised: February 10, 2016; May 26, 2016Accepted: June 2, 2016Published Online in Articles in Advance:November 3, 2016


Copyright: © 2016 INFORMS

Abstract. Implicit contracts can mitigate moral hazard in labor, credit, and product mar-kets. The enforcement mechanism underlying an implicit contract is the threat of exclu-sion: the agent fears that he will lose future income if the principal breaks off the rela-tionship. This threat may be very weak in environments where an agent can appropriateincome-generating resources provided by the principal. For example, in credit marketswith weak creditor protection, borrowers may be able to appropriate borrowed fundsand generate investment income without requiring further loans. We examine implicitcontracting in a lending experiment where the threat of exclusion is exogenously varied.We find that weak exclusion undermines implicit contracting: it leads to a more frequentbreakdown of credit relationships as well as to smaller loans.

History: Accepted by John List, behavioral economics.Funding: This project was funded by internal grants from CentER at Tilburg University, the University

of St. Gallen, and the University of California, San Diego.Supplemental Material: Data and the online appendix are available at https://doi.org/10.1287/

mnsc.2016.2572.

Keywords: economics • microeconomic behavior • behavior and behavioral decision making • finance • corporate finance • implicit contracting

1. IntroductionEconomic theory suggests that self-enforcing agree-ments, i.e., implicit contracts, can mitigate moral haz-ard in labor, credit, andproductmarkets (e.g., Bull 1987,Boot and Thakor 1994, Klein and Leffler 1981). Existingexperimental evidence documents that self-enforcingagreements emerge and are efficiency enhancing inbilateral contracting settings as well as in market con-texts with endogenous partner choice (Brown et al.2004, Fehr et al. 2009). For managers, implicit con-tracting implies that conflicts of interest with employ-ees, creditors, or suppliers may be resolved throughrepeated interaction rather than through monitoring,incentive contracts, or a reallocation of ownership.The enforcement mechanism underlying an implicit

contract is the threat of exclusion: the agent fears thathe will lose future income if the principal breaks offthe relationship. In this paper, we emphasize that insome markets and business relations, the threat ofexclusion is inherently weak. In these environments,implicit contracting may not be an effective instrumentto mitigate moral hazard, and managers may thereforeneed to resort to more formal and costly enforcementmechanisms.

The threat of exclusion is especially weak in envi-ronments where the agent can appropriate income-generating resources from the principal and canindependently put these resources to productive use.For example, in credit environments with weak credi-tor protection, borrowersmay appropriate and reinvestborrowed funds (Bond and Krishnamurthy 2004,

Bulow and Rogoff 1989). In the context of foreign directinvestment, local investment partners (e.g., the hostgovernment) may expropriate the physical and finan-cial capital of foreign investors (Thomas and Worrall1994). In professional services such as consulting, legaladvice, or wealthmanagement, advisors may persuadethe firm’s clients to follow them when they leave thefirm or set up their own business.1 In such environ-ments, the agent (borrower, investee, employee) mayno longer need to contract with the principal (lender,investor, employer) to maintain income generation.

We implement a laboratory experiment to investigatehow implicit contracting is affected when the threat ofexclusion is weak. Our main treatments study implicitcontracting in the context of repeated, bilateral lend-ing. In each period, the lender decides how much tolend to the borrower and what repayment to request.The borrower earns a nonstochastic investment returnthat depends on the loan size and can decide whetherto strategically default or not. In our main treatment,the weak exclusion (WE) treatment, a borrower whodefaults can continue to use the borrowed funds toinvest in future periods. In our control treatment, thestrong exclusion (SE) treatment, a defaulting borrowermust liquidate his investment and consume the pro-ceeds in the same period. If he wants to invest in sub-sequent periods, the borrower must go back to thelender for a new loan. This treatment closely resem-bles the design of existing experimental studies thatstudy repeated investment games (for an overview,see Camerer 2003). By comparing the outcomes of the

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Brown and Serra-Garcia: The Threat of Exclusion and Implicit Contracting4082 Management Science, 2017, vol. 63, no. 12, pp. 4081–4100, ©2016 INFORMS

WE and SE treatments, we examine how the ability oflenders to exclude defaulting borrowers from futureincome generation affects implicit contracting.We derive predictions under the assumption that

there is a share of nonidentifiable social borrowerswho repay loans even in a one-shot situation (Krepset al. 1982).2 In the SE treatment, an implicit contractingequilibrium with maximum loan sizes and full repay-ment until the penultimate period is feasible. Borrow-ers have a strong incentive to repay, since they willotherwise be cut off from future loans and thus invest-ment. By contrast, in the WE treatment, the threat ofdiscontinuing a credit relationship is a weaker dis-ciplining device, since, upon default, borrowers cancontinue to invest the funds already borrowed. Twodifferent types of equilibria can emerge: first, implicitcontracting equilibria in which lenders “start small”(offer low initial loans and repayment-contingent loanincreases to establish dynamic incentives for borrow-ers to repay), and second, screening equilibria in whichlenders offer high initial loans to borrowers to screenout selfish agents (who will default). Hence, from atheoretical perspective, we show that weak exclusioncan lead to either smaller loan sizes or an earlier break-down of credit relationships.Our results show both predicted effects of weak

exclusion. First, we find that credit relationships aremore likely to break down in the WE treatment. By theend of the first period, only 44% of all relationships arecharacterized by a loan offered, accepted, and repaidin the WE treatment, compared to 73% in the SE treat-ment. In accordance with screening equilibria, we findthat in the initial period of the WE treatment (but notthe SE treatment), default is more likely for large loansizes. Second, we find that credit relationships in theWE treatment feature smaller loans than those in theSE treatment. In accordance with the implicit contract-ing equilibria, a larger fraction of lenders in the WEtreatment offer small loan sizes in the initial period.

In robustness tests, we document that our maintreatment effects are moderated in competitive marketconditions. We replicate our experiment with lendercompetition; i.e., each borrower is matched with twolenders who can make competing loan offers in eachperiod. Under lender competition, we find that self-enforcing credit relationships are also less frequentand loan sizes are smaller in the weak exclusioncondition than in the strong exclusion condition. How-ever, lender competition mitigates the negative treat-ment effect of weak exclusion on the early breakdownof credit relationships. This can be explained by thefact that screening equilibria are no longer feasibleunder lender competition. Moreover, competition low-ers interest rates and thus reduces the incentives ofborrowers to default in the weak exclusion condition.

The main contribution of this paper is to provideevidence that the threat of exclusion is crucial to

the efficacy of self-enforcing agreements. The exist-ing experimental literature has explored two condi-tions under which implicit contracting may not be aperfect substitute for third-party enforcement: lendercompetition and stochastic investment returns. Com-petition between lenders could potentially weaken bor-rowers’ incentives to repay a given lender as they mayturn to other lenders after default. Similarly, stochasticinvestment returns may limit the scope for relationalcontracts as lenders cannot perfectly identify and pun-ish strategic defaults. Brown and Zehnder (2007) showthat, even in the presence of competition, relationalcontracts emerge and lead to large volumes of credit.Fehr and Zehnder (2009) find that even with stochas-tic investment returns, relational contracts emerge andsustain high credit volumes. In contrast to these stud-ies, we document that when agents can appropriateincome-generating resources from principals, implicitcontracting may be seriously impaired.3The second contribution of our study is that we

examine how the threat of exclusion impacts on thetime structure of implicit contracts. Previous theoreticalwork has examined the time structure of self-enforcingagreements and suggested that asymmetric informa-tion about players’ types may explain “starting small”in investment contexts (Ghosh and Ray 1996, 2016;Rauch and Watson 2003; Sobel 1985) and in prison-ers’ dilemmas (see Watson 1999, 2002; Andreoni andSamuelson 2006). Starting small—or “progressive lend-ing,” as it is often termed in credit market contexts—iscommonly observed in environments with weak cred-itor protection, for example, in microfinance (Morduch1999, Armendariz and Morduch 2006). However, thereis no evidence to date documenting that weak creditorprotection is a determinant of “progressive lending.”Our results suggest that weak creditor protection canlead to smaller loan offers. However, we find “progres-sive lending,” i.e., increasing loan sizes over time, inde-pendent of the threat of exclusion.4

The rest of this paper is organized as follows. InSection 2, we describe the experimental design. In Sec-tion 3, we outline the predictions. We report our exper-imental results in Sections 4 and 5. Section 6 concludes.

2. Experimental DesignWe study the consequences of the threat of exclusionfor self-enforcing agreements by focusing on repeated,bilateral lending (and use a credit market framinghenceforth). We implement two treatments, based on arepeated investment game (Berg et al. 1995). In robust-ness tests, we adapt our main treatments to allow forlender competition. We report on these competitiontreatments in Section 5.

2.1. Strong Exclusion TreatmentIn the strong exclusion treatment, one lender and oneborrower are paired for seven periods. We choose a

Brown and Serra-Garcia: The Threat of Exclusion and Implicit ContractingManagement Science, 2017, vol. 63, no. 12, pp. 4081–4100, ©2016 INFORMS 4083

finite horizon game because it allows us to identify theemergence of self-enforcing implicit agreements.5 Wechoose seven periods rather than two or three to beable to clearly separate “starting small” in loan sizesfrom the potential end-game effect, i.e., a reduction ofloan sizes in the last periods of the game.In each period t � {1, . . . , 7}, the borrower has an

investment opportunity: he can invest the amountIt ∈ {0, 1, 2, 3, . . . , 10}, which yields a certain grossreturn of vIt , with v � 3 in our experiment. We restrictthe maximum investment size to 10 in each period.The investment amount of the borrower in each periodIt � Ct + St is equal to his capital Ct and the loan sizeSt he receives from the lender. In all periods of the SEtreatment, the borrower has zero capital Ct � 0. Thus,in accordance with previous experiments on repeatedinvestment games (e.g., Cochard et al. 2004), borrowersin the SE treatment start from scratch in each periodand can only invest if they obtain a loan.The decision structure in each period is as

follows:• Loan offer: The lender receives an endowment of

10 units at the beginning of each period. The lendercan offer a loan size of St ∈ [0, 10] to the borrower. Thelender also chooses her requested repayment Rt , whereRt ∈ [0, vSt].

• Loan acceptance: If the lender chooses an offer witha strictly positive loan St > 0, the borrower must decidewhether to accept (At � 1) or reject the offer (At � 0).

• Repayment decision: If the borrower accepts a loanoffer (St ,Rt), he decides whether to make the repay-ment requested by the lender (Dt � 0) or default(Dt � 1).6Both the lender and the borrower receive a sym-

metric “reservation” income of 10 points per period, ifthey decide not to trade. This design choice was madeso that asymmetric reservation payoffswould not affectthe decisions of lenders to offer credit. The incomeof the lender in each period is equal to her reserva-tion payoff plus her net income from lending as shownbelow:

πt �

10 if no loan (St � 0 or At � 0),10− St +Rt

if loan repaid (St > 0,At � 1,Dt � 0),10− St if loan default (St > 0,At � 1,Dt � 1).

The income of the borrower is equal to his reserva-tion payoff plus his investment income v · It � v · Stminus the repayment he makes to the lender Rt :

ut �

10 if no loan (St �0 or At �0),10+ v ·St −Rt

if loan repaid (St > 0,At �1,Dt �0),10+ v ·St if loan default (St > 0,At �1,Dt �1).

At the end of each period, the lender is informed aboutthe borrower’s repayment decision. The lender and theborrower are informed of their own and their partner’spayoffs for the period. They also see an overview ofthe history of their bilateral interactions in previousperiods, showing past loan sizes and requested repay-ments of the lender, and acceptance and repaymentsby the borrower.

2.2. Weak Exclusion TreatmentIn the weak exclusion treatment a lender and a bor-rower are also paired for seven periods and make thesame decisions as in the SE treatment in each period.The WE treatment differs from the SE treatment onlywith respect to the consequences of a loan default forthe borrower’s current period payoff and his capital.In the WE treatment, the borrower has zero capitalin period 1. However, if the borrower receives a loanand does not repay it, he can keep the lender’s fundsfor future investment. We assume that borrowers whodefault in period t automatically have the loan princi-pal St added to their capital for all subsequent periods.The borrower liquidates his capital (and consumes theproceeds) in the final period. The capital of a borrowerin periods t � {2, . . . , 7} thus equals the sum of the bor-rowed funds which he did not repay:

Ct �

t−1∑k�1

Dk · Sk .

The fact that we force borrowers to reinvest fundsthat they keep after default, rather than allowing themto decide whether to consume or reinvest them, seemsrestrictive. We chose this design for two reasons. First,we wanted to simplify the game as much as possibleby abstracting from endogenous consumption/savingdecisions.7 Second, reinvestment of loaned funds is theoptimal strategy of a borrower who has defaulted.

The income of the borrower in periods t � {1, . . . , 6}is equal to his reservation payoff plus his investmentincome v · It , minus the repayment he makes to thelender (Rt) and minus the capital that he keeps forthe subsequent period, Ct+1 � Ct + Dt · St . In periodst � {1, . . . , 6}, the capital is thus deducted from theinvestment income and transferred to the subsequentperiod, leading to the following payoffs:

ut�1,...,6�

10+ (v−1) ·Ct if no loan (St �0 or At �0),10+ (v−1) ·Ct + v ·St −Rt

if loan repaid (St > 0,At �1,Dt �0),10+ (v−1) · (Ct +St)

if loan default (St > 0,At �1,Dt �1).

At the end of period 7, the borrower liquidates hiscapital and consumes it. We make this assumption toensure that repayment behavior in the final period of


the WE treatment has the same payoff implications asin the SE treatment. His payoff in this period is thus

ut�7 �

10+ v ·Ct if no loan (St � 0 or At � 0),10+ v · (Ct + St) −Rt

if loan repaid (St > 0,At � 1,Dt � 0),10+ v · (Ct + St)

if loan default (St > 0,At � 1,Dt � 1).

As in the SE treatment, both the lender and the bor-rower are provided with an overview of the history ofthe relationship, including any capital accumulated bythe borrower.

2.3. DiscussionSome features of our experimental design warrantdetailed discussion. First, it is important to clarify theunderlying assumptions about the debt-enforcementenvironment in our two treatments. In both theWE andthe SE treatment, borrowers can strategically defaulton their loans. If the borrower defaults, the lender can-not recover any part of the loaned funds. This designfeature is common to previous experimental studiesof repeated investment games (e.g., Cochard et al.2004) and relational contracting in credit markets (e.g.,Brown and Zehnder 2007). The assumption of a zerorecovery rate implies either a very costly process ofenforcing debt or legal impediments to seizing assetsof borrowers.

The World Bank Doing Business database docu-ments that inmany countries the judicial procedures toenforce debt are indeed very costly, even when lendershave secured claims.8 In 91 of 198 countries, the esti-mated recovery rate on a secured loan amounts to lessthan one-third of the claim. Costly debt enforcementis particularly prevalent in low-income and emergingeconomies and negatively impacts on credit marketdevelopment (Djankov et al. 2008). Recovery rates maybe low in high-income countries as well. For exam-ple, in many U.S. states, a broad range of householdassets are exempt from the bankruptcy process (see,e.g., White 1998),9 with negative consequences for thesupply of consumer credit (Gropp et al. 1997) andsmall business finance (Cerqueiro and Penas 2017).Moreover, corporate borrowers may be able to tun-nel assets out of their current business (Johnson et al.2000, Jiang et al. 2010). Thus, in both low-income andhigh-income countries, the assumption of a low recov-ery rate on defaulted loans seems reasonable for manycredit markets.The difference between the SE and WE treatments

lies in what a borrower can do with the funds whenhe defaults. In the SE treatment, if the borrowerdefaults, he must liquidate his investment and con-sume the proceeds within the same period. This treat-ment inherently implies that although the recovery

rate for lenders is low, the debt enforcement pro-cess is very fast. Borrowers cannot hold on to andreinvest appropriated funds. By contrast, in the WEtreatment, a defaulting borrower can retain borrowedfunds and reinvest these in future periods. This treat-ment assumes that the debt enforcement process isnot only very costly, but also very slow. The DoingBusiness database documents that, especially in low-income countries, the debt enforcement process is veryslow. For example, in 109 of 198 countries, the judi-cial enforcement process for secured claims takes morethan two years in the case of a bankruptcy. And unsur-prisingly, those countries with low recovery rates onsecured debt are typically characterized by lengthyenforcement processes. Our WE treatment capturesthis environment by allowing a defaulting borrower tocontinue to use borrowed funds for future investmentwithout having to surrender either his assets or prof-its to the lender. Anecdotal evidence suggests that incountries with weak creditor protection, borrowers doappropriate and continue to use borrowed funds, forexample, by tunneling them out of existing businessesinto new ones.10

A further assumption that warrants discussion is theinvestment limit for borrowers. We hold the invest-ment opportunity of the borrower constant over time toexamine credit rationing over the course of a relation-ship. If, for example, we observe that a lender offers asmall loan in period 1 and she increases it over time,we know that the borrower was credit constrained inperiod 1. By contrast, when field studies observe ris-ing loan schedules over time (Ioannidou and Ongena2010, Kirschenmann 2016), they typically cannot dis-tinguish whether this is due to improved investmentopportunities of the borrower or a relaxation of creditconstraints.

2.4. ProceduresWe implement our two main treatments in a labora-tory experiment. A total 186 students participated inthe WE and SE treatments. Our first set of sessions wasimplemented at Tilburg University (90 participants).Our second set of sessions was implemented at theUniversity of California, San Diego (96 participants).Each subject could only participate in one session, andin each session, only one of the treatments was imple-mented. As shown in Online Appendix D, we do notobserve a significant difference in behavior in the lend-ing game across locations, except for a small differencein acceptance rates in the SE treatment. We thus poolthe observations from Tilburg University and UC SanDiego. Additionally, we include a location fixed effectin all regressions.

At the beginning of each session, participants wererandomly assigned to the role of either a borroweror a lender. These roles were fixed for the whole ses-sion. Each player formed part of a matching group,


composed of three lenders and three borrowers. Eachplayer played three rounds of our lending game: eachlender (borrower) repeated the lending game with thethree different borrowers (lenders) in her or his match-ing group. As a consequence, we observe nine lender–borrower relationships for each matching group. In theWE treatment there were 15 matching groups, and inthe SE treatment there were 16 matching groups. Thisimplies that we observe 135 lender–borrower relation-ships in the WE treatment and 144 relationships in theSE treatment.The experiment was programmed and conducted

with the experimental software z-Tree (Fischbacher2007). All sessions lasted approximately 90 minutes.Subjects at TilburgUniversity received a show-up fee ofe5 and an additional e1 for every 25 points earned dur-ing the experiment. Subjects at UC San Diego receiveda show-up fee of US$10 and an additional US$1 forevery 20 points earned during the experiment. Onaverage, subjects earned e20.9 or US$30.0 for theirparticipation.11Before starting our lending experiment, each sub-

ject read a detailed set of instructions. The instructionscan be found in Online Appendix A. The experimen-tal instructions were framed in a credit context.12 Afterreading the instructions, participants had to pass a testwith control questions. The lending game did not startuntil all subjects had correctly answered all controlquestions.Behavior in our lending game might be affected by

individual behavioral traits. First, individual risk pref-erences affect decisions in investment games (Eckel andWilson 2004, Schechter 2007, Houser et al. 2010). Sec-ond, the level of strategic reasoning, i.e., the antici-pation of what other subjects in the matching groupmight do, can affect behavior significantly (Nagel1995). Third, social preferences, i.e., reciprocal motivesand fairness preferences of the borrower, as well asthe anticipation of these preferences, i.e., trust by thelender, should affect behavior in our experiment (see,e.g., Roe and Wu 2009).

Participants took part in three “games” aimed atmeasuring their levels of risk aversion (using a mul-tiple choice list with a fixed lottery and increasingfixed payments), strategic reasoning (using a guess-ing game), and trust and trustworthiness (using a one-shot strategy-method trust game). In our first set ofsessions (Tilburg), these games took place before themain experiment (we label them “preexperiment”). Inour second set of sessions (San Diego), the games tookplace after the main experiment (we label them “post-experiment”).13 Online Appendix B describes thesepre- and postexperiment games and provides sum-mary statistics for their outcomes in our two treat-ments. We find no significant differences in behavior inthese games across treatments in either location.14

3. PredictionsUnder the assumption of common knowledge of ratio-nality and selfishness of all market participants, thepredictions for all three treatments are straightforward.Since repayments are not enforceable, a borrower’s bestresponse is to never repay a loan in a one-period game.As it is public knowledge that the WE treatment andthe SE treatment last for a finite number of periods, abackward induction argument ensures that there is nolending in any period of either treatment.

A broad body of experimental evidence suggests,however, that not all people will maximize monetarypayoffs in our experiment. Social preferences basedon reciprocity (Dufwenberg and Kirchsteiger 2004) ordistributional concerns (Fehr and Schmidt 1999) caninduce borrowers to repay loans even in one-shot inter-actions. Evidence from one-period investment gamesin the lab (Berg et al. 1995) and in the field (Karlan 2005)suggests that a substantial share of second movers, i.e.,borrowers in our context, exhibit such social prefer-ences and repay.

In the following we establish predictions for ourtreatments under the assumption that some (noniden-tifiable) borrowers are conditionally reciprocal: theyare willing to repay a loan in a one-shot situation, aslong as the repayment requested by the lender does notexceed a threshold value. We assume that this thresh-old r̄ can be characterized by the maximum (gross)interest rate it � Rt/St ≤ r̄ that a social borrower is will-ing to pay. We assume that the remaining borrowersare selfish in the sense that they never repay loans ina one-shot situation. The share of social borrowers pis assumed to be 1/r̄T ≤ p < 1/r̄. The assumption thatp < 1/r̄ implies that it is not profitable for risk-neutrallenders to lend in a one-shot game. The assumptionp ≥ 1/r̄T implies that a repeated game equilibrium inwhich selfish borrowers repay with positive probabil-ity in initial periods exists.15

The outcomes of our preexperimental and postex-perimental games, documented in Online Appendix B,suggests that there is a substantial share of social bor-rowers in both treatments. In particular, behavior inthe one-shot, strategy-method trust game suggests thatless than 15% of the subjects in the roles of borrowerscan be characterized as pure money maximizers, whoalways default in a one-shot situation. By comparison,more than 25% of the subjects behave as social bor-rowers who are willing to repay a loan as long as thedesired repayment implies that they earn at least one-half of the surplus. Applied to our experiment, thisfinding would imply that the above conditions on theshare of social borrowers is satisfied in our sample.16In the following we outline the main predictions for

both treatments. All proofs are presented in OnlineAppendix C.17 Since borrower types are a prioriindistinguishable, the WE and SE treatments can be


characterized as finitely repeated games of incom-plete information. Such games have multiple equilib-ria (Kreps et al. 1982). We distinguish between twotypes of equilibria and, within each type, concentrateon the profit-maximizing equilibria for the lender (as inThomas and Worrall 1994). In implicit contracting equi-libria, selfish borrowers imitate the behavior of socialborrowers during the first periods but default towardthe end of the game. In screening equilibria, selfish bor-rowers default in the first period, and from period 2onward the lender only extends credit to (now iden-tified) social borrowers. It is important to note that inboth treatments, the one-shot equilibrium of no lend-ing is also feasible.In the SE treatment, the profit-maximizing (and

surplus-maximizing) implicit contracting equilibriumfeatures loans of maximum size 10 in periods 1–6 anda smaller loan of 10 · r̄/v in period 7. The interest rateis it � r̄ in each period. Loan offers in periods t �

{2, . . . , 7} are contingent on the borrower repaying allpast loans. The incentive constraint of a selfish bor-rower in period t is as follows:

T−1∑k�t

(v − ik) · Sk + v · ST ≥ v · St . (ICSE)

Since loans are of size 10 for periods 1–6, ICSE issatisfied with inequality in these periods. The smallerloan size in period 7 implies that the constraint is satis-fied with equality in period 6. Thus, in this period theselfish borrower is indifferent between repaying anddefaulting, and defaults with a strictly positive prob-ability. This allows the lender to learn about the bor-rower’s type in period 6 and to break even in period 7.A screening equilibrium is not feasible in the SE

treatment. By definition, in such an equilibrium, self-ish borrowers would default with certainty in the firstperiod of the game. In the following periods, the lenderwould offer maximum loans of 10 to the borrowerswho did not default, i.e., social borrowers. However,given that the lender offers maximum loans in sub-sequent periods, a selfish borrower has no incentiveto default in the first period. It is impossible for thelender to offer a contract that does not meet ICSE in theinitial period if i1 ≤ r̄. We summarize these results inProposition 1.Proposition 1. In the SE treatment, the profit-maximizingimplicit contracting equilibrium features the maximumcredit volume in periods 1–6 and no defaults in periods 1–5.A screening equilibrium is not feasible in this treatment.In the WE treatment, the potential to reinvest bor-

rowed funds in future periods increases the borrower’sincentive to default. This can be seen from the selfishborrower’s incentive constraint for this treatment:

T−1∑k�t

(v − ik) · Sk + v · ST ≥ v · St +

T−1∑k�t

(v − 1) · St . (ICWE)

Implicit contracting equilibria are also feasible in theWE treatment. However, these equilibria must be char-acterized by “progressive lending”: to meet the bor-rower’s incentive constraint, the lender must start withnonmaximum loans and increase the loan size offeredto the borrower if he repays. The intuition for this resultis simple: if the lender offers the maximum loan of 10in period 1, a selfish borrower could default and rein-vest these funds in all future periods without payinginterest. The selfish borrower only stands to gain fromrepaying initial loans if future loans are higher.

In contrast to the SE treatment, a screening equilib-rium exists in the WE treatment. If the lender offersa large enough loan in the first period, a selfish bor-rower prefers to default straight away. For example,from ICWE we see that a selfish borrower will not repaya loan offer with S1 � 10 and i1 � r̄, while a social bor-rower will repay such a loan. These results are broughttogether in Proposition 2.

Proposition 2. In the WE treatment, an implicit contract-ing equilibrium must feature “progressive lending.” Loanoffers increase gradually over time and there are no defaultsin periods 1–5. In this treatment, a screening equilibrium isalso feasible in which selfish borrowers default with certaintyin the first period.

Based on the above predictions, we establish the fol-lowing empirical hypotheses. Our null hypothesis isthat there is no difference in observed lending out-comes between the SE and WE treatments: The sharesof self-enforcing credit relationships in which loans areoffered, accepted, and repaid for at least the first fiveperiods are similar. Moreover, the average loan sizesand interest rates are alike. Our alternative hypothesisis that we will observe a marked difference in lend-ing outcomes between the WE and SE treatments. Thenature of this difference will depend on the type ofequilibria that dominate empirically in the WE treat-ment. We outline the expected impact of weak exclu-sion if mainly implicit contracting equilibria emerge inthe WE treatment (H1) and if mainly screening equi-libria emerge (H2). Empirically, a combination of thesetwo types of equilibria is likely to occur.18

Hypothesis 1 (H1) (Implicit Contracting Dominates in theWE Treatment). In both treatments there is a similar shareof self-enforcing credit relationships, i.e., credit relationshipsthat are characterized by loan offers and loan repayment upto at least period 5. The average loan size in the SE treat-ment is higher than that in the WE treatment, as the WEtreatment is characterized by progressive lending. Loan sizesrise steadily in the WE treatment, while they exhibit a dropin the last period in the SE treatment. Interest rates do notdiffer between the treatments.

Hypothesis 2 (H2) (Screening Dominates in the WETreatment). In the WE treatment there is a lower share of


self-enforcing credit relationships than in the SE treatment.Loan sizes and interest rates offered by lenders do not dif-fer between the SE and WE treatments (except for the finalperiod).

4. Main Results4.1. Credit Relationships and Credit TermsIn this section, we test our main hypotheses by com-paring three outcomes of interest across the WE andSE treatments: the share of self-enforcing credit rela-tionships, i.e., relationships in which a loan is offered,accepted, and repaid for at least the first five periods,19as well as the average Loan size and the average Inter-est rate (requested repayment/loan size) for acceptedloan offers. Our unit of observation is matching-group averages. We hereby compare the outcomes ofthe 15 matching groups in the WE treatment to the16 matching groups in the SE treatment using two-sided nonparametric and parametric tests. Since weare comparing three outcomes, we correct for multi-ple hypothesis testing using Bonferroni adjustmentson nonparametric Mann–Whitney (MW) tests and theadjustment proposed by List et al. (2016) on parametrict-tests.20Figure 1 displays the share of credit relationships

in which a loan was offered, accepted, and repaid ineach period. Figure 1 reveals that credit relationshipsbreak down much more frequently in the WE treat-ment compared to the SE treatment. In the first period,

Figure 1. (Color online) Loans Offered, Accepted, and Repaid

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Notes. This figure displays the share of credit relationships that are characterized by a loan offer, a loan acceptance, and a loan repaymentin each period by treatment. The means and standard errors are calculated considering each matching group average as one independentobservation. The total number of credit relationships (matching groups) is 135 (15) in the WE treatment and 144 (16) in the SE treatment.

only 44% of the 135 relationships in the WE treatmentare characterized by a loan being offered, accepted, andrepaid, compared to 73% of the 144 relationships inthe SE treatment. This difference is driven by a lowernumber of loans offered (90% versus 99%), a loweracceptance ratio of offersmade (76% versus 89%), and alower repayment rate for offers that have been accepted(65% versus 84%) in the WE treatment.

The share of relationships featuring a loan offer inperiod 2 is 78% in the WE treatment and 92% in the SEtreatment. Thus, lenders not only continue those rela-tionships that survive the first period, but also attemptto restart many of the relationships that break down inperiod 1 (61% and 72% of the relationships that breakdown in period 1 in the WE and SE treatments, respec-tively, feature a loan offer in period 2). However, theshare of relationships in which the period 2 offer is alsoaccepted and repaid again declines to 44% in the WEtreatment and 71% in the SE treatment. This patternrepeats itself through period 6.21

Figure 1 suggests that the SE treatment is character-ized by more self-enforcing credit relationships thanthe WE treatment. This conclusion is confirmed by theend-game behavior in period 7. In the SE treatment, themajority of credit relationships fall subject to the end-game effect: Borrowers default more frequently, andmore lenders refrain from offering credit in the finalperiod.

In line with Figure 1, we observe a substantialdifference in the share of self-enforcing contracting


Table 1. Main Treatment Effects

Mean Mann–Whitney test t-test

Bonferroni List et al. (2016)Outcome variable WE treatment SE treatment Naïve p-value adjusted p-value Naïve p-value adjusted p-value

Share of self-enforcing relationships 0.12 0.48 0.0000 0.0000 0.0003 0.0003Loan size 5.00 6.90 0.0044 0.0132 0.0043 0.0083Interest rate 1.95 1.94 0.9842 1.0000 0.9290 0.9290

Notes. This table presents the means of our three main outcome variables for each treatment. We also present the results of the Mann–Whitneytest on the treatment differences, including the naive p-values and the Bonferroni adjusted p-values for multiple hypothesis testing. We alsopresent the results of t-tests for the treatment differences, including the naive p-values and the p-values using the adjustment for multiplehypothesis testing proposed by List et al. (2016).

relationships, i.e., relationships in which a loan isoffered, accepted, and repaid for at least the first fiveperiods, between the SE treatment (48%) andWE treat-ment (12%). Table 1 displays the results of the non-parametric and parametric tests, which reveal that thistreatment difference is statistically significant.Figure 2 presents the credit terms for accepted loan

offers, showing the average Loan size (panel A) and theaverage Interest rate (panel B) by period. The treatmentdifference between the average loan size increases fromperiod 1 (5.20 versus 5.97) to period 7 (5.25 versus 7.89).Over all periods, the average loan size is significantlysmaller in the WE treatment (5.00) than in the SE treat-ment (6.90). As shown in Table 1, this difference isstatistically significant. Panel B of Figure 2 documentsthat the average interest rate is similar in all periodsin both treatments. Average interest rates do not differsignificantly between the WE treatment (1.94) and theSE treatment (1.95), as shown in Table 1. The observedinterest implies (upon repayment) an equal sharing ofsurplus between the lender and borrower, in accor-dance with our behavioral assumptions.

Figure 2. (Color online) Contract Terms of Accepted Loan Offers

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Notes. This figure displays the contract terms of accepted loan offers by period and treatment. Panel A shows the Loan size. Panel B shows theInterest rate (requested repayment/loan size). The means and standard errors are calculated considering each matching group average as oneindependent observation.

The impact of the WE treatment on credit relation-ships and credit terms has implications for the distri-bution of payoffs between the lender and the borrower.Lenders earn less in the WE treatment than in the SEtreatment (10.74 versus 13.04 per period). In contrast,borrowers earn more in the WE treatment than in theSE treatment (20.20 versus 17.98 per period).

Result 1 (Credit Relationships and Credit Terms). In theWE treatment there is a lower share of self-enforcing creditrelationships than in the SE treatment. The average loan sizeis also smaller in theWE treatment than in the SE treatment.Interest rates do not differ across treatments.

To what extent are the findings presented in Result 1noteworthy? Maniadis et al. (2014) argue that thejudgment of novel empirical findings should not relysolely on an assessment of statistical significance. Theyemphasize that the probability that a significant treat-ment effect represents a true association dependson the level of significance (α) and power of ourempirical test (1 − β) as well as our prior (π) aboutthe probability with which our alternative hypothesis


Table 2. Poststudy Probability Calculations

Power (1− β)

Prior (π) 0.75 0.8 0.9 0.95 0.99

0.1 0.63 0.64 0.67 0.68 0.690.2 0.79 0.80 0.82 0.83 0.830.3 0.87 0.87 0.89 0.89 0.890.4 0.91 0.91 0.92 0.93 0.930.5 0.94 0.94 0.95 0.95 0.95

Notes. This table illustrates the significance of the treatment differ-ences between the WE and SE treatments by calculating the PSP forone of our outcome variables: the share of self-enforcing relation-ships. The PSP is calculated in line with Maniadis et al. (2014) as(1− β) ∗π/((1− β) ∗π+α ∗ (1−π)), where α is the level of significance(0.05), 1 − β is the ex ante power of our empirical test, and π is ourprior about the probability of the alternative hypothesis occurring.

holds. The poststudy probability (PSP) informs usabout the probability that a treatment difference thatwe declare as statistically significant is actually a trueassociation.We illustrate the strength of our main treatment

effects by calculating the PSP � (1− β) · π/((1− β) · π +

α · (1− π)) for one prominent finding from Table 1: theshare of self-enforcing credit relationships in which aloan is offered, accepted, and repaid for at least thefirst five periods. For this outcome we yield a largeand statistically significant difference between the WE(12%) and the SE (48%) treatments. Simulations sug-gest that, given an ex ante level of significance ofα � 0.05, the power of our experimental design (1− β)for this outcome exceeds 0.75.22 Table 2 presents thePSP for varying levels of priors π and for different lev-els of power (1− β) that are consistent with our simula-tions.23 We conclude from the table that for reasonablelevels of ex ante priors, our observed treatment dif-ference shifts priors substantially. For example, if we

Figure 3. (Color online) First-Period Loan Offers

Notes. This figure displays the period 1 loan offers by treatment. Panel A displays the cumulative frequency of offers by Loan size. Panel Bdisplays the cumulative frequency of offers by Interest rate (requested repayment/loan size).

believed prior to the study that there was a 30% chanceof the WE treatment undermining the emergence ofself-enforcing contracts, then our observed treatmenteffect would move this prior to at least 87%. Likewise,if we believed prior to the study that there was a 50%chance of the WE treatment undermining the emer-gence of self-enforcing contracts, then our observedtreatment effect would move this prior to at least 94%.

4.2. Lender BehaviorOur above findings show more loan defaults in ini-tial periods in the WE treatment than in the SE treat-ment, suggesting less implicit contracting and morescreening in the WE treatment. However, we also findsmaller loans in theWE treatment, suggesting that self-enforcing agreements were (at least) attempted in thistreatment. If lenders attempt to initiate implicit con-tracts in both treatments, we should see lower initialloan sizes offered in the WE treatment than in the SEtreatment. Panel A of Figure 3 displays the empiri-cal cumulative distribution function of the Loan sizeoffered by lenders to borrowers in the first period in theWE and SE treatments. The figure reveals that smallloans are more frequent in the WE treatment, whereclose to 70% of lenders offer a loan smaller than 5. Bycontrast, in the SE treatment, only 49% of lenders offera loan smaller than 5. Panel B of Figure 3 shows thatthe distribution of Interest rate offered in first-periodloan offers is similar in the WE and SE treatments. Inboth treatments, the surplus sharing interest rate of 2is most common.

Table 3 reports the results of a multivariate anal-ysis relating first-period loan offers to the treatment(WE or SE) and characteristics of the lender.24 The esti-mated coefficient of the dummy variableWE Treatmentin column (3) confirms that first-period loans in theWE


Table 3. First-Period Loan Offers

(1) (2) (3) (4) (5) (6) (7) (8)

Dependent variable: Loan size Interest rate

Treatment: WE SE WE and SE WE and SE WE SE WE and SE WE and SE

WE −1.333∗∗ 0.218 0.024 −0.022[0.553] [0.547] [0.083] [0.132]

WE×Round 2 −1.829∗∗∗ 0.132[0.483] [0.126]

WE×Round 3 −2.824∗∗∗ 0.006[0.591] [0.135]

Round 2 −0.933∗ 0.896∗∗∗ 0.011 0.896∗∗∗ 0.231∗∗ 0.096 0.158∗∗ 0.095[0.437] [0.232] [0.291] [0.227] [0.098] [0.084] [0.064] [0.082]

Round 3 −1.844∗∗∗ 0.979∗∗ −0.387 0.979∗∗ 0.124 0.116 0.119∗ 0.115[0.429] [0.427] [0.394] [0.418] [0.115] [0.073] [0.065] [0.073]

Risk aversion −0.420∗∗∗ −0.300 −0.383∗∗∗ −0.383∗∗∗ 0.014 −0.015 0.004 0.004[0.111] [0.257] [0.114] [0.114] [0.029] [0.033] [0.022] [0.022]

Strategic reasoning 0.000 0.031 0.014 0.014 −0.003 −0.003 −0.004 −0.004[0.029] [0.039] [0.023] [0.023] [0.003] [0.004] [0.002] [0.002]

Trust 0.336∗∗ 0.166 0.242∗∗ 0.242∗∗ 0.006 0.005 0.008 0.008[0.118] [0.149] [0.098] [0.098] [0.029] [0.013] [0.015] [0.015]

Constant 5.927∗∗ 4.483 6.235∗∗∗ 5.484∗∗ 2.133∗∗∗ 2.185∗∗∗ 2.132∗∗∗ 2.154∗∗∗[2.655] [2.964] [2.100] [2.103] [0.354] [0.388] [0.279] [0.284]

Method OLS OLS OLS OLS OLS OLS OLS OLSObservations 135 144 279 279 122 142 264 264Number of lenders 45 48 93 93 45 48 93 93R2 0.228 0.096 0.143 0.172 0.110 0.032 0.058 0.062

Notes. This table reports ordinary least squares (OLS) estimates for the dependent variables Loan size (columns (1)–(4)) and Interest rate(columns (5)–(8)) using observations from first-period loan offers only. Loan size is the loan offered by lenders, taking values from 0 to 10.Interest rate is the repayment requested divided by loan size and takes values 0 to 3. WE is a dummy variable that is 1 for all observationsfrom the WE treatment and 0 for those from the SE treatment. All regressions include round fixed effects, whereby round 1 is the omittedcategory, and location fixed effects, where Tilburg University is the omitted category. The variables Risk aversion, Strategic reasoning, and Trustare lender-specific measures elicited from pre- and postexperiment games. Standard errors are reported in brackets and are corrected forclustering at the matching group level.∗, ∗∗, ∗∗∗ indicate significance at the 10%, 5%, and 1% levels, respectively.

treatment are on average 1.3 points lower than in the SEtreatment. The coefficients of Round 2 and Round 3 incolumns (1) and (2) and those of the interaction termsWE treatment×Round 2 and WE treatment×Round 3 incolumn (4) suggest that the treatment effect is strength-ened as subjects become more experienced.The variation in initial loan offers across lenders is

related to individual risk attitudes of lenders as wellas the degree to which they trust other participants.In Table 3 we control for three measures of lendercharacteristics—Risk aversion, Strategic reasoning, andTrust—using data from the pre- and postexperimentgames discussed in Section 2.4. We find that lenderswith higher indicators of Risk aversion and lenders whoexhibit less Trust in other participants offer smallerperiod 1 loans in both treatments, but that this iseffect is larger and more precisely estimated in the WEtreatment.25

For periods 2–7, we predict that in both treatmentsthe renewal of loan offers by lenders from one periodto another should be strongly contingent on the repay-ment of past loans. Moreover, as implicit contractsmust be characterized by progressive lending in the

WE treatment, we expect that—conditional on pastloan repayment—the offered loan size increases morestrongly over time in the WE treatment than in the SEtreatment.

We find that loan offers are strongly contingent onpast repayment in both treatments. If the borrowerrepaid a loan in the previous period, lenders offer aloan in the next period in 98% of the cases in the WEtreatment and 97% of the cases in the SE treatment. Bycontrast, if the borrower defaulted, lenders offer a loanin 61% of the cases in the WE treatment and 62% of thecases in the SE treatment.26In Table 4 we examine whether—conditional on

repayment in all past periods—the Loan size offeredby lenders increases over time.27 Our explanatory vari-ables are the dummy variables Period 2–3, Period 4–5,and Period 6–7, which indicate whether the averageloan size offered to borrowers is higher in these periodscompared to the baseline period 1. The results showthat offered loan sizes increase over time in both treat-ments (columns (1) and (2)). In the WE treatment aswell as in the SE treatment, the offered loan size peaksin periods 4 and 5, where offered loans are 1.5–2 points


Table 4. Dynamics of Loan Offers

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

Dependent variable: Loan size

Treatment: WE SE WE and SE WE and SE

Period 2–3 0.998∗∗∗ 1.274∗∗∗ 1.179∗∗∗ 1.273∗∗∗[0.112] [0.219] [0.141] [0.217]

Period 4–5 1.553∗∗∗ 2.032∗∗∗ 1.912∗∗∗ 2.027∗∗∗[0.239] [0.335] [0.234] [0.332]

Period 6–7 1.248∗∗∗ 1.047∗ 1.058∗∗ 1.040∗[0.328] [0.565] [0.427] [0.557]

WE −1.472∗∗∗ −0.805[0.476] [0.517]

WE×Period 2–3 −0.248[0.246]

WE×Period 4–5 −0.432[0.402]

WE×Period 6–7 0.255[0.639]

Constant 5.092∗∗ 4.941∗∗∗ 5.950∗∗∗ 5.727∗∗∗[2.205] [1.902] [1.524] [1.544]

Method OLS OLS OLS OLSLender characteristics Yes Yes Yes YesRound fixed effects Yes Yes Yes YesObservations 307 604 911 911Number of lenders 45 48 93 93Overall R2 0.338 0.178 0.250 0.257

Notes. This table reports panel estimates for Loan size for periods 1–7in relationships without past default. The dependent variable is Loansize and ranges from 0 to 10. Period 2–3, Period 4–5, and Period 6–7 aredummy variables denoting the corresponding period of the relation-ship (period 1 is the omitted category).WE is a dummy variable thatis 1 for all observations from the WE treatment and 0 for those fromthe SE treatment. All regressions include lender characteristics (Riskaversion, Strategic reasoning, and Trust), round fixed effects, the inter-action of round fixed effects with the treatment dummy (columns (3)and (4) only), and location fixed effects, where Tilburg University isthe omitted category. Standard errors are clustered at the matchinggroup level and reported in brackets.∗, ∗∗, ∗∗∗ indicate significance at the 10%, 5%, and 1% levels,

respectively.

higher than in period 1. The negative coefficient ofWE treatment (column (3)) indicates that the loan sizeoffered to borrowers who repaid in the past is signifi-cantly lower in the WE than in the SE treatment. Thenegative (but insignificant) interaction terms of WE ×Period 2–3 and WE × Period 4–5 (column (4)) suggestthat the loan sizes offered to borrowers do not increasefaster in the WE treatment than in the SE treatment.In Table 5, we compare the resulting time struc-

ture of loan sizes within credit relationships acrossthe two treatments. We define the ultimate length ofa relationship as the number of periods for whichthe relationship survived, i.e., loans were offered,accepted, and repaid in every previous period. A rela-tionship in which a loan was offered and accepted inperiod 1 but not repaid is defined as having an ultimatelength of zero periods. By contrast, a relationship thatinvolved positive loan offers in all periods and inwhichthe borrower always accepted and repaid the loan has

an ultimate length of seven periods. We define a long-term relationship as a relationship with an ultimateduration of at least five periods. In line with the resultspresented in Figure 1, only 16 of 135 relationships inthe WE treatment (12%) are long term, compared to 69of 144 relationships in the SE treatment (48%).

Long-term relationships in the WE treatment startoff with somewhat smaller loan sizes than long-termrelationships in the SE treatment. The average first-period loan for these relationships is 5.8 in the WEtreatment compared to 6.5 in the SE treatment. Thisdifference is, however, not statistically significant.28 Byperiod five, the average loan size in long-term relation-ships in theWE treatment increases by 1.8 points to 7.6.This confirms our prediction that long-term relationsin the WE treatment should, on average, be character-ized by increasing loan sizes. However, we find a sim-ilar pattern in the SE treatment. In this treatment, theaverage loan size in period 5 is 8.6, implying an evenstronger increase of 2.3 points from period one.

Result 2 (Lender Behavior). Lenders in the WE treatmentoffer smaller loans in the first period of a relationship com-pared to those in the SE treatment. Long-term credit rela-tionships in the WE treatment display an increase in loansizes over time. However, “progressive lending” is observedto a similar degree in the SE treatment.

Result 2 supports the conjecture that a substantialfraction of lenders attempt to start implicit agreementswith small loan sizes in the WE treatment.29 However,the long-term relationships that emerge do not exhibitsubstantially lower initial loan sizes or a stronger timetrend in the WE compared to the SE treatment. Twocentral features in the data seem to explain this behav-ior. First, as we will see in the next subsection, borrow-ers in the WE treatment are significantly more likelyto reject small loan offers in the initial period of a rela-tionship. Second, loan sizes exhibit an increasing timetrend in the SE treatment as well, a finding that hasbeen documented previously in finitely repeated trustgames (Anderhub et al. 2002, Cochard et al. 2004, King-Casas et al. 2005, Bornhorst et al. 2010). Our results arein line with these previous findings and suggest thata weak threat of exclusion is not a necessary conditionfor progressive lending in credit relationships plaguedby moral hazard.

4.3. Borrower BehaviorFigure 4 displays the frequency with which borrow-ers reject loan offers (panel A) and default on acceptedloans (panel B) in period 1 by treatment. Table 6presents results of a corresponding multivariate analy-sis of borrower behavior in period 1.30

In period 1, 25% of all loan offers are rejected inthe WE treatment, while 11% of the loan offers inthe SE treatment are rejected (see Figure 1). For both


Table 5. Time Structure of Relationships

Loan size offered in periodRelationship lengthin periods N 1 2 3 4 5 6 7

Panel A. WE treatment0 75 4.21–2 34 4.7 5.53–4 10 5.5 6.5 7.2 7.05–7 16 5.8 6.5 6.9 7.4 7.6 7.8 6.8

Panel B. SE treatment0 39 5.91–2 24 4.4 5.2 8.23–4 12 5.5 6.3 7.2 8.25–7 69 6.5 7.7 8.2 8.5 8.8 9.0 9.5

Notes. This table displays the average Loan size offered by lenders by period conditional on the relationship length.Relationship length is determined by the number of periods in which a loan is offered, accepted, and repaid. Ifno loan is offered, accepted, or repaid in period 1, the relationship length is 0. If a loan is offered, accepted, andrepaid in period 1, but not in period 2, the relationship length is 1. If a loan is offered, accepted, and repaid allperiods, the relationship length is 7. Panel A displays results for the WE treatment, and panel B displays resultsfor the SE treatment. N reports the number of relations by relationship length per treatment.

treatments, Figure 4 displays the highest rejection rateamong credit offerswith Interest rate above 2 (58% in theWE treatment, 50% in the SE treatment). These offerspropose an unequal split of surplus to the disadvan-tage of the borrower. This is in line with our predic-tions that “social” borrowers will not accept unfair loanoffers. The regression results in Table 6 confirm thatloan offers that propose Interest rate> 2 are significantlymore likely to be rejected than loan offers that pro-pose an equal share of surplus to the borrower. Thereis no difference in the rejection rate of “unfair” offersbetween the WE and SE treatments, as captured by theinsignificant interaction term WE × Interest rate > 2 incolumn (4) of Table 6. By contrast, loan size is treateddifferently by borrowers in the WE and SE treatments.The estimate for WE × Loan < 5 in column (4) revealsthat offers with small loan sizes are significantly morelikely to be rejected in the WE treatment than in theSE treatment. This finding suggests that some lenderswho attempted to start with small loans could not doso due to borrower rejections.The default rate on first-period loans that are

accepted by borrowers is 35% in the WE treatmentcompared to 16% in the SE treatment. Panel B of Fig-ure 3 shows that in the WE treatment, the default rateon first-period loans is especially high for larger loansand for loans that propose an “unfair” split of surplus.This result is confirmed by the column (5) estimatesin Table 6. In the WE treatment, accepted offers witha loan size of less than 5 (Loan < 5) are 19 percentagepoints less likely to suffer a default, while offers withInterest rate > 2 are 25 percentage points more likelyto suffer a default. While both of these coefficientsare imprecisely estimated, they are jointly significant(F-test � 0.020), suggesting that large loans with high

interest rates are 45 percentage points more likely to bedefaulted on than small loans with low interest rates inthe WE treatment. In the SE treatment, by contrast, wefind only aweak impact of the loan size and the interestrate on first-period loan defaults. The estimated coef-ficients for Loan size < 5 and Interest rate > 2 are jointlyinsignificant (F-test� 0.764). These results suggest thatdynamic incentives to repay are substantially strongerin the initial periods of the SE treatment.Result 3 (Borrower Behavior in Period 1). In the initialperiod, borrowers in both treatments are more likely to rejectloan offers that propose an unfair sharing of surplus. In theWE treatment, borrowers are also more likely to reject period1 loan offers with small loan sizes. Borrowers in the WEtreatment are much more likely to default on large loans withhigh interest rates than borrowers in the SE treatment.

The default behavior reported in Result 3 points toscreening in the WE treatment. Borrowers that wereoffered larger loan sizes are more likely to default.At the same time, rejection behavior indicates thatimplicit contracts are more difficult to establish inthe WE treatment. Our findings show that borrow-ers in the WE treatment often reject the low initialloan offers inherent to progressive lending. One expla-nation for the prevalence of this behavior is that inthe WE treatment, social borrowers prefer screeningequilibria (in which they receive maximum loan sizesin all periods) to implicit contracting equilibria, whichfeature progressive lending. Thus, they may have triedto signal a desire to be tested with larger loans—a testthat is only meaningful in this treatment.

5. Lender CompetitionWeak exclusion has important effects on implicit con-tracting in bilateral credit relationships, as shown thus


Figure 4. (Color online) Borrower Behavior in Period 1

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Notes. Panel A displays the average Rejection rate in period 1 over Loan size (left) and over Interest rate (right), by treatment. Panel B displaysthe average Default rate over Loan size (left) and over Interest rate (right), by treatment. The average rejection and default rates are calculatedconsidering each matching group average as one independent observation.


Table 6. Borrower Behavior in Period 1

(1) (2) (3) (4) (5) (6) (7) (8)

Dependent variable: Reject Default

Treatment: WE SE WE and SE WE and SE WE SE WE and SE WE and SE

Loan size < 5 0.127 −0.050 0.033 −0.050 −0.192∗ −0.034 −0.121∗ −0.034[0.086] [0.052] [0.052] [0.052] [0.102] [0.087] [0.068] [0.086]

Interest rate > 2 0.376∗∗ 0.471∗∗∗ 0.413∗∗∗ 0.471∗∗∗ 0.256 −0.074 0.116 −0.074[0.144] [0.092] [0.090] [0.091] [0.166] [0.110] [0.108] [0.108]

WE 0.087∗ 0.114 0.188∗∗∗ 0.270∗∗[0.046] [0.075] [0.066] [0.124]

WE×Loan < 5 0.178∗ −0.158[0.099] [0.132]

WE× Interest rate > 2 −0.095 0.330[0.168] [0.196]

Constant 0.189∗∗∗ 0.076 0.092∗∗ 0.076∗ 0.436∗∗∗ 0.166∗∗ 0.205∗∗∗ 0.166∗∗[0.062] [0.044] [0.040] [0.044] [0.103] [0.072] [0.063] [0.072]

Method OLS OLS OLS OLS OLS OLS OLS OLSBorrower characteristics No No No No No No No NoRound fixed effects Yes Yes Yes Yes Yes Yes Yes YesObservations 122 142 264 264 92 126 218 218Number of lenders 45 48 93 93 43 48 91 91Overall R2 0.197 0.282 0.231 0.254 0.088 0.013 0.072 0.095

Notes. This table reports panel estimates for Reject (columns (1)–(4)) and Default (columns (5)–(8)) in surviving relationships in period 1. Rejectis a dummy variable that takes the value 1 if the borrower rejects the lender’s offer and 0 otherwise. Default is a dummy variable that takes thevalue 1 if the borrower does not repay an accepted loan offer. Loan size < 5 is a dummy variable that takes the value 1 if the loan size is 1–4and 0 otherwise. Interest rate > 2 is a dummy variable that takes the value 1 if Interest rate (requested repayment/loan size) exceeds the surplussharing rate of 2 and 0 otherwise.WE is a dummy variable that is 1 for all observations from the WE treatment and zero for those from the SEtreatment. All regressions include round fixed effects and the interaction of round fixed effects with the treatment dummy (columns (3), (4),(7), and (8)). Standard errors are clustered at the matching group level and reported in brackets. OLS, ordinary least squares.∗, ∗∗, ∗∗∗ indicate significance at the 10%, 5%, and 1% levels, respectively.

far. In this section, we examine whether weak exclu-sion has a similar effect on credit relationships in acompetitive environment. Specifically, we examine theeffects of weak exclusion when lenders compete forborrowers. We study lender competition (rather than,e.g., borrower competition) as theory suggests thatcompetition between lenders may strongly influencethe emergence and time structure of credit relation-ships. For example, Sharpe (1990) and Petersen andRajan (1995) show that competition between banksmay undermine the ability of lenders to earn quasirents in ongoing lending relationships, and thereforemay reduce their incentive to engage in such relation-ships from the outset.

We implement lender competition by pairing twolenders with one borrower.31 The lending game isidentical to that without competition, except for thefollowing changes: First, both lenders make a creditoffer to the borrower simultaneously at the beginningof each period. Second, the borrower can accept oneoffer (or none). Third, at the beginning of each period,each lender is informed about the past credit volumeaccepted by the borrower and his repayment behav-ior, but not the interest rate.32 We implement a treat-ment with lender competition for our weak exclusioncondition (WE Competition treatment) and our strongexclusion condition (SE Competition treatment).

5.1. PredictionsIn this section, we discuss the main differences in pre-dictions for the WE Competition and SE Competi-tion treatments compared to our main treatments withbilateral interaction. Detailed predictions are providedin Online Appendix E.

Implicit contracting in the SE Competition treatmentexhibits a similar pattern of loan sizes compared to ourmain SE treatment with bilateral interaction. Implicitcontracting equilibria are characterized by maximalloan offers throughout the first six periods and a dropin period 7. However, interest rates are lower withlender competition: they are at the break even rate(it � 1), rather than the surplus sharing rate (r̄ � 2),since lenders compete to attract the borrower. Note thatsince there are two symmetrical lenders with identicalinformation about past repayment, a relationship canemerge with one of the lenders or there can be switch-ing between lenders.We refer to an active credit marketas an environment in which at least one offer is madeand one offer is accepted and repaid in each period.33The set of equilibria in the WE Competition treat-

ment changes compared to our WE treatment withbilateral trading. In particular, screening equilibria donot exist under weak exclusion with lender competi-tion. The reason is that, as both lenders are equally


informed about past repayment behavior, borrow-ers are not informationally captured by their incum-bent lender.34 In expectation, therefore, lenders cannotrecoup losses from defaulting selfish borrowers in thefirst period by earning quasi rents on social borrowersin subsequent periods. In the WE Competition treat-ment, implicit contracting equilibria exist, but exhibita different time pattern of loan volumes. Instead ofprogressively increasing loan volumes, lenders offer aconstant loan volume from periods one to six, which isstrictly smaller than the maximal loan offer. In the lastperiod, they increase their loan offer, offering the max-imal loan size, to induce indifference between repay-ment and default among borrowers in period 6. Theconstant loan size in nonfinal periods is self-enforcing,as lenders demand the break-even interest rate (it � 1).Our null hypothesis for the comparison of the WE

Competition and SE Competition treatments is againthat we observe no differences in lending outcomes.Our alternative hypothesis suggests that we observedifferences in loan sizes, but not in the frequency ofself-enforcing credit relationships:

Hypothesis 3 (H3) (Lender Competition). Self-enforcingcredit relationships, i.e., credit relationships in which loansare offered, accepted, and repaid for at least five periods,are equally likely in the WE Competition and SE Competi-tion treatments. The average loan size is, however, lower in

Figure 5. (Color online) Loans Offered, Accepted, and Repaid—Competition Treatments

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Notes. This figure displays the share of credit markets that are characterized by a loan offer, a loan acceptance, and a loan repayment ineach period for both competition treatments. The means and standard errors are calculated considering each matching group average as oneindependent observation. The total number of credit markets (matching groups) is 54 (6) in the WE competition treatment and 54 (6) in the SEcompetition treatment.

the WE Competition treatment than in the SE Competitiontreatment. Interest rates are similar in both treatments.

5.2. ProceduresThe treatments with lender competition were designedand implemented following the same procedures asour bilateral trading treatments. The only major dif-ference was that two lenders were matched with oneborrower in each round. To keep the perfect strangermatching used in the main experiment, each matchinggroup consisted of 12 (instead of 6) subjects.

We ran 12 sessions with lender competition at UCSan Diego with one matching group per session.A total of 144 subjects participated in these sessions,whereby each subject participated in one treatmentonly.35 Six sessions, i.e., matching groups, were run forthe WE Competition treatment and six sessions wererun for the SE Competition treatment. After the sub-jects completed three seven-period rounds of the lend-ing game, they played the postexperiment games asoutlined above.

5.3. ResultsOur aim in this section is to examine whether the maintreatment differences documented for our main WEand SE treatments also hold with lender competition.Our discussion of the results for the SE Competitionand WE Competition treatments is therefore limited


Table 7. Treatment Effects with Lender Competition

Mean Mann–Whitney test

WE competition SE competition BonferroniOutcome variable treatment treatment Naïve p-value adjusted p-value

Share of self-enforcing relationships 0.35 0.50 0.0609 0.1827Loan size 7.40 8.52 0.0250 0.0750Interest rate 1.27 1.31 0.7488 1.0000

Notes. This table presents the means of our three main outcome variables for each lender competition treatment. We also present the results oftheMann–Whitney test on the treatment differences, including the naive p-values and the Bonferroni adjusted p-values for multiple hypothesistesting.

to replicating the analyses presented in Section 4.1. Aswe did there, we compare three outcomes: the shareof self-enforcing credit relationships, i.e., relationshipsin which a loan is offered, accepted, and repaid for atleast the first five periods, and the average Loan size andInterest rate for accepted loan offers. We measure ouroutcome variables again at the matching group leveland thus compare six observations for the WE Com-petition treatment against six observations for the SECompetition treatment. Because of the lower numberof observations for this robustness test, we confine ourtests to nonparametric methods (Mann–Whitney test)and account for multiple hypothesis testing by adjust-ing p-values using the Bonferroni method.

Figure 5 displays the share of creditmarkets inwhicha loan is offered, accepted, and repaid by period in theWE Competition and SE Competition treatments. Inthe WE Competition treatment, 72% of the credit mar-kets survive period 1 (i.e., a loan is offered, accepted,and repaid), while this is the case for 82% of the mar-kets in the SE Competition treatment. By period 3, thegap in credit market performance widens. In the WE

Figure 6. (Color online) Credit Terms of Accepted Loan Offers in the Competition Treatments

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Notes. This figure displays the average contract terms of accepted loan offers in the competition treatments by period and treatment. Panel Ashows the Loan size. Panel B shows the Interest rate (requested repayment/loan size). The means and standard errors are calculated consideringeach matching group average as one independent observation.

Competition treatment, 53% of the markets feature arepaid loan, while 75% of the markets do so in the SECompetition treatment. This gap remains until the endof period 5. By periods 6 and 7, the gap between theWE and SE Competition treatments closes again due tothe end-game effect in the SE Competition treatment.

Table 7 summarizes our treatment effects underlender competition. In line with Figure 5, we find asmaller share of self-enforcing relationships in the WEtreatment (35%) compared to the SE treatment (50%).However, the nonparametric tests presented in Table 7reveal that this treatment difference is not statisticallysignificant after adjusting for multiple hypothesis test-ing (MW test, adjusted p-value� 0.183).Figure 6 displays the credit terms of accepted loan

offers in the competition treatments. In line with ourpredictions, accepted loan offers are smaller in allperiods in the WE Competition compared to the SECompetition treatment. By contrast, interest rates aresimilar in both treatments. Table 7 shows that the aver-age Loan size of accepted loan offers over all periodsis 7.40 in the WE Competition treatment compared to


8.52 in SE Competition treatment (MW test, adjusted p-value � 0.075). Table 7 reveals no difference in averageinterest rates in the WE Competition treatment (1.27)compared to the SE Competition treatment (1.31; MWtest, adjusted p-value� 1.00).

Comparing the treatment effect of weak exclusionon lending in competitive credit markets (Table 7) rel-ative to bilateral trading environments (Table 1), wefind in both cases a negative effect on the share ofself-enforcing credit relationships and on average loansizes. The magnitude of the effect of weak exclusionon the average loan size is similar in the both trad-ing environments. However, in line with Hypothesis 3,the magnitude of the effect of weak exclusion on theshare of self-enforcing contracts is substantially smallerunder competition (15 percentage points) than underbilateral trading (36 percentage points) and has muchweaker statistical significance.36

Result 4 (Lender Competition). Under lender competition,weak exclusion is associated with smaller loan sizes and asmall, nonsignificant decrease in the share of self-enforcingrelationships. Compared to a bilateral trading environment,the magnitude of the effect of weak exclusion on the shareof self-enforcing credit relationships is weaker under lendercompetition.

6. ConclusionIn this paper, we examine how the threat of exclusionimpacts on self-enforcing agreements in contractingenvironments plagued by moral hazard. The results ofour lending experiment suggest that weak exclusionleads to a more frequent breakdown of lending rela-tionships as well as to smaller loan sizes. These effectsare substantial with bilateral trading, and are moder-ated with lender competition. Our findings provide anew perspective on the conditions under which self-enforcing agreements may—or may not—be a viableinstrument for managers to mitigate conflicts of inter-est with employees, creditors, and clients. Implicitcontracting is an effective enforcement strategy whenagents value the relationship with their current trad-ing partner. This may not be the case when agents canappropriate income-generating resources provided tothem by principals. In this case, the threat of exclu-sion is weak, and our experiment suggests that implicitcontracting is impaired.

Whichmarkets and business relations aremost likelyto be subject to aweak threat of exclusion? This threat isparticularly weak when (i) agents (employees, debtors,suppliers) use income-generating resources providedto them by the principal, (ii) a weak legal environ-ment enables agents to appropriate these resources,and (iii) agents do not rely on the continued cooper-ation of the principal to generate future income withthese resources. Bank lending in environments with

weak creditor protection—the context of interest inour experiment—is a prime example of these condi-tions. Joint ventures in foreign direct investment areanother—especially when the foreign partner has thetechnical know-how to use common assets indepen-dently. Likewise, investment relations with upstreamfirms may be subject to a weak exclusion threat ifthe supplier can appropriate technology and supplycompeting firms. Professional services, such as wealthmanagement or consulting, in which employees maypoach clients is another environment where a weakthreat of exclusion may undermine incentives. In suchmarkets and business relations, managers may need toresort to formal and costly enforcement mechanisms,e.g., monitoring, incentive contracts, or a reallocationof ownership, to mitigate conflicts of interest.

AcknowledgmentsThe authors thank Eric van Damme, Hans Degryse, JohnDuffy, Karolin Kirschenmann, Ola Kvaloy, Sera Linardi, JanPotters, Joel Sobel, and Stefan Trautmann, as well as semi-nar participants at Maastricht University, Simon Fraser Uni-versity, Tilburg University, the University of East Anglia,the University of Nottingham, the University of Osnabrueck,Universitat Autonoma de Barcelona, Universitat PompeuFabra, the University of Zurich, the XIX Finance Forum,CESifo Munich, the International Meeting on Experimen-tal and Behavioral Economics 2011, and the First LeeXInternational Conference on Theoretical and ExperimentalMacroeconomics at Universitat Pompeu Fabra for commentsand suggestions. The authors also thank John List (depart-ment editor) and three anonymous referees for very helpfulcomments.

Endnotes1 It is, for example, estimated that 60%–90% of wealth managementclients follow their advisor when they change firms (Gudz 2013).2Such an assumption has been shown to hold in a wide range ofexperiments. Furthermore, evidence of such types has been found intrust games and has been linked to actual repayment decisions in thefield (Karlan 2005).3Falk et al. (2015) show that dismissal barriers can undermine rela-tional contracting in labor markets. Thus similar to our paper, theyexamine how institutions affect the emergence of implicit agree-ments. In contrast to their paper, we examine institutional featuresinherent to the credit market (debt enforcement) and not only exam-ine whether these institutions affect the emergence of implicit agree-ments, but also how these agreements are structured over time.4Starting small can also be rationalized by profit maximization ofthe principal who increases the stakes toward the end of the rela-tionship such that he can extract a greater surplus in the beginning(e.g., Ray 2002), or by borrowing constraints that are endogenous tothe dynamics of debt and thus make increasing loan sizes optimal(Albuquerque and Hopenhayn 2004).5While reputation concerns are constant in an infinite horizon, theyare strong at the beginning and very weak at the end with a finitehorizon. As shown, for example, by Brown and Zehnder (2007),self-enforcing credit agreements can be identified as relationships inwhich the borrower repays in nonfinal periods and then defaults inthe final period.


6Partial repayments are not possible. In reality, some borrowers obvi-ously become delinquent without fully defaulting. However, becauseof the deterministic nature of investment earnings in our design, weexclude partial repayments.7Relative to existing experimental studies, we introduce only onechange, i.e., that a defaulting borrower can reinvest borrowed funds,and hence there are no endogenous savings/consumption decisionsin any of the treatments.8The Doing Business indicators of “Resolving Insolvency” comparethe costs, time, and processes involved in a bank enforcing a securedclaim on a nonfinancial firm that enters bankruptcy procedures.For details of the methodology and data, see http://www.doingbusiness.org/data/exploretopics/resolving-insolvency (accessedOctober 13, 2016).9For example, in the United States, when individuals file for personalbankruptcy under Chapters 7 or 13, several personal assets can beexcluded from seizure during bankruptcy (e.g., owner-occupied res-idences, personal property, and retirement accounts). White (1998,p. 689) argues that “because few debtors have nonexempt assets,more than 90 percent of Chapter 7 cases involve no repayment atall, and the average repayment rate in Chapter 7 cases is less than3 percent.”10A recent Economist article on bankruptcy proceedings in Indiareports that ”At the moment, creditors cannot take any legal actionagainst a defaulter until a restructuring plan is in place, which usu-ally takes between three and ten years. In the meantime, the ownersof sick firms retain day-to-day management control; and while theydrag out court proceedings, creditors see their assets dwindle. Inmany cases, says a lawyer who works on such cases, the owners startup a fresh company in the name of a relative, and siphon off businessfrom the old one” (The Economist 2015).11We chose to pay a higher show-up fee to subjects and decreasethe exchange rate for two reasons. First, because of the euro to U.S.dollar exchange rate, which was 0.78 USD/EUR on October 29, 2014,shortly before we ran the sessions at UC San Diego. Second, weintended to add sessions with lender competition at UC San Diego(as will be detailed in Section 5), in which participants would makesignificantly less money for a similar amount of time in the labora-tory. To avoid differential selection into sessions, we set the show-upfee to US$10 for all sessions conducted at UC San Diego.12The reason why we chose a context-specific and not a neutralframing was that the experiment was relatively complex. In complexexperiments, a completely neutral language bears the danger thatsubjects will create their own (potentially misleading) interpretationof the decision environment. Thus, the context-specific framing givesus control over what our participants have in mind.13Because of logistical constraints, the location (Tilburg or SanDiego) varied simultaneously with the order of the additional games(pre- versus postexperiment). We thus acknowledge that we can onlymeasure the joint effect of location and order and cannot rule outthat countervailing order and location effects partly offset each other.Our results suggest that location and order do not exert a significantjoint effect on behavior in the additional games (as shown in OnlineAppendix B) or the lending game (as shown in Online Appendix D).14Throughout the pre- and postexperimental games, subjectsreceived no feedback. They were not informed about other sub-jects’ decisions or their own payoffs until the end of the experiment.Subjects also knew that the decisions in each preexperimental/postexperimental game had no effect on the lending game (andvice versa). The instructions for these games are available from theauthors upon request. We find that choices in the preexperiment ver-sus postexperiment games are not significantly different in the riskelicitation task and guessing game. We find differences in the trustgame in the SE but not the WE treatment. The higher trust and trust-worthiness in the postexperiment games in the SE treatment suggests

there was a spillover from successful interaction in the lending gameonto the trust game.15As we outline in Online Appendix C, lending relationships witha positive repayment probability for selfish borrowers in nonfinalperiods and certain default by selfish borrowers in the final periodare feasible if T ≥ 2 and p ≥ 1/r̄T . The higher the share of socialborrowers p in the population and the larger the number of periodsT, the more periods with full repayment by all borrowers can besustained.16 In our experiment, it � 2 is the interest rate that generates the samepayoffs for the lender and borrower if the borrower repays a loan.With v � 3, it �Rt/St � 2 implies that Rt −St � v ·St −Rt . If we assumethat r̄ � 2 and p � 0.25, then as T � 7, the condition 1/r̄T ≤ p < 1/r̄is met.17 In deriving these predictions, we assume a finite horizon and riskneutrality of the lenders to simplify the analysis. These assumptionsdo not change the qualitative effects of weak exclusion, as we discussin Online Appendix C.18Whether the profit-maximizing implicit contracting equilibriumor the profit-maximizing screening equilibrium yields higher profitsto the lender depends on the gross return from investment (v) andthe share of social borrowers. As shown in Online Appendix C.4,given the choice of v � 3 in our experiment and the assumption thatthe share of social borrowers is p < 1/r̄, where r̄ � 2, the implicitcontracting equilibrium yields higher profits to the lender than thescreening equilibrium.19The strength of implicit contracting can also be measured by theaverage length of relationships in which there offers have been con-tinuously made, accepted, and repaid, or, more generally, the aver-age number of periods in which a loan has been offered, accepted,and repaid. Results remain the same if we use these alternativedefinitions.20 In Sections 4.2 and 4.3, where we analyze individual lender andborrower behavior, we do not adjust p-values formultiple hypothesistesting. We follow this approach because the purpose of studyingindividual behavior is to understand the mechanisms underlyingthe treatment effects on our main outcome variables, rather than toexamine additional hypotheses and outcomes.21Out of those relationships that break down in a given period t,27% and 33% are restarted in the next period (t + 1) in the WE andSE treatments, respectively. Most restarts occur after a rejection inthe previous period (45% and 37% of the restarts observed in theWE and SE treatments, respectively); 35% and 36% of the restartsoccur after a default, while 20% and 26% of the restarts occur after nooffer was made in the previous period in the WE and SE treatments,respectively.22Our statistical inference is based on comparing the outcomes of15 matching groups in the WE treatment to 16 matching groups inthe SE treatment using two-sided nonparametric (Mann–Whitney)tests. The power (1 − β) of these tests is a function of the level ofsignificance (α � 0.05) and the assumed distribution of (matching-group-level) outcomes under the null and alternative hypotheses. Ineach matching group, there are nine relationships. We thus modelthe outcome of each matching group as drawn from a binomialdistribution where n � 9 is the number of draws and q is the prob-ability that a loan is offered, accepted, and repaid in at least fiveperiods. To estimate the power of our test, we need to specify qfor the null hypotheses (SE � WE) and alternative hypotheses (SE ,WE). Based on evidence provided by Brown and Zehnder (2007),we assume that in the SE treatment, two-thirds of the relationshipsfeature implicit contracting so that qnull � 0.66. The predicted proba-bility for theWE treatment under the alternative hypothesis dependson the share of relationships that feature implicit contracting ϕ1,the share that feature screening ϕ2, and the share of social typesp (as only they repay in a screening equilibrium): qalternative � ϕ1 +

http://www.doingbusiness.org/data/exploretopics/resolving-insolvency

http://www.doingbusiness.org/data/exploretopics/resolving-insolvency


ϕ2 · p. For consistency, we assume that there are similar shares ofrelationships in the SE and WE treatments that feature repeatedcontracting, ϕ1 + ϕ2 � 0.66, and that both implicit contracting andscreening are present in the WE treatment, ϕ1 , ϕ2 ∈ [0.22, 0.44].In line with evidence provided by Brown and Zehnder (2007), wefurther assume that the share of social types is p � 0.3. Together,these assumptions imply that qalternative ∈ [0.35, 0.5]. With qnull � 0.66and qalternative ∈ [0.35, 0.5], we yield power estimates of (1 − β) ∈[0.77, 0.99] for our Mann–Whitney tests. We simulate the power ofour test using the software PASS. When simulating, we approximatethe binomial distribution for matching group outcomes with a cor-responding normal distribution.23Guided by our theoretical predictions, our empirical prior π is thatweak exclusion should influence credit relationships in our experi-ment. However, existing experimental studies indicate that implicitcontracting can be robust to institutional changes (e.g., competition,stochastic incomes) that appear relevant from a theory perspective(Brown and Zehnder 2007, Fehr and Zehnder 2009). Thus, it is fea-sible that weak exclusion has a negligible impact on credit relation-ships in our experiment as well.24Since the correlation between loan sizes and interest is not sig-nificantly different from zero, we analyze these two variables sep-arately (Spearman’s rho � −0.34, p-value � 0.21 in the WE treat-ment; Spearman’s rho�−0.0721, p-value� 0.79 in the SE treatment).Results remain qualitatively the same if we estimate both regressionssimultaneously instead. Furthermore, results remain qualitativelythe samewhen the decision to make a loan offer is studied separatelyfrom the loan size, conditional on making an offer. The results areavailable from the authors.25Existing studies provide mixed evidence on the relation betweenrisk aversion, trust, and first-mover behavior in investment games.Schechter (2007), for example, provides field evidence that first-mover behavior in trust games is significantly related to individ-ual risk attitudes. By contrast, the evidence provided by Eckel andWilson (2004) or Houser et al. (2010) suggests that trust in othersrather than risk attitudes is associated with first-mover behavior. Wefind that both factors affect first-mover behavior.26There is no significant difference in contract renewal rates acrosstreatments, conditional on past repayment or conditional on pastdefault. Regression results are available from the authors uponrequest.27The regression results reported in Table 4 include individuallender characteristics as well as round fixed effects. Results remainqualitatively the same if we use lender fixed effects.28We conduct a Mann–Whitney test at the relationship level. Thep-value obtained is 0.776.29A further piece of evidence that is consistent with this conjec-ture is lender beliefs. While lenders waited for borrowers’ decisionson the acceptance and repayment of loans, we elicited their beliefsabout repayment. These were not incentivized to avoid increasingthe complexity of the experiment for participants. Lenders simplyanswered the question “How probable do you think it is that theborrower will make the desired repayment?” with a scale from 1,“very unlikely,” to 6, “very likely.” Overall all rounds, in the WEtreatment, lenders who offered loans of 1–4 in the first period statedthat repayment was likely or very likely in 40% of the cases, whilelenders who offered loans of 5–10 did the same in 38% of the cases.By contrast, in the SE treatment, these percentages were 18% of thecases for loans of 1–4, and 42% for loans of 5–10. By round 3, lendersin the WE treatment seemed to expect a strategy of “starting small”to be more successful in inducing repayment by borrowers. In 50%of the cases, they believed repayment to be likely or very likely afteran offer of size 1–4, compared to 40% after an offer of size 5–10. Thecorresponding percentages were 0% and 38% in the SE treatment.30Because of our interest in the interaction effects of treatment dum-mies and other variables, we choose to use linear probability models

rather than probit or logit models (see Ai and Norton 2003 for adiscussion of the difficulty of interpreting the marginal effects ofinteraction terms in nonlinear models). An analysis of loan rejectionand repayment for periods 2–7, as shown in Online Appendix D(Table D.2), reveals that rejection and default are significantly morelikely if the interest rate is above 2, while default is more likely forsmaller loans in the SE treatment (and not in the WE treatment).31We chose this type of design because the presence of two lendersis enough to generate the effects of competition. Our focus is on theeffect of weak exclusion on credit offers and repayment behavior,rather than the endogenous formation of credit relationships.32This information setting mirrors the functioning of public creditregistries and private credit bureaus in many developed and devel-oping countries (Jappelli and Pagano 2002, Miller 2003), wherelenders have access to the volume of credit upon which the borrowerdefaulted, while not knowing the interest that was required for thatloan.33We term the two lender and one borrower environment a mar-ket, following terminology used by Roth et al. (1991), among others,to describe environments in which multiple buyers (lenders, in ourcase) make offers to a single seller (borrower, in our case).34See the model by Sharpe (1990) for a game of endogenous asym-metric information between lenders in which borrowers are infor-mationally captured by their incumbent bank.35Additionally, no subject that participated in the sessions in UC SanDiego participated in either of the bilateral contracting treatments.36Given the smaller number of observations in the competition treat-ments (six matching groups per treatment) compared to our mainbilateral trading treatments, one may worry that the lack of signif-icance of an effect of weak exclusion is due to the low number ofobservations. We performed ex post power calculations to assessthis concern. First, if the magnitude of the treatment effect of weakexclusion were the same as in the main treatments (12 versus 48 per-centage points), we would be powered to detect a significant effect(the power would be 93% with six matching groups). Second, giventhe observed magnitude of the treatment effect in the competitiontreatments (35 versus 50 percentage points), our power level wouldbe merely 62% even if we increase the number of observations to15 per treatment (as in our main treatments). Given the observedmagnitude of the treatment effect in the competition treatments,27 matching groups per treatment would be needed in each treat-ment to obtain a power of 80% given a significance level of 0.05.

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http://wealthmanagement.com/viewpoints/will-your-clients-follow-you

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The Threat of Exclusion and Implicit Contracting Threat of Exclusion.pdf · BrownandSerra-Garcia: The Threat of Exclusion and Implicit Contracting ManagementScience,2017,vol.63,no.12,pp.4081–4100,©2016INFORMS