credit-output interlinked contracts: the relationships

CREDIT-OUTPUT INTERLINKED CONTRACTS: THE RELATIONSHIPS BETWEEN TRADERS AND FARMERS

BY NARDA LIZETTE SOTOMAYOR

Licenciado, Ponti cia Universidad Catolica del Peru, 1987 M.S., The Ohio State University, 1992

THESIS

Submitted in partial ful llment of the requirements for the degree of Doctor of Philosophy in Agricultural Economics in the Graduate College of the University of Illinois at Urbana-Champaign, 1998

Urbana, Illinois

c Copyright by Narda Lizette Sotomayor, 1998

Abstract In Peru, as in many other developing countries, the absence or imperfections of credit and insurance markets characterizes the environment of formal market institutions. However, when formal market institutions fail to meet some demands, informal arrangements, such as market interlinkages, may help to ll in the gaps. This dissertation analyzes credit-output interlinked contracts (COIC), based on detailed surveys of wholesale traders and farmers in a typical valley of Peru. After identifying a typical COIC, we explain how the structure of behavior of contracting parties who interact repeatedly can sustain mutually bene cial outcomes. COIC accomplishes the role of making credit available to small farmers and, at least, partially insures the participants of the contract. Long-term personal relationships allow trust and reputation to develop and help to overcome the problems caused by asymmetric information. The permanent threat of punishment by breaking the relationship makes immediate gains from deviations smaller than the losses in the future. Thus, in equilibrium, the parties always cooperate and the contract is repeated, only while mutual economic gains from the relationship exists. COIC, as observed in Coastal Peru. are modeled using a repeated game approach. We accommodate to our speci c case study Radner's review strategies model, which makes the farmer's compensation in any one period depend on the average outcome over a number of periods. That is, small deviations are not punished. Tolerance is required because of the inability of the trader to distinguish if a low outcome was due to uncontrollable random variables or to the lack of cooperation. In this way, repetition allows the trader to reduce the farmer's risk without reducing his incentive to cooperate in the contract. Within the repeated game framework, changes in the length of the review period, the farmer's probability of success, the reservation utilities of the parties, and their risk aversion are analyzed. These changes aect the system of incentives designed to promote contract compliance, and therefore, the behavior of the parties and the conditions of the contracts. iii

A Pepe y a esa vida que vendra...

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Acknowledgments I would like to express my sincere appreciation to Professor Carl Nelson, my advisor, for his guidance, patience, and valuable discussions throughout my doctoral program and during the realization of this research. I am also indebted to the other members of my committee. My appreciation goes to Professor Bruce Sherrick, for his important comments on my manuscripts and his support during the realization of this dissertation, through the University of Illinois Research Board. My gratitude goes to Professor David Bullock for providing me my rst assistantship in this Department and for his trust and encouragement. And, thank you to Professor Charles Kahn, for his insights in the modeling chapter of this dissertation. I also would like to acknowledge my indebtedness to the Ford Foundation, who nanced the rst two years of my Ph.D. studies, and to those who contributed to the realization of the eld research of this dissertation. The Social Science Research Council provided nancial support for conducting the eld research. The farmers in the Huaral Valley and the traders in the wholesale market of Lima gave me great insights about how credit-output interlinkage works, without which the realization of this study would not be possible. CEPES, in Lima, a non-governmental research institution, gave me the institutional support at the beginning of my eld research. Juana Davila, my eld assistant, made the conduction of the surveys a gratifying task, with her persistence and good sense of humor. In addition, I would like to extend my gratitude to my friends in the Ph.D. program who have made my graduate career enjoyable. Special thanks go to Molly Bhattacharyya for her valuable friendship, and to Muhammad Mushtaq with whom I have taken most of the course work, playing cooperatively despite the non-cooperative setting. I also own special thanks to Edward Durkin for his beautiful music and refreshing chats. Last but most, I am deeply grateful to my husband, Jose Tavera, for his contribution to my career, his patience, sacri ces, and unshakable support; and, to my parents for their faith in me and continuous encouragement. v

Contents 1 Introduction

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2 A Review of the Literature

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1.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Objectives of the Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Dissertation Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Literature Review on Market Interlinkages . . . . . . . . . . . . . 2.1.1 Reasons for Interlinking . . . . . . . . . . . . . . . . . . . 2.1.2 Modeling Approaches . . . . . . . . . . . . . . . . . . . . 2.1.3 Determination of Contractual Parameters . . . . . . . . . 2.1.4 Weaknesses in the Literature of Market Interlinkages . . . 2.2 Literature Review on Repeated Games Theory . . . . . . . . . . 2.2.1 What is Special about Repeated Games? . . . . . . . . . 2.2.2 Repeated Games with Imperfect Observability of Actions

3 Brief Background of the Peruvian Agricultural Sector 3.1 3.2 3.3 3.4 3.5

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Agriculture and the Peruvian Economy . . . . . . . . . . . . . . . . . . . . Endowments and Natural Preconditions . . . . . . . . . . . . . . . . . . . . Tenancy System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Financial Services in Rural Peru . . . . . . . . . . . . . . . . . . . . . . . . Commercialization of Agricultural Products in the Coastal Region of Peru .

4 Linked Contracts in the Huaral Valley

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4.1 The Study Area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Survey Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Personal Characteristics of the Participants of the Contract . . . . . . . . . . vi

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4.3.1 Trader-Lenders Characteristics . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Farmer-Borrowers Characteristics. . . . . . . . . . . . . . . . . . . . . 4.4 Interlinked Contracts: Trader-Lender and Farmer-Borrower Relationships . . 4.4.1 The Screening Process . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Motivation for Contract Participation . . . . . . . . . . . . . . . . . . 4.4.3 Terms and Conditions of the Contracts: Implicit and Explicit Conditions 4.4.4 Contract Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.5 Default Events and Coercive Actions. . . . . . . . . . . . . . . . . . . 4.5 Main Economic Issues that the Formal Model Should Address. . . . . . . . .

5 Modeling Credit-Output Interlinked Contracts 5.1 Credit-Output Interlinked Contracts as Games 5.1.1 Description of the Stage Game . . . . . 5.1.2 The In nitely Repeated Game . . . . . 5.2 A Model of Review Strategies . . . . . . . . . . 5.2.1 The Stage Game . . . . . . . . . . . . . 5.2.2 The Repeated Game . . . . . . . . . . . 5.2.3 Equilibrium Review Strategies . . . . .

6 An Exercise Applying Review Strategies

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6.1 De ning the Empirical Model . . . . . . . . . . . . . . . . . 6.2 Review Strategies: Comparative Statics . . . . . . . . . . . 6.2.1 Changes in the Length of the Review Period . . . . 6.2.2 Changes in the Trader's Reservation Utility . . . . . 6.2.3 Changes in the Farmer's Reservation Utility . . . . . 6.2.4 Changes in the Probability of Success in Each Stage 6.2.5 Changes in the Farmer's Risk Aversion . . . . . . . vii

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6.2.6 Changes in the Trader's Risk Aversion . . . . . . . . . . . . . . . . . . 105

7 Conclusions and Policy Implications

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References

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Vita

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7.1 Policy Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

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List of Tables 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Access of Rural Households to Formal Credit . . . . . . . . . . . . . . . . . . Hydrological Cycles of the Chancay-Huaral River . . . . . . . . . . . . . . . . Land Aptitude for Agriculture . . . . . . . . . . . . . . . . . . . . . . . . . . Distribution of Crop Cultivation in the Huaral Valley . . . . . . . . . . . . . Agricultural Season for Tomatoes and Sweet Corn . . . . . . . . . . . . . . . Supply of tomatoes and Sweet Corn of the Huaral Valley to the Wholesale Market of Lima . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Marketing Characteristics by Type of Crop . . . . . . . . . . . . . . . . . . . Composition of the Sample by Number of Respondents and Contracts . . . . Trader's Personal Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . Distribution of Sample Household by Size Group of Holdings . . . . . . . . . Farmer's Participation in the Credit Market by Size of Holding . . . . . . . . Loan Characteristics as Reported by Producers . . . . . . . . . . . . . . . . . Loan Characteristics as Reported by Traders . . . . . . . . . . . . . . . . . . Default Events and Coercive Actions . . . . . . . . . . . . . . . . . . . . . . . Changes in the Length of the Review Period . . . . . . . . . . . . . . . . . . . Changes in Trader's Reservation Utility . . . . . . . . . . . . . . . . . . . . . Changes in Farmer's Reservation Utility . . . . . . . . . . . . . . . . . . . . . Changes in the Probability of Success in Each Stage ( ) . . . . . . . . . . . . Changes in Farmer's Risk Aversion . . . . . . . . . . . . . . . . . . . . . . . . Changes in Trader's Risk Aversion . . . . . . . . . . . . . . . . . . . . . . . .

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32 35 36 37 37 38 39 40 41 43 44 49 50 55 98 100 101 102 104 106

List of Figures 1 2 3

Extensive representation of the interlinked contract game . . . . . . . . . . . Representation of trader's strategy by machines . . . . . . . . . . . . . . . . . Representation of farmer's strategy by machines . . . . . . . . . . . . . . . .

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1 Introduction Over the last decades, many low income countries, including Peru, have allocated large amounts of resources to rural nancial market projects. The justi cation of these interventions has been threefold. First, the fact that there is limited access for small producers to formal credit sources. In general, private nancial institutions are reluctant to lend to small producers in rural areas, because lenders nd it too costly: a) to gather information on the likelihood of a borrower's default on a loan; b) to monitor the borrower's actions after the loan is given; and c) to ensure repayment. In addition, the fact that the average administrative and operational costs increase as the size of the loan decreases, puts small borrowers in a disadvantaged position relative to large borrowers. Second, there has been a popular belief that small rural producers pay excessive interest rates in informal credit markets. Finally, the conviction of policy-makers that the lack of nancial alternatives constrains growth and development. Given these premises, a rational policy response was to make credit available to rural producers at subsidized interest rates. However, the result of many of these interventions has been disappointing from the point of view of eciency and distribution. 1 There was little success in reaching small farmers (those without collateral or with below average income); the default rates were high, which together with the subsidized interest rates (often negative in real terms) led to the bankruptcy and consequent liquidation of most of these programs. At the same time, traditional moneylenders and other informal institutions stand strong. They are still active, and perform the function of meeting the credit needs that formal institutions have left un lled. The perverse results of these interventions have been extensively documented. See for example GonzalezVega (1977), Pischke and Adams (1980). 1

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1.1 Problem Statement In recent years, the economic development literature has shifted the focus of research on the rural sector of developing countries, toward understanding the role of institutions as well as the behavior of individuals and families in rural areas (Binswanger & Rosenzweig, 1984). The main concern has been to explain the existence of rural institutions that appear to contradict the implications of competitive markets. The literature explaining sharecropping relationships that extend beyond agreements over the use of land is especially extensive. 2 Landlord and tenant often enter into several transactions at the same time: renting land; contracting labor; purchasing inputs; and marketing output, generating what is known as interlinked transactions in the agrarian literature (Bardhan, 1980). An interlinked transaction is one in which two parties trade in at least two markets, and the elements of trade in one market are used to enforce a contract in the other market. Market interlinkages have been shown to be ubiquitous and take diverse forms in less developed countries. 3 While several studies have considered linked transactions involving sharecropping relationships, little economic research has examined one form of interlinkage that is probably more prevalent and important in practice. 4 This interlinkage is the one between the marketing of a crop and the provision of credit nancing the working capital for its production. 5 In a credit-output interlinked contract, a trader commonly provides loans to a producer on the condition that the latter sells part or all of his crop to the former. As with other types of interlinked contracts, credit-output contracts dier from the impersonal Arrow-Debreu market setting where individuals make trades with the \market" See for example Newbery and Stiglitz (1979) and Binswanger and Rosenzweig (1984). For a survey on interlinked contracts see Bardhan (1980), Binswanger and Rosenzweig (1984), and Bell (1988). 4 See for example Newbery and Stiglitz (1979), Braverman and Stiglitz (1982), and Hayami and Otsuka (1993). 5 Some of the few studies on theoretical aspects of output-credit interlinkages are those of Gangopadhyay and Sengupta (1987), Bell and Srinivasan (1989), and Esguerra, Nagarajan, and Meyer (1993). Floro and Yotopoulus (1991) oer an empirical study of informal credit markets in the Philippines. Among other rural institutions, credit-output interlinkages are analyzed. 2 3

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(Hart & Holmstrom, 1987). Interlinked contracts are to some extent relationship-speci c. That is, once transactions are made they have much higher value inside the relationship than outside (Williamson, 1985). A clear understanding of the nature of these relations is undoubtedly important in any policy agenda of institutional reforms. These observations raise a number of important questions that motivate this dissertation. Why do interlinkages between credit and output markets exist? What are the economic incentives for market intermediaries to provide loans to producers, and for agricultural producers to borrow from traders instead of other sources? What are the enforcement mechanisms of this kind of arrangement? What are the eect of these transactions on the welfare of the parties? How ecient is market interlinking in relation to the alternative of the parties transacting in separate markets? This study of interlinked credit relationships provides a better understanding of the behavior of economic agents in an environment of uncertainty and poorly functioning formal institutions, as often exists in rural areas of less developed countries. As a consequence, lessons are extracted for policy making and economic development eorts.

1.2 Objectives of the Research While the literature on market interlinkage has focused on the causes of interlinking and in the contractual choice, this study assumes that the choice of a credit-output interlinked contract was already made. Thus, the analysis starts after the contract is sealed. The general objectives of this dissertation are twofold. The rst objective is to identify and to model the terms and conditions of credit-output linked contracts (loan size, amount of crop bonded, interest rate, commission charges, etc.) and their enforcement mechanism. A second objective is to explain the structure of behavior when the parties interact repeatedly and to show how this structure can sustain mutually bene cial outcomes. These objectives are accomplished through detailed surveys, aimed to capture information about the speci cs of 3

credit-output linked contracts performed between wholesale traders and farmers of a typical valley in the Coastal region of Peru. Credit-output interlinkages in Peru seem to be widespread, particularly in the coastal region, whose production is basically market oriented. A recent study on credit markets in a Coastal valley of Peru reports that about 67.3 percent of agricultural producers interviewed borrowed from market intermediaries (Alvarado, 1994). This observation is consistent with the extant evidence on this form of interlinking, which apparently grows stronger with commercialization (Bell, 1988). The speci c objectives of this study are:

 To characterize the participants of credit-output interlinked contracts.  To capture the details about credit-output interlinked contracts in the coastal region of Peru (price and non-price covenants).

 To quantify and explain the determination of the main elements of a credit-output interlinked contract in the coastal region of Peru: loan size, duration, use of the loans, explicit and/or implicit interest rates, commission rates, output prices, and volume of crop involved.

 To identify: (i) the factors that provide incentives to the parties to honor the contract; and (ii) the factors that may induce producers to breach the contract by failing to deliver part or all of the crop \promised".

 To characterize typical contract enforcement procedures, when the actions of the contracting parties are not observable; and there is no legal mechanism for contract enforcement, or it is ineective.

 To identify the elements of the credit-output interlinked contracts likely to contribute to the development of rural nancial systems. 4

1.3 Dissertation Organization The following section is arranged in two parts. The rst part provides a review of current research on market interlinkages in general, focusing on the questions that motivated most of the literature. That is, why do market interlinkages occur and what are the eects on the allocation of resources and on the welfare of the parties? In addition, the most frequent modeling approaches assumed are surveyed, identifying the main weakness in the literature on market interlinkages and suggesting themes for further research. The second part of Section 5.2 oers a review of the literature on repeated game theory, emphasizing the aspects relevant to this study. Before concentrating on the results of the case study, background information on the Peruvian Agricultural Sector is provided in Section 3. Section 4 reports the results from the survey of farmers in a typical valley of the Coastal region of Peru and of traders in a wholesale market of Lima. The characteristics of creditoutput interlinked arrangements are presented, as well as the motivation for participation, the terms and conditions of contracts, and the enforcement mechanisms. The aim is to identify the features that enable credit-output interlinked contracts to constitute an equilibrium. Section 5 provides a formal model of the credit-output interlinked contracts as observed in Coastal Peru, using a repeated games approach. The sucient conditions for the parameters of the contract to constitute an  ; equilibrium, characterized by cooperation, are derived. Based on a review strategy model, Section 6 presents comparative statics based on the information provided by the surveys. Finally, Section 7 concludes with a brief summary of the issues and ndings of the study, identifying features of the interlinked contracts that can be assimilated to further the development of rural nancial markets in Peru.

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2 A Review of the Literature This Section is organized in two parts. The rst part surveys the literature on market interlinkages and the modeling approaches most frequently used. The second part reviews the literature on repeated game theory, with emphasis on cases of imperfect monitoring when the agents discount the future.

2.1 Literature Review on Market Interlinkages In the past three decades, the literature on agrarian institutions has made it clear that the standard theory of perfect competition, full information, and complete markets is insucient to explain a number of important economic phenomena. It is now well recognized that a complete set of contingent claim markets, in the Arrow-Debreu sense, does not exist and that the non-market institutions have a very important in uence on resource allocation (Bell & Srinivasan, 1989). In agrarian economies, transactions are far from being performed in an anonymous setting, as much mainstream neoclassical economics assumes. Long- term personal and economic relationships are important elements in transactions involving uncertainty (Floro & Yotopoulus, 1991). Furthermore, a pair of related agents often deliberately trade with each other in more than one market generating the so-called market interlinkages. The need to understand the nature of the interlinkage of markets has been increasingly recognized in the agrarian development literature, focusing on the interlinkages between land, credit, and labor markets. 6 When this type of interlinkage is involved, the landlord typically provides consumption credit to the sharecropper in return for the latter agreeing to provide labor services. The possible impacts of policies such as land reform, in the form of land distribution and intervention in the land market, was one of the concerns behind the study of these types of contracts. Much less attention has been given to the study of the interSee for example Bhaduri (1973, 1977, 1979), Bardhan and Rudra (1978), Bell and Zusman (1976), Braverman and Stiglitz (1981), Braverman and Guash (1984), and Srinivasan (1989). 6

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linkage between credit and output markets. Studies on credit-output interlinkages include Gangopadhyay and Sengupta (1987), Bell and Srinivasan (1989), and Floro and Yotopoulus (1991). 7 This insucient attention in the literature to credit-output interlinkages contrasts with the existing empirical evidence showing its importance. Bell and Srinivasan (1985), based on information on some Indian villages, argue that interlinkages between credit and output markets may be more prevalent and signi cant in terms of volume of credit than those between credit and tenancy or labor. Jones (1980) arrives at similar conclusions in a study examining West Africa. The discussion in the literature on market interlinkages, including those in which sharecropping relationships are involved, will provide insights into the understanding of creditoutput relationships. Two questions motivate the literature on market interlinkages. The rst question focuses on the reasons for interlinking and the eect of market interlinkage on the allocation of resources and the welfare of the parties. The second question concerns two stylized facts: (i) output and input costs are shared equally between landlord and tenant (Binswanger & Rosenzweig, 1984; Bell & Srinivasan, 1985; Nabi, 1986); and (ii) with interlinkages, interest rates on production loans tend to be lower than the market rates, or even zero (Bardhan & Rudra, 1980; Nabi, 1986; Gangopadhyay & Sengupta, 1986). Although these two puzzles are speci c to sharecropping relationships, they will be reviewed later, for they motivated theoretical work about how the contractual parameters of interlinked contracts are determined.

2.1.1 Reasons for Interlinking Traditionally, interlinked transactions were viewed as an instrument used by one party to better extract the surplus from the other (Bhaduri, 1973, 1977, 1979). It was argued that an interlinked arrangement enhances the exploitative power of a landlord, much more than 7

Floro and Yotopoulus study this arrangement among many other in informal credit markets.

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what one would have enjoyed otherwise in only a single market (see for example, Wharton (1962) and Basu (1984)). Alternative theoretical explanations come from the transaction cost economics (TCE) and the imperfect information (IMI) approaches, which view market interlinkage as a consequence of signi cant transaction costs and information asymmetries. Although the TCE and the IMI approaches have developed independently from one another, both are complementary rather than con icting. Stiglitz (1985a) argues that information costs are a special case of transaction costs. When private information exists on the side of one party, this party may take actions to increase his/her bene ts at the expense of the other party. The second party, who is aware of this risk, will incur costs when generating information and taking actions to minimize his/her loss. From the TCE approach, transaction costs exist and are incorporated in market prices. These costs are not normally included in the conventional production costs of neoclassical theory and are partly explained by the existence of incomplete property rights. The hypothesis in TCE framework, is that institutions, in general, are cost minimizing devices that may change and evolve with changes in the nature and sources of transaction costs (Coase, 1937; Williamson, 1975, 1985, 1989; Demsetz, 1988). When transaction costs are high, contracting parties are compelled to make use of non-price strategies, such as quantity rationing and market interlinkage (Floro & Yotopoulus, 1991). In particular, consider the case of a creditoutput interlinkage. Suppose that a trader oers credit to cultivators, on the same terms available to them from alternative sources, but tied to marketing services for their crop at a market commission charge. In accepting, cultivators will not be worse o than transacting in separate markets. Moreover, they will have lower transaction costs than had they been operating in separate markets. Cultivators transacting in separate markets would have to search for a source of credit, likely with no other collateral than their future income, the crop, and would have to look for someone to market their crop. Thus, when transaction costs depend on the number of separate occasions an individual attempts a transaction and on the 8

number of other parties with whom one deals, market interlinkage is a solution where at least one of the parties will bene t (Bell, 1988). Moreover, linked contracts, based on long-term personal relationships, tend to increase the costs of terminating a contract in the event of possible discovery of opportunistic or dishonest behavior (Bardhan, 1989; Hayami & Otsuka, 1993). The IMI approach stresses the fact that information is imperfect and costly (Akerlof, 1970; Newbery & Stiglitz, 1979; Stiglitz, 1985b, 1986). When there are information asymmetries, the parties of a transaction face the problem of not knowing what type of person one is dealing with (\adverse selection" or \hidden information" in Arrow's (Arrow, 1985) terminology), and not knowing what actions that person may take once the contract is sealed (\moral hazard" or \hidden action" in Arrow's (Arrow, 1985) terminology). Bardhan (1980) argues that, in these circumstances, credit systems based on personal trust and interlocking obligations in dierent markets between the same parties is a way to insure against either party ending up with too many of Akerlof's \lemons" (Akerlof, 1970). However, most contract theories restrict attention to the analysis of cases in which informational asymmetries arise only subsequent to contracting, after assuming that the parties seal the transaction at some initial date (Hart & Holmstrom, 1987). Bell (1988) claims that when there is a good deal of repeated business, which is the case in a village, few personal attributes of any economic signi cance are hidden. 8 When moral hazard problems are emphasized, market interlinkages are explained as an instrument to create incentives for contract performing and to permit one agent to exercise a better control over the actions of the other. Braverman and Stiglitz (1982), and Mitra (1983), analyzing interlinked credit and tenancy contracts, emphasize the incentive eect of a tenant's borrowing on his unenforceable work-eort. For example, an interlinked credit and tenancy arrangement with a bonded labor clause states that if the borrower fails to repay the loan, he/she must provide labor services to the lender (Braverman & Stiglitz, 1981). Thus, Because the choice of contracts and how the parties get involved is not the main issue in this study, the emphasis will be on moral hazard problems. 8

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there is an incentive for the borrower to increase his/her eort to avoid situations that will raise the probability of loan default. Because tenant's work eort and landlord's income are positively related, the landlord may do better by acting as a moneylender as well. Similarly, in the case of credit-output interlinkage, if credit aects the output that the cultivator is able to obtain, and, therefore, the volume of marketable surplus, traders may do better by providing credit. As Stiglitz (1986) asserts, where there appear to be signi cant externalities between the actions of one party and the actions of the other, a natural market solution is to internalize the externality, and that is what interlinkage of markets does. However, Hayami and Otsuka (1993), argue that the choice of interlinked over independent contracts cannot be explained by the above mentioned incentive eect alone, because the loan can be replaced by an implicit xed payment. A more plausible explanation is found in the asymmetric access of agents to credit markets. If interest charges dier between better and less endowed agents, there is a possibility of mutually advantageous trade. The imperfection of credit markets in rural areas and the absence of insurance markets appear strongly, in the literature, as factors explaining market interlinkages. 9 Because imperfect information leads to adverse selection and moral hazard problems, the lending activity entails incurring costs oriented to the solution of three basic problems: the screening; the incentives; and the enforcement problem (Ho & Stiglitz, 1990). These problems are in general a characteristic of credit markets, but they are felt much more acutely in rural credit markets and in developing countries than in other contexts. In addition, dealing with small borrowers results in a high unit cost in processing and administering the loans. If the solution of these problems is oered at too high a cost, then credit rationing will occur. Simply increasing the interest rate such that the associated costs of lending are covered is not always a solution, because high interest rates may attract high-return, high-risk projects increasing the probability of default of loans. In short, credit rationing occurs because the interest rate 9

See for example, Braverman and Srinivasan (1981, 1984), and Ray and Sengupta (1989).

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serves both the function of price, as well as an instrument to in uence the composition of the lender's loan portfolio (Stigler, 1989; Stiglitz & Weiss, 1981). One instrument used by lenders to ameliorate the consequences of information asymmetries is collateral, which, once pledged, reduces the borrower's incentive to undertake projects that increase the probability of default. In particular, land has traditionally been an ideal collateral asset because of its attributes of immobility and immunity to damage (Binswanger & Rosenzweig, 1984). Small cultivators, however, may have few assets acceptable as collateral by traditional lenders, and thus their access to commercial loans is limited. The landlord (or the trader, in the case of this study), in contrast, is likely to have better access (to cheaper credit sources) than the landless tenants and laborers (Hayami & Otsuka, 1993). Interlinked contracts are likely to be a response to credit market imperfections, and may provide a means to alleviate screening, incentive, and enforcement problems (Ho & Stiglitz, 1990). For example, in a tenancy-credit contract, landlords will accept the tenancy itself as collateral. Moreover, they are in the best position to enforce the repayment at the time of harvest (Bardhan, 1980). Similarly, in the credit-output linked contract, for the trader, the promise of the future output oered as collateral has higher value or is less costly to dispose of in the case of default than it is for traditional lenders (Sherrick & Lubben, 1994). In fact, since the collateral is actually intended to serve as the repayment stream, a market conversion to cash need not be conducted prior to payment. In the absence of insurance markets, interlinkage is viewed as a risk-sharing device. For example, a laborer may be employed during the peak season, and may be unemployed during the lean season. In an interlinked arrangement, a landlord may provide a loan to the laborer during the lean season on the condition that the laborer will work for the landlord during the peak season, when labor is needed (Ray & Sengupta, 1989). In an credit-output interlinkage, traders solve the uncertainty about the volume of crop they will be able to intermediate. Producers assure a channel to market their crop and also share the risk of poor production. 11

Thus, a number of factors may explain the prevalence of interlinkages in agrarian markets, where the terms of the contracts consist of price and non-price elements. It is likely that more than one of the above considerations are present in an interlinked contract. However, the necessary conditions for interlinkage to occur have not been clearly established in the literature. As Hayami and Otsuka (1993) point out, the incentive eect of a producer's borrowing on his/her unenforceable work eort is not enough to justify interlinking. The loan in an interlinked contract can be replaced by an implicit xed payment to generate the same incentive. These authors argue that a better explanation can be found in the imperfections of credit markets expressed in the dierent interest rates faced by greater and lesser endowed agents. This asymmetry would engender an arbitrage opportunity. However, this argument still does not explain interlinking. The greater endowed agent need not be somebody who interlinks, but could be a moneylender or any other relatively well-endowed agent engaging in pure money lending. As Ray and Sengupta (1989) assert, there must be another ingredient that creates the interlocker's advantage. These authors propose alternative assumptions that explain the advantage of interlinking: (i) the lenders are restricted to oer only linear contracts (prices independent of quantities); (ii) the interlocker has an advantage on the market(s) where he/she is active; and (iii) the pure moneylender by virtue of his/her specialized occupation can observe the realization of a smaller number of variables than the interlocker can. The two last assumptions, which are very much related, seem to be particularly relevant for the case of trader-producer relationships. A trader's activity assumes an endless human capital investment, which improves his/her ability to take advantage of market opportunities. Part of this investment is the continuous interaction with producers, which allows the trader to observe variables not observable to a pure moneylender. Some of the variables explaining credit-output interlinkage are the knowledge about the diverse market channels available to the farmer, the farmer's ability to procure a regular harvest, and the expected market value for the crops being planted. The real value of these variables in explaining credit-output interlinkages can only be determined through empirical work. 12

2.1.2 Modeling Approaches The formal analysis in the theoretical literature about market interlinkages commonly utilizes agency models (see for example, Braverman and Stiglitz (1982), Braverman and Srinivasan (1984), and Bell and Srinivasan (1989)), and occasionally utilizes a Nash bargaining approach (Zusman & Bell, 1985; Bell, 1988). As shown later, the derived eciency and welfare eects from these models do not always agree. Because informational and other restrictions are at the heart of the analysis, optimality in these approaches is not understood in a rst-best sense, but rather in a constrained or second-best sense (Hart & Holmstrom, 1987). Greenwald and Stiglitz (1986) have shown that when there is market incompleteness and information is imperfect, market allocation is constrained Pareto-inecient. In this case, pervasive externalities; i.e., actions by one individual that aect the welfare of the others can be partially internalized through market interlinking (Braverman & Stiglitz, 1982). When agency models are employed, the interlocker (landlord or trader-lender) is the principal and the producer-borrower is the agent. Most of the studies assume that there is a single monopolist lender. The fact that an interlocker has an advantage over pure moneylenders is often regarded as self-evident in much of the literature. 10 The eciency and welfare eects are analyzed, and the terms of the interlinked contracts are the variables to explain (see for example Mitra (1983), Braverman and Srinivasan (1984) and Bell (1988)). Emphasizing one reason at a time to explain the prevalence of interlinked contracts, diverse studies show that interlinking transactions is an ecient economic response to asymmetric information. Mitra (1983) and Braverman and Stiglitz (1982), assuming prohibitive monitoring costs, emphasize the incentive eect of a tenant's borrowing on his/her work-eort. A second-best allocation is found, provided that the landlord prohibits farmers from unrestricted access to 10 An exception to this is found in Ray and Sengupta (1989). These authors discuss the conditions under which an interlocker may gain advantage over a pure moneylender or another interlocker active in a dierent market. Also, Floro and Yotopoulus (1991) consider similar issues.

13

the organized market (Mitra, 1983). Braverman and Srinivasan (1984) identify as a key element the imperfection of credit markets. The policy implication of these results is that banning interlinked arrangements, ceteris paribus, can be Pareto-inferior for rural economic agents. In a Nash bargaining framework, Bell and Zusman (1976) assume that the allocation of tenants among landlords is brought about with a cooperative bilateral bargaining between each landlord and each of the quali ed potential tenants. The bargaining centeres around all feasible arrangements, and the terms of the contract depend on technology as well as on the parties' preferences and bargaining strengths. The eect of interlinking transactions is to shift the utility possibility frontier outward. The authors show that, if the disagreement payos are independent of the contractual parameters, it is always possible to nd an interlinked contract that yields a higher value for the Nash product of the changes in expected utility of the parties than the maximum value of that product when interlinking is not allowed (Bell, 1988). The welfare eects of interlinking are not clear in the literature. On one hand, principalagent models nd that equilibrium in interlinked arrangements will be characterized by utility equivalent contracts (Braverman & Srinivasan, 1984; Cheung, 1969). That is, in equilibrium a producer-borrower's utility obtained through interlinking will be the same as his/her reservation utility; i.e., that which he could have obtained dealing in separate markets. On the other hand, in a bargaining framework, Bell (1988) shows that the producer-borrower may be worse o with an interlinked contract than transacting in separate markets. The eect depends on the way the utility possibility frontier shifts and the position of the disagreement point relative to the origin. However, when there is transferable utility, a dicult situation to conceive, both parties gain equally in a cooperative outcome whether there is interlinking or not.

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2.1.3 Determination of Contractual Parameters As mentioned in Section 2.1, the frequently observed 50:50 sharing rule and the low interest rates associated with interlinked contracts inspired the study of how contractual parameters are determined. Dealing with these issues, in an agency framework, the leading models on interlinked contracts (Braverman & Stiglitz, 1982; Braverman & Srinivasan, 1984; Bell & Srinivasan, 1989) assume that the crop season consists of the two periods of planting and harvesting. Producers receive credit to nance the rst period expenses, as they receive income only in the second period and do not have savings. The amount provided is usually controlled by the principal and it is independent of the producer's future income. Thus, rst period consumption is perfectly controlled by lenders (Hayami & Otsuka, 1993). Assuming production certainty, Braverman and Srinivasan (1984) and Gangopadhyay and Sengupta (1987), analyzing interlinked contracts within sharecropping relations, arrive to an indeterminacy of the interest rate and the sharing rule. Bell and Srinivasan (1989), in a context of production uncertainty and credit-output interlinkage, derived a similar result. The optimum contract will specify a pure commission on sales or interest charges but not both. When both variables are under the control of the lender-interlocker, it is shown that one is redundant. This indeterminacy, however, is necessary but not sucient to explain the observed interest rates associated with interlinked contracts and the prevalence of a 50:50 sharing rule. Murrel (1983) argues that it must rst be assumed that the 50:50 sharing rule served traditionally as a community \golden rule" of justice and its alteration may generate social distress. Then, the low interest rates are explained as follows. Because increased borrowing will increase the producer's eort, and, hence, the landlord-lender's return, the latter will insure that the former gets credit from the cheapest source. Thus, the landlord will provide credit only in a situation where it will lower the cost of credit to the tenant. This result occurs when the landlord's opportunity cost of his/her money is lower than the prevailing rate in the tenant's alternative source of credit (Braverman & Srinivasan, 1984). 15

Bell and Srinivasan (1989), in a credit-output interlinkage context, show that in the absence of moral hazard, and even if the probability of default is high, a household's (producer's) optimal contract will involve only commission charges and no interest rate. This same result is found when moral hazard is introduced and the incentive condition for labor input is not binding. If it is binding, either pure commission charges or interest rates will be paid but not both. Interest rates are charged only if incentive considerations are pressing and the probability of default is suciently great. These results are consistent with the fact that only commission charges are speci ed in credit-output interlinkage. The study assumes riskneutral agents, however. Given the importance of uncertainty about prices and quantities in an agrarian economy, the introduction of risk aversion would be a more realistic assumption. Also, the role of price uncertainty, which may be particularly important in interlinked contracts where marketing is involved, is missing in the analysis.

2.1.4 Weaknesses in the Literature of Market Interlinkages Diverse studies in the literature have been able to partially explain the stylized facts mentioned at the beginning of this literature review. The assumptions in the models reviewed, however, can be made more realistic. In a context of credit-output interlinkage in an agrarian economy, both price and quantity uncertainty are important elements to be considered, for each may in uence the contract performance. In addition, the literature on interlinked contracts does not address issues that are particularly important in informal rural institutions. First, the interlinked contracts take place in an environment where property rights are not well de ned and contracts are not (cannot be) legally enforceable. Contracts are informal, and legal systems in less developed countries are inecient. This fact makes the costs of legal enforcement (i.e. fees, time) too high to resort to it, and so the mechanisms available for contract enforcement are reduced to extralegal mechanisms. 16

Second, contracts are incomplete. They are not state contingent, because of the agents' inability to foresee later contingencies or, as Williamson (1979) argues, because it is too costly to specify actions to be taken in every event. Often, contracts do not even specify prices and volume of crop involved in the contract. Traders form expectations about the crop volume to be delivered to him/her, but this provision is not speci ed in the contract and hence it is not strictly enforceable. There are production risks and the interlocker's share in the crop harvested is subject to a farmer's manipulation. Thus, important questions are: (i) in an environment of inecient legal enforcement, does interlinkage give any advantage for contract enforcement? (ii) how do interlinked contracts reduce the costs of bargaining and negotiation over events not agreed upon? and (iii) how are contracts enforced when the collateral is not tangible? Third, the inability of the farmer to commit to the contract and that of the trader to observe trades has not been addressed in the literature about market interlinkages. The models of interlinked contracts reviewed point to a monopolistic arrangement where the principal will insist on an exclusive contract. However, in marketing credit interlinkage, it is often observed that producers borrow from diverse sources (for instance, from more than one trader), thus engaging in more than one commitment. In these circumstances, the question of how the contracts are enforced is again relevant. Personal relationships involved in interlinked contracts and reputation eects help explain the enforcement problem. These points need much more study, especially in the sense of relating them to the economic value of the alternatives to the contract. Finally, as explained earlier in this review, agency models applied to interlinked contracts focus on moral hazard problems, where private information is on the side of the agent. The usual models assume completely uninformed principals. However, in a credit-marketing contract, there are at least two ways in which traders may be informed principals. First, information such as the various commercialization channels available to producers, a particular crop's market prospects, and the average production yields in a speci c region, is 17

available to traders. This awareness may help the researcher to identify the interlocker's advantage over pure moneylenders. Second, an information asymmetry arises on the side of the trader-principal at the time of marketing the crop, when the output price is revealed to her/him. Producers do not usually observe this information, so they have to rely on the trader's report. Where price information does not easily ow, which is usually the case of less developed economies, this information asymmetry can be important. In the best scenario, producers are informed about a relevant range of prices, a range over which marketers can advantageously manipulate the information. Although the per-unit under-pricing may not be important, there may be important gains when the volume of output involved is considered. It is clear that all the weaknesses of the literature, pointed out in this review, cannot be resolved in a single study. However, there are at least two promising lines of inquiry that can be taken. One attempts to explain the contractual choice; i.e., why a credit-output interlinked contract is chosen in the economic, social and technological environment of a particular agrarian economy. This approach would require a broad survey covering all types of contractual alternatives. A second line of research concentrates on the credit-output interlinked contract, assuming that the choice was already made. Thus, the analysis starts after the contract is sealed. This study takes the second approach. Consistent with this choice, the issues raised above about the incompleteness of these contracts, the farmer's inability to honor the contract without engaging in side trading, and the existence of private information on the side of the trader (principal), are especially important for this study. Arrow (1974) has argued that the absence of contingent state contracts is related to the existence of asymmetric information. If a contract is contingent on an event, then the event has to be easily veri able by both parties. However, this information is likely to be observable to only one party of the contract. In a credit-output interlinked contract, there are degrees of observability for both parties. Traders fully observe prices but not quantities. Producers, on the other hand, fully observe quantities but not prices. Each one has the ability to manipulate the variable better observed. In this scenario, a question 18

arises about the impact of asymmetric information on the distribution of revenue.

2.2 Literature Review on Repeated Games Theory An important element in interlinked contracts is the repeated interaction of two agents who behave strategically to maximize their own objectives. Consequently, this study uses \repeated games theory" as the modeling approach. A brief review on this topic follows, focusing on the aspects relevant to our study. Myerson (1991) de nes game theory as the study of mathematical models of con ict and cooperation between intelligent and rational decision-makers (commonly called players), whose decisions will aect one another' s welfare. Rationality implies that players choose their best action in terms of \sel sh" utility maximization. Consequently, if the game is played only once, a cooperative strategy cannot be sustained as a Nash equilibrium (Sabourian, 1989). This result changes when the game is repeated in nitely.

2.2.1 What is Special about Repeated Games? Repeated games are those in which players face the same \stage game" in every period, and the players' overall payo is a weighted average of the payos in each stage (Fudenberg & Tirole, 1991). Repetition can be nite or in nite. In any nite repetition of the game, the only Nash equilibrium is that of the stage game (Osborne & Rubinstein, 1994). In contrast, in an in nite repeated game, cooperation can be sustained as an equilibrium. This result was the main motivation for economists to further study repeated games. A stylized fact is that the terms and conditions on which individuals interact are not, in general, determined by fully explicit enforceable contracts. Moreover, in many economies, legal enforcement mechanisms do not exist or are ineective. However, the fact that in many economic and social situations parties interact repeatedly implies that implicit, self-enforcing contracts respond to a certain rationale. When a repeated game has an in nite horizon, 19

because no move is necessarily the last, or because the players believe that there is a high probability that they will play again (Myerson, 1991), agents have an incentive to conform to an implicit agreement today, because they believe that this will in uence the nature of subsequent interactions (Pearce, 1992). Thus, repetition enables cooperation. This may be the simplest but most important result in models of in nitely repeated games. The typical example is provided using the well-known prisoner's dilemma, where the stage outcome results in a Nash equilibrium characterized by non-cooperation by the parties. Repetition of the game, however, may allow new equilibria. In the simplest case, when the actions of the players are observable at the end of each stage game, players can condition their moves on the information they have received in previous stages. For instance, players may agree to play a sequence of moves that will result in a particular payo in the long run, while threatening each other with reverting forever to a non-cooperative behavior as soon as a deviation of the opponent has been observed. Therefore, a player must always consider the eect that her/his current action may have on the information and, thus, the action of their opponents in the future. Again, the outcome of repetition is cooperation. Osborne and Rubinstein (1994) stress that the primary achievement of the theory was to isolate the set of strategies (what they call social norms) that support mutually desirable payo pro les. However, most of the results in the literature concern the set of payos that can be achieved under certain conditions, which are summarized in the so-called Folk Theorems. Pertaining to the structure of the equilibrium strategies, the theory speci es the necessity of credible punishment threats and players that have the incentive to carry out the punishment and who will do so when required. The magnitude and the eectiveness of the punishment depend on how players value the future. The simplest assumption is that players value the future as much as the present. But, a more general assumption is that players discount future utilities with the discount factor,  , where (0; 1], which measures the patience, or time attitude of the players. A value of  close to zero corresponds to impatient players who 20

are mainly concerned about current or near-future payos (Myerson, 1991). In this case, larger threats of punishment would be required to enforce cooperation, than in the case in which the discount factor is close to one. The remaining portion of the review assumes the more general case of discounting. When discounting is assumed, the Folk Theorem for Repeated Games states that under a full dimensionality condition, any feasible payos that give all players more than their minmax values can be achieved by a perfect equilibrium if the players are patient enough (Fudenberg & Maskin, 1986). In the limit of extreme patience, repetition allows virtually any payo to be an equilibrium (Fudenberg & Tirole, 1991). Thus, in a repeated game, the problem is not, as in the one shot game, the existence of an equilibrium, but rather the existence of too many equilibrium outcomes. The possibility of punishment and thus the existence of many equilibria occurs because players can condition their actions on the history of the game. However, because there are large numbers of possible histories, one can construct many equilibrium strategies in repeated games (Sabourian, 1989).

2.2.2 Repeated Games with Imperfect Observability of Actions The folk theorem above holds for repeated games with complete information and when the actions of the players are perfectly observed. Studies that assume that some information is not available to the players can be roughly classi ed into two categories. First, when the payos of the game and/or the individual characteristics of the players are not common knowledge (as the complete information models assume) we have models with incomplete information, which in the insurance literature are referred to as adverse selection models (Mertens, 1989). In economics, the literature on models of incomplete information is substantial, and will not be reviewed here. Some references on this topic include Harsanyi's seminal paper (Harsanyi, 1967-1968), where ctional moves of nature that select \types" was rst introduced, allowing the description of a game of incomplete information as a game of 21

imperfect information; Akerlof (1970), who explained market failures caused by information asymmetry; Kreps and Wilson (1982), Milgrom and Roberts (1982), and Fudenberg (1992), who explored the eects of reputation in games with incomplete information. Secondly, when the absence of perfect observability of moves is assumed, there are problems of imperfect monitoring, which are known as moral hazard problems in the insurance literature. What follows focuses on studies that assume imperfect monitoring. Imperfect monitoring occurs when players are able to observe only signals of the moves, not the moves themselves. Results in these models were rst obtained for the cases of nondiscounting (Pearce, 1992), and the question of eciency in the presence of moral hazard was an important issue in these studies. When the actions are observable, players can threaten each other with punishment if deviation has occurred and they will be sure that no punishment will occur in equilibrium. However, when there is imperfect observability of moves, and a player appears to have deviated, even if she/he has not, punishment may have to be applied just to deter opportunistic behavior. Thus, the bene ts from deterring opportunistic behavior have to be balanced with the costs that the threats of punishment may impose (Myerson, 1991). The pioneering papers of Rubinstein (1979), Radner (1981), and Rubinstein and Yaari (1983) proved that in principal agent games, with one-sided asymmetric information, in nite repetition makes it possible to approach eciency in the presence of moral hazard. Radner (1981, 1985) and Rubinstein (1979), in a repeated principal agent game with one-sided asymmetric information introduced the concept of review strategies. This technique assumes a review period after which a test is conducted by the principal, in order to determine the probability that the agent has deviated from the cooperative behavior. The test allows some margin of error, so that small deviations are not punished. When there is positive discounting, Radner (1985) showed that for a discount factor suciently high, equilibria in which the agent plays cooperatively in a high fraction of periods is possible. When contracts involve two-sided moral hazard, it is still possible to use the standard 22

principal-agent model with one-sided asymmetric information. Al-Najjar (1997) provided the theoretical foundations for this simpli cation. He analyzes the case of a principal that simultaneously participates in contracts with N independent agents. Participants of each contract do not observe each other's actions. Assuming that there are no informational linkages, Al-Najjar shows that optimal incentive schemes eliminate the principal's incentive problem when the number of agents are suciently large. Green and Porter (1984) and Porter (1983) rst introduced discounting in imperfect monitoring models, to explain price wars in oligopolistic competition, where rms observed only their own actions (individual output) but not the actions of the other rms. The interest was to explain how cooperation can be achieved. The authors assumed the existence of public information, de ned as a commonly observable outcome that depends on the rms' actions and on a random variable. In the case they analyze, the market price is public information and depends on the total supply (the sum of individual rms supply) and on the stochastic aggregate demand. The public outcome is interpreted as an imperfect signal of the rm's actions, such that a fall in the market price might be due either to an unexpected fall in the demand or to an unexpected increase in a rm's production. Porter (1983) analyzed cooperative symmetric equilibria that result from a restricted set of trigger strategies. A price lower than a predetermined price level triggers a t-period punishment that results in the Cournot equilibrium price. A key element for the strategy to constitute an equilibrium is that, once there is an indication that deviation has occurred, all rms will have the incentive to implement the punishment and will do so. After t periods of punishment, cooperation resumes and will continue, unless the price falls below the trigger level, in which case the Cournot equilibrium (punishment period) is established, and so on. A more general solution to Porter's (1983) model was provided by Abreu, Pearce, and Stachetti (1986), who showed the existence of equilibria in a symmetric discounted repeated games with imperfect monitoring. Later, Abreu, Pearce, and Stachetti (1990) generalized their results for a broad class of asymmetric games. Following Kreps and Wilson (1982), 23

they studied sequential equilibria in which each player conditions her/his actions on other players past signals and not on her/his own previous actions. After any rst period history, a sequential equilibrium induces a \continuation pro le", and because rst period realization is publicly observed, this pro le is common knowledge and is itself a sequential equilibrium (Abreu et al., 1990). These authors use as a tool of analysis the concept of \self-generation", which is a generalization of the principle of optimality of discounted dynamic programming that provides a sucient condition for a vector of payos to be the maximal present value obtainable at the beginning of the game (Fudenberg & Tirole, 1991). Their most important result is that the super-game equilibria can be, and for the sake of eciency, must be under certain conditions, restricted to sequential equilibria whose continuation values are extreme points of the set of sequential equilibrium payo vectors. Thus, after one period of the best equilibrium, players will either restart the best equilibrium or move to the worst equilibrium. The intuition is that when creating incentives to enforce cooperation, the players should be aggressive going all the way to the extreme of the set of sequential equilibrium payos. In order to preserve the \recursive structure" of the super-game equilibria, the analysis of Abreu et al. (1990) is con ned to the cases in which players receive no private signals, use only pure strategies, and the commonly observed signal has a constant support (Pearce, 1992). Fudenberg, Levine, and Maskin (1994) show that the Folk Theorem extends to repeated games with moral hazard on all sides, i.e. there is no ineciency, so long as the public information permits the statistical identi cation of a deviator. This is equivalent to require that the vector of actions satisfy pairwise identi ability; that is, \for every pair of players, the distribution over public outcomes induced by one player's unilateral deviations from this vector are distinct from those induced by others' deviations, so that the player's deviations can be distinguished statistically" (Fudenberg et al., 1994, p. 998). In general, once deviation has been observed, punishment must occur for the Folk Theorem to hold. When there is imperfect public information, a commonly observable signal, players 24

can agree on when a deviation has occurred and so when a punishment must be implemented. However, it is often the case that the agents receive dierent signals so that they may disagree on the need for punishment. This is the case of imperfect private information studied by Fudenberg and Levine (1991), which includes games of imperfect public information as a special case. These authors show that when an informational linkage is satis ed, a partial Folk Theorem can be stated for the approximate equilibria. 11 The informational linkage ensures that all players can communicate with each other and can correctly interpret the communication. In a strategy similar to Radner's (1986) review strategies, at a certain point in time, each player calculates a statistic that de nes a threshold level below which deviation is suspected. Test statistics results are communicated to the other players through signals, informing them as to whether or not the review was passed. To summarize and highlight the relevant results for our study, the most important result in models of in nitely repeated games is that repetition enables cooperation. Even if the stage game has a unique Nash equilibrium characterized by non-cooperation of the parties, repetition may allow new cooperative equilibria. For each party, the future bene ts from a continued relationship can outweigh the short-term bene ts obtained by deviating from cooperation. Thus, equilibria is found by isolating the set of strategies that support mutually desirable payo pro les (Osborne & Rubinstein, 1994). The theory speci es the need of credible punishment threats that are carried out when a deviation of a player has been observed. However, when there is imperfect observability of moves, the agents will have to rely on imperfect signals, which are commonly observable and depend on the agents' acts and on a random variable, to determine when punishment is needed (Green & Porter, 1984; Porter, 1983; Abreu et al., 1986, 1990; Fudenberg et al., Partial Folk Theorem in the sense that the mutually enforceable payos may be a strictly smaller set than the individually rational socially feasible ones (Fudenberg & Levine, 1991). 11

25

1994). If such a public outcome does not exist, then the existence of an informational linkage that ensures that the players can communicate with each other and can correctly interpret the communication will be needed (Fudenberg & Levine, 1991). In any case, a key element for the strategies to constitute an equilibrium is that once there is deviation or an indication that deviation has occurred (even if it has not), all players have the incentives to implement the punishment. When the actions are not observable, and the players have to rely on imperfect signals, the principal-agent review strategies model allows a ne-tuning of the assessment of the principal over the action of the agent. Allowing a margin of error, small deviations are not punished. Moreover, because the agent's compensation depends on the history over the review period, the agent obtains a partial insurance over the negative outcomes caused by random uctuations (Radner, 1981, 1985; Rubinstein, 1979). Although this model assumes one-sided asymmetric information, it can still be used when there is double-sided asymmetric information if the principal contracts simultaneously with a suciently large number of agents, which give rise to an aggregation of information about the actions of the principal (Al-Najjar, 1997).

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3 Brief Background of the Peruvian Agricultural Sector Market interlinkages in general are ubiquitous; and, in particular, the incidence of creditoutput interlinkages apparently grows with commercialization. The details of the contracts, however, may vary according to technological factors, social relations, and economic conditions. Peru is a highly heterogeneous country in terms of ethnic, geographical, social, and economic characteristics. The empirical part of this study focuses on credit-output interlinkages in a typical valley of Coastal Peru, where small farmers are the participants. Thus, the results here presented are representative of the linked arrangements that take place in the Coastal region of Peru, and cannot be generalized to other regions. Before presenting the surveys' results on credit-output interlinkages (Section 4), a brief background on the Peruvian Agricultural Sector is presented. The assumption is that the environment in which the parties interact may condition the terms of their transactions. This Section is organized as follows. The importance of agriculture in the Peruvian economy is rst described, together with a coarse description of the macroeconomic situation at the time the surveys were undertaken. Then, brief background information on the endowments and natural conditions, the tenancy system, rural nancial services, and the commercialization of agricultural products follows.

3.1 Agriculture and the Peruvian Economy Although the performance of the Peruvian Agricultural Sector has not been satisfactory over the last decades, agriculture is still an important sector in the Peruvian economy. Its production, in the aggregate, has not kept up with the growth of population. Furthermore, agriculture's share of the country's gross domestic product (GDP) fell from 14.2 percent to 12.2 percent from 1970 to 1995 (Instituto Nacional de Estadistica e Informacion , 1997). Despite this downward trend in agricultural production, agriculture still provides employment to about 32 percent of the labor force. Obstacles to increasing agricultural production include 27

the country's poor quality of resources and the negative eects of macroeconomic policies, which have persistently favored urban consumers at the expense of rural producers (Hudson, 1992). Since August 1990, the Peruvian economy has undergone radical reforms implemented by then newly elected president Fujimori. Extremely austere monetary and scal policies were implemented to stabilize the economy, which had been experiencing rampant in ation. Trade restrictions, output price controls, interest rate ceilings, and subsidies were slashed, and the government embarked on a sweeping privatization. In addition, all development banks were eliminated, and restrictions on land sales were removed, except on those imposed on communal properties. After annual in ation of 2,775 percent in 1989 and 7,650 percent in 1990, in ation dropped to 56.7 percent in 1992 (Banco Central de Reserva, 1992). The end of the hyperin ation, however, had come with a sharp decrease in real wages, a decrease in the real exchange rate, and a generalized recession in activities oriented to both domestic and external markets. The eects on agriculture were detrimental. The demand for agricultural products fell dramatically and agricultural relative prices sharply decreased. Agricultural production fell 13 percent in 1992 with respect to 1990, and relative prices dropped 13.5 percent in 1992 with respect to 1989. However, during the recovery period which started in 1993, the agricultural sector outpaced the performance of the economy as a whole. The agricultural sector grew 14.6 percent in 1993, 16.6 percent in 1994, and 6.3 percent in 1995, while the correspondent rates of growth for the gross national product were 6.4, 13.1, and 7 percent, respectively.

3.2 Endowments and Natural Preconditions Peru is a country that encompasses such a variety of geographic and climatic characteristics that 84 of the 103 possible ecological zones can be found in its territory. This diversity allows 28

the cultivation of a large variety of crops (The World Bank, 1989). Despite this fact, Peruvian agriculture encounters a severe limitation in the quality of its land endowment; 3.81 percent of its territory can be counted as arable, 2.11 percent is considered appropriate for perennial crops, 13.94 percent for pasture, 37.89 percent for forestry, and 42.25 percent is not adequate for agricultural production (ONERN: O cina Nacional de Recursos Naturales , 1982). In general, geographical, cultural, and ethnic determinants make Peru a highly heterogeneous country. This is particularly clear in the agricultural sector, which has three distinct agricultural regions. The coast (Costa), a desert strip located between the Paci c Ocean and Andean highlands, is relatively better endowed with agricultural production factors than other regions. The best land quality can be found in coastal valleys, and most agriculture there is irrigated. The coast accounted for 12 percent of the cultivated land area and for 46 percent of the total agriculture gross product in 1987 (Instituto Nacional de Estadistica , 1988). The main crops are cotton, yellow maize, sugar cane, potatoes, and rice. In contrast to the coast, the highlands (sierra), which are made up of the valleys and western plateaus of the Andean mountains, has only a small portion of irrigated land. Sierra agriculture heavily depends on irregular rainfall. In 1987, the sierra accounted for 49 percent of the cultivated land area, and for 29 percent of the total agricultural gross product (Instituto Nacional de Estadistica , 1988). The main products are potatoes, white maize, wheat, beans, and barley, as well as several Andean crops (quinua, canigua, olluco, oca, and kiwicha among others). Finally, there is the jungle (Selva) composed of valleys and eastern plateaus of the Andes and the Amazon basin. Year-round rainfall promotes the cultivation of coee, rice, and yellow maize. The Selva region accounted, in 1987, for 39 percent of the total cultivated land and 25 percent of the agricultural gross output (Instituto Nacional de Estadistica , 1988). Because the empirical study focuses in the Coastal region of Peru, the remainder of this section concentrates on the characteristics of this region.

29

3.3 Tenancy System In Peru, as in many other Latin American countries, agricultural reforms in the form of land redistribution were an important element in rural development programs. The last reform was the one carried out, between 1969 and 1976, by the military regime of General Velazco-Alvarado. The eects of this reform, however, have been unsatisfactory from the economic point of view. Large properties (haciendas) found mainly in the coastal region, and operating eciently, were expropriated and transformed into Agricultural Production Cooperatives (CAPS). Nonetheless, the newly created CAPS, with ex-hacienda laborers as their associates, failed to meet expectations, and soon they were facing a nancial crisis. Naturally, by the early 1980s, a process of subdivision emerged in coastal cooperatives. It is dicult to say whether the cooperatives' crisis re ected intrinsic problems of the cooperative model or dierent macroeconomic circumstances. Most likely, it re ected a complex interaction of both (Melmed & Carter, 1991). To date, nearly all collectively-owned CAPS have been subdivided into individually owned and cultivated landholding (Carter & Alvarez, 1989). The 1994 Agricultural Census found that 89 percent of agricultural land was under the ownership system, 1.17 percent under leasing, and 7.42 percent under communal property. More than 70 percent of agricultural units were less than 5 hectares. Nevertheless, farmers are not a homogeneous group, but they vary by degree of mechanization, specialization, labor use and income. In the coastal region, the degree of mechanization is larger than other regions.

3.4 Financial Services in Rural Peru Like many other governments in developing countries, the Peruvian government has intervened heavily in rural credit markets, through administrative allocation of funds, interest rate ceilings, and the establishment of specialized agricultural institutions, the most important being a governmental bank, the Banco Agrario del Peru (BAP). 30

The eorts to channel capital sources to rural areas have used the traditional approach of granting loans at subsidized interest rates. This was a response to the government's objective of improving the income distribution of rural areas, especially in the Andean region. Although the BAP had earned, among international lending institutions, a reputation of being a reasonably eective specialized credit agency, the in ationary burst in the middle 1980s, which was not matched by increases in nominal interest rates, ensured the rapid de-capitalization of BAP's revolving fund. BAP's closure in 1991 left agricultural producers without any formal source of nancing. However, the eect of BAP's closure was not uniform among farmers because, as in other experiences of subsidized loans, credit rationing occurred in BAP's loans, in favor of better endowed agents, thereby crowding-out small producers. As a consequence, market-oriented small and medium farmers, particularly those in the coastal region, are the most aected by BAP's liquidation. Large farmers, on the other hand, can move easily to commercial banks. Campesinos in the sierra region are probably not much worse o than before, because their access to BAP's loans was already very limited. As shown in Table 1, the results of the 1994 Agricultural Census show a correlation between the landholding size and the access to credit (captured by the question about ever receiving credit). Moreover, there seems to be a self-selection process on the side of small farmers, as the incidence of producers who have requested a loan in the year prior to the census increases with land size. However, the uneven access to credit is a secondary problem if farmers' global access to credit sources is considered. As indicated in Table 1, only 15.33 percent of the agricultural producers ever received a formal loan, and 6.14 percent requested and obtained a loan in the census year. In general, the Peruvian formal rural nancial sector is small and incomplete, weak and inecient. Only a small part of the rural population has access to nancial services, basically credit services. In order to ll in the absence of formal nancing to agriculture, recently, the government has created rural local banks, cajas rurales. However, their coverage is limited and some of them are already facing institutional viability problems. In addition, the so-called 31

semi-formal sector that comprises non-governmental organizations (NGO) is still dependent on donations and soft loans (Sotomayor, 1995). NGOs, however, are the most active sector in terms of credit technology development, although their outreach is marginal. Table 1: Access of Rural Households to Formal Credit

farm size(L) percentage that percentage with percentage that ever in hectares applied for a loan application approved received a formal loan TOTAL 8.01 6.14 15.33 2.97 2.04 6.25 L 21 1 10Ha: Source:

4.4 Interlinked Contracts: Trader-Lender and Farmer-Borrower Relationships The purpose of this sub-section is to provide a detailed description of the trader-lenders and farmer-borrowers relationships observed in the Huaral Valley and in the wholesale market of 44

vegetables in Lima. The terms and conditions of the contracts, the screening, monitoring, and enforcement mechanisms are depicted, together with the motivation of the parties for contract participation.

4.4.1 The Screening Process The relationship between traders and lenders in the credit and output markets is not casual. It is a personal and a long-term relationship, which is typically the result of social interaction and repeated transactions. The survey results indicate that on average, the parties knew each other for about nine years. Furthermore, they were involved in previous interlinked contracts, on average, in six opportunities. Typically, the parties of an interlinked contract in the study area start their relationship in just one market, the output market. Once the farmer is known by the trader to be honest and a good crop supplier (quality and consistency in the supply of crop is what traders highlight), the farmer is in a good position to request credit when needed, or the trader oers the farmer some working capital. Negotiations take place in the eld or in the trader's kiosk, and once the parties have reached an agreement, the loan is promptly granted, usually in more than one installment, or according to farmers' needs. In the few cases in which the relationship was new, potential borrowers were introduced to the trader by a farmer-borrower who already had an enduring relationship with the trader-lender. Farmers providing recommendations are not nancially accountable for new borrowers' debts. However, in practice, they understand they have a moral obligation to make sure that his/her sponsored farmer complies with the contract.

4.4.2 Motivation for Contract Participation What makes the parties participate in an interlinked contract? The results of the survey indicate that farmers and traders freely decide to participate in an interlinked contract, which suggests that there must be gains from the transaction for both parties. A common belief 45

about the relationship between farmers and traders is that it is an exploitative relationship, where the farmer is the party who loses. Interestingly, when farmers were put in the hypothetical position of actually being able to choose a lender, more than 50 percent indicated the crop traders as the most preferred lender 16 (see Table 11). The opportunity of the loan, its exibility, and the implicit possibility of deferring the repayment of the loan to the next season in the event that output is not realized were some of the elements pointed to by farmers that make traders' loans attractive. Thus, from the farmer's perspective, an important gain in an interlinked contract is not only the access to capital sources but also the access to exible and opportune loans. The presence of a liquidity constraint aects farmer's decisions about the optimal combination of inputs resulting in lower output levels than those obtained in the absence of liquidity constraints. Credit may then increase the level of output. However, o time loans and high transaction costs may oset the gains of relaxing the liquidity constraint. Sources of credit available to farmers, other than that of the wholesale traders, are loans from commercial banks mediated by specialized non-governmental organizations and loans from agricultural input retail stores. However, the loans from these sources lack one or more of the attributes ascribed to traders' loans. Loans from commercial banks take time to process, require collateral, usually follow (at least in the study area) a group lending approach, and typically specify the crop to be nanced. Moreover, farmers' responses to the survey's questionnaire suggest the existence of a self-selection process that keeps farmers away from commercial banks' loans, particularly when risky crops (as perceived by the farmers themselves) are involved in the contracts. As farmers expressed, it would not be rational to risk their land, oered as collateral for a commercial bank loan, to cultivate a risky crop. Loans provided by input suppliers are closer to traders' loans. They do not require The next preferred lender was a government bank. However, currently this option does not exist. The agricultural bank had consistently high rates of default and nally went bankrupt and was liquidated in 1991. Most of its clientele were farmers in the coastal region. 16

46

collateral and, although there is always a document to certify the loan, they are basically based on trust and repeated transactions in the input market. However, loan maturity is typically shorter than that of wholesale traders' loans. In addition, contracts with input suppliers specify cash repayments independently of whether there has been a good harvest or not. This feature diers from the contracts with wholesale traders, which leave room for postponing the repayment of the loan in adverse situations, implicitly providing a crop insurance. The cost of the loans does not seem to be an issue and may not be an important source of divergence among alternatives to nance crop production. When funding comes from interlinked contracts, farmers are to some extent conscious about the implicit interest rate they may pay if the trader under-prices the crop. What are the gains for traders from participating in an interlinked contract? Traders mention as the most important gain the fact that they can secure business in advance of the harvest, saving all searching problems when their time is more valuable. The attributes that traders look for in an interlinked relationship are volume and quality of crop and consistency in its supply. The above explanation about the linked transaction is consistent with the observation that a larger incidence of interlinked contracts exists in the market for tomatoes than in the market for sweet corn. This dierence can be attributed to at least two reasons. First, the per hectare cultivation of tomatoes requires a larger volume of working capital than sweet corn. Therefore, assuming that farmers in the study valley are similar in their liquidity position, farmers' needs of working capital are more pressing in the case of tomatoes than in the case of sweet corn. Thus, it is more likely that tomato farmers will engage in interlinked contracts more often than sweet corn farmers will. Secondly, the varieties of sweet corn coming from the coastal region (where the study area is located) are not valued by consumers as much as the varieties coming from the sierra region. Therefore, in the case of sweet corn, traders' gains from interlinked contracts with farmers 47

in the coastal region are expected to be lower than those with farmers in the sierra region. In the case of tomatoes, this regional dierentiation does not occur, as most of the tomatoes supplied by the wholesale market of Lima originate in the coastal region. In particular, in 1995, the Huaral Valley's share in the total supply of tomatoes in the wholesale market of Lima was, on average, 30 percent, reaching 40 percent from January to April (EMMSA, 1995). Overall, the supply of tomatoes from the study area is not only substantial, but also consistent. In contrast, the importance of the Huaral Valley in the supply of sweet corn is small, on average 3.5 percent, and it is only signi cant from June to December. Thus, the importance of the crop in the market is one of the incentives for participating in the linked contract. Summarizing, the attributes that traders look for are in general more evident in the case of tomatoes than in the case of sweet corn. In addition, farmers' needs for liquidity are more pressing in the rst case than in the second one. Therefore, it is reasonable to nd a larger incidence of interlinked contracts in the tomato case than in the sweet corn case.

4.4.3 Terms and Conditions of the Contracts: Implicit and Explicit Conditions Tables 12 and 13 show some characteristics of interlinked contracts as reported by farmers and traders, respectively. As shown in these tables, interlinked contracts in the study area are basically incomplete, informal contracts, based on trust developed after years of conducting business. Most of the time, there is not a loan document or there is just an informal receipt specifying only the amount and date of loan granted. Typically, contracts take place without a witness or guarantor.

48

Table 12: Loan Characteristics as Reported by Producers Description Loan contract: - none - letter - informal receipt - loan contract Loan form: - cash only - kind only - both Crop supervision: - yes - no Contract terms: - loan size (nuevos soles*) - loan size per hectare - maturity (weeks) - length of relationship ...with the trader (years) - percentage of harvest ...promised to the trader

tomato producers

cases

percentage

21 4 10 1

sweet corn producers cases

percentage

58.3 11.1 27.8 2.8

24 0 10 0

70.6 0 29.4 0

35 1 -

97.2 2.8 -

15 5 15

42.9 14.3 42.9

29 7

80.6 19.4

22 12

64.7 35.3

observations

mean

observations

mean

36 36 36

2283 1346 12

35 35 35

929 553 14

36

8.38

35

8.04

36

77

35

100.00

Survey to farmers, conducted in the February 1995 - August 1995 period. (*) During the survey period, on average, 1 sol=0.45 US$ Source:

Some terms and conditions of the contract are made explicit orally and some others are just implicit conditions. The fact that the loan has to be repaid with the harvest and within an agreed upon period of time (harvest time) is one condition usually made explicit. There are not explicit interest rates. Implicit conditions are understood as a result of customary practice, which usually varies according to the type of crop. Some of these conditions are: the amount of crop involved in the contract, the understanding of who is responsible for the harvest of the crop and for its bagging, loading, and transportation costs, and the time at 49

which prices are determined. Table 13: Loan Characteristics as Reported by Traders Description Loan contract: - none - letter - informal receipt - loan contract Loan form: - cash only - kind only - both Crop supervision: - yes - no Technical assistance: - yes - no Contract terms: - loan size (nuevos soles*) - loan size per hectare - maturity (weeks) - length of relationship ...with the farmer (years) - percentage of harvest ...bonded in the contract

tomato producers

cases

percentage

50 55 39 0

sweet corn producers cases

percentage

34.7 38.2 27.1 0

16 10 26 0

30.8 19.2 50.0 0

111 4 29

77.1 2.8 20.1

5 10 35

10 20.0 70.0

111 33

77.1 22.9

33 19

63.5 36.5

46 98

31.9 68.1

23 29

44.2 55.8

observations

mean

observations

mean

140 138 106

1856 955 11

48 48 51

1591 532 15

149

8.93

53

9.54

144

94.03

52

100.00

Survey to farmers, conducted in the February 1995 - August 1995 period. (*) During the survey period, on average, 1 sol=0.45 US$ Source:

Implicit conditions, however, are not always clear. For instance, in the case of tomatoes, there is a discrepancy between the farmer's and the trader's report about the percentage of harvested crop bonded in the interlinked contract. Farmers reported a lower percentage than traders did, as can be seen by comparing Table 12 and Table 13. This discrepancy does 50

not occur in the case of sweet corn. There are at least two reasons that can explain this discrepancy between parties and across crops. First, farmers determine this implicit amount of crop, taking into account the size of the loan (relative to total production costs), and the time in the production period at which the loan was granted. The larger the participation of the loan in total production costs and the earlier the participation of the trader in nancing the production, the larger is the trader's share in the harvest. The share of the loans in total production costs are about the same for the two crops; but loans are granted earlier in the production period in the case of sweet corn than in the case of tomatoes. Secondly, since tomato demands a larger investment per hectare than sweet corn, it is more likely that a tomato farmer will engage in interlinked contracts with more than one trader to cover all the costs of production. In this case, it is more comfortable for farmers to report that they understand that not all the harvest was bonded with one trader in order not to appear dishonest. The actions to be taken in default events are not speci ed, for that would be understood as a signal of lack of trust. However, farmers expect that if the harvest is poor, both parties will be able to come out with some reasonable way of loan repayment. Loans may be granted in cash or in-kind or in a combination. The in-kind component more frequently consists of seeds and eventually fertilizer and pesticides. In-kind loans were basically found in the case of sweet corn, while loans for tomato cultivation were typically granted in cash. A possible explanation for this fact is that sweet corn traders actually trade two types of goods, fresh harvested sweet corn and sweet corn seed. Traders usually held inventories of sweet corn seed, which is bought from farmers or accumulated from the corn not sold when fresh. Moreover, not infrequently, when the market prices of fresh harvested sweet corn are too low, traders will prefer to save the merchandise for later sale as seed. Therefore, the fact that wholesale traders provide in-kind loans (mostly seed) to sweet corn producers can also be understood as an additional channel for traders to sell their merchandise. The price of sweet corn seed charged to the farmer-borrower is, in most of the cases, equal or lower 51

than the prevailing price in retail stores. Out of 21 sweet corn farmers who had received inkind loans, only two reported an excess in the input price charged by the trader-lender. In contrast, tomato seed is not usually commercialized by tomato traders. Imported and domestic seed previously treated is mostly sold by input suppliers. The average size of the loans is generally small. Aside from a few cases in which loans were granted in dollar units, loans are typically granted in the domestic currency (nuevos soles), in two or three installments or according to farmers' needs. Traders reported that frequently they had to provide larger amounts of capital than they initially expected, in order not to lose the initial investment. These unexpected loans occur when there is an imminent risk of crop loss due to pest infestation and the farmer lacks working capital. The alternative to increasing the loan would be to let the farmer borrow from another trader and then to share the harvest with the other lender. The maturity of the loans usually spans the production period. However, in the case of tomatoes, trader's participation in crop nancing starts on average four to six weeks after seeding. Tomato traders reported that because tomatoes are a risky crop and demand signi cant amounts of nancing per hectare, they need to have a signal about farmers' ability. This signal is the health of the tomato plant after four to six weeks. The survey reveals that crop supervision is an important element in interlinked contracts. Monitoring provides information about farmers' nancial needs and a basis to judge contract performance. The cost of crop supervision is not as high as it would be for a specialized lender, because trader-lenders supervise the crop while searching for merchandise. The time at which the price of the crop is determined is more part of the usual practice in a particular commodity market than an explicit element in the interlinked contract. In the case of sweet corn, for example, prices received by farmers are set at harvest time or a few days before harvest. In the case of tomatoes, however, prices are revealed to the farmer after the trader sells the crop, that is, the price is more directly related to the spot market. This dierence is related to the fact that traders take the responsibility of the single harvest 52

of sweet corn, while producers are in charge of the multiple harvests of tomatoes, which in contrast with the sweet corn are more exible in terms of harvest timing. Sweet corn has an exact maturity day, and traders try to secure that harvest by paying in advance or right before harvest.

4.4.4 Contract Performance The survey results show that the established form of repayment was, in general, honored by borrowers, although the number of defaulters as a percentage of total current borrowers was about 20 percent. Default cases were those in which the farmer was unable or unwilling to pay the loan. The cases in which the amount of harvest received was below the trader's expected level were not considered (by traders) default cases as long as a \reasonable" amount of crop was received and the loan was recovered. However, when the crop delivered was below the trader's expectations, traders report giving warnings to the producer making explicit their awareness that the full amount of crop produced was not delivered. These warnings are given to induce better behavior in the next season. Default was more frequent in the case of tomatoes (27.98 percent) than in the case of sweet corn (18.50 percent). Furthermore, the percentage of contracts in which traders reported they had not received the expected amounts of crop is 30.8 percent in the case of tomatoes and 15.8 percent in the case of sweet corn. In view of the characteristics of the cultivation, harvest, and marketing of tomatoes and sweet corn, this nding is not surprising. Again, the fact that tomatoes demand larger amounts of money per hectare of production makes it more plausible for the farmer to establish a nancial relationship with more than one trader. In addition, the multiple harvest of tomatoes carried out by producers leaves more room for opportunistic behavior than in the case of sweet corn in which the one-time harvest is performed by the trader. This situation is acknowledged by the traders who, in order to reduce crop deviation, typically participate in the harvests in which the quality and the amount of tomatoes peak. 53

It is also the traders' practice not to charge for loan recovery until the good harvests are delivered. This practice is to keep the farmer \bonded". From the farmer's point of view, traders' compliance with the linked contract can be considered satisfactory, although 54 percent of the farmers reported that they were paid for the crop below the price they could have obtained if they were debt free. This practice, however, was considered by most producers to be reasonable as long as crop under-pricing was small. In addition, 41 percent of the farmers thought they had received the same price as farmers without debt. 17

4.4.5 Default Events and Coercive Actions. Because the boundary between the inability and unwillingness to comply with contractual obligations is not clear, traders have to design an enforcement mechanism suciently strong so as to deter opportunistic behavior. However, because the environment in which farmers work is very uncertain, enforcement cannot be too strong because it may eliminate bona de trade (Fafchamps, 1996). The survey results seem to support this point. In order to take measures to discourage opportunistic behavior while not being so harsh as to deter contracts with good farmers, traders have to assess whether the breach of contract was due to unforeseen events or to dishonesty or incompetence. The fact that linked contracts are long-term relationships is a key element. It allows one party to gather valuable information about the other party's type, and to better derive inferences about true performance. In the case of the trader-lender, this information is complemented with her knowledge about the performance of other farmers in the same area, or, when monitoring was more intense, with the information gathered in eld visits during the production period. The assessments made by traders about farmers' default cases are shown in Table 14, 17 Out of the 72 respondents, there were three farmers who reported the trader refused to pay them what was owned.

54

which displays the traders' classi cation of defaults as \involuntary" and \voluntary". In general, the majority of defaults were considered to be involuntary, and basically caused by poor harvest and/or low market prices. Table 14: Default Events and Coercive Actions current farmer-borrowers borrowers in defaults default as a percentage of ...current borrowers involuntary default voluntary default

Actions taken in default events: - debt payment postponed - money back - legal enforcement - pending - loan is considered lost

Source:

valid total as percent mean median cases of defaults

63 57

716 146

100.0

11 3

7 2

54 55

20.4 109 37

74.6 25.3

2 1

2 0

55 55 55 53 55

95 10 0 32 9

65.0 6.8 0.0 21.9 6.2

2 0 0 1 0

0 0 0 0 0

Survey to traders, conducted in the February 1995 - August 1995 period.

In most cases, when the traders' assessment was that the default of the farmer-borrower was involuntary, the payment of the loan was postponed to the next season. In a very few cases, however, the postponement of loan repayment was the action taken as the last resort to the alternative of declaring the loan lost. In exceptional occasions, those who might be considered premium farmer-borrowers received a new loan for help to nance next season's crop cultivation, and to facilitate the loan repayment. The fact that the loan was returned in cash (\money back") was not necessarily associated with the willingness or unwillingness to comply with contractual obligations. If a farmer had a bad harvest of the crop nanced with an interlinked arrangement, but had income ows from another crop cultivation or another activity, he was still able to repay the loan. \Pending" meant that the trader-lender and the defaulter did not reach an agreement 55

about how the loan should be repaid. Traders reported that the situation was \pending" in two cases: when farmers opportunistically (voluntarily, according to the trader's assessment) breached the contract, and when (to the knowledge of the trader) the farmer refused to repay the loan although he had income ows from other sources (such as the cultivation of other crop or from other income generating activity). \Pending" does not mean lack of action; it usually meant harassment through implicit or explicit threats. As expected, legal actions were not taken when the interlinked contract was breached, because it is too costly, monetarily and in terms of time. The fact that, according to the survey, 33.2 percent of the contracts involved a commercial letter (which is accepted in court as proof) did not imply the use of legal actions to enforce the loan. Formal documents were used only to compel loan repayment through threats of resorting to court. 18 The loan was considered lost in two kinds of situations: (i) the size of the loan was small so that traders did not consider it cost eective to exert eorts to recover the loan, (ii) traders were unable to nd the debtor because he/she was cropping in a rented land for the period in which interlinkage took place. In these cases, the relationship was terminated. In general, when the trader highly suspects that the farmer-borrower breached the contract as a consequence of dishonest behavior or incompetence, she decides to terminate the relationship. Pertaining to the farmer's assessments about the trader's behavior, farmers in the Huaral Valley have to rely on the imperfect sources of information they have, which are relatively good for areas with easy access to Lima. Because the Huaral Valley is near Lima and the road conditions are good, most farmers may have at least average daily price information, which is published daily in the wholesale market. In addition, farmers can get information from other producers, from truckers, and from traders other than their lender. The selection of partners continues as the relationship is built. When asked about their participation in future interlinked contracts, 91.4 percent of the traders reported that they However, for those farmers who were well informed about legal procedures, this threat is ineective since, by law, debt is not a reason for imprisonment. 18

56

will continue the nancial relationship only with those farmers who they knew were honest and who knew how to work.

4.5 Main Economic Issues that the Formal Model Should Address. Results from the survey suggest the need to highlight in the model the following characteristics of interlinked contracts, as observed in a Peruvian coastal valley.

 The characteristic of linked contracts of being long-term relationships makes opportunistic behavior costlier, because the parties have too much to lose in the future.

 Farmers engage in interlinked contracts with wholesale traders not just because these

contracts allow them the access to (any) loans but rather because interlinked contracts permit them the access to loans with certain attributes: promptness and exibility. Farmers understand exibility mainly in the sense that there is room for negotiation and postponement of the loan repayment in bad states. Thus, farmers value the access to loans as well as the possibility of risk shifting.

 The right mix of severity and exibility allows the traders not to scare o honest and

ecient farmers who can provide a good and regular supply of crop that can increase the traders' share in the market. When the trader's assessment is that the farmer defaulted in the loan because of opportunistic behavior, the relationship is ended. However, \ exible" terms are oered to those whose default was assessed as involuntary.

 Farmers who have a high probability of revising the contract in bad states, postponing the repayment of the loan, are usually farmers in good standing, with a long-term relationship with the traders and who have gained a good reputation.

 Traders who are engaged in a long-term relationship with farmers are those with a reputation of being \fair". 57

5 Modeling Credit-Output Interlinked Contracts In this section, game theory is used as a tool to analyze credit-output interlinked contracts as an in nitely repeated game model. The purpose is to improve the understanding of these informal arrangements. Section 5.1 provides a detailed description of credit-output interlinked contracts in game theoretic terms. The general results, particularly the gains from contract participation and those from interacting repeatedly as opposed to a one time interaction, are presented. Section 5.2 focuses on better explaining the structural behavior of the contracting parties that results in cooperative strategies being an -equilibrium. Radner's (1985) model of review strategies is adapted to represent the speci c contracting problem analyzed in this study.

5.1 Credit-Output Interlinked Contracts as Games As the survey results show, interlinked contracts involve two individuals whose payos depend not only on their preferences and the technology but also on the other party's preferences and choice of action. Because of this situation, agents behave strategically in an attempt to optimize their own objectives. Game theory provides a systematic way of analyzing problems of strategic behavior where one agent's action depends essentially on what the other agents may do (Eatwell, Milgate, & Newman, 1989). Game theory by itself does not help understand economic phenomena. Its purpose is to help economists understand and predict what will happen in an economic context (Kreps, 1990). In particular, game theory is used in this chapter to understand the structural behavior of the contracting parties engaged in a creditoutput interlinked arrangement. The fact that credit-output interlinked contracts are long-term relationships makes repeated games a convenient approach to model these contracts. In particular, when trust and social pressure are important to enforce mutually bene cial informal agreements without legally enforced contracts, repeated games may be a good approximation (Fudenberg & 58

Tirole, 1991, p.145). If the game (the contract) is repeated in nitely, or if the players, in every stage of the game, think that the game will continue, repetition makes possible credible promises and threats to enforce the terms of the contract. In the case to be modeled here, in each stage of the repeated game, the moves of the trader and farmer are sequential, and the players do not directly observe the opponent's action. They observe only signals of those actions, which are used to form beliefs about actual behavior. The unobserved action of the trader consists of the charges she applies to determine the price of the crop to be paid to the farmer. The unobserved action of the farmer is the choice of the fraction of the harvested crop to be delivered to the trader. It is assumed that the trader has successfully screened good (skillful) farmers from bad (incompetent) farmers. Thus, farmer's skills or low eort are not a source of moral hazard.

5.1.1 Description of the Stage Game The game that will be modeled here is one of incomplete information. The players' payo functions are not common knowledge, and at some moves in the game, the player with the move does not know the whole history of the game. Figure 1 shows a representation of the game in an extensive form. The extensive form was selected because it provides insights beyond those generated by analysis of the equilibrium based on a strategic form representation. The game involves two players, a trader and a farmer, hereafter she and he, respectively. The moves of nature are considered exogenous. The timing of the game is as follows: 1. The game begins with a decision node for the trader, who chooses between lending (L) or not lending ( L) an amount of money \L" to the farmer. The trader decides to continue or not with the game. If she decides not to lend, the game is over, and the payos of the players are given by their reservation utilities, u for the trader and v  for the farmer. If she decides to lend, it will be under the condition that the farmer 59

sells all of his crop to (through) her. The trader promises the farmer to pay market price for the crop, after crop delivery, with the deduction of charge for the loan and the average commission trade. 2. If a loan is forwarded, a decision node is reached by nature. Assume that the yield Y depends only on the loan and on nature's moves, represented by a random variable y ; i.e. Y = y (L; y ). For simplicity, it is assumed that y can take two values that result in high output (Yh ) or low output (Yl ). 3. After nature's move, the uncertainty on output is resolved and it is observed only by the farmer, who then decides about the fraction \a " (0  a  1) of the harvested crop to be sold to the trader-lender. Thus, a expresses the action of the farmer. He can either cooperate (C ) or not cooperate ( C ). Cooperation means that he sells all the crop to the trader-lender (a = 1). No cooperation occurs when the farmer sells (diverts) part or all the crop to a pure trader (a < 1), expecting to obtain better prices. 4. Once the trader-lender observes the amount of crop delivered to her, she knows she has reached an information set, but she is unable to distinguish the information nodes in this set. If the farmer delivers to the trader-lender an amount of crop below her expectations, the trader will not know whether nature has played Yl and the farmer has cooperated or whether nature has played Yh and the farmer has chosen not to cooperate. However, there are two sets of information that can be distinguished by the trader:

 The information set where the move of nature resulted in high output and the farmer has chosen to cooperate. This is because the average volume of crop that a hectare of land can produce in optimal conditions is common knowledge; and

 The information set that summarizes the occurrence of bad output and noncooperation by the farmer. In fact, we can assume that this node will never be 60

reached. The farmer nds a deviation to be pro table only if a signi cant amount of crop is at stake. The existence of economies of scale in transporting the crop from the eld to the wholesale market makes deviation unpro table when there is low production. In addition, low volume of crop is usually associated with low quality of crop, which is priced lower in the market. Thus, it is expected that a farmer who has observed low output will cooperate with the trader. The extent to which the trader is informed, is illustrated in Figure 1 wich shows the trader with three information sets. The two singleton sets are those that contain perfectly identi able information nodes. The non-singleton set shows the trader's inability to distinguish between the information nodes corresponding to the events of high output and farmer's non-cooperation, and low output and farmer's cooperation. These nodes are connected with a dotted line. 5. The last move in the stage game corresponds to the trader-lender. She has to calculate the share of the farmer as a payment for the bonded crop. She does this after observing the realization of the spot prices, which are exogenously determined by: P = p(p ), where p is a random variable. However, because the observation of the spot price is private to her, she may calculate the price to be paid to the farmer as follows:

P I = (1 ; c ;  ; )P (p ); where P I is the interlinked price, P is the spot price, c is a nancial charge for loan recovery, accepted by the farmer as a \reasonable" charge,  covers the marketing costs at the average commission trade, and  is a possible surcharge that equals zero if the trader-lender acts cooperatively, and that is larger than zero otherwise. Thus, the trader's action is expressed by the choice of . 61

 L  L  

Figure 1: Extensive representation of the interlinked contract game T

- (u; v )

?

N

HHH  H Yh HH Yl   H   j H

    C C         F

J J J J





C



T

J

J

J

J C

J 

^ J

J ^ J

T


A
A C
A C
A
A
A



F

T


A
A C
A C
A
A
A


C







T


A A A

C A A A


A
A C
A C
A
A
A

(A,B) (A+,b) (a,B+) (A-,B-) (a,c) (a+,c-) (0,0)

Trader's payo ranking: A+, A, A-, a+, a, 0. Farmer's payo ranking: B+, B, B-, b, c, c-, 0.

62



(0,0)

From the description above, it is important to highlight that there is double-sided asymmetric information. First, in contrast to the farmer who observes the realization of yield, the trader-lender observes only the crop delivered by the farmer to her. Second, in contrast to the trader who observes all the components of P I , the farmer observes only P I . This information asymmetry leaves room for opportunistic behavior on both sides. The farmer may sell part of his crop to a pure trader (choose a < 1) and report to the trader-lender that the harvest was low. The trader-lender may claim she has observed a lower price than the realized market price, when in fact she is playing non-cooperatively (choosing  > 0).

Proposition 1 (Nash Equilibrium of the Stage Game) In the Nash equilibrium of the stage game described above, the players will fail to agree on an interlinked contract. Both trader and farmer will maximize their short-term gains; and, as a result, they will obtain their reservation utilities, u and v  , respectively.

Assume that agents freely decide to participate in the game (the interlinked contract). The decision is made rationally, by comparing the expected utilities in the game with their reservation utilities; i.e. with the expected utilities they can obtain if they do not participate in the game. On this account, agents can choose not to participate if the expected rewards from the game fall below their reservation values. These values constitute a rst lower bound for the expected utilities in the game. Rationality implies that players in the stage game will be interested only in the maximization of their individual immediate payos. Because the environment in which these contracts take place either does not provide legal mechanisms to enforce them or those mechanisms are ineective, in the stage game there are no credible threats of being punished if the terms of the contract are not honored, or there are no credible commitments to act cooperatively. The way equilibrium is reached can be better explained by backwards induction. Starting from the last move in the game. A rational strategy for the trader-lender is not to cooperate; i.e. to make  large enough so that P I = 0. Because the farmer assumes 63

that the trader is a rational individual, he will expect her to behave non-cooperatively, and therefore he will decide not to cooperate (a = 0). In turn, the trader assumes rationality of the farmer and will anticipate a non-cooperative behavior from him, and therefore will decide not to forward the loan in the rst place (L = 0). The expected utilities of the game, u and v, will be zero. As a result, the Nash equilibrium of the stage game is not to sign an interlinked contract, and the players get their reservation payos, u and v . Without loss of generality, we can assume that u > 0 and v  > 0, so that the decision not to enter in the game is clear. However, if no contract is signed, the farmer will have to nance his production with loans from other sources, at higher interest rates. The trader will not have secured a volume of crop to market. We can argue that, under certain conditions, the equilibrium utilities u and v  are smaller than the utilities the players may have obtained in the interlinked contract had they cooperated.

Proposition 2 (Player's Welfare in the Stage Game Equilibrium) i) a risk averse farmer will be worse o without the interlinked contract provided that he has to resort to more expensive capital sources, and that his utility function presents decreasing absolute risk aversion (DARA); ii) a trader will be worse o without the interlinked contract than with the interlinked contract if the expected costs of searching merchandise exceed the opportunity cost of the loan granted.

i. Consider a farmer who must borrow to nance crop production. The loan is received at planting time and paid back, with interest, at harvest. Let: ( (L; p; y ) ; rL) be the

farmer's pro t, over the crop season period, where \ " is the farmer's income from crop sales; p and y are, as before, i.i.d. random variables aecting prices and yield, respectively; \L" are loans, and \r" is the interest rate on loans. Note that the principal received and repaid cancels out in the time frame considered. De ne:  = (p y ). Then, the farmer's problem of maximizing his expected utility can be written as: 64

max EV ( (L; ) ; rL) L The rst order condition (FOC) is:   E V 0 (:)( L ; r) = 0

The second order condition (SOC) is: h i E V 00(:)( L ; r)2 + V 0 (:) LL < 0

The failure to sign the contract implies that the farmer will have to nance his production with loans from other sources, at higher interest rates. Thus, the farmer will be worse o if : @EV (:) = E V 0(:)  @ @L ; L  0 @r @L @r By assumption: V 0 > 0, and @ =@L > 0. Thus, the farmer is worse o if :

@L < 0: @r From the total dierentiation of the rst order condition it follows: h i   E V 00( L ; r)2 + V 0 LL dL ; E V 00( L ; r)L + V 0 dr = 0

dL = E [V 00( L ; r)L + V 0] dr SOC

65

where SOC < 0. Therefore, dL=dr < 0 if:

E [V 00( L ; r)L] > 0: Assuming that  > 0 and that L > 0, take w de ned by  such that L = r. Let rA(w) be the absolute risk aversion coecient, and assume DARA. This implies:

rA (w) ) rA(w)( L ; r) rA (w) ) rA(w)( L ; r) ) (V 00(:)( L ; r) ) E [V 00( L ; r)L]

> > < > > >

rA (w); : : :if : L > r rA(w)( L ; r); rA(w); : : :if : L < r rA (w)( L ; r) ;rA(w)V 0( L ; r) : : : 8 0:

ii. Assume a crop trader who has a capital surplus ` `L", which can be deposited in a commer-

cial bank receiving an interest rate ro , or may be lent to farmers through an interlinked contract. If no contract is signed, the trader incurs costs of searching for merchandise, which are s per unit of output marketed. The trader receives in her marketing activity the average commission trade \ 00. If an interlinked contract is signed, assume that the trader does not earn any explicit interest on the capital lent, but reduces her cost of searching merchandise to zero. In addition, she earns the average commission trade and, if found pro table, an additional margin  that she could seize from the farmer. Further, assume that in the interlinked arrangement the farmer cooperates, so that all the farmer's crop production (Y ) is marketed by the trader. Therefore, the trader's expected returns without the interlinked contract (ERw=o) and with it (ERw) 66

are, respectively:

ERw=o = E [ (P:Y ; s:Y + ro L] ERw = ( + )E (P:Y ):

The trader will prefer the interlinked contract if ERw > ERw=o which is equivalent to:

E (P:Y ) > E [roL ; s:Y ]: Furthermore, if the trader cooperates; i.e.  = 0, s:Y > roL, which says that if the trader-lender does not underprice the farmer's crop, for interlinkage to be preferred, it suces that the expected total search costs exceed the foregone capital gains when lending L to the farmer. In general, searching costs include information gathering about opportunities and arrangement of individual transactions. Costs in searching opportunities include the money and time expended by the trader in information collection about when and where crops are being harvested, so that potential parties in a transaction are located. Once the potential parties meet there are negotiation processes that involves costs. In addition, typically traders will want to form a \clientele" of good crop suppliers. This involves continuous investment through repeated transactions and social interaction, which is costly. On the other hand, the foregone capital gains of the trader when lending to the farmer may not be so important. The relevant variable to analyze foregone gains for the trader is the deposit interest rate net of the transaction costs incurred by the trader when making deposits and withdrawals of her funds to and from formal nancial institutions. Inconvenient oce locations and banking hours, and bureaucratic procedures often adopted by formal institutions, especially when withdrawing funds, make transaction 67

costs high; thus, net deposit interest rates are low. Liquidity is highly valued by traders because any delay in the capital needed may imply losing opportunities to increase the volume of crop marketed. These problems were mentioned by traders in the survey, when they were asked to explain their low participation in formal capital markets. From the arguments above, it can be expected that the trader will nd it more pro table to allocate any capital surplus into an interlinked arrangement with a farmer than to deposit it in a formal nancial institution.

5.1.2 The In nitely Repeated Game Suppose now that the one-stage game described above is repeated in nitely often. The resulting game is called the supergame. In each stage game t = 1; 2; 3;


; 1, agents face a new environment and choose a one-period strategy. The main result of in nitely repeated games is that players can in uence their opponents' behavior by promising rewards and credible threats. As a consequence, a strong result of in nitely repeated games is that \if the stage game has a unique Nash equilibrium, there may be sub-game perfect outcomes of the in nitely repeated game in which no stage's outcome is a Nash equilibrium of the in nitely repeated game" (Gibbons, 1992, p.78). In particular, in the game studied here, a new equilibria that involves cooperation between the trader and the farmer emerges. This result holds as long as each player has a long-term horizon and takes into account how her/his behavior and that of the opponent aects the payos in the future. The survey provides information about the importance of a long-term horizon to sustain an interlinked contract. As mentioned before, the parties involved in an interlinked contract have been transacting, on average, for nine years. Moreover, traders who previously were engaged in an interlinked contract but were working independently at the time of the survey, reported high farmers' default as a reason for stopping the interlinked transaction. The fact that those traders were in their late sixties suggests that farmers envisioned that the end of 68

the \game" was approaching.

Proposition 3 (Results of the In nitely Repeated Game) If the nature of the interlinked contracts is that of an in nitely repeated game, it is possible for the parties to induce cooperation, and so to approach an ecient equilibrium.

First of all, the assumptions about how much information the players have available before making their decisions need to be restated. Through time and as the game is played over and over, the players accumulate information that can help to infer their opponent's behavior. The rules of each period game remain constant; but the environment, the realization of crop quantities, and their market prices change randomly. It is assumed that the random variables are independent and identically distributed. The farmer (trader-lender) perfectly observes the realization of quantities (prices) but not the realization of prices (quantities). However, neither player is totally uninformed about the variable not observed. The farmer can learn about the ranges over which prices have varied in a particular day. The trader, through her dealings with other farmers, can observe aggregate shocks, but not idiosyncratic shocks aecting the farmer's nanced crop. Based on these observations and on the signals sent by the opponent, players can make assessments about the other party's behavior, which will help them to design incentive mechanisms to induce cooperation. In particular, there are two ways in which the trader can induce cooperation and make the interlinked contract a mutually bene cial choice. First, because the trader moves second in the sub-game that starts with a loan, she can punish any alleged deviation of the farmer and reward a supposed cooperation. More speci cally, at the time of crop delivery, the trader who is unable to distinguish the nodes in her information set, may devote herself to the following strategy: \if, after receiving the crop, I believe the farmer has cooperated, I will pay him, discounting from the market price only the average market trade margin  ; but, if I believe he has deviated, I will discount an additional margin ". Secondly, as time goes on and the game is played repeatedly, the trader will be able to update her assessments about the 69

farmer's behavior, and base her decisions, about forwarding or not forwarding a loan to the farmer, on these assessments. After a certain number of periods, she can review the history of the farmer and decide whether to continue with the contract or to break the relationship. On the other hand, the farmer has only one way to aect the outcome of the game; i.e. through his decisions about the amount of crop delivered. If the farmer believes the relationship is not worthwhile for him (if he believes he has been cheated on prices), he will punish the trader in the next period by receiving a loan and not cooperating. This action will later in uence the assessment of the trader, and eventually result in a termination of the relationship. The strategy above depicted is a rst approach to describe the enforcement mechanism as observed in Coastal Peru. However, the threat maintained by the trader in the stage game may have two con icting eects. It may eectively deter a possible opportunistic behavior of the farmer, or it may produce a reaction from the farmer in the next season (by deviating from cooperation) if he has been punished unfairly. This behavior would eventually force the termination of the relationship. As noted before in this study, in the presence of uncertainty, the trader has to be severe enough to enforce compliance, but not too harsh to discourage good farmers. Therefore, by being more lenient, the trader would avoid making mistakes and could improve contract performance. This is what the review strategies model presented below captures very well by assuming a review period within which the trader always cooperates, independently of the farmer's behavior, and punishes only if the farmer fails a test that is based on the accumulated information during the review period. In what follows, a model of review strategies is used to rigorously show that cooperative behavior of the contracting parties can produce a set of equilibria. However, the review strategies is just one possible set of equilibria among many others that the theory of repeated games will predict. Unfortunately, the theory does not help in selecting one equilibrium that may be considered the solution. The fact that the agents adopt a particular way of \playing the game" is related to past relevant experiences and to the notion of how individuals in 70

general behave. However, how these expectations are formed, how and why they persist, are questions still unexplained by formal mathematical game theory (Kreps, 1990). The review strategies was chosen because it better re ects the behavior of the participants of the interlinked contract in our study case.

5.2 A Model of Review Strategies The following model is based on Radner's (1985) paper on repeated principal-agent games with discounting. In the case of the interlinked contract game, the trader-lender is considered to be the principal and the farmer-borrower the agent. The model outlined below is, in general, consistent with the assumptions in the previous section, except in one aspect. Radner's model assumes one-sided asymmetric information. His model features unobservable actions of the agent, and a stochastic outcome which is correlated with players' actions. In the interlinked contracts as observed in Coastal Peru, asymmetric information exists on both sides: the trader (the principal) and the farmer (the agent). Because a trader contracts with multiple farmers, a result of Al-Najjar (1997) provides a theoretical justi cation for using a one-sided asymmetric information model. The attributes of the interlinked contract are closely related to those of the contracting problem studied by Al-Najjar. In a static setting, he assumes a principal contracting in two-sided moral hazards with N independent agents. Although there is no common uncertainty in the agents' performance that can be used to improve the agents' incentives through relative performance evaluation, optimal incentive schemes eliminate the incentive problem of the principal when the number of agents is suciently large. There are reputation-like eects that are formed through an aggregation of information on the action of the principal, reducing the doublesided moral hazard problem to the simple principal-agent model with private information on the side of the agent. More precisely, and in terms of the problem being analyzed here, traders typically enter 71

into interlinked arrangements in the same agricultural season with large groups of farmers, operating in the same geographical area. Assume that the trader can costlessly commit himself to taking an action of his choice with all farmers. Each farmer is informed about the distribution of crop market prices, but not the exact price at which the trader sold his crop. Based on the information available, a test statistic is de ned. A low value of the test statistic will be interpreted as evidence that the trader has deviated. Therefore, given that a particular action has been taken by the trader, his private information is eliminated through an aggregation of information about his actions; thus, reducing the problem to one-sided asymmetric information. However, if it is not possible to provide an incentive for the trader to apply a single action for all farmers, the incentive scheme would be such that the trader will deviate with a small fraction of farmers and will do this randomly. Given the argument above, Radner's (1985) model, with some adjustments, is appropriate to understand the behavioral structure of credit-output interlinked contracts, as observed in Coastal Peru. Speci c changes in the assumptions of Radner's model were made to better t the characteristics of the study case. These changes are as follows:

 First, in this study, instead of assuming a risk-neutral principal and a risk-averse agent, both players are assumed to be risk-averse.

 Second, in this study, the farmer (the agent) chooses in each period an action which

depends on the information he receives about the realization of a random variable, determined by nature. In Radner's model, there is no previous information about the environment available to the agent at the time of making the choice of action.

 Third, the moves of the players are sequential. 19 As a result of these changes, there are modi cations of the proofs, but the main results found in Radner's paper hold. 19

The rst two assumptions were suggested for a more general model in Radner (1985).

72

In a review strategy, the trader periodically evaluates the performance of the farmer over a pre-determined period (a review period). If the result of the evaluation is satisfactory, a new review period is started. Otherwise, the agents enter a punishment phase, after which a new review period is initiated. During the review period, the trader assigns herself the strategy of choosing a cooperative action independently of the outcome in every stage of the review period. The farmer enforces the trader's cooperative action by a constant threat of optimizing myopically (maximizing short-term gains) in the next stage, if the trader ever deviates from the cooperative behavior. During the punishment phase, the agents optimize myopically and the equilibrium is that of the stage game; i.e. no contract is signed. Section 5.2.1 further de nes and speci es the assumptions of the stage game, which are consistent with the description in the previous section. Section 5.2.2 de nes the repeated game, specifying the discounted expected utilities for the contracting parties in a review strategies game. Finally, Section 5.2.3 shows that equilibria can be approached with a review strategies model. This is accomplished by showing that, given the farmer's optimal response, the trader's optimal response is a review strategy.

5.2.1 The Stage Game The description of the stage game is basically the same as that in the previous section. The notation of the variables also applies. However, further de nitions and a speci cation of the assumptions are needed. This follows:

 Denote G as the two person stage game. The players have nite strategy sets A and W . A corresponds to the farmer and W to the trader.  The farmer's strategy is a mapping  that determines his action ( the share of crop to deliver to the trader-lender), as a function of his private information on the realization

73

of output; and his expected share in the interlinked contract (! e ); i.e.:

A = (Y (); !e):

(1)

 The trader-lender's strategy for a given action a is: W = ! (; a; );

(2)

which is undertaken by choosing . Recall that strictly positive values of  imply that the trader is applying a surcharge over the price of the bonded crop, and that  = 0 says that the trader plays cooperatively. The random variable  is the total revenue involved in the interlinked contract, which is distributed between farmer and trader. It is parameterized by the farmer's action and by the random variable .

 (a; ) = aPY (; L)

(3)

where, as before, L is the amount of the loan granted to the farmer.

 Assume that in every stage of the game, only two states can occur. Call a state success if the farmer meets the trader's expectations about the crop delivered. Otherwise, the state is called failure. Let the probability of success be  (; a), which depends on nature's moves and on the farmer's actions.

 De ne the farmer's share from the total revenue of the interlinked contract, in the crop season period, as:

W = !( (a); ; ) =  (a) ; (P ; P I )aPY = aP I Y

(4)

where \P I " is the price of the crop received by the farmer in the interlinked arrangement 74

and is de ned as before; i.e:

P I = (1 ; c ;  ; )P (p );

(5)

c can be understood as an implicit interest rate (considered \reasonable" by the farmer) obtained through crop underpricing; that is, cPY = rL;  covers the marketing costs at the average commission trade, and  is a possible surcharge that equals zero if the trader-lender acts cooperatively, and that is larger than zero otherwise. Thus, the farmer's share can be expressed as:

W = (1 ; c ;  ; )aPY:

(6)

Note that the loan received by the farmer at planting period and paid back at harvest cancel out. Also note that the farmer's share involves a cost of taking the action \a". If the portion aY of the crop were sold to a pure trader rather than to the trader-lender, the farmer could have earned '(a; ) = a(1 ;  )PY . Thus, we could de ne:

E (a; ; ) = '(a; ) ; (! (a; ; ) ; L) as the foregone gains (the \eort") of the farmer when he takes the action a .

 The trader's share in the interlinked contract is:  (a; ) ; ! ((a); ):

(7)

 Assume that both parties are risk averse, and the utilities for the trader and farmer are, respectively:

U ((a) ; W ); 75

(8)

and

V (W )

(9)

where, both U and V are strictly increasing and strictly concave.

 For given strategies ! and , the expected utilities for the trader-lender and the farmer can be de ned as: u = EU and v = EV . If the players at time t do not believe that they will meet again at time t + 1, they will be only concerned about immediate payos. Each player will choose a non-cooperative action anticipating that the opponent will do the same. As explained in the previous section, the fact that the players assume short-term gains as their objective, results in a Nash equilibrium characterized by the failure to sign the contract. Denote the pair of the short-term strategies: (! , a ); where !  is the best response of the trader-lender to the strategy a, and a is the best response of the farmer to the trader's strategy ! . The corresponding equilibrium utilities are just the reservation utilities, u and v , for the trader and the farmer respectively. However, this equilibrium is inecient. Let (^! ; a^) be a more ecient pair of strategies associated with the cooperative behavior in the one period game, and (^u; v^) the corresponding utilities, where u^ > u and v^ > v  . Later, it will be shown that when repetition is allowed, the agents can achieve a more ecient result than the resul achieved in the stage game. Short-term gains are oset by the spillover eects threatening future transactions. In our study case, repetition is an important characteristic.

5.2.2 The Repeated Game  Assume that the one-period game G described above is repeated in nitely. Let G1( ; ) be the resulting in nitely repeated game de ned by the component G and the traderlender's ( ) and the farmer's ( ) discount factors, ; (0; 1).

 The pair of strategies (; & ) are chosen by the players in each stage t = 1; 2;


; 1, 76

based on the information they have available. The trader-lender's strategy is  and the farmer's is & .

 Let i, i = f; t, be the information history available for the farmer (f ) and the trader(t) at the stage t, at decision time.

f = (HtY ; HtP;1; HtP;I1; Ht!;1; HtA;1)

(10)

where:

HtY HtP;1 HtP;I1 Ht!;1 HtA;1

= (Y1 ; : : :; Yt) = (P1 ; : : :; Pt;1 ) = (P1I ; : : :; PtI;1)

= (H1! ; : : :; Ht!;1) = (A1; : : :; At;1)

where P is the average spot price of the crop at harvest time.

t = (HtP ; HtY ; Ht ; Ht!;1)

(11)

where,

HtP = (P1; : : :; Pt) HtY = (Y1; : : :; Yt ) H  = (1; : : :; t) where Yt is the expected yield conjectured by the trader after observing aggregate shocks aecting crop production. Her observation of all other farmers with whom she 77

is associated in similar interlinked contracts improves her conjectures on the output to be expected from a particular farmer. In a review strategies model, the trader will commit herself to play cooperatively during review periods 1 through \R", independently of the farmer's behavior; i.e. she will choose  = 0. Suppose that this action implies for the farmer a reward, !^ , for a given action of the farmer. At time Rt+1 , the trader will review the performance of the farmer. De ne Gt = U ( ; !^ ) as the utility obtained by the trader-lender in stage t; and let

E (Gt= t; t = ^ ) = u^ be the expected utility of the trader given the information available to her, and given her assumption that the farmer is playing cooperatively. De ne

SR = G1 + G2 +


+ GR: The trader-lender reviews the farmer's performance by applying the following test: 8 >
:

pass : if SR  Ru^ ; B fail : otherwise

Thus, the trader estimates the farmer's performance by comparing the utility she has obtained during the review period with her own expected utility, estimated under the assumption that the farmer has played cooperatively. B is interpreted as a \margin of error" in performance allowed to the farmer by the trader. At the end of the rst review period, if the farmer passes the test there is renewal of the contract, and a new review period is initiated. However, if the agent fails the review, a punishment phase that lasts M periods starts. At 78

time (R + M + 1), another review period is initiated for R stages, after which the review policy is applied, and so on. Note that the trader bases the review test on the observation of her own utility, which is not observable by the farmer. The implicit assumption here is that the trader has means to signal to the farmer the results of the test and her intent to continue or stop the relationship. In the study case, this actually happens. Even at the end of each stage game, there is communication among the parties. If the trader believes that the crop delivered to her was below her expectations, she warns the farmer about her knowing of crop diversion. For simplicity, this is not captured in the formal model. If during any stage of the review period, the trader deviates from her cooperative behavior, the farmer responds by choosing a non-cooperative action in the next stage, after the trader's deviation, and continues with the non-cooperative action for the remainder of the review period and for M 0 additional periods. Thus, a punishment phase is initiated by the farmer. Recall that the equilibrium in the punishment period is that of the one stage game; i.e. players interrupt the relationship, and obtain only their reservation utilities. Figures 2 and 3 are graphical representations of players' strategies through machine games, which abstract the process by which a player implements a strategy in a repeated game. Each box corresponds to a state (phase), inside each box is the name of the state followed (after the colon) by the action that the machine takes in that state. The box with the heavy boundary corresponds to the initial state (Osborne & Rubinstein, 1994). We denote with \C" the cooperative phase and with \NC" the punishment (non-cooperative) phase. The arrows correspond to the transitions from one state to another. Adjacent to each arrow is the set of outcomes that induces the transition.

79

Figure 2: Representation of trader's strategy by machines if SR  Ru^ ; B ??

C :=0

-

C :  = 0 if S < Ru^ ;-B NC :  > 0 R

R periods

-

M periods

Figure 3: Representation of farmer's strategy by machines

if  = 0 ? ?

C : a^

if  > 0

-

(R-t) periods

NC : a < 1

-

M0 periods

80

NC : a < 1

NC :  > 0

Discounted Expected Utilities for Review Strategies To show that in a review strategies model, cooperation can be supported as an equilibrium, it is necessary to demonstrate that cooperation yields traders and farmers at least the same expected utilities as their reservation values and that it is a best response. For this purpose, and given the assumption about players' time attitude, it is essential to de ne the players' discounted expected utilities. Because each stage t begins a sub-game, it is possible to compute players' expected utilities from period t on. However, in order to make the utilities of period t comparable with those of the following periods, the payos should be normalized, as will be shown later.

 Let u( ) and v() be the normalized discounted expected utilities of the trader-lender and farmer, respectively.

 Denote (a; ) the probability that the farmer fails the rst review, which depends on the farmer's action and on the randomness of the environment. For any pair of strategies (!; ), the trader's normalized discounted expected utility can be written as:

u( ) = (1 ; )

R X t=1

t;1(EGt) + [ R(1 ; M )u + R+M u( )] + (1 ; ) Ru( )

(12)

where, as de ned before, EGt is the immediate reward or expected utility of the trader in state t. The second and third elements on the right-hand side develop the expected future payos of the trader. First, with probability  the farmer fails the review after R periods, forcing a punishment phase for M periods; i.e. no contract is signed. While punishment is implemented, the trader gets just her reservation utility u until cooperation resumes with a payo u( ). Secondly, with probability (1 ; ), the farmer passes R periods of review, and cooperation continues for another R periods, with payo u( ). Note that each payo is 81

adjusted by the corresponding time discount factor. The normalization factor (1 ; ) is used in order to measure the stage game and the repeated game payos in the same units. The normalized value of 1 util per period is (1=(1 ; )) utils (Fudenberg & Tirole, 1991). Then, solving Equation( 12) for u( ) yields: R t;1EG +  R(1 ; M )u t t=1 u( ) = (1 ; ) 1 ;  R+M ; (1 ; ) R P

(13)

Similar to the trader's utility, the farmer's utility is:

v( ) = (1 ; )

R X t;1

t;1EVt + [R(1 ; M )v  +  R+M v ( ) + (1 ; ) Rv ()

(14)

which, solving for v ( ) gives: P (1 ;  ) Rt;1  t;1 EVt +  R (1 ;  M )v  v( ) = 1 ;  R+M ; (1 ; ) R

(15)

The optimal discounted expected utilities, for the trader-lender and for the farmerborrower, are found by maximizing Equation (13) and Equation (15). Denote these optimal values as u~( ) and v~( ).

Optimal Review Strategies for the Farmer Suppose that, during the review period, the farmer chooses a cooperative action, called a^, which induces a probability of passing the review period of ^. Recall that a cooperative action is not enough to induce, with certainty, the success state. Random variables that aect the farmer's production are also explanatory variables of the outcome. Then, for a given cooperative action of the trader-lender, the farmer's choice results in an expected utility EVt = v^. This discounted expected utility v^( ) constitutes a lower bound of the

82

optimal value v~( ):

R R M  v^() = (1 ;  ^ )^Rv ++M (1 ; ^ R)v 1 ;  ; (1 ; )

(16)

(v ; v^) + K (u ; u^)  0:

(17)

In order to de ne an upper bound for the farmer's optimal discounted expected utility, assume that there is a positive K such that for every farmer's strategy, if the principal uses !^ , then the following relation holds:

Thus, for any strategy of the agent and any period t during the review phase:

E (Vt= f )  v^ + K [^u ; E (Gt= t)]

(18)

it follows from this and Equation 15 that: PR R t;1 u ; EGt) +  R(1 ;  M )v  v()  (1 ;  )^v + (1 ; 1)K; tR=1+M ;(^ (1 ; ) R

De ne:

f (x; y) 

y X t;1

(1 ; xt;1 ) = y ; 11;;xx ; : : : 0  x < 1 y

(19) (20)

Because ju^ ; EGtj  L; it follows that: R X

R X t ; 1  (^u ; EGt) ; (^u ; EGt)  L f (; R) t=1 t=1

Let A be the left hand side of the above equation, which can then be rewritten as:

;Lf (; R) < A < Lf (; R)

83

(21)

or:

R X t=1

which yields:

 t;1(^u ; EGt) 

R X t;1

R X t=1

(^u ; EGt) + Lf (; R)

t;1 (^u ; EGt)  Ru^ ; ESR + Lf (; R)

(22)

Since  = Prob[SR < Ru^ ; B ], and SR  0, it follows that:

Ru^ ; ESR  Ru^ + (1 ; )B

(23)

Using Equation (22) to modify Equation (19), and then utilizing (23) it follows that:

v ( )  vo ( );

(24)

where, R v +  R (1 ;  M )v  vo() = (1(1;; )^ R ) +  R (1 ;  M ) [Ru^ + (1 ; )B + Lf (; R)] + (1 ;  )K (1 ;  R ) +  R (1 ;  M )

(25)

Thus, vo ( ) is an upper bound for v ( ). Note that the rst term of the above equation is the same as the lower bound shown in Equation (16) after rearranging terms in the denominator. Thus, the second term of the above equation is what makes the dierence between the lower and upper bounds.

5.2.3 Equilibrium Review Strategies The review strategies are characterized by the parameters R, B, M, and M 0 . Let us reiterate and be more precise about these parameters. R is an instrument used by the trader to gather more accurate information about the farmer's behavior, and evaluate him in such a way 84

that both parties of the contract can agree on the outcome of the review. The parameter B measures the level of tolerance allowed by the trader; she does not punish small alleged deviations. Because of the presence of random variables, small average deviations of the observed outcome with respect to the expected outcome may occur even when the farmer has played cooperatively in every stage. In the survey, farmers were particularly eloquent about the

exibility of traders before claiming that a situation is a default. Farmers described this as a characteristic that distinguishes trader-lenders from commercial lenders. The parameters M and M 0 , the length of punishment initiated by the traders and the farmer, respectively, are necessary for the strategy to be sustained as an equilibrium. Punishment must be implemented in order to generate reputation about the determination of the parties to enforce the contract. The following relations are de ned for analytical convenience:

De ne

B = R;


> 0; : : : 1=2 <  < 1 M = R;


 > 0

(26)

k^  V ar(t=At = ^a) = ^(1 ; ^)

(28)

(27)

Let  be a number xed such that:

and x  so that:

0 <  < v^ ; v  ;

(29)

 > v^ ;Kv u^; 

(30)

The pair (; & ) describes a class of review strategies, where each element is characterized by the parameters R, B , M , and M 0 . A pair of review strategies is an equilibrium of the 85

game if  (R; M 0) is optimal against & (; R; M 0), and vice-versa. For the trader-lender's strategy to be optimal against the farmer's strategy, we need to show that the trader-lender will not nd it pro table to deviate (not cooperate) during the review period. Suppose the trader-lender chooses not to cooperate at the stage t of the rst review period that lasts R stages; i.e. t < R, and follows the review strategy thereafter. Recall, that if the trader deviates (i.e., discounts from the market crop price beyond the average commission trade and what would be considered a fair charge for loan recovery), and the farmer knows he has been cheated, he will start a penalty phase in the stage t + 1 through the stage R. He does this by optimizing as he would do in a single stage game (selling his harvest to any other trader with the expectation of obtaining better prices), and he will continue non-cooperating for the next M 0 stages. Therefore, the trader's discounted expected utility will be given by: (1 ; R;t+M 0 )u + R;t+M 0 ( )

(31)

Note that, for simplicity, we are assuming that the trader gets her reservation value, even when she is being punished by the farmer within the review period. In fact, within the review period, if the farmer sells all his crop to any other trader, the trader-lender will lose not only the gains from marketing the crop but also the capital forwarded to the farmer. The nal payo should be lower than the trader's reservation utility. However, as will be obvious later, this simpli cation does not aect the results of the comparison between the trader's payos when cooperation occurs and when it does not. If the trader does not deviate from the cooperative behavior during the review period and follows the review policy, her discounted expected utility will be:

E [(1 ; )(

RX ;t n=1

n;1Ut+n ) + R;t(1 ; M (Hr))u + R;t+M (HR)u( )=Ht] 86

(32)

where 8 >
:

0 : if SR  Ru^ ; B M : if SR < Ru^ ; B

9 > = > ;

For the trader's strategy to be optimal, it is sucient that her discounted expected utility expressed in (31) be less than the one in (32); for each (t = 0; : : :; R ; 1). Because !  is a feasible strategy for the trader, u( )  u . Also, in (32), Ut+n  0 (33) so that replacing M (HR) by M cannot increase (32). Thus, (32) is at least as large as:

R;t(1 ; M )u + R;T +M u( )

(34)

Therefore, a sucient condition for the trader's strategy to be an equilibrium is that (31) be strictly less than (34); i.e.:

R;t( M ; M 0 )(u( ) ; u) > (1 ; R;t)(u); : : :; for(t = 0; : : :; R ; 1):

(35)

But u( ) > u , so this is equivalent to:

R( M ; M 0 )(u( ) ; u) > (1 ; R)(u) u( ) > u

(36)

For the second line of (36) to hold, it is sucient that:

uo ( ) > u 87

(37)

where uo ( ) is the lower bound of u( ): R u +  R(1 ; M )u (1 ; )[Ru^ + (1 ; )B + f ( ; LR)] uo ( )  (1(1;; )^ R) +  R(1 ; M ) ; (1 ; R) +  R(1 ; M )

(38)

and was derived similarly to 25. Thus, (1 ; R)(^u ; u) ; (1 ; )[Ru^ + (1 ; )B + LR] + (1 ; LR) > 0 which implies:

(; R)^u + [1 ; (; R)]B + LR < u^ ; u

(39)

The rst part of the inequality (36) can be rewritten as:

M 0 < R ; (1 ;

R)Z ( )

(40)

 Z ( )  u ( u) ; u

(41)

R

where,

o

Inequality (40) is satis ed for a suciently large M 0 provided that the right-hand side is positive, or that:

(1+)R > Z ( ) (42) 1 ; R) To express the conditions above in another way, de ne: [ inf (; R)] < 1, for each  and R, to be the in mum of , such that (37) and (42) hold.

M 0inf (; ; R) to be the in mum of M 0 satisfying (40).

88

These results can be summarized as:

Theorem 1 (Equilibrium of the Supergame) If  and R satisfy Inequality (39), >

inf (; R) and M 0 > M 0inf (; ; R), then the review strategies (R; M 0) and & (; ; R) form an equilibrium of the supergame.

89

6 An Exercise Applying Review Strategies 6.1 De ning the Empirical Model The purpose of this section is to better understand the role of and the relationship between the diverse parameters that de ne a review strategy, as presented in the previous chapter. When the information was available, proportional values to those found in the survey were used for the exercise. Thus, rather than emphasizing magnitudes, we focus on relationships. We begin by making the following assumptions:

 Assume that the trader-lender and the farmer-borrower both have an attitude towards risk such that their utility functions show constant relative risk aversion (CRRA). Take the following functional forms to represent the agent's utilities for a payo W:

U (W ) = Ai + (1=(1 ; i))(W )(1; i)

(43)

where (i = t; f ). t denotes the trader and f the farmer. The Ai s are constant scalars and the i s are constant relative risk aversion coecients.

 Assume that the lender's and the farmer's reservation utilities are strictly positive; i.e., u > 0; : : :and : : :v > 0: For traders, the alternative to participating in a particular interlinked contract is to initiate similar relationships with other farmers or to allocate any cash surplus in an alternative activity. However, the substitution of one farmer-borrower for another is costly, because an interlinked arrangement comes after repeated interactions and unlinked transactions between a potential borrower and the trader. Thus, u is smaller than the expected utility in the interlinked arrangement. In addition, although, in the 90

traders' survey, nearly 30 percent of the traders reported having a second activity, they also revealed that their rst priority was crop-trading. In the farmer's case, the alternative to a credit-output interlinked contract is to nance the crop production with alternative more expensive sources, if available. In addition, about 50 percent of farmers surveyed reported they were involved in a second income generating activity, other than agriculture. However, the time assigned to this second activity was conditional on the labor needs for crop cultivation. Thus, it can be assumed that v  is smaller than the farmer's expected utility in the interlinked arrangement.

 The trader-lender (the principal) maximizes her expected utility from participating in the interlinked contract subject to the farmer's participation constraint. As before, the trader-lender's payo from the interlinked contract is ( (a) ; ! ( )), and that of the farmer is ! ( ). For the sake of generality, consider the case in which the farmer does not sell all his crop to the trader-lender; i.e. a < 1. If so, the farmer will have another source of income, from the sale of the (1 ; a) portion of the harvested crop to a pure trader. Denote this part of the farmer's total payo as '0(a). Thus, the trader's optimization problem is: max EU [ (a) ; ! ( )] (44) subject to:

EV [!() + '0(a)]  v 

(45)

;EU 0[(a) ; !()] + EU 0[!() + '0(a)] = 0

(46)

The rst order condition is:

Assuming that the utility functions take the structural form considered in Equation 91

( 43), the rst order condition can be written as: [ (a) ; ! ( )]; t = [! ( ) + '0 (a)]; f

; t ln((a) ; !()) = ; f ln  ; f ln(!() + '0(a)) where  is the Lagrange multiplier corresponding to the farmer's participation constraint.

 Assume that the interlinked contract, the game, follows the review strategies model, and that the players adhere to the optimal policy. That is, they both cooperate. This assumption implies that '0 = 0, as a = 1. Furthermore, if the players have equal negotiation power; i.e.  = 1, it follows that:

t ln( (a) ; ! ( )) = f ln(! ())

(47)

This relation will dictate the interlinked contract's sharing rule, where the farmer gets ! and the trader gets ( ; !). For given values of f and t , we can approximate the sharing rule. For the comparative static exercise on review strategies, some assumptions about parameters' values are also needed.

 Assume that the farmer is more risk averse than the trader. This assumption derives from the idea that individuals with capacity to bear risk are less risk averse. In the Huaral Valley, as in most of Peru, small farmers are in a less favorable economic situation than traders. Unfortunately, there are no studies that estimate individuals' risk aversion in Peru. Fafchamps and Pender (1997) compute maximum likelihood estimates of the coecient of relative risk aversion of Indian farmers. Their estimates revert around 1.8-3.1. Taking these values as reference, we assume f = 2:5 and t = 1:5, for the 92

farmer and trader, respectively. Later, changes in these coecients are considered.

 Following the simplifying assumptions of the theoretical model, the revenue distributed between the contracting parties can take only two values, a high value (h ) or a low value (l), which are assumed to be h = 10, and l = 2:5. The relation between these

high and low values are proportional to those found in the surveys. Farmers without major cultivation problems were able (or expected) to obtain, on average, 1,000 boxes of tomatoes, and those farmers who reported they had lost their harvest to pest infestation were still able to obtain, on average, 250 boxes of tomatoes from the initial harvest(s). Given the assumption that the farmer cooperates (a = 1), a situation of success or failure in a particular stage will depend only on nature's moves. Thus, there is success when h is observed.

 Let the probability of success in a particular stage be 80 percent; i.e. ^ = 0:8, provided

that the farmer cooperates. Once again, when the farmer cooperates, this probability depends only on the randomness of nature, which in the Huaral Valley does not imply much volatility. Weather conditions are somewhat predictable, and water availability is not much of a problem. The most important hazard is the possibility of pest infestation, which, to a certain degree, is controllable with good farming practices.

 Trader's and farmer's reservation utilities are arbitrarily taken, and assumed to be: u = 0:20 and v = 0:10, respectively. Changes in these variables are later considered.  The initial value assumed for the length of the review strategy is R = 3. Later, for a comparative static analysis, R = 4; 5, and 6 are also considered. Results from the surveys show that, on average, farmers and traders knew each other for nine years, and that they were involved in an interlinked arrangement during 6 agricultural seasons. This justi es the value of the maximum length of the review period considered. Note that each stage of the review lasts from 4 to 6 months. Tomatoes take about 6 months 93

from the planting day to the last harvest, and farmers typically engage in an interlinked arrangement at about the second month of the cycle. Longer review periods would be unreasonable, particularly in an economy just coming out from experiencing high levels of in ation. In 1995, the survey year, the increase in prices were relatively low, an annual 10.2 percent. However, the in ation rate in 1990 reached a peak of 7649 percent, and the average in ation rate from 1991 to 1994 was 60.7 percent. Economic agents take time to gain con dence in the stability of the new environment, and thus they take time to adjust. The remaining variables and parameters come from the review strategies model, and were determined as follows:

 Given the high and low values that the total revenue  can take, and for given risk aversion coecients is, the expected utilities of the players are calculated assuming a

Von-Newman Morgenstern utility; using for the utility functions the structural functional form assumed in Equation ( 43), which shows constant relative risk aversion ( CRRA).

 From the Equation ( 26) that de nes the relationship between the length of the review period, R, and the margin of error of the review test, B , assume a value for = 0:2, where was only constrained to be strictly positive. In addition, from the values that  can take (0:5 <  < 1), pick  = 0:8. Then, for a given R, B is de ned.  A set of values for the parameter  are given by Equation (29). Given v^ and v,  can take any value between 0 and (^v ; v  ). By convention, o was selected such that o = (^v ; v ), where  = 3=4.  Assuming a positive value for k and given o, Equation (30) de nes feasible values for . From those values, a particular o , was chosen such that it approaches the lower bound of  with two decimals, and it de nes an integer number for the length of the 94

punishment period imposed by the trader (M ). The purpose of selecting a  close to its lower bound, was to solve for M, at its smallest value.

 The probability that the farmer fails the review can be drawn from a binomial probability distribution, with parameters ^, R, and s, where s is the minimum number of successes required by the trader during the review period. s can be found as follows: Recall that SR is the trader's accumulated realized utility during the review period, which the trader compares with her own expected utility. SR can be written as: SR = s:U (S ) + f:U (F ) or : SR = s:U (S ) + (R ; s)U (F )

(48)

where, S (F) means success (failure) in meeting the trader's expectations in a particular stage during the review period R; and s(f) is the number of successes (failures) in the review period. Then, replacing ( 48) in the de nition of the review policy, a lower bound for s can be found:

SR (sU (S ) + (R ; s)U (F )) s(U (S ) ; U (F )) + RU (F ) s

   

Ru^ ; B Ru^ ; B Ru^ ; B R(^u ; U (F )) ; B U (S ) ; U (F )

(49)

Knowing the values of  and the agent's utility functions, the expected utility under cooperation, u^; and the utilities of success, U(S), and that of failure, U(F), can be calculated. For a given R, B is already known; thus the lower bound for s is de ned. Then, pick the smallest integer that satis es Inequality ( 49). 95

 Finally, for the review strategies to constitute an  ; equilibrium, some inequalities must hold, which allows one to further specify the rest of the parameters. Inequality (39) and the second part of Inequality (36) have to hold. These inequalities impose constraints over the trader's discount factor, . Inequality (40) further reduces the feasible set of , by requiring that its right hand side be positive. The minimum is selected and its value replaced in Inequality (40) to obtain the length of the punishment period imposed by the farmer, M 0 .

6.2 Review Strategies: Comparative Statics Before analyzing changes in diverse parameters, and as a way of summarizing the assumptions in the previous section, the baseline case is rst stated.

 Let the high and low outcomes be: h = 10, l = 2:5, the probability of success in each stage:  = 0:8 and the risk aversion coecients: t = 1:5, f = 2:5:  Assume the length of the review period R = 3.  Then, the sharing rule obtained from Equation (47) is: !h = 3:17 and !l = 1:18 for the farmer, and (h ; !h ) = 6:83 and (l ; ! ) = 1:32 for the trader, in the states of high

outcome and low outcome, respectively. Given the utility functions, and assuming a cooperative behavior from the agents, the expected utilities are: v^ = 1:73 and u^ = 2:04, for the farmer and trader respectively. In addition, let the reservation values be v  = 0:1 and u = 0:2, for the farmer and the trader, respectively.

 The value of the parameter K is obtained from Equation (17), which we repeat here: (v ; v^) + K (u ; u^)  0 96

which holds for some positive K for every farmer's strategy, given that the principal uses !^ . If the farmer cooperates v = v^ = 1:73 and u = u^ = 2:04, the inequality holds for any positive value of K . If the farmer does not cooperate, the trader always gets her share of the low output state, independently of which state had been revealed to the farmer. Recall that, earlier we have argued that the farmer will nd it pro table to deviate only in the high output state, where he may claim that a low state has occurred when a high state has been actually revealed. If deviation occurs, the farmer's share in the high output will be the total crop revenue in the high state minus the trader's share in the low state; i.e. (10 ; 1:32) = 8:68. The corresponding expected utilities for the farmer and trader are, respectively, v = 1:88 and u = 1:25. Replacing the relevant values in (17), we obtain: K  0:095, and we pick the value at the equality.

 M is determined as follows: 0 <  < v^ ; v = 1:63 Select o = (^v ; v ), and let  = 3=4. Thus, o = 1:22  > min = v^;vku^; = 0:48 Thus, M  [(min + 0:01)R] = 1:46 Select M = Ceiling [1:46] = 2, Thus, o = M=R = 2=3 o

 Given the constraints in Equations ( 26), assume  = 0:8 and = 0:17, which de nes B = R = 0:41.  From the assumptions above and using the review test equation, the minimum number of successes required of the farmer is S = 2.  Thus, (3; 2; 0:8) = 0:104  Given L = 0:5, Equations ( 36) and ( 40) require a minimum discount factor = 0:70. For this , the requirement for the length of punishment imposed by the farmer is: M 0  16:57. 97

However, from the information in the surveys, a trader's discount factor of = 0:83 was estimated, which satis es the constraints. 20 For = 0:83, M 0  4:54.

6.2.1 Changes in the Length of the Review Period Let's assume increases in the length of the review period. Table 15 summarizes the eect of these changes in the relevant parameters de ning the review strategy. Table 15: Changes in the Length of the Review Period

R

3

o M B S 

for the minimum feasible :

M0



M0



for the observed = 0:83:

4

5

6

2/3 1/2 2 2 0.41 0.51 2 3 0.104 0.18

3/5 3 0.62 4 0.26

5/6 5 0.71 5 0.34

0.70 0.78 16.57 11.59

0.85 16.83

0.89 20.25

4.54

6.49 can't support can't support

The rst eect is over the level of tolerance, or margin of error (B ), allowed to the farmer by the trader. By de nition, this margin is directly related to the length of the review, through the parameters  and . Thus, B increases as R increases. In addition, the probability that the agent fails the review also increases. This probability was calculated from a binomial distribution for a minimum number of successes (S). As before, the minimum S has been chosen using the review test equation so that S is an integer number. As shown in Table 15, as R increases the proportion of successes required over the length of the review period increases. Thus, the test becomes stier with increases in R.

= 0:83 was obtained from the information provided by farmers on the implicit interest rate on the loan charged by traders through crop underpricing. 20

98

The length of punishment imposed by the trader, M , is directly related to R (recall that M = R). Only when the review period increases from 3 to 4 stages, M does not increase in response to an increase in R. For the same set of feasible s, the increase in R is not large enough to increase M . Note that M is estimated from the relation: M = o R, where o is the smallest feasible  that produces an integer value for M . To analyze the eect of increases in R over the length of the punishment imposed by the farmer, M 0, the discount factor is kept at the level observed in the eld, = 0:83. In general, longer review periods are associated with a longer length of punishment threatened by the farmer if non-cooperation occurs. This eect is reinforced by the increasing M that is positively related to M 0 . As intuition would suggest, longer review periods are associated with a higher trader's discount factor (more patient traders). Note that in our case study, long review periods, such as ve stages or more, cannot be supported as equilibrium at the discount factor of the traders observed in the eld.

6.2.2 Changes in the Trader's Reservation Utility Consider increases in the trader's reservation utility. Such increases may occur due to a reduction in the costs of searching merchandise, to an improvement in the gains of an alternative activity, or to an easiness in replacing one farmer-borrower for another. The main eects of increases in the trader's reservation utility are summarized in Table 16. Although the values of M are not aected by changes in u , they are included in the table to compare them with the values of M 0 .

99

Table 16: Changes in Trader's Reservation Utility

u M

0.2



for the minimum feasible :

M0



M0



for the observed = 0:83:

2

0.3 2

0.4 2

0.70 0.78 0.82 16.57 10.27 17.13 4.54

0.5 2

0.86 30.87

7.07 13.66 can't support

Increases in the trader's reservation utility requires more patient traders to sustain an equilibrium, as expressed by the increasing minimum as u increases. In addition, for a given trader's discount factor, such as the observed = 0:83, the length of punishment imposed by the farmer increases with increases in the trader's reservation utility. The dierence between the expected utility from the contract and the reservation utility of a particular agent is a measure of the importance of the contract for a contracting party. An increase in the trader's reservation utility; i.e., a decrease in (^u ; u ) reduces her incentives to honor the contract, because a given punishment produces smaller losses than those corresponding to a lower reservation utility. Recall that punishments refer to the termination of the relationship. Therefore, if the trader's reservation utility is higher, ceteris paribus her time preference, the farmer has to threaten her with longer periods of punishment if the cooperative behavior is to be enforced. In the case that the trader's reservation utility is as high as u = 0:4 or more, the threat of punishment is an actual termination of the relationship. Moreover, these levels of trader's reservation utility are not consistent with the trader's discount factor observed in the eld.

6.2.3 Changes in the Farmer's Reservation Utility Consider now an increase in the farmer's reservation utility. This may occur, for instance, due to an improvement in the farmer's access to alternative sources of working capital, or to 100

an increased ability of the farmer to switch from one trader to another, or to an improvement in the rewards produced by his alternative activity to crop production. Table 17 summarizes the eect of increases in the farmer's reservation utility. Similarly to the case of increases in u, an increase in the farmer's reservation utility (v ), ceteris paribus, reduces his losses in the event of contract termination, and with that, reduces his incentive (^v ; v  ) to comply with the contract. Therefore, the trader may need to threaten the farmer with longer periods of punishment in the event of non-cooperation. This is re ected in the higher values of M caused by changes in the parameter , which varies inversely with (^v ; v ), as shown in the following expression:

@ = ; K u^  @ (^v ; v ) (1 ; )(^v ; v  )2  0 For a given discount factor, the length of punishment imposed by the farmer (M 0) increases, since it is directly related to M. Therefore, we could expect that policies that aect the farmers' reservation value, for instance the improvement of farmers' access to other capital sources, will imply threats of more severe punishment within the interlinked contracts.

Table 17: Changes in Farmer's Reservation Utility

v  o M

0.1



for the minimum feasible :

M0



M0



for the observed = 0:83:

1.63 2/3 2

0.3

1.43 2/3 2

0.6

1.13 1 3

0.9

0.83 1 3

1.2

0.53 5/3 5

0.70 0.70 0.74 0.74 0.81 16.57 16.59 15.67 15.67 13.00 4.54

101

4.54

6.25

6.25 10.78

6.2.4 Changes in the Probability of Success in Each Stage Table 18 summarizes the main eects of decreases in the probability of success. Table 18: Changes in the Probability of Success in Each Stage ( )  v^ o M u^ 

0.9



for the minimum feasible :

M0



M0



for the observed = 0:83:

0.8

1.78 1.73 2/3 2/3 2 2 2.14 2.04 0.03 0.10

0.7 0.65

1.69 2/3 2 1.94 0.22

1.67 2/3 2 1.89 0.28

0.68 0.70 0.75 0.77 9.18 16.56 11.04 16.34 4.02 4.54

4.69

6.92

For given risk aversion coecients, the share of the parties remains constant. However, the changes in the probability of success in each stage aect farmer's and trader's expected utility. A decrease in  reduces both the expected utility of the farmer (^v ) and that of the trader (^u), as shown in Table 18, and as explained by the following expressions:

@ v^ = V (!h ) ; V (! l)  0: @ @ u^ = U ((!h) ; ! h ) ; U ((! l) ; !l )  0: @ The eect of changes in  over M , the length of punishment threatened to the farmer, is less immediate. Intuitively, a decrease in  that decreases the farmer's expected utility and so his incentives to honor the contract and to avoid punishments, should increase the need of longer punishment periods. However, decreases in the trader's expected utility should decrease , and so the length of punishment imposed to the farmer. The eect over M can 102

be shown through the impact of changes in  over the feasible set for the parameter  (recall that M = R). That is,

@ = k @@u^ (^v ; v  ;  ) ; @@v^ K u^ @ (^v ; v  ;  )2 because the denominator is always positive, the sign of the derivative depends on the numerator. Thus, @ @  ()0 if: #  @ (^v ; v ;  )  ()1 @ v^ u^ @

" @u ^

or:



@ u^ k  ()  @ v^   @ @ o

In the exercise here, for the changes in probability considered, the weighted eect of the changes in the probability of success in each stage over the expected utility of the farmer was not signi cantly dierent from the weighted eect over the trader's expected utility. Thus, as  decreases we could still pick the same o so that M remained unchanged. The immediate direct eect of decreases in  is on the probability  that the farmer fails the review. This probability increases. In turn, as the chances that the farmer will fail the review increases, the minimum trader's discount factor required to sustain an equilibrium increases, i.e., more patient traders are needed. For a given discount factor, such as the observed = 0:83, decreases in  imply increases in the length of punishment, M 0 , imposed by the farmer in the event of the trader's noncooperation. As explained before, decreases in  reduces the trader's expected utility. Given the trader's reservation utility, a lower expected utility weakens her incentives to comply with the contract. Thus, the farmer has to threaten her with longer periods of punishment to restore the incentives for a cooperative behavior. 103

6.2.5 Changes in the Farmer's Risk Aversion We have considered changes in the risk aversion coecient. Risk aversion behavior does not necessarily follow from a physiological aversion to risk. Masson (1972) shows how riskaverse behavior may follow from institutional characteristics of the economy, such as market imperfections. He demonstrates how a risk neutral individual who faces imperfect markets will behave on gambles involving present income as if he were maximizing expected utility. Thus, we can think of changes in the agent's risk aversion behavior as a result of changes in the institutional environment, not uncommon in developing countries. Table 19 summarizes the eect of increases in the farmer's risk aversion over diverse variables of the review strategy model. Table 19: Changes in Farmer's Risk Aversion !h !l v^  o M u^

2

f



for the minimum feasible :

M0



M0



for the observed = 0:83:

3.89 1.21 1.88 1.78 2/3 2 2.00

2.5

3.17 1.18 1.73 1.63 2/3 2 2.04

3

2.70 1.16 1.65 1.55 2/3 2 2.06

3.5

2.39 1.14 1.60 1.50 2/3 2 2.07

0.71 0.70 0.70 0.70 10.36 16.56 12.76 11.69 4.62

4.54

4.49

4.46

An increase in the farmer's risk aversion, ceteris-paribus, implies for the farmer a smaller share of the revenue to be distributed. The farmer's share decreases proportionally less in the state of low outcome than in that of high outcome. In terms of utility and expected utility, the increase in risk aversion produces two opposite eects. First, the valuation of a given level of wealth increases as the risk aversion coecient increases; thus augmenting the 104

expected utility. Secondly, a decline in the farmer's share due to an increase in risk aversion implies lower utility and expected utility. For the particular parameters being considered in this exercise, the outcome of these two eects is a lower expected utility for the farmer. In contrast, the trader's share increases, given a constant risk aversion coecient. Thus, her expected utility also increases. Given that the reservation utilities remain unchanged, changes in expected utility decrease (increase) the farmer's (trader's) incentive to cooperate at each stage. The decrease in the farmer's incentive to cooperate should imply greater values for  and thus for M. That is, in order to compensate for the changes in the dierence of the farmer's expected utilities and his reservation utilities (which is a measure of the losses of being punished), threats of longer punishment periods are required against the farmer. Moreover,  is positively related to u^, which is increasing. However, these two eects are not shown in Table 19. Although the set of feasible values for  are higher when the farmer's risk aversion increases, we could still pick o = 2=3 that gives the smallest integer number for M . Similarly, for a given trader's discount factor , the increase in the trader's incentive to cooperate should imply that the farmer will need to threaten her with shorter punishment periods (M 0). However, M 0 is also directly related to M , which is non-decreasing. The nal impact on M 0 thus depends on the relative strength of the eect of the increase in (^v ; v ) and that of M . In our exercise, as we move to larger risk aversion coecients, and with M unchanged, M 0 decreases as a response to increases in (^v ; v  ).

6.2.6 Changes in the Trader's Risk Aversion The results of increasing the trader's risk aversion are summarized in Table 20. Increases in the trader's risk aversion increases the farmer's share in the revenue to be distributed, and so decreases that of the trader. Note that when the trader's risk aversion equals that of the farmer ( t = f = 2:5), both agents share the revenue equally (recall that  h = 10 105

and  l = 5). Similar to the farmer's case, the increase in risk aversion produces two opposite eects: a larger utility for a given level of wealth when t increases; and a lower utility for the trader caused by the decreases in his share of the revenue. In this case, the rst eect dominates, and the trader's expected utility increases. Because the farmer's risk aversion is kept constant and his share in the revenue has increased, the farmer's expected utility increases with the trader's risk aversion. Table 20: Changes in Trader's Risk Aversion !h !l v^  o M u^ So

1.3

t

M0



M0



for the observed = 0:83:

2

4.12 1.22 1.77 1.67 1/3 1 2.71 2

2.5

3.17 1.18 1.73 1.63 1/3 1 2.04 2

0.86 20.32

0.70 0.66 0.65 16.57 8.46 5.53

can't support

4.54 3.64 3.30



for the minimum feasible :

1.5

2.79 1.16 1.71 1.61 1/3 1 0.91 2

5 1.25 1.79 1.69 2/3 2 2.86 1

Given that both the trader's and the farmer's reservation utility has remained unchanged, while their expected utilities have increased, the incentive to cooperate at each stage increases for the parties. Consequently, the need for longer punishment threats, imposed by both the farmer and the trader, should decline with increases in the trader's risk aversion. However, the increase in the trader's expected utility raises the set of values for , and thus for M . In this exercise, both eects have similar weights except when the trader's risk aversion increases from 2 to 2.5, where the second eect dominates. Moreover, increases in M directly aect M 0 . Thus, this eect has to be weighted against 106

the eect of the net expected utility of the trader. In this exercise, the incentive eect dominates. Thus, M 0 decreases.

107

7 Conclusions and Policy Implications In Peru as in many other developing countries, the absence or imperfection of credit and insurance markets characterizes the environment of formal market institutions. Economic agents, without perfect information when engaging in a trade, incur transaction costs by generating information about the parties and taking preventive actions to reduce the risk involved in the transaction. If these costs are too high, it can lead to the absence of a complete set of contingent claims. However, when formal market institutions fail to meet some demands, informal arrangements may help to ll in the gaps left by formal institutions. This study has provided a clear understanding of a form of market interlinkage that accomplishes the role of making credit available to small farmers and, at least, partially insures the participants of the contract. This is the interlinkage between the marketing of a crop and the provision of credit for nancing the working capital of its production, as observed in a Coastal valley of Peru. Marketing and production activities both involve risk and uncertainty. First, traders have no assurance regarding the volume of trade they will be able to intermediate in a certain period. Second, producers face the risk inherent in agriculture and the uncertainty of not being able to market their production. However, insurance markets that would mitigate the problem of the resulting income uncertainty of both traders and producers are absent. In addition, small agricultural producers lack access to commercial bank loans because it is too costly for traditional lenders to overcome the costs of informational asymmetries. In this scenario, credit-output interlinkage serves a role. It improves trader-lenders' ability to plan ahead and to be able to maintain a relatively stable volume of trade. In addition, producer-borrowers are able to satisfy their credit needs, to assure a channel by which their output is commercialized, and to obtain partial insurance against unfavorable moves of nature. A salient feature of this type of contract is that it is not a casual relationship; rather it is a personalistic relationship, typically the result of social interaction and repeated transactions. 108

This attribute, which allows trust and reputation to develop, helps to overcome the informational barrier and the moral hazard problem that makes transactions in formal markets infeasible. Moreover, in an environment of inecient legal enforcement, as in rural Peru, credit-output interlinkage gives an advantage for contract enforcement, because repetition allows cooperation. This study has provided a characterization of the participants of the contracts and a detailed description of the terms and conditions, as surveyed in the Huaral Valley, in Coastal Peru. It was observed that screening, monitoring, and enforcement problems are solved by trader-lenders at lower costs than those incurred by commercial lenders. The screening of the contract participants is undertaken through previous repeated unlinked transactions that allow the identi cation of trustworthy and reliable partners. Once trust has been established, some conditions in the interlinked contract are made explicit orally. There are also implicit conditions, which are the result of customary practice. Loans are mainly provided in cash in the case of tomatoes and in kind (seed) in the case of sweet corn. The loan size is small, equivalent to about one third of the total crop production costs. The maturity period does not exceed that of the production. Other than the promise of the farmer to deliver the crop at harvest, no collateral or guarantee is involved in the contract. There are no explicit interest rates. However, crop underpricing by traders is not uncommon, particularly when the quality of the crop delivered is not competitive. Under a certain range, farmers consider crop underpricing reasonable. Crop supervision is an important element in interlinked contracts. The traders interviewed reported that crop supervision provides them with information about farmers' nancial needs and a basis to judge contract performance. The way the contract is enforced depends on the judgment of the trader. When the trader's assessment is that the farmer's default was involuntary, the payment of the loan is postponed to the next season. If the assessment is that the default was voluntary, the relationship is broken. Traders reported that in the case of non-compliance, legal actions are not taken, as this would imply a waste of monetary and 109

time resources. When the size of the loan justi es the costs of recovery, the loan recovery is accomplished using non-traditional methods; including persuasion and intimidation. The surveys in this study has focused on two crops, sweet corn and tomatoes. It was shown that incentives to participate in interlinked contracts vary across crops. First, traders have more incentives to engage in interlinked contracts with farmers producing a (variety of) crop that is important in the relevant output market. Second, farmers producing a crop that has high requirements for working capital and/or those who have higher risk of losses are more willing to participate in a credit-output interlinked contract. Under both considerations, the gains for the parties from contract participation were found to be larger in the case of tomatoes than in the case of sweet corn. Consequently, a higher incidence of interlinked contracts was found in the case of tomatoes than in that of sweet corn. However, in general, the existence of gains in an interlinked contract does not guarantee the repetition of the relationship. Because there exists double-sided asymmetric information, there is room for opportunistic behavior that can cancel the gains, unless there is a breach deterrence mechanism. A key question this study aimed to answer concerned the enforcement procedure that makes the parties honor the contract, even when some variables of the contract are not speci ed and no provisions are made for loan default. We have answered this question using a repeated game approach that allows one to comprehend the consequences of the observed long-term relationships on the performance of the contract. Long-term relationships make opportunistic behavior costlier. The permanent threat of punishment by breaking the relationship makes immediate gains from deviations smaller than the losses in the future. Thus, in equilibrium, the parties always cooperate and the contract is repeated, only while mutual economic gains from the relationship exist. More speci cally, interlinked contracts were modeled using a principal-agent game with discounting. The existence of a large enough number of farmers that enter into independent contracts with a trader gives rise to reputation-like eects, which are formed through an aggregation of information on the actions of the trader, reducing the double-sided moral 110

hazard problem to a one-sided situation with private information on the side of the agent (AlNajjar, 1997). This allowed us to accommodate Radner's (1985) review strategy model in our problem. The review strategy model captures the structure of the equilibrium strategy consistent with the observed behavior of traders and farmers in Coastal Peru. A review strategy makes the farmer's compensation in any one period depend on the average outcome over a number of periods. By instituting a review period and establishing the requirement that the farmer, on average, delivers an output consistent with the trader's expectations, the trader can make more accurate decisions about the farmer's performance, while allowing a level of tolerance. Tolerance is required because of the inability of the trader to distinguish if a low outcome was due to uncontrollable random variables aecting the farmer's production or to the lack of cooperation. In this way, the trader partially insures the farmer against unfavorable movements of the random variables aecting production. Thus, repetition allows the trader to reduce the farmer's risk without reducing his incentive to cooperate in the contract. In order to better understand the structural behavior of the contracting parties and the way diverse parameters in the review strategy model in uence such behavior, the last part of the study included some comparative statics exercises. In general, changes in parameters aect the behavior of the parties and thus the conditions of the contracts through the eects on the system of incentives designed to promote contract compliance. We summarize some of the results. First, as the length of the review period increases and the margin of error adjusts in a smaller proportion, the probability that the agent fails the review increases. The new equilibrium is achieved with higher punishment periods imposed by both the farmer and the trader. Second, it can be expected that changes in a contracting party's reservation utility will aect her/his incentives for cooperation, because the dierence between the expected utility of the contract and the reservation utility is altered. For instance, an increase in the farmer's 111

reservation utility that may be caused by an improvement in the farmer's access to capital sources, reduces his incentives to comply with the interlinked contract. The losses from a rupture of the relationship if non-cooperation is detected become smaller. Consequently, the length of the penalty phase threatened by the trader to the farmer has to be longer to restore the system of incentives for contract compliance. Third, the study analyzed increases in the farmer's probability of success, which may be increased by factors such as an improvement in cropping techniques and irrigation technologies that aect the quantity risk involved in agriculture. The expected utilities of both the farmer and the trader vary directly with changes in the stage probability of success. Thus, with unchanged reservation utilities and for a given trader's discount factor, the length of punishment threatened by the parties in the event of non-cooperation has to be higher to re-establish the system of incentives. Finally, we have considered changes in the contracting parties' risk aversion. Changes in the agent's risk aversion may occur as a result of changes in the institutional environment, not uncommon in developing countries. In general, an increase in the risk aversion coecient of one of the contracting parties reduces her/his share of the revenue to be distributed. But at the same time, the party's valuation of a given level of wealth increases. The relative strength of these two eects de nes the nal impact over the party's expected utility. The expected utility of the other party (with unchanged risk aversion) moves together with the party's changing risk aversion coecient. For instance, and for the particular case analyzed in this study, increases in the risk aversion coecient of the farmer lower his expected utility, while increasing the trader's expected utility. Hence, the farmer's (trader's) incentive to cooperate decreases (increases), and the required length of the punishment threatened to the farmer (trader) by the trader (farmer) is longer (shorter).

112

7.1 Policy Implications This study will enable development economists, both theorists and practitioners, to better understand how informal interlinked arrangements respond to market imperfections, by overcoming the informational problems through repeated transactions and personal relationships. As a consequence, lessons can be extracted for policy making. The evidence presented in this study shows support for the now predominant view that informal institutions may play a useful role in developing countries (Meyer & Nagarajan, 1991). Credit-output interlinked contracts exist because they are bene cial for the parties involved, rather than being a mechanism for exploitation, as previously thought. Moreover, credit-output interlinked contracts nance the production of crops that would not, otherwise, be nanced by commercial lenders, because these crops are considered risky compared to those oriented to external markets. Furthermore, because informational problems are less costly to overcome for trader-lenders than for commercial lenders, credit and partial insurance are made available to farmers at low costs. Thus, if the purpose is to facilitate the access of small farmers to capital sources, credit-output relationships should not be condemned, but rather promoted. First, formal nancial institutions can put the trader-lenders' informational advantage on their side by employing them as intermediaries to channel working capital to small producers. Bell (1990) and Wells (1978) report on this proposed arrangement being used in North Arcot and in Malaysia, by banks and private fertilizer companies and by an Agricultural Bank, respectively. However, the incentive scheme needs to be carefully designed taking into account not only the new agency problem that arises but also the case-speci c economic and socio-cultural factors. The new agency problem refers to the fact that the trader-lender may be more prone to relax the screening process to take on borrowers; or traders and farmers may collude and take actions that jeopardize the interest of commercial lenders. In addition, when traders were asked to comment on this approach, some of them mention the fact that the 113

personal relationship between themselves and farmers may be disrupted once a commercial bank's interest is involved. Second, another (indirect) way to facilitate the access to credit by small farmers is to ease the access of traders to formal loans. As reported in the survey's results section, traderlenders typically nance their marketing and lending activities with their own sources; and whenever there are liquidity constraints, these are commonly relaxed with high-interest rate short-maturity loans from informal moneylenders. Traders are unwilling to apply for formal loans because of the high transaction costs that the loan application procedure in formal nancial markets imply for the borrower. The heavy paperwork, the lengthy procedure, the inconvenient oce location and hours, among other factors, impose additional costs for potential borrowers. Thus, the loan application and delivery procedures have to be made more ecient to make traders participate in formal capital markets. The informational problems that may arise when lending to crop wholesale traders would be easier to overcome by commercial lenders than those problems arising when lending to small producers. Traders are registered concessionaires at the wholesale market in Lima, and typically own assets that can be oered as collateral. However, the expected results of the approaches above described cannot be overstated. Traders reported in the survey a 20 percent rate of default, from which 75 percent was judged to be involuntary. That is, not all moral hazard problems were solved by traders; ve percent of the farmers voluntarily defaulted. In addition, the high percentage of involuntary default provides an idea of the risk conditions in the production and marketing of the crops here analyzed. This observation suggests that there is a role for the government, in the form of scal policy. First, actions are needed to reduce the conditions of uncertainty and risk under which agriculture takes place. Such actions are the improvement of economic infrastructure (repair and maintenance of irrigation works, road infrastructure, crop storage facilities, etc.) and the provision of information on prices and distribution of crops planted. From the features of the interlinked contracts, we can draw out principles that can fur114

ther the development of formal nancial institutions. First, we have learned that generating the right incentives is the most eective way to promote cooperation, rather than policing borrowers. This is particularly important in an environment where the legal system is ineffective. Relating availability of credit to past performance is a key element in encouraging contract compliance, and threats of credible punishments are necessary to deter opportunistic behavior. However, rewards and punishments can be eective only if there is repetition that allows the development of a long-term relationship. The main aws of many credit programs in Peru oriented to agricultural producers have arisen from ignoring these observations. Past credit programs were understood as short-term projects, and borrowers were selected based on some targeting criteria, independent of their past history. Moreover, constant forgiveness of loans driven by political pressures made punishment of the defaulters not credible. Not surprisingly, high default rates and the bankruptcy of the institutions implementing the programs were the results. Second, one part of the right incentives to promote cooperation is some level of tolerance. Because contracts take place in an uncertain environment and lenders are unable to determine whether a default was due to unfavorable movements of the random variables aecting production or to the borrowers' lack of cooperation, a level of tolerance of a certain target with high probability is required to reduce the borrower's risk without reducing his incentives to cooperate. Commercial lenders may need to establish some sort of insurance to bear the costs of being tolerant. Third, traders are able to oer to the farmers a speci c nancial product at conditions that are aordable to them. Once the relationship is established, traders' loans are easy to access, are promptly delivered, and provide some partial insurance for unforeseen events. These characteristics should be considered by lenders who want to capture farmers as their clientele. During the last seven years, the current government of Peru has taken a free market approach that has implied an increase in competition in the formal nancial market, mainly due 115

to the increasing participation of foreign capital. As the process progresses, one can expect that the largest banks will capture the prime clientele in the market while smaller banks will have to direct their ventures (as some are already doing now) to sectors of the market not served before, such as small scale rms and small and medium agricultural producers. For this purpose, they will have to tailor their nancial products to the needs of that so far neglected demand. An issue that needs further research and more careful quanti cation is the cost of the loan (for farmers) under interlinked contracts. This measurement will help to determine the exact welfare eects of these contracts. This study provided only an approximation of the cost of loans, which is dicult to capture. Farmers are unable to observe the actual price at which their crop was sold to retailers by wholesale traders. The information they provided was based on their knowledge of average daily prices and their interaction with other farmers. On the other hand, traders have no incentive and they are wary about providing us with that information. However, the results of the survey show that the usual crop underpricing, on average, is not perceived by farmers as exploitative, but rather as a fair price to pay for the service received. Nevertheless, an improvement on price information systems can ameliorate the negotiation power of the farmer and make the terms of the transaction more transparent.

116

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Vita Narda Lizette Sotomayor was born in Apurimac, Peru. She obtained her Bachelor's degree in Social Sciences, and her title of Licentiate in Economics at the Ponti cia Universidad Catolica del Peru (PUCP) in 1985 and 1987, respectively. Upon graduation she worked at the Department of Economics of the PUCP. In 1992, she earned her Master's degree in Agricultural Economics at The Ohio State University. Her master's thesis was on the relationship between credit and productivity. The empirical application was based on a survey of small scale rms in Ecuador. In 1992, Narda started the Ph.D. program as a Ford Foundation fellow at the Department of Agricultural Economics at the University of Illinois at Urbana-Champaign. In 1993 and 1994, she participated in the summer employment program at The World Bank. The rst time she was appointed to go on mission to Ecuador to study the potential economic eects of a proposal of land reform. The second time, she went on a mission to Bolivia to study the availability of nancial services for the rural population. She wrote mission reports on both occasions, with the ndings and recommendations. In 1994, Narda was awarded a Tinker Foundation grant to perform a pilot survey on the nancial relationships between traders and farmers in Coastal Peru. Based on this pilot study, she conducted her dissertation surveys to wholesalers and small farmers in 1995. The eld research was founded with a Social Science Research Council Grant. In the same year, she also worked as a consultant on rural nancial issues for the Ministry of Economy and Finance of Peru. She successfully defended her dissertation in October, 1997. Narda's research areas of interest are rural nancial markets and institutions, the economics of information, and applied theory of contracts and incentives.

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