Role of risk sharing and transaction costs in contract choice: Theory and evidence from groundwater contracts

Transcription

1 Journal of Economic Behavior & Organization Vol. 63 (2007) Role of risk sharing and transaction costs in contract choice: Theory and evidence from groundwater contracts Rimjhim M. Aggarwal Department of Economics, 3300 Dyer Street, Suite 301, Southern Methodist University, Dallas, TX , United States Received 6 December 2002; received in revised form 2 June 2005; accepted 15 June 2005 Available online 19 May 2006 Abstract Empirical modeling of contract choice has been problematic because routine large-scale surveys do not contain sufficient information on matched partners and on contractual terms. This paper is based on a primary level survey of groundwater contracts in India. We discuss several different measures for riskiness and transaction costs and use them to test for alternative theories of contract choice. Although the risk sharing explanation has been most popular in the theoretical literature, it is not found to be significant. The data are more consistent with a double-sided incentive model, where the need for giving proper incentives to the buyer and the seller determines contract choice Elsevier B.V. All rights reserved. JEL classification: O12; Q12; D82 Keywords: Contracts; Risk; Transaction costs; Groundwater; Agriculture; India 1. Introduction With the spread of contracting all over the world, there has been a growing interest in examining the determinants of contract choice. Theoretical research on the subject has analyzed the role of a wide array of factors, such as risk sharing, moral hazard, capital constraints and transaction costs on contract choice (Cheung, 1969; Stiglitz, 1974; Grossman and Hart, 1983; Eswaran and Kotwal, 1985; Laffontaine, 1992; Laffont and Matoussi, 1995). However, it is important to recognize that Tel.: ; fax: address: aggarwal@smu.edu /$ see front matter 2006 Elsevier B.V. All rights reserved. doi: /j.jebo

2 476 R.M. Aggarwal / J. of Economic Behavior & Org. 63 (2007) most of the results derived from these models hold only under very specific assumptions regarding the functional forms and the strategy space of the agent (Holmstrom and Milgrom, 1987). Thus, it is widely recognized that careful empirical work is critical in our understanding about the accuracy and generality of the theoretical results. Empirical research on contract choice has proved to be quite challenging for several reasons. At the core lies the difficulty in finding appropriate empirical measures for theoretical constructs, such as risk attitudes of contracting parties, riskiness of technology, monitoring, enforcement and other transaction costs. Most of the theoretically interesting variables are either not observed or only partially observed. Given this problem, the empirical methodology used most often is to regress contract choice on a range of proxies relating to the characteristics of the contracting parties and crops (alternatively, jobs/technology). The estimated coefficients on these proxies are then used to test hypothesis regarding contract choice. In a recent paper, Ackerberg and Botticini (2002) point out that this methodology could lead to misleading results if the potential endogeneity of contracting parties is not given adequate attention. In their study of land tenure contracts in Renaissance Tuscany, they found that the omitted variable bias due to endogenous matching can be quite serious and casts doubt on results from previous empirical papers that have neglected this issue. Most large-scale surveys contain, at best, very scanty information on matched partners. An additional difficulty in the study of agrarian contracts is that contractual terms tend to be qualitative and often closely enmeshed with social norms. Thus, these are generally missed in routine largescale surveys, leaving the researcher with an incomplete picture of the contractual structure. On the other hand, surveys that are specifically designed to capture contractual intricacies tend to be limited in their geographical coverage and often cover just 1 year of data. To estimate the contract choice equation, one needs proxies for contractual determinants (such as riskiness of alternative crops or their input intensities) that are exogenous to the contract itself. Such proxies are difficult to construct from the available data. The present paper uses data from a specially designed primary level survey to examine the determinants of contract choice in groundwater contracts in western India. An important externality associated with this data is that the villages surveyed belong to the same agroclimatic region in western India in which ICRISAT also collected panel data on production conditions. 1 The existence of this supplementary data together with the primary level survey provides us with a unique setting to address the problems generally encountered in doing empirical research on contract choice, as discussed above. We also believe that groundwater contracts provide an interesting avenue to revisit some of the ongoing controversies in contract literature, such as those regarding the role of risk sharing in contract choice, as well as provide new perspectives on the working of agrarian institutions. Existing empirical research on contract choice in agriculture has almost exclusively focused on the case of land tenure. With the spread of irrigated agriculture across the developing world, groundwater transactions between farmers who own wells and their neighbors have become quite widespread, particularly in South Asia. Numerous case studies on water markets from South Asia have pointed to how these markets are changing the structure of the agrarian economy. 2 However, to the best of our knowledge, contract theory has not been systematically applied to understand contract choice in groundwater transactions. 1 See footnote 6 for more details on the ICRISAT data. 2 In particular, these studies have pointed to how social and economic prestige are now more closely related to ownership of a productive well rather than landownership per se. Studies on groundwater markets include Janakarajan (1992), Shah and Ballabh (1997), Dubash (2002), Shah (1993), Kajisa and Sakurai (2003) for India; Meinzen-Dick and Sullins (1994) for Pakistan; Wood and Palmer-Jones (1990) and Fujita and Hossain (1995) for Bangladesh.

3 R.M. Aggarwal / J. of Economic Behavior & Org. 63 (2007) Given the vast theoretical literature that already exists on contract choice, we do not present any new theoretical models in this paper. Instead the focus of this paper is on analyzing the institutional environment and testing among existing theoretical explanations that seem relevant to our case. In the theoretical literature on contract choice, risk sharing was long believed to be the primary motivation for share contracts. 3 However, evidence from empirical studies on contract choice is somewhat mixed with only a very few studies finding risk sharing explanation to be significant. 4 This has led to a lot of controversy regarding appropriate measures of riskiness of technology and other econometric issues, such as the endogeneity bias discussed earlier. In this paper, we propose two different measures of crop riskiness and use these measures in our contract choice equations. The pseudo fixed nature of our data enables us to control for the omitted variable bias that has plagued earlier empirical studies on contract choice. Interestingly, we do not find the risk sharing explanation to be significant in any of the fixed effect models that we estimated. Our data seems to be somewhat more consistent with a double-sided incentive model, which assumes both parties to be risk neutral and explains contract choice as arising from the tradeoffs between incentive provision to both the buyer and the seller for the provision of their inputs. The rest of the paper is organized as follows. Section 2 provides a brief description of the sample villages and the survey methodology. In Section 3, we review some theories on contract choice and discuss their empirical implications. In Section 4, we discuss the empirical methodology and in Section 5 we present the results. Finally, in Section 6, we conclude. 2. Survey methodology and the sample villages Groundwater transactions in the South Asian context are very different from the formal water trades widely observed in developed countries where property rights on groundwater are relatively well defined. 5 In India, as also in several other developing countries, property rights on groundwater are quite poorly defined. Legally as long as water remains underground no one owns it, but once pumped to the surface, it belongs to the owner of the plot to which it is lifted. Thus access to groundwater is the prerogative of the owner of the land above and often entails a large and risky investment in drilling a well and buying the pumping equipment. Given the imperfect nature of rural credit markets, it is only the relatively large landowners that can get access to the necessary credit. The situation in most parts of South Asia is further complicated by the fact that the average farm size is very small, and generally consists of two or more non-contiguous 3 In their survey of land and labor contracts, Otsuka et al. (1992:2012) argue that this model provides the most consistent explanation for the existence of a share contract. 4 For instance, Rao (1971) found in his study in southern India that crops with high yield and profit variance tended to be under fixed payment contracts. Similarly, Allen and Lueck (1995) found that natural riskiness could not explain modern crop share contracts for corn and wheat in Midwestern USA. Studies on contracts from non-farm settings (such as franchising) also find little support for the risk sharing explanation for share contracts (see Allen and Lueck for a survey). Ackerberg and Botticini argue that these previous papers have not paid sufficient attention to the problem of endogenous matching. In their study of land tenure contracts in Renaissance Tuscany they found that after controlling for endogeneity, risk sharing does seem to play a significant role in explaining share contracts. A recent study by Kajisa and Sakurai on groundwater markets in India found water price to be higher under crop sharing contracts. They argue that this is presumably due to a risk premium payment from the buyer to the sellers (p. 27). However, they do not provide any independent analysis of why crop sharing contracts arise and why these coexist with other contractual forms. 5 In developed country contexts, the commodity transacted in groundwater markets is the right to a well-defined share of the underlying aquifer among wellowners drawing upon a common aquifer. For a comparative discussion on different types of groundwater rights, see Saleth (1998).

4 478 R.M. Aggarwal / J. of Economic Behavior & Org. 63 (2007) Table 1 Summary statistics Particulars Mean Standard deviation Maximum Minimum Land owned by buyers (acres) Land owned by sellers (acres) Number of potential buyers per seller Number of potential sellers per buyer Diameter of sample wells (ft) Depth of sample wells (ft) Horsepower of installed pump Fixed cash payment per hour of water pumped (rupees) Source: Survey data. plots. Modern pumping technology, on the other hand, has a built-in indivisibility and has the capacity to pump water at considerably higher rates per unit of time than that required by even the relatively larger sized farms. Under such circumstances, an interesting institutional innovation in recent years has been the evolution of various kinds of informal agreements amongst well-owning farmers and their neighbors to buy and sell water for irrigation. The present analysis is based on a primary level survey we conducted to study these groundwater contracts in Sabarkantha district, in the state of Gujarat in western India, for the agricultural year The structure of the water market in a given region is very sensitive to the soil, climate, topography and the socioeconomic conditions that prevail in that region. Thus, in order to focus the analysis on the main economic determinants of contract choice and to be able to draw meaningful comparative inferences, we surveyed two villages from within the same agroclimatic region. The two villages chosen were Ambavada (village A) and Boriya (village B). Village B has been part of ICRISAT s village level studies. 6 Table 1 shows some summary statistics pertaining to these villages. Both villages are part of the rocky semi-arid region of India. The average rainfall is around 760 mm of which 90 percent is received during the southwest monsoon months of June September. One can distinguish three seasons in the agricultural calendar in this region. The first is the Kharif (rainy) season, which stretches from late June/early July to October. The main Kharif crops are paddy, castor, fennel, groundnut, maize and pearl millet. The second is the Rabi season, which stretches from November to March. The main Rabi crops are wheat and tobacco. The third is the summer season from April to June, in which pearl millet is sometimes grown; otherwise the field is left fallow. Most of this region is characterized by sandy soils, with low moisture retention and requiring very frequent irrigation, crucially in the seasons of Rabi and summer when rainfall is scanty and unpredictable. Groundwater is the only source of irrigation in both the villages, and it is provided through privately owned borewells drilled to a depth of at least 100 ft below ground level. There were a total of 24 effectively functioning borewells in village A and 30 in village B at the time of the survey. 7 All of these borewells are fitted with submersible electric pumps with horsepower ranging 6 In these village level studies, panel data was collected by ICRISAT in to and then again in , on a sample of 40 households on various socio-economic variables of the farming system. The existence of this vast database and the experience of ICRISAT s village investigators who have stayed for many years in this village strongly influenced our choice of this sample village. A summary description of the various agro-economic features of village B is given in Singh and Singh (1982). 7 The older dug wells in the two villages have dried up as water levels have fallen over the years.

5 R.M. Aggarwal / J. of Economic Behavior & Org. 63 (2007) from 5 to 25 (see Table 1). There is a fixed annual charge for electricity, which depends on the horsepower of installed pump but is not dependent on the actual usage of electricity. Electricity supply is highly erratic in this region, both in terms of when electricity is available and the voltage of supply. Sharp fluctuations in the voltage often lead to pump failures. In a survey of cultivating households in village B, Pender and Asokan (1993) found that financial constraints are cited most often as the reason for not investing in wells. The second most common reason is not having enough land. 8 Very often these two factors are correlated since land is the main collateral against which credit is offered in rural credit markets. Thus, it is mostly the small and marginal farmers who cannot invest in their own wells and are more likely to be water purchasers (see Table 1). 9 Two separate questionnaires were canvassed in these villages, one to be answered by the water sellers and the other by water buyers. The selection of buyers and sellers in the sample was done in the following way. First, a census of the well owning households was conducted which found a total of 54 such households in the two villages. All of these households reported selling at least some part of the water pumped out of their wells every year. From this census, a sample of 30 households who owned wells in different locations within the two villages was selected in the first stage of sampling. Then, in the second stage of sampling, we selected a sample of 40 households who had bought water in the past year from the well owners selected in the first stage of sampling. This two-stage sampling methodology provided us information on both sides of the contract and also provided a natural consistency check by being able to match the responses of both parties to the transaction. Data was collected on all the groundwater contracts agreed upon between this set of buyers and sellers for the different seasons in the agricultural year Information on 100 contracts was collected, from which 2 had to be dropped because of inconsistent responses. Two main types of contractual arrangements were observed in the sample villages. The first is the fixed payment contract wherein, before the season begins, the water seller promises to supply a certain specified amount of irrigation to the water buyer in exchange for a fixed cash payment per hour of water pumped, to be paid at the end of the season. The contract is quite vague about the timing of these irrigations. In Section 3, we will examine how the incompleteness of the contract in this respect affects contract choice. The buyer provides all other inputs, except for irrigation. The second type of contract is the cropsharing contract in which the seller supplies irrigation in exchange for a certain specified proportion of the output to be paid at the end of the season. In some cases, the seller also shares the cost of fertilizers and seeds with the water buyer. Note that in both types of contracts, payment is made at the end of the season. Mixing of contracts in the form of a positive output share together with a certain (non-zero) fixed payment was not observed. Separate contracts are agreed upon for the different crops to be irrigated, and all the contracts were observed to be seasonal in duration. Interlinkage of groundwater contracts with other contracts, such as that for credit, labor or land was not observed. 10 All the buyers in the sample, except one, owned the plot of land on which irrigation was sought. Table 2 shows a set of cross tabulations of contract type with major characteristics of the crops. As is evident from this table, there are some crops, like maize and millet grown in the Kharif (rainy) season, that are almost always found under fixed payment contracts. On the other hand, 8 Joint investment in new wells was not observed in these villages. 9 Sometimes large landowners who own plots of land in different locations also resort to water buying if they cannot transport water from their own well to all their fields. However, there has been a tendency for well owners to buy or rent additional land near their well and sell off their plots of land in other locations. 10 Interlinked contracts with land tenure and/or credit have been reported in some other contexts, such as in Tamilnadu state in South India (Janakarajan) and Bangladesh (Fujita and Hossain).

6 Table 2 Crop characteristics and contract type in sample villages Crops Maize Groundnut Paddy Millet (Kharif) Fennel Castor Wheat Tobacco Millet summer Average for all crops Crop characteristics Main growing season Kharif Kharif Kharif Kharif Kharif Rabi a Khari Rabi a Rabi Rabi Summer Irrigation elasticity b Labor elasticity b Risk (1) b Risk (2) b Contract type: cropsharing contracts as percent of total for each crop Village A c (0.447) (0.378) 50 (0.577) n.a. d (0.488) 12.5 (0.353) 83.3 (0.408) 80 (0.548) 100 (0) Village B c 0 (0) (0.577) (0.516) 0 (0) 50 (0.548) 12.5 (0.353) 88.8 (0.333) 50 (0.707) 100 (0) Total number of contracts under crop Source: Survey data and ICRISAT VLS studies. a Fennel and Castor are sown in the Kharif season and harvested towards the end of Rabi season. b Details regarding the measurement of irrigation and labor elasticity and the two measures of risk are discussed in the methodology section. c Figures in parenthesis show standard deviation in contract type in each village. d There were no observations on millet grown during the Kharif season in village A. 480 R.M. Aggarwal / J. of Economic Behavior & Org. 63 (2007)

7 R.M. Aggarwal / J. of Economic Behavior & Org. 63 (2007) Table 3 Results of a linear regression model on determination of contractual terms Independent variables Parameter estimate (S.E.) Intercept (3.2701) Depth of well (0.0120) Horsepower of installed pump ** (0.1356) Village dummy ** (2.0506) R Adjusted R Number of observations 40 Dependent variable = fixed payment per hour of water pumped. Source: Survey data. ** Significant at 1 percent level. there are other important crops like paddy and fennel (spice crop) that are also grown during the same season, but for these crops there is considerable intravillage variation in contract type. Wheat is an important food crop grown during the Rabi (post-rainy season), and it is almost always associated with a cropsharing contract. Tobacco is another important crop of this season, but there is much greater intravillage variation in the type of contract associated with it. Millet is the only crop grown during the summer season, and it is always associated with a crop-sharing contract in both villages. An important point to bear in mind when examining groundwater transactions is the fragmented nature of this market. Depending on the topography, soil conditions and technology of transporting water, there is a limited area around the well over which it is economically feasible to transport water. Each water seller was observed to have, on an average, around six to seven potential customers (as shown in Table 1). The water buyers also, in general, do not have much choice regarding the sellers from whom they can buy water. Around 50 percent of water buyer respondents in our sample reported that there was only one well in their vicinity. Given the highly fragmented nature of this market one would, a priori, expect to find a significant intra-village variation in the fixed payment and crop share parameter. As also noted in several other studies on water markets in South Asia, we observed very little variation in these parameters. 11 Some summary statistics pertaining to the observed values of the fixed cash payment parameter are presented in Table 1. Most of the observed variation in this parameter is explained by wellspecific factors, such as depth of the well and horsepower of installed pump, as shown in Table 3. This is to be expected given that the payment for irrigation is made on a per hour basis and the horsepower of the pump and the depth of the well are important determinants of the flow of water in a given unit of time. Once these well-specific factors are controlled for, there is very little residual variation in the fixed payment parameter within a village. Table 4 shows the frequency distribution of the output shares observed in the two villages. Again, as is evident from this table, output shares do not vary much within a village. However, with regard to sharing of input costs, the picture is quite varied and complex. In the case of all share contracts involving wheat, the cost of seeds and fertilizers was observed to be shared in the same proportion as output. In case of other crops, there was no systematic pattern with sometimes no input sharing and sometimes only the cost of seeds or only the cost of fertilizers being shared. 11 See, for example, Meinzein Dick and Sullins for Pakistan; Wood and Palmer-Jones for Bangladesh; Dubash and Shah for India.

8 482 R.M. Aggarwal / J. of Economic Behavior & Org. 63 (2007) Table 4 Variation of crop shares across the sample villages Crop share Percentage of cases when observed Village A Village B One-third share to water seller No input sharing 0 29 With input sharing 0 13 Half share to water seller No input sharing 23 7 With input sharing Source: Survey data. Default rates on the payment for water under both types of contracts was observed to be very low (there were two reported cases under fixed payment contracts and none under crop share contracts). The threat of not getting water in the next season if previous payments had not been made seems to work as an effective enforcement device. 3. Review of existing theories on contractual choice In the preceding section, we have pointed to two main types of contracts that were observed in the sample villages, namely, fixed payment and cropsharing contracts. Several models have been formulated in the land tenancy literature to explain the coexistence of alternative contractual forms. 12 In this paper, we will focus on two specific classes of models from this literature that seem to be most relevant for the case of groundwater contracts The insurance-incentive tradeoff (IIT) model One of the most important arguments for share contracts has been that it allows risk sharing (Cheung). In contrast to this, a fixed payment contract provides the best incentives to the agent but places the entire production risk on him. This tradeoff between insurance provision and incentive provision determines the optimal contract (Stiglitz, 1974; Holmstrom and Milgrom, 1987; Otsuka et al., 1992). In terms of insurance provision, it follows from models of this kind that contract choice would differ across (a) households depending on their ability to bear risks and (b) across crops depending on their riskiness. In particular, for the case of groundwater contracts, this theory would suggest that for any given crop, the more risk averse is the water buyer (seller) the more likely it is that a cropsharing (fixed payment) contract would be chosen. Similarly given any two parties to the contract, a cropsharing (fixed payment) contract is more likely to be chosen for crops, which are perceived to be more (less) risky. Given these risk factors, contract choice is also likely to differ across water sellers depending on their monitoring abilities. In a cropsharing contract, the water buyer gets only a part of his marginal 12 For a survey, see Binswanger and Rosenzweig, Otsuka et al. and Singh. 13 Various kinds of screening models have also been used in the land tenancy literature (see Singh for a survey). An important assumption underlying these models is regarding asymmetric information about the abilities of the tenant. This assumption seems unreasonable for the case of groundwater transactions, which involve only owners of neighboring fields. Hence, we do not examine screening models in this paper.

9 R.M. Aggarwal / J. of Economic Behavior & Org. 63 (2007) product and thus has the incentive to shirk in the application of labor and other inputs. Therefore, other things being equal, the water seller is more likely to choose the cropsharing alternative when his ability to monitor the buyer is better. Furthermore, given his ability to monitor, he will be less likely to choose the cropsharing alternative when the incentive for the buyer to shirk is higher Double-sided incentive (DSI) model The insurance-incentive tradeoff model discussed earlier assumes moral hazard only on the part of the agent. Formalizing some of the ideas in Reid (1976), Eswaran and Kotwal develop a model in which there is an incentive problem associated with both parties to the contract. Models of this kind typically assume both parties to be risk neutral, thus abstracting away from risk sharing considerations and focusing instead on both parties need for incentives given the costs of monitoring and enforcement. 14 In Eswaran and Kotwal s model, the incentive problem arises because of the high costs of quality enforcement with respect to two kinds of labor inputs: supervisory input and managerial input. In their model, the principal (landlord) has a relative advantage in the supply of managerial labor while the agent (tenant) has a relative advantage in the supply of supervisory labor. Different contracts are chosen depending on the incentives that these provide to each of the parties. In the context of groundwater transactions, it can similarly be argued that incentive problems may arise with regard to inputs provided by both the water buyer and the water seller. Incentive problem in the provision of labor by the buyer has already been discussed. Let us now look at how incentive problems may arise in the provision of irrigation input by the seller. For many irrigated crops, particularly the high yielding varieties of wheat and rice, crop yields are highly sensitive not only to the amount of irrigation, but more importantly, to the timing of the various irrigations. This is what we shall refer to as the quality dimension in irrigation supply to distinguish it from the quantity dimension, which is a volumetric measure of the amount of water supplied. Timeliness is often defined in the irrigation literature as the correspondence of water deliveries to crop needs. Hukkeri and Pandey (1977) in their extensive research on this subject report that the most practical criterion commonly adopted by farmers for scheduling of irrigations is one based on the physiological growth stages critical in the demand for water. Some stages during the crop cycle can tolerate moisture stress to a certain extent while in case of other stages (such as the crown root initiation stage in wheat that occurs shortly after sowing), any shortfall in water deliveries results in a significant loss in the yield. Crops vary in their sensitivity to the timeliness of irrigation supply. In case of some crops, water stress in certain stages of growth can be compensated by more water in other stages, while in case of other crops it cannot. For these latter set of crops, proper timing of irrigations is very critical. 15 Our interviews with farmers suggested that they perceive the timeliness issue in irrigation supply to be very critical and, in fact, give this as an important reason for why public irriga- 14 Models of this kind are also sometimes called transaction cost based models since these ignore risk preferences and focus more on asset specificity and various forms of transaction costs. Other examples include Allen and Lueck (1995), Laffont and Matoussi (1995) and Laffontaine (1992). 15 The importance of timing in irrigation supply has been emphasized in a number of studies that compare the performance of alternative irrigation sources and find crop yields under bureaucratically or community managed systems to be significantly lower than that under private wells, see Shah for a survey. Meinzen-Dick (1995) estimated a production function for paddy and found that incorporating measures of timeliness explains much more of the variability in agricultural production than simple quantitative measures of irrigation supply over a season.

10 484 R.M. Aggarwal / J. of Economic Behavior & Org. 63 (2007) tion schemes are associated with poor agricultural productivity. However, interestingly, we found that the contracts agreed upon between the buyers and sellers are quite vague with respect to the issue of timeliness of irrigation supply. Thus, for example, contracting parties may agree on some broad stipulation, such as the requirement that irrigation has to be given once every days. However, the contract is largely silent with respect to what happens if, for instance, there is unexpected event, such as pump failure or power outage, excessive overdraft from neighboring wells, or a drought. Optimal timing is contingent upon a host of factors that are revealed gradually, and it is prohibitively costly to specify a complete contract regarding timing of water deliveries. One may argue that real world contracts are rarely complete in the sense of specifying appropriate actions to be taken under every possible contingency. This is particularly true of agricultural contracts that tend to be quite informal. However, as opposed to other agricultural contracts, one important difference in case of groundwater contracts is that these are a relatively new institutional innovation. 16 Thus farmers are much lower down on their learning curves. Most theoretical models of contract choice begin by assuming complete contracts and thus ignore the role of learning by doing in contract design and implementation. Very often, a shared history of contract enforcement provides informal guidelines or codes of behavior that fill up some of the missing provisions. In our field study, we observed that social norms play an important role in specifying some broad stipulations on fairness in irrigation supply, such as requiring water sellers to provide all their customers with water by turn. However, for crops that are very sensitive to timing of irrigation, more fine-tuning may be required. 17 The fact that the seller owns the well implies that he has the residual rights of control over all aspects of irrigation timing not specified in the contract. Thus, given an unexpected contingency, such as power outage, the seller has the flexibility within the broad specifications of the contract of prioritizing the timing of irrigation supply between his own field and the fields of different buyers. 18 In such a situation, a cropsharing contract gives better incentives than a fixed payment contract to the seller to provide timely irrigations. This is because the seller gets a share of the output under a cropsharing contract while under a fixed payment contract he gets a pre-specified fixed amount, as long as he adheres to the broad specifications of the contract. The extent to which the buyer is affected by these actions of the seller depends on the sensitivity of the crop grown to the fineness in detail about the timing of irrigations. There is, therefore, a double-sided incentive problem here, where the need for giving proper incentives to both the buyer and the seller determines the choice between a cropsharing and fixed 16 Intensive use of groundwater irrigation through electrically operated borewells became widespread around the mid 1980s in this largely semi-arid region. Information on aquifer characteristics and water requirements of different crops is still quite poor. 17 Once the state of nature reveals itself, renegotiations may increase ex post surplus. However, there are several reasons why renegotiation of contracts is likely to be very costly in this setting. The sample villages lie in a hard rock region where the groundwater aquifer is highly discontinuous. Under such a scenario it is reasonable to assume that the seller has private information about the recharge rate of his well. The presence of private information makes renegotiation of contracts very costly (Al-Najjar, 1995). Moreover, once the ex post state is revealed, production decisions must be made rapidly, leaving insufficient time to agree upon a new contract. Disputes over the proper division of the ex post surplus might well delay or even prevent renegotiations from occurring. 18 In our survey interviews, all the sellers pointed out that they follow the convention of a strict rotation schedule in the allocation of water between their fields and the fields of the different buyers. Under such a schedule, everyone is supposed to get water by turns and any shortages are equally shared. The buyers, however, reported several cases of discrimination in which buyers with larger land endowments or those having the option of buying from another seller had been favored.

11 R.M. Aggarwal / J. of Economic Behavior & Org. 63 (2007) payment contract. While a cropsharing contract provides better incentives to the seller to provide timely irrigations, it provides fewer incentives than a fixed payment contract to the buyer. A long-term relationship between the buyer and the seller may reduce the severity of these incentive problems, but may not completely eliminate them. The testable implication that follows from this double-sided incentive problem is the following. A cropsharing (fixed payment) contract is more likely to be chosen, the more important is the incentive problem in the input provided by the seller (buyer). In the next section, we explain in greater detail what we mean by the incentive problem in the provision of different inputs and the associated measurement issues. To summarize, the insurance-incentive tradeoff model explains contract choice as a balance between risk sharing and a one-sided incentive problem while the double-sided incentive model abstracts away from risk sharing considerations and explains contract choice as a balance between incentive provision along multiple margins. While these different theories have emphasized different factors, it is plausible that in many situations these factors supplement each other rather than being exclusive. Building upon the model of Eswaran and Kotwal, Agrawal (1999) develops a generalized double-sided moral hazard model in which the assumption of risk neutrality of the agents is dropped, thus allowing for risk sharing considerations as well as shirking by both agents. In Agrawal s model, the optimal contract maximizes the output net of the risk-bearing and agency costs. In the next section, we develop a general reduced form empirical model that allows us to test for the significance of these different factors in the context of groundwater contracts. 4. Empirical model It is instructive to start with a simple contract choice equation of the following nature: Y = β S X S + β B X B + β C X C + ε (1) where Y is a binary contract choice variable (which takes the value one if a share contract is observed and zero if a fixed payment contract is observed). X S, X B and X C are the fundamental characteristics of the seller, buyer and the crop, respectively, which according to theory determine contract choice. β S, β B and β C are the corresponding vectors of unknown coefficients. ε is assumed to be the random error term that is distributed independently and identically with mean zero and variance σ 2. If all the relevant characteristics of buyer, seller and the crop (X S, X B and X C ) are fully observed and are uncorrelated with ε, then a multinomial logit estimation of (1) would give consistent estimates. The estimated coefficients could then be used to test hypotheses derived from the above-discussed theories Endogenous matching and crop choice An important problem with econometric estimation of (1) is that some or all of the elements of X S and X B may be only partially observed or may not be observed at all. Some examples include risk attitudes of buyer and seller and their monitoring abilities. It is common in empirical work on contractual choice to use suitable proxies for such unobserved or partially observed characteristics. Following Ackerberg and Botticini, the underlying proxy equations can be written as X S = α S P S + η S (2) X B = α B P B + η B (3)

12 486 R.M. Aggarwal / J. of Economic Behavior & Org. 63 (2007) where P S and P B are observed proxy variables for characteristics of the seller and buyer, respectively, and α S and α B are the corresponding proxy coefficients. η S and η B are the proxy errors that are mean independent of P S and P B. 19 Using the proxy Eqs. (2) and (3), the contract Eq. (1) can be rewritten as Y = β S P S + β B P B + β C X C + (β S η S + β B η B + ε) (4) where β S = α S β S and β B = α B β B. Estimation of Eq. (4) by a multinomial logit model is likely to lead to biased estimates because it is unlikely that buyers and sellers are matched completely randomly. Since the characteristics of a buyer matter to the seller, it is likely that he will look for an appropriate buyer and vice versa. For instance, sellers who have poor monitoring abilities may seek out buyers who have a reputation for being hardworking and trustworthy. Similarly, buyers who are highly risk averse may seek out sellers who are willing to bear some of their risks at low cost. One of the questions in the survey asked the sellers to rank the most desirable characteristics they seek in a buyer. Reputation of being hardworking and trustworthy ranked amongst the top two attributes. Thus matches are expected to be equilibrium outcomes implying that buyer characteristics (X B ) and seller characteristics (X S ) are likely to be correlated. This implies that since η B is a part of X B, it is also likely to be correlated with X S and hence also with the seller proxy variables P S. Similarly, η S is likely to be correlated with P B. This suggests that using a multinomial logit model to estimate (4) would lead to biased estimates of β S and β B. In addition, if it is true that crop choice is endogenous to contract choice then some of the omitted variables relating to buyer and seller characteristics may also be correlated with X C, leading to biased estimates of β C. For instance, it is plausible that water buyers who are relatively more risk averse (due to some unobserved characteristic) prefer crops that are relatively safer. Similarly, sellers with high-unobserved monitoring costs may prefer crops that require less monitoring. In the rest of this subsection, we discuss how important these problems are likely to be in our context and offer some plausible solutions. Most empirical studies of contractual choice have not paid sufficient attention to the problem of biased estimates due to endogenous matching. An important exception is the study, cited earlier, by Ackerberg and Botticini (A B) on land tenure contracts. In such contracts, each party has a reasonably large set of choices regarding its potential partner, so the matching of parties is likely to be a purposive one. Thus, it is not entirely surprising that A B found the problem of omitted variable bias to be quite serious in their study. In contrast to this, in the case of groundwater transactions, the choice set of potential partners is quite limited. This is because once the well is dug, there is a restricted area over which it is economically feasible to transport water. 20 As was pointed out earlier, around 50 percent of water buyer respondents in our sample reported that there was only one well in their vicinity. The sellers, on the other hand, seem to have somewhat greater choice. Each water seller in our sample was observed to have on an average around seven potential customers in his command area. In a typical year, around four customers would get irrigation in the rainy season while two would get irrigation in the other 19 Note that the above formulation of the proxy equation in (4) allows for several different possibilities, such as: (i) more than one proxy for a specific buyer/seller characteristic, (ii) no proxy for some specific buyer/seller characteristic and (iii) the possibility that the true value of some buyer/seller characteristic is actually observed. 20 Neither the land sales nor the land tenure market was found to be very active in the sample villages.

13 R.M. Aggarwal / J. of Economic Behavior & Org. 63 (2007) seasons. 21 Because of this rather limited choice set of partners, we expect the problem of endogenous matching to be less serious for groundwater transactions. However, it would be presumptuous of us to assume that buyer and seller characteristics are uncorrelated, and so we turn now to some plausible solutions for this problem of endogenous matching. A B argue that the preferred solution to the problem of endogenous matching revolves around finding a suitable set of instrument variables that affect the matching equation but do not affect the contract choice equation or the proxy equation. This is generally quite tricky. A B argue that if the observations come from different geographical regions (representing isolated markets) with different population distributions of tenants or landlords, then the matching equation is likely to differ across these regions. One can then use region dummies and region dummies interacted with tenant characteristics as instruments. As alluded above, for identification it is important that the instruments that are chosen affect the matching equation but do not affect the contract choice equation or the proxy equation. A B argue that the region dummies and their interaction with tenant characteristics affects who gets matched with whom, but has only second order effects on the contract choice and the proxy equations. In our view, it is very difficult to justify the exclusion of region dummies from the contract choice equation. Thus, for instance, the region of residence affects the reservation utility of an agent, which is likely to affect not only who is matched with whom but also the choice of contract (as numerous theoretical models of contract choice typically assume). Similarly, a farmer s decision regarding which set of crops to grow is generally quite complex, and it is difficult to find instruments that can identify this choice. Most theoretical as well as empirical models assume crop choice to be exogenous. Previous agronomic studies in our study area have found that proper sequencing of crops across seasons, in accordance with crop rotation requirements and the particular nature of the soil, is a very important determinant of crop choice in this region with low soil fertility (Singh and Singh). It has also been observed that farmers tend to grow a diverse set of crops in any given season to spread risks and to meet diverse needs, such as for food, fodder and cash. Further, note that the crops that we actually observe being grown under groundwater contracts depend not only on what the buyer would like to grow but also on whether the seller finds it attractive to enter into a contract for that crop, given his other alternatives. In our data, we have information only on the crops that were actually observed to be grown under existing contracts. Thus, we have a truncated sample, and identification here requires us to make a convincing case for a separation between the truncation variables and the variables in the structural equation. This is very difficult to do given the data. Given these problems with finding suitable instruments, one alternative would be to make use of the pseudo-panel nature of our data set and estimate a fixed effect model. Almost all of the sample buyers and sellers in our data set entered into two or more separate contracts for different crops either with the same or different partners. Thus to control for the unobserved characteristics of the buyer and the seller, we can treat each unique buyer seller configuration as a group and look at the within-group estimator. 22 The underlying assumption here is that the unobserved 21 We also observed that sellers tend to give irrigation to different set of buyers in different seasons so that almost all the potential buyers get irrigation in at least some seasons. This may be because sellers like to have a large clientele and do not wish to turn down requests for an essential resource like water. One can also speculate that by providing some irrigation to their neighbors, existing well owners try to discourage their neighbors from digging their own wells in the future. 22 As pointed out earlier, there are separate contracts for each crop, and each observation in our data set represents a unique buyer seller crop configuration. There were 48 unique buyer seller groups in our data set, out of which 43 were observed to have two or more contracts.

14 488 R.M. Aggarwal / J. of Economic Behavior & Org. 63 (2007) Table 5a Determinants of the probability of choosing a cropsharing (CS) contract: results of a logistic regression model using risk (1) measure Explanatory variables Model I (pooled data) Model II (party fixed effect) Model III (buyer fixed effect) Model IV (seller fixed effect) Intercept (1.587) Buyer s land (0.091) (0.15) Buyer s occupation a (0.609) (1.1) Seller s land (0.044) (0.076) Seller s occupation a (0.633) (1.46) Riskiness of crop (0.018) (0.024) (0.023) (0.019) Irrigation *** (4.6) *** (5.46) *** (5.819) *** (4.129) Labor *** (0.763) (0.925) (0.969) 1.99 ** (0.941) Village dummy (0.613) Log likelihood function Number of groups Figures in parenthesis are standard errors. a Occupation dummy = 1 if agriculture is the main occupation, 0 otherwise. ** Significant at 5 percent. *** Significant at 1 percent. characteristics of the buyers and sellers are fixed constants across contracts for the same agents. To estimate this fixed effect model, we use Chamberlain (1984) s approach of maximizing a conditional likelihood function. The results are presented in Tables 5a and 5b (model II). This formulation helps us to minimize the bias arising due to unobserved characteristics of the buyers and the sellers. However, it has an important limitation. The effects of the observed characteristics of the buyer and the seller (e.g. their occupation or their land endowments), that do not vary across contracts, are not identified in this model. Table 5b Determinants of the probability of choosing a cropsharing (CS) contract: results of a logistic regression model using risk (2) measure Explanatory variables Model I (pooled data) Model II (party fixed effect) Model III (buyer fixed effect) Model IV (seller fixed effect) Intercept (1.337) Buyer s land 0.02 (0.09) (0.156) Buyer s occupation a (0.617) (1.108) Seller s land (0.047) (0.096) Seller s occupation a (0.63) 1.53 (1.691) Riskiness of crop * (0.892) (1.683) 2.31 (1.696) (0.982) Irrigation *** (6.504) ** (11.108) ** (11.278) *** (6.039) Labor * (0.814) (1.197) 0.14 (1.277) (0.959) Village dummy (0.638) Log likelihood function Number of groups Figures in parenthesis are standard errors. a Occupation dummy = 1 if agriculture is the main occupation, 0 otherwise. * Significant at 10 percent probability level. ** Significant at 5 percent. *** Significant at 1 percent.