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Journal of Economic Behavior & OrganizationVol. 63 (2007) 475–496

Role of risk sharing and transaction costs incontract choice: Theory and evidence

from groundwater contracts

Rimjhim M. Aggarwal ∗Department of Economics, 3300 Dyer Street, Suite 301, Southern Methodist University,

Dallas, TX 75275-0496, United States

Received 6 December 2002; received in revised form 2 June 2005; accepted 15 June 2005Available online 19 May 2006

Abstract

Empirical modeling of contract choice has been problematic because routine large-scale surveys do notcontain sufficient information on matched partners and on contractual terms. This paper is based on aprimary level survey of groundwater contracts in India. We discuss several different measures for riskinessand transaction costs and use them to test for alternative theories of contract choice. Although the risk sharingexplanation has been most popular in the theoretical literature, it is not found to be significant. The dataare more consistent with a double-sided incentive model, where the need for giving proper incentives to thebuyer and the seller determines contract choice.© 2006 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 examiningthe determinants of contract choice. Theoretical research on the subject has analyzed the role of awide array of factors, such as risk sharing, moral hazard, capital constraints and transaction costson 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

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476 R.M. Aggarwal / J. of Economic Behavior & Org. 63 (2007) 475–496

most of the results derived from these models hold only under very specific assumptions regardingthe functional forms and the strategy space of the agent (Holmstrom and Milgrom, 1987). Thus, itis widely recognized that careful empirical work is critical in our understanding about the accuracyand generality of the theoretical results.

Empirical research on contract choice has proved to be quite challenging for several reasons. Atthe core lies the difficulty in finding appropriate empirical measures for theoretical constructs, suchas risk attitudes of contracting parties, riskiness of technology, monitoring, enforcement and othertransaction costs. Most of the theoretically interesting variables are either not observed or onlypartially observed. Given this problem, the empirical methodology used most often is to regresscontract choice on a range of proxies relating to the characteristics of the contracting parties andcrops (alternatively, jobs/technology). The estimated coefficients on these proxies are then usedto 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 ofcontracting parties is not given adequate attention. In their study of land tenure contracts in Renais-sance Tuscany, they found that the omitted variable bias due to endogenous matching can be quiteserious 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. Anadditional difficulty in the study of agrarian contracts is that contractual terms tend to be qualitativeand often closely enmeshed with social norms. Thus, these are generally missed in routine large-scale surveys, leaving the researcher with an incomplete picture of the contractual structure. Onthe other hand, surveys that are specifically designed to capture contractual intricacies tend to belimited in their geographical coverage and often cover just 1 year of data. To estimate the contractchoice equation, one needs proxies for contractual determinants (such as riskiness of alternativecrops or their input intensities) that are exogenous to the contract itself. Such proxies are difficultto construct from the available data.

The present paper uses data from a specially designed primary level survey to examine thedeterminants of contract choice in groundwater contracts in western India. An important exter-nality associated with this data is that the villages surveyed belong to the same agroclimaticregion 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 witha unique setting to address the problems generally encountered in doing empirical research oncontract choice, as discussed above. We also believe that groundwater contracts provide an inter-esting avenue to revisit some of the ongoing controversies in contract literature, such as thoseregarding the role of risk sharing in contract choice, as well as provide new perspectives on theworking of agrarian institutions. Existing empirical research on contract choice in agriculture hasalmost exclusively focused on the case of land tenure. With the spread of irrigated agricultureacross the developing world, groundwater transactions between farmers who own wells and theirneighbors have become quite widespread, particularly in South Asia. Numerous case studies onwater markets from South Asia have pointed to how these markets are changing the structureof the agrarian economy.2 However, to the best of our knowledge, contract theory has not beensystematically 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), Shahand 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.

R.M. Aggarwal / J. of Economic Behavior & Org. 63 (2007) 475–496 477

Given the vast theoretical literature that already exists on contract choice, we do not present anynew theoretical models in this paper. Instead the focus of this paper is on analyzing the institutionalenvironment 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 primarymotivation for share contracts.3 However, evidence from empirical studies on contract choice issomewhat 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 technologyand other econometric issues, such as the endogeneity bias discussed earlier. In this paper, wepropose two different measures of crop riskiness and use these measures in our contract choiceequations. The pseudo fixed nature of our data enables us to control for the omitted variable biasthat has plagued earlier empirical studies on contract choice. Interestingly, we do not find therisk sharing explanation to be significant in any of the fixed effect models that we estimated. Ourdata seems to be somewhat more consistent with a double-sided incentive model, which assumesboth parties to be risk neutral and explains contract choice as arising from the tradeoffs betweenincentive 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 samplevillages and the survey methodology. In Section 3, we review some theories on contract choiceand discuss their empirical implications. In Section 4, we discuss the empirical methodology andin 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 watertrades widely observed in developed countries where property rights on groundwater are rela-tively well defined.5 In India, as also in several other developing countries, property rights ongroundwater are quite poorly defined. Legally as long as water remains underground no one ownsit, but once pumped to the surface, it belongs to the owner of the plot to which it is lifted. Thusaccess to groundwater is the prerogative of the owner of the land above and often entails a largeand risky investment in drilling a well and buying the pumping equipment. Given the imperfectnature of rural credit markets, it is only the relatively large landowners that can get access tothe necessary credit. The situation in most parts of South Asia is further complicated by the factthat 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 consistentexplanation 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 tendedto be under fixed payment contracts. Similarly, Allen and Lueck (1995) found that natural riskiness could not explainmodern crop share contracts for corn and wheat in Midwestern USA. Studies on contracts from non-farm settings (suchas franchising) also find little support for the risk sharing explanation for share contracts (see Allen and Lueck for asurvey). Ackerberg and Botticini argue that these previous papers have not paid sufficient attention to the problem ofendogenous matching. In their study of land tenure contracts in Renaissance Tuscany they found that after controlling forendogeneity, risk sharing does seem to play a significant role in explaining share contracts. A recent study by Kajisa andSakurai on groundwater markets in India found water price to be higher under crop sharing contracts. They argue that thisis “presumably due to a risk premium payment from the buyer to the sellers” (p. 27). However, they do not provide anyindependent 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 shareof the underlying aquifer among wellowners drawing upon a common aquifer. For a comparative discussion on differenttypes of groundwater rights, see Saleth (1998).


Table 1Summary statistics

Particulars Mean Standard deviation Maximum Minimum

Land owned by buyers (acres) 5.071 3.552 12 1Land owned by sellers (acres) 11.859 7.0456 30 1.5Number of potential buyers per seller 6.621 3.529 10 2Number of potential sellers per buyer 1.952 0.9362 3 1Diameter of sample wells (ft) 0.67 0 0.67 0.67Depth of sample wells (ft) 258.448 118.767 450 135Horsepower of installed pump 13.973 5.772 25 5Fixed cash payment per hour of water pumped (rupees) 18.683 3.959 25 10

Source: Survey data.

plots. Modern pumping technology, on the other hand, has a built-in indivisibility and has thecapacity to pump water at considerably higher rates per unit of time than that required by even therelatively larger sized farms. Under such circumstances, an interesting institutional innovation inrecent years has been the evolution of various kinds of informal agreements amongst well-owningfarmers 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 groundwatercontracts in Sabarkantha district, in the state of Gujarat in western India, for the agricultural year1993–1994. 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 orderto focus the analysis on the main economic determinants of contract choice and to be able to drawmeaningful comparative inferences, we surveyed two villages from within the same agroclimaticregion. The two villages chosen were Ambavada (village A) and Boriya (village B). Village Bhas been part of ICRISAT’s village level studies.6

Table 1 shows some summary statistics pertaining to these villages. Both villages are part ofthe rocky semi-arid region of India. The average rainfall is around 760 mm of which 90 percentis received during the southwest monsoon months of June–September. One can distinguish threeseasons in the agricultural calendar in this region. The first is the Kharif (rainy) season, whichstretches 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 Novemberto March. The main Rabi crops are wheat and tobacco. The third is the summer season from Aprilto June, in which pearl millet is sometimes grown; otherwise the field is left fallow. Most of thisregion is characterized by sandy soils, with low moisture retention and requiring very frequentirrigation, 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 throughprivately owned borewells drilled to a depth of at least 100 ft below ground level. There were atotal of 24 effectively functioning borewells in village A and 30 in village B at the time of thesurvey.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 1980–1981 to 1984–1985 and then again in1989–1990, on a sample of 40 households on various socio-economic variables of the farming system. The existence ofthis vast database and the experience of ICRISAT’s village investigators who have stayed for many years in this villagestrongly influenced our choice of this sample village. A summary description of the various agro-economic features ofvillage 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.


from 5 to 25 (see Table 1). There is a fixed annual charge for electricity, which depends on thehorsepower of installed pump but is not dependent on the actual usage of electricity. Electricitysupply is highly erratic in this region, both in terms of when electricity is available and the voltageof supply. Sharp fluctuations in the voltage often lead to pump failures. In a survey of cultivatinghouseholds in village B, Pender and Asokan (1993) found that financial constraints are cited mostoften as the reason for not investing in wells. The second most common reason is not havingenough land.8 Very often these two factors are correlated since land is the main collateral againstwhich credit is offered in rural credit markets. Thus, it is mostly the small and marginal farmerswho 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 watersellers and the other by water buyers. The selection of buyers and sellers in the sample was donein the following way. First, a census of the well owning households was conducted which founda total of 54 such households in the two villages. All of these households reported selling at leastsome part of the water pumped out of their wells every year. From this census, a sample of 30households who owned wells in different locations within the two villages was selected in the firststage of sampling. Then, in the second stage of sampling, we selected a sample of 40 householdswho 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 andalso provided a natural consistency check by being able to match the responses of both parties tothe transaction. Data was collected on all the groundwater contracts agreed upon between this setof buyers and sellers for the different seasons in the agricultural year 1993–1994. Information on100 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 isthe fixed payment contract wherein, before the season begins, the water seller promises to supplya certain specified amount of irrigation to the water buyer in exchange for a fixed cash paymentper hour of water pumped, to be paid at the end of the season. The contract is quite vague about thetiming of these irrigations. In Section 3, we will examine how the incompleteness of the contractin 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 inexchange for a certain specified proportion of the output to be paid at the end of the season. Insome cases, the seller also shares the cost of fertilizers and seeds with the water buyer. Note thatin both types of contracts, payment is made at the end of the season. Mixing of contracts in theform 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 wereobserved 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 rentadditional 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).

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Table 2Crop characteristics and contract type in sample villages

Crops

Maize Groundnut Paddy Millet (Kharif) Fennel Castor Wheat Tobacco Milletsummer

Average forall crops

Crop characteristicsMain growing season Kharif Kharif Kharif Kharif Kharif–Rabia Khari–Rabia Rabi Rabi SummerIrrigation elasticityb 0.01 0.0004 0.031 0.001 0.198 0.027 0.160 0.104 0.279 0.097Labor elasticityb 1.945 0.842 0.6995 1.759 1.104 1.626 0.235 1.345 1.315 1.1395Risk (1)b 2.198 41.018 71.606 10.024 43.2503 35.484 26.619 38.001 52.159 35.595Risk (2)b 6.605 0.369 1.049 5.582 1.628 0.545 0.298 0.81 0.073 1.883

Contract type: cropsharing contracts as percent of total for each cropVillage Ac 16.67 (0.447) 14.29 (0.378) 50 (0.577) n.a.d 71.43 (0.488) 12.5 (0.353) 83.3 (0.408) 80 (0.548) 100 (0)Village Bc 0 (0) 33.33 (0.577) 33.33 (0.516) 0 (0) 50 (0.548) 12.5 (0.353) 88.8 (0.333) 50 (0.707) 100 (0)

Total number of contractsunder crop

10 10 10 6 12 16 15 7 14

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.


Table 3Results of a linear regression model on determination of contractual terms

Independent variables Parameter estimate (S.E.)

Intercept 2.1445 (3.2701)Depth of well 0.0203 (0.0120)Horsepower of installed pump 0.4932** (0.1356)Village dummy 6.0438** (2.0506)

R2 0.6461Adjusted R2 0.6167Number 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 duringthe 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 almostalways 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 isthe only crop grown during the summer season, and it is always associated with a crop-sharingcontract in both villages.

An important point to bear in mind when examining groundwater transactions is the fragmentednature of this market. Depending on the topography, soil conditions and technology of transportingwater, there is a limited area around the well over which it is economically feasible to transportwater. Each water seller was observed to have, on an average, around six to seven potentialcustomers (as shown in Table 1). The water buyers also, in general, do not have much choiceregarding the sellers from whom they can buy water. Around 50 percent of water buyer respondentsin 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 significantintra-village variation in the fixed payment and crop share parameter. As also noted in several otherstudies 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 parameterare presented in Table 1. Most of the observed variation in this parameter is explained by well-specific 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 thehorsepower of the pump and the depth of the well are important determinants of the flow of waterin a given unit of time. Once these well-specific factors are controlled for, there is very littleresidual 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 allshare contracts involving wheat, the cost of seeds and fertilizers was observed to be shared in thesame proportion as output. In case of other crops, there was no systematic pattern with sometimesno 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 Shahfor India.


Table 4Variation of crop shares across the sample villages

Crop share Percentage of cases when observed

Village A Village B

One-third share to water sellerNo input sharing 0 29With input sharing 0 13

Half share to water sellerNo input sharing 23 7With input sharing 77 51

Source: Survey data.

Default rates on the payment for water under both types of contracts was observed to be verylow (there were two reported cases under fixed payment contracts and none under crop sharecontracts). The threat of not getting water in the next season if previous payments had not beenmade 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 observedin the sample villages, namely, fixed payment and cropsharing contracts. Several models havebeen formulated in the land tenancy literature to explain the coexistence of alternative contractualforms.12 In this paper, we will focus on two specific classes of models from this literature thatseem to be most relevant for the case of groundwater contracts.13

3.1. 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 butplaces the entire production risk on him. This tradeoff between insurance provision and incentiveprovision determines the optimal contract (Stiglitz, 1974; Holmstrom and Milgrom, 1987; Otsukaet al., 1992). In terms of insurance provision, it follows from models of this kind that contractchoice would differ across (a) households depending on their ability to bear risks and (b) acrosscrops depending on their riskiness. In particular, for the case of groundwater contracts, this theorywould suggest that for any given crop, the more risk averse is the water buyer (seller) the morelikely it is that a cropsharing (fixed payment) contract would be chosen. Similarly given any twoparties to the contract, a cropsharing (fixed payment) contract is more likely to be chosen forcrops, which are perceived to be more (less) risky.

Given these risk factors, contract choice is also likely to differ across water sellers depending ontheir 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. Thisassumption 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.


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 alternativewhen his ability to monitor the buyer is better. Furthermore, given his ability to monitor, he willbe less likely to choose the cropsharing alternative when the incentive for the buyer to shirk ishigher.

3.2. Double-sided incentive (DSI) model

The insurance-incentive tradeoff model discussed earlier assumes moral hazard only on thepart of the agent. Formalizing some of the ideas in Reid (1976), Eswaran and Kotwal developa 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 fromrisk sharing considerations and focusing instead on both parties’ need for incentives given thecosts of monitoring and enforcement.14 In Eswaran and Kotwal’s model, the incentive problemarises 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 relativeadvantage in the supply of managerial labor while the agent (tenant) has a relative advantage inthe supply of supervisory labor. Different contracts are chosen depending on the incentives thatthese provide to each of the parties.

In the context of groundwater transactions, it can similarly be argued that incentive problemsmay arise with regard to inputs provided by both the water buyer and the water seller. Incentiveproblem in the provision of labor by the buyer has already been discussed. Let us now look athow 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 yieldsare highly sensitive not only to the amount of irrigation, but more importantly, to the timing of thevarious irrigations. This is what we shall refer to as the quality dimension in irrigation supply todistinguish it from the quantity dimension, which is a volumetric measure of the amount of watersupplied. Timeliness is often defined in the irrigation literature as the correspondence of waterdeliveries to crop needs. Hukkeri and Pandey (1977) in their extensive research on this subjectreport that the most practical criterion commonly adopted by farmers for scheduling of irrigationsis one based on the physiological growth stages critical in the demand for water. Some stagesduring 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 shortfallin water deliveries results in a significant loss in the yield. Crops vary in their sensitivity to thetimeliness of irrigation supply. In case of some crops, water stress in certain stages of growth canbe compensated by more water in other stages, while in case of other crops it cannot. For theselatter set of crops, proper timing of irrigations is very critical.15

Our interviews with farmers suggested that they perceive the timeliness issue in irrigationsupply 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 andfocus 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 perfor-

mance of alternative irrigation sources and find crop yields under bureaucratically or community managed systems to besignificantly lower than that under private wells, see Shah for a survey. Meinzen-Dick (1995) estimated a production func-tion for paddy and found that incorporating measures of timeliness explains much more of the variability in agriculturalproduction than simple quantitative measures of irrigation supply over a season.


tion schemes are associated with poor agricultural productivity. However, interestingly, we foundthat the contracts agreed upon between the buyers and sellers are quite vague with respect tothe issue of timeliness of irrigation supply. Thus, for example, contracting parties may agree onsome broad stipulation, such as the requirement that irrigation has to be given once every 10–15days. However, the contract is largely silent with respect to what happens if, for instance, thereis unexpected event, such as pump failure or power outage, excessive overdraft from neighbor-ing wells, or a drought. Optimal timing is contingent upon a host of factors that are revealedgradually, and it is prohibitively costly to specify a complete contract regarding timing of waterdeliveries.

One may argue that real world contracts are rarely complete in the sense of specifying appro-priate actions to be taken under every possible contingency. This is particularly true of agriculturalcontracts that tend to be quite informal. However, as opposed to other agricultural contracts, oneimportant difference in case of groundwater contracts is that these are a relatively new institutionalinnovation.16 Thus farmers are much lower down on their learning curves. Most theoretical mod-els of contract choice begin by assuming complete contracts and thus ignore the role of learning bydoing in contract design and implementation. Very often, a shared history of contract enforcementprovides informal guidelines or codes of behavior that fill up some of the missing provisions. Inour field study, we observed that social norms play an important role in specifying some broadstipulations on “fairness” in irrigation supply, such as requiring water sellers to provide all theircustomers 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 allaspects 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 contractof prioritizing the timing of irrigation supply between his own field and the fields of differentbuyers.18 In such a situation, a cropsharing contract gives better incentives than a fixed paymentcontract to the seller to provide timely irrigations. This is because the seller gets a share of theoutput under a cropsharing contract while under a fixed payment contract he gets a pre-specifiedfixed amount, as long as he adheres to the broad specifications of the contract. The extent to whichthe buyer is affected by these actions of the seller depends on the sensitivity of the crop grown tothe fineness in detail about the timing of irrigations.

There is, therefore, a double-sided incentive problem here, where the need for giving properincentives 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 mid1980s in this largely semi-arid region. Information on aquifer characteristics and water requirements of different crops isstill 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 regionwhere the groundwater aquifer is highly discontinuous. Under such a scenario it is reasonable to assume that the sellerhas private information about the recharge rate of his well. The presence of private information makes renegotiation ofcontracts very costly (Al-Najjar, 1995). Moreover, once the ex post state is revealed, production decisions must be maderapidly, leaving insufficient time to agree upon a new contract. Disputes over the proper division of the ex post surplusmight 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 supposedto get water by turns and any shortages are equally shared. The buyers, however, reported several cases of discriminationin which buyers with larger land endowments or those having the option of buying from another seller had been favored.


payment contract. While a cropsharing contract provides better incentives to the seller to providetimely irrigations, it provides fewer incentives than a fixed payment contract to the buyer. Along-term relationship between the buyer and the seller may reduce the severity of these incentiveproblems, but may not completely eliminate them. The testable implication that follows from thisdouble-sided incentive problem is the following. A cropsharing (fixed payment) contract is morelikely 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 problemin the provision of different inputs and the associated measurement issues.

To summarize, the insurance-incentive tradeoff model explains contract choice as a balancebetween risk sharing and a one-sided incentive problem while the double-sided incentive modelabstracts away from risk sharing considerations and explains contract choice as a balance betweenincentive provision along multiple margins. While these different theories have emphasized dif-ferent factors, it is plausible that in many situations these factors supplement each other ratherthan being exclusive. Building upon the model of Eswaran and Kotwal, Agrawal (1999) developsa “generalized double-sided moral hazard model” in which the assumption of risk neutrality ofthe agents is dropped, thus allowing for risk sharing considerations as well as shirking by bothagents. In Agrawal’s model, the optimal contract maximizes the output net of the risk-bearingand agency costs. In the next section, we develop a general reduced form empirical model thatallows us to test for the significance of these different factors in the context of groundwatercontracts.

4. Empirical model

It is instructive to start with a simple contract choice equation of the following nature:

Y = βSXS + βBXB + βCXC + ε (1)

where Y is a binary contract choice variable (which takes the value one if a share contract isobserved and zero if a fixed payment contract is observed). XS, XB and XC are the fundamentalcharacteristics of the seller, buyer and the crop, respectively, which according to theory determinecontract choice. βS, βB and βC are the corresponding vectors of unknown coefficients. ε is assumedto be the random error term that is distributed independently and identically with mean zero andvariance σ2. If all the relevant characteristics of buyer, seller and the crop (XS, XB and XC) arefully observed and are uncorrelated with ε, then a multinomial logit estimation of (1) would giveconsistent estimates. The estimated coefficients could then be used to test hypotheses derivedfrom the above-discussed theories.

4.1. Endogenous matching and crop choice

An important problem with econometric estimation of (1) is that some or all of the elements ofXS and XB may be only partially observed or may not be observed at all. Some examples includerisk attitudes of buyer and seller and their monitoring abilities. It is common in empirical work oncontractual choice to use suitable proxies for such unobserved or partially observed characteristics.Following Ackerberg and Botticini, the underlying proxy equations can be written as

XS = αSPS + ηS (2)

XB = αBPB + ηB (3)


where PS and PB are observed proxy variables for characteristics of the seller and buyer, respec-tively, and αS and αB are the corresponding proxy coefficients. ηS and ηB are the proxy errorsthat are mean independent of PS and PB.19

Using the proxy Eqs. (2) and (3), the contract Eq. (1) can be rewritten as

Y = β′SPS + β′BPB + βCXC + (βSηS + βBηB + ε) (4)

where β′S = αSβS and β′B = αBβB. Estimation of Eq. (4) by a multinomial logit model is likelyto lead to biased estimates because it is unlikely that buyers and sellers are matched completelyrandomly. Since the characteristics of a buyer matter to the seller, it is likely that he will lookfor an appropriate buyer and vice versa. For instance, sellers who have poor monitoring abilitiesmay 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 theirrisks at low cost. One of the questions in the survey asked the sellers to rank the most desir-able 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 outcomesimplying that buyer characteristics (XB) and seller characteristics (XS) are likely to be correlated.This implies that since ηB is a part of XB, it is also likely to be correlated with XS and hencealso with the seller proxy variables PS. Similarly, ηS is likely to be correlated with PB. Thissuggests that using a multinomial logit model to estimate (4) would lead to biased estimatesof β′S and β′B.

In addition, if it is true that crop choice is endogenous to contract choice then some of the omittedvariables relating to buyer and seller characteristics may also be correlated with XC, leading tobiased estimates of βC. For instance, it is plausible that water buyers who are relatively more riskaverse (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. Inthe rest of this subsection, we discuss how important these problems are likely to be in our contextand offer some plausible solutions.

Most empirical studies of contractual choice have not paid sufficient attention to the problemof biased estimates due to endogenous matching. An important exception is the study, citedearlier, by Ackerberg and Botticini (A–B) on land tenure contracts. In such contracts, each partyhas a reasonably large set of choices regarding its potential partner, so the matching of partiesis likely to be a purposive one. Thus, it is not entirely surprising that A–B found the problemof omitted variable bias to be quite serious in their study. In contrast to this, in the case ofgroundwater transactions, the choice set of potential partners is quite limited. This is becauseonce the well is dug, there is a restricted area over which it is economically feasible to transportwater.20 As was pointed out earlier, around 50 percent of water buyer respondents in our samplereported that there was only one well in their vicinity. The sellers, on the other hand, seem tohave somewhat greater choice. Each water seller in our sample was observed to have on anaverage around seven potential customers in his command area. In a typical year, around fourcustomers 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) morethan 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.


seasons.21 Because of this rather limited choice set of partners, we expect the problem ofendogenous matching to be less serious for groundwater transactions. However, it would bepresumptuous of us to assume that buyer and seller characteristics are uncorrelated, and so weturn 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 aroundfinding a suitable set of instrument variables that affect the matching equation but do not affect thecontract choice equation or the proxy equation. This is generally quite tricky. A–B argue that if theobservations come from different geographical regions (representing isolated markets) with dif-ferent population distributions of tenants or landlords, then the matching equation is likely to differacross these regions. One can then use region dummies and region dummies interacted with tenantcharacteristics as instruments. As alluded above, for identification it is important that the instru-ments that are chosen affect the matching equation but do not affect the contract choice equationor the proxy equation. A–B argue that the region dummies and their interaction with tenant char-acteristics affects who gets matched with whom, but has only second order effects on the contractchoice and the proxy equations. In our view, it is very difficult to justify the exclusion of regiondummies from the contract choice equation. Thus, for instance, the region of residence affects thereservation utility of an agent, which is likely to affect not only who is matched with whom butalso 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 asempirical models assume crop choice to be exogenous. Previous agronomic studies in our studyarea have found that proper sequencing of crops across seasons, in accordance with crop rotationrequirements and the particular nature of the soil, is a very important determinant of crop choicein this region with low soil fertility (Singh and Singh). It has also been observed that farmerstend 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 beinggrown under groundwater contracts depend not only on what the buyer would like to grow butalso on whether the seller finds it attractive to enter into a contract for that crop, given his otheralternatives. In our data, we have information only on the crops that were actually observed to begrown under existing contracts. Thus, we have a truncated sample, and identification here requiresus to make a convincing case for a separation between the truncation variables and the variablesin 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 useof the pseudo-panel nature of our data set and estimate a fixed effect model. Almost all of thesample buyers and sellers in our data set entered into two or more separate contracts for differentcrops either with the same or different partners. Thus to control for the unobserved characteristicsof the buyer and the seller, we can treat each unique “buyer–seller” configuration as a groupand 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 allthe potential buyers get irrigation in at least some seasons. This may be because sellers like to have a large clientele anddo not wish to turn down requests for an essential resource like water. One can also speculate that by providing someirrigation to their neighbors, existing well owners try to discourage their neighbors from digging their own wells in thefuture.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 wereobserved to have two or more contracts.


Table 5aDeterminants 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 (partyfixed effect)

Model III (buyerfixed effect)

Model IV (sellerfixed effect)

Intercept 0.793 (1.587)Buyer’s land −0.021 (0.091) 0.143 (0.15)Buyer’s occupationa 0.532 (0.609) 0.216 (1.1)Seller’s land −0.036 (0.044) −0.066 (0.076)Seller’s occupationa 0.777 (0.633) 1.532 (1.46)Riskiness of crop −0.006 (0.018) −0.0036 (0.024) −0.004 (0.023) −0.007 (0.019)Irrigation 20.951*** (4.6) 15.95*** (5.46) 19.078*** (5.819) 16.423*** (4.129)Labor −2.234*** (0.763) −0.801 (0.925) −1.091 (0.969) −1.99** (0.941)Village dummy −0.192 (0.613)Log likelihood function −37.259 −10.655 −12.293 −18.833Number of groups 98 43 33 21

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). Thisformulation helps us to minimize the bias arising due to unobserved characteristics of the buyersand the sellers. However, it has an important limitation. The effects of the observed characteristicsof the buyer and the seller (e.g. their occupation or their land endowments), that do not vary acrosscontracts, are not identified in this model.

Table 5bDeterminants 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 (partyfixed effect)

Model III (buyerfixed effect)

Model IV (sellerfixed effect)

Intercept 0.785 (1.337)Buyer’s land −0.02 (0.09) 0.136 (0.156)Buyer’s occupationa 0.571 (0.617) 0.365 (1.108)Seller’s land −0.041 (0.047) −0.071 (0.096)Seller’s occupationa 0.667 (0.63) 1.53 (1.691)Riskiness of crop −1.543* (0.892) −2.325 (1.683) −2.31 (1.696) −1.401 (0.982)Irrigation 24.436*** (6.504) 23.122** (11.108) 26.682** (11.278) 19.324*** (6.039)Labor −1.472* (0.814) 0.054 (1.197) 0.14 (1.277) −1.365 (0.959)Village dummy −0.129 (0.638)Log likelihood function −34.613 −7.977 −9.469 −16.261Number of groups 98 43 33 21

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.


To gain further insights into the relative importance of the buyer and seller fixed effects, wetried two other models. In model III in Tables 5a and 5b, we take each unique “buyer” as agroup and estimate the within-buyer estimator. Since each buyer may have multiple contractswith either the same or different sellers, the estimates obtained through this model are differentfrom those obtained by looking at each unique “buyer–seller” group. In model IV, we follow asimilar procedure taking each unique “seller” as a group. A comparison of model III with model I(pooled logit model) would give us some idea of the bias arising due to buyer unobserved effectswhile a comparison of model IV with model I would give us some idea of the bias arising dueto seller unobserved effects. Next, we turn to a discussion of the plausible set of explanatoryvariables to include in these models, given the above theories.

4.2. Measurement of risk and incentive problems

The risk sharing motivation for cropsharing has been the most popular argument in thetheoretical literature, but ironically it is also the most difficult to test empirically. One of theproblems with testing its validity is that risk preferences are very difficult to measure. Binswangerand Sillers (1983) in their experimental work in India found farmers to have fairly homoge-neous risk preferences. Following upon this work, Eswaran and Kotwal (1985) showed that ifagents have similar risk preferences but the capital market is imperfect, then the agent withbetter access to credit will behave as if he is less risk averse. Access to credit in the ruralcredit market is largely determined by the amount of land that can be offered as collateral.This means that farmers with smaller land endowments would behave as if they are more riskaverse than farmers with larger land endowments. As shown earlier, the average land endow-ment of buyers is much lower than that of sellers, so they are expected to be more risk aversethan the sellers. This leads to the following testable hypothesis. The smaller (larger) is the landendowment of the buyer (seller), the more likely it is that a cropsharing contract would bechosen.

Given the two parties to the contract, contract choice may also differ across crops depend-ing on their riskiness. Quantifying the risks associated with different crops is a difficult task.The most widely used method in the literature has been to use some measure of the observedvariance in output. The latter, in turn, is a function of contract choice, and this introduces asimultaneity problem. Note that it is the exogenous part that is the parameter of interest inprincipal-agent models. Canjels (1996) in his study of sharecropping in U.S. agriculture usedparametrically specified parsimonious models from the agronomy literature to estimate the effectof various weather variables on yields. These models typically break up the growing season intodifferent stages of plant growth and allow for interaction effects between precipitation and tem-perature (and other climatic variables when available). For our study area, we are not aware ofany such models that allow a parsimonious representation of various weather related variables.Moreover, time-series data is not available for any of the pertinent weather variables, apart fromrainfall.

Given these limitations, one simple alternative would be to look at the sensitivity of yieldsof different crops to rainfall variation after controlling for individual and time fixed effects.Accordingly, we estimate the following model for each crop in our sample using data fromICRISAT’s village level studies for this agroclimatic region for the years 1980–1991 to 1984–1985and 1989–1990:

Qit = βRit + λi + λt + uit (5)


where subscript i indexes farm households and t indexes the year. Qit is the yield per acre, Rit therainfall, λi and λt are, respectively, the household and time fixed effects and uit is the random errorterm.23 Our proposed measure of risk here (RISK1) is the standard deviation of bRit, where b isthe estimate of β. In Table 2, we report these risk estimates for the different crops. In this table,we also report the likelihood ratio (LR) test statistic (and the associated probability value) for theunrestricted model estimated in (5), against a restricted version with only the time and individualfixed effects. The LR statistic basically tests for fit in the regression once the fixed effects havebeen controlled for. As can be seen from Table 2, the fit is significant for some of the crops, suchas rainy season millet, summer millet, castor and groundnut. Interestingly, all these crops (exceptsummer millet) are sown during the rainy season, although for castor the growing season extendsinto the Rabi season as well.

One can argue that the measure for risk proposed above incorporates only one dimensionof risk, namely that arising from rainfall variation. There may be other sources of exogenousrisk, such as those related to temperature variation or pests that also affect crop yields. In mosttheoretical models, including Stiglitz’s insurance-incentive tradeoff model, a measure of risk isderived from the specification of a stochastic production function of the following kind:

Q = F (X, α)ε (6)

where Q is the crop output, X the vector of inputs, α a vector of parameters and ε is a random errorterm with mean equal to one and variance given as σ2. Given this specification of the technology,σ2 is generally used as the measure of riskiness.24

One can derive estimates of σ2 by estimating the production function in (6) for each cropusing ICRISAT data on inputs and outputs for farms in this agroclimatic region. However, directestimators of production functions may be inconsistent because inputs may be endogenous. Analternative technique would be to estimate the dual specification in which technology is representedin the form of a profit function whose derivatives are the input demand functions and the outputsupply function, all expressed as functions of prices. However, an important problem here is thatthere is very little variation in prices faced by farmers in our data set.

Another option is to use the within primal estimator since we have panel data available in thiscase. Under the assumption that the unobserved heterogeneity takes the form of additive fixedeffects, the within primal estimator is consistent.25 Accordingly, we estimated a Cobb–Douglasspecification of the production function in (6) using the fixed effects model.26 The vector X in ourestimation included the following inputs: land, labor, irrigation, fertilizers and bullock hours. Themeasure of risk derived from this estimation is referred to as RISK2. Results of these productionfunction estimations are reported in Table 6.

Next let us turn to the measurement of the incentive problem on the buyer’s and seller’s sides.One can envision two main components in the measurement of the incentive problem here. The

23 For crops grown during the rainy season, the rainfall variable includes rainfall recorded during the rainy season. Forcrops grown in other seasons, the rainfall variable includes the rainfall recorded during the preceding rainy season andthe growing season of the crop.24 It is well known that variance has limitations as a measure of risk. However, Meyer (1987) shows that for the class of

models where the outcome variable is specified as a positive linear function of the random parameter (as in (6)), the twomoment decision models are consistent with expected utility maximization.25 Mundlak (1996) has shown that, in general, the within primal estimator is superior to the dual estimator.26 Some other specifications of the production function, such as the translog specification were also tried. The results

did not differ qualitatively from the Cobb–Douglas (C–D) case.

R.M

.Aggarw

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(2007)475–496

491

Table 6Production function estimates for different crops

Crops

Millet (Kharif) Maize Paddy Fennel Castor Millet (summer) Groundnut Wheat

Land 2.548** (0.757) 4.57 (2.44) 0.43 (0.428) 0.108 (0.785) 0.413* (0.202) −0.351 (0.201) 1.173 (1.18) 0.39 (0.218)Labor 1.759** (0.607) 1.945 (1.583) 0.6995* (0.348) 1.104 (1.057) 1.626** (0.228) 1.315* (0.246) 0.842 (0.715) 0.235 (0.241)Fertilizer 0.36** (0.087) 0.018 (0.181) 0.065* (0.029) −0.019 (0.389) 0.066** (0.015) 0.148** (0.087) 0.001 (0.001) 0.139** (0.037)Irrigation 0.001 (0.003) 0.01 (0.232) 0.031 (0.034) 0.198 (0.437) 0.027 (0.02) 0.279 (0.249) 0.0004 (0.0005) 0.160** (0.044)Bullock hours 0.183 (0.391) −1.845 (2.408) 0.026 (0.061) 0.062 (0.915) −0.382 (0.23) −0.379 (0.114) −1.061 (1.512) −0.045 (0.061)

Model F 11.01** 2.13 182.35** 3.831* 31.05** 38.991** 1.81 103.13**

No. of observations 119 47 49 43 85 43 49 149

Figures in parenthesis are standard errors.* Significant at 5 percent probability level.

** Significant at 1 percent.


first is some measure of the importance of the input provided by each party in the productionprocess of each crop, and the second is the ability of the each party to monitor the provisionof this input. To measure the second component, we have used data on the principal occupationof the buyer and the seller. The underlying rationale here is that the ability of each party tomonitor the other is likely to be better if agriculture is their primary occupation. To measure thefirst component, namely the importance of different inputs in the production process of differentcrops, we used the estimated coefficients on the labor and irrigation input in (6). As a measureof the labor input in (6), we used ICRISAT data on aggregate adult family and hired labor hoursused in the production of each crop. The advantage of using ICRISAT’s panel data based on astratified sample, different from the one we used in our survey, is that it gives us a measure ofinput elasticity that is determined more closely by technological considerations and can be treatedas an exogenously given characteristic of the crop.

Similarly, to measure the irrigation input, one possibility is to use data on the total num-ber of hours for which irrigation was supplied. However, this is a purely quantitative measureof the irrigation input and may not adequately reflect the issue of timeliness in irrigation sup-ply. As argued earlier, the issue of timeliness in irrigation supply is very critical in explainingthe seller’s incentive problem. The sensitivity of different crops to the timeliness of irrigationsupply is very difficult to estimate empirically. The most extensive discussion on timeliness isfound in studies that compare the irrigation performance of alternative irrigation systems (seeRao, 1993 for a survey). Here, the standard procedure is to compare the impact of a unit of irri-gation provided by different irrigation systems on the productivity of a particular crop aftercontrolling for all other factors, such as differences in soil fertility and other input applica-tions. The timeliness dimension emerges as a residual factor here. There are very few studiesthat have formulated an explicit measure of timeliness. One such study is by Meinzen-Dickwho divides the growing season for paddy into 10 day periods (decades) and formulates indicesfor timeliness that relate water deliveries to water requirements for each of these decades. Theindices she proposes are useful for paddy because depth of water application is relatively easyto measure for paddy with standing water, but they have limited applicability for dry-footedcrops.

For these other crops, it is much harder to find a single measure of timeliness. Irrigationspecialists suggest that to measure the sensitivity of different crops to moisture stress, the followingfactors should be included: soil moisture holding capacity, rooting depth, previous history ofwetting and drying of the soil, and time since the last irrigation. However, given that data maynot be available on all these factors, there is a simpler solution if our interest lies in the relativeranking of different crops rather than an absolute measure of each crop’s sensitivity to moisturestress. In this case, it would be pertinent to look at the relative sensitivity of different cropsto the number of irrigations applied during the growing season. This measure would give arough indication of how long each crop could go, under the given set of conditions, betweenirrigations.

The merit of this measure can be illustrated by comparing the irrigation requirement of paddywith that of wheat. Both crops are heavily irrigated crops. Paddy is grown during the Kharif (rainy)season while wheat is grown during the Rabi (post-rainy) season. In the case of wheat, frequentirrigations need to be given at regular intervals, generally 8–10 irrigations are given every 10–15days. In comparison to this, paddy requires fewer irrigations but in each irrigation, the field needsto be flooded. Thus, although both crops are heavily irrigated crops, the incompleteness of thecontract in defining the timing of irrigations is likely to be more critical for wheat than for paddy.Based on the above arguments, we use ICRISAT data on the number of irrigations given to each


crop as a measure of the irrigation input. The estimated coefficient on this irrigation input is thenused as a measure of the incentive problem in the supply of irrigation.27

5. Results

Tables 5a and 5b present the results from four different specifications of the binary logit modelof contractual choice. To test for the significance of buyer fixed effects in model III, we conducteda simple Hausman specification test of the following kind. Under the null hypothesis of fixedeffects, the pooled logit estimator is inconsistent while Chamberlain’s estimator (model III) isconsistent and efficient. However, if the null is incorrect, then both estimators are consistent andChamberlain’s estimator is inefficient. Using this test, we found that the null hypothesis of buyerfixed effects could not be rejected at the 1 percent level. However, a similar procedure to test forseller fixed effects in model IV rejected the null hypothesis of seller fixed effects.

As is evident from Tables 5a and 5b, contract choice is not found to be significantly relatedto either the risk-bearing abilities of the two parties or to the two measures of crop riskiness.This result is robust across the different specifications we tried. Some other empirical studies thathave isolated a similar result are Rao (1971) and Allen and Lueck (1995) for land tenancy, andLaffontaine for the case of franchising in U.S. It is worth noting that the importance of the risksharing motivation in any form of output sharing contract is likely to depend on the availabilityof other options to stabilize consumption over time. Diversification of holdings, intertemporalholding of grains, purchase and sales of assets, borrowing and lending, and gifts and transfers aresome other examples of risk sharing institutions that have been found to be quite important in suchsemi-arid environments (Townsend, 1994). It is also important to keep in mind that larger riskassociated with a particular crop could have several different implications besides the need forinsurance provision. For instance, a larger risk in terms of increased variability in output could beinterpreted as exacerbating the observability problem, thus leading to the choice of fixed paymentcontracts. Similarly, as argued by Rao (1971), greater uncertainty associated with a particularcrop could lead to a greater role for entrepreneurship, thus making the issue of incentives for thebuyer even more important.

Our measure of the incentive problem in irrigation supply is highly significant across all thespecifications. This is also evident in Table 2, which shows that crops like wheat, tobacco andsummer millet that have a high irrigation elasticity tend to be under cropsharing contracts whilecrops like maize, groundnut and millet that have a low irrigation elasticity are largely found underfixed payment contracts. Interestingly enough, Meinzen-Dick and Sullins in their study on watermarkets in Pakistan also observed the same empirical regularity. They found cropsharing contractsto be common for crops, such as tomatoes and onions, which are very sensitive to moisture stressat critical periods.

The effect of labor elasticity of the crop, which we use as a measure of the incentive problemon the buyer’s side, is found to be negative but significant in only some specifications. It issignificant in model I with pooled data, and in model IV with seller fixed effects. However,

27 This measure needs to be interpreted with caution. Note that the number of irrigations to be given during the growingseason can be specified in the contract, so the sensitivity of different crops to the number of irrigations is not a directmeasure of the incentive problem. The severity of the incentive problem here arises from the sensitivity of output to anymistiming in irrigation supply due to the incompleteness of the contract. This elasticity is difficult to measure directlybut is likely to be highly correlated with the measure we use. This is well illustrated by the example on paddy and wheatgiven above.


interestingly enough, once we control for buyer fixed effects in specifications II and III, the effectis no longer significant. This gives support to our earlier conjecture that sellers may purposivelyselect buyers who are known to be hardworking and trustworthy, thus reducing the severity ofthe incentive problem on the buyer’s side. Finally, the dummies for buyer’s and seller’s primaryoccupation are not found to be significant determinants of contract choice. This may be becausethese are somewhat crude measures of the incentive problem. Overall these results provide somesupport to a model based on a double-sided incentive problem where the need for giving properincentives to both the buyer and the seller determines contract choice.

6. Summary and conclusions

In this paper, we have analyzed the structure of groundwater contracts and tested for alternativetheories on the rationale for contract choice. Both fixed payment and cropsharing contracts werefound to coexist in the sample villages. To explain this coexistence of contract types, the insurance-incentive tradeoff model that emphasizes the tradeoffs between risk sharing and incentive provi-sion to the cultivator was compared with the double-sided incentive model that emphasizes therole of transaction costs in contract choice and the associated incentive problem on both sides.

The challenge in testing for these theories stems from the difficulty in finding appropriateempirical measures for theoretical constructs, such as riskiness of different crops, risk preferencesand the moral hazard problem. The commonly used procedure of using suitable proxies forpartially observed or unobserved explanatory variables may result in biased estimates due toendogenous matching. In our study, we discussed several alternative solutions to ameliorate theseproblems. A couple of different measures of riskiness of crops and the incentive problems werediscussed and estimated using panel data from ICRISAT’s VLS studies. To control for the omittedvariable bias we made use of the pseudo panel nature of our data set and estimated different fixedeffect models. Neither the riskiness of crops nor the risk-bearing abilities of the two parties wasfound to be significant in explaining the probability of share contracts. Interestingly, the irrigationelasticity of the crop (which we use a measure of the seller’s incentive problem) was found to behighly significant, and this result was found to be quite robust across the different specificationswe tried, including the pooled sample and different fixed effect models. On the other hand, thelabor elasticity of the crop was found to be significant in only some of the specifications. To theextent that these labor and irrigation elasticities adequately capture the actual incentive problemfaced by buyer and seller, respectively, these results provide some support to a model based ona double-sided incentive problem where the need for giving proper incentives to both the buyerand the seller determines contract choice.

It is also worth noting that we observed some aspects of the contract structure to be at variancewith both the theoretical models reviewed here. Thus, for instance, both models predict fairlycomplex incentive schemes that are in sharp contrast to the simple linear contracts observedin our sample villages, as also in many other empirical studies. We also observed very littlevariation in the fixed payment and share parameter, which is also at variance with the finely tunedrules predicted by these two theories. Wood and Palmer-Jones in their study on water markets inBangladesh found a similar pattern and suggest that pressures for conformity within the villagegenerally override plot-derived calculations based on economic and ecological criteria. Anotherpossibility suggested by Holmstrom and Milgrom is that the usual agency models are overlysimplistic and fail to account for the need to have schemes that perform well under a variety ofconditions (i.e. schemes that are more robust). They propose an agency model in which linearschemes are optimal because the agent is assumed to have a rather rich action space.


Most formal models of contracting also begin by assuming that both parties can write (orverbally agree on) contracts that provide a complete description of the rights and obligations ofeach party under every possible contingency. Most real world contracts, on the other hand, arenot only very simple but also quite coarse. In this paper, we have shown how the incompletenessof the contract in specifying the timing of irrigations makes the seller’s incentive problem verycritical. At the policy level, one may conjecture that this incentive problem also helps to explainwhy there has been an exponential growth in private well investment (in spite of the lumpinessof investment and high risks) while pubic investment (as also group/cooperative investment inwells) has stagnated.

To the extent that the incompleteness of groundwater contracts arises from incomplete knowl-edge regarding aquifer characteristics, groundwater dynamics and electricity supply conditions, itis expected that as farmers learn by doing, it may become less costly to agree upon more completecontracts. Accumulated knowledge over time may also lead to evolution of norms of behavior thatgovern what happens under a wider range of contingencies. Anecdotal evidence from the villagesthat we surveyed in 1993–1994 suggests that share contracts are now being slowly replaced bymore fixed payment contracts. A recent case study by Dubash of two villages in western Indiaalso found that share contracts in groundwater are giving way to fixed payment contracts overtime. Analyzing these historical trends in contract choice could provide further insights into thedeterminants of contract choice.

Acknowledgements

I would like to thank Erik Thorbecke, Robert Chambers, Suzi Kerr, Alain de Janvry, RamonLopez, Keijoro Otsuka, John Quiggin and an anonymous referee for their comments on an earlierversion of this paper. I am grateful to M. Asokan and Anil Patel for their help with the data collec-tion work. The Comparative Economic Development Program, Cornell University and ICRISATprovided financial assistance for the field research.

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