Journal of Economic Behavior & Organization
Vol. 63 (2007) 475–496
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 75275-0496, 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.
© 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 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
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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 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.
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.
2
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 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).
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R.M. Aggarwal / J. of Economic Behavior & Org. 63 (2007) 475–496
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)
5.071
11.859
6.621
1.952
0.67
258.448
13.973
18.683
3.552
7.0456
3.529
0.9362
0
118.767
5.772
3.959
12
30
10
3
0.67
450
25
25
1
1.5
2
1
0.67
135
5
10
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
1993–1994. 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 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 1980–1981 to 1984–1985 and then again in
1989–1990, 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.
R.M. Aggarwal / J. of Economic Behavior & Org. 63 (2007) 475–496
479
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 1993–1994. 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.
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).
9
480
Crops
Crop characteristics
Main growing season
Irrigation elasticityb
Labor elasticityb
Risk (1)b
Risk (2)b
Maize
Groundnut
Paddy
Millet (Kharif) Fennel
Kharif
0.01
1.945
2.198
6.605
Kharif
0.0004
0.842
41.018
0.369
Kharif
0.031
0.6995
71.606
1.049
Kharif
0.001
1.759
10.024
5.582
Contract type: cropsharing contracts as percent of total for each crop
16.67 (0.447) 14.29 (0.378) 50 (0.577)
n.a.d
Village Ac
0 (0)
33.33 (0.577) 33.33 (0.516) 0 (0)
Village Bc
Total number of contracts
under crop
10
10
10
6
Kharif–Rabia
0.198
1.104
43.2503
1.628
Castor
Wheat
Tobacco
Millet
summer
Average for
all crops
Khari–Rabia
0.027
1.626
35.484
0.545
Rabi
0.160
0.235
26.619
0.298
Rabi
0.104
1.345
38.001
0.81
Summer
0.279
1.315
52.159
0.073
0.097
1.1395
35.595
1.883
71.43 (0.488) 12.5 (0.353)
50 (0.548)
12.5 (0.353)
83.3 (0.408) 80 (0.548) 100 (0)
88.8 (0.333) 50 (0.707) 100 (0)
12
15
16
7
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.
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Table 2
Crop characteristics and contract type in sample villages
R.M. Aggarwal / J. of Economic Behavior & Org. 63 (2007) 475–496
481
Table 3
Results of a linear regression model on determination of contractual terms
Independent variables
Intercept
Depth of well
Horsepower of installed pump
Village dummy
R2
Adjusted R2
Number of observations
Parameter estimate (S.E.)
2.1445 (3.2701)
0.0203 (0.0120)
0.4932** (0.1356)
6.0438** (2.0506)
0.6461
0.6167
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.
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R.M. Aggarwal / J. of Economic Behavior & Org. 63 (2007) 475–496
Table 4
Variation of crop shares across the sample villages
Crop share
Percentage of cases when observed
Village A
One-third share to water seller
No input sharing
With input sharing
Half share to water seller
No input sharing
With input sharing
Village B
0
0
29
13
23
77
7
51
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.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 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.
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.
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483
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.
3.2. 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 irriga14 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.
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R.M. Aggarwal / J. of Economic Behavior & Org. 63 (2007) 475–496
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 10–15
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.
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485
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 XS + β B XB + β C XC + 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). XS , XB and XC are the fundamental
characteristics of the seller, buyer and the crop, respectively, which according to theory determine
contract choice. βS , βB and βC 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 (XS , XB and XC ) 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.
4.1. Endogenous matching and crop choice
An important problem with econometric estimation of (1) is that some or all of the elements of
XS and XB 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 = αS P S + η S
(2)
XB = αB P B + ηB
(3)
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where PS and PB are observed proxy variables for characteristics of the seller and buyer, respectively, and αS and αB are the corresponding proxy coefficients. ηS and ηB are the proxy errors
that 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 P S + β P B + βC XC + (βS ηS + βB ηB + ε)
S
B
(4)
where β S = αS βS and β B = αB βB . 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 (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 hence
also with the seller proxy variables PS . Similarly, ηS is likely to be correlated with PB . 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 XC , leading to
biased estimates of βC . 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.
R.M. Aggarwal / J. of Economic Behavior & Org. 63 (2007) 475–496
487
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.
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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)
Intercept
Buyer’s land
Buyer’s occupationa
Seller’s land
Seller’s occupationa
Riskiness of crop
Irrigation
Labor
Village dummy
Log likelihood function
Number of groups
0.793 (1.587)
−0.021 (0.091)
0.532 (0.609)
−0.036 (0.044)
0.777 (0.633)
−0.006 (0.018)
20.951*** (4.6)
−2.234*** (0.763)
−0.192 (0.613)
−37.259
98
Model II (party
fixed effect)
Model III (buyer
fixed effect)
Model IV (seller
fixed effect)
0.143 (0.15)
0.216 (1.1)
−0.066 (0.076)
1.532 (1.46)
−0.004 (0.023)
19.078*** (5.819)
−1.091 (0.969)
−0.0036 (0.024)
15.95*** (5.46)
−0.801 (0.925)
−10.655
43
−12.293
33
−0.007 (0.019)
16.423*** (4.129)
−1.99** (0.941)
−18.833
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). 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)
Intercept
Buyer’s land
Buyer’s occupationa
Seller’s land
Seller’s occupationa
Riskiness of crop
Irrigation
Labor
Village dummy
Log likelihood function
Number of groups
0.785 (1.337)
−0.02 (0.09)
0.571 (0.617)
−0.041 (0.047)
0.667 (0.63)
−1.543* (0.892)
24.436*** (6.504)
−1.472* (0.814)
−0.129 (0.638)
−34.613
98
Model II (party
fixed effect)
Model III (buyer
fixed effect)
Model IV (seller
fixed effect)
0.136 (0.156)
0.365 (1.108)
−2.325 (1.683)
23.122** (11.108)
0.054 (1.197)
−0.071 (0.096)
1.53 (1.691)
−2.31 (1.696)
26.682** (11.278)
0.14 (1.277)
−7.977
43
−9.469
33
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.
−1.401 (0.982)
19.324*** (6.039)
−1.365 (0.959)
−16.261
21
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489
To gain further insights into the relative importance of the buyer and seller fixed effects, we
tried two other models. In model III in Tables 5a and 5b, we take each unique “buyer” as a
group and estimate the within-buyer estimator. Since each buyer may have multiple contracts
with either the same or different sellers, the estimates obtained through this model are different
from those obtained by looking at each unique “buyer–seller” group. In model IV, we follow a
similar 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 effects
while a comparison of model IV with model I would give us some idea of the bias arising due
to seller unobserved effects. Next, we turn to a discussion of the plausible set of explanatory
variables 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 the
theoretical literature, but ironically it is also the most difficult to test empirically. One of the
problems with testing its validity is that risk preferences are very difficult to measure. Binswanger
and Sillers (1983) in their experimental work in India found farmers to have fairly homogeneous risk preferences. Following upon this work, Eswaran and Kotwal (1985) showed that if
agents have similar risk preferences but the capital market is imperfect, then the agent with
better access to credit will behave as if he is less risk averse. Access to credit in the rural
credit 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 risk
averse than farmers with larger land endowments. As shown earlier, the average land endowment of buyers is much lower than that of sellers, so they are expected to be more risk averse
than the sellers. This leads to the following testable hypothesis. The smaller (larger) is the land
endowment of the buyer (seller), the more likely it is that a cropsharing contract would be
chosen.
Given the two parties to the contract, contract choice may also differ across crops depending 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 observed
variance in output. The latter, in turn, is a function of contract choice, and this introduces a
simultaneity problem. Note that it is the exogenous part that is the parameter of interest in
principal-agent models. Canjels (1996) in his study of sharecropping in U.S. agriculture used
parametrically specified parsimonious models from the agronomy literature to estimate the effect
of various weather variables on yields. These models typically break up the growing season into
different stages of plant growth and allow for interaction effects between precipitation and temperature (and other climatic variables when available). For our study area, we are not aware of
any 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 from
rainfall.
Given these limitations, one simple alternative would be to look at the sensitivity of yields
of 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 from
ICRISAT’s village level studies for this agroclimatic region for the years 1980–1991 to 1984–1985
and 1989–1990:
Qit = βRit + λi + λt + uit
(5)
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where subscript i indexes farm households and t indexes the year. Qit is the yield per acre, Rit the
rainfall, λi and λt are, respectively, the household and time fixed effects and uit is the random error
term.23 Our proposed measure of risk here (RISK1) is the standard deviation of bRit , where b is
the 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 the
unrestricted model estimated in (5), against a restricted version with only the time and individual
fixed effects. The LR statistic basically tests for fit in the regression once the fixed effects have
been controlled for. As can be seen from Table 2, the fit is significant for some of the crops, such
as rainy season millet, summer millet, castor and groundnut. Interestingly, all these crops (except
summer millet) are sown during the rainy season, although for castor the growing season extends
into the Rabi season as well.
One can argue that the measure for risk proposed above incorporates only one dimension
of risk, namely that arising from rainfall variation. There may be other sources of exogenous
risk, such as those related to temperature variation or pests that also affect crop yields. In most
theoretical models, including Stiglitz’s insurance-incentive tradeoff model, a measure of risk is
derived 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 error
term with mean equal to one and variance given as σ 2 . Given this specification of the technology,
σ 2 is generally used as the measure of riskiness.24
One can derive estimates of σ 2 by estimating the production function in (6) for each crop
using ICRISAT data on inputs and outputs for farms in this agroclimatic region. However, direct
estimators of production functions may be inconsistent because inputs may be endogenous. An
alternative technique would be to estimate the dual specification in which technology is represented
in the form of a profit function whose derivatives are the input demand functions and the output
supply function, all expressed as functions of prices. However, an important problem here is that
there 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 this
case. Under the assumption that the unobserved heterogeneity takes the form of additive fixed
effects, the within primal estimator is consistent.25 Accordingly, we estimated a Cobb–Douglas
specification of the production function in (6) using the fixed effects model.26 The vector X in our
estimation included the following inputs: land, labor, irrigation, fertilizers and bullock hours. The
measure of risk derived from this estimation is referred to as RISK2. Results of these production
function 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. For
crops grown in other seasons, the rainfall variable includes the rainfall recorded during the preceding rainy season and
the 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 two
moment 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.
Crops
Millet (Kharif)
Land
Labor
Fertilizer
Irrigation
Bullock hours
Maize
2.548** (0.757) 4.57 (2.44)
1.759** (0.607) 1.945 (1.583)
0.36** (0.087)
0.018 (0.181)
0.001 (0.003)
0.01 (0.232)
0.183 (0.391) −1.845 (2.408)
Model F
11.01**
No. of observations 119
2.13
47
Figures in parenthesis are standard errors.
* Significant at 5 percent probability level.
** Significant at 1 percent.
Paddy
Fennel
0.43 (0.428)
0.108 (0.785)
0.6995* (0.348) 1.104 (1.057)
0.065* (0.029) −0.019 (0.389)
0.031 (0.034)
0.198 (0.437)
0.026 (0.061)
0.062 (0.915)
182.35**
49
3.831*
43
Castor
Millet (summer)
Groundnut
Wheat
0.413* (0.202) −0.351 (0.201)
1.173 (1.18)
1.626** (0.228) 1.315* (0.246)
0.842 (0.715)
0.066** (0.015) 0.148** (0.087) 0.001 (0.001)
0.027 (0.02)
0.279 (0.249)
0.0004 (0.0005)
−0.382 (0.23)
−0.379 (0.114) −1.061 (1.512)
0.39 (0.218)
0.235 (0.241)
0.139** (0.037)
0.160** (0.044)
−0.045 (0.061)
31.05**
85
103.13**
149
38.991**
43
1.81
49
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Table 6
Production function estimates for different crops
491
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first is some measure of the importance of the input provided by each party in the production
process of each crop, and the second is the ability of the each party to monitor the provision
of this input. To measure the second component, we have used data on the principal occupation
of the buyer and the seller. The underlying rationale here is that the ability of each party to
monitor the other is likely to be better if agriculture is their primary occupation. To measure the
first component, namely the importance of different inputs in the production process of different
crops, we used the estimated coefficients on the labor and irrigation input in (6). As a measure
of the labor input in (6), we used ICRISAT data on aggregate adult family and hired labor hours
used in the production of each crop. The advantage of using ICRISAT’s panel data based on a
stratified sample, different from the one we used in our survey, is that it gives us a measure of
input elasticity that is determined more closely by technological considerations and can be treated
as an exogenously given characteristic of the crop.
Similarly, to measure the irrigation input, one possibility is to use data on the total number of hours for which irrigation was supplied. However, this is a purely quantitative measure
of the irrigation input and may not adequately reflect the issue of timeliness in irrigation supply. As argued earlier, the issue of timeliness in irrigation supply is very critical in explaining
the seller’s incentive problem. The sensitivity of different crops to the timeliness of irrigation
supply is very difficult to estimate empirically. The most extensive discussion on timeliness is
found in studies that compare the irrigation performance of alternative irrigation systems (see
Rao, 1993 for a survey). Here, the standard procedure is to compare the impact of a unit of irrigation provided by different irrigation systems on the productivity of a particular crop after
controlling for all other factors, such as differences in soil fertility and other input applications. The timeliness dimension emerges as a residual factor here. There are very few studies
that have formulated an explicit measure of timeliness. One such study is by Meinzen-Dick
who divides the growing season for paddy into 10 day periods (decades) and formulates indices
for timeliness that relate water deliveries to water requirements for each of these decades. The
indices she proposes are useful for paddy because depth of water application is relatively easy
to measure for paddy with standing water, but they have limited applicability for dry-footed
crops.
For these other crops, it is much harder to find a single measure of timeliness. Irrigation
specialists suggest that to measure the sensitivity of different crops to moisture stress, the following
factors should be included: soil moisture holding capacity, rooting depth, previous history of
wetting and drying of the soil, and time since the last irrigation. However, given that data may
not be available on all these factors, there is a simpler solution if our interest lies in the relative
ranking of different crops rather than an absolute measure of each crop’s sensitivity to moisture
stress. In this case, it would be pertinent to look at the relative sensitivity of different crops
to the number of irrigations applied during the growing season. This measure would give a
rough indication of how long each crop could go, under the given set of conditions, between
irrigations.
The merit of this measure can be illustrated by comparing the irrigation requirement of paddy
with 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, frequent
irrigations need to be given at regular intervals, generally 8–10 irrigations are given every 10–15
days. In comparison to this, paddy requires fewer irrigations but in each irrigation, the field needs
to be flooded. Thus, although both crops are heavily irrigated crops, the incompleteness of the
contract 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
R.M. Aggarwal / J. of Economic Behavior & Org. 63 (2007) 475–496
493
crop as a measure of the irrigation input. The estimated coefficient on this irrigation input is then
used 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 model
of contractual choice. To test for the significance of buyer fixed effects in model III, we conducted
a simple Hausman specification test of the following kind. Under the null hypothesis of fixed
effects, the pooled logit estimator is inconsistent while Chamberlain’s estimator (model III) is
consistent and efficient. However, if the null is incorrect, then both estimators are consistent and
Chamberlain’s estimator is inefficient. Using this test, we found that the null hypothesis of buyer
fixed effects could not be rejected at the 1 percent level. However, a similar procedure to test for
seller 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 related
to 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 that
have isolated a similar result are Rao (1971) and Allen and Lueck (1995) for land tenancy, and
Laffontaine for the case of franchising in U.S. It is worth noting that the importance of the risk
sharing motivation in any form of output sharing contract is likely to depend on the availability
of other options to stabilize consumption over time. Diversification of holdings, intertemporal
holding of grains, purchase and sales of assets, borrowing and lending, and gifts and transfers are
some other examples of risk sharing institutions that have been found to be quite important in such
semi-arid environments (Townsend, 1994). It is also important to keep in mind that larger risk
associated with a particular crop could have several different implications besides the need for
insurance provision. For instance, a larger risk in terms of increased variability in output could be
interpreted as exacerbating the observability problem, thus leading to the choice of fixed payment
contracts. Similarly, as argued by Rao (1971), greater uncertainty associated with a particular
crop could lead to a greater role for entrepreneurship, thus making the issue of incentives for the
buyer even more important.
Our measure of the incentive problem in irrigation supply is highly significant across all the
specifications. This is also evident in Table 2, which shows that crops like wheat, tobacco and
summer millet that have a high irrigation elasticity tend to be under cropsharing contracts while
crops like maize, groundnut and millet that have a low irrigation elasticity are largely found under
fixed payment contracts. Interestingly enough, Meinzen-Dick and Sullins in their study on water
markets in Pakistan also observed the same empirical regularity. They found cropsharing contracts
to be common for crops, such as tomatoes and onions, which are very sensitive to moisture stress
at critical periods.
The effect of labor elasticity of the crop, which we use as a measure of the incentive problem
on the buyer’s side, is found to be negative but significant in only some specifications. It is
significant 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 growing
season can be specified in the contract, so the sensitivity of different crops to the number of irrigations is not a direct
measure of the incentive problem. The severity of the incentive problem here arises from the sensitivity of output to any
mistiming in irrigation supply due to the incompleteness of the contract. This elasticity is difficult to measure directly
but is likely to be highly correlated with the measure we use. This is well illustrated by the example on paddy and wheat
given above.
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R.M. Aggarwal / J. of Economic Behavior & Org. 63 (2007) 475–496
interestingly enough, once we control for buyer fixed effects in specifications II and III, the effect
is no longer significant. This gives support to our earlier conjecture that sellers may purposively
select buyers who are known to be hardworking and trustworthy, thus reducing the severity of
the incentive problem on the buyer’s side. Finally, the dummies for buyer’s and seller’s primary
occupation are not found to be significant determinants of contract choice. This may be because
these are somewhat crude measures of the incentive problem. Overall these results provide some
support to a model based on a double-sided incentive problem where the need for giving proper
incentives 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 alternative
theories on the rationale for contract choice. Both fixed payment and cropsharing contracts were
found to coexist in the sample villages. To explain this coexistence of contract types, the insuranceincentive tradeoff model that emphasizes the tradeoffs between risk sharing and incentive provision to the cultivator was compared with the double-sided incentive model that emphasizes the
role 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 appropriate
empirical measures for theoretical constructs, such as riskiness of different crops, risk preferences
and the moral hazard problem. The commonly used procedure of using suitable proxies for
partially observed or unobserved explanatory variables may result in biased estimates due to
endogenous matching. In our study, we discussed several alternative solutions to ameliorate these
problems. A couple of different measures of riskiness of crops and the incentive problems were
discussed and estimated using panel data from ICRISAT’s VLS studies. To control for the omitted
variable bias we made use of the pseudo panel nature of our data set and estimated different fixed
effect models. Neither the riskiness of crops nor the risk-bearing abilities of the two parties was
found to be significant in explaining the probability of share contracts. Interestingly, the irrigation
elasticity of the crop (which we use a measure of the seller’s incentive problem) was found to be
highly significant, and this result was found to be quite robust across the different specifications
we tried, including the pooled sample and different fixed effect models. On the other hand, the
labor elasticity of the crop was found to be significant in only some of the specifications. To the
extent that these labor and irrigation elasticities adequately capture the actual incentive problem
faced by buyer and seller, respectively, these results provide some support to a model based on
a double-sided incentive problem where the need for giving proper incentives to both the buyer
and the seller determines contract choice.
It is also worth noting that we observed some aspects of the contract structure to be at variance
with both the theoretical models reviewed here. Thus, for instance, both models predict fairly
complex incentive schemes that are in sharp contrast to the simple linear contracts observed
in our sample villages, as also in many other empirical studies. We also observed very little
variation in the fixed payment and share parameter, which is also at variance with the finely tuned
rules predicted by these two theories. Wood and Palmer-Jones in their study on water markets in
Bangladesh found a similar pattern and suggest that pressures for conformity within the village
generally override plot-derived calculations based on economic and ecological criteria. Another
possibility suggested by Holmstrom and Milgrom is that the usual agency models are overly
simplistic and fail to account for the need to have schemes that perform well under a variety of
conditions (i.e. schemes that are more robust). They propose an agency model in which linear
schemes are optimal because the agent is assumed to have a rather rich action space.
R.M. Aggarwal / J. of Economic Behavior & Org. 63 (2007) 475–496
495
Most formal models of contracting also begin by assuming that both parties can write (or
verbally agree on) contracts that provide a complete description of the rights and obligations of
each party under every possible contingency. Most real world contracts, on the other hand, are
not only very simple but also quite coarse. In this paper, we have shown how the incompleteness
of the contract in specifying the timing of irrigations makes the seller’s incentive problem very
critical. At the policy level, one may conjecture that this incentive problem also helps to explain
why there has been an exponential growth in private well investment (in spite of the lumpiness
of investment and high risks) while pubic investment (as also group/cooperative investment in
wells) has stagnated.
To the extent that the incompleteness of groundwater contracts arises from incomplete knowledge regarding aquifer characteristics, groundwater dynamics and electricity supply conditions, it
is expected that as farmers learn by doing, it may become less costly to agree upon more complete
contracts. Accumulated knowledge over time may also lead to evolution of norms of behavior that
govern what happens under a wider range of contingencies. Anecdotal evidence from the villages
that we surveyed in 1993–1994 suggests that share contracts are now being slowly replaced by
more fixed payment contracts. A recent case study by Dubash of two villages in western India
also found that share contracts in groundwater are giving way to fixed payment contracts over
time. Analyzing these historical trends in contract choice could provide further insights into the
determinants of contract choice.
Acknowledgements
I would like to thank Erik Thorbecke, Robert Chambers, Suzi Kerr, Alain de Janvry, Ramon
Lopez, Keijoro Otsuka, John Quiggin and an anonymous referee for their comments on an earlier
version of this paper. I am grateful to M. Asokan and Anil Patel for their help with the data collection work. The Comparative Economic Development Program, Cornell University and ICRISAT
provided financial assistance for the field research.
References
Ackerberg, D.A., Botticini, M., 2002. Endogenous matching and the empirical determinants of contract form. Journal of
Political Economy 110, 564–591.
Agrawal, P., 1999. Contractual structure in agriculture. Journal of Economic Behavior and Organization 39, 293–325.
Allen, D., Lueck, D., 1995. Risk preferences and economics of contracts. American Economic Review 85, 437–441.
Al-Najjar, N., 1995. Incomplete contracts and the governance of complex contractual relationships. American Economic
Review 85, 432–436.
Binswanger, H.P., Sillers, D., 1983. Risk-aversion and credit constraints in farmers’ decision-making: a reinterpretation.
Journal of Development Studies 20, 5–21.
Binswanger, H.P., Rosenzweig, M.R., 1984. Contractual Arrangements, Employment, and Wages in Rural Labor Markets
in Asia. Yale University Press, New Haven.
Canjels, E., 1996. Risk and Incentives in Sharecropping—Evidence from Modern U.S. Agriculture. Northwestern University, Mimeo.
Chamberlain, G., 1984. Panel data. In: Griliches, Z., Intriligator, M.D. (Eds.), Handbook of Econometrics, vol. 2. North
Holland, Amsterdam, pp. 1247–1318.
Cheung, S., 1969. Transaction costs, risk aversion, and the choice of contractual arrangements. Journal of Law and
Economics 12, 23–42.
Dubash, N.K., 2002. Tubewell Capitalism: Groundwater Development and Agrarian Change in Gujarat. Oxford University
Press, New Delhi.
Eswaran, M., Kotwal, A., 1985. A theory of contractual structure in agriculture. American Economic Review 75, 352–367.
496
R.M. Aggarwal / J. of Economic Behavior & Org. 63 (2007) 475–496
Fujita, K., Hossain, F., 1995. Role of groundwater markets in agricultural development and income distribution: a case
study in a northwest Bangladesh village. Developing Economies 33, 442–463.
Grossman, S.J., Hart, O.D., 1983. An analysis of the principal-agent problem. Econometrica 51, 7–46.
Holmstrom, B., Milgrom, P., 1987. Aggregation and linearity in the provision of intertemporal incentives. Econometrica
55, 303–328.
Hukkeri, S.B., Pandey, S.L., 1977. Water Requirement and Irrigation of Crops. I.A.R.I. Monograph, vol. 4. Water Technology Centre, New Delhi.
Janakarajan, S., 1992. Interlinked transactions and the market for water in the agrarian economy of a Tamilnadu village.
In: Subramanian, S. (Ed.), Themes in Development Economics. Oxford University Press, New Delhi, pp. 151–201.
Kajisa, K., Sakurai, T., 2003. Determinants of groundwater price under bilateral bargaining with multiple modes of
contracts: a case from Madhya Pradesh, India. Japanes Journal of Rural Economics 5, 1–11.
Laffont, J., Matoussi, M.S., 1995. Moral hazard, financial constraints, and sharecropping in El Oulja. Review of Economic
Studies 62, 381–399.
Laffontaine, F., 1992. Agency theory and franchising: some empirical results. RAND Journal of Economics 23, 263–283.
Meinzen-Dick, R., Sullins, M., 1994. Water Markets in Pakistan: Participation and Productivity. International Food Policy
Research Institute, Washington, DC.
Meinzen-Dick, R., 1995. Timeliness of irrigation: performance indicators and impact on agricultural production in the
Sone irrigation system, Bihar. Irrigation and Drainage Systems 9, 371–387.
Meyer, J., 1987. Two-moment decision models and expected utility maximization. American Economic Review 77,
421–430.
Mundlak, Y., 1996. Production function estimation: reviving the primal. Econometrica 64, 431–438.
Otsuka, K., Chuma, H., Hayami, Y., 1992. Land and labor contracts in agrarian economies: theories and facts. Journal of
Economic Literature 30, 1965–2018.
Pender, J., Asokan, M., 1993. Farmers Irrigation Investments in South India. Department of Economics, University of
Utah (Working Paper No. 93–13).
Rao, C.H.H., 1971. Uncertainty, entrepreneurship and sharecropping in India. Journal of Political Economy 85, 578–595.
Rao, P.S., 1993. Review of Selected Literature on Indicators of Irrigation Performance. International Irrigation Management Institute, Colombo.
Reid, J.D., 1976. Sharecropping and agricultural uncertainity. Economic Development and Cultural Change 24, 549–576.
Saleth, R.M., 1998. Water markets in India: economic and institutional aspects. In: Easter, K.W., Dinar, A., Rosegrant,
M.W. (Eds.), Markets for Water: Potential and Performance. Kluwer Academic Publishers, Boston, pp. 187–206.
Shah, T., 1993. Groundwater Markets and Irrigation Development: Political Economy and Practical Policy. Oxford University Press, Bombay.
Shah, T., Ballabh, V., 1997. Water markets in North Bihar. six village studies in Muzzaffarpur district. Economic and
Political Weekly 27, A183–A190.
Singh, R.P., Singh, S.B., 1982. Features of traditional farming systems in two villages of Gujarat. Economics Program
Progress Report-35. ICRISAT, India.
Singh, N., 1989. Theories of sharecropping. In: Bardhan, P. (Ed.), The Economic Theory of Agrarian Institutions. Clarendon Press, Oxford, pp. 33–72.
Stiglitz, J., 1974. Incentives and risk sharing in sharecropping. Review of Economic Studies 41, 219–255.
Townsend, R., 1994. Risk and insurance in village India. Econometrica 62, 539–591.
Wood, G.D., Palmer-Jones, R., 1990. The Water Sellers: a Cooperative Venture by the Rural Poor. Kumarian Press,
Connecticut.