Determinants of collective action on the local commons: a model with evidence from Mexico

Journal of Development Economics Vol. 62 Ž2000. 181–208 www.elsevier.comrlocatereconbase

Determinants of collective action on the local commons: a model with evidence from Mexico Jeff Dayton-Johnson Department of Economics, Dalhousie UniÕersity, Halifax, NoÕa Scotia, Canada B3H 3J5

Abstract I develop a model of cooperation in small irrigation systems. I give conditions under which an equalizing redistribution of wealth increases the level of equilibrium cooperation, but also show that some redistributions that increase inequality can also increase cooperation. The distributiÕe rule, a combination of arrangements for maintenance-cost sharing and water allocation, also affects the cooperation level. I estimate statistical models of cooperation for three maintenance indicators using field data from a study of Mexican irrigation societies. Social heterogeneity and landholding inequality are significantly associated with lower maintenance. Distributive rules that allocate water proportionally to landholding size likewise reduce maintenance. q 2000 Elsevier Science B.V. All rights reserved. JEL classification: D70; O12; O13; O17; Q25 Keywords: Common property; Cooperation; Irrigation

1. Introduction Management of the local commons — small-scale common-pool resources such as community in-shore fisheries, forests, pasturelands, and irrigation systems — is critically important to economic well-being and environmental conditions in the rural sector of developing economies Žsee, e.g., Jodha, 1986.. The systematic study of group characteristics and group performance in these self-governed

E-mail address: [email protected] ŽJ. Dayton-Johnson.. 0304-3878r00r$ - see front matterq 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 3 8 7 8 Ž 0 0 . 0 0 0 8 0 - 8

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resource-using communities can shed light on the determinants of successful collective action. What group characteristics — e.g., group size, inequality — favor or hinder the supply of cooperative effort to maintain these collectively owned assets? Moreover, what effect do local rules to govern the commons have on the success with which local resources are husbanded? In this paper, I answer these questions using a theoretical model and the results of a field study of farmer-managed irrigation systems in the Mexican state of Guanajuato. 1 In the theoretical portion of the paper, I use a simple model to explore the relationship between structural characteristics of the resource-using community and its environment Že.g., group size, various measures of heterogeneity, water availability. and the system’s equilibrium level of cooperative effort. I show how these relationships depend on the particular set of rules adopted by the community. In the empirical section of the paper, I draw on these theoretical results to formulate a statistical model of cooperation, based on the Mexican survey data. I estimate three ordered-logit models of cooperative effort, each with a different measure of quality of infrastructure maintenance Žthe maintenance of canal side-slopes, the state of repair of field-intake structures, and the degree of control of water leakage around the canals.. The set of independent variables includes group size, economic inequality, social heterogeneity, the local wage, and irrigation availability; I also include the predicted distributive rule estimated for each surveyed system. Social heterogeneity — the number of agrarian-reform communities from which the members of an irrigation system are drawn — has a consistently negative impact on group performance. Inequality in landholding also has a negative, though complicated, effect. The choice of distributive rule has a quantitatively larger impact on the level of infrastructure maintenance, controlling for other factors, than the direct effect of structural characteristics such as group size or inequality. Given that those structural characteristics also determine the distributive rule, I conclude the paper with a calculation of their full effect on observed maintenance effort: directly through their effect on cooperation, and indirectly through their effect on choice of rules. Field studies that analyze a single common-pool resource system Že.g., an in-shore fishery, a community forest, or a locally managed irrigation system. dominate the empirical literature Žsummarized in Ostrom, 1990.. In many cases, these studies provide deeply detailed description of the rules and institutions that govern resource use. Unfortunately, small numbers of observations Žgenerally only one. and consequently too few degrees of freedom preclude these studies from

1 I surveyed farmers and inspected the canal infrastructure in 54 farmer-managed irrigation systems in the central Mexican state of Guanajuato during 1995 and 1996. The design and results of the survey are summarized in Dayton-Johnson Ž1999..

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making statistically based statements regarding the relationship between institutions, cooperation, and system performance. Recent empirical studies have analyzed larger-scale data sets, beginning with the study of Wade Ž1987. of 41 irrigating villages in Andhra Pradesh, India. Tang Ž1992. systematically assesses a large number of case studies of agency-managed and farmer-managed irrigation systems to establish empirical regularities regarding their organization and performance. Closest in spirit to this paper is the study of Lam Ž1998. of a class of irrigation systems in Nepal. In a different resource domain, Seabright Ž1997. analyzes cooperation among 69 milk producers’ cooperative societies in Tamil Nadu, India, in the context of a repeated-game model. Banerjee et al. Ž1997. analyze cooperation among nearly 100 sugar cooperatives in Maharashtra, India; they find that economic inequality significantly reduces efficiency. This paper seeks to add to this recent work, complementing the case-study focus of the existing literature with a larger-scale statistical study of collective action among an entire class of resource-using systems.

2. Structural characteristics and cooperative effort: theory Consider a simple model of the farmer-managed irrigation system. The irrigation system comprises a set of n farming households i s 1, . . . ,n; let I s  1, . . . ,n4 . Each household i is endowed with an amount of irrigable land l i . The users collectively have access to reservoir water for irrigation. The quantity of water captured by the reservoir is W. Let L ' Ý i g I l i be the aggregate land in the system; thus l irL is i’s share of the reservoir’s command area. The ‘‘sequence’’ of moves is as follows. Ž1. At some point prior to the playing of the game, the governing council of the water users’ association chooses the maximum number of hours of collective labor Ž X . and the water-allocation and cost-sharing arrangements Ždescribed below. that specify each irrigating household’s share of the costs and benefits of systemmaintenance efforts.2 Ž2. A second set of variables exogenous to the model is chosen each period by Nature: the water captured in the reservoir this season ŽW .; the output price Ž p .; and the unit cost of cooperation Ž c .. The values of these parameters are known to all. Ž3. All irrigating households i that are members of the water users’ association choose contribution levels of canal-cleaning and maintenance effort x i . The collective-maintenance activities typically required in small irrigation systems 2 X is largely determined by the physical extension of the canal network and the average productivity of labor. This paper does not assume that X is chosen according to any maximizing logic, only that the nearer the realized X is to X, the higher is equilibrium maintenance and output.

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include constructing and maintaining canals and field channels, and desilting, weeding and stopping encroachments in reservoir beds. The total amount of cooperative effort is thus determined: X ' Ý i g I x i . Ž4. Payoffs are realized: the ‘‘effective water supply’’ XW is distributed according to the water-allocation arrangement. Each household i that contributed the required amount of canal-cleaning in the previous stage receives its share, and all others receive nothing. Each contributing household’s agricultural output is strictly increasing in the aggregate amount of cooperative effort X. Output is sold at price p. Although this is a one-period model, in practice, steps a2 through a4 are repeated year after year; step a1 might be revisited irregularly. The description of the payoffs in step a4 implies that each farmer’s output is linear in irrigation supply. This in turn implies that the marginal product of irrigation water is independent of landholding size. ŽIf not, output would be concave in water inputs.. This specification is consistent with a production technology in which water and land are strict complements and each household Žregardless of parcel size. is severely water-constrained. Indeed, the irrigators in the Mexican sample, given available rainfall and their choice of crops, face severe shortfalls in irrigation supply.3 In that case, an additional cubic meter of water would yield similar increments to crop output, ceteris paribus, on small and large parcels. Nevertheless, it must be emphasized that linearity of output in water is a special assumption that has non-trivial consequences for household decision-making. As is customary Žthough not necessarily justified. in the research on local regulation of the commons ŽJohnson and Libecap, 1982; Kanbur, 1991., I assume that side payments are impossible. Households that benefit from collective canalcleaning cannot transfer income to equilibrium non-contributors in exchange for canal-cleaning effort by the latter. The distributiÕe rule combines a cost-sharing arrangement g i 4i g I , which specifies the maintenance-cost share g i X of household i, and a water-allocation arrangement  a i 4i g I , which specifies household i’s water share a i XW if i complies with the cost-sharing arrangement. Note that for all i g I, a i ) 0 and g i ) 0, and Ý i g I a i s Ý i g I g i s 1. I consider four distributive rules. Equal-diÕision: Costs and water are equally divided Ž a i s g i s 1rn, for all i g I .. Proportional: Costs and water are allocated proportionally to landholding Ž a i s g i s l irL, for all i g I .. Proportional-allocation: Water allocation is proportional to landholding and costs are equally divided Ž a i s l irL, g i s 1rn, for all i g I .. Proportional-cost-sharing: Cost sharing is proportional to landholding and water is

3 Dayton-Johnson Ž1999. calculates the relatiÕe water supply ŽLevine, 1982. of the Mexican systems, and shows that the average lies below values observed in the case-study literature for Asia and Africa.

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Table 1 Joint distribution of characteristics of distributive rules in 49 Mexican farmer-managed irrigation systems Each cell reports the number of irrigation systems with that pair of characteristics. ŽThree systems have different canal-cleaning regimes; therefore the numbers in the fifth and sixth columns sum only to 46.. Source: Dayton-Johnson Ž1999.. Cost sharing Proportional Water allocation Proportional 8 Equal-division 1 Cost sharing Proportional Equal-division Water distributor Present Absent

Water distributor

Canal cleaning

Equal-division

Present

Absent

Collective

Household

23 17

25 10

6 8

11 9

18 8

8 27

1 13

0 20

8 18

12 8

21 5

equally divided Ž a i s 1rn,g i s l irL, for all i g I .. These are the four rules encountered in the Mexican field data. Table 1 presents the distribution of characteristics of the distributive rules across the irrigation systems in the Mexican field study. Forty-nine of the 51 operational irrigation systems in the sample can be classified into one of the four categories developed above.4 Table 2 also presents information on the presence or absence of a water distributor Žcharged with the physical distribution of irrigation water to parcels., and the labor-mobilization regime for canal-cleaning Žwhich is either carried out collectively, or individually by households.. Let DŽ L. ' Ž l 1rL,l 2rL, . . . ,l nrL.< l i ) 0,; i g I,Ý nis1 l irL s 14 be the set of landholding distributions. I restrict attention to distributions of landholding that assign a positive share to each household: households with no irrigable land would not be members of the water users’ association. For l g DŽ L., let X r) Ž l . be the largest amount of collective effort supplied in equilibrium when the distribution of landholding is l and the distributive rule is r Žwhere r g  proportional, equal-division, proportional-allocation, proportional-cost-sharing4 . I will frequently suppress subscripts and arguments for X ) in what follows.

4 In the two operational systems excised from Table 1, irrigators have abandoned collective canal-cleaning effort and simply collect money from the member households to hire laborers to do the work.

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Table 2 Predicted signs of the effects of variables on cooperation, for four distributive rules

c p W n Lr n Inequality Social heterogeneity

Equal-division

Proportional

Proportionalallocation

Proportionalcost-sharing

y q q 0 0 0 y

y q q 0 0 0 y

y q q qry 0 qry y

y q q qry 0 qry y

In this section, I determine the effect of various exogenous variables — including irrigation supply, unit cost of cooperation, group size, mean landholding, economic inequality and social heterogeneity — on the highest-observable level of cooperative effort X ) . 2.1. Output price, unit cost of cooperation, and irrigation supply Proposition 1 details the relationship between equilibrium cooperative effort and the exogenous variables in the model. A higher output price or a higher irrigation supply raise the return to cooperative effort; a lower unit cost of cooperation similarly increases the net return to cooperative effort. Proposition 1. (a) Under any of the distributiÕe rules, X ) is (weakly) greater, the higher the output price p, the larger the reserÕoir leÕel W, and the lower the unit cost of contribution c. (b) Under the proportional and equal-diÕision rules, X ) is equal to X as long as pW G c. Household i’s return to complying with the rule is

a i p w Xyi q x i x W y cx i

Ž 1.

where Xyi ' Ý j/ i x j . Then this return rises with p and W, and declines with c. To motivate part Žb. of the proposition, let a i s g i in Eq. Ž1.. Under full compliance with the rule, Xyi q x i s X and x i s g i X. If pW ) c, then X s X is an equilibrium outcome.5 5 A referee points out that this result would not necessarily hold if each household’s output were not linear in irrigation supply. Suppose that condition Ž1. is equal to zero for two households i and j. If, contrary to the assumptions of my model, output were strictly increasing in landholding size, then a redistribution of land from i to j, with no change in water allocation, would reduce i’s output and thus its returns from complying with the distributive rule. But the value of Eq. Ž1. would remain unchanged.

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2.2. Group size A well-known hypothesis of Olson Ž1965. asserts that the larger the number of members in a group, the less likely that the group will exhibit successful collective action: as group size increases, the benefit to the individual from cooperation decreases, while the benefit of ‘‘free-riding’’ on the cooperative efforts of others does not. In the Mexican unidades and other local-commons management regimes world-wide, resource users have managed to resolve some, but not all, of the collective-action problems inherent in the commons. For example, they have designed regulatory institutions, but there remain externalities in the supply of maintenance effort. Will group size inhibit cooperative effort in this sphere? To assess the effect of an increase in group size on cooperation, I need to specify which other variables are held constant. That is, one could consider group-size increases accompanied by changes in reservoir command area Ž L., irrigation supply ŽW ., or maintenance labor Ž X .. I will hold those variables unchanged, but change instead the distribution of landholding l so that it reduces the land held by the original members and assigns a strictly positive amount of land to each of the new members. Consider the effects of such a change in n and l under the proportional rule or equal-division rule. Whatever the new distribution of landholding after the increase in n, there is no change in X ) as long as pW is still no smaller than c. Under the proportional-allocation rule, if the largest set of equilibrium contributors is initially a strict subset of group members, the effect of an increase in n is ambiguous. Under this rule, any equilibrium contributor has higher landholding wealth than any non-contributor. ŽThis is demonstrated in the proof of Proposition 3 below.. There is a ‘‘contribution threshold’’ level of wealth. The aggregate contribution of canal-cleaning effort by the original contributors must be weakly less after the increase in n, given that some or all might now fall below that wealth threshold. However, this could be offset by contributions by the new members. Hence, the effect of increasing group size is a priori ambiguous. ŽThe effect is similarly ambiguous for the proportional-cost-sharing rule.. 2.3. Mean landholding wealth Is there a wealth effect associated with cooperative effort? Consider an increase in the reservoir command area L to LX : this increases mean wealth to LXrn. Change the distribution of landholding to lX , where for each i, lXi is set such that lXi X

L

s

li L

Under such a ‘‘inequality-preserving’’ change in mean wealth, there is no effect on equilibrium cooperative effort under the proportional and equal-division

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rules, since p, W, and c are unchanged. Neither will X ) change under the proportional-allocation or proportional-cost-sharing rules. Consider, for example, the proportional-allocation rule: Any household that initially contributes canalcleaning effort will continue to do so with higher mean wealth. The condition for contributing must still be met since lXrLX s l jrL. Furthermore, the size of each contributors’ contribution is unchanged. 2.4. Inequality Proposition 2 states that under the proportional and equal-division rules, mean-preserving spreads of the landholding distribution have no effect on the aggregate amount of equilibrium contributions to canal-cleaning effort. Proposition 2. Let a i s g i for all i g I, and let the distribution of landholding be l g D(L). If lX is a mean-preserÕing spread of l, then X ) (lX ) s X ) (l). Proof. Even if the landholding distribution becomes more unequal, each household i continues to face the same participation condition. Under the proportional rule, conditional on contribution of maintenance effort by all other households, i contributes if: li L

X w pW y c x G 0

Under the equal-division rule, the corresponding condition is: 1 n

X w pW y c x G 0

In either case, the participation decision is non-negative if pW G c and is unchanged by the change in the wealth distribution; thus X ) Ž lX . s X ) Ž l .. If pW - c, then initially X ) s 0, and a change in the landholding distribution will similarly have no effect on households’ decisions to cooperate. B The stark results of Proposition 2 would not necessarily hold if crop output were increasing in wealth. Given that the assumed independence of output on parcel size is motivated by severe irrigation-water shortage, this suggests that the effect of inequality on equilibrium cooperation would be even more complicated in irrigation communities with relatively greater availability of irrigation water. Under the proportional-allocation or the proportional-cost-sharing rules, changes in inequality can have an effect on equilibrium cooperation. Propositions 3 and 4 consider the case of the proportional-allocation rule given that it is the most commonly observed rule in the Mexican field study. Proposition 3 gives sufficient conditions such that there exists a redistribution of landholding that reduces inequality and increases equilibrium cooperation. Proposition 4 gives conditions

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under which redistributions that increase inequality also increase equilibrium cooperation. Proposition 3. Let a i s l i r L and g i s 1 r n for all i g I, and let the distribution of landholding be giÕen by l g D(L). Let J ; I denote the set of n J equilibrium contributors. Define lˆ' max{l i N i g I}. If lj

lˆ

c

Ý L y pW G

jgJ

c

1

y L

pW n J q 1

Ž 2.

there exists an equalizing redistribution of landholding l˜g D(L) such that X ) (l˜) ) X ) (l). Proof. First, I show that each equilibrium contributor j g J has a landholding share such that: lj

1

c

G

L

n J pW

.

Ž 3.

If some group J of n J households contributes maintenance effort, then for any j g J, compliance must at least weakly dominate non-compliance: lj L

p

nJ n

X Wyc

1 n

X G 0.

This condition simplifies Ždividing through by Ž1rn. X and rearranging. to condition Ž3.. Also, condition Ž3. will not hold for any non-contributor. Sum the difference between the right-hand and left-hand sides of Eq. Ž3. over all j g J: this yields the left-hand side of the expression in Eq. Ž2.. This is the maximum amount of wealth that can be transferred from initial contributors without changing their compliance decision. The right-hand side of Eq. Ž2. is the shortfall of the wealth share of the wealthiest initial non-contributor. If Eq. Ž2. is satisfied, then wealth can be transferred to the wealthiest non-contributing household i such that i will now contribute. Thus, X ) Ž l˜. s

nJq1 n

X)

nJ n

XsX ) Ž l.

so that aggregate cooperative effort in equilibrium is increased.

B

Condition Ž2. is sufficient but not necessary for an equalizing landholding redistribution to increase equilibrium cooperative effort. In particular, if landholding is transferred from initial contributors to initial non-contributors, then n J increases on the left-hand side of Eq. Ž3., lowering the minimum ‘‘contribution threshold’’ share of landholding, so that more land than that considered in Proposition 3 could be transferred with a qualitatively similar result.

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Proposition 4. Let a i s l i r L and g i s 1 r n for all i g I, and let the distribution of landholding be giÕen by l g D(L). Define lˆ' max{l i N i g I _ J}. Finally, let K be the set of households with landholding less than l.ˆ If

Ý kgK

lk L

yeG

lˆ

1

c

y L

n J q 1 pW

Ž 4.

for e ) 0 small, then there exists a mean-preserÕing spread of landholding lX such that X ) (lX ) ) X ) (l). Proof. The right-hand side of Eq. Ž4. is the share of landholding that, if transferred to the non-contributor with the largest landholding, would induce the latter to contribute. The left-hand side is Žalmost. the total amount of landholding of households with lower landholding than the wealthiest non-contributor. If Eq. Ž4. is satisfied, then there exists sufficient landholding among the least wealthy households to transfer to the wealthiest non-contributor and thereby induce the latter to contribute. Call this new distribution lX . All initial contributors j g J continue to contribute under lX . Thus, X ) Ž lX . s X ) Ž l . q Ž1rn. X. B Propositions 3 and 4 illustrate that under the proportional-allocation rule, the relationship between inequality and cooperation is not monotonic. Proposition 3 gives the conditions under which there exists a transfer of land from equilibrium contributors to a non-contributor such that equilibrium cooperation increases. As long as initial contributors have landholding shares sufficiently above the contribution threshold, then that they can give land to a non-contributing household, and this will raise aggregate maintenance effort and reduce inequality. Proposition 4, in contrast, gives the conditions under which there exists a redistribution of landholding among non-contributors that raises aggregate cooperative effort. Finally, in the proof of Proposition 3, it was shown that whenever there is an equilibrium under the proportional-allocation rule in which the contributors form a strict and nonempty subset of the group, contributors and non-contributors can be wealth-ranked: any contributor has larger landholding than any non-contributor. This is because there is a ‘‘threshold share’’ of landholding above which the household contributes cooperative effort. This threshold is a function of the set of contributors: the larger the number of contributors, the lower is the wealth threshold. The wealth threshold is also related Žinversely. to W, the water captured in the reservoir.6 Proposition 2 showed that under the proportional and equal-division rules, wealth redistributions among non-contributors or among contributors have no effect on equilibrium cooperation: any redistribution there amounts to a redistribu6

Similarly, under the proportional-cost-sharing rule, if contributors form a strict subset of households, any contributor has lower wealth than any non-contributor.

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tion among contributors Žwhen X ) s X . or among non-contributors Žwhen X ) s 0..7 2.5. Social heterogeneity The model assumes both perfect monitoring and perfect enforcement of the distributive rule. Both assumptions are plausible in the information-rich village economy. If the water users in a particular system are drawn from more than one village, however, the costs of monitoring and enforcement might be higher than in a single-village irrigation system. To the extent that monitoring and enforcement rely on informal norms of cooperation, those norms lose force when they cross village boundaries. In the Mexican field study, the relevant indicator of this social heterogeneity is the number of ejidos represented among unidad members. Ejidos are the quasi-communal farming communities created by Mexico’s agrarian reform: to a first approximation, ejidos correspond to villages.8 The number of villages represented among irrigation-system members, then, shifts up the systemwide cost function for cooperation and ceteris paribus will reduce the level of cooperative effort in equilibrium. The aforementioned study of Wade Ž1987. of Indian villages found that irrigation organization was more successful where the management organization overlapped with other structures of authority. Thus, if there is a significant overlap between the ejido and the unidad Žand consequently fewer ejidos per unidad ., then the unidad can draw on the institutional legitimacy and authority of the ejido. For all these reasons, one ejido is better than two or more, but it is an open question whether zero ejidos are better than one. If water users are not members of any ejido, there is little organization that can be exploited by the unidad. If so, the relationship between the number of ejidos and performance rise from zero to one, and falls thereafter. ŽFortunately, for the estimation exercise, among the 48 systems included in the statistical analysis, only one is completely ejido-free.. Table 2 summarizes the theoretical discussion in Sections 2.1–2.5: it shows the expected sign of the effect of each of the structural characteristics on cooperation, for each of the four distributive rules observed in the field. 7

In the pure public-goods problem with free riding, these neutrality results are associated with Warr Ž1983., Bergstrom et al. Ž1986. significantly generalize Warr’s neutrality theorem, and show conditions where it is not true. 8 I cannot improve upon the explanation of ejidos given by Stephen Ž1997, fn. 1.: ‘‘Ejido refers to agrarian reform communities granted land taken from large landowners as a result of the agrarian struggles during the Mexican Revolution Ž1910–1917. . . . Such land is held corporately by the persons who make up the ejido. Originally, the ejido bestowed use rights on a list of recipients, while the state retained ultimate property rights. Ejido land could not be sold or rented, but holders could pass their use rights on to relatives. As a result, many families have worked the same parcels of land for several generations. In 1992, changes amending Article 27 of the Mexican Constitution made it possible to privatize ejido land following a complex process of land measurement, certification, and individual titling.’’

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2.6. The distributiÕe rule Propositions 1–4 illustrate that the effect of various structural characteristics on cooperation is mediated by the particular distributive rule in place. What leads a group of water users to choose a given rule? 9 North Ž1990. argues that institutions — like regulatory regimes for the commons — evolve in the direction of ever-greater efficiency. Does the underlying selection mechanism for distributive rules in Mexican unidades follow this logic? If so, is there a single best distributive rule for all unidades? Two forces are at work in determining the distributive rule that leads to the highest possible agricultural output. First, distributive rules with ‘‘congruence’’ between cost-sharing and water-allocation arrangements will always exhibit high maintenance Ž X ) s X . in equilibrium, as long as pW G c. ŽThis was shown in Proposition 1, for the congruent proportional and equal-division rules.. There exist partial-compliance equilibria under the proportional-allocation and proportionalcost-sharing rules, a consequence of the contribution threshold level of wealth discussed earlier. This confirms the assertion of Ostrom Ž1990, p. 92. that congruent rules characterize successful commons-management regimes. At the same time, there are transaction costs associated with each distributive rule, costs of record-keeping and accounting, monitoring and enforcement, and negotiation. These costs are probably higher under the proportional-allocation rule than under the equal-division rule, and highest of all under the proportional rule. Different water-delivery volumes and different maintenance-cost shares impose higher costs of running the system and greater scope for disagreements. The equal-division rule imposes the lowest transaction costs and elicits the highest level of maintenance effort. The proportional rule also elicits high effort, but at a greater cost. Under certain conditions, the maintenance shortfall of the proportional-allocation rule relative to the proportional rule can be smaller than the transaction-cost saving. The real question is why a system would choose either of the latter rules over the equal-division rule. Table 1 shows that seventeen of 49 unidades have chosen the equal-division rule, but 31 chose the proportional Žeight. or proportional-allocation Ž23. rules. Where there is significant landholding inequality, wealthier households might press for the proportionalrproportional-allocation rules. The proportional-allocation rule raises the difference between their return Ž a i s l irL. and their cost Žg i s 1rn. relative to the equal-division rule. If the marginal product of water is higher on larger farms, the proportionalrproportional-allocation rules will increase wealthier farmers’ payoffs more than proportionally. To the extent that larger landholders’ preferences receive more weight in the rule-selection process, greater 9

The material in this subsection borrows substantially from Dayton-Johnson Ž2000., where these issues are discussed at greater length.

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Table 3 Distribution of levels of canal-maintenance performance, along three dimensions Condition of . . .

Side-slopes Field intakes Filtration

Number of systems Good

Fair

Poor

Total

7 13 7

20 22 18

21 5 18

48 40 42

inequality should be correlated with proportionalrproportional-allocation rules. This will be the case even if those rules do not mobilize the same level of maintenance effort as the equal-division rule. In sum, the proportionalrproportional-allocation rules involve higher transaction costs and will be associated, ceteris paribus, with lower maintenance levels than the equal-division rule.

3. Evidence In this section, I consider my Mexican field data in light of the theoretical model in Section 2. I use the following measures of canal-cleaning performance: Ø the state of repair of field intakes, the small and simple structures that regulate the flow of irrigation water into individual parcels, Ø the degree of definition of canal side-slopes Žimportant since almost all are earthen canals, unlined with cement or concrete., Ø the degree of filtration Žleakage. of water around the canals. These three measures are part of a larger set of indicators of the quality of system maintenance collected during a canal inspection at each of the sampled systems. I did not observe directly the level of cooperative effort provided at each system. I assume that the observed quality of maintenance in each case increases with the level of cooperation in cost sharing. For each indicator, each irrigation system was given a score of ‘‘3’’ Žgood., ‘‘2’’ Žfair., or ‘‘1’’ Žbad..10 The scores for the surveyed systems are summarized in Table 3. With each of these indicators, I estimate an ordered-logit model using the explanatory variables listed below. The independent variables in the canal-maintenance performance models are listed below. ŽTable 2 reported the predicted sign of each variable’s effect according to the theoretical model.. Summary statistics for these variables are listed in Table 4. 10

For the filtration variables, the meaning of the scores is slightly different: ‘‘1’’ indicates generalized filtration; ‘‘2’’ filtration in a few stretches; ‘‘3’’, none.

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Table 4 Mean values of independent variables used in the canal-cleaning performance models These summary characteristics are limited to the subsample of 48 systems on the basis of which the maintenance models are estimated. dˆ is the estimated probability of choosing a proportional or proportional-allocation rule. Variable

Units

Mean

Std. Dev.

Min

Max

dˆ Households Gini coefficient No. of ejidos Command area Wage Irrigation supply Government-constructed

probability no. % no. ha. pesosrday 1000 m3 Ž0,1.

0.65 125 27.2 1.8 454 26.7 1659 0.83

0.39 141 24.6 1.6 940 6.4 5448 0.38

0.0006 15 0 0 16 13.5 0 0

0.9999 676 74.7 8 6014 45 37,500 1

Predicted probability of obserÕing a proportional or proportional-allocation distributiÕe rule. I derived several assertions about the level of canal-maintenance performance in Section 2, many conditional on the presence of a particular distributive rule. However, I cannot include the observed distributive rule on the right-hand side of the performance equations since the observed rule is endogenous. Therefore, I include the predicted probability of observing a proportional or proportional-allocation rule. The results of a logit model of rule choice are shown in Table 5. The model predicts, for each of the surveyed systems, the probability that the system will adopt either the proportional or proportional-allocation distributive rule, rather than the equal-division rule. Unidades that have adopted either the proportional or proportional-allocation rule are collapsed into a single category for

Table 5 Results of a logit model predicting the choice of a proportional water-allocation rule Each of the independent variables has been normalized with mean zero and standard deviation equal to one. Source: Dayton-Johnson Ž2000.. Log-likelihoodsy11.83

N s 48, x 2 Ž7. s 38.73, Prob.) x 2 s 0.0000, Pseudo-R 2 s 0.62

Variable

Coefficient

Std. error

t-ratio

Gini No. of households No. of ejidos WUA age Water depth Ratio of smallest parcel to wage Lined share of canals Constant

2.8839 2.1657 y0.1890 1.6156 y1.0819 0.2344 0.8775 1.7708

1.0879 2.5888 1.3329 0.9087 0.8765 1.7506 0.6294 1.1951

2.65 0.84 y0.14 1.79 y1.23 0.13 1.39 1.48

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the empirical work. This is justified by the reasons given in Section 2.6: proportional- and proportional-allocation-rule systems have similarly complex rules and high transaction costs relative to the equal-division rule. There is a also practical reason. Only eight systems have chosen the proportional rule, a very small number in a sample of 48. The single system that adopted the proportionalcost-sharing rule is dropped from the analysis. Thus, the predicted probability is the estimated likelihood that a given system will adopt proportional water-allocation arrangement.11 Number of households. As noted in Section 2.2, Olson Ž1965. posits that the level of collective action is declining in the number of group members; my model predicts that there is no effect under the equal-division or proportional rule. Under the proportional-allocation rule, group size affects cooperative effort, although the sign of the effect is indeterminate. In addition to including the number of households that are members of the water users’ association, I also interact that number with the predicted probability dˆ : a coefficient on this interaction term significantly different from zero is consistent with my model. Economic inequality (Gini coefficient calculated on the basis of landholding in the reserÕoir’s command area). Section 2 illustrated that the relationship between inequality and canal-cleaning performance under the frequently observed proportional-allocation rule is complicated. The sign of this effect must be established empirically. Accordingly, I include both the Gini coefficient and its square as right-hand-side variables, in order to capture the possibility of a U-shaped relationship. I also include an interaction term between the predicted probability dˆ of adopting a proportional or proportional-allocation rule and the Gini coefficient in case the effect of inequality on cooperation is mediated by the rule in place. ŽSuch an effect is suggested by Proposition 2.. Number of ejidos. On average, over 80% of the households in the irrigation system are ejidatarios, members of an ejido Žthat is, beneficiaries of the agrarian reform.. The irrigation systems studied here frequently straddle more than one ejido: I hypothesize that performance in such systems will be worse, ceteris paribus, than in those systems where all users are from a single farming community.12

11

If crop output is a concave, rather than linear, function of water, then this collapsing of categories is less tenable, as a referee has pointed out. Diminishing marginal productivity of water implies that aggregate crop output will be higher under proportional water allocation than under equal division. Households with small landholdings derive a smaller return from their equal share of the effective water supply than do households with larger landholdings. 12 Frequently, all or most members of an ejido have equal-sized plots, but different ejidos have a different plot size. Thus, it might be supposed that as a measure of social heterogeneity, the number of ejidos is merely capturing the economic heterogeneity of different asset sizes among water users from different ejidos. However, the correlation between the number of ejidos represented in the water users’ association and the Gini coefficient based on landholding size is only 0.32.

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ReserÕoir command area (hectares). In Section 2, I showed that there should be no wealth effect of increasing the mean irrigated parcel size. Controlling for the number of households, I expect no significant effect of command-area size Local wage (pesos per day). This is a proxy for the unit cost of cooperation c: for many farmers, it is the opportunity cost of time spent cleaning canals, while for farmers who hire laborers to do their canal-cleaning, it is the direct cost. From Proposition 1, I expect that this will be negatively associated with performance. Irrigation supply (thousands of cubic meters). Irrigation supply measures the water available in the reservoir at the beginning of the irrigation season, not the water available at the field intakes. From Proposition 1, I expect this to be positively associated with canal-cleaning performance. GoÕernment-constructed system. This is an indicator variable equal to one if the government constructed the system infrastructure, and zero otherwise. Where government agents have a higher level of involvement, farmers are more likely to learn about more profitable crops and improved seed varieties, about more lucrative marketing opportunities, and about government-sponsored support programs, should they exist. Thus, I expect government support of the water users’ association in general to raise the marginal return to cooperative effort, and to be positively associated with system performance. However, ‘‘government support’’ could be endogenous: better-performing systems might attract government involvement, or only truly disastrous systems might receive attention. Therefore, I include this limited but exogenous indicator of government support, which I expect to be positively associated with both measures of performance.13 ŽSome writers believe that government involvement weakens the incentive toward cooperative effort among resource users, as in the evaluation of Byrnes Ž1992. of assistance to collective Pakistani watercourses, where collective effort declined following the program.. In the following sections, I report the results of the models of canal-cleaning performance. The use of the predicted probability dˆ of observing a proportionalrproportional-allocation rule as an explanatory variable is not entirely appropriate in the ordered-logit model, which is non-linear; accordingly, I also run least-squares regressions with the same explanatory variables, treating the performance indicators as if they were continuous variables. It is appropriate to include the estimated probabilities dˆ in a linear regression, but because the dependent variable is categorical, the errors will not be normally distributed. Thus, I report the results of both the ordered-logit and least-squares models; fortunately, the sign 13

The alternative to government construction is not user construction: unlike the cases of farmermanaged irrigation systems in other latitudes ŽBacdayan, 1980; Lewis, 1980; Athukorale et al., 1994; Yoder, 1994., there are no examples of irrigation systems in my sample wholly constructed by the water users. Many of the government-constructed systems were built in partnership with the local farmers, who were often paid for their labor. The systems not constructed by the government were built by large land-holders — hacendados — in the years before the agrarian reform.

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and magnitude of the estimated coefficients are similar for both models. The interpretation of results is based on the ordered-logit models. 3.1. Maintenance of canal side-slopes Table 6 presents the results of estimation of the ordered-logit and least-squares models of side-slope definition. The relative magnitudes and signs of the coefficients are similar between the two models, with two exceptions: the estimated coefficient on the Gini term is positive in the ordered-logit model, and negative in the least-squares regression; and the estimated coefficient on the interaction between dˆ and the Gini coefficient is negative in the ordered-logit model, and positive in the least-squares model. ŽThese two exceptions are not independent, of course.. The consistency between the two sets of results suggests that the potential problems of the modeling strategy discussed above are not serious. The following coefficients reported in Table 6 are significant at or above the 85% level.

Table 6 Results of two statistical models of the definition of side-slopes The dependent variable is a three-level ordered qualitative variable Ž‘‘good’’, ‘‘fair’’, ‘‘poor’’. based on a canal inspection of each irrigation system. The two left-most columns of numbers report results of an ordered-logit model; the two right-most columns of numbers report results of least-squares regression on the same set of explanatory variables. dˆ is the estimated probability of choosing a proportional or proportional-allocation rule. Dependent variablesdefinition of side-slopes Variable

No. of households Gini coefficient Gini squared No. of ejidos Command area Wage Irrigation supply Government-constructed

dˆ =households dˆ =Gini dˆ Constant

Ordered logit

OLS

Coefficient

t-Ratio

Coefficient

t-Ratio

y0.0107 0.0087 0.0014 y0.6916 0.0023 y0.1123 y0.0004 1.4298

y0.7 0.1 1.2 y2.3 1.1 y1.3 y1.5 1.8

y0.0044 y0.0210 0.0004 y0.1774 0.0005 y0.0218 y0.0001 0.4604

y0.8 y0.5 0.6 y1.9 0.9 y0.9 y1.1 1.5

0.0133

0.8

0.0049

0.8

y0.1016

y0.7

0.0012

0.0

0.8587

0.5

N s 48 x 2 Ž11. s11.88 Prob.) x 2 s 0.373 Pseudo-R 2 s 0.1228 log likelihoodsy42.4

0.2034 0.292 2.8221 3.5 N s 48 F Ž11,36. s 0.8 Prob.) F s 0.6407 R 2 s 0.1961 R2 sy0.0495

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Table 7 Marginal effect of changes in independent variables on side-slope definition The marginal effect is evaluated at the mean value of the independent variables, and the full effect of group size, inequality, and the choice of distributive rule account for interactions and squared terms, as described in the text. dˆ is the estimated probability of choosing a proportionalrproportional-allocation rule. Variable

Marginal effect Ž%.

Full effect Ž%.

No. of households Gini coefficient Gini squared No. of ejidos Command area Wage Irrigation supply Government-constructed

y0.0702 0.0571 0.0092 y4.5380 0.0151 y0.7369 y0.0026 9.3818

y0.0139 y0.1238

dˆ =households dˆ =Gini dˆ

y0.6667

0.0873 5.6344

y1.5626

Ø The effect of an increase in the number of ejidos, an index of social heterogeneity, is large and negative, confirming expectations. ŽThe level of significance is 97.9%.. The marginal effect of an additional ejido among the group members reduces the probability that side-slope maintenance increases one level by 4.5%. Ø Irrigation supply has a negative, though very small, effect on side-slope maintenance, contrary to expectations. ŽThe level of significance is 86%.. The marginal effect is y0.003%. Ø If the irrigation system was constructed by the government, this has a positive and very large impact on side-slope maintenance. ŽThe level of significance is 92.4%.. The marginal effect is 9.4%. In part, this captures the fact that the lined share of the canal network is higher among such systems, and thus the condition of canal side-slopes is better practically by definition.14 Table 7 reports the full effects of group size, inequality, and the choice of distributive rule, accounting for the inclusion of interaction and squared terms on the right-hand side of the estimated equations. I calculate the full effect of the number of households as: f Ž xXbˆ . bˆ HH q bˆd HH mdˆ

ž

/

Ž 5.

where: f ŽP. is the density function of the logistic distribution, evaluated at the vector xX of mean values of the independent variables; bˆ HH is the estimated 14

Among the 29 government-constructed systems, the lined share of the canal network is 36%, while among the other systems, the lined share is 5%.

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coefficient on the number of households; bˆd HH is the coefficient on the interaction term between households and the estimated probability dˆ ; and mdˆ is the mean value of the estimated probability dˆ. The direct effect of the number of households on side-slope definition Ž bˆ HH . is negative Žy0.07%.; the full effect, as defined in Eq. Ž5., is negative and smaller Žy0.01%.. The full effect of the Gini coefficient on side-slope maintenance is given by: f Ž xXbˆ . bˆGINI q bˆGINISQ mGINI q bˆd GINI mdˆ

ž

Ž 6.

/

in Table 7, where f ŽP. is defined as above; bˆGINI is the estimated coefficient on the Gini term; bˆGINISQ is the estimated coefficient on the square of the Gini term; mGINI is the mean value of the Gini term; and bˆd GINI mdˆ is the estimated coefficient on the interaction between the Gini coefficient and the estimated probability dˆ, multiplied by mdˆ . Thus, while the direct effect of the Gini coefficient Ž bˆGINI . is positive but small Ž0.06%., the full effect as defined in Eq. Ž6. is negative and approximately twice the magnitude of the direct effect Žy0.12%..

Table 8 Results of two statistical models of the condition of field intakes The dependent variable is a three-level ordered qualitative variable Ž‘‘good’’, ‘‘fair’’, ‘‘poor’’. based on a canal inspection of each irrigation system. The two left-most columns of numbers report results of an ordered-logit model; the two right-most columns of numbers report results of least-squares regression on the same set of explanatory variables. dˆ is the estimated probability of choosing a proportional or proportional-allocation rule. Dependent variables condition of field intakes Variable

Ordered logit

OLS

Coefficient

t-Ratio

Coefficient

t-Ratio

No. of households Gini coefficient Gini squared No. of ejidos Command area Wage Irrigation supply Government-constructed

0.0112 0.1305 0.0051 y0.7392 0.0023 y0.0688 y0.0004 y0.2095

0.7 0.9 2.7 y2.0 1.1 y0.8 y1.3 y0.2

0.0027 0.0378 0.0010 y0.1448 0.0004 y0.0104 y0.0001 y0.0286

0.6 0.9 3.0 y1.8 0.7 y0.5 y0.9 y0.1

dˆ =households dˆ =Gini dˆ Constant

y0.0121

y0.7

y0.0027

y0.5

y0.4814

y2.5

y0.1070

y2.3

7.0442

2.6

N s 40 x 2 Ž11. s19.67 Prob) x 2 s 0.0501 Pseudo-R 2 s 0.2577 log likelihoodsy28.3

1.4267 1.6259 N s 40 F Ž11,28. s1.58 Prob) F s 0.1603 R 2 s 0.3826 R 2 s 0.1400

2.4 2.3

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The estimated full effect, finally, of having chosen a proportional or proportional-allocation rule is: f Ž xXbˆ . bˆd q bˆd HH m HH q bˆd GINI mGINI

ž

Ž 7.

/

where the terms are those defined in Eqs. Ž5. and Ž6., as well as m HH , the average number of households in the surveyed systems. While the direct effect of the proportionalrproportional-allocation rule Ž bˆd ., relative to the equal-division rule, is positive and large Ž5.6%., the full effect, as defined in Ž7., is negative and a fraction of the absolute magnitude Žy1.6%.. 3.2. Condition of field intakes Table 8 reports the results of the ordered-logit and least-squares models of the condition of field intakes; Table 9 gives the marginal effect of each independent variable, evaluated at the vector xX of mean values of the independent variables, on the estimated probability. The signs of the estimated coefficients of the ordered-logit and least-squares models are the same, with one exception: the coefficient on the predicted probability dˆ of adopting a proportional or proportional-allocation rule is negative and insignificant in the ordered-logit results, and positive Žand significant. in the regression results. The following coefficients in Table 9 are significant at or above the 95% level. Ø The coefficient on the square of the Gini term is positive. ŽThe level of significance is 99.2%.. The marginal effect is 0.13%. This indicates that the direct effect of inequality on field-intake maintenance — not mediated by the choice of distributive rule — is larger at higher levels of inequality.

Table 9 Marginal effect of changes in independent variables on field-intake maintenance The effect is evaluated at the mean value of the independent variables, and the full effect of group size, inequality, and the choice of distributive rule account for interactions and squared terms, as described in the text. dˆ is the estimated probability of choosing a proportional or proportional-allocation rule. Variable

Marginal effect Ž%.

No. of households Gini coefficient Gini squared No. of ejidos Command area Wage Irrigation supply Government-constructed

0.2759 3.2148 0.1256 y18.2097 0.0567 y1.6948 y0.0099 y7.1563

dˆ =households dˆ =Gini dˆ

y11.8590

Full effect Ž%. 0.0834 y1.0293

y0.2981 173.5293

y186.1150

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Ø Social heterogeneity — the number of ejidos represented among water users’ association members — has a negative impact on field-intake maintenance, as expected. The magnitude of the coefficient is large. ŽThe level of significance is 95.8%.. The marginal effect is y18.2%. Ø The coefficient on the interaction between the estimated dˆ and the Gini term is large and negative: this supports Proposition 2. ŽThe level of significance is 98.8%.. The marginal effect is y11.9%. The effect of inequality on field-intake maintenance is stronger in those systems with proportionalrproportional-allocation rules. Table 9 gives the full effect of group size, inequality, and the choice of distributive rule on field-intake maintenance. The direct impact of the number of households is positive Ž0.28%., while the full effect, as defined in Eq. Ž5. is less than a third as large Ž0.08%.. The direct impact of the Gini coefficient is positive Ž3.2%.. The effect of the interaction between the Gini and the predicted probability dˆ is negative, and much larger in absolute value Žy11.9%.. The full effect of the Gini coefficient Žas defined in Eq. 6. is negative Žy1.03%.. As in the case of the side-slope model, the full effect of choosing a proportional or proportional-alTable 10 Results of two statistical models of the degree of control of filtration The dependent variable is a three-level ordered qualitative variable Ž‘‘good’’, ‘‘fair’’, ‘‘poor’’. based on a canal inspection of each irrigation system. The two left-most columns of numbers report results of an ordered-logit model; the two right-most columns of numbers report results of least-squares regression on the same set of explanatory variables. dˆ is the estimated probability of choosing a proportional or proportional-allocation rule. Dependent variables control of filtration Ordered logit

OLS

Variable

Coefficient

t-Ratio

Coefficient

t-Ratio

No. of households Gini coefficient Gini squared No. of ejidos Command area Wage Irrigation supply Government-constructed

0.0125 y0.0314 0.0040 y0.6795 0.0047 y0.2392 y0.0003 y0.0992

0.8 y0.2 2.4 y2.3 2.5 y2.4 y0.7 y0.1

0.0031 0.0005 0.0008 y0.1513 0.0011 y0.0573 y0.0001 y0.0089

0.5 0.0 1.8 y1.6 2.0 y2.2 y1.7 y0.0

dˆ =households dˆ =Gini dˆ Constant

y0.0187

y1.1

y0.0047

y0.8

y0.1968

y1.2

y0.0464

y0.8

2.2328

1.0

N s 43 x 2 Ž11. s15.72 Prob) x 2 s 0.1518 Pseudo-R 2 s 0.1784 log likelihoodsy36.2

0.6243 3.6166 N s 43 F Ž11,31. s 0.89 Prob) F s 0.5584 R 2 sy0.2403 R 2 sy0.0293

0.8 4.0

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location rule is negative and larger in absolute value than any other coefficient, but this time it is enormous Žy186%.. The direct effect Ž173%. is very nearly equal in absolute value to the full effect. 3.3. Filtration Finally, Table 10 presents the results of the ordered-logit and least-squares models of system performance in the control of water filtration around the canal network. Table 11 gives the marginal effect of each independent variable, evaluated at the vector xX of mean values of the independent variables, on the estimated probability that maintenance increases one level. Here, there is one discrepancy in the signs of the estimated coefficients in the two models: the coefficient on the Gini term is negative in the logit model, and positive in the least-squares regression. These estimated coefficients are significant at a level above 95%. Ø As in the field-intake model, the coefficient on the square of the Gini term is positive. ŽThe level of significance is 98.3%.. The marginal effect is a low 0.002%. Ø As in both the side-slope and field-intake models, a larger number of constituent ejidos has a negative impact on performance Žy0.27%.. ŽThe level of significance is 97.9%.. Ø The effect of the size of the command area is positive Ž0.002%., suggesting a positive wealth effect on performance. ŽThe level of significance is 98.7%.. Ø The effect of the local wage is negative Žy0.09%., as posited in Proposition Ž 1. The level of significance is 98.4%..

Table 11 Marginal effect of changes in independent variables on the control of filtration The effect is evaluated at the mean value of the independent variables, and the full effect of group size, inequality, and the choice of distributive rule account for interactions and squared terms, as described in the text. dˆ is the estimated probability of choosing a proportionalrproportional-allocation rule. Variable

Marginal effect Ž%.

No. of households Gini coefficient Gini squared No. of ejidos Command area Wage Irrigation supply Government-constructed

0.0049 y0.0124 0.0016 y0.26837 0.0019 y0.0944 y0.0001 y0.0392

dˆ =households dˆ =Gini dˆ

y0.0074

Full effect Ž%. 0.0002 y0.0197

y0.0777 0.8816

y2.1545

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The full effect of group size is positive but very small Ž0.0002%.. The full effect of inequality, as measured by the Gini coefficient, is negative Žy0.02%., like the direct effect. The full effect of the choice of a proportionalrproportionalallocation distributive rule is negative and large in absolute value Žy2.16%.. 3.4. The determinants of cooperation Here, I summarize the economic significance of the empirical results presented in Tables 6–11 regarding the determinants of cooperation in the management of these common-pool resources. Social heterogeneity lowers cooperatiÕe effort. In all three cooperation models, social heterogeneity — the number of ejidos represented in the unidad — is associated with lower maintenance levels. Controlling for other factors, costs associated with organizing irrigation across ejido boundaries lower aggregate cooperative effort. Moreover, the quantitative importance of this form of social inequality is larger than that of economic inequality. Economic inequality lowers cooperatiÕe effort. Economic inequality reduces the level of cooperative effort. The full effect of the Gini coefficient is negative in each of the three maintenance models. The components of this full effect, however, do not all have negative signs. The estimated coefficient on the square of the Gini term is positive in all cases, suggesting a positive effect of inequality on canal maintenance that is higher at higher levels of inequality. The estimated coefficient on the interaction between predicted distributive rule dˆ and the Gini term is negative: conditional on having chosen a proportional or proportional-allocation rule, increasing inequality reduces the level of cooperative effort. Higher wages reduce the leÕel of infrastructure maintenance. System maintenance is a labor-intensive activity, and accordingly when the cost of providing cooperative effort rises, ceteris paribus the observed level of repair of the canal network falls. ŽThe effect is statistically significant only in the filtration model.. The largest quantitatiÕe determinant of cooperatiÕe effort is the distributiÕe rule in place at the irrigation system. The full effect of the estimated probability dˆ of having chosen a proportionalrproportional-allocation distributive rule on cooperative effort is quantitatively greater than that of structural characteristics such as group size or heterogeneity. Since many of those same structural characteristics determine the probability of choosing the proportional or proportional-allocation rule, this result means that the indirect effect of these variables via their impact on rule choice is quantitatively larger than their direct effect on cooperation. I will quantify these direct and indirect effect of group size, inequality, and the number of ejidos in Section 3.5 below. Moreover, controlling for other factors, systems that have chosen the proportionalrproportional-allocation distributive rules exhibit lower levels of infrastructure maintenance. Contrary to the model’s prediction, the effect of larger irrigation supply in the most recent crop cycle is negative Žthough not significant.. Proposition 2 states

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Table 12 Total effects of changes in the Gini coefficient, number of households, and number of ejidos on three indicators of canal maintenance These computations include both the direct effect of each variable, and its indirect effect via its impact on the choice of rules. Model

A

B

C

D

E

Effect on dˆ

Effect on dˆ

Indirect effect ŽA=B.

Direct effect

Total effect ŽCqD.

35.85 35.85 35.85

y1.56 y186.12 y2.16

y0.56 y66.71 y0.77

y3.04 y25.31 y0.48

y3.60 y92.02 y1.26

Number of households Side-slopes 26.92 Field intakes 26.92 Filtration 26.92

y1.56 y186.12 y2.16

y0.42 y50.10 y0.58

y1.95 11.73 0.02

y2.37 y38.37 y0.56

Number of ejidos Side-slopes y2.35 Field intakes y2.35 Filtration y2.35

y1.56 y186.12 y2.16

0.04 4.37 0.05

y7.29 y29.26 y43.10

y7.25 y24.88 y0.38

Gini coefficient Side-slopes Field intakes Filtration

that increases in W, by increasing the incremental return to cooperative effort, increase aggregate cooperative effort.15 As I hypothesized, the effect of group size is small Žrelative to the effect of inequality or the choice of rule, for example.. The effect of mean landholding Žcaptured by the coefficient on the reservoir command area. is significant only in the filtration model, but is very small even there. 3.5. Direct and indirect effects on cooperation Some structural characteristics of the unidades that I used to explain the choice of distributive rule in Table 4 are also used to explain the level of maintenance effort in Tables 6–11: namely, the number of households, the Gini coefficient, and the number of ejidos. It remains, thus, to combine the estimation results of the rule-choice and maintenance models to compute the total effect of these three variables on cooperative effort. Inequality Žthe Gini coefficient., for example, has a direct Žnegative. effect on cooperative effort. At the same time, inequality has a Žpositive. effect on the likelihood that the unidad chooses a proportionalrproportional-allocation rule. The proportionalrproportional-allocation rules, meanwhile, have a Žnegative. effect on cooperative effort. Thus, inequality’s indirect effect on 15

This result, however, is consistent with an alternative, U-shaped, relationship between resource scarcity and cooperation.

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cooperation operates via its effect on the choice of distributive rule. Table 12 computes the direct and indirect effects of inequality ŽGini coefficient., group size Žnumber of households., and social heterogeneity Žnumber of ejidos .. The table reveals that economic inequality and group size have larger indirect than direct effects on cooperative effort. ŽBoth the direct and indirect effects of these variables on cooperation are negative.. These variables play a larger role in the arena of institutional design than in season-to-season operation of the irrigation system. Social heterogeneity makes it less likely that a group will select the more poorly performing proportionalrproportional-allocation rules, so that its effect on cooperation is positiÕe. The direct effect of social heterogeneity, however, is negative.

4. Concluding remarks 4.1. Relation to other work on cooperation on the commons The theoretical model of cooperation in this paper analyzes a different problem from other studies of cooperation on the commons. Most of the theoretical literature analyzes the conditions under which resource users like irrigators or fishers voluntarily conserve the resource in the hope of gaining future benefits. Thus, for example, Levhari and Mirman Ž1980. showed that multiple equilibria might exist in a dynamic fishing game, relying on ‘‘trigger strategies’’: one player credibly threatens to overfish forever if the other overfishes. The optimal outcome might be among the equilibria of the fishing game; Benhabib and Radner Ž1992. show that under alternative specifications of the production technology, the optimal outcome is an equilibrium only for certain initial levels of the resource stock. ŽThe possibility of multiple equilibria in the community-grazing context had earlier been raised by Runge Ž1981., who focused on the prisoners dilemma and the assurance-game outcomes.. The application of these repeated-game models to the problem of resource conservation on the local commons is thoroughly explored by Seabright Ž1993.. In all of these cases, non-cooperators cannot be excluded from consuming units of the resource, and can only be punished by future non-cooperative behavior by other resource users. Nevertheless, this strand of the literature made explicit the conditions under which cooperation on the commons was a self-enforcing equilibrium outcome. The synthesis of Ostrom Ž1990. of the case-study literature demonstrated that in practice, non-cooperators and others frequently are excluded from consuming the resource, and that rules are enforced by local sanctions other than the threat of future non-cooperation. ŽBaland and Platteau Ž1998. explore these issues in a microeconomic framework.. The field study of Mexican unidades analyzed in the empirical part of this paper provides an example of a class of resource-using systems governed by local rules. Moreover, the trigger strategies that underlie

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cooperative outcomes in repeated games little resemble the graduated sanctions observed in the field. The empirical and theoretical recognition of local regulatory regimes for the commons raises new issues. What types of governance structures will perform better? What group characteristics are associated with higher levels of cooperation in a setting of local regulation? The present paper, then, seeks to understand cooperation on the commons where local regulation exists. One important question is whether the characteristics associated with cooperative outcomes in the self-enforcing-cooperation framework are also conducive to cooperation in the regulatory framework. For example, the classic impediments of Olson Ž1965. to collective action are group size and inequality. This paper shows that conditional on having successfully formed a water users’ association, Mexican unidades cooperate less in more-unequal environments, but the effect of group size is small. 4.2. Summary of results This paper develops a simple model of individual households’ incentives to provide collective-maintenance effort in a communally owned irrigation system. Monitoring and enforcement of the rules is assumed to be perfect. ŽThis assumption is less likely to be justified in multi-village irrigation systems; there, imperfect monitoring and enforcement likely reduce the level of cooperative effort.. The model shows that the effect of economic inequality is complicated and not monotonic: I give conditions under which an equalizing redistribution of wealth increases the level of cooperative effort in equilibrium, but also show that some redistributions that increase inequality can also increase equilibrium cooperation. Higher output prices and irrigation supply are predicted to favor cooperation, while higher local wages reduce cooperative effort. The distributiÕe rule, a combination of arrangements for maintenance-cost sharing and irrigation-water allocation, also affects the level of maintenance. I include a brief discussion of why some systems might have chosen less-than-optimal distributive rules. The theoretical model is confronted with field data from a study of Mexican farmer-managed irrigation systems known as unidades de riego. I estimate three ordered-logit models of the quality of maintenance of the unidad infrastructure. Three indicators of maintenance — degree of definition of canal side-slopes, state of repair of field intakes, and degree of control of leakage around the canals — are taken to be measures of the level of cooperative effort supplied by unidad members. I find that social heterogeneity, measured by the number of different villages from which the users of a given system are drawn, is consistently and significantly associated with lower levels of infrastructure maintenance. Inequality in landholding has a negative, though complicated, effect on maintenance. Having chosen a distributive rule that allocates irrigation water to households in proportion to landholding size likewise has a negative effect on observed maintenance.

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Acknowledgements This paper is based on a chapter from my doctoral dissertation in economics from the University of California, Berkeley. Thanks are due to Pranab Bardhan, Charles Clarke, Alain de Janvry, Juan Pablo Flores Perez, Sam H. Johnson III, ´ Matthew Rabin, and two anonymous referees. The research received generous financial support from the MacArthur Foundation’s Research Network on Inequality and Economic Performance. References Athukorale, K., Merrey, D.J., 1994. Effectiveness of non-government organizations in developing local irrigation organizations: a case study from Sri Lanka, IIMI Country Paper, Sri Lanka, No. 12 ŽInternational Irrigation Management Institute, Colombo, Sri Lanka.. Bacdayan, A.S., 1980. Mountain irrigators in the Philippines. In: Coward, E.W. Jr. ŽEd.., Irrigation and Agricultural Development in Asia: Perspectives from the Social Sciences. Cornell Univ. Press, Ithaca, pp. 172–185. Baland, J.-M., Platteau, J.-P., 1998. Wealth inequality and efficiency in the commons: ii. The regulated case. Oxford Economic Papers 50, 1–22. Banerjee, A., Mookherjee, D., Munshi, K., Ray, D., 1997. Inequality, control rights and efficiency: a study of sugar cooperatives in Western Maharashtra, Discussion Paper No. 80, Institute for Economic Development, Boston University. Benhabib, J., Radner, R., 1992. The joint exploitation of a productive asset: a game-theoretic approach. Economic Theory 2, 155–190. Bergstrom, T.C., Blume, L., Varian, H., 1986. On the private provision of public goods. Journal of Public Economics 29, 25–49. Byrnes, K.J., 1992. Water users associations in World Bank-Assisted irrigation projects in Pakistan, Technical Paper No. 173 ŽThe World Bank, Washington, DC.. Dayton-Johnson, J., 1999. Irrigation organization in Mexican unidades de riego: results of a field study. Irrigation and Drainage Systems 13, 55–74. Dayton-Johnson, J., 2000. Choosing rules to govern the commons: a model with evidence from Mexico. Journal of Economic Behavior and Organization, forthcoming. Jodha, N.S., 1986. Common property resources and rural poor in dry regions of India. Economic and Political Weekly 21, 1169–1181. Johnson, R.N., Libecap, G.D., 1982. Contracting problems and regulation: the case of the fishery. American Economic Review 72, 1005–1022. Kanbur, R., 1991. Heterogeneity, distribution and cooperation in common property resource management, background paper for the 1992 World Development Report, The World Bank. Lam, W.F., 1998. Governing Irrigation Systems in Nepal: Institutions, Infrastructure, and Collective Action. ICS Press, Oakland, CA. Levhari, D., Mirman, L.J., 1980. The great fish war. Bell Journal of Economics 11, 244–322. Levine, G., 1982. Relative water supply: An explanatory variable for irrigation systems, The Determinants of Irrigation Project Problems in Developing Countries, Technical Report No. 6 ŽCornell and Rutgers Universities, Ithaca, NY, and New Brunswick, NJ.. Lewis, H.T., 1980. Irrigation societies in the Northern Philippines. In: Coward, E.W. Jr. ŽEd.., Irrigation and Agricultural Development in Asia: Perspectives from the Social Sciences. Cornell Univ. Press, Ithaca, pp. 153–171. Olson, M., 1965. The Logic of Collective Action: Public Goods and the Theory of Groups. Harvard Univ. Press, Cambridge, MA, Harvard Economic Studies No. 124.

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