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Testing Between Competing Theoriesof Reverse Share Tenancy
Marc F. Bellemare∗
July 12, 2007
Abstract
Reverse share tenancy, i.e., sharecropping between a poor landlordand a rich tenant, is common throughout the developing world. Yetit can only fit the canonical principal-agent model of sharecroppingunder specific circumstances. This paper develops and tests betweenthree theoretical explanations for reverse share tenancy based respec-tively on (i) risk-aversion on the part of both the landlord and thetenant; (ii) asset risk, or weak property rights; and (iii) limited liabil-ity. Survey data from Madagascar offer strong support for the assetrisk hypothesis, pointing to the need to broaden the canonical share-cropping model to account for reverse share tenancy.
JEL Classification Codes: D86, O12, Q12, Q15.
∗Assistant Professor of Public Policy and Economics, Terry Sanford Institute of PublicPolicy, Duke University, 201 Science Drive, Box 90239, Durham, NC, 27708-0239, (919)613-7405, [email protected].
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1 Introduction
Sharecropping, an agrarian contract by which a landlord leases out land toa tenant in exchange for a share of the crop, has been studied by economistsever since Adam Smith’s The Wealth of Nations. Almost two and a halfcenturies later, the canonical explanation for the existence of sharecropping,following Cheung (1969a), Stiglitz (1974) and Newbery (1977), is that sharetenancy matches a relatively richer landlord, whose comparative advantagelies in risk-bearing, with a tenant whose comparative advantage lies in la-bor monitoring. By trading off incentives and risk-sharing, sharecropping candominate both fixed rent contracts that are considered too risky by the ten-ant and wage contracts that predictably lead to underprovision of effort bythe laborer.1
There nevertheless exists situations of reverse share tenancy,2 in which apoor, presumably risk-averse landlord contracts with a rich, presumably risk-neutral tenant on shares. Such situations do not fit the canonical model ofsharecropping because the poorer landlord no longer holds comparative ad-vantage in risk-bearing over the tenant, a situation in which the principal-agent model predicts a fixed rent contract. Indeed, few of the extant modelsof sharecropping are consistent with the oft-observed phenomenon of reverseshare tenancy.3
In this paper, three theoretical explanations are presented that are consis-tent with both reverse share tenancy and traditional sharecropping contracts.The first model simply the canonical risk-sharing explanation in which both
1Another strand in the literature on sharecropping is that on transactions cost, whichstarted with Cheung (1968, 1969b) and whose best empirical representations are a pair ofpapers by Allen and Lueck (1992, 1993) looking at US farm data. The transactions costapproach to modeling sharecropping contracts assumes that the landlord can enforce theoptimal level of effort, making sharecropping first-best.
2A distinction is made between “reverse share tenancy” and “reverse tenancy”, sincethe latter term could refer to both fixed rent and sharecropping contracts.
3Worldwide statistics on the prevalence of reverse share tenancy are unavailable, butsuch statistics are presented below for the empirical application at hand. Reverse tenancyhas received some attention due to its prevalence in Lesotho (Lawry, 1993), South Africa(Lyne and Thomson, 1995), Eritrea (Tikabo and Holden, 2003), Ethiopia (Little et al.,2003; Bezabih, 2007), Bangladesh (Pearce, 1983), Malaysia (Pearce, 1983), India (Pearce,1983; Singh, 1989), and the Philippines (Roumasset, 2002).
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parties are risk-averse. In this case, sharecropping can emerge as the optimalcontract even when the landlord is poorer than the tenant. The second modelexplains sharecropping as the result of asset risk, or weak property rights:assuming that the strength of the landlord’s claim on her land is an increas-ing function of the share of the crop she receives as rent – a situation that isnot unlikely in places where property rights are weak or insecure – she mightchoose to offer her tenant a sharecropping even though such a contract wouldpredictably lead to moral hazard.4 Finally, the third model, due to Ghatakand Pandey (2000), explains sharecropping as the result of limited liability:if the landlord expects her tenant’s limited liability constraint to bind (i.e.,if it is likely that the tenant will default on paying the cash rent), and ifthe tenant can choose among various techniques that differ in their expectedyields and variances, the landlord will choose a sharecropping contract inorder to mitigate the tenant’s risk-taking behavior.5
After presenting these competing theoretical explanations for reverse sharetenancy, this paper tests them empirically using field data from Lac Alao-tra, Madagascar’s most important rice-producing region. In Lac Alaotra,37 percent of plots are under some form of land tenancy (i.e., fixed rent orsharecropping), and 24 percent of plots are sharecropped. In addition, reversetenancy (a precise definition of which is given in section 5.3 below) occurson almost 19 percent of plots, and over 12 of plots are under reverse sharetenancy.6 The data strongly support the asset risk hypothesis, indicating theneed to broaden the canonical model to account for reverse share tenancy.
This paper thus offers a threefold contribution to the literature. First, andof most general interest, it sheds light, both theoretical and empirical, on arelatively common phenomenon that has so far been ignored by developmenteconomists, as described above. Second, this paper contributes to both theempirical contracting literature and the empirical sharecropping literatureby testing whether observed contracts correspond to the predictions of the
4This special case of the adverse possession (Shavell, 2004; Posner, 2007) rule for landis empirically motivated and discussed at length in section 2.2 below.
5Although the limited liability constraint is less likely to bind for richer tenants, section2.3 discusses how even if the average tenant household liquidated all of its assets, it stillwould not be able to afford the cash rent.
6All estimates are significant at the 1 percent level. These statistics are probability-weighted means, as described in section 4.
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theory rather than by testing whether agents respond to incentives (Pren-dergast, 1999).7 As such, it is most closely related to two recent papers: oneby Dubois (2002), who develops a dynamic principal-agent model in whichlandlords choose sharecropping agreements in order to trade off moral haz-ard and incentives to overuse land; and the other by Pandey (2004), whotests whether the principal-agent model accurately predicts how sharecrop-ping contracts change with technology. Finally, by finding that insecure landrights motivate the emergence of sharecropping in Lac Alaotra, this papercan inform land policy in Madagascar and in other places with similar fea-tures. As such, this paper is perhaps closest in spirit to recent works byMacours (2004), who shows how heterogeneity among ethnic groups com-bined with weak enforcement of property rights causes landlords to contractwith partners from the same ethnic group; Macours et al. (2004), who showhow insecure property rights cause landlords to only lease out to a restrictedcircle of acquaintances; and Conning and Robinson (2007), who develop andtest a general equilibrium model of agrarian organization and property rights.
The rest of the paper follows is organized as follows. Section 2 presentsthe three theoretical models of sharecropping described above. In section3, the empirical framework and identification strategy is discussed. Section 4presents the survey methodology as well as descriptive statistics for the dataused in the empirical application. In section 5, the estimation results arepresented and analyzed, along with a number of robustness checks. Section6 concludes and briefly discusses implications for policy.
2 Theoretical Framework
2.1 Standard Model and Risk-Sharing Hypothesis
Consider the canonical model of sharecropping. A principal whose utilityfunction is V (·), with V ′ > 0 and V ′′ ≤ 0, contracts with an agent whose
7Following Marshall (1920), the moral hazard problem associated with sharecroppingbecame known as Marshallian inefficiency. For the most part, the empirical literature onsharecropping has aimed at determining whether agents indeed do respond to incentives insharecropping contracts. Notable contributions include Bell (1977), Shaban (1987), Laffontand Matoussi (1995), Pender and Fafchamps (2006), and Arcand et al. (2007). In mostcases, the null hypothesis of no moral hazard is in favor of the alternative hypothesis ofMarshallian inefficiency.
4
utility function is U(·), with U ′ > 0 and U ′′ ≤ 0. Assume that the princi-pal and the agent’s utility functions both exhibit decreasing absolute riskaversion (ARA). The principal hires the agent to exploit a plot of land andproduce output q ∈ [q, q]. The level of output is stochastic, and its realiza-tion depends on the effort of the agent, e ∈ E. Both output and effort arelinked through the probability density function f(q|e), which describes thelikelihood of observing output level q given effort level e. The agent’s payofffrom accepting the contract offered by the principal is additively separablein the utility derived from the contract and in the cost of effort, which is rep-resented by the twice continuously differentiable function ψ(e), with ψ′ > 0and ψ′′ > 0.
As in the standard principal-agent model (Bolton and Dewatripont, 2005),the principal must solve the following problem by offering a contract {w(q)}to the agent:
maxw(q)
∫ q
q
V [q − w(q)]f(q|e)dq, subject to (1)
∫ q
q
U [w(q)]f(q|e)dq − ψ(e) ≥ U (IR) (2)
e ∈ argmaxe∈E
{∫ q
q
U [w(q)]f(q|e)dq − ψ(e)
}(IC), (3)
where the first constraint is the agent’s individual rationality (IR) constraintand the second constraint is his incentive compatibility (IC) constraint. As-sume that the agent’s maximization problem has a unique solution. Since hisutility is the sum of concave functions, one can then apply the first-orderapproach (Rogerson, 1985) and replace IC by its first-order condition (IC’).The principal’s problem then becomes
maxw(q)
∫ q
q
V [q − w(q)]f(q|e)dq, subject to (4)
∫ q
q
U [w(q)]f(q|e)dq − ψ(e) ≥ U (IR) (5)
∫ q
q
U [w(q)]fe(q|e)dq − ψ′(e) = 0 (IC’), (6)
5
where fe(q|e) = ∂f(q|e)∂e
. Forming the Kuhn-Tucker maximization problem anddifferentiating inside the integral sign with respect to w(q) and the multipliersassociated with each constraint yields the following first-order conditions:
−V ′[q − w(q)]f(q|e) + λU ′[w(q)]f(q|e) + µU ′[w(q)]fe(q|e) = 0 (7)
λ{U [w(q)]f(q|e)dq − ψ(e)− U} = 0 (8)
µ{U [w(q)]fe(q|e)dq − ψ′(e)} = 0 (9)
Assuming for now that the multipliers λ and µ are both positive, i.e., assum-ing that the IR and IC’ constraints both bind, rearranging the first-ordercondition with respect to w(q) yields
V ′[q − w(q)]
U ′[w(q)]= λ + µ
fe(q|e)f(q|e) , (10)
a familiar result in contract theory which summarizes the trade-off betweenrisk-sharing and incentives. If the IC’ constraint does not bind, i.e., if µ = 0,implying no moral hazard, then the ratio of marginal utilities of the princi-pal and the agent is constant and equal to λ, and the principal offers a wagecontract w which the agent accepts. If, however, the IC’ constraint binds,i.e., if µ > 0, then one either observes a sharecropping contract or a fixedrent contract.
This paper focuses on linear contracts, i.e., contracts of the form w(q) =aq + b, where a ∈ [0, 1] is the share of the crop that goes to the agent, andb ∈ R is a side payment from the principal to the agent, i.e., a fixed rent if b isnegative, and a fixed wage if b is positive. The reason for doing so is twofold.First, landlords and tenants overwhelmingly tend to use linear sharecroppingcontracts in practice, as is the case in the empirical application in the sec-ond part of this paper. Second, behavioral evidence suggests that individualstend to use heuristics in order to reduce complex decision-making problemsinto tractable ones, and the use of linear contracts represents either the useof such a heuristic or an example of bounded rationality (Simon, 1957), adiscussion of which is beyond the scope of this paper.8
8Holmstrom and Milgrom (1987) have identified conditions under which a linear con-tract is optimal.
6
Differentiating equation 10 with respect to q yields
w′(q) =µ(U ′)2 d
dq
[fe(q|e)f(q|e)
]− V ′′U ′
−V ′′U ′ − U ′′V ′ , (11)
which is the slope of the contract w(q) = aq + b. In other words, w′(q) is theshare of the crop that goes to the agent as his payment for exploiting theland, i.e., a. Since the side payment parameter b enters the contract linearly,the principal will adjust it in order to make the agent’s IR constraint bind(Stiglitz, 1974).
Assume now that both the principal and the agent are risk averse, i.e., V ′′ < 0and U ′′ < 0. Assume further that d
dq
[fe(q|e)f(q|e)
] ≥ 0, i.e., the monotone likelihood
ratio property holds. Then, w′(q) > 0, i.e., the agent gets a strictly positiveshare of output q.
Multiplying each term of the numerator and each term of the denominatorin equation 11 by U ′V ′ yields
w′(q) =µU ′
V ′ddq
[fe(q|e)f(q|e)
]+ RL
RL + RT
, (12)
where RL = −V ′′V ′ and RT = −U ′′
U ′ are the Arrow-Pratt coefficients of absoluterisk-aversion of the principal and the agent, respectively. Given equation 12,the following result obtains.
Proposition 1 (Impossibility Result) Under the assumptions made sofar, reverse share tenancy is impossible. That is, when the principal is risk-averse and the agent is risk-neutral, one observes a fixed rent contract.
Proof See appendix A.
This is the prime motivation behind this paper: whereas reverse share tenancyhas been observed the world over, economic theory has yet to explain suchcontracts. Moreover, Proposition 1 shows that under the standard principal-agent model, sharecropping is impossible between a sufficiently poor principaland a sufficiently rich agent, i.e., the model needs additional assumptions inorder for reverse share tenancy to be possible. Before presenting theoreticalexplanations for reverse share tenancy, however, one can state the following.
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Proposition 2 (Standard Optimal Contract) Given the above assump-tions: (i) If the principal is risk-neutral and the agent is risk-averse, theprincipal offers a sharecropping contract; and (ii) under some conditions, theslope of the contract is monotonically decreasing in the relative degrees of ab-solute risk aversion of the agent and the principal. Thus, if the principal andthe agent are both risk-averse, the principal offers a sharecropping contract.
Proof See appendix A.
Both Propositions 1 and 2 make intuitive sense. First, under the present as-sumptions, one should not expect a sharecropping agreement to be signedbetween a risk-averse principal and a risk-neutral agent since in such a case,the principal no longer has a comparative advantage in risk-bearing, whichnow resides with the agent. Therefore, since the agent also has a comparativeadvantage in terms of monitoring labor effort, one should expect the agentto be full residual claimant on the output. Second, that a risk-averse agent isoffered a sharecropping contract by a risk-neutral principal is a well-knownresult of contract theory (Bolton and Dewatripont, 2005) and of developmentmicroeconomics (Stiglitz, 1974). Third, the monotonicity of the contract slopein the relative degree of absolute risk-aversion of the parties to the contractis non-trivial, since it clearly establishes the trade-off between insurance andincentives: the more risk-averse the principal is relative to the agent, thehigher the incentives faced by the agent, and vice versa.
Finally, the above framework allows one to derive the first testable impli-cation, i.e., when both parties to the contract are risk-averse, sharecroppingcan emerges as the optimal contract. This will be the risk-sharing hypothesis,against which the other theoretical explanations will be tested. This is thefirst candidate explanation for the existence of reverse share tenancy con-tracts. If, however, the tenant is risk-neutral, then one needs to broaden thestandard framework to accommodate the existence of reverse share tenancy.The two following sub-sections do so.
2.2 Asset Risk Hypothesis
This section develops a model in which sharecropping can emerge as theoptimal contract when the principal is risk-averse and the agent is risk-neutral. This result hinges upon the asset risk assumption, i.e., the stronger
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the agent’s incentives, the weaker the principal’s subsequent claim to thecontracted plot of land. This is empirically justified in Madagascar by localcustoms, which hold that taking the risk inherent in agricultural productionas well as taking possession of the fruits of the land both ensure continuedaccess to the land, much as direct cultivation of the land does under moretraditional property rights. This special case of the adverse possession rule(Shavell, 2004; Posner, 2007) was mentioned landowners in Lac Alaotra dur-ing preliminary visits to the field. Under such conditions, the incentive toreduce asset risk motivates (reverse) share tenancy. Note that this closelyresembles “use it or lose it” water rights in the Western United States (Mil-grom and Roberts, 1992).
Note that this paper does not study the choice between a rental contractand hiring an agent on a fixed wage. Indeed, it would simply suffice to as-sume that the principal is sufficiently liquidity-constrained to rule out suchcases. Alternatively, and just as important, there is an important empiricaldifference between leasing out a plot of land on a fixed rent or a sharecrop-ping contract and exploiting one’s own plot using wage laborers, which isdiscussed further in section 3.1.
The following model is closely related to that of Dubois (2002), with animportant difference: in Dubois’ model the agent’s effort could influence fu-ture production possibilities, whereas here the terms of the contract directlyaffect the principal’s land value. Let the production function be linear ho-mogeneous with respect to land (Otsuka et al., 1992), and let ht be the plotarea. For a fixed amount of land, let the production function be such thatqt = νtf(et), where ν is a multiplicative shock with mean equal to one andf(·) is a production function with fe > 0, fee < 0, and f(·) is twice continu-ously differentiable.
Moreover, let ht = s(at)ht−1 +εt and E(ht) = E[s(at)ht−1], where ε is a shockwith mean equal to zero which is assumed to be additive for tractability, ais the share of output that goes to the agent.9 This equation is the law ofmotion for land, and s(·) represents the principal’s claim to the land (or the
9Once again, the focus is on linear contracts, both for the reasons mentioned aboveand because the tools of contract theory do not allow one to determine the shape of theoptimal contract in a dynamic setting (Dubois, 2002).
9
strength of her property right), with sa < 0. In addition, assume that thesecond-order effects of a on s(a) are negligible, i.e., saa = 0.
Assuming the principal is risk-averse and the agent is risk-neutral, the agent’sexpected payoff is
atE[νf(et)] + bt − ψ(et). (13)
Then, the principal’s expected payoff is
EU [(1− at)νf(et)− bt], (14)
where U(·) is a bounded von Neumann-Morgenstern utility function. Finally,let U denote the agent’s reservation utility.
The principal’s problem is to solve
v0(h) = maxat,bt
Eνt,εt
∞∑t=0
δtEU [(1− at)νf(et)− bt] (15)
subject to, for all t ≥ 0,
atE[νf(et)] + bt − ψ(et) ≥ U (IR), (16)
et ∈ argmaxe∈EatE[νf(et)] + bt − ψ(et) (IC), and (17)
E(ht) = s(at)ht−1 + εt, (18)
where δ ∈ (0, 1) is the principal’s discount factor and the two constraints arerespectively the agent’s individual rationality and incentive compatibilityconstraints. Applying the first-order approach, one can rewrite the latterconstraint as
atE[νfe]− ψe = 0 (IC’). (19)
The Bellman equation for the above problem is then
v0(h0) = maxa,b
{EU [(1− a)νf(e)− b + δEv0(h1)]
}, (20)
subject to
aE[νf(e)] + b− ψ(e) ≥ U , and (21)
aEνfe − ψe = 0, (22)
where h0 denotes the initial plot area, and h1 = s(a)h0 + ε. Before derivingthe optimal contract, it is necessary to establish the following result.
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Lemma 1 Agent effort is increasing in crop share, i.e., ea > 0.
Proof See appendix A.
In order to solve the Bellman equation, it is necessary to establish the fol-lowing result, which will be useful in substituting for b using the agent’s IRconstraint.
Lemma 2 The side payment is decreasing in crop share, i.e., ba < 0.
Proof See appendix A.
This leaves us with the following expression for the Bellman equation:
v0(h) = maxa
{EU [(1− a)νf(e(a))− b(a)] + δEv0[s(a)h + ε]
}, (23)
The following lemma is the last necessary step in establishing the result ofProposition 3.
Lemma 3 The function v0(·) is strictly increasing.
Proof See appendix A.
Proposition 3 (Asset Risk Optimal Contract) In the presence of assetrisk, sharecropping emerges as the optimal contract between a risk-averseprincipal and a risk-neutral agent.
Proof See appendix A.
The following proposition provides a useful testable implication for appliedwork.
Proposition 4 (Comparative Statics) If the strength of the landlord’sproperty right does not vary with the slope of the contract, the principal offersthe agent a sequence of fixed rent contracts. Moreover, the slope of the opti-mal contract is decreasing in the sensitivity of the strength of the landlord’sproperty right to the slope of the contract.
Proof See appendix A.
Proposition 4 provides an important result: given a data set that featuresenough variation in the perception of the strength of one’s property right
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and in the shape of the contract chosen by the principal, one can test thenull hypothesis that asset risk has no effect on the probability of observinga sharecropping contract relative to the probability of observing a fixed rentcontract. This is the second candidate explanation for the existence of reverseshare tenancy contracts.
2.3 Limited Liability Hypothesis
The model presented here, due to Ghatak and Pandey (2000), assumes risk-neutral agents.10 The agent has a limited liability constraint, i.e., there existsan output threshold below which he cannot repay the principal, and he hastwo choice variables, effort in labor, e ∈ [e, e], where e > e ≥ 0, and a level ofrisk r ∈ [r, r], where r > r ≥ 0. The former variable incorporates Marshallianinefficiency into the model, while the latter incorporates “technical” moralhazard (Basu, 1992).
Before discussing the model, note that intuition suggests that the limited lia-bility constraint is likely to bind for poor tenants only, and that if the tenantis rich, a collateral requirement on the part of the landlord may eliminate thenegative consequences of limited liability. In the data, however, it turns outthat while tenants in reverse tenancy arrangements are significantly wealthierthan their landlords, the value of the average tenant’s wealth is not enoughto cover the monetary value of the rent (either cash or crop) once liquidated.The limited liability model is thus not implausible in the application at hand.
Production requires one unit of land and one unit of labor, respectively ownedby the principal and the agent. Given the agent’s choices of e and r, naturechooses an output q ∈ [q, q]. The distribution function of output is F (q|e, r),and the bounds of the support of q are assumed not to depend on e and r, andthe cumulative distribution function F (·) is twice continuously differentiable.Further,
∂F (q|e, r)∂q
= f(q|e, r), and (24)
∂
∂q
[fe(q|e, r)f(q|e, r)
]≥ 0. (25)
10Assuming that the landlord is risk-averse would only strengthen the conclusions ofthis model.
12
In other words, the monotone likelihood ratio property holds, i.e., an increasein labor effort will result in a new output which first-order stochastically dom-inates the previous output.
As for r, the riskiness of the project undertaken by the agent, the modelassumes that an increase in r causes a mean-preserving spread in the dis-tribution of output. That is, an increase in the level of risk chosen by theagent, holding the effort level constant, causes a mean-preserving spread inthe distribution of output. Thus, an increase in r will symmetrically shiftprobability mass towards the tails of the output distribution, ceteris paribus.
As regards labor effort and risk, the agent incurs a private cost ψ(e, r), whereψ(·) is twice continuously differentiable, ψe > 0, ψr > 0, ψee > 0, ψrr > 0,ψer ≥ 0 and ψ(0, 0) = 0. The principal cannot observe the agent’s provisionof labor effort and his choice of risk. She must thus rely on the realization ofoutput q to obtain information on these two variables.
As in the previous two models, the agent receives aq + b from the contract.Thus, the principal’s and the agent’s incomes from the contract are
yL = min{(1− a)q − b, q}, and (26)
yT = max{aq + b, 0} (27)
Thus, Ghatak and Pandey implicitly assume that the limited liability con-straint binds at q = −b/a. The principal and the agent’s expected payoffsare thus:
UL = E(q)−∫ q
q
[aq + b]f(q|e, r)dq, and (28)
UT =
∫ q
q
[aq + b]f(q|e, r)dq − ψ(e, r). (29)
Letting the agent’s reservation utility be equal to U , it is obvious that theagent’s individual rationality (IR) constraint is that UT ≥ U . The agent’schoice of e and r are given by the following incentive constraints (IC):
−a
∫ q
q
Fe(q|e, r)dq = ψe(e, r), and (30)
13
−a
∫ q
q
Fr(q|e, r)dq = ψr(e, r). (31)
Ghatak and Pandey then characterize the full information benchmark, i.e.,the case in which both effort and risk are contractible. After deriving propo-sitions characterizing what happens when the principal can enforce e and r,they present the following two propositions, which are of interest in studyingreverse share tenancy.11
Proposition 5 When neither e nor r can be enforced by the principal, acontract in which a = 0 cannot be optimal. Thus, the optimal contract issuch that 0 < a ≤ 1. That is, the optimal contract is either a fixed rent or asharecropping contract.
The idea behind the Ghatak and Pandey model, however, is to characterizethe conditions under which sharecropping emerges as the dominant tenurialagreement. Ghatak and Pandey’s last proposition characterizes this.
Proposition 6 When neither e nor r can be enforced by the principal, ifthe distribution of q is less sensitive to changes in e than to changes in r,sharecropping emerges as the optimal contract.
In order to test the limited liability hypothesis, one would only need to testthe null hypothesis that the presence of a limited liability clause has noeffect on the probability of choosing a sharecropping contract relative to theprobability of choosing a fixed rent contract. This is the third candidateexplanation for the existence of reverse share tenancy contracts.
3 Empirical Framework
In order to test three hypotheses presented above against one another, thefollowing empirical strategy is adopted. First, the method proposed by Acker-berg and Botticini (2002) is used to test for the possibility of endogenous (i.e.,non-random) matching between landlords and tenants. Finding little, if any,evidence of endogenous matching, a simple test of whether the landlord’sdecision to lease out and her contract choice decision are correlated is im-plemented using the coefficient of correlation from a bivariate probit with
11The reader interested in the proofs of these propositions is invited to read the originalarticle by Ghatak and Pandey (2000).
14
selection. Since both decision stages turn out to be uncorrelated, univari-ate probits are estimated, i.e., one for the decision to lease out, and one forthe contract choice decision. The following section discusses the identifica-tion strategy adopted in testing between the competing hypotheses presentedabove.
3.1 Identification Strategy
In order to properly test between the above hypotheses, the landlord’s choiceof contract (i.e., an indicator equal to one if she chose a sharecropping con-tract and equal to zero if she chose a fixed rent contract) is regressed onplot-, landlord household-, tenant household-, and contract-level controls aswell as on the following variables of interest: (i) proxies for the landlord’sand the tenant’s levels of risk aversion; (ii) the slope of the landlord’s assetrisk function; and (iii) an indicator equal to one if there is an explicit limitedliability clause in the contract and equal to zero otherwise.
Following Laffont and Matoussi (1995) and assuming decreasing absolute riskaversion (DARA), the landlord and tenant households’ wealth levels are usedas proxies for their levels of income risk aversion.12 Thus the test of the risk-sharing hypothesis proceeds as follows. In the contract choice equation, letβWL
and βWTdenote the regression coefficients on the landlord’s (principal)
and the tenant’s (agent) levels of assets, respectively. To test whether riskmatters for both parties, one can simply test the null hypothesis that H0:βWL
= 0 and βWT= 0 versus the alternative hypothesis that HA: βWL
> 0and βWT
< 0. While this is not a test that the landlord is risk-averse and thetenant is risk-neutral per se, it is the best one can do given that the data donot allow computing Arrow-Pratt coefficients of absolute risk aversion.
Given that the landlord’s optimal choice of contract in the asset risk modeldepends on sa, the slope of the function representing the strength of the land-lord’s claim to her land, rather than on s(a), the value of the strength of herproperty right, the following identification strategy was adopted. The land-lords’ subjective perceptions of asset risk (i.e., r(a) = 1− s(a)) were elicited.Given the contract signed by the landlord with her tenant, the landlord was
12See section 4 for a precise definition of what “wealth” means in the context of thispaper.
15
given 20 tokens and was asked to distribute them between two boxes, onelabeled with “0”, and one labeled with “1”. The landlord was told that thelatter box represented a state of the world where she lost her claim to theland as a result of the contract signed, whereas the former box representeda state of the world where she kept her claim to the land. Data on the land-lord’s hypothetical perception of asset risk under the alternate contract werealso collected.13 This allows computing the discrete change in r(a), due tothe (hypothetical) move from a fixed rent to a sharecropping contract. Todo so, let r(1) and r(0.5) denote the perceived asset risk of a landlord enter-ing a fixed rent or sharecropping contract, respectively, and rh(1) and rh(0.5)denote the hypothetical asset risk of a landlord entering a fixed rent or share-cropping contract, respectively.14 Thus, ra (the inverse of sa) was computedsuch that
ra =∆r(a)
∆a=
(rh(1)− r(0.5)
1− 0.5
)I(a=0.5)(r(1)− rh(0.5)
1− 0.5
)I(a=1)
, (32)
where I(·) is an indicator variable equal to one if the condition betweenparentheses is true and equal to zero otherwise. Note that because a takeson only two discrete values in the data, the functions r(a) and s(a) have nocurvature per se, i.e., raa = saa = 0. This allows one to assume that ra isexogenous to the dependent variable in the contract choice equation below.In addition, recall that da∗/dsa > 0 in the theoretical model of section 2.2,i.e., as the landlord’s claim to the land is strengthened, the likelihood shewill choose a fixed rent contract increases. Since the data relies on ra, i.e., theeffective asset risk (i.e., the inverse of sa) and the dependent variable in thecontract choice equation was coded as a one if a sharecropping contract wasobserved and as a zero if a fixed rent contract was observed, the test becomesa test of the null hypothesis that d(1−a∗)/dra = 0 versus the alternative thatd(1− a∗)/dra > 0, i.e., a test of whether asset risk increases the likelihood ofobserving a sharecropping contract.
13This is simply the landlords’ perception of asset risk were they to sign the alternativecontract. The two asset risk questions were asked in two separate survey instrumentsfielded four months apart. This eliminates the risk of anchoring one answer to the other(Tversky and Kahneman, 1982), thereby eliminating any spurious correlation betweenperceived and hypothetical price risk.
14Note that a = 0.5 in all sharecropping contracts in the data.
16
Finally, as regards the limited liability variable, a dummy variable is usedthat is equal to one if there was an explicit limited liability clause in the con-tract and equal to zero if there was no such clause. The presence of such alimited liability clause was determined by asking landlords whether there wassuch an explicit (i.e., common knowledge) provision in the contract. AlthoughGhatak and Pandey (2000) assume that limited liability is a primitive of theirmodel, and therefore exogenous to contract choice, limited liability is likelyto be determined jointly with contract choice, so one needs to instrument forit. The instrument used here is the number of cultivation techniques availableon the plot other than the one chosen. Indeed, in the Ghatak-Pandey frame-work, the scope for technical moral hazard is non-decreasing in the numberof available cultivation techniques, as is the likelihood of observing a limitedliability clause. In addition, provided the presence of limited liability is con-trolled for in the equation of interest, there is no reason why the number ofother available cultivation techniques should affect contract choice, given thatlimited liability is the mechanism through which it affects contract choice.
4 Data and Descriptive Statistics
The data used in this paper were collected in Lac Alaotra, Madagascar, be-tween March and August 2004. Lac Alaotra lies about 300 km northeast ofAntananarivo, the country’s capital, and is the country’s most importantrice-producing region. Sharecropping being mainly observed on rice plots inMadagascar, it makes sense to choose this region to conduct the first em-pirical studies of share tenancy in Madagascar.15 In addition, since rice isthe staple of Malagasy diet, focusing on the country’s most important rice-growing region may be informative for policy reasons.
The survey methodology was as follows. First, the six communes16 with thehighest density of sharecropping around Lac Alaotra were selected from a2001 commune census conducted by Cornell University in collaboration withMadagascar’s Institut national de la statistique (INSTAT) and Centre na-
15The only other studies of share tenancy in Madagascar were conducted by Jarosz (1991,1994), also in Lac Alaotra, and consist of case studies. This paper is the first to combinesformal theoretical modeling with econometric evidence on sharecropping in Madagascar.
16A commune is an administrative unit that is roughly equivalent to a district in theUnited States.
17
tional de la recherche appliquee au developpement (FOFIFA) (Minten andRazafindraibe, 2003). Then, the two villages with the highest density of share-cropping were chosen in each commune after determining the density of share-cropping in each village by going through communal records. In an effort tooversample sharecropping so as to increase precision, five households knownnot to lease in or lease out land were selected, five households known to leasein or lease out under a fixed rent contract were selected, and 15 householdsknown to lease in or lease out under a sharecropping contract were selectedin each village. All households were from within the sampling frame in eachvillage, and the end result is a sample of 300 selected households.17
For each selected household, plot-, household- and contract-level data werecollected. Household- and (leased-in) plot-level data for the tenants of the300 selected households as well as household-level and contract-level datafor the landlords of the 300 selected households were then collected, whichmakes for a richer data set. A detailed discussion of the survey methodologyis available upon request.
Table 1 presents plot-level summary statistics, and note that L denotes thelandowner. Almost 40 percent of plots are leased out,18 and the average plotcovers 1.3 hectares. The vast majority of plots are in rice paddies, with only21 percent of plots being tanety (hillside plots) and 12 percent of plots beingbas-fonds.19 The average distance between the plot and the landowner’s house(in walking minutes) is about 40 minutes, and over 30 percent of plots havebeen previously owned by the landowner’s family, i.e., passed down throughbequest or intra-family gift. The average number of fady days on the plot forthe landlord is about one day per week, usually Thursday.20
17The estimation results in this paper control for the oversampling of households thatenter sharecropping agreements by incorporating sampling weights. Ideally, one would alsocontrol for the choice-based nature of the sample (Manski and Lerman, 1977). Unfortu-nately, population proportions at the contract-level have never been collected in Mada-gascar, making the choice-based sampling correction impossible to implement.
18These are unweighted descriptive statistics, which explains the slight discrepanciesbetween the numbers presented in tables 1 and 2 and the numbers cited in the introduction.
19In this study, bas-fond refers to a plot located at the bottom of a valley on whichrice is not grown. Although the term bas-fond means rice paddy in the High Plateaux ofMadagascar, it has a different meaning in coastal areas, such as Lac Alaotra.
20Fady roughly translates as “prohibition” or “taboo”. Agricultural work is prohibitedon fady days, both at the individual and at the household level. For an interesting account
18
Turning to household-level covariates, the average household size is a littleover six individuals, and the average household’s dependency ratio is over0.4.21 The average household head is 50 years of age and has about five yearsof formal education and 25 years of agricultural experience. Moreover, ap-proximately ten percent of household heads are female. Finally, the averagehousehold head estimated his opportunity cost of time to be about $0.15 perhour; household income was about 117,000 ariary, or $60 per capita22 in theyear preceding the survey; and the average household has about $150 worthof assets per capita and about $450 worth of working capital .23
Table 2 presents similar descriptive statistics for the sub-sample of rentedplots. Over two-thirds of plots are sharecropped, the average leased out plotcovers a little over one hectare, about 85 percent of contracted plots are riceplots, and the average leased out plot is about 30 walking minutes from thelandlord’s house, i.e., slightly closer than the average plot. Also note thatone fifth of leased out plots were previously owned by the landlord’s familybefore she took possession of her plot.
Comparing landlord (L) and tenant households (T) , household characteris-tics are essentially the same between parties to the contract but landlordstend to be significantly older than their tenants,24 and while tenant house-holds have more working capital than landlord households, the latter have
of the multiple fady observed by the Malagasy, see Ruud (1960). For a study of the effectof fady days on agricultural productivity, see Stifel et al. (2007).
21The dependency ratio is the sum of the number of individuals under 15 and the numberof individuals over 64 divided by the total number of individuals in the household.
22US$1 ≈ 2,000 ariary.23Household income is defined as the sum of the incomes from animal sales, agricultural
and non-agricultural wages, and proceeds from leases of cattle and equipment; householdincome is net of income from land leases to avoid biasing the income value in favor ofthe landlords. The value of the household’s working capital is then defined as the sumof the values of its hoe, harrow, cart, plow, tractor, and small tractor. Finally, the valueof the household’s assets is defined as the sum of the values of its non-productive assets,i.e., house, television, radio, car, and bank account balance. The value of landholdings isomitted because of the near impossibility of obtaining accurate values from respondents.The land sales market is extremely thin in Madagascar, given that sales tend to occur forthe most part in distress situations (Randrianarisoa and Minten, 2001).
24Given that there were only six female tenants in the sample, the tenant gender indi-cator is omitted from estimation.
19
Figure 1: Nonparametric Regression of Contract Choice on Asset Risk.
Kernel regression, bw = 15, k = 6
Grid points−24 40
.655786
.75127
higher incomes and more assets per capita than the former.25 Turning to thevariables of interest, while the measure of the slope of the asset risk functionra should be positive on the basis of the theoretical model of section 2.2, itsmean is negative but not significantly different from zero at the 90 percentconfidence level. In figure 1, however, a nonparametric regression of contractchoice on ra with bandwidth equal to 15 using the Gaussian kernel, showsprima facie evidence in favor of the asset risk hypothesis. Finally, 55 percentof contracts include an explicit limited liability clause. A mean comparisontest shows that the the proportion of limited liability is higher in sharecrop-ping than in fixed rent, offering prima facie evidence in favor of the limitedliability hypothesis as well.
25In section 5.3, comparisons are made between landlords and tenants in the full andreverse tenancy samples and establish that while wealth differences between landlords andtenants are not significant in the full sample, they are significant in the reverse tenancysample. In other words, landlords generally enjoy wealth levels comparable to their tenantsin Lac Alaotra, except in reverse tenancy cases, where tenants are significantly richer thantheir landlords.
20
5 Estimation Results and Analysis
This section presents the estimation results for the estimation sequence out-lined in section 3. It first presents the results of the Ackerberg and Botticini(2002) test of endogenous matching. A bivariate probit with selection is thenestimated in which the first stage models the landlord’s leasing out deci-sion and the second stage models her contract choice decision, conditional onhaving chosen to lease out in the first stage. This model is estimated bothwith and without the Ackerberg-Botticini endogenous matching correction,only to find that there is no difference between both sets of estimated co-efficients. Proceeding with the assumption of no endogenous matching, theresults of a bivariate probit model indicate that both decision stages are un-correlated. This leads to the estimation of univariate probits (i.e., one for thefull sample of land tenancy contracts, one and for the restricted sample ofreverse tenancy), the results of which show that the asset risk hypothesis isstrongly supported by the data. This finding is then confirmed by a series ofrobustness checks.
5.1 Endogenous Matching
Following Ackerberg and Botticini (2002), it is likely that landlords and ten-ants are not randomly matched with one another. If non-random matchingturns out to be true in the data, coefficient estimates for the contract choiceequation are then be biased given the use of imperfect proxies for risk aver-sion. In order to identify whether there may be endogenous matching betweenthe landlords and tenants in the data, the landlord (tenant) household’s levelof assets per capita was regressed on the tenant (landlord) household’s char-acteristics. Table 3 presents the estimation results of a regression of the ten-ant household assets per capita on the characteristics of the principal andher household.26 These results indicate that some characteristics of the prin-cipal are significant in determining the proxy for the agent’s level of riskaversion, so that there may be some endogenous matching. The estimationresults presented in table 3, however, come from an atheoretical regression,and computing correlation coefficients between the tenant household’s level
26In the interest of brevity, the inverse regression (i.e., the regression of the landlordhousehold’s level of assets per capita on the tenant household’s characteristics) is notshown, as it yielded statistically insignificant results: all coefficients were individually in-significant, and the p-value of a test of their joint significance was equal to 0.87.
21
of assets per capita and the landlord household’s characteristics yields nosignificant correlations, even at the 10 percent significance level. It is thusnot clear whether landlords and tenants are truly endogenously matched inthese data.
Still, to control for the possibility of endogenous matching, the method intro-duced by Ackerberg and Botticini was adopted, which consists in estimatinga matching equation using geographical dummies and their interactions withthe principal’s level of risk aversion as instruments for the tenant’s risk aver-sion. Indeed, assuming that the contract choice equation below is correctlyspecified, the market (here, the commune) in which a contract is signed shouldnot causally influence contract choice and can thus be omitted from the con-tract choice equation. Moreover, in these data, the levels of migration areextremely low: in ten out of 12 villages, the number of individuals movingin and out of the village over the last five years was less than ten. It is thushighly unlikely that individuals move from one commune to another on thebasis of expected contract choice given that the transactions costs of movingare prohibitively high and reputations take a long time to form (Platteau,1994a; 1994b).
Table 4 presents the estimation results for the matching equation. Perhapsunsurprisingly, the commune dummies, along with their interaction with theprincipal’s risk aversion proxy, turn out to be jointly significant at the 1 per-cent level, with an F(10,343)-statistic equal to 2.40. The matching equationalso had an adjusted R2 of 0.36, which rules out overfitting.
In order to definitively establish whether there is endogenous matching inthese data, two bivariate probit with selections were estimated for the canon-ical model (i.e., omitting the measure of asset risk and the limited liabilitydummy): a naıve version of the model, and one in which the endogenousmatching correction has been implemented. Before presenting these estima-tion results, however, a discussion of the exclusionary restrictions (i.e., thevariables excluded from the contract choice equation but included in the leas-ing out equation so as to explain selection into being a landlord) is in order.Given that the Ackerberg and Botticini framework excludes commune dum-mies from the contract choice equation, these are de facto included amongthe exclusionary restrictions. Relying on geographical dummies, however, isa somewhat weak strategy, so the landlord’s number of fady days on the plot
22
from is also excluded from the contract choice equation, since the numberof days the landlord cannot work on her plot should have no bearing on thecontract she chooses, but it very likely motivates her decision to lease out theplot. Indeed, if a landlord cannot work on a given plot two days per week,she can avoid bearing the cost of the fady by renting it out.
That said, table 5 uses the results of both bivariate probits (with and withoutthe endogenous matching correction) in computing, for each coefficient, theratio β/βEM , where the numerator is the coefficient estimate from the naıveregression and the denominator is the coefficient estimate from the bivariateprobit with endogenous matching (EM) correction.27 Standard errors werecomputed using the delta method, and the null hypothesis that each coeffi-cient is equal to one was then tested. In no case could it be rejected, so thatit appears that there is only a negligible amount of endogenous matching,which is likely due to the fact that about 65 percent of landlords contractwith kin, and 53 percent of landlords who could choose their tenant reportchoosing the present tenant because of kinship. The rest of this paper thusproceeds under the assumption of no endogenous matching.
5.2 Bivariate Probit with Selection
The next step is to estimate the full model incorporating both the asset riskand the limited liability hypotheses into the canonical model. Before doingso, however, table 6 presents the instrumenting regression for the limitedliability dummy. Note that the instrument for the limited liability dummy(i.e., the number of cultivation techniques available other than the one cho-sen by the tenant) is jointly significant at the 1 percent level, as are the jointcoefficients, and the adjusted R2 measure is equal to 0.11, which rules outoverfitting. In the interest of brevity, these estimation results are not dis-cussed further.
Table 8 presents the estimation results for the bivariate probit with selection.Note first that these estimates were bootstrapped over 250 replications so asto obtain consistent standard errors given the use of fitted value for thelimited liability dummy. Second, note that the exclusionary restrictions arejointly significant at the 1 percent level, with a χ2(6) statistic of 33.51, but
27Both these sets of results are omitted for brevity but are available upon request.
23
that the risk-sharing hypothesis is not, with a χ2(2) statistic of 0.61. Finally,note that the coefficient of correlation between the contract choice and leasingout equations is not significantly different from zero and that its 95 percentconfidence interval is the set (-1, 0.999). As a result, univariate probits forthe contract choice equation are estimated in the remainder of this paper.
5.3 Univariate Probits
In the interest of brevity, the estimation results of a univariate probit for thefirst-stage (i.e., leasing out equation) are not reported. Instead, the focus ofthis section is on full-information maximum likelihood (FIML) instrumentalvariable (IV) probits of the second-stage contract choice equation for thefull sample;28 the restricted sample of reverse tenancy cases; and robustnesschecks based on an alternative definition of wealth and on a different speci-fication.
Table 8 presents estimation results for the full-sample IV probit, i.e., thecontract choice equation estimated on the sample of all land tenancy cases inthe data. Although first-stage estimates are omitted for brevity, the numberof cultivation techniques other than the one chosen by the tenant (i.e., theinstrument for the limited liability dummy) was significant at the 1 percentlevel in the first-stage equation. Moving on to the contract choice equation,one gets to the core result of this paper: ra, the change in asset risk due to achange in the contract, has the expected effect on contract choice and is sig-nificant at the 1 percent significance level. In addition, note that the landlordand tenant’s risk aversion proxies turn out to be jointly insignificant, as isthe limited liability variable, which constitutes a rejection of the risk-sharinghypothesis as well as of the limited liability hypothesis. In other words, inthe full-sample, risk preferences and limited liability do not seem to drivecontract choice, but asset risk does.
Looking at the estimated coefficients for the control variables, first note thatnone of the individual characteristics of the landlord of the tenant are signifi-cant. Irrigated plots, however, are more likely to be leased out on a fixed rentcontract. Finally, the longer a landlord has been contracting with a particu-
28The FIML estimator is used given that Newey’s (1984) two-step estimator cannotaccommodate the use of probability weights.
24
lar tenant, the more likely the landlord is to offer a sharecropping contract.This finding echoes that of Laffont and Matoussi (1995), who interpret itas follows. The longer the landlord and the tenant have been contractingtogether, the more information the landlord has on the tenant’s ability, sothat large departures from the expected level of output can be ascribed toshirking rather than a stochastic shock. In other words, because the landlordcan detect moral hazard better after contracting with the agent longer, thelikelihood of observing a sharecropping contract increases with relationshiplength. This is an intuitive result.
Turning to reverse tenancy, first note that “wealth” is defined here as a house-hold’s level of (non-productive) assets per capita. The per capita measure isused instead of the level measure so as to avoid biasing the comparison iflandlord and tenant households differ systematically by size. As preliminarysteps to the analysis of the reverse tenancy sample, the probability-weightedmean of the difference between agent household assets per capita and princi-pal household assets per capita were computed. In the full sample, the meandifference is not statistically significant at the 5 percent level, i.e., in theland tenancy sample, landlords and tenants are seemingly equally wealthy,and this does not differ by type of contract. In the reverse tenancy sample,however, the difference is statistically significant at the 1 percent level, i.e., inthe reverse tenancy sample, landlords are indeed poorer than their tenants,and this result does not vary by contract type.
Table 9 presents estimation results for the reverse tenancy sample. Onceagain, ra has the expected effect on contract choice and is significant at the1 percent level. Moreover, the risk aversion proxies turn out to be jointly in-significant, which constitutes a rejection of the risk-sharing hypothesis, butwith a fairly low p-value of 0.12. In other words, in the reverse tenancy sam-ple, it is not clear whether risk preferences affect contract choice, but as inthe full sample, an increase in the level of asset risk increases the likelihoodof observing a sharecropping contract, as predicted by the theoretical modelof section 2.2.
Turning to the control variables, note that whether a plot is irrigated has thesame effect as in the full sample. The main difference, however, is that thecharacteristics of the landlord and the tenant turn out to be significant inthis case. Contrary to a conventional wisdom in Madagascar, which says that
25
single, older women are usually the landlords in sharecropping agreements,it turns out that older women are more likely to offer a fixed rent contract(recall that the indicator for whether the landlord is single was omitted dueto almost perfect collinearity with the female indicator). In addition, thelandlord household’s assets per capita has the expected sign and significancepredicted by the risk-sharing hypothesis, i.e., as the landlord household getsricher, the landlord is more likely to choose a sharecropping contract. Onthe tenant’s side, however, assets per capita are insignificant, with the jointsignificance discussed above. Thus, one should not reject the risk-sharinghypothesis outright in the restricted sample of reverse tenancy. Finally, thetenant household’s dependency ratio increases the likelihood of sharecrop-ping, a result for which the theoretical model offers no ready explanation.
Because of the relatively small size of the reverse tenancy sample, the fol-lowing robustness checks were also performed, the results of which are notshown for brevity but are available upon request: (i) using the sum of ahousehold’s non-productive assets and working capital as wealth; (ii) usingabsolute rather than per capita levels of assets; (iii) using absolute ratherthan per capita levels of assets plus working capital; (iv) using per capitaincome; (v) using absolute income; and (vi) excluding the limited liabilityindicator (i.e., its fitted values) from the right-hand side of the contract-choice equation while preserving assets per capita as wealth. The asset riskhypothesis was significant at the 1 percent level in cases (i), (ii), and (iii),at the 5 percent level in case (iv), and at the 10 percent level in case (v).In case (vi), the asset risk explanation was significant at the 1 percent levelin both univariate IV probits (i.e., the full sample and the reverse tenancysample) and in the bivariate probit with selection, since in this case, the co-efficient of correlation turned out to be significantly different from zero andthe exclusionary restrictions were jointly significant.
The data thus offer strong support for the hypothesis that asset risk drives theemergence of both forms of sharecropping as well as the broader hypothesisthat the canonical risk-sharing model of sharecropping fails to explain theemergence of reverse share tenancy in Lac Alaotra.
26
6 Conclusion
Using data from Madagascar’s most important rice-producing region, this pa-per has presented and tested among three theoretical explanations to accountfor the existence of reverse share tenancy contracts. Estimation results indi-cate that asset risk drives both traditional sharecropping and reverse sharetenancy contracts, but that the canonical risk-sharing explanation cannotexplain either institution. Although the tests of risk-sharing conducted inthis paper have low power and rely on proxies for risk aversion, the strongempirical support for the asset risk model points, at the very least, to thenecessity of broadening the canonical Stiglitzian model to account for theexistence of reverse share tenancy.
From a policy perspective, the empirical results indicate that weak propertyrights have a significant impact in Lac Alaotra, Madagascar most importantrice-growing region. After the country moved from being a net exporter tobeing an net importer of rice over the last 20 years, the Malagasy govern-ment has declared food sufficiency to be one of its goals. The literature onsharecropping in developing countries, however, is fairly convincing in show-ing that sharecropping contracts do entail inefficiencies due to Marshallianinefficiency (Bell, 1977; Shaban, 1987; Laffont and Matoussi, 1995; Penderand Fafchamps, 2006; Arcand et al., 2007). As a result, it seems like theremight be scope for a policy intervention aiming to strengthen land rights.Indeed, although Jacoby and Minten (2005) find that titles have little to noeffect on investment by landowners and plot values in Lac Alaotra, it mighthave a subtler effect on the behavior of landowners involved in land tenancy.
To the author’s knowledge, this paper is the first study to combine formaltheoretical modeling with empirical evidence in discussing the oft-observedphenomenon of reverse share tenancy. This opens up an important area ofempirical research, as reverse share tenancy has been discussed in the contextof several other countries. Further studies similar to this one should thus beundertaken in these other countries, aiming at a general understanding ofthe scope and nature of reverse share tenancy.
27
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[42] Shaban, R.A. (1987), “Testing Between Competing Models of Share-cropping”, Journal of Political Economy, Volume 95, pages 893-920.
[43] Shavell, S. (2004), Foundations of Economic Analysis of Law, Cam-bridge, MA: Belknap Press.
[44] Simon, H. (1957), Models of Man, New York, NY: Wiley.
[45] Singh, I. (1989), “Reverse Tenancy in Punjab Agriculture: Impact ofTechnological Change”, Economic and Political Weekly, Volume 24.
31
[46] Stifel, D., M. Fafchamps, and B. Minten (2007), “Taboos, Agriculture,and Productivity”, Working Paper, Lafayette College.
[47] Stiglitz, J.E. (1974), “Incentives and Risk-Sharing in Sharecropping”,Review of Economic Studies, Volume 41, pages 219-255.
[48] Stokey, N.L., and R.E. Lucas, Jr. (1989), Recursive Methods in EconomicDynamics, Cambridge, MA: Harvard University Press.
[49] Tikabo, M.O. and S.T. Holden (2003), “Land Contract Choice: PoorLandlords and Rich Tenants Evidence from the Highlands of Eritrea”,Working Paper, Department of Economics and Social Sciences, Agricul-tural University of Norway.
[50] Tversky, A. and D. Kahneman (1982), “Judgment under Uncertainty:Heuristics and Biases” in D. Kahneman, P. Slovic, and A. Tversky, eds.,Judgment under Uncertainty: Heuristics and Biases, Cambridge: Cam-bridge University Press.
32
Table 1: First-Stage Descriptive Statistics
Variable Mean Std. Dev. NPlot Leased Out Dummy 0.39 (0.49) 1029Plot Size (Ares) 132.63 (395.88) 1005Tanety Dummy 0.21 (0.41) 1029Bas-Fond Dummy 0.12 (0.33) 1029Irrigated Plot Dummy 0.56 (0.50) 1005Family-Owned Plot Dummy 0.32 (0.47) 1029Distance between Plot and House (Minutes) 38.68 (46.67) 1005Plot Fady Days (Days Per Year) 54.35 (44.18) 997L Household Dependency Ratio 0.42 (0.22) 1005L Household Size (Individuals) 6.18 (2.75) 1005L Age (Years) 49.96 (14.20) 1005L Female Dummy 0.11 (0.31) 1005L Education (Completed Years) 5.53 (3.67) 1005L Agricultural Experience (Years) 25.78 (15.03) 915L Hourly Wage (Ariary) 306.43 (214.20) 949L Household Income Per Capita (100,000 Ariary) 1.17 (2.57) 998L Household Assets Per Capita 3.04 (6.25) 989L Household Working Capital (100,000 Ariary) 9.04 (28.88) 998Commune 1 0.21 (0.40) 1029Commune 2 0.18 (0.38) 1029Commune 3 0.18 (0.38) 1029Commune 4 0.15 (0.35) 1029Commune 5 0.17 (0.37) 1029Commune 6 0.13 (0.33) 1029
33
Table 2: Second-Stage Descriptive Statistics
Variable Mean (Std. Dev.) NSharecropping Dummy 0.69 (0.46) 387Plot Size 108.83 (84.76) 397Tanety 0.07 (0.25) 397Bas-Fond 0.09 (0.28) 397Irrigated Plot Dummy 0.75 (0.43) 397Distance between House and Plot 33.69 (37.22) 397L Household Size 5.48 (2.80) 389L Household Dependency Ratio 0.45 (0.25) 389L Age 53.31 (16.37) 389L Female 0.20 (0.40) 389L Household Income Per Capita 1.16 (2.34) 388L Household Assets Per Capita 12.22 (32.17) 382L Household Working Capital 5.31 (25.87) 388Relationship Length 2.54 (3.64) 388Kin Contract 0.63 (0.48) 397T Household Size 5.77 (2.56) 394T Household Dependency Ratio 0.41 (0.22) 394T Age 39.08 (11.10) 394T Agricultural Experience 17.95 (11.04) 385T Household Income Per Capita 0.94 (1.50) 393T Household Assets Per Capita 8.78 (14.96) 393T Household Working Capital 6.03 (16.73) 393ra -0.26 (3.96) 387Limited Liability Dummy 0.55 (0.50) 388
34
Table 3: Estimation Results for Ackerberg-Botticini Testof Endogenous Matching
Variable Coefficient (Std. Err.)Dependent Variable: T Household Assets Per CapitaL Household Size -0.056 (0.063)L Household Dependency Ratio -1.095† (0.574)L Age 0.015† (0.008)L Female -0.156 (0.368)L Education 0.047 (0.039)L Household Working Capital 0.003† (0.002)L Household Assets Per Capita -0.018 (0.024)L Household Income Per Capita -0.119∗∗ (0.043)Intercept 1.626∗ (0.680)N 379R2 0.03F(8,370) 2.02p-value 0.04Significance levels : † : 10% ∗ : 5% ∗∗ : 1%
35
Table 4: Estimation Results for Ackerberg-Botticini In-strumenting Regression
Variable Coefficient (Std. Err.)Dependent Variable: T Household Assets Per CapitaFamily-Owned Plot -1.043∗∗ (0.272)Plot Size -0.000 (0.002)Tanety 0.194 (0.655)Bas-Fond -0.029 (0.633)Irrigated Plot 0.169 (0.433)Distance between House and Plot -0.012∗∗ (0.004)L Household Size -0.030 (0.057)L Household Dependency Ratio -0.516 (0.660)L Age -0.013 (0.008)L Female -0.161 (0.426)L Education -0.031 (0.052)L Household Income Per Capita -0.119∗∗ (0.046)L Household Assets Per Capita 0.036∗ (0.018)L Household Working Capital 0.003 (0.003)Relationship Length 0.004 (0.057)Kin Contract -0.098 (0.282)T Household Size -0.253∗∗ (0.082)T Household Dependency Ratio -1.920∗∗ (0.632)T Age 0.020 (0.160)T Education 0.092∗ (0.045)T Household Income Per Capita 0.312∗ (0.126)T Household Working Capital 0.054∗∗ (0.016)ra -0.022 (0.046)Commune 2 0.095 (0.395)Commune 3 -0.719∗ (0.313)Commune 4 0.844 (0.768)Commune 5 0.580 (0.356)Commune 6 0.132 (0.435)Commune 2*L Household Assets Per Capita 0.402 (0.264)Commune 3*L Household Assets Per Capita -0.056 (0.056)Commune 4*L Household Assets Per Capita -0.105∗ (0.048)
Continued on next page...
36
... table 4 continued
Variable Coefficient (Std. Err.)Commune 5*L Household Assets Per Capita -0.064∗ (0.032)Commune 6*L Household Assets Per Capita 0.015 (0.059)Intercept 3.840∗∗ (1.063)N 377R2 0.36F(33,343) 3.60p-value 0.00F(10,343) (Instruments) 2.44p-value (Instruments) 0.00
37
Table 5: Estimation Results for Full-Sample IV Probit
Variable Coefficient (Std. Err.)
(β/βEM) (Delta)Dependent Variable: Sharecropping DummyFamily-Owned Plot -0.056 (303.073)Plot Size 1.030 (284.612)Tanety 1.040 (18.949)Bas-Fond 1.113 (10.286)Irrigated Plot 0.997 (0.568)Distance between House and Plot 1.966 (79767.125)L Household Size 0.962 (7.061)L Household Dependency Ratio 1.128 (3.611)L Age 1.009 (13.794)L Female 0.902 (8.356)L Education 0.987 (15.585)L Household Income Per Capita 1.061 (46.081)L Household Assets Per Capita 0.999 (52.088)L Household Working Capital 1.145 (1509.145)Relationship Length 0.922 (12.777)Kin Contract 0.914 (11.184)T Household Size 1.013 (8.594)T Household Dependency Ratio 0.939 (0.693)T Age 0.815 (493.694)T Education 1.519 (2516.590)T Agricultural Experience 0.838 (125.110)T Household Income Per Capita 0.924 (10.664)T Household Assets Per Capita 0.611 (35.035)T Household Working Capital -12.909 (1564477.442)Intercept 1.041 (0.270)
38
Table 6: Estimation Results for Limited Liability Instru-menting Regression
Variable Coefficient (Std. Err.)Dependent Variable: Limited Liability DummyFamily-Owned Plot 0.052 (0.064)Plot Size 0.000 (0.000)Tanety 0.381∗∗ (0.134)Bas-Fond 0.199 (0.123)Irrigated Plot -0.149† (0.081)Distance between House and Plot -0.000 (0.001)L Household Size -0.001 (0.010)L Household Dependency Ratio -0.001 (0.106)L Age 0.002 (0.002)L Female 0.041 (0.067)L Education -0.011 (0.008)L Household Income Per Capita 0.022† (0.012)L Household Assets Per Capita -0.008† (0.004)L Household Working Capital 0.001 (0.001)Relationship Length 0.005 (0.007)Kin Contract -0.011 (0.055)T Household Size 0.011 (0.014)T Household Dependency Ratio -0.189 (0.138)T Age -0.007∗ (0.003)T Education 0.006 (0.008)T Household Income Per Capita -0.008 (0.018)T Household Assets Per Capita 0.027∗ (0.011)T Household Working Capital 0.001 (0.002)ra 0.001 (0.007)Number of Other Cultivation Techniques 0.185∗∗ (0.031)Intercept 0.306 (0.223)N 377R2 0.17F(25,351) 2.86p-value 0.00p-value (Instrument) 0.00
39
Table 7: Estimation Results for the Bivariate Probit withSelection
Variable Coefficient (Std. Err.)Dependent Variable: Sharecropping DummyFamily-Owned Plot 0.023 (0.229)Plot Size 0.003 (0.002)Tanety 0.149 (1.686)Bas-Fond -0.355 (0.607)Irrigated Plot -1.135∗ (0.535)Distance between House and Plot -0.001 (0.004)L Household Size 0.081 (0.051)L Household Dependency Ratio -0.544 (0.641)L Age -0.028∗∗ (0.009)L Female -0.154 (0.375)L Education -0.066 (0.047)L Household Income Per Capita -0.033 (0.089)L Household Assets Per Capita 0.029 (0.060)L Household Working Capital 0.003 (0.016)Relationship Length 0.074 (0.062)Kin Contract -0.121 (0.250)T Household Size -0.099 (0.069)T Household Dependency Ratio 1.023 (0.694)T Age -0.011 (0.017)T Education 0.011 (0.041)T Agricultural Experience 0.012 (0.016)T Household Income Per Capita -0.094 (0.088)T Household Assets Per Capita 0.057 (0.069)T Household Working Capital 0.000 (0.011)ra 0.072 (0.057)Limited Liability Dummy (Fitted Values) -0.396 (0.820)Intercept 3.702∗∗ (1.341)Dependent Variable: Plot Leased Out DummyPlot Size -0.001† (0.001)Tanety -1.098∗∗ (0.249)Bas-Fond -0.344 (0.233)Irrigated Plot 0.505∗ (0.198)
Continued on next page...
40
... table 7 continued
Variable Coefficient (Std. Err.)Family-Owned Plot -0.187 (0.153)Distance between House and Plot -0.001 (0.002)Plot Fady Days 0.003 (0.002)L Household Dependency Ratio 0.686∗ (0.301)L Household Size -0.091∗∗ (0.028)L Age 0.025∗∗ (0.008)L Female 0.708∗∗ (0.221)L Education -0.008 (0.027)L Agricultural Experience -0.012† (0.006)L Household Income Per Capita 0.072† (0.044)L Household Assets Per Capita -0.049† (0.029)L Household Working Capital -0.000 (0.016)Commune 2 0.286 (0.243)Commune 3 0.192 (0.239)Commune 4 -0.499∗ (0.251)Commune 5 0.120 (0.227)Commune 6 -0.653∗ (0.309)Intercept -1.092∗ (0.538)ρ -0.895 (1.178)N 877Log-Likelihood -549.55χ2
(26) 28.6
p-value 0.33p-value (Exclusionary Restrictions) 0.00p-value (Risk-Sharing Hypothesis) 0.61
41
Table 8: Estimation Results for Full-Sample IV Probit
Variable Coefficient (Std. Err.)Dependent Variable: Sharecropping DummyFamily-Owned Plot -0.108 (0.195)Plot Size 0.001 (0.002)Tanety -0.447 (0.596)Bas-Fond -0.543 (0.402)Irrigated Plot -0.779∗ (0.303)Distance between House and Plot -0.000 (0.003)L Household Size 0.007 (0.034)L Household Dependency Ratio 0.111 (0.377)L Age -0.010 (0.006)L Female -0.077 (0.233)L Household Income Per Capita 0.002 (0.040)L Household Assets Per Capita -0.010 (0.011)L Household Working Capital 0.003 (0.004)Relationship Length 0.073† (0.038)Kin Contract -0.201 (0.203)T Household Size -0.082 (0.056)T Household Dependency Ratio 0.888 (0.556)T Age -0.013 (0.013)T Agricultural Experience 0.003 (0.011)T Household Income Per Capita -0.087 (0.058)T Household Assets Per Capita 0.027 (0.036)T Household Working Capital -0.005 (0.007)ra 0.098∗∗ (0.034)Limited Liability (Fitted Values) -0.422 (0.510)Intercept 2.346∗∗ (0.647)N 368Log-Likelihood -384.11χ2
(24) 53.37
p-value 0.00p-value (Risk-Sharing Hypothesis) 0.48
42
Table 9: Estimation Results for Reverse Tenancy Sample(Assets Per Capita) IV Probit
Variable Coefficient (Std. Err.)Dependent Variable: Sharecropping DummyFamily-Owned Plot 0.159 (0.261)Plot Size 0.001 (0.002)Tanety -0.465 (0.820)Bas-Fond -0.001 (0.543)Irrigated Plot -0.674† (0.383)Distance between House and Plot 0.001 (0.003)L Household Size -0.031 (0.049)L Household Dependency Ratio 0.257 (0.656)L Age -0.018† (0.009)L Female -0.622† (0.328)L Household Income Per Capita -0.093 (0.228)L Household Assets Per Capita 0.392∗ (0.190)L Household Working Capital 0.001 (0.003)Relationship Length 0.031 (0.051)Kin Contract -0.419 (0.290)T Household Size -0.137 (0.093)T Household Dependency Ratio 1.677∗ (0.823)T Age 0.026 (0.018)T Agricultural Experience -0.026 (0.017)T Household Income Per Capita -0.101 (0.078)T Household Assets Per Capita -0.013 (0.042)T Household Working Capital 0.007 (0.007)ra 0.114∗∗ (0.044)Limited Liability (Fitted Values) -0.525 (0.697)Intercept 1.858† (0.969)N 181Log-Likelihood -181.46χ2
(24) 49.41
p-value 0.00p-value (Risk-Sharing Hypothesis) 0.12
43
A Proofs of Propositions
Proof of Proposition 1 When the principal is risk-averse and the agentis risk-neutral, RL > 0 and RT goes to zero. The slope of the contract thusbecomes
limRT→0
w′(q) =µU ′
V ′ddq
[fe(q|e)f(q|e)
]+ RL
RL
≥ 1, (33)
but since the share of the output that the agent can get from the contractlies in the [0, 1] interval, then w′(q) = 1, and a fixed rent contract obtains. ¥
Proof of Proposition 2 Before proving the two parts of the proposition,let ρ ≡ RT /RL capture the degree of risk aversion of the agent relative tothe degree of risk aversion of the principal, such that
w′(q) =
µRL
U ′V ′
ddq
[fe(q|e)f(q|e)
]+ 1
1 + ρ. (34)
We can establish part (i) by setting V ′′ = 0 in equation 11 above. This yields
w′(q) =µ(U ′)2 d
dq
[fe(q|e)f(q|e)
]
−U ′′V ′ > 0, (35)
i.e., when the principal is risk-neutral and the agent is risk-averse, a share-cropping contract obtains. This is the well-known Stiglitzian result.
Turning to part (ii), note that simply calculating dw′(q)dρ
from equation 15cannot establish this part of the proposition since, as ρ varies, so does theratio of marginal utilities in w′(q). The proof must therefore proceed in aroundabout way, first showing that an increase in agent wealth is equiva-lent to a decrease in ρ, and then showing that an increase in agent wealthleads to an increase in w′(q) if the agent is sufficiently decreasingly absolutelyrisk-averse. Thus, as agent wealth increases, the lower his level of absoluterisk aversion. As he gets less risk-averse, the more production risk he bears.29
29Part (ii) could also be established by looking at the principal’s side of things, but thatwould only unnecessarily complicate the algebra.
44
Let z denote agent wealth. We first need first need to establish that dρdz
< 0,i.e., that the richer the agent, the lower his degree of risk aversion relative tothat of the principal. Since decreasing ARA of the agent has been assumedabove, we have that
dRT (z)
dz=
[R2
T −U ′′′(z)
U ′(z)
]< 0. (36)
But then
dρ
dz=
[U ′′′(z)
U ′(z)−R2
T
]V ′′
V ′ < 0, (37)
i.e., the richer the agent, the less absolutely risk-averse he is relative to theprincipal. But then, recall from equation 12 that
w′(q) =µU ′(z)
V ′ddq
[fe(q|e)f(q|e)
]− V ′′V ′
−V ′′V ′ − U ′′(z)
U ′(z)
. (38)
Let Ψ = ddq
[fe(q|e)f(q|e)
]to simplify notation. Taking the derivative of w′(q) with
respect to z yields
dw′(q)dz
=
[µU ′′(z)
V ′ Ψ][− V ′′
V ′ − U ′′(z)U ′(z)
]− [R2
T − U ′′′(z)U ′(z)
][µU ′(z)
V ′ Ψ− V ′′V ′
][− V ′′
V ′ − U ′′(z)U ′(z)
]2 . (39)
Since the denominator is positive, the first term of the numerator is negative,and the second bracket of the second term of the numerator is also positive,the sign of dw′(q)
dzhinges upon the sign of the first bracket of the second term
of the numerator, i.e., on the sign of[R2
T − U ′′′(z)U ′(z)
], which is the derivative
of the agent’s level of absolute risk aversion with respect to his wealth, asin equation 16. Three cases are possible: (a) the tenant’s utility functionexhibits decreasing ARA; (b) it exhibits constant ARA; or (c) it exhibitsincreasing ARA.
It should be obvious that in cases (b) and (c), dw′(q)dz
< 0. In case (a), how-
ever, the sign of dw′(q)dz
is ambiguous. If the agent is sufficiently decreasingly
absolute risk-averse, then dw′(q)dz
> 0, i.e., the richer the agent gets, the moreproduction risk he will bear through a higher share of the output. If, how-ever, the agent is not sufficiently decreasingly absolutely risk-averse, then
45
dw′(q)dz
≤ 0. Thus, the slope of the contract is monotonically decreasing in therelative degrees of absolute risk aversion of the agent and the principal onlywhen the agent’s preferences exhibit a sufficiently decreasing level of ARA.
Finally, that a risk-averse principal offers a sharecropping contract to a risk-averse agent follows from the first two parts of the proposition.¥
Proof of Lemma 1 From the agent’s incentive compatibility constraint,one gets that a = ψe/E[νfe]. Thus, as a increases, the ratio ψe/E[νfe] alsoincreases. Since ψee > 0 and fee < 0, this means that as a increases, e(a) alsoincreases, so that ea > 0. ¥
Proof of Lemma 2 From the agent’s IR constraint, one gets that
b(a) = U + ψ(e(a))− aE[νf(e(a))]. (40)
But then, ba = −ea(aE[νfe] − ψe) − E[νf(e)], and from the agent’s ICconstraint, the bracketed expression is identical to zero. Therefore, ba =−E[νf(e)] < 0. ¥
Proof of Lemma 3 When faced with the following problem
v0(x) = maxx′∈Γ(x)
{F (x, x′) + δv0(x
′)}, (41)
v0(·) is strictly increasing if (i) the state space X, which includes x and x′,is a convex subset or R` and the correspondence Γ : X → X is nonempty,compact-valued, and continuous; (ii) F : A → R is bounded and continuousand δ ∈ (0, 1); (iii) For all y, F (·, y) is strictly increasing in each of its first `arguments; and (iv) Γ is monotonic (Stokey and Lucas, 1989, p.80).
That the state space – the land area of a given plot, h – is a subset of R is ob-vious. The Γ(·) correspondence, in this case the law of motion, is nonempty,compact-valued, and its expectation is continuous. The returns function F (·),in this case the utility function of the principal, is assumed bounded and iscontinuous by virtue of being a von Neumann-Morgenstern utility function,and it is also increasing in its one argument, i.e., the principal’s income. Also,δ ∈ (0, 1) by assumption. Finally, the law of motion is monotonic in expec-tation, so that v0(·) is strictly increasing. ¥
46
Proof of Proposition 3 In order to maximize the Bellman equation, oneneeds to take the derivative with respect to a. Doing this and using thesubstitution method to solve yields the following expression for a∗, the cropshare in the optimal contract:
a∗ = 1 +δEv′0sah
EνU ′feea
, (42)
where the first term represents the first-best contract and the second termrepresents the effect of introducing asset risk (or strength of the landlord’sclaim to her asset, in this case) in the model. Since all the variables in thesecond term are positive except for sa, the optimal contract is lower-poweredthan the first-best contract, so that sharecropping emerges as the optimalsolution. ¥
Proof Taking the derivative of the slope of the optimal contract with respect
to the asset risk parameter yields da∗/dsa =δEv′0h
EνU ′feea> 0, which means that
as the sensitivity to the slope of the contract of the landlord’s claim to theland increases, the slope of the optimal contract increases, i.e., the greatersa, the higher a∗. In the limit, sa = 0 and a∗ = 1, i.e., when the landlord’sclaim to the land does not vary at all because of the slope of the contract, thefirst-best contract obtains because the second term in equation 42 is equalto zero. ¥
47