Abstract
Most studies of tenurial insecurity focus on its effects on investment. This paper studies the hitherto unexplored relationship between tenurial insecurity and land tenancy contracts. Based on distinct features of formal law and customary rights in Madagascar, this paper augments the canonical model of sharecropping by making the strength of the landlord’s property right increasing in the amount of risk she bears within the contract. Using data on landlords’ subjective perceptions in rural Madagascar, empirical tests support the hypothesis that insecure property rights drive contract choice but offer little support in favor of the canonical risk sharing hypothesis. (JEL K11, Q15)
I. Introduction
What are the impacts of tenurial insecurity on the behavior of individuals and households in developing countries? Do weak property rights push landowners to underinvest in improving their plots of land? Does tenurial insecurity make landowners who no longer can or want to exploit their land think twice about leasing out their plots of land and becoming landlords? Do weak property rights force landlords to discriminate between potential tenants? More generally, what actions, if any, are taken by landowners in developing countries to hedge against the risk of losing their claim to their land?
Although there exists an important literature on the impacts of tenurial insecurity on the investment behavior of landowners (see Besley 1995 and Brasselle, Gaspart, and Platteau 2002 for key studies; see Carter and Olinto 2003; Deininger and Jin 2003, 2006; Goldstein and Udry 2008; and Fenske 2010 for recent studies), the impacts of tenurial insecurity on other aspects of the land market (i.e., land sales, land tenancy, etc.) are relatively less well known. Conning and Robinson (2007) develop a general equilibrium model in which landowners adopt inefficient measures in an effort to curb tenurial insecurity and find support for their model when testing it using data from India. Similarly, Deininger, Ali, and Alemu (2009) report evidence that suggests that tenurial insecurity prevents the land lease market from functioning efficiently in Ethiopia, a finding echoed by Lunduka, Holden, and Øygard (2009), who find that tenurial insecurity also constrains the functioning of the land market in Malawi. Finally, Macours, de Janvry, and Sadoulet (2010) find that tenurial insecurity adversely affects the matching of landlords and tenants in Nicaragua, as it forces landlords to contract with socioeconomically similar tenants.
This paper studies the impact of tenurial insecurity on the tenancy contracts landlords offer their tenants. Based on field observations as well as conversations with rural landowners in Madagascar, this paper first develops a transaction cost–based alternative hypothesis to the canonical risk sharing explanation. Indeed, since the seminal contribution of Stiglitz (1974), the canonical explanation for the existence of sharecropping has been that it balances out risk sharing and incentives. So when the landlord is risk-neutral or risk-averse and the tenant is risk-averse, a sharecropping contract dominates a fixed rent contract because it partially insures the tenant against production risk while still tying pay to performance. When the tenant is risk-neutral, however, there is no longer a need to insure the tenant against production risk, so that a fixed rent contract becomes optimal.
Because sharecropping has been observed in both high- and low-risk environments, however, another school of thought—the transaction costs school of thought—posits that sharecropping emerges because the presence of one or more transaction costs make sharecropping more attractive relative to fixed rent (Cheung 1968; Allen and Lueck 2002). It could be the case, for example, that the tenant is risk-neutral but that a fixed rent contract would push him to deplete soil fertility by virtue of providing him with stronger incentives given that he gets to keep the entire crop. In this case, the landlord could choose a sharecropping contract in order to preserve soil fertility, a hypothesis for which Dubois (2002) has found empirical support in the Philippines.
The conceptual framework developed in this paper explains sharecropping as a result of an important transaction cost, namely, tenurial insecurity. That is, if the strength of the landlord’s property right is an increasing function of the production risk she chooses to bear (e.g., as she would in a sharecropping contract relative to a fixed rent contract), she might choose a sharecropping contract even when the tenant is risk-neutral, even though such a contract leaves her exposed to a suboptimal amount of production risk and leads to moral hazard, at least in principle.1
The hypothesis developed in this paper is rooted in the interaction between the formal legal system and customary rights in Madagascar. Indeed, both the law and custom hold that property is a reward that varies in proportion with the effort one puts in cultivating the land, and economists have long recognized the disincentive effects of sharecropping relative to rental contracts when it comes to agricultural productivity. Moreover, the administration of lands is often left to village elders in Madagascar, and it appears that these elders often enforce a social norm according to which landlords should bear some of the risk inherent to agricultural production on their own plots, as in the case of a sharecropping contract. Indeed, in a sharecropping contract, the landlord shares production risk at a rate equal to the rate at which she shares output with the tenant, by definition. So for example, a landlord who keeps 50% of the output as rent bears 50% of the production risk.
After incorporating tenurial insecurity in the canonical model, this paper then uses data on the landlords’ subjective perceptions of tenurial insecurity to test whether these drive contract choice. Using plot-level data from Lac Alaotra, Madagascar’s premier ricegrowing region, contract choice equations are estimated that control for both the matching process and the match between the landlord and the tenant. The data ultimately strongly support the hypothesis that tenurial insecurity drives contract choice but offer little to no support in favor of the canonical risk sharing hypothesis. In short, for a 1% increase in the landlord’s subjective assessment of the likelihood that she will lose her plot of land as a result of the contract she chose to offer her tenant, the likelihood of observing a sharecropping contract increases by 2% on average. The empirical results thus ultimately support a transaction cost–based explanation, as described by Allen and Lueck (2002).
This paper therefore offers a threefold contribution to the literature. First and foremost, whereas the majority of studies looking at tenurial insecurity focus on investment, this paper studies the hitherto unexplored relationship between tenurial insecurity and contract choice on the land tenancy market.
Second, this paper contributes to the growing literature on subjective expectations in development economics (Luseno et al. 2003; Doss, McPeak, and Barrett 2006; Lybbert et al. 2007; Cardenas and Carpenter 2008; see Delavande, Giné, and McKenzie 2011 for a survey of the literature) by eliciting subjective assessments of tenurial insecurity from landlords and using these to test the implications of the theory. Moreover, this paper is the first to incorporate subjective expectations in an applied contract-theoretic setting, in this case the subjective expectations of the principal regarding her risk of losing a productive asset contracted upon.2
Third, this paper studies the oft-observed yet relatively unknown institution known as “reverse tenancy,” in other words, land tenancy in which the landlord is poorer than the tenant, which is very frequent in Madagascar (Minten and Razafindraibe 2003) and which has also been observed in places as diverse as Bangladesh (Pearce 1983), Eritrea (Tikabo 2003), Ethiopia (Bezabih 2007), India (Singh 1989), Lesotho (Lawry 1993), Malaysia (Pearce 1983), the Philippines (Roumasset 2002), and South Africa (Lyne and Thomson 1995). In such cases, however, if tenants are risk-neutral (or act as if risk-neutral because they have better opportunities for diversifying risk or better access to insurance by virtue of being wealthier), the canonical model is inconsistent with the existence of reverse share tenancy, and it needs to be modified to account for whatever makes the existence of reverse share tenancy possible. This paper modifies the canonical model so as to accommodate the existence of reverse share tenancy if tenants can indeed be assumed to be risk-neutral.3 Moreover, if the tenurial insecurity hypothesis developed in this paper is supported by the data, it may be useful to know whether tenurial insecurity plays a more important role for landlords who are poorer than their tenants than for the average landlord.
II. Background and Contractual Environment
The tenurial insecurity hypothesis put forth in this paper may seem prima facie surprising. Although the impacts of eviction threats on tenant behavior have been explored both theoretically (Banerjee and Ghatak 2004) and empirically (Kassie and Holden 2007, 2009), the hypothesis that the strength of a landlord’s claim to her plot of land could be a function of how much risk she chooses to bear when leasing her plot out is unheard of under more familiar (i.e., Western) legal systems. Yet this was the reason invoked by several landowners for choosing sharecropping over fixed rent during preliminary visits to Madagascar, where landlords who choose not to bear any production risk appear to be perceived as uncooperative and unwilling to contribute to social welfare and are thus often discussed with contempt by third parties. A formal theoretical model of the conceptual argument developed in this section that will provide some structure for the empirical work below can be found in Appendix A.
In his chapter on tenure security in Madagascar, Teyssier (1998) notes how the Lac Alaotra region, where the data used in this paper have been collected, has been attracting migrants since the nineteenth century. For the Sihanaka (the dominant ethnic group in Lac Alaotra), the land belongs to the individuals who were born on it. The land where one was born is therefore not perceived only as a simple production input: in a country where the cult of the ancestors regiments one’s existence, it also serves as a link between one and one’s ancestors. Teyssier (1998, 586) writes that for other ethnic groups, who have composed the bulk of the immigration to Lac Alaotra, however, “the land belongs to the individual who cultivates it. This conception is also that of the central government, for whom the titling of a portion of the private national domain in an individual’s name is necessarily associated with previous cultivation by the same individual. Property is thus conceived of as a ‘reward’ that varies in proportion to the effort put in cultivating the land.” (Emphasis added.)
Recall that in the canonical principal-agent model of land tenancy (Stiglitz 1974), the provision of effort by the tenant is curbed by the weaker incentives provided by a sharecropping contract relative to a fixed rent contract. It is likely that this is directly taken into account by landlords when contemplating whether to offer their tenants a sharecropping or a fixed rent contract. In his descriptive study of sharecropping in Lac Alaotra, Charmes (1975) notes how landlords in sharecropping contracts are almost always involved in some aspect of production (e.g., plowing, transplanting, harvesting, threshing, husking, and milling), whereas the involvement of landlords in fixed rent contracts is consists only in providing the plot of land on which production takes place.
Likewise, in his case study of the informal economy of lower Antananarivo, Turcotte (2006, 330) hints at the fact that tenurial insecurity drives contract choice, when he writes that “access to rice is related to the property rights which some individuals still have on inherited plots. … Although it occurs that rice plots owned in the countryside (or in town) are not exploited or are exploited by and for someone else, one is more likely to lease out such plots under a sharecropping agreement to one’s kin or to someone whom one trusts.” (Author’s translation.)
What conditions lead to the emergence of a land rights system in which the terms of the contract chosen by the landlord affect her likelihood of retaining her claim to the land? As is often the case in Sub-Saharan Africa (Platteau 1994, 2000), formal legal institutions coexist with customary rights in Madagascar. According to Karsenty and Le Roy (1996), land is conceived of as the land of the ancestors in Madagascar, and in rural areas, the activities of the living largely focus on preserving the land of the ancestors. Consequently, land can become private property only if it is titled, the process leading to which is not only extremely slow and costly in terms of both time and money, but also perceived as useless by 25% of Minten and Razafindraibe’s (2003) respondents. In many communities the administration of plots is left to the village elders, who allocate plots to members of the clan. Further, Malagasy tradition holds that taking possession of the fruits of the land, and bearing agricultural risk both ensure continued access to the land, much as direct cultivation does under more familiar property rights regimes.
Formal institutions that may have been put in place so as to make informal institutions official also contribute to the landlords’ perceptions of tenurial insecurity in Madagascar. First, under Western property rights regimes, one often encounters the legal doctrine of adverse possession (Posner 2007), which holds that an individual may take possession of a plot of land belonging to another by occupying or exploiting it for a certain amount of time (see Baker et al. 2001 for an empirical study). In Madagascar, Keck, Sharma, and Feder (1994, 47) write that “in 1962 and 1964, legislation defined property rights as more than a right to enjoy and dispense of one’s property in an absolute sense; property rights represented an ensemble of prerogatives defined by the greater public good. Thus, property took on a more prominent social function; individuals unable to use the land had no right to keep it, and the land was to be transferred to a more productive owner/user.”
It is thus possible for a tenant to obtain his landlord’s plot legally through adverse possession, which is often dependent on the general attitude toward rights to future use, about which Posner (2007, 49) writes that it is itself “related to the age-old hostility to speculation—the purchase of a good not to use but to hold in the hope that it will appreciate in value.”
Given that legal recourse is often prohibitively costly in Madagascar (Fafchamps and Minten 2001), the frequency with which tenants claim their landlords’ plots through formal adverse possession is most likely very low, although a survey respondent did tell the author that about 70% of the cases heard at the local communal court were about land issues. What likely occurs more often is informal adverse possession, that is, land redistribution by the village elders.
This begs the question, however, of why village elders would want to redistribute lands between community members. Unfortunately, this is a question on which the extant literature on land in Madagascar is silent. During the fieldwork for the data collection effort that led to this paper, the author was repeatedly told by landlords that they chose share tenancy “to help the family” or “to help others.” While this is an admittedly vague answer, it does suggest that the village elders are enforcing a norm of risk sharing among members of the same family, if not among members of the same community. This is especially likely in a context where most people are risk-averse, and in which a risk-averse landlord who chooses a fixed rent contract so as to avoid taking any risk is perceived as leaving all of the production risk associated with cultivation of her plot of land to her tenant, who is also most likely risk-averse. Similarly to Posner’s argument that the law evolves in a way that maximizes efficiency, Ellickson (1989, 1994) develops a hypothesis according to which social norms evolve so as to maximize wealth (or minimize transaction costs).4 It is thus likely that the norm of land redistribution in Madagascar has evolved so as to maximize social welfare by spreading risk across individuals. In other words, it looks as though sharecropping emerges as a result of a social norm aimed at providing social insurance. Unfortunately, the data used in this paper do not lend themselves to testing this hypothesis, and so it must remain speculative.
Equally important for the tenurial insecurity hypothesis, Keck, Sharma, and Feder (1994, 48) note further that “ordinance 74-022 developed additional specifications for land improvement in rural areas. … Once the land improvement work was complete, the beneficiary could either become the owner or remain as a land user. In either case, the beneficiary was expected to work the land in a ‘rational fashion’ in keeping with a set of pre-established conditions.”
Adam Smith (1776/1976) himself had intuited that sharecroppers face fewer incentives to make improvements to the land than fixed renters, as formalized by Johnson (1950). In this sense, according to the formal legal system in Madagascar, if a landlord wishes to maximize her chances of keeping her claim to her plot of land, she may be better off bearing some production risk by offering her tenant a sharecropping rather than a fixed rent contract. In the data used in the application below, 48% of fixed rent tenants versus 40% of sharecroppers had invested in improving the land.
Lastly, the land sales market is exceptionally thin in Madagascar, where only 3% of households in the nationally representative data set used by Randrianarisoa and Minten (2001) reported having sold land in the last five years and only 13% of the plots in the nationally representative data set used by Minten and Razafindraibe (2003) had been purchased by their owners. The land rental market is comparatively more active, with almost 8% of cultivated land under some form of tenancy. According to Randrianarisoa and Minten, the land rental market mostly allows households from the middle of the income distribution to lease in land from both poorer and wealthier households.
The data used in the application below show that in Lac Alaotra, 37% of all plots are leased out, and 24% of all plots are sharecropped. In addition, reverse tenancy occurs on 22% of plots if one looks at household wealth levels (a precise definition of which is given below; this number and the core findings in this paper do not change substantially whether one looks at household wealth in levels, per capita, or per adult equivalent), and over 15% of plots are under reverse share tenancy, that is, sharecropping in which the landlord is poorer than the tenant.
III. Empirical Framework
The core specification of the contract choice equation to be estimated in this paper is such that
1where i denotes the plot; yi = 1 if plot i is under fixed rent and yi = 0 if it is under sharecropping; xP, xl, and xt are vectors of plot-, landlord household-, and tenant household-specific characteristics; sa captures the landlord’s subjective perceptions of (contract-dependent) tenurial insecurity and is the variable of interest, the origins of which can be found in Appendix A and a discussion of which can be found below; and ϵ is an error term with mean zero. Equation [1] is estimated by ordinary least squares with robust standard errors, and thus constitutes a reduced form linear probability model (LPM) of contract choice.
One could estimate a probit or a logit instead of an LPM, but the latter is chosen so as to simplify the interpretation of the estimated coefficients. In the LPM defined by equation [1], each estimated coefficient can be interpreted as the percentage change in the likelihood of observing a fixed rent contract rather than a sharecropping contract resulting from a unit change in the explanatory variable it is attached to, whereas the coefficients of a probit or logit need to be transformed in order to obtain marginal effects. The LPM is adopted here because it allows for a more direct interpretation of the estimated coefficients. In addition, its use is relatively harmless given the data pattern. Specifically, while it is common to estimate equation [1] by estimating a probit or a logit because (1) the predictions of the LPM can in principle lie outside the [0,1] interval, and (2) its error term is heteroskedastic, the goal of this paper is not to forecast contract choice but rather to study the structural relationships between contract choice and a few key explanatory variables, and all equations are estimated with robust standard errors, which takes care of the heteroskedasticity problem posed by the LPM. The following sections discuss, in turn, the identification and testing strategies relied upon in this paper.
Identification Strategy
Estimating equation [1] would pose no particular problem if ϵi were orthogonal to xP, xl, xt, and sa. In practice, however, endogeneity problems plague the cross-sectional analysis of contracts.
A well-known problem is the endogenous matching between landlords and tenants (Ackerberg and Botticini 2002). In this context, an endogenous matching problem could arise because wealth is used as a proxy for risk aversion. Let wl and wt denote the wealth levels of the landlord and the tenant, which are used here as proxies for risk preferences. In other words, wl = rL + ζl, and wt = rT + ζT, where rl and rT are the landlord and the tenant’s coefficients of absolute or relative risk aversion and ζL and ζT are error terms included in ϵi when relying on wealth as a proxy for risk aversion. But then, if the landlord and the tenant match along risk preferences (i.e., if wl is correlated with ζT or wt is correlated with ζL,), the estimated coefficients for the wealth levels are biased.
In order to control for the possibility that there is endogenous matching in the data, two types of controls are included. The first is a set of dummy variables that control for how the landlord and the tenant came to know each other. The second is a set of dummy variables that control for why the landlord chose this particular tenant. These two sets of dummy variables are discussed further below, when describing the data.
For some, another potentially important endogeneity problem could result from the selection of landowners into landlord status. Indeed, Dubois (2002) estimates a two-stage empirical model in which the first-stage equation accounts for the landowner’s selection into landlord status (i.e., the decision to lease the plot out) and in which the second-stage equation accounts for the landlord’s choice of contract. This paper does not model the decision to lease out and focuses instead on contract choice conditional on the fact that the landowner has chosen to become a landlord.
Indeed, it is important for the econometrician to control for selection in a context where he wishes to generalize his findings to an entire population. For example, when one wants to know whether the vitamin C absorbed from consuming orange juice has positive effects on health, one needs to estimate those impacts for everyone in the population, and not just in the subset of the population that already consumes orange juice, and may be consuming orange juice because this set’s members are a priori more health-conscious individuals. In this context, however, it makes little sense to want to generalize the findings of the contract choice equation to everybody, since not every landowner is a potential landlord. Consequently, because no attempt is made at controlling for the selection of landowners into landlord status, it stands to reason that the findings in Section V below are valid only for the subset of the landowner population that selects into landlord status.
Ultimately, clean identification is difficult if not impossible to obtain when conducting applied work on contracts using cross-sectional data. To generalize to an entire population of landlords, the ideal observational data set would include (1) experimentally derived (rather than estimated) measures of risk aversion for each landlord and each tenant (Lybbert and Just 2007), and (2) multiple observations for each landlord, each tenant, and each landlord-tenant match so as to allow controlling for the unobserved heterogeneity between landlords, tenants, and matches via landlord, tenant, and match fixed effects. Such an ideal data set, however, would be extremely costly and time-consuming to collect, and nothing guarantees that there would be enough variation in the contracts entered into by each party or in the landlord-tenant matches observed. People tend to contract with the same partners, and they tend to enter into the same contracts over and over. As a consequence, in most cases, the best one can do is to include a rich enough set of controls.
Testing Strategy
This section discusses how the tenurial insecurity hypothesis developed above is tested along with the canonical risk sharing hypothesis concurrently in this paper.
To test the risk sharing hypothesis, the landlord’s choice of contract is regressed on proxies for the landlord and the tenant’s risk preferences, as done by Laffont and Matoussi (1995), Ackerberg and Botticini (2002), Dubois (2002), and Fukunaga and Huffman (2009). Following Bellemare and Brown (2010), however, when using wealth or income as a proxy for risk aversion, one can only test that (1) the landlord is risk-neutral or her preferences exhibit constant absolute risk aversion (CARA), and (2) the agent is risk-neutral.5 Letting 
and 
denote the coefficients attached to the landlord and the tenant’s wealth levels, one can therefore only test the null hypothesis 
and 
versus the alternative hypothesis 
and 
. This means that a rejection of the null is not very informative in this context, as it only serves to reject that the landlord is risk-neutral or her preferences exhibit CARA and the tenant is risk-neutral. Moreover, we know from first principles that failing to reject the null is not informative, given that it does not allow one to accept the null. At best, failing to reject the null suggests that the conditions posed in the null hypothesis may hold in the data.
Turning to the tenurial insecurity hypothesis, given that the landlord’s optimal choice of contract in the tenurial insecurity model depends on sa rather than on s(a) (see the theoretical framework presented in Appendix A), the following identification strategy is adopted. The landlords’ subjective perceptions of tenurial insecurity (i.e., the inverse of s(a); that is, 1 − s(a)) were elicited as follows during the survey.
Given the contract signed by the landlord with her tenant, the following strategy was adopted to elicit her subjective assessment of the likelihood that she would lose her plot as a consequence of this contract. The landlord was given 20 tokens and asked to distribute them between two boxes, one labeled “0” and one labeled “1.” The landlord was told that the latter box—labeled “1” because it represented a 100% probability of losing the land—represented a state of the world where she lost her claim to the land as a result of the contract signed, whereas the former box—labeled “0” because it represented a 0% probability of losing the land—represented a state of the world where she kept her claim to the land. The landlord was also informed of various representations. For example, she was told that if she distributed her token evenly between the two boxes (i.e., 10 tokens in box “0” and 10 tokens in box “1”), it meant that her subjective assessment of the probability that she would lose her plot of land as a result of the contract signed with her tenant was 50%. Likewise, data on the landlord’s hypothetical perception of tenurial insecurity under the alternate contract (i.e., the contract not chosen) were also collected in the same fashion, since sharecropping and fixed rent are mutually exclusive and collectively exhaustive contractual forms in this context.6 This allows computing the discrete change in s(a) due to a (hypothetical) change of contracts from sharecropping to fixed rent.
To do so, let s(1) and s(0.5), respectively, denote the perceived security of tenure of a landlord entering a fixed rent or sharecropping contract, and sh(1) and sh(0.5), respectively, denote the hypothetical security of tenure of a landlord entering a fixed rent or sharecropping contract.7 The variable of interest in testing the tenurial insecurity hypothesis (i.e., sa) can then be computed as follows:
2where I( · ) is an indicator function equal to one if the condition between the parentheses is true and equal to zero otherwise.
Because a takes only two discrete values in the data, s(a) has no curvature, in other words, saa = (Δ2s(a))/(Δa2) is undefined. This allows assuming that sa is exogenous in the contract choice equation. Intuitively, because there are only two possible values of contract choice, which contract is chosen has no effect on the rate at which the likelihood of keeping the land changes as contract choice changes, because such a rate is undefined. There are no second-order effects of y on s, so that the rate of change in the landlord’s perceived likelihood of keeping her plot due to a change of contract choice is exogenous to contract choice.
In other words, the landlord’s perception of tenure security does not depend on the chosen contract but is driven by social norms. The exogeneity of sa is further justified by the fact that almost 80% of landlords have been involved in land tenancy in the past, and so their subjective expectations of tenure security were already formed prior to signing the current contract.
For sa then, the null hypothesis is thus H0: ∂y/∂sa = 0 versus the alternative hypothesis H0: ∂y/∂sa ≠ 0, that is, a test of whether the change in perceived security of tenure due to a change in contract decreases the likelihood of observing a sharecropping contract. Consequently, rejecting the null in favor of H0 : ∂y/∂sa > 0 will provide support in favor of the tenurial insecurity hypothesis. Lastly, γ = ∂y/∂sa can be interpreted below as the change in the likelihood of observing sharecropping over fixed rent due to a 100% increase in sa, so γ/100 gives the percentage change in the likelihood of observing sharecropping over fixed rent due to a 1% increase in sa.
IV. Data and Descriptive Statistics
The data used in this paper were collected by the author in Lac Alaotra, Madagascar, between March and August 2004. Lac Alaotra, which lies about 300 km to the northeast Antananarivo, is the country’s premier region for rice cultivation. Since sharecropping is mostly observed on rice plots in Madagascar (Karsenty and Le Roy 1996), rice is the Malagasy staple, and previous studies of sharecropping in Madagascar focused on Lac Alaotra, it is natural to focus on that region for the first formal empirical study of share tenancy in Madagascar.8
The survey methodology was as follows. First, the six communes with the highest density of sharecropping around Lac Alaotra were selected from the 2001 commune census conducted by Cornell University in collaboration with Madagascar’s Institut National de la Statistique and Centre National de la Recherche Appliquée au Développement (Minten and Razafindraibe 2003).9 Then, the two villages with the highest density of sharecropping were chosen in each commune, after determining the density of sharecropping in each village by going through communal records. In an effort to oversample sharecropping so as to increase precision, five households known not to lease in or lease out land were selected, five households known to lease in or lease out under a fixed rent contract were selected, and 15 households known to lease in or lease out under a sharecropping contract were selected in each village. All households were within the sampling frame in each village, and so the end result is a sample of 300 selected households.10
For each selected household, data were collected at the plot, household, and contract levels. Household- and (leased-in) plot-level data for the tenants of the 300 selected households and household-level and contract-level data for the landlords of the 300 selected households were then collected. The data covered a total of 1,029 plots, 387 of which were under land tenancy. Because of missing data, the empirical application below retains a sample of 353 land tenancy contracts. Table 1 defines some of the variables used in the estimation.
Data Description for Selected Variables
Table 2 presents descriptive statistics for the variables used in the contract choice equation. Almost 70% of the plots are sharecropped, with the remaining 30% leased out under a fixed rent contract. The average plot covers a little over 1 ha and is worth about $650 to its owner,11 and roughly 40% of the plots are titled.12 Almost 87% of the plots in the data are rice plots, with the remainder split two to one between lowland and hillside plots, and the average plot is 33 walking minutes away from the landlord’s house.
Descriptive Statistics (n = 353)
The average landlord household is composed of 5.5 individuals, a little under half of whom are dependents (i.e., under the age of 15 or over the age of 64). About 15% of landlords are female, and the average landlord is 53 years old and has five years of formal education. In terms of resources, the average landlord household has $107 worth of assets per capita, and an annual income per capita of $53.13 Lastly, 25% of landlords report being liquidity-constrained, proxied here by whether the landlord or the landlord’s spouse requested a formal or informal loan in the 12 months preceding the survey.
Turning to tenants, the average tenant household is composed of 5.7 individuals, a little under half of whom are dependents. The average tenant is 39 years old and has six years of formal education. In terms of resources, the average tenant household has $150 worth of assets per capita and an annual income of $54 per capita. Lastly, 37% of tenants report being liquidity-constrained, also proxied here by whether the tenant or the tenant’s spouse requested a formal or informal loan in the 12 months preceding the survey.
Comparing landlords and tenants, household characteristics are mostly similar between parties to the contract, but while the levels of income per capita of landlord and tenant households are similar, tenants are on average 41% wealthier than landlords, given their respective levels of assets per capita. This fact is in agreement with much of the extant literature on land in Madagascar, which discusses how “reverse tenancy” (i.e., land tenancy between poor landlords and rich tenants, or land tenancy in which the wealth ordering is reversed with respect to the usual scenario found in the literature, in which landlords are wealthier and more educated and own more land) is common throughout the country (Minten and Razafindraibe 2003; Bellemare 2009). The tenurial insecurity hypothesis developed in this paper (see Appendix A) can lead to such cases of reverse tenancy.
Although tenants are on average wealthier than landlords, tenants are more likely to be liquidity-constrained. This is not inconsistent with the fact that landlords are poorer than their tenants in these data. Indeed, the liquidity constraint dummies measure whether household heads or their spouses have requested a formal or informal loan during the 12 months preceding the survey. As such, landlords were simply less likely to request loans than their tenants, so that the liquidity constraint dummies are really lower bounds.
As regards the match and the matching process between the average landlord and the average tenant, 65% of land tenancy agreements in the data are signed between kin (i.e., between members of the same extended family, which in this context includes one’s grandparents, parents, siblings, children, aunts, uncles, cousins, nieces, and nephews), with the remainder signed between the landlord and a friend (27%). or a stranger introduced by kin (5%), or someone else (3%). The high proportion of kin contracts is consistent with the theoretical hypothesis of tenurial insecurity. Indeed, with tenurial insecurity, contracting with kin might offer partial insurance against adverse possession. Of course, this is merely suggestive, as it does not control for confounding factors.
In cases where the landlord was considering more than one potential tenant, she chose the current tenant for his honesty in 14% of cases, for his wealth in 8% of cases, for his ability to bear risk in less than 1% of cases, to return a favor in less than 1% of cases, and for other reasons in the remainder of cases. The average landlord spent 1.2 days looking for a tenant and considered 1.5 other potential tenants, and the average landlord-tenant match has lasted for two years.
Tables 3 and 4 report descriptive statistics for the same variables, respectively, by contract choice (i.e., by whether an observation is a sharecropping or a fixed rent contract) and by type of tenancy (i.e., by whether an observation constitutes a case of “regular” tenancy, in which the landlord is wealthier than the tenant, or a case of reverse tenancy, in which the landlord is poorer than the tenant).
Descriptive Statistics by Type of Contract
Descriptive Statistics by Type of Land Tenancy
Table 3 indicates that hillside plots are more likely to be leased out under a sharecropping contract. If the tenurial insecurity hypothesis developed in this paper turns out to be supported by the data, this would be consistent with Teyssier’s (1998) observation that hillside plots are among the most-contested ones in Lac Alaotra. Irrigated plots are more likely to be leased out under a fixed rent contract. Although landlord individual and household characteristics do not differ significantly between sharecropping and fixed rent contracts, sharecroppers tend to be less educated and their households tend to have higher dependency ratios than tenants in fixed rent contracts. Sharecroppers also have lower incomes per capita than tenants in fixed rent contracts, suggesting that as his income increases, a tenant becomes more likely to accept bearing more risk. This presupposes, however, that risk aversion is decreasing in income, and that income is a valid proxy for risk aversion. Lastly, when the landlord chooses her tenant in order to return a favor, she is more likely to choose a sharecropping contract.
Similarly, Table 4 indicates that plots under reverse tenancy agreements are more likely to be titled than plots under regular tenancy and that plots under reverse tenancy agreements are on average farther away from the landlord’s house than plots under regular tenancy. Leaving aside the wealth difference between landlord and tenants (along which the concepts of regular and reverse tenancy are defined in this paper, so that the wealth ordering observed in Table 4 is true by construction), landlords in reverse tenancy agreements are significantly older and less educated, and they have substantially lower incomes than landlords in regular tenancy agreements. Although landlords in reverse tenancy agreements are less likely to report being liquidity-constrained than landlords in regular tenancy agreements, recall that this variable only measures whether the landlord has requested a formal or an informal loan that was then denied during the 12 months preceding the survey. Consequently, the sign of the difference likely reflects the landlord selection into requesting loans. Tenants in reverse tenancy agreements have significantly smaller households and are more educated than tenants in regular tenancy agreements, and they also have substantially higher incomes than tenants in regular tenancy agreements. Surprisingly, landlords in sharecropping agreements (Table 3) or in reverse tenancy (Table 4) are neither more likely to be female nor more likely to be elderly, two findings that contradict the conventional wisdom about land tenancy in Madagascar (Jarosz 1990, 1991) and about reverse tenancy elsewhere (Bezabih 2007), which often talks of landlords in reverse share tenancy agreements being disproportionately single, elderly women.
Looking at the differences between the landlord-tenant match and the matching process between the landlord and the tenant between the regular and reverse tenancy subsamples, the landlord and the tenant are slightly more likely to be kin under regular than under reverse tenancy, but while this difference is statistically significant, it barely registers as economically significant. Lastly, tenants in regular tenancy agreements are more likely to have been chosen for their honesty or because the landlord owed them a favor than tenants in reverse tenancy agreements.
Finally, turning to the variable of interest in this paper, namely, the subjective expectations of the landlord, Table 5 reports the average landlord’s perceptions of tenurial security, in other words, her subjective perception of the likelihood that she will retain her claim to the land. Table 5 is split into three panels. The upper panel of Table 5 reports subjective expectations for the full sample of all land tenancy contracts in the data. Then, because there is a large proportion of reverse tenancy (i.e., contracts in which the landlord is poorer than the tenant) in the data, the middle and bottom panels of Table 5, respectively, report subjective expectations for the “regular” tenancy (i.e., contracts in which the landlord is wealthier than the tenant) and reverse tenancy subsamples.
Subjective Expectations of the Landlord
In all three panels, landlords are highly confident that they will retain their plot of land whether one considers actual (i.e., under the contract signed) tenure security s(a), hypothetical (i.e., under the alternative contract) tenure security sh(a), tenure security under sharecropping s(0.5), or tenure security under fixed rent s(1).
Indeed, in all cases, landlords report subjective perceptions of tenure security above 98%. Such high percentages are not inconsistent with the theoretical model of Section II, since the experimental literature has found that individuals commonly overreact to small-probability events (i.e., they behave as though small probabilities are in fact much higher and are thus seen as overweighing those small probabilities; see Kahneman and Tversky 1979). This thus seems to be the case here, but two additional examples come to mind. First, Nagin et al. (2002) conducted a field experiment in which even a likelihood as low as 3% of being monitored managed to induce optimal effort on the part of call center employees, and recent field experiments in China have shown that farmers significantly overweigh small-probability events (Liu 2011) when deciding whether to adopt improved varieties of cotton. In this case, if the tenurial insecurity hypothesis for the emergence of share tenancy developed in Section II is true, landlords seemingly overweight the probability of losing their plots.
More telling is the change in sa associated with a move from sharecropping to fixed rent. In all three panels of Table 5, a positive change in sa is associated with a move from sharecropping to fixed rent. Using the notation of Section IV, this suggests that ∂y/∂sa > 0, which is the empirical equivalent of Proposition 2 in Appendix A. Of course, this merely suggests that the hypothesized relationship between tenurial insecurity and land tenancy holds in these data, given that it fails to control for confounding factors. The next section investigates the relationship between tenurial insecurity and land tenancy more rigorously.
V. Estimation Results
Table 6 presents estimation results for the contract choice equation presented in equation [1]. The first column reports estimation results for a naïve specification that fails to control for the match and the matching process between the landlord and the tenant, and the second column reports estimation results for a specification that controls for the match and the matching process between the landlord and the tenant.
Linear Probability Models of Contract Choice in the Full Sample (n = 353)
In the naïve specification in Column 1, irrigated plots are over 20% more likely to be leased out under fixed rent than nonirrigated plots, perhaps because production is less risky on irrigated plots than it is on rain-fed plots, given the uncertainty over rainfall. On the landlord’s side, every additional year of age increases by 0.5% the likelihood of observing a fixed rent contract, and every additional year of education increases it by 2%. This last finding could mean that better-educated landlords have a better knowledge of the law and are thus in a better position to face adverse possession claims by their tenants.
On the tenant’s side, a 10% increase in the dependency ratio, which roughly measures labor quality within the household, implies a 3.1% decrease in the likelihood of observing a fixed rent contract, and for every additional $50 of income, the likelihood of observing a fixed rent contract increases by 5%.
This last finding offers some support for the risk sharing hypothesis, as it suggests that as tenants get wealthier, they are more likely to bear more production risk. It is important to note, however, that expected utility is defined in theory on final wealth rather than on income (Bellemare and Brown 2010), so this is merely suggestive. Perhaps more importantly, this interpretation would implicitly assume that the preferences of the tenant exhibit decreasing absolute risk aversion. The wealth levels of the landlord and the tenant, however, are neither jointly nor separately significant in this naïve specification, so that if one considers wealth, it is not possible to reject that the landlord is risk-neutral or her preferences exhibit CARA and that the tenant is risk-neutral. If one considers income, however, the income levels of the landlord and the tenant are barely significant at the 10% level.
More importantly, the tenurial insecurity hypothesis is supported by the data in this specification. Specifically, a 1% increase in the landlord’s subjective perception of tenurial security (i.e., sa) increases the likelihood of observing a fixed rent contract by 1.9%, and this finding is significant at the 1% level.
Few things change in the specification controlling for the characteristics of the match and of the matching process between the landlord and the tenant in Column 2. At the plot level, larger plots are less likely to be leased out under a fixed rent contract, but while this is statistically significant, it is only marginally economically significant: for every additional 100 m2 of plot size, the likelihood of observing a fixed rent contract decreases by 0.1%. Moreover, whereas the presence of irrigation on the plot entailed a 20% increase in the likelihood of observing a fixed rent contract in the previous specification, this is no longer significant when controlling for the characteristics of the match and the matching process. Likewise, the age of the landlord is no longer significant once the match and the matching process are accounted for.
As regards the landlord-tenant match, for every additional year the landlord and the tenant have been contracting together, the likelihood of observing a sharecropping contract increases by 2.4%. Laffont and Matoussi (1995) report a similar finding, with their interpretation being that successful repeated interactions lead to landlords trusting tenants a little bit more not to shirk in the face of the weaker incentives provided by a sharecropping relative to fixed rent. As for the matching process between the landlord and the tenant, for every additional potential tenant the landlord has considered before settling on her current tenant, the likelihood that she chooses a fixed rent contract decreases by 2%. This suggests that the more potential tenants there are, the more valuable a plot is perceived to be, and so the broader the scope for adverse possession, ceteris paribus.
More importantly, the tenurial insecurity hypothesis is once again supported by the data: a 1% increase in sa increases the likelihood of observing a fixed rent contract by 2.2%, a finding that is significant at the 1% level. As for the risk sharing hypothesis, it is once again the case that for every additional $50 of tenant income, the likelihood of observing a fixed rent contract increases by 5%, which again offers some partial support for the risk sharing hypothesis. In this specification, however, one fails to reject the null hypothesis that the risk preferences of the landlord and the tenant jointly determine contract choice both when risk preferences are proxied for by wealth and when they are proxied for by income.
Table 7 is almost identical to Table 6, except that it presents estimation results for the subsample of reverse tenancy, that is, for the subsample of cases where the landlord is poorer than the tenant, which is a defining feature of land tenancy in Madagascar. In the interest of brevity, the remainder of this section focuses on the variables of interest, namely, the change in the landlord’s perception of tenurial security and the proxies for the risk preferences of the landlord and of the tenant.
Linear Probability Models of Contract Choice in the Reverse Tenancy Sample (n = 225)
Once again, the tenurial insecurity hypothesis is supported by the data at the 1% significance level in the reverse tenancy subsample. The important difference between Tables 5 and 7 is that tenurial insecurity has a stronger impact than in the reverse tenancy sample than it does in the full sample. Whereas in the naïve specification, which fails to control for the characteristics of the landlord-tenant match and matching process, a 1% increase in sa increased the likelihood of observing a fixed rent contract by 1.9% in the full sample, and a 1% increase in sa increased the likelihood of observing a fixed rent contract by 2.4% in the reverse tenancy sample. Likewise, whereas in the specification that controls for the characteristics of the landlord-tenant match and matching process, a 1% increase in sa increased the likelihood of observing a fixed rent contract by 2.2% in the full sample, and a 1% increase in sa increased the likelihood of observing a fixed rent contract by 3.9% in the reverse tenancy sample.
This strengthening of this paper’s core result when considering the reverse tenancy sample suggests that landlords whose tenants are wealthier than they are perceive that their claim to their own plot of land is weaker than it is for the average landlord, in other words, that landlords in reverse tenancy agreements believe they have less bargaining power than the average landlord.
Finally, as regards the risk sharing hypothesis in the reverse tenancy sample, it is once again the case that for every additional $50 of tenant income, the likelihood of observing a fixed rent contract increases significantly. The magnitude of this impact, however, is decreased slightly, from 5% in Table 6 to 4% in Table 7. While this once again offers partial support in favor of the risk sharing hypothesis, in neither specification can one reject the null hypothesis that the risk preferences of the landlord and the tenant jointly determine contract choice in Table 7, both when one uses wealth or income as a proxy for risk preferences.
The results in Tables 6 and 7 thus offer strong support for the hypothesis that tenurial insecurity drives the emergence of sharecropping in these data, especially since sa has the expected effect, and one cannot reject the hypothesis that the risk preferences of the landlord and the tenant do not jointly determine contract choice.
Indeed, following Bellemare and Brown (2010), and allowing for the possibility that risk preferences are defined over income rather than over final wealth, the results in Tables 6 and 7 lead one to (1) fail to reject the null that the average landlord is risk-neutral or that her preferences exhibit CARA, and (2) reject the null that the average tenant is risk-neutral. To conclude that this is empirical support for the canonical risk sharing hypothesis, however, one would need to make the additional assumption that tenant preferences exhibit decreasing absolute risk aversion (DARA). But then, there is no reason to believe that tenant preferences exhibit DARA, especially since there is a failure to reject the hypothesis that the average landlord’s preferences exhibit CARA in Tables 6 and 7.
The results in Tables 6 and 7 are thus especially favorable to the theoretical model in Appendix A, given that one rejects the null hypothesis that tenurial insecurity plays no role in explaining contract choice while finding little support for the canonical risk sharing hypothesis. So even though Bellemare (2011) finds that formal land titles have no impact on agricultural productivity in Madagascar, it appears that tenurial insecurity does shape some aspects of economic behavior in the region. Indeed, Bellemare also shows that while formal land rights—land titles—indeed have no impact on agricultural productivity in Madagascar, landowners’ subjective perceptions of their informal land rights—what they can or cannot do with their plots—do affect productivity. The findings in this paper thus do not contradict those on formal titles. Indeed, the conclusion that land titles do not increase tenurial security does not mean that there is no tenurial insecurity, the effects of which have been shown empirically in this paper to be considerable on the land tenancy market.
VI. Conclusion
This paper has developed a hypothesis and subsequent theoretical explanation for the emergence of sharecropping in Lac Alaotra, Madagascar’s most important rice-growing region. In this setting, conversations with landowners during preliminary visits to the field have shown that some landlords perceive more tenurial insecurity when leasing out under a fixed rent contract than when leasing out under a sharecropping contract. The conceptual framework developed in this paper thus dynamicizes the canonical principal-agent model of sharecropping (Stiglitz 1974) and augments it by incorporating an important transaction cost, namely, the risk that the landlord will lose her plot as a result of the contract she chooses to sign with her tenant.
Then, using data on the landlords’ subjective perceptions of tenurial insecurity and incorporating recent advances in applied contract theory (Bellemare and Brown 2010), this paper has concurrently tested the hypotheses that (1) contract-dependent tenurial insecurity drives contract choice, and (2) risk preferences drive contract choice. The data strongly support the tenurial insecurity hypothesis developed in this paper at the expense of the risk sharing hypothesis, showing that a 1% increase in the landlords’ subjective perception of tenurial insecurity (i.e., the likelihood she will lose her claim to her plot of land) increases the likelihood of observing a sharecropping contract by about 2%. This finding is robust to whether one considers the full sample of land tenancy or the restricted sample of reverse tenancy, that is, land tenancy contracts in which the landlord is poorer than the tenant, a form of tenancy that is the norm rather than the exception in this context. This finding is strengthened when controlling for the characteristics of the landlord-tenant match and of the matching process between the landlord and the tenant (Ackerberg and Botticini 2002).
When comparing to previous empirical studies of land tenancy, what is distinct about the study context is the apparent presence of a social norm that associates different land tenancy contracts with different degrees of tenurial insecurity, as well as the prevalence of reverse share tenancy agreements. Although the former appears to be specific to Madagascar, more in-depth empirical investigations of land tenancy markets in other countries might reveal that similar social norm exists elsewhere. The latter, however, is common throughout the world. Indeed, instances of reverse tenancy have been observed in Bangladesh (Pearce 1983), Eritrea (Tikabo 2003), Ethiopia (Bezabih 2007), India (Singh 1989), Lesotho (Lawry 1993), Malaysia (Pearce 1983), the Philippines (Roumasset 2002), and South Africa (Lyne and Thomson 1995). It is likely that tenurial insecurity plays a role in shaping land tenancy in some of those countries. In Ethiopia, for example, all lands belong to the state, which periodically redistributes lands. More generally, the conceptual framework developed in this paper would apply to any rental market—land or otherwise—in which there is a significant likelihood that the lessor will lose the asset being rented to the lessee as a consequence of the terms of the contract.
One shortcoming of the empirical analysis in this paper is that it is impossible to fully control for the unobserved heterogeneity between landlords, tenants, and landlord-tenant matches using the data at hand. In fairness, this is common to almost all empirical investigations of contract theory. An exception to this would be Karlan and Zinman’s (2009) recent randomized study of the credit market in South Africa, the design of which allows disentangling the effects of adverse selection and moral hazard.
Another, perhaps more important, shortcoming of the empirical analysis of this paper is that it could not investigate the precise reason why tenurial insecurity affects contract choice. Institutions—that is, both specific provisions of the formal legal system and informal provisions of social norms—are conducive to contract choice affecting one’s subjective perception of tenurial insecurity in Madagascar, but it is impossible to identify the exact mechanism through which this happens. Addressing this concern would require a careful investigation of the way individuals form their expectations regarding tenurial insecurity.
Acknowledgments
I am grateful to Chris Barrett, Pierre Dubois, David Just, Ravi Kanbur, and Bart Minten for their guidance, as well as several seminar audiences and conference participants for comments and suggestions. I am also indebted to Nate Engle for patiently sharing his extensive knowledge of Lac Alaotra, as well as to Mamy Randrianarisoa and his survey team for data assistance. I have benefited from the generous financial support received from the National Science Foundation through Doctoral Dissertation Improvement Grant SES-0350713; from USAID through grant LAG-A-00-96-90016-00 to the BASIS CRSP; and from the Social Science Research Council’s Program in Applied Economics with funds provided from the John D. and Catherine T. MacArthur Foundation. All remaining errors are mine.
Appendix A: Theoretical Framework
This section develops a dynamic principal-agent model in which sharecropping can emerge as the optimal contract even when the tenant is risk-neutral. This result hinges upon the presence of tenurial insecurity in a way such that the more (less) production risk is borne by the landlord, the stronger (weaker) her subsequent claim to the land.
The model developed in this section thus nests both the canonical principal-agent model of share tenancy as well as the transaction cost–based explanation developed in this paper. As such, it is closely related to that of Dubois (2002), but with one important difference: whereas in Dubois’s model, the terms of the contract influence future production possibilities via tenant effort, in this paper, the terms of the contract affect the landlord’s (expected) plot value.
Assume a production technology f(et), where et is effort in period t, fe > 0, fee < 0, and f ( · ) is twice continuously differentiable. Assume further that f ( · ) is linear homogeneous with respect to land. For a fixed amount of land ht, the production function is such that qt = υtf (et), where υt is an exogenous shock with E(υt) = 1.
The law of motion for the plot under contract is ht = s(at)ht − 1 + ϵ, where a is the share of output that goes to the tenant and ϵ is an exogenous shock with E(ϵt) = 0 so that E(ht) = s(at)ht − 1.14 The function s( · ) represents the strength of the landlord’s property right (i.e., her tenurial security), with Sa < 0.
Assume that the landlord is risk-averse and, without any loss of generality, that the tenant is risk-neutral. The tenant’s expected payoff is then such that
A1where bt is a side payment and ψ( · ) is the agent’s effort cost function, ψe > 0, ψee > 0, and ψ( · ) is twice continuously differentiable. When bt > 0, the side payment is a fixed wage paid by the landlord to the tenant. Alternatively, when bt < 0, the side payment is a fixed rent paid by the tenant to the landlord. And although this side payment is usually set equal to zero in practice in the context of a share tenancy contract, it is in principle possible for such a side payment to take place even outside of fixed rent and wage contracts. In other words, the model can accommodate cases where a ∈ (0,1) and bt ≠ 0.
Likewise, the landlord’s expected payoff is such that
A2where U( · ) is a von Neumann-Morgenstern utility function such that U′ > 0, U″ < 0, and U( · ) is twice continuously differentiable. Finally, let Ū denote the tenant’s reservation utility. Then, the landlord’s problem is to solve
A3
A4
A5
A6where δ ∈ (0,1) is the landlord’s discount factor.
Applying the first-order approach (Rogerson 1985; Jewitt 1987), one can rewrite the agent’s incentive compatibility constraint as
A7The Bellman equation for the above problem is then
A8
A9
A10where h0 denotes initial plot size, and h1 = s(a)h0 + ϵ. Before deriving the optimal contract, however, it is necessary to establish the following results.
Lemma 1: Tenant effort is increasing in crop share, that is, ea > 0.
Proof: From equation [A7], a = ψe/E[υfe]. As a increases, ψe/E[υfe] also increases. Since ψee > 0 and fee < 0, this means that as a increases, e(a) also increases, so that ea > 0.
Lemma 2: The side payment is decreasing in crop share, that is, ba < 0.
Proof: From equation [A4], the side payment is such that b(a) = Ū + ψ(e(a) − aE[vf (e(a))]. But then,
ba = − ea {aE[υfe] − Ψe} − E[υf (e)], and from equation [A7], aE[vfe] − ψe = 0 at an optimum, so that ba = − E[vf (e)] < 0.
Lemma 3: The value function is strictly increasing, that is, 
.
Proof: See Stokey and Lucas (1989).
Lemma 4: The value function is strictly concave, that is, 
.
Proof: See Stokey and Lucas (1989).
These intermediate results then lead to the following results.
Proposition 1 (optimal contract): Given the assumptions made so far, in the presence of tenurial insecurity, sharecropping emerges as the optimal contract between a risk-averse landlord and a risk-neutral tenant.
Proof: To solve the Bellman equation, one must compute the first-order condition with respect to a. Using the substitution method to solve it yields the crop share in the optimal contract, a, such that 
, where the first term is the first-best (i.e., fixed rent) contract and the second term is the effect of tenurial insecurity, that is, the strength of the landlord’s claim to the land. Since all the variables in the second term are positive except for sa, the incentives are weaker than under the first-best contract, and sharecropping emerges as the optimal solution.
Proposition 2 (comparative statics): Given the assumptions made so far, in the absence of tenurial insecurity, the landlord offers the tenant a sequence of fixed rent contracts, that is, a* = 1 in all time periods. With tenurial insecurity, (da*)/(dsa) > 0, that is, the stronger the landlord’s claim to the land, the more likely she is to offer the tenant a fixed rent contract. Conversely, the weaker her claim to the land, the more likely she is to offer a sharecropping contract.
Proof: Taking the derivative of the slope of the optimal contract with respect to sa yields 
. So as sa increases, the slope of the optimal contract increases. Because sa < 0, in the limit, sa = 0 and a* = 1; that is, without tenurial insecurity, a fixed rent (i.e., first-best) contract obtains between a risk-averse landlord and a risk-neutral tenant. With tenurial insecurity, however, a* < 1.
Proposition 2 provides a useful testable implication: given data on both the landlords’ perception of tenurial insecurity and on the contracts they choose, one can test the null hypothesis that tenurial insecurity has no effect on the probability of observing a sharecropping contract relative to the probability of observing a fixed rent contract. In this paper, this hypothesis is tested alongside the usual risk sharing hypothesis so as to determine which of these two hypotheses drives contract choice in the data.
Appendix B: Imputed Variables
Imputations of Land Value and Formal Title
Footnotes
The author is assistant professor, Sanford School of Public Policy, Duke University, Durham, North Carolina.
↵1 See Shaban (1987) and Arcand, Ai, and Éthier (2007) for evidence in favor of moral hazard in India and Tunisia, respectively. Sadoulet, de Janvry, and Fukui (1997), however, find that contracts between kin eliminate the moral hazard problem in the Philippines. Likewise, Kassie and Holden (2007) find that the threat of eviction eliminates moral hazard in Ethiopia, but that this effect disappears in contracts between kin. Lastly, Braido (2008) finds no evidence of moral hazard due to sharecropping in India, finding instead that the efficiency loss arises because sharecropping typically occurs on lower-quality land than does fixed rent. Given data limitations, it is not possible to conduct a cleanly identified test of moral hazard in the present context.
↵2 Given that data collection focused on the contracts themselves and not on land redistribution mechanisms or village-level institutions, this paper takes tenurial insecurity as given. Although it would be of interest to open the “black box” of tenurial insecurity and land redistribution, it is beyond the scope of this paper to do so. Bellemare (2009) studies the determinants of the subjective expectations used in this paper and finds that few, if any, variables explain how these subjective expectations are formed.
↵3 Indeed, if no one could be assumed risk-neutral or to act as if risk-neutral because of better opportunities for risk diversification or better access to insurance, one would never observe fixed rent contracts in the real world.
↵4 Ellickson then illustrates his hypothesis by discussing case studies of the norms that developed in the whaling industry (Ellickson 1989) and among the cattle ranchers of Shasta county in California (Ellickson 1994).
↵5 See Section IV for a precise definition of wealth in the context of this paper.
↵6 This is the perception of tenurial insecurity under the alternative contract. The two tenurial insecurity questions were asked four months apart to eliminate the risk of anchoring (Tversky and Kahneman 1982).
↵7 For all sharecropping contracts in the data, a = 0.5.
↵8 See the descriptive studies of sharecropping in Lac Alaotra by Charmes (1975) and Jarosz (1990, 1991).
↵9 A commune is roughly the equivalent of a district in the United States.
↵10 All descriptive statistics and estimation results control for the oversampling of households that enter sharecropping agreements by using sampling weights. Ideally, one should also control for the choice-based nature of the sample (Manski and Lerman 1977). Unfortunately, population proportions at the contract level have never been collected in Madagascar, making the choice-based sampling correction impossible to implement.
↵11 Dollars are U.S. dollars; $1 ≈ 2,000 ariary.
↵12 Due to an error in survey design, both the plot value and the formal title dummy variables had to be imputed. See Appendix Table B1 for the imputations. Robustness checks were conducted that omitted these imputed variables, which did not change the core findings of this paper.
↵13 The value of landholdings is omitted from wealth calculations given that land markets are extremely thin in Madagascar. Minten and Razafindraibe (2003) report that only 13% of the plots in their nationally representative sample had been purchased by their owners, and that 73% of plots had been inherited. While it is easy to recover land value in the former case, it is near impossible in the latter case, and although a household’s landholdings are an important factor in determining its wealth, its livestock holdings, which are included in this paper’s measure of assets, are often a better indicator of household wealth (Minten and Razafindraibe 2003).
↵14 As with Dubois (2002), this section focuses on linear contracts, both because the tools of contract theory do not allow determining the shape of the optimal contract in a dynamic setting and because linear contracts are used in the vast majority of land tenancy agreements in the real world, probably as a means of eliminating contracting costs.
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