Sharecropping And Uncertainty The Risk Sharing Rationale Economics Essay
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In rural agriculture we observe the existence of various forms of contracts in the cultivation of land. More specifically, we distinguish between three forms of contractual agreements. In fixed-rent contracts the tenant pays a fixed sum of money to the landlord, the rent, and obtains the right to cultivate land in return. In a fixed-wage contract the tenant is paid a constant wage by the landlord. Finally, with sharecropping the tenant receives an agreed upon share of the output he has produced and passes the remaining share on to the landlord. 
Empirically, we widely observe the prevalence of sharecropping in particular in South Asia, where it is the dominant agricultural contract.  The wide-spread existence of sharecropping has puzzled economists since Alfred Marshall demonstrated that share contracts in terms of the efficiency of agricultural production are clearly inferior to fixed-rent tenancy.  In fact, Marshall showed that all contracts but a fixed-rent contract will lead to an undersupply of labour by the tenant and thereby make agricultural production diverge from its efficient level. 
The fact that the existence of sharecropping cannot be explained in terms of efficiency considerations has led many scholars to seek alternative explanations. The predominant rationale has been risk-sharing between the landlord and the tenant. Nevertheless, with constant returns to scale it can be shown that sharecropping has no extra-risk-sharing advantage over a suitable mix of fixed-rent tenancy and wage-labour contracts.
In this essay, in a first step I will outline the relationship between sharecropping and risk-sharing. Furthermore, I will discuss the argument refuting this rationale and possible qualifications of its results. Lastly, I will demonstrate that sharecropping is underpinned by other rationales, such as incentive provision and screening, making share contracts not only a response to uncertainty but also to problems arising from information asymmetries, such as moral hazard and adverse selection.
Sharecropping and uncertainty: the risk-sharing rationale
Risk-sharing as a rationale for sharecropping
The existence of sharecropping has commonly been explained in terms of risk-sharing. Even though a tenant could yield a higher return by a fixed-rent contract and overall economic surplus would be superior, because the output of the tenant does not fully depend on his labour input (but say on weather conditions or other stochastic variables), the tenant will not be willing to bear all the risk arising from agricultural production. Uncertainty is a crucial factor in the determination of output  and because of imperfections in the insurance market the tenant cannot obtain insurance and usually has no other means of diversifying risk.
On this backdrop, in a share contract risk associated with agricultural production accrues in part both to the tenant and to the landlord and sharecropping may therefore emerge if both the tenant and the landlord are risk-averse. This has first been outlined by Cheung who suggested that sharecropping contracts have risk-sharing advantages over fixed-rent and wage contracts.  To formally display the risk-sharing argument we can follow Ray in conceptualising the fixed-rent and sharecropping contracts as two risky gambles between which the tenant chooses.  Here, the landlord and the tenant are expected to be risk-neutral and risk-averse respectively. We assume a binomial distribution of output where the good and bad levels of output are denoted by and , each having a probability attached to them. In the case of the fixed-rent contract, where is the fixed rent paid by the tenant to the landlord, irrespective of output, the landlord's return is , while the tenant receives or . With a sharecropping contract that yields the same expected return of the landlord the latter will receive
which is set equal to , determining the share for the landlord as
The landlord, because he is risk-neutral is indifferent between those two contracts that would yield him . The tenant in the good state receives in the fixed-rent contract and with the sharecropping alternative. By substituting we get
The sharecropping contract lowers the return to the tenant in the good state, but since the share has been chosen such that the expected monetary values are the same to either party under the two contracts, the tenant's return under the bad state is increased relative to fixed rent. Therefore, while sharecropping and fixed-rent contracts have the same expected value, the spread of returns to the tenant is narrower under sharecropping. He would therefore prefer a share contract and the landlord knowing this can create a larger expected payoff by cutting the tenant's share to a point where the tenant still prefers the sharecropping contract.
A critique of the risk-sharing argument
Several authors, first among them Newbery in a response to Cheung's observations, have brought forward a critique of the risk-sharing argument for the existence of share contracts.  Stiglitz notes the following:
"[If] workers and landlords can mix contracts [i.e. workers can work for several different landlords and landlords hire workers on several different 'contracts'], the pure sharecropping contract can be dispensed with, in the sense that all the risk-sharing opportunities could be provided by combining pure wage and pure rental contracts." 
We can formalise this argument following Bardhan/Udry.  We assume a production function , where denotes cultivated land, is labour input and is a random parameter that stands for uncertainty in agricultural production. The production function exhibits constant returns to scale for any . denotes the share of output that accrues to the tenant with the remaining share being passed on to the landlord. The rental and wage rates are and respectively.
In the model, the landlord rents out a fraction to the tenant and hires wage labour for the remaining fraction of land. The tenant, in return devotes a fraction of his labour to cultivating land under a fixed-rent contract and the remaining fraction to doing so under a wage contract. The tenant's income will then be
The landlord's income is given by
, as .
The landlord is better off under the sharecropping arrangement than under the mixed contract if , whereas the tenant is better off with a share contract if . Therefore, the only possible solution for a sharecropping contract to emerge is in which case, both incomes for the landlord and the tenant are equal to the income received under sharecropping. Share contracts then have no risk-sharing advantages of a suitable mix of fixed-rent and wage contracts.
Several qualifications of this result have been pointed out by Singh.  Firstly, we may add to the above analysis the factor of how the wage rate, the rental rate and the share are determined. If we do this we find that potential inefficiencies arise with wage and fixed-rent contracts alone which lead to a situation where sharecropping can be advantageous in terms of risk management. If we imagine, for example, a monopoly situation in the land market where the landlord chooses the rental rate in response to demand and both the landlord and the tenant take the wage rate as given, we observe a monopolistic inefficiency situation and a sharecropping contract with a side payment would make both parties better off.
A further qualification is made by Singh on the basis that the refutation of the risk-sharing rationale for sharecropping only considers linear share assignments: "Any linear function of output will slope between 0 and 1 and constant term between and can be attained for the tenant through a mix of fixed-rent and wage contracts."  However, by assuming linear share assignments we may fail to take into account risk-sharing advantages provided by non-linear share contracts over fixed-rent and wage contracts.
A third qualification of the statement is made on the basis that refuting risk-sharing advantages of share contracts mostly limit their observations to uncertainty in output. However, often we have reason to believe that input is also risky. This has been argued by Newbery who specifically looks at labour market imperfections that might affect risk in input. 
Sharecropping and information asymmetries: incentives and screening
Incentive Provision and Sharecropping
So far we have looked at sharecropping contracts as a response to uncertainty in agricultural production and we have seen that share contracts may provide certain risk-sharing advantages that under certain circumstances, however, can equally be provided by a mix of fixed-rent and wage contracts.
In fact, risk-sharing is not the only rationale for the existence of sharecropping and we may understand share contracts as a response to information asymmetries existing in agricultural production. One problem arising from such information asymmetries is moral hazard. Often labour input by the tenant cannot be observed by the landlord, but only output produced, leading to a situation in which the tenant can 'shirk' and undersupply labour input. The landlord and the tenant will find themselves in a principal agent relationship where any contractual form will have to deal with the problem of inducing high effort exerted by the tenant through adequate incentive provision. 
There are various models explaining share contracts in terms of the presence of incentive problems arising from labour as an unobservable input. These include the incentive insurance trade-off model, the two-sided incentive model as well as limited liability models pointing to wealth constraints on the part of the tenants.  We will look at the two-sided inventive problem put forward by Eswaran and Kotwal in more detail.
Eswaran and Kotwal show that sharecropping may emerge as a contractual form when both the landlord and the tenant provide labour inputs that are not observable to the other party.  In their model both the tenant and the landlord are risk-neutral and the amount of land is given, such that the land variable is ignored. The production function is given by where is managerial input, is effective labour input, is expected output and is a random variable with expected value 1. We define effective labour input in terms of two elements ), where is supervisory input, is labour hired and is a parameter that denotes the relative importance of supervision in one unit of effective labour. If we substitute into the initial production function we obtain .
It is assumed in the model that hired labour can be easily observed, whereas managerial and supervisory effort cannot and that the tenant and the landlord possess different abilities in exerting these efforts. More specifically, the landlord is in a position where he has more managerial qualities through access to markets, information and institutions and therefore can conduct management more efficiently. The reverse holds true for the tenant who can better provide the supervision of family labour. This relationship is expressed in terms of two parameters and which denote the fraction of the landlord's time spent on management equivalent to one hour of the tenant's time spent so and the fraction of the tenant's time spent on supervision equivalent to the landlord's time spent so respectively. 
Eswaran and Kotwal perform numerical calculations to look at the outcomes, i.e. the expected net income of the landlord, of three different contractual forms, where in the first type of contract the landlord cultivates his land through hired labour and provides management and supervision efforts himself. A further possibility is for the landlord to lease out his land to a tenant to provide and while hiring labour . Lastly, the landlord and the tenant can provide and respectively, each drawing on their comparative advantage in their specialised field, in which case they enter a sharecropping contract. Since neither will obtain their full marginal product and effort is unobservable as outlined at the outset incentive problems arise.
The results obtained from the model indicate that the choice of contract will depend on the values that the parameters and take. If they are low, sharecropping will be preferable to the landlord, while if only or are high he will choose a fixed-rent or a fixed-wage contract respectively. This means that a sharecropping contract will emerge if the landlord and the tenant display considerable advantages in their field. More generally, the model allows us to conclude that sharecropping contracts can be seen as a response to moral hazard problems arising from a pooling of labour inputs by the landlord and the tenant.
Adverse selection: screening as a rationale for sharecropping
Another rationale that has been advanced for the existence of sharecropping is screening.  While explaining share contracts in terms of moral hazard problems arising from information asymmetries, screening is a device to respond to adverse selection problems, similarly occurred through asymmetric information. The argument for sharecropping that relies on adverse selection states that there are tenants with different types of abilities and share contracts can be used to screen tenants according to these abilities. The assumption is that by offering a set of different contracts different ability tenants will choose the contract that best fits their ability. Sharecropping then has a role to play in the set of different contracts that are offered for screening and will most likely be chosen by low ability tenants. 
To demonstrate this, we follow Hallagan's argument formalised by Singh where a single landlord has two identical plots of land and several potential tenants, one of which is of higher ability than the others.  Since the plots cannot be cultivated by one tenant the landlord aims to attract a higher ability and a lower ability tenant. The expected output of the high ability and the low ability tenant are and respectively, with output being stochastic such that ability cannot be derived from output. Because of this, the landlord cannot discriminate between two tenants by charging them different rents: with their types being hidden the high ability tenant would claim to be of a lower ability and demand a lower rent.
The model shows that the landlord can do best if he chooses a set of contracts that offers a fixed-rent and a share contract to be chosen by the high ability and the low ability tenant respectively. For the desired contract selection to occur, the tenants' respective incentive compatibility constraints and must hold. We see that the high ability tenant prefers the fixed-rent contract whereas the low ability tenant will prefer the share contract, as on rearranging we obtain which if preferences were reversed would not hold.
The landlord maximises his expected income by choosing subject to the tenants' incentive compatibility and participation constraints and . We first consider the participation constraint of the high ability tenant to be binding, such that with the landlord's expected income . In this case the this expected income is maximised by setting so that the low ability tenant just accepts the share contract and the high ability tenant is better off than with the alternative
The landlord then receives
If the low ability tenant is indifferent between the two contracts, then . Since from the participation constraints must be the same, the landlord's expected income is
which is lower and therefore the landlord is better off with the first possibility.
In fact, the participation constraint will be binding for the tenant who has an incentive to pretend to be a different type when offered two different contracts. For the landlord the screening contract is better as opposed to the alternative of charging a low rent or a high rent, under the condition that the difference in productivity between the high ability and the low ability tenant are not too striking. As a result, we can conclude that share contracts can provide a response to the existence information asymmetries, and more specifically hidden types of tenants in agriculture.
In this essay, we have departed from the principle of Marshallian inefficiency of sharecropping as a basis to look at one of the predominant rationales for sharecropping which has been risk-sharing between the tenant and the landlord as a response to uncertainty in agricultural production. We have discussed the critique of this rationale for sharecropping which consists in demonstrating that under constant returns to scale sharecropping arrangements have no extra risk-sharing advantages over a suitable mix of fixed-rent and wage contracts and have argued that under certain circumstance the risk-sharing role of sharecropping can be upheld.
As opposed to the rationale derived from uncertainty, we have looked at those rationales underlying share contracts that deal with asymmetric information to explain the persistence of sharecropping among agricultural contractual forms. We have first looked at moral hazard issues arising from the non-observability of labour input or hidden action by the tenant on the part of the landlord and have identified sharecropping as a response to this problem through incentive provision.
Furthermore, we have considered the second problem arising from information asymmetries when the types of potential tenants are hidden. We have outlined how screening as a response to adverse selection problems can involve the offering of sharecropping contracts co-existing with other kinds of contracts leading tenants to self-select themselves for an appropriate type of contract. We can therefore conclude, that given the existence of information asymmetries, sharecropping contracts may provide desired contractual outcomes which can explain their prevalence in agricultural production.
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