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Bargaining and Efficiency in Sharecropping


Jon Reiersen*

Vestfold College

P.O. Box 2243, N-3103 Tønsberg

Norway

E-mail: jon.reiersen@hive.no



Abstract: The paper uses a generalized Nash bargaining to derive solutions for the rental share and labor input in sharecropping. The bargaining is modeled as a two stage process. There is first a bargain about the rental share, and then a bargain about labor input. The power of the landlord to ensure an outcome favorable to himself may differ in the two stages. By imposing particular assumptions about these bargaining powers, some popular models of sharecropping that have been treated as completely separate in the literature, can be derived as special cases in our model. However, we also generate a new class of models. It is also demonstrated that it is not the tenant’s influence in the labor input decision per se which causes inefficiency in sharecropping, but differences in the tenant’s influence over different issues in the contract. This is in contrast to the popular view which states that if the tenant controls the level of labor input, sharecropping will result in an inefficient resource allocation.

* Previous versions of this paper have been presented at the 17th National Meeting of Economists, University of Bergen, January 1997 and at the workshop Institutions in Development, University of Copenhagen, June 1997. I am indebted to Kalle Moene for helpful discussions and valuable advice at various stages of preparing this paper. I have also benefited from comments by Turid Bøe, James Godbolt, Steinar Holden, Jon Strand, and seminar participants at the University of Copenhagen and at the University of Oslo. Financial support from the Norwegian Research Council is gratefully acknowledged.



1. Introduction
Sharecropping is widely observed in developing countries. In Bangladesh, for example, about 21 percent of all farmland is cultivated under different tenurial arrangements, of which 91 percent is cultivated under sharecropping. In the Philippines about 79 percent of all tenanted land are sharecropped, while the figure in Indonesia is 60 percent (Hayami and Otsuka, 1993).1 In spite of a lot of theoretical and empirical work in recent years, there has been little convergence among economists in the opinion on sharecropping. As will be further discussed in this paper, the divergence has been especially great in the understanding of how this contractual arrangement affects resource allocation and efficiency in agriculture. Although a large number of models of sharecropping have been developed in recent years, the literature has basically followed two approaches to modeling such contracts.2 The first portrays the institution of sharecropping as inefficient. The argument runs as follows: A tenant whose contract stipulates only the share to be paid as a rent, will have an incentive to use variable inputs, in particular his labor, less intensively than an owner-operator or a tenant leasing in land on a fixed- rent basis. Production will accordingly be lower on cropshared land compared to fixed-rent tenancy and owner cultivation. Such an approach, often called Marshallian analysis, characterizes the works of Bardhan and Srinivasan (1971), Stiglitz (1974), Bell and Zusman (1976), Lucas (1979), and Shetty (1988), among others. The second approach to modeling sharecropping is based on the work of Cheung. This approach argues that the contract offered by the landlord will not only stipulate the tenant’s share of output, but also the labor input to be applied on the land. A conclusion from this analysis is that productive efficiency prevails as the intensity of cultivation and the marginal product of labor are equated across lands that are owned or rented. Major advocates of the Cheungian thesis are Cheung (1968, 1969) and Newbery (1974; 1975).

In the literature, the Marshallian and Cheungian approach have been treated as competing models of sharecropping. A large number of empirical studies have therefore been carried out in order to test which one is the appropriate model.3 The results of these studies are, however, mixed, so the existing empirical evidence has not yet been able to settle the issue.



In this paper we argue that the difference between the Marshallian and the Cheungian model of sharecropping is somewhat exaggerated. Our aim is to show that the two models can be viewed as special cases of a more general model of sharecropping. The way we integrate the two models is to look at a sequential bargaining framework, developed in another setting by Manning (1987). We look at a bargain between a non-cultivating landlord and a landless tenant. The bargain is modeled as a two-stage process: In the first stage the rental share is determined and in the second stage labor input. The power of the landlord to ensure an outcome favorable to himself may differ in the two stages.

As will be shown, this model can be helpful in interpreting a number of aspects of sharecropping. First, it is demonstrated that some popular models of sharecropping can be derived as special cases, by imposing particular assumptions about the two parties bargaining power. However, we also generate a new class of models.

Secondly, the model provides a new perspective on the relationship between the tenant’s influence in the labor input decision and efficiency in sharecropping. It is shown that it is not the tenant’s control over labor input per se which causes inefficiency, but differences in the tenant’s influence over different issues in the contract. This is contrary to the popular (Marshallian) view which states that if the tenant controls the level of labor input, sharecropping will result in an inefficient resource allocation.

This last result also has some implications for the interpretation of recent empirical work on sharecropping (e.g. Bell, 1977; Bliss and Stern, 1982; Nabi, 1986; Shaban, 1987; and Bhuiyan 1987). As mentioned, a central aspect of this work has been to test which is the appropriate model of sharecropping; the Marshallian or the Cheungain. The tests have essentially been based on an examination of whether the intensity of cultivation is lower on sharecropped land compared to land that is owner cultivated or cultivated on a fixed-rent basis. If it is not, the Marshallian inefficiency hypothesis of sharecropping is rejected and the Cheungian hypothesis is accepted. Although the first part of this test is satisfactory, the rejection of the Marshallian model does not, however, automatically justify acceptance of the Cheungian model - if one accept the framework used in this paper. This also applies for the opposite. A rejection of the Cheungian model does not automatically justify acceptance of the Marshallian model. We therefore argue that the existing empirical studies of sharecropping seems to suffer from an “identification” problem.



The structure of the paper is as follows. In the next section we sketch out more formally the essential features of the Marshallian and Cheungian approach to sharecropping. In the third section, a two-stage bargaining model is presented, and it is demonstrated how the models reviewed in section two can be seen as special cases of this more general model of sharecropping. In section four we introduce some specific utility functions in order to illustrate some implications of the framework developed. In particular we look at the relationship between the power of the landlord and efficiency in sharecropping. Section five concludes the paper.

2. Models of sharecropping


The essential features of the Marshallian and the Cheungian analysis of sharecropping can be captured by considering a single tenant cultivating a given plot of land on the agreement that he must give the landlord a fraction (a) of the total output (x). Output depends on the tenant’s labor input, (L), and there is no uncertainty involved.4 The tenant’s income is then y=af(L), while the landlords gets (1-a)f(L). The utility of the tenant (U) and the landlord (V) depend on income (y) and the tenant’s labor input (L)




2.1 The Marshallian model
In the traditional Marshallian model it is assumed that the tenant determines the level of labor input to be provided on the sharecropped land. For a given a, the tenant then maximizes U(y,L) with respect to L, implying the first-order condition




(2) states that resource allocation under sharecropping is not first-best efficient, since the marginal product of labor f’(L) is not equated with the marginal rate of substitution between labor input and income (-U2 /U1). Since the tenant only receives a fraction of his marginal product of labor, labor input will be to low.

More recent tenancy models in the Marshallian tradition, derive equation (2) under the assumption that a is decided by the landlord, taking into account the effect of changes in a on L, i.e.




According to this characterization of the problem, the landlord can affect the tenant’s level of labor input only by manipulating a.




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