Under the assumption that the landlord is risk-neutral and the tenant is risk-averse, sharecropping is second-best in that it trades off risk sharing and incentives. Many, however, have reported instances of reverse share tenancy, or sharecropping in which the landlord is considerably poorer than the tenant. This note shows that reverse share tenancy is impossible under the canonical Stiglitzian model of sharecropping but becomes possible if and only if (i) both the landlord and the tenant can be assumed risk-averse; or (ii) there exist significant transactions costs making sharecropping more desirable than either a wage or fixed rent contract.Sharecropping; Reverse Share Tenancy; Transactions Cost

Bellemare, Marc F.

English

Research Papers in Economics

 
 
The (Im)Possibility of Reverse Share Tenancy 
Marc F. Bellemare
† 
December 4, 2009 
 
Under the assumption that the landlord is risk-neutral and the tenant is risk-
averse, sharecropping is second-best in that it trades off risk sharing and 
incentives. Many, however, have reported instances of reverse share tenancy, or 
sharecropping in which the landlord is considerably poorer than the tenant. This 
note shows that reverse share tenancy is impossible under the canonical 
Stiglitzian model of sharecropping but becomes possible if and only if (i) both the 
landlord and the tenant can be assumed risk-averse; or (ii) there exist significant 
transactions costs making sharecropping more desirable than either a wage or 
fixed rent contract. 
 
JEL Classification Codes: D23, D86, O12, Q12 
 
Keywords: Sharecropping, Reverse Share Tenancy, Transactions Cost. 
 
 
                                                 
† Assistant Professor, Sanford School of Public Policy, Duke University, Box 90312, Durham, NC, 27708-
0312, United States, Telephone: 919-613-9382, Facsimile: 919-684-9940, marc.bellemare@duke.edu. The (Im)Possibility of Reverse Share Tenancy 
 
1. Introduction 
Under the assumption that the landlord is risk-neutral and the tenant is risk-averse, the 
principal-agent model predicts that the landlord will choose a sharecropping contract, 
which trades off risk-sharing and incentives (Stiglitz, 1974). Indeed, when the tenant’s 
effort is unobservable by the landlord, the tenant faces little or no incentive to provide 
effort under a wage contract but bears too much risk under a fixed rent contract. 
Sharecropping thus emerges as the second-best contract. 
 
The risk preferences assumed in the canonical model stem from the stylized facts. In 
most cases, landlords are wealthier than their tenants, and so it is only natural to assume 
that they are risk-neutral and their tenants risk-averse. Yet, several instances of 
sharecropping in which landlords are considerably poorer than their tenants have been 
reported in the social sciences. Such reverse share tenancy agreements have been found 
to be widespread in places as diverse as Lesotho (Lawry, 1993), South Africa (Lyne and 
Thomson, 1995), Eritrea (Tikabo, 2003), Ethiopia (Bezabih, 2007), Bangladesh (Pearce, 
1983), Madagascar (Bellemare, 2009), Malaysia (Pearce, 1983), India (Singh, 1989), as 
well as the Philippines (Roumasset, 2002). Under the assumption of decreasing absolute 
risk aversion (DARA), assuming that landlords are risk-neutral and tenants are risk-
averse is ill-advised in such contexts. 
 
This paper establishes in section 2 that reverse share tenancy is impossible under the 
canonical model of sharecropping unless both landlord and tenant can be assumed risk-averse. Section 3 suggests ways in which transactions costs can be incorporated in the 
canonical model to account for the emergence of reverse share tenancy. Section 4 
concludes by providing directions for future research. 
 
2. Theoretical Framework and Impossibility Result 
Consider the following general principal-agent model. A landlord whose utility function 
is  ) ( V , with  0 ' V  and  0 ' '  V , contracts with a tenant whose utility function is  ) ( U , 
with  0 ' U  and  0 " U . The landlord and the tenant’s utility functions both exhibit 
DARA. The landlord hires the tenant to cultivate her plot and produce output 
Q q q q   ] , [ , which is stochastic and depends on the tenant’s effort  E e  through the 
conditional probability density function  ) | ( e q f , which describes the likelihood of 
observing output level q given effort level e. The tenant’s payoff from accepting the 
contract offered by the principal is additively separable in the utility derived from the 
contract and the cost of effort, which is represented by the twice continuously 
differentiable function  ) (e  , with  0 '   and  0 "  .  
 
As in the standard principal-agent model with (Bolton and Dewatripont, 2005), the 
landlord maximizes her objective function by offering a contract  ) (q w  to the tenant. 
Assuming that the tenant’s maximization problem has a unique solution, and because his 
utility is the sum of concave functions, one can apply the first-order approach (Rogerson, 
1985) and replace his incentive compatibility constraint by its first-order condition. 
Letting    and   be the multipliers associated with the tenant’s individual rationality (IR) and incentive compatibility (IC) constraints, forming the maximization problem, and 
solving yields 
  ,
) | (
) | (
)] ( [ '
)] ( [ '
e q f
e q f
q w U
q w q V e    

       ( 1 )  
a familiar result in contract theory summarizing the trade-off between risk-sharing and 
incentives. 
 
Focusing on linear contracts, i.e., contracts of the form  b aq q w   ) ( , where 
] 1 , 0 [  a  is the share of the crop that goes to the tenant, and  R b  is a side payment from 
the landlord to the tenant, i.e., a fixed rent if b is negative, and a wage if b is positive,
1 
one can differentiate equation 1 with respect to q to obtain 
 
' " ' "
' "
) | (
) | (
'
) ( '
2
V U U V
U V
e q f
e q f
dq
d
U
q w
e
 
 







,        ( 2 )  
the slope of the contract  b aq q w   ) ( . In other words,  ) ( ' q w  is the share of the crop 
that goes to the tenant. Since side payment b enters the contract linearly, the landlord will 
adjust it so as to make the agent's IR constraint bind (Stiglitz, 1974). 
 
Assuming that the monotone likelihood ratio property holds, i.e.,  0
) | (
) | (
 





e q f
e q f
dq
d e , 
the agent gets a strictly positive share of output q, i.e.,  0 ) ( '  q w . Multiplying each term 
of the numerator and the denominator in equation 2 by  ' 'V U  yields 
                                                 
1 The reason for assuming linear contracts is twofold. First, landlords overwhelmingly tend to use such 
contracts in practice. Second, behavioral evidence suggests that individuals use heuristics to reduce 
complex problems into tractable ones. The use of linear contracts most likely represents the use of such a 
heuristic or an example of bounded rationality (Simon, 1957), a discussion of which is beyond the scope of 
this paper. Holmström and Milgrom (1987) derive conditions under which a linear contract is optimal. T L
L
e
A A
A
e q f
e q f
dq
d
V
U
q w

 






) | (
) | (
'
'
) ( '

,        ( 3 )  
where  ' / " V V AL    and  ' / " U U AT    are the coefficients of absolute risk aversion of 
the landlord and the tenant, respectively. The following results then obtain. 
 
Proposition 1 When the landlord is risk-averse and the tenant is risk-neutral, share 
tenancy cannot emerge as the optimal contract in the principal-agent model. 
Proof When the landlord is risk-averse and the tenant is risk-neutral,  0  L A  and 
0  T A . The slope of the contract thus becomes 
  1
) | (
) | (
'
'
) ( ' lim
0 

 







T L
L
e
A A A
A
e q f
e q f
dq
d
V
U
q w
T

.       ( 4 )  
But since the share of the output that the tenant can get from the contract lies in the [0,1] 
interval, 1 ) ( '  q w , i.e., a fixed rent contract obtains. ◄ 
 
Proposition 2 (Optimal Contract) When the landlord and the tenant are both risk-
averse, the principal offers a sharecropping contract. Moreover, the share of the crop 
that goes to the agent is strictly decreasing (weakly increasing) in the absolute risk 
aversion of the tenant (landlord). 
Proof From equation 4, 
  1
) | (
) | (
'
'
) ( ' lim
0 

 







T L
L
e
A A A
A
e q f
e q f
dq
d
V
U
q w
T

.       ( 5 )  But then,  0
) ( '



T A
q w
, which implies that starting from a risk-averse landlord and a risk-
neutral tenant risk-neutral, as the tenant gets more risk-averse, sharecropping becomes 
more likely. Further, let  





 
) | (
) | (
'
'
e q f
e q f
dq
d
V
U e  . Then, 
 
2 ) (
) ( '
T L
T
L A A
A
A
q w

 



.        ( 6 )  
But since  1 ) ( ' 

 

T L
L
A A
A
q w ,  T A   , so that  0
) ( '



L A
q w
. ◄ 
 
Both results are intuitive. With a risk-averse landlord and a risk-neutral tenant, the 
landlord no longer has a comparative advantage in risk-bearing. Since the tenant has a 
comparative advantage in both risk-bearing and in effort monitoring, he should bear all 
the risk. The second proposition provides another intuitive result: when both the landlord 
and the tenant are risk-averse, each party bears some of the risk. 
 
3. Reverse Share Tenancy in Practice 
Propositions 1 and 2 respectively show that reverse share tenancy is impossible if the 
landlord is risk-averse and the tenant is risk-neutral, but that it can emerge when both are 
risk-averse, no matter their wealth ordering. Although two-sided risk aversion is a prima 
facie more realistic than assuming risk neutrality of one party (Holt and Laury, 2002), it 
is also possible to retain the assumption that the tenant is risk-neutral if significant 
transactions costs drive risk-averse landlords to choose to bear some risk. 
 For example, Ghatak and Pandey (2000) extend the model of section 2 by introducing 
limited liability on the part of the tenant. The landlord may then choose sharecropping 
over fixed rent in an effort to curb the tenant’s risk-taking behavior. Likewise, Dubois 
(2002) introduces fertility dynamics in the canonical model. Because landlords sign 
short-term contracts, the strong incentives implied by fixed rent contracts push tenants to 
overuse the land, so landlords may choose sharecropping in order to preserve the fertility 
of their plots, a hypothesis that is supported by data from the Philippines. Finally, 
Bellemare (2009) finds that in Madagascar, a landlord’s subjective probability that she 
will lose claim to her plot is often higher under fixed rent than under sharecropping, and 
so landlords may choose sharecropping in order to minimize the risk of expropriation. 
One could come up with several such departures from the canonical model of section 2 in 
order to explain reverse share tenancy. 
 
Thus, although Ghatak and Pandey (2000) and Dubois (2002) do not explicitly set out 
to study reverse share tenancy, their transactions costs-based theoretical frameworks 
provide excellent candidate explanations for the emergence of such an institution, and 
both Dubois’ (2002) and Bellemare’s (2009) transactions costs-based explanations are 
supported by their data.  
 
As a result, if landlords are risk-averse and tenants are risk-neutral, the canonical 
model must be augmented by including transactions costs in order to successfully 
describe the emergence of reverse share tenancy. Whether the explanation for reverse share tenancy lies on the side of two-sided risk aversion or of transactions costs, however, 
is ultimately an empirical question. 
 
4. Conclusion 
This paper has established that the existence of reverse share tenancy (i.e., sharecropping 
between a poor landlord and a rich tenant) is inconsistent with the assumption that the 
landlord is risk-neutral and the tenant is risk-averse in the principal-agent model. It has 
then shown that reverse share tenancy is possible if and only if (i) both the landlord and 
the tenant are risk-averse in the principal-agent model; or (ii) significant transactions 
costs make sharecropping more attractive than fixed rent for a risk-averse landlord. 
 
What are the implications of these results? The first thing to acknowledge is that 
which of these two possible causes of reverse share tenancy prevails is an empirical 
question. On the one hand, two-sided risk aversion is more realistic than assuming that 
one party is risk-neutral, but it is extremely difficult to test this assumption empirically, 
both because relying on proxies for risk preferences leads to unidentified tests (Bellemare 
and Brown, forthcoming) and because estimated rather than experimentally-derived risk 
preferences lead to spurious correlation between wealth and risk aversion (Lybbert and 
Just, 2007). On the other hand, although transactions costs-based explanations lend 
themselves more naturally to empirical tests, they also depend much on the specific 
context. Ultimately, it appears that it may be necessary to derive structural empirical 
models from the theory which nest competing explanations for reverse share tenancy. 
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The (Im)Possibility of Reverse Share Tenancy

The (Im)Possibility of Reverse Share Tenancy

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