Was Marshall Wrong:
Sharecropping and Productive Efficiency
Christopher L. Gilbert
University of Trento
Presentation prepared for the 5th - Summer School in Development Economics, Alba di
Canazei (TN), 15-19 July 2013.
Thanks are due to Luciano Andreozzi, Ken Binmore and Joe Stiglitz.
Introduction
Sharecropping is a land tenure arrangement in which the tenant farmer pays rent to the
landlord at least partly in kind. It is common form of contracting in much of developing Asia
and historically, it was common across much of southern Europe (mezzadria, métayage,
mediero). It emerged in the post-Reconstruction U.S. south.
Both Adam Smith and Marshall regarded sharecropping as an inefficient form of contracting
which results in the persistence of low agricultural yields. The modern literature (Stiglitz, 1974;
Ishikawa, 1975; Newbery, 1977; Newbery and Stiglitz, 1979) does not dispute yield inefficiency
but emphasizes the risk-sharing benefits of sharecropping.
We often observe that sharecropping contracts involve a 50:50 division of the crop between
the landlord and the farmer. Recently, some social norm theorists have made the analogy with
the dictator game to argue that this division reflects a fairness social norm.
1
Questions
1.
Are the risk-sharing benefits from share-cropping sufficient to offset reduced
yield efficiency?
2.
We observe that sharecropping tends to give way to pure rental contracts as
countries get richer? Why is this?
3.
(Equivalently) why is sharecropping a topic in development economics and not in
agricultural economics?
4.
Where sharecropping is present, why do we frequently observe a 50:50 division
of the crop between landlord and farmer?
2
Framework: contract types
Write farm revenue as Y = f ( L ) with f ' > 0 , f " < 0 and f ( 0 ) = 0 and where the tilde indicates
a variable which is unknown at the time of contracting.
The farmer contracts to pay X to the landlord. There are three pure contract forms (Stiglitz,
1974):
1.
Pure rental contract: X = R where R is a fixed rental.
2.
Contract farming: the farmer receives a fixed payment W so X= Y − W
3.
Sharecropping: the farmer gives a fixed percentage β (typically, but not invariably, 50%)
to the landlord so X = βY
In the general case, X = α + βY . Contract farming is the polar case in which β =1 (so W = −α )
and pure rental the polar case in which β =0 (so R = α ). Pure sharecropping has α = 0
The case of β > 0 and α > 0 corresponds to a mixed sharecropping-rental contract.
The case of β > 0 and α < 0 corresponds to contract farming with incentive payments.
.
3
Marshallian inefficiency
Marshall (Principles, VI.x.4) argued that
economic efficiency requires β =0 - i.e. pure
Q
rental contracts:
“… if then he [a French metayer] is free to
cultivate as he chooses, he will cultivate far less
intensively than on the English plains”.
Consider sharecropping in which the farmer
retains share 1-β.
Farmers equate the marginal product of their
efforts on to that on other activities – working
L
L**
L*
as hired labour or on their own land.
L* is the efficient labour input but under share-cropping this falls to L**.
4
Compare this to the situation in which the
Q
farmer pays a fixed rent R.
Here, the farmer’s labour input is unaffected
by the payment and output is at the “first
best” level.
R
According to this view, sharecropping results
in poor incentives to the farmer.
Competition will ensure that landowners can
obtain more by offering fixed rental contracts.
The Marshallian puzzle: Why then do we still
observe sharecropping, and even contract
L*
L
farming?
Marshall was echoing Adam Smith (Wealth of Nations, p.248) who had argued that sharecropping, even in the eighteenth century, was a hangover from the past: fixed rents plus well
defined tenant rights “contributed more to the present grandeur of England than all their
well-boasted regulations of commerce taken together”.
5
Evidence on sharecropping yields
My reading of the evidence strongly supports the view that sharecropping is inefficient.
•
The major empirical difficulty is to control for unobserved heterogeneity of land and
households – some households may be more efficient than others and some land may be
more productive. It is possible that these households choose fixed rent contracts or own
their own land and that the least productive land is more often sharecropped, creating a
false impression that sharecropping is inefficient.
•
Shaban (1987) studied Indian sharecropping households who also owned or rented land.
 Input and output intensities are higher on owned crops than on sharecropped land –
19%-55% for inputs and 33% for outputs.
 Some of this difference is explained by better irrigation of land owned by the
household.
 Controlling for soil quality and irrigation, there are no productivity differences
between owned and rented land, but both are more productive than sharecropped
land.
•
This is all in line with the Marshallian theory.
6
Transactions costs and monitoring
One approach to resolving the Marshallian paradox, anticipated by Marshall himself, is via
consideration of transaction costs.
If the landlord were able to efficiently monitor labour and other inputs, he could condition
contracts on the appropriate level of input. It follows that if shareholding is inefficient, this
must be because there inadequate monitoring is costly or inadequate.
“[The] landlord has to spend much time and trouble, either of his own or of a paid
agent, in keeping the tenant to his work, …” (Marshall, Principles, VI,x,4)
Contract farming always requires supervision. The landowner generally provides non-labour
inputs but needs to ensure that the farmer provides labour. Under sharecropping, the farmer
generally provides non-labour inputs although this provision may also be shared. The farmer
requires less supervision since he has an incentive to provide inputs.
7
Eswaran and Kotwal (1985) modelled tenants as prone to shirking on work and landlords as
prone to shirking on management. The tenant is better placed to supervise inputs and the
landlord is better at managing. They argue that sharecropping gives the best outcome if the
landlord cannot efficiently supervise inputs and the tenant cannot make efficient management
decisions.
I conclude that contract farming is only feasible if the land-owner has a feasible supervision
technology. The premise of the sharecropping literature is that supervision is either infeasible
or too costly. I therefore rule out the case of wage payments to contract farmers (i.e. α < 0).
Any model of contract farming would need to include a specification of the landowner’s
supervision function.
8
Sharecropping and risk-sharing
The second approach in the literature is based around risk aversion. This was emphasized by
the Japanese development economist Ishikawa (1975).
We can think of sharecropping as an arrangement whereby the landlord rents land to his
tenant but also packages crop and price insurance with the land.
The justification for this is
a)
the landlord is richer than the tenant and can more easily bear the risk,
b)
the landlord can use the land as collateral and can thus smooth consumption by lending
and borrowing, with the result that risk has a lower impact on him.
The resulting benefit, which may be entirely or partially captured by the landlord in terms of a
higher average payment, may imply that sharecropping offers a superior welfare outcome to
the fixed rental contract even allowing for Marshallian inefficiency. (Stiglitz, 1974; Newbery,
1977; Newbery and Stiglitz, 1979).
9
Example: The farmer’s income=
is Y z. f ( L ) + a where z is zero with probability p (crop failure)
and one with probability 1-p. (a is other income). Expected income is E (Y ) =
(1 − p ) f ( L ) + a
First consider the case if the farmer pays fixed rent R.
The household has one unit of labour available. Non-farm (wage) income is w (1 − L ) .
The farmer maximizes expected utility
Eu (Y ) = (1 − p ) u ( f ( L ) + w (1 − L ) − R + a ) + pu (w (1 − L ) − R + a )
His first order condition is
0
(1 − p ) uY ( f ( L ) + w (1 − L ) − R + a ).  fL ( L ) − w  − puY (w (1 − L ) − R + a )w =
or
0
(1 − p )  fL ( L ) − w  uY1 − pwuY0 =
where uY1 and uY0 are his marginal utilities for a normal and failing crop respectively.
*
u
L
(
)> w
w
Y
=
by fL ( L* )
It follows that the farmer chooses labour supply L* given
1 − p uY1 ( L* ) 1 − p
where uY =(1 − p ) uY1 + puY0 > uY1 , the farmers marginal utility averaged across the two states.
The farmer substitutes towards the riskless outside option to ensure higher utility in the case
of crop failure.
10
Because of missing insurance markets, there is inefficiency even under the fixed rent contract.
Now suppose the farmer can choose a sharecropping contract in which he pays α + βY .
We initially require the landlord has the same expected rent under the sharecropping contract,
i.e. α + βE (Y ) = R . Call this the β contract. It induces the farmer to supply Lβ units of labour
implying α= R − β (1 − p ) f ( Lβ ) . This gives the entire benefit of sharecropping to the tenant.
I take it that the landlord has a large number of tenants and offers them common contracts.
The farmers are unable to bargain with the landlord and take α as given.
His first order condition gives
fL ( Lβ ) =
w
uY ( Lβ )
(1 − p )(1 − β ) uY1 ( Lβ )
The solution of this equation defines the labour input Lβ than the farmer will provide under the
β contract.
11
It is tempting but incorrect to argue that a move from a pure rental contract to a sharecropping
*
w uY ( L )
fL ( L* )
=
>
contract will inevitably reduce efficiency,
i.e. fL ( Lβ )
1
1 *
(1 − p )(1 − β ) uY ( Lβ ) (1 − p ) uY ( L )
w
because
w
(1 − p )(1 − β )
risk so that
uY ( Lβ )
u ( Lβ )
1
Y
<
>
w
. This is incorrect because sharecropping reduces the farmer’s
1
p
−
(
)
uY ( L* )
u (L )
1
Y
uY ( Lβ )
*
. It is not immediately clear whether the inefficiency effect
dominates the risk reduction effect. Using the farmer’s first order condition I can derive

dLβ
 p 1
w
1
1 0 0 
u − p
r uY +
r uY  
=
2 Y
1 
dβ fLL ( Lβ ) uY  (1 − p )(1 − β )
1 −β
1−p
 
where u = βu1 + (1 − β ) u0 , the β-weighted average of the famer’s marginal utilities and
Y
r= −
Y
Y
f ( L ) uYY
, the farmer’s coefficient of partial risk aversion, which I allow to vary with the
uY
level of production. Since fLL ( Lβ ) < 0 , the first term is negative and the second positive.
12
The sign of the net effect is ambiguous. However, the first (negative) term will be increasing (in
absolute value) with β while the second term will be large when β is zero or very low (since uY0
and uY will both be very high. If there is a positive labour supply response, it will therefore be
for low values of β.
13
The social planner’s problem
The farmer takes the cash component α of the sharecropping contract as given. The social
planner chooses the value of β to maximize the farmer’s expected utility changing α to keep
the landlord’s expected rent receipts unchanged. Write the farmer’s expected utility as
v (β ) = Eu (Y ) β =
(1 − p ) u1 (β ) + pu0 (β )
The planner chooses β to maximize the farmer’s expected utility subject to α= R − βE (Y ) . The
first order condition is
dv (β )

dL 
dL
= p (1 − p ) ( uY0 (β ) − uY1 (β ) )  f ( L ) + βfL ( L )  + (1 − p ) uY1 (β ) fL ( L ) − uY (β ) w 
dβ
dβ 
dβ

Using the farmer’s first order condition replace L by Lβ, the second term in this equation can be
re-expressed as
dL  w
dL
dv (β )

== p (1 − p ) ( uY0 (β ) − uY1 (β ) )  f ( Lβ ) + βfL ( Lβ ) β  +
uY (β ) β
dβ
dβ  1 − β
dβ

The sign of this derivative is again ambiguous but will be positive if
dLβ
dβ
> 0.
14
Numerical Example
I take f ( L ) = 10 L and u ( C ) =
1 1−ρ
C (CRRA). The probability p of crop failure is 0.1.
1−ρ
The household has unit labour time and non-farm income 4. The land rental R = 3 and the
farmer’s outside wage w = 5.
If there were no uncertainty (p = 0), the famer would set =
fL
5
= 5 implying L = 1, i.e. he
L
devotes the whole of his labour time to the farm. If the farmer were risk neutral
=
fL
5
w
5
giving L = 0.81 and f ( L ) = 9 . We now take the farmer to be risk averse
=
=
1
0.9
−
p
L
with constant relative risk aversion ρ = 2.5, a relatively high value. Faced with a pure rental
contract (β = 0), we obtain L* = 0.30 with f ( L* ) = 5.50 so that the farmer, Soviet-style, is
devoting 70% of his time to off-farm activities. The yield is 61% of the efficient case.
15
The figure plots the
farmer’s labour input
Lβ and farm output
f ( Lβ ) against β.
The curves have a
maximum at β = 0.01
consistent with my
argument that allows
dL
may be positive
dβ
for low values of β.
The farmer’s utility is maximized at β = 0.29 since the utility value to
him of the associated risk reduction outweighs the benefit of
increased output.
16
Labour Input and Farm Output under Sharecropping Contracts
Risk
Pure rental contract Yield maximizing contract Utility maximizing contract
Labour
Output
Labour Output
Labour Output
a-R
β
β
ρ
L0
f(L0)
Lβ
f(Lβ)
Lβ
f(Lβ)
1.0 1.0
0.54
7.36
0.00
0.54
7.36
0.15
0.47
6.83
2.5 1.0
0.30
5.50
0.01
0.30
5.51
0.29
0.27
5.19
5.0 1.0
0.14
3.78
0.28
0.17
4.07
0.45
0.15
3.86
1.0 0.1
0.50
7.07
0.00
0.50
7.07
0.17
0.43
6.57
2.5 0.1
0.26
5.14
0.11
0.27
5.23
0.31
0.25
4.97
5.0 0.1
0.12
3.45
0.33
0.15
3.82
0.45
0.14
3.72
The “first best” has L = 0.81 and f(L) = 9.00
The table shows the computed yield maximizing and utility maximizing labour inputs and farm
outputs for a lower and a higher degree of risk aversion. For ρ = 1 (log utility), a move from a
pure rental contract to a share-cropping contract always reduces farm yields while for ρ = 5, a
relatively high value, yields are maximized at β = 0.29. I also report the results of experiments
in which non-farm income a is reduced from 4.0 to 3.1, leaving only 0.1 available for
consumption after paying a rental R = 3.0. The impact is to increase the optimal values for β,
but these changes are small relative to those from changes in the risk aversion coefficient ρ.
17
An alternative approach
The contract considered above leaves the landlord with exactly the same expected payment as
the pure rental contract. However, the landlord can extract the farmer’s utility gain as
additional rent δ such that the total payment becomes α + βE (Y )= R + δ .
The farmer’s utility is now v (β, δ ) . The landlord extracts the total utility gain obtained by the
farmers by setting v (β, δ ) =v ( 0,0 ) so that the farmer has the same expected utility under
sharecropping as under a pure rental contract.
18
Seed and fertilizer inputs
An important issue under share-cropping is, Who pays for the inputs?
There are two arguments for the landlord to bear these costs:
a)
Inputs are applied at or around the time of planting. Their cost is repaid after the
harvest. Poor credit access will imply that the landlord can bear these costs better.
b)
If the landlord owns several farms, he will be able to take advantage of bulk purchase
to buy at a lower price than the farmer.
On the other hand
c)
The cost to the landlord is that the farmer may sell inputs or apply them to his own
land.
Responsibility for input purchase is often divided between the farmer and the landlord with
the farmer having responsibility for inputs for which there is a ready resale market and where
monitoring is difficult (e.g. fertilizers).
If the landlord provides inputs, this increases the incentive to the farmer to devote his labour
time to the farm.
19
Modified numerical example
I now suppose I take f ( L, S ) = 15.2L0.5 S 0.25 where S is the seed input. I initially set the seed price
to q = 12 irrespective of who purchases it. The constant on the production function is set such
that, under the same parametric conditions as previously, the efficient labour input is 0.81 and
the resulting efficient output is 9, exactly as in the earlier example. I take risk aversion ρ = 2.5
and non-labour income a = 4 throughout.
I consider three cases:
a)
The farmer pays for inputs.
b)
The landlord pays. However, I adjust the rental he receives such that his expected rental
receipt is the same under the sharecropping and pure rental contracts.
c)
The farmer and landlord divide the input payments in the proportion β:1-β.
20
Labour and Seed Input and Farm Output under Sharecropping Contracts
Pure rental contract
Utility maximizing contract
Who
Seed
pays for price Labour
Seed
Output
Labour
Seed Output
β
inputs?
q
L0
S0
f(L0, S0)
Lβ
Sβ
f(Lβ,Sβ)
Farmer
12
0.19
0.07
3.44
0.13
0.17
0.07
3.12
Landlord
12
0.38
0.11
5.42
0.22
0.38
0.11
5.40
Landlord
8
0.39
0.20
6.32
0.28
0.42
0.21
6.69
Shared
12
0.38
0.11
5.42
0.05
0.37
0.11
5.36
Shared
12/8
0.39
0.20
6.32
0.01
0.39
0.20
6.32
The “first best” for q = 12 has L = 0.81, S = 0.19 and f(L,S) = 9.00
In the case in which seed payment is shared, the farmer pays the proportion β.
• Sharecropping raises the farmer’s utility irrespective of whether he pays for the inputs or
whether the landlord pays.
• Efficiency is greater when the landlord pays for the inputs, even if he pays the same price
as the farmer. In the pure rental case, this arises because the landlord is risk-neutral.
• If the landlord pays a lower price for inputs this further increases efficiency and
strengthens the case for sharecropping.
• If input payments are divided between the farmer and the landlord, the farmer prefers to
push almost the entire input cost onto the landlord – sharecropping gives him little.
21
Sharecropping and development
The modern literature argued that risk-sharing considerations can make sharecropping
attractive even if yields are diminished.
This view is limited for two reasons:
1.
If farmers have a riskless off-farm option, sharecropping can increase yields by inducing
the farmer to devote more of his labour time to the farm.
2.
Missing insurance markets are just one feature of the difficult environment in which
developing country farmers find themselves. Poorly developed credit markets are possibly
more important. Low yields in part reflect inadequate input provision. Under
sharecropping, the farmer and the landlord assume joint responsibility for input provision
– the farmer providing labour and the landlord sees and fertilizer inputs.
These problems become less acute as countries develop – rural credit becomes more easily
available and farm households have enough non-labour income or accumulate sufficient
wealth to be able to survive poor or even disastrous harvests. Sharecropping therefore gives
way to pure rental contracts as countries get richer – as happened in southern Europe.
22
Was Marshall wrong?
Marshall was correct in arguing that sharecropping is generally inefficient. However, if farmers
have off-farm options, low-β sharecropping contracts can raise yields by making it more
attractive for risk-averse farmers to devote time to farm activities.
Marshall argued that English agriculture was more prosperous than French agriculture because
the French used sharecropping contracts. My belief if the reverse – the English used pure
rental agreements because English agriculture was more prosperous than its French
counterpart.
The implication for the developing world is that the persistence of sharecropping is more a
consequence than a cause of low yields.
23
The Dictator Game
The Dictator Game (DG) is a so-called degenerate game (degenerate because it is not strategic)
in which a cake (say a $10 bill) is divided between a proponent and a respondent. The
proponent proposes a division (whole numbers of dollars) and the respondent either accepts
this division or rejected. If he rejects, both parties get zero. The “rational” proposal is that the
proponent proposes ($9, $1) and the respondent accepts.
Extensive experimental evidence indicates that respondents generally reject ($9, $1).
These rejections are interpreted by some as evidence of non-rationality and by other of
evidence of a fairness “social norm”. If the proponent acts in accordance with a Kantian
universifiability principle, he must ask how what he would wish the respondent to propose if
he had been selected as proponent. This suggests a fair ($5, $5) division.
24
Sharecropping as a social norm?
The simulations I have undertaken suggest that where sharecropping is optimal, it involves a
more moderate degree of risk-sharing than the standard 50/50 split. In all my simulations, the
50/50 split results in substantial efficiency reduction.
Social norm theorists argue that optimization is difficult. These difficulties are amplified in the
presence of heterogeneity (here, risk aversion coefficients and the extent of non-labour
income) which would require re-optimization for each contract. The 50/50 fairness norm is
suggested by the experimental literature on the Dictator Game (DG).
•
My reading of the DG literature is that 50/50 is not the only norm to emerge. 60/40 and
70/30 are also possible outcomes as the opponent acknowledges that the game structure
gives the dictator some ownership rights.
•
Fairness may be more important to the social norm theorists than to their experimental
subjects. Landlords are unlikely to see themselves in the position of poor farmers.
•
Optimization is indeed difficult but 50/50 is the sharecropping context seems too far from
the likely range in which the optimum will lie to be justified as a plausible heuristic.
25
Repetition
The analogy with repeated the Prisoners’ Dilemma game suggests that repetition may support
a 50:50 sharecropping division.
Suppose contracts last for a period of years but the landlord then has the right to alter the
contract.
In the numerical example (ρ = 2.5, q = 12, farmer pays for inputs) the β-contract has β = 0.22. It
yields (scaled) expected utility EUβ = 7.35. The “first best” contract with β = 0.50 but in which
the farmer sets Lopt = 0.81 yields expected utility EUopt = 6.97. It raises the landlord’s rent from
3.00 to 4.50. If the farmer accepts that contract but applies his individually optimal labour
input of L0.5 = 0.19, he gets expected utility EU0.5 = 7.60 so the farmer has an incentive to
renege.
26
If the farmer reneges, with probability π he loses his tenancy and with probability 1 - π he has
to accept the β-contract and pay for inputs in the next period.
Suppose contracts last 5 years so d = 25% is a reasonable discount rate.
If the farmer adheres to the contract, his valuation function Wcoop is W=
EUopt +
coop
1
Wcoop
1+d
1

implying Wcoop=  1 +  EUopt = 34.87.
d

If, instead, the farmer reneges his valuation function is Wnon−=
EU0.5 +
coop
W
=
EUβ +
β
1
Wβ where
1+d
1
Wβ = 36.76 implying Wnon−coop = 37.01.
1+d
The 50:50 allocation is not supported. However, reworking the numbers with the farmer taking
two thirds of the output gives Wcoop = 38.28 and Wnon-coop = 37.13. The landlord’s expected
receipt is unchanged at 3.00.
Repetition can support sharecropping but this depends on specific parameter values.
27
Conclusions
1.
Sharecropping can raise yields for low values of the β parameter but will generally reduce
yields (Marshall was mostly right).
2.
The persistence of sharecropping can be rationalized in terms of poorly functioning credit
markets as well as missing insurance markets.
3.
Sharecropping is likely to be displaced by pure rental contracts as farmers become richer
and gain enhanced access to credit.
4.
Even in the absence of these markets, it seems difficult to find situations in which the
standard 50:50 division of the crop is close to optimal.
5.
It may be the case that repeated contracting can explain the frequently observed 50:50
sharecropping division but social norm analogies with the Dictator Game appear forced.
Thank you for your attention (and comments).
28