Lecture Notes - Agricultural Organization
1
Introduction
• look at markets and institutions that form the agricultural sector in developing economies
- important - many people employed, large fraction of GDP
• stress the role of information, incentives, contracts
— important factors in the context of missing markets - prevalent in developing
countries
— lie at the heart of informal institutions that arise in developing countries
• Examples:
— lack of information - landlord and tenant - tenant’s effort/labor unobservable
— incentives - under imperfect markets/information some first best contracts may not
be compatible with incentives - e.g. can’t have fixed wage for the tenant if effort is
unobservable. Also - bad incentives to invest in workers given short run contracts.
2
Overview of the Land and Labor Markets in Developing Countries
• unequal distribution of land while more equal distribution of labor endowments - small
owners of land will have excess supply of labor, big owners - excess demand - thus need
for input markets for land (leasing, selling) and agricultural labor
• why both markets exist? (under perfect competition & info, CRS - just one will be
enough (Why?)) - these assumptions not likely to hold in LDCs or in agriculture in
general (e.g. there may be IRS at low land sizes)
• Need for contracts between landlords and tenants - tenancy contracts - crucial ingredient for understanding developing countries agricultural sector.
• Major characteristics of agricultural production:
— land and labor are the two major factors of production. Production is done through
a sequence of tasks (sowing, fertilizing, harvesting, etc.)
— there is a lot of exogenous uncertainty (weather, pests, etc.) while no formal
insurance markets usually exist
— major form of agricultural production in LDCs is small farms but there also exist
landless laborers or wealthy absentee landlords
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• Data:
— huge proportion of the rural population in LDCs is either landless or owns small
plots (table 12.1, p.416); Gini coefficients of land distribution - very high (0.45 - 0.6
in Asia; 0.8-0.9 in Latin America)
— Asia: many small plots (average farm size 2-3 ha; 70-90% of all farms < 5ha), 86%
owner cultivated
— Latin America: most land in very large farms cultivated by hired labor
— Africa: a lot of land is communal - badly defined property rights
3
Tenancy Contracts
• tenancy contracts take various forms - will study what determines them, their efficiency,
role for policy and its potential impact
• Contractual forms:
— suppose output is Y and R is what the tenant (T) pays to the landlord (LL) (can be
negative in which case the landlord pays the tenant). We can then write a general
tenancy contrast as
R = αY + F
where α is a number between 0 and 1.
— 1. Fixed Rent Contract - the tenant gets the output, pays a fixed (independent
of output) amount of rent to the landlord; this corresponds to α = 0, F > 0; notice
that all risk is with the tenant
— 2. Sharecropping Contract (SC)- the tenant gets fraction α of the output, the
rest remains for the landlord; 0 < α < 1, F = 0; risk is shared
— 3. Fixed Wage Contract - the output is collected by the landlord while the tenant
gets a fixed wage; α = 0, F < 0; all risk is with the landlord
• All of the above contractual forms are observed throughout the world; in Latin America
fixed rent is most popular (small land owners giving their land to cultivation to bigger);
Asia - lots of sharecropping
• Inefficiency of Sharecropping?
— the wide-spread predominance of sharecropping has bothered economists since Adam
Smith and Marshall
— the idea is that SC should be inefficient since the tenant gets only a fraction
of the marginal benefit from putting more effort (since output is shared and not
profits SC is like a tax on labor effort - distorts choices). Thus fixed rent should be
always chosen over SC since tenant receives 100% of extra output if he puts in more
effort.
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— Formally:
√
— Example: Suppose labor, l is the only input and Y = 2 l, cost of labor effort
2
c(l) = l2 . Suppose also effort cannot be enforced (e.g. it is unobservable). Then,
under fixed rent the tenant will choose effort to solve:
√
l2
max 2 l − − F
l
2
set the derivative to zero:
1
√ =l
l
with a solution: lF R = 1. Total output is then Y F R = 2.
If instead the tenant obtains a fraction s (e.g. 1/2) from the output, his utility
maximization problem is:
1 √
l2
max (2 l) −
l
2
2
setting the derivative to zero:
1
√ =l
2 l
or, lSC = ( 12 )2/3 ≈ 0.63 which is much less than before. Convince yourself that this
result obtains for general forms Y = F (l) and c(l) when s ∈ (0, 1). Once again, the
idea is that incentives to supply effort are distorted under SC.
— Thus the tenant would apply less effort and output will be lower under SC compared
to FR - why is sharecropping then used? Important question - shows us that there are
some other factors that necessitate use of SC - hence if we remove them - efficiency
will increase.
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Theories of Tenancy
• next we explain different theories of why one would observe different contractual forms
in tenancy
• we also show that sharecropping may be chosen under various types of environments
despite its inherent inefficiency. Thus, despite SC being first best inefficient it can be
second best efficient under various conditions as explained below
• We evaluate different tenancy theories on the basis of the following factors:
— contractual diversity - can we observe different contracts (FR, SC, FW) dependent
on the environment?
— efficiency - does the theory predict any differences in production efficiency across
different contract forms?
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— effects of variations in technology - e.g. what happens to the optimal contract
as riskiness of output changes?
— effects of variations in preferences - e.g. what happens if attitudes towards risk
change
4.1
Sharing Costs of Inputs
• Remember sharecropping was shown to be inefficient because the tenant incurs the full
marginal cost of his actions but enjoys only a fraction of the marginal benefits.
• Thus if costs are also shared efficiency can be recovered
• Formally, take the same model as before but assume that l now is some input like e.g.
fertilizer with a price p and suppose the landlord and the tenant share the costs of fertilizer
in the same ratio as output. Then the tenant will solve:
√
max s(2 l) − spl
l
• setting the derivative to 0:
s
√ = sp
l
or, l∗ = 1/p2 - independent of s. Clearly that would be the efficient amount of the input
if there was no sharing (s = 1).
• The intuition about why the above works - sharing both costs and output is like sharing
profits - remember that a profit tax (as opposed to income tax) does not distort input
choice.
• Thus, according to this story sharecropping can be observed together with cost sharing
(e.g. the landlord giving seeds to the tenant for free, etc.)
4.2
A Risk Sharing Model of Sharecropping
• suppose that there is no insurance market. Then one can argue that SC would be an
optimal contract form if both the tenant and landlord are risk averse
• remember, being risk averse means that you prefer a sure income of m to a lottery that
yields m on average. E.g. prefer $50 to an activity that yields you $100 with probability
50% and 0 with probability 50%. Technically risk aversion implies that an agent’s utility
is strictly concave function of income (consumption).
• Suppose output is given by: Y = l + ε, where l is effort put by the tenant and ε is a
random shock with mean 0 and variance σ 2 .
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• Both the tenant and landlord are risk averse with utility function:
U(c) = E(c) −
ri
V ar(c)
2
where c is consumption (income), ri is a measure of risk aversion (i = L, T for the landlord
and tenant respectively), E(c) is expected consumption and V ar(c) is the variance in
consumption, i.e. V ar(c) = (c − E(c))2 .
• The tenant has a cost of effort c(l) = 12 l2 .
• Restrict attention to linear contracts, i.e. tenant’s income is a linear function of output:
cT = sY − F
where s is a share of output and F (can be >0, <0 or 0 - to be determined) is a fixed
component.
• Notice that then we’ll have
E(cT ) = E(sY − F ) = sE(Y ) − F = sl − F
V ar(cT ) = V ar(sY − F ) = s2 V ar(Y ) = s2 σ 2
• The tenant’s utility then is:
U T (l, s, F ) = E(cT ) −
rT
rT
1
V ar(cT ) = sl − F − s2 σ 2 − l2
2
2
2
• Similarly, the landlord will have income
cL = (1 − s)Y + F
and expected utility of:
U L (l, s, F ) = (1 − s)l + F −
rL
(1 − s)2 σ 2
2
• The optimal contract will be chosen to maximize the sum of the two parties’ expected
utilities (total surplus) (we suppose effort is enforceable and everything is contractible).
At this moment we do not care how the total surplus (i.e. expected profits) will be
distributed:
rT
rL
1
max S = U L + U T = l − s2 σ 2 − (1 − s)2 σ 2 − l2
s,l
2
2
2
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• taking the partial derivatives and setting to zero:
1−l = 0
−srT σ + rL (1 − s)σ 2 = 0
2
rL
. Notice that the optimal contract will be a sharecropping
rL + rT
one in general. The size of F will be determined according to bargaining power between
the two parties. For example, if the landlord has all the bargaining power (as is usually
assumed) he will set F in such way as to make the tenant exactly as well off as the
tenant’s opportunity cost which is his utility if the tenant leaves and goes to his second
best alternative (i.e. the landlord extracts all rents from the relationship). Formally,
suppose that tenant’s reservation utility is ūT , i.e. he’ll enter the contract only if
or, l∗ = 1 and s∗ =
U T ≥ ūT
if the landlord has all the bargaining power he’ll choose F to make U T (l∗ , s∗ , F ) = ūT . Solve
this equation for F.
• Thus mutual need for insurance makes the sharecropping contract optimal for the two
parties despite its production inefficiency.
• Notice that if rT = 0 (the tenant is risk neutral - i.e. does not care about the variance,
only about the mean income) the optimal contract is fixed rent, while if rL = 0 it is fixed
wage. Thus this model can explain coexistence of all three contractual forms based on
the preferences of the two parties (e.g. does not depend on the riskiness of output, σ 2 )
• Notice also that effort is at the efficient level - no production inefficiency (this is because
it is assumed contractible)
• Criticisms:
— no endogenous explanation of why insurance markets missing
— highly implausible to get a share of 1/2 - the most commonly observed one.
4.3
A Risk Sharing Versus Incentives Model of Sharecropping
• Suppose tenant’s effort cannot be contracted upon - e.g. it is unobservable. Then
the tenant will need incentives to put in effort
• It automatically follows that a fixed wage contract will not work - if a tenant is paid the
same no matter how much he works, he will not work - a moral hazard problem. Thus
the tenant’s reward must depend on output somehow.
• A fixed rent contract seems perfect in terms of incentives (remember that under FR
contract the tenant gets the full marginal benefit of extra effort) but may be bad if the
tenant is risk averse (since all the output risk is borne by the tenant).
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• Thus a sharecropping contract may be a good trade-off between provision of incentives and insurance when tenants are risk averse and effort is unobservable.
• Since l cannot be directly stipulated, the landlord can only influence it by choice of s and
F. Output is still l + ε and we look at linear contracts.
• For given s and F the tenant will choose the effort level ˆl that solves:
max sl − F −
l
rT 2 2 1 2
sσ − l
2
2
i..e
ˆl = s
(ICC)
Notice that this is lower than the efficient effort level whenever s < 1.
• The landlord knows that l will be chosen in that way and will take it into account when
deciding on the s since s influences the level of effort that the tenant will put in. Thus
ˆl = s puts a constraint on what the optimal contract looks like. It is called - incentive
compatibility constraint. It says that the optimal contract must take into account the
incentives (optimal action) of the tenant. The maximization of joint profits then proceed
subject to this constraint. (think why it did not exist when effort was observable!)
• To solve for the optimal contract look at total profits which in this case are (after substituting in for ˆl which cannot be chosen independently of s here):
Ŝ = s −
rT 2 2 rL
1
s σ − (1 − s)2 − s2
2
2
2
notice that unlike the previous case l cannot be chosen! - the landlord has to implement it
through the choice of s.
• Maximizing Ŝ with respect to s we set the derivative to zero:
1 − rT sσ 2 + rL (1 − s)σ 2 − s = 0
or,
ŝ =
1 + rL σ 2
1 + rL σ 2 + rT σ 2
• Notice that if rT > 0 (which is what we assume), the above share is less than 1 and hence
a sharecropping contract is optimal. Only if σ 2 = 0 or rT = 0 will fixed rent be optimal.
To get a fixed wage contract we need rT → ∞ which is unrealistic. The contractual form
(the share) depends on both attitudes toward risk and the variance of output. As σ 2
(riskiness) goes up, the share of the tenant and effort go down (explain why!)
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• Notice also that the effort level in the model above is less than the first best one (l = 1)
that would obtain under fixed rent. The reason is the ”agency cost” due to the missing
information (non-contractibility) for effort.
• Criticisms:
— some people have argues that this explanation of SC is not very probable as closeknit rural societies are unlikely to feature such informational asymmetries/costly
monitoring - can be settled empirically
— why not the tenant buy the land (using a loan) and achieve efficiency - not good
criticism - the bank is also subject to the same moral hazard problem - the landlord
himself could have set s = 0, F > 0 - i.e. selling the land but chose not to.
4.4
Limited Liability Model of Sharecropping
• If the tenant is poor and output is uncertain - may not be able to implement the optimal
fixed rent contract because the tenant maybe be unable to pay the required rent.
• Take the previous model (unobserved effort) but make 2 modifications: 1.) both landlord
and tenant are risk neutral, i.e. don’t care about risk, 2.) there is a limited liability
constraint on the tenant - i.e. it is assumed that he has to pay the rent in advance but
can’t pay more than wT (his wealth). This introduces an additional constraint called the
limited liability constraint:
F ≤ wT
• As before, incentive compatibility requires that l = s. Thus the landlord solves:
max s(1 − s) + F
s,F
2
s
− F ≥ ūT (participation)
2
F ≤ wT (limited liability)
s.t. U T =
• Suppose first the LL constraint does not bind. Then, since the tenant doesn’t mind risk it
is best for incentives (and maximum profits) to set s = 1 (i.e. do a fixed rent arrangement)
and F = 12 − ūT from the participation constraint (PC). (convince yourself this is true)
• Suppose however, wT < 12 − ūT i.e. the tenant has not enough wealth to pay this optimal
rent and thus the limited liability constraint binds: F = wT . The landlord then has two
options:
— 1. keep s = 1 for efficiency reasons but allow the PC constraint not to bind - i.e.
leave some rents to the tenant by setting F = wT < 12 − ūT .
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— 2. reduce s and secure some of the rents the tenant is earning - in this case we can
find s from the binding PC (i.e. no rents for the tenant)
s2 = 2(wT + ūT )
— given that wT < 12 − ūT the above implies s < 1 i.e. there is sharecropping even
when both parties are risk neutral!
— can this (reducing s) continue to be optimal as wT gets smaller and smaller? No,
the cost on incentives becomes too high at some point and it will be optimal to just
max profits without caring about the PC, i.e. set s = 1/2. (show as an exercise that
this is optimal if 2(wT + ūT ) < 1/2). Notice that this model can predict (under some
conditions) an optimal share of 1/2 for tenants with different wT , ūT .
• This model implies that we should observe more fixed rent contracts the richer are the
tenants (e.g. South America).
• other implications: the model never predicts wage contracts; uncertainty doesn’t matter
for the optimal tenancy contract; effort is often suboptimal; the higher the tenant’s wealth
the greater the landlord’s profit (show this!) and the higher efficiency and the share.
• the tenant can be earning rents (i.e. utility over his opportunity cost or reservation
utility) in the optimal contract - can make eviction threats useful (see more on this
below)
• Another implication - limited liability creates incentives for the tenant to overinvest in
risky methods of production since he bears no downside risk
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Tenancy and Eviction Threats
• Eviction: another option that landlords can use - not renew the contract
• eviction can be used to alleviate efficiency problems - provides incentives to tenants to
put in more effort
• However: introduces a new risk for the tenant (need to compensate for it); less incentive
for tenant to do long term investments (e.g. fertilizer)
• Notice that the threat of eviction will only bite if the tenant is earning rent (i.e. his
utility in the tenancy contract is higher than his best outside alternative) - thus eviction
may have more bite under limited liability problems - i.e. for poorer tenants.
• Are tenants worse off with eviction?
— remember for eviction threats to be used employed tenants must be earning rents.
Thus if eviction is banned (e.g. by law) this transfers more bargaining power
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to the current tenants - incumbents are better off. However, new potential
tenants are worse off - knowing that they cannot use eviction threats the landlords
can drive them to their reservation utility by making take-it-or-leave-it offers before
signing a contract.
— banning eviction can increase productive efficiency due to the transfer of bargaining power to the tenant. Why didn’t the landlord do the same before - he doesn’t
care about productivity but his own profits which are lower when eviction is banned.
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Development Economics 855
Lecture Notes 6
Agricultural Organization – Data and Empirical Studies
Introduction
-----------------• We will investigate two main issues:
o agricultural productivity across different tenancy contracts (incl.
testing the theory about inefficiency of sharecropping)
o the relationship between land inequality/land size and
productivity/efficiency
History of Land Inequality
--------------------------------------• in distant past – labor was scarce factor, as population grew land became
scarce, property rights emerge – communal followed by private
• lords emerge promising to protect property rights for a fee – later embedded
into norms, legal system
• Factors contributing to land inequality:
o Large pieces of land given to members of ruling class as reward for
favors
o Differentially high taxes imposed on free peasants & subsidies to
members of ruling class
o Restricting the market for agricultural output
• Questions:
o Is such inequality compatible with production efficiency?
o If there is efficiency loss can it be repaired through a land rental
market (we looked at this question already)
o Would a land sales market repair the inefficiency?
o What is the role of a land reform (redistribution of land from rich to
poor)
I. Land Size and Productivity
--------------------------------------------• Do small farms have production functions that “lie beyond” those of large
farms?
• Hard to compare: do not use same inputs; existence of non-monitored inputs
• Will compare efficiency: output per acre
• Differences in productivity can come from two main sources: 1. technology
and 2. incentive problems due to imperfect info/markets
Technology:
- large plots are more suitable for mechanization (indivisibilities – need
1 animal, 1 tractor, etc.; rental market for animals – not well
developed – can overwork them, hard to monitor)
-
conclusion: it seems that large plots should be more productive from
technological point of view (also – can always split into small if
needed)
Incentives – see below
II. Imperfect Insurance Markets and Productivity in Small Farms
• typically in developing countries: tenants are risk averse but there are no
insurance markets – thus landlords can make money trying to insure them via
sharecropping contracts that however fail to achieve production efficiency
• why doesn’t the landlord reap those productivity gains? He would if there
were perfect insurance markets, however in an imperfect world the efficient
contract (fixed rental) puts too much risk on the tenant and the latter is willing
to give up money to be insured. As a result the landlord makes more under the
SC contract although efficiency is destroyed.
• Thus: we expect to see plots farmed by family labor (small) to have efficiency
advantage over bigger plots using tenants
III. Imperfect Labor Markets and Small Farm Productivity
• imperfect credit/insurance markets – force the labor/land market to act double
duty and serve insurance role as well. In trying to do two things – fails to do
both in the best possible way (insurance – incentives trade-off)
• similar outcome if labor market is imperfect – e.g. if there is unemployment
• at full employment – cost of hiring an additional unit of labor is the going
wage, w which is also the opportunity cost of 1 unit of own labor
• if there is unemployment – still costs w to hire additional unit on the market
but opp. cost. of own labor is less than w (b/c of probability of being
unemployed)
• thus: easy to see that small farms can put in more labor per acre (MC is lower)
IV. Pooling Land
• Why not small farms (no incentive problems) pool and take advantage of
technological returns as well?
• Pooling itself creates incentive problems – free riding problem – in joint
production you do not reap the full benefits of your extra effort but bear full
costs
• Evidence: decollectivization in China – led to huge gains in productivity.
To conclude: theory suggests that technology favors larger farms but incentive
problems favor smaller ones – not clear ex ante what the result in terms of productivity
comparison will be – has to be decided by data.
Evidence on the link between land size and productivity
-----------------------------------------------------------------------------• most of the empirical evidence suggests that productivity gains arising
through incentives (in an imperfect markets setting, i.e. not applicable to
USA, Canada) outweigh technological gains
•
•
developing country data: owner cultivated small farms are most productive,
followed by large mechanized farms using wage labor. Sharecropping is least
productive (measure is output per acre)
o Sen (1981) – finds a negative relationship between productivity and
farm size; productivity on owned land exceeds productivity on
sharecropped land by as much as 50%
o Berry-Cline: study Brazil – find that larger differences in farm size
imply larger productivity differences, e.g. in north-east Brazil – small
farms are 5 times more productive than largest
o Rosenzweig-Binswanger – find that smaller farms are more productive
but their advantage is smaller in high risk environments (where
insurance in crucial but family farms lack it)
Caveat: there are reasons to believe that small plots may be of higher quality
(e.g. fragment good land more for inheritance purposes; sell off bad land in
distress)
Relationship Between Land Size and Productivity - Asuncao & Ghatak (2003)
model
 Idea: explain the inverse relationship between farm size and productivity by endogenous
occupational choice and heterogeneity with respect to farming skills without relying on
diminishing returns or incentive problems.
 Model
- assume no credit markets
- population mass 1, wealth distribution Ga
- all individuals have 1 unit of labor supplied inelastically either on their own farm or
on someone else’s as wage worker
- agents are heterogeneous in farming skills, for any given wealth level there are 
skilled, 1   unskilled
- production f-n: requires 1 worker per unit of land, output is q s or q u (skilled vs.
unskilled) per unit of land
- w is wage, p is rental rate of land, thus wealth a buys you a/p units of land (can’t
borrow)
- a worker thus earns c W  a  w
q w
- a farmer earns: c F  ip a, i  s, u
 each agent chooses the occupation that gives him more income (consumption). Thus the
level of wealth at which an i type agent will be indifferent between the two occupations is
wp
ai  qi  w  p
 note that q s  q u implies that for all positive w, a s  a u i.e. a skilled person would choose
to be a farmer at a lower wealth level
 Given the above AG prove: the average farm size of skilled farmers is smaller than that of
unskilled.
 intuition: given that skill is uncorrelated with wealth all guys in the wealth interval a s , a u 
will be skilled farmers, while the people with a  a u i.e. the ones with high farm sizes
(remember farm size is a/p will be both skilled and unskilled.
 thus if one looks at the relationship between farm size and productivity (output per unit of
land) without controlling for farmer skill we will find that small farms are more productive
on average than large farms.
 implication: one needs to control for farmer heterogeneity when doing such regressions very hard to do.