The Review of Economic Studies Ltd.
Moral Hazard, Financial Constraints and Sharecropping in El Oulja
Author(s): Jean-Jacques Laffont and Mohamed Salah Matoussi
Source: The Review of Economic Studies, Vol. 62, No. 3 (Jul., 1995), pp. 381-399
Published by: Oxford University Press
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Reviewof EconomicStudies(1995) 62, 381-399
C 1995The Reviewof EconomicStudiesLimited
Moral
0034-6527/95/00170381$02.00
azard
Financia
Constraints and
in
Sharecropping
EOulja
JEAN-JACQUESLAFFONT
GREMAQ and IDEI, Universit des Sciences Sociales de Toulouse
and
MOHAMED SALAH MATOUSSI
GREQE, Universite'de Tunis
First version received August 1990; final version accepted April 1995(Eds.)
This paperdevelopsa theory of sharecroppingwhich emphasizesthe dual role of moral
hazardin the provisionof effortand financialconstraints.The model is compatiblewith a large
varietyof contractsas observedin the regionof El Ouljain Tunisia.Using an originaldata set
includingfinancialdata, varioustests of the theoryareundertaken.Productionfunctionsstressing
the role of effortare estimated.The data supportthe theorywhichpredictslowerefficiencywhen
the tenant'sshareof outputis lower.The role of financialconstraintsin explainingwhichtype of
contractis selected(as well as the implicationsthat financialconstraintshave upon effort and
thereforeoutput)are supportedby the data.
1. INTRODUCTION
FollowingAdam Smith, all economistsuntil Johnson (1950) have consideredsharecropping to be a "practicewhich is hurtfulto the whole society", an unexplainedfailureof
the invisiblehand that should be eitherdiscouragedby taxation (A. Smith) or improved
by appropriatesharing of variablefactors (Schickele(1941), Heady (1947)). Johnson
(1950) startsfrom the empiricalobservationthat "the deviationsfrom optimum(induced
by sharecroppingcontracts)are not immediatelyobvious from a cursoryexaminationof
Americanfarmsoperatingunderdifferenttypes of tenurearrangements".He then argues
that the landlordcan approachthe desiredintensityof cultivationby detailedcontracting
and monitoring,by providingother inputs and keeping the size of the individualunit
small, to decrease(by an income effect) the farmer'smarginaldisutilityof effort, or by
the use of short-termcontracts.However,he admitsthat his theorydoes not quiteexplain
why sharecroppingcontractsseem to do as well as rentalcontracts.
The next main step' in the understandingof sharecroppingwas achievedby stressing
tenants'riskaversion.The rentalcontractdoes not providean appropriatesharingof risk.
Sharecroppingresults from the trade-off beween incentives and risk sharing (Stiglitz
1. The solutionproposedby Cheung(1968) amountsto assumingthat labourintensitycan be chosenby
the landlord.Bardhanand Srinivasan(1971), in an otherwiseunsatisfactorymodel, correctlystress that the
landlordcannotdecidehow muchlabourthe sharecropperputs in his land. Shaban(1987) providesempirical
evidenceagainstthe idea that landlordscan completelymonitoreffort.
381
382
REVIEWOF ECONOMICSTUDIES
(1974), Newbery (1977))2. A positive role for sharecropping is finally found as a second-
best way of inducingeffort by risk-aversetenants.Bravermanand Stiglitz(1982) extend
this insightby showing,as second-besttheorysuggests,that the landlordshouldintervene
in all markets(creditmarketand input markets)in which the tenant transacts,in order
to mitigatethe inefficiencyresultingfrom the above trade-off.
More recently,variouspapers(see Singh(1987) for a survey)focus on an asymmetry
of informationbetweentenantsand landlords.Tenantsare screenedfor their ability (or
someothervariableof privateinformation)by the variouscontracts.However,the stability
of thepopulationin the villagewe study(El Oulja)makestheseinformationalexplanations
quiteunconvincing.Everybodyseemsto be awareof the abilitiesof everymemberof the
village.
Othermodels stressthe imperfectionsof some marketsto explainvariousfeaturesof
tenancychoices, for examplemissingmarketsfor some inputssuch as bullocks,technical
know-how,family labour (Eswaranand Kotwal (1985), Bliss and Stern (1982), Pant
(1983), Reid (1976)).
Our main emphasiswill be on missing credit markets3when effort levels are not
observable.We are not the firstones to stressthesefeatures.However,with one exception
we became aware of after writing a first draft of this work, papers discussingcredit
constraintsdo not use these constraintsas an explanationof sharecropping.Braverman
and Srinivasan(1981) show that preventingeither landlordsfrom providingcredit to
tenantsor the provisionof creditby the governmentdoes not affectthe welfareof tenants.
This is due to the fact that in their model landlordscan control effort levels by varying
the size of the plot given to a tenant.The authors"takeit as given that the only form of
tenancyis sharecropping".Jaynes (1982) has also emphasizedcredit constraintsbut by
assumingthat landlordsare more constrainedthan tenants4.
In a contributionwhich is the closest to our paper Shetty (1988) developsa model
wheresharecroppingis explainedby an ex post liabilityconstraint.In bad statesof nature,
the rent cannot be paid completely.Even with risk-neutraltenantslimitedliabilityintroducesnon-concavitiesin the landlord'sand tenant'spayofffunctions.Sharecroppingmitigates within the relationshipthe associatedinsuranceproblem.Shetty'sassumptionthat
tenants'assetscan be appropriatedcostlesslyby landlordsis inadequatefor the villagewe
observe.We are led insteadto write an ex ante financialconstraintwhich, in the absence
of moral hazard,explainsthe emergenceof sharecropping,but not inefficientoutcomes.
An ex ante financialconstraintandmoral hazardwill be the two main buildingblocks of
our stylizedmodel.
The data are brieflydescribedin Section2 (the Appendixgives summarystatisticsof
the data). Section 3 describesthe interactionof moral hazardin the tenant'seffort level
and of the financialconstraintin the designof efficientcontracts.The model of Section3
is extendedin Section4 to accountfor the landlord'sfinancialconstraints,variablesizes
of plots, risk aversion,repeatedrelationships,etc. Section 5 is devotedto the estimation
of productionfunctionsincludingan effortvariable.Strongempiricalsupportis given to
the need for consideringincentivesin the estimationof productionor cost functions.
Section 6 providesan empiricalanalysis for the choices of contractsand confirmsthe
contractcan then be
2. Risk aversionalone is not enough.As shownby severalauthorsa sharecropping
mimickedby an appropriatecombinationof rentand wagecontracts.
3. See Bravermanand Guasch(1986) for empiricalevidenceon the difficultiesto provideruralcreditin
LDC's.
permitsan "individualwho
4. A refereepointedout a referenceto Marxwho stressedthat sharecropping
is not himselfa capitalistto have a capitalistfor a partner"in Jaynes(1982).
LAFFONT & MATOUSSI
SHARECROPPING IN EL OULJA
383
importantrole playedby financialvariablesin explainingthe type of contractselectedby
a landlordand a tenant.Concludingcommentsare gatheredin Section7.
2. THE DATA
A surveycarriedout with the help of the TunisianNational Institutefor Statisticshas
been conductedin 1986 in a ruralarea known as El Oulja,40 miles west of Tunis. One
hundredfamilieshave beenconcernedwith this surveywhichincludesthreetypes of data.
(i) Generalinformationabout the familieswith, in particular,the numberof days
workedin agriculture.
(ii) Informationabout each plot of land definedas a piece of land whereonly one
type of crop is carriedout each season. Data includesize of plot, type of crop,
type of labourcontractused (eitherwage contractor fix rent contractor sharecroppingcontract),productionlevels,preciseamountsof labourinputs as well
as preciseamountsof other inputs.
(iii) Wealthand incomedata for each family.
A similarsurveywas undertakenin 1988with somewhatless care. We will use data
from it only to test the robustnessof our results(see the appendixfor more on the data).
3. CONTRACTINGWITH FINANCIAL CONSTRAINTSAND
MORAL HAZARD
As recognizednow in the literature(see Reid (1987), Singh (1987)), the theoryof sharecroppingis best viewedas a sub-fieldof the theory of the firm.One cannot expect "one
particularexplanationof managerialstructureto be uniquelypowerfulover a long period
of time and acrossmany cases" (Reid (1987), p. 565). Any model of sharecroppingmust
stressspecificfeaturesof the data to be explored.The purposeof this sectionis to develop
a simplemodel incorporatingthe basic ideas we found usefulin explainingthe characteristics of sharecroppingin El Oulja. The model will then be enrichedto account for a
numberof interestingbut secondaryaspectsof the contractingproblemwe study and to
relax some assumptionsof the basic model.
The productionfunctionof an elementarypiece of land, called a plot, is written:
y5=f(le, x) + -,
f increasingandconcave,
(1)
wherey is output, 1is the amountof labourinput, e is the averagelevel of effortapplied
to these units of labour (le= 1 is labour in efficiencyunits), x is the amount of other
materialinputs,and E is a zero-meanrandomvariable.
Land is owned by landlordswho contractwith tenants to organizeproduction.A
generalcontractis definedby threeparameters(a, ,B, r) whichare, respectively,the share
of the productkept by the tenant,the shareof materialinputspaid by the tenantand the
certainpaymentmadeby the tenantto the landlord.This generalformof contractencompasses all types of contractsused.
A pure rentalcontract(RC) is associatedwith a = 1, ,B=1, and r> 0.
A pure wage contract(WC) is associatedwith a = 0, ,B=0, and r <0.
A sharecropping contract (SC, a; ,B) is associated with a e (0, 1), /Be (0, 1) and r>0.
If we denote yi(le), with yv(0)= 0, ' > 0, y" > 0 the disutilityof labourfor the tenant
his utility level for a contract(a, /B,r) when he works le in efficiencyunits is, assuming
REVIEWOF ECONOMICSTUDIES
384
risk neutrality:
af(le, x)-f3xyf(le)-r-w
where w denotes his living expensesat the subsistencelevel without working.Note also
that, as we are going to use only a cross-sectionof data, all priceshave been normalized
to one.
First,assumethat the landlordcan observeall variables.If the landlordis riskneutral,
the efficientcontractssolve the followingmaximizationprogramme:
max (1-a)f(1,
(2)
x)-(1 -/3)x+r
(a,/J,r,l,x)
subjectto
af(l,x) -/3ix - y(l) - r - w >
(A)
(3)
whereu is the alternativelevel of utility the tenant can achieve.The main interiorfirstorderconditionsof this programmeare:
Lfx) + A.[adf(l x) - Vt'1)]
]=
(I-a) -.f(1
(I -a)
(I,x)-(l-fl)+A
Ox
(4)
ad (1,x)-fl =0
LOxI
I - A= 0
(5)
(6)
or
-,i(1,x) = VV1) and
' (1,x)= I
(7)
i.e. the efficientallocationof resourcesis achieved.
If 1*, x* denote the efficientallocationof resources,(a, /3, r) are chosen so that:
af (l
(8)
*, x*)-/3x*-yV(l1*)-r-w=-u
i.e.,
a = 1,= 3 = 1
a =O,3=O
r (
r=-u-aY(i*)-w
-w
for a RC,
for a WC,
any combinationa, ,B,r satisfying(8) for a SC. In the observedsharecontractswe have
r=O.
Any type of contract can thereforefulfill the first-orderconditions at the efficient
allocationof resources.
Assumenow that, becauseof imperfectionsin the creditmarket,the workingcapital
R of the tenantis limited.In definingan optimalcontract,we must add the constraint:
w+/3x*+ rR
(9)
but there remain multiple optimal contracts implementingthe efficient allocation of
resources.
Remark. Constraint(9) is an ex ante financialconstraint.It says that the tenant
mustpay for his livingexpenses(w), for his shareof input (,Bx*)and for an eventualrent
LAFFONT & MATOUSSI
SHARECROPPING IN EL OULJA
385
(r). The rent r may be negativeand it is then interpretedas a wage. From the point of
view of the sharecropperwhat mattersis the aggregateamountof money r + ,Bx*he must
disburse.As ,Bandx* areobservableP does not playany independentrolein the theoretical
analysis.Our way of writingthe financialconstraintimpliesthat any delayedpaymentto
the landlordtakesplaceonly in the formof a shareof output(1- a)(f+ s). An alternative
(followedby Shetty(1988)) wouldbe to ask for an ex post rentr and obtainmin (r, f+ ?).
Our unmodelledargumentto exclude this possibility is that the transactioncosts for
monitoringoutput would then be as great as in sharecroppingwhile at the same time
inducingless effort of the landlord(who can give to the tenant all sorts of advicesand
helps). A completeinvestigationof this questionwould requireintroducingmoralhazard
in the insurancewith limitedliabilitymodelof Shetty.Also, this alternativeway of sharing
ex post output appearsextremelyconflictualin the cases of bad crops. The landlordthen
gets all of the productioninsteadof sharingthe consequencesof bad statesof naturewith
the tenant.
The logic of the behaviourwe postulatefor the landlordis to obtain as much cash
advancesfrom the tenantas possiblein the form of rentor materialinputs.He then picks
the lowest a compatiblewith the tenant'sindividualrationalityconstraint.
From (8) and (9) we have:
a <f(l*
*)
(10)
.
Rental contractsand sharecroppingcontractswith a high shareof the productgiven
to the tenantmay be excludedby financialconstraintsand the constraint(10) is tight. It
predictsa positivecorrelationbetweena and R that is easy to observein the data.
So far the modelpredictsefficientproduction,but we pursuethe analysisby assuming
that the tenants'seffort levels are unobservableby the landlord(at least beyond some
monitorablelevel). We continue to assume that materialinputs, x, and labour, 1, are
observableand consequentlycan be chosen by the landlord.However,e is chosen by the
tenant. Hence, the moral hazardconstraint5:
Of
at
a ,f (le, x) = yV'(1e).
(11
If no financialconstraintexisted, then risk neutralitywould enable the landlordto
achieve an efficientallocation of resourcesby choosing a rental contract (a = 1). The
tenantwould then benefitfrom all his effortand would choose a sociallyoptimallevel of
effort.
Considernow the landlord'soptimizationprogrammewhen both a financialconstraintfor the tenant and the moral hazardconstraint(11) exist:
max (1-a)f(le,x)-(1-f,)x+r
(12)
(a,fl,r,l,e,x)
subjectto
af(le, x)-f3x-r-
y-(le)-w
R-fJx-r-w>0
a a--(le, x) -
V'(le)= 0.
>
(13)
(14)
(15)
5. As f is concavein I and yrconvex,the first-ordercondition(11) is sufficientto characterizethe choice
of effortlevel.
REVIEWOF ECONOMICSTUDIES
386
Clearly,if R is largeenough (14) is not bindingand a rent contractis selectedwith
the highestpossiblevalue of r which saturatesthe individualrationalityconstraint.
Let us now focus on the case wherethe financialconstraintis binding;(14) can be
used to substitutethe value of r+ w+ fix to give:
max (1-a)f(le,x)-x+R-w
(16)
(a,le,x)
subjectto
> u+ R
af (le, x)-y/(le)
a ,f (le, x) - V'(1e)=0.
01
(A)
(17)
(1l)
(18)
We obtain the first-orderinteriorconditions6:
(I -a) 4(le, x) + p a 42(le,x)- I"(le)l=O
LOl2
81
(19)
Of
~~~~~~~02f
(I - a) af(le, x) - I + Aa ,f (le, x) + pa - - (le, x) =?
(20)
(A - 1)f (le, x) + ll 'f(le, x) = O.
(21)
Ox
Ox
alox
01
Using (15) and (21) in (19) (20), we finallyget, leavingout argumentsin the functions:
Of=
+
( -a O2f)
(22)
01~~~2
Of
Ox
l -ua
dt
alax
(23)
OfI
Il-ua a>/f
The allocationis now inefficient,p >07, the marginalproductivityof labour in efficiencyunits is too high; the marginalproductivityof inputsis also too low (if labourand
materialinputsare not complementary)with an ambiguousresultif they are complementary. The completecomparativestatics of this model is actuallyquite complexand will
not be derived.
However,we can obtain the followingpropositionwhich summarizesthe main predictionsof the model.
Proposition1.
(i) The landlord's utility level increases with the tenant's working capital R.
(ii) Conditionally on the level of other inputs x, the level of effective labour le, and
therefore the production level, y, are increasing in R.
6. We assumebelowthat the individualrationalityconstraintis binding.For R smallenougheitherthere
willbe a switchto a wagecontract(seebelow)or the landlordwillprefernot to saturatethe individualrationality
constraintto inducesome effort.For a fixedx it can easilybe checkedthat dA/dR<0. Thereforedependingon
the productionfunctioneitherthe constraintis alwaysbindingor it is not bindingfor R smallerthana threshold
value.This helpsexplainwhy in practicethe shareof the productleft to the workeris neverless than 1/2.
7. Look at (19), and use the concavityoff and the convexityof yV.
LAFFONT & MATOUSSI
SHARECROPPING IN EL OULJA
387
Landlord'sutilitylevel
RC
SC
a=1
WC
a/
/
a =O
R
FIGURE I
(iii) Conditionally on the level of other inputs x, the tenant's share of output a is
increasing in R.
Proof. (i) Follows from the envelope theorem and (ii) and (iii) from a straightforwarddifferentiationof the first-orderconditionsfor the landlord'sprogramme. 11
Since we have assumed that the tenant's individual rationalitylevel of utility is
independent8of his workingcapital,the level of utilityfor the landlordis decreasingwhen
the tenant'sworkingcapitalR decreases.Thencomesa point at whichthe landlordprefers
to incur some monitoringcost9 to ensure a minimaleffort level and switch to a wage
contract.The model so obtainedis then compatiblewith the co-existenceof all types of
contractsthat we observein El Oulja'?.
In Proposition1, the monotonicityof y and a in R is obtainedonly conditionallyon
x. This will be enoughfor the empiricalwork. The predictionof Proposition1 (ii) will be
exploredin Section5 wherewe estimateproductionfunctionstestingfor a positivedependence of productionon R or a conditionallyon x. Proposition1 (iii) will be used to test
in Section6 the positivedependenceof the contractchoice on R conditionallyon x (and
also unconditionally).Figure 1 summarizesthe analysis.What has not been provedis the
8. We may also expect(dependingon the relativenumbersof landlordsand tenants)that the tenantswith
a lot of workingcapitalwill be able to extractmore incomethan the others.In Figure I we have assumedthat
the bargainingpowerwas in the hands of landlords,tenantsbeing all kept at the dilevel. The other extreme
situationwould be the one wherelandlordswould be kept at the same level and the increaseof utilitydue to
moreeffort(due to highershares(due to higherworkingcapital))would benefittenants.(see Bell (1989) for a
bargainingmodel of sharecropping).In this paperwe stay in the principalagent frameworkwith u exogenous
on the groundsthat an excesssupplyof labouris endemicin El Oulja.
9. If af/la is boundedabove, and the tenant is very poor (a very small), sharecroppingincentivesfor
effortare very low.
10. Actually,we observeonly the values of 1/2, 2/3 and 3/4 for the parametera in the sharecropping
contracts.
REVIEW OF ECONOMIC STUDIES
388
monotonicityof a in R unconditionallyas we can expectin generaland as illustratedin
the figure.
4. EXTENDING THE BASIC FRAMEWORK
(i) Financial constraints of the landlords
If the tenantdoes not have any financialconstraint,then the optimalcontractis the rental
contract.It remainsthe solution even if the landlordhas financialconstraintssince this
contractdoes not requireany financialparticipationof the landlord.
Considernow the case wherethe tenant'sfinancialconstraintis binding.If R'denotes
the availableworkingcapital of the landowner,indexingnow by t, the tenant'sworking
capital,his optimizationprogrammeis:
max (1- a)f(le, x)-(1 -,B)x+r
(a,le,f3,x,r)
subjectto
fix - r-
af(le,-
(le) >
R'-,Bx-r-w_O
a - (le, x)- V'(le) = 0
R'-(1 -/3)x+r?0.
From the two tight financialconstraintswe derive:
x =R'+
R - w
r=
((1 -,)R'-JJR'-(1
-/B)w.
The maximizationprogrammeis reducedto:
max (1 -a) f (le, R'+R'- w)-R'
(a,je)
af (le, R'+ R' -w)-R'+
w-t(le)
a af(le, R + R'- w) - yg'(le) =0.
al
>a
(A)
(p)
(24)
(25)
Restrictingthe analysisto the case whereboth constraintsare bindingwe obtain by
differentiation
straightforward
da _Of/Ox<0
dR'
f
da
I-aaf/lax
dRt
f
SHARECROPPINGIN EL OULJA
LAFFONT & MATOUSSI
389
(if the marginalproductivityof other inputsis not too far from the optimum)and
da _ da >011
dRt dR'
The effect of the landlord'swealth on effort or labour alloction in efficiencyunits
depends on the sign of a2f/lalx. If labour and materialinputs are not complementary
(a2f/alax< 0), labouris increased.The effectis ambiguousif they are complementaryand
null for a Cobb-Douglas productionfunction.
We will use these resultsto test that the landlord'swealth has a negativeeffect on
the tenant'sshareand that the landlord'sworkingcapitalhas no effecton productionfor
a Cobb-Douglas specification.
(ii) Variablesize of plots, hiredlabour
Let h be the size of the plot alloted to a given head of family who can use lf units of
familialwork wherelf is first supposedto be observable.He can also hire an amountI of
labourat a wagev witha normalizedeffortlevelof one enforcedby the tenant'smonitoring.
Being essentiallynon-verifiableby the landlordthis labour input is not usually shared.
(We ignore the subsistencelevel in this next model).
The landlord'sincome is then:
Ife+ l, x)-(1 -/)x+
(1 -a)f(h,
r.
Let VI(e)denote now the disutilityof effortfor each memberof the familywho has
an outside opportunityequal to a.
The utility level of the familyis:
af (h, lf e + 1,x)-,Bix -vl- r - (e)lf .
The landlord'smaximizationprogrammebecomesthen:
max
{(1 -a)f(h,
(ac,3,1h,e,j,x,r)
lf e, 1,x)-(1 -/P)x+r}
af(h, Ife, 1,x) -,fx-vl-r-ra Of =
a
V/I(e)lif Ifu
'(e) (if If> 0)
v (if 1>0)
R'-f3x-vl-r
_O.
By limitingthe size or the plot, one might think that the landlordis able to obtain a
high level of effort from the tenant (Bravermanand Srinivasan(1981), Johnson (1950),
Cheung(1969)). However,if lf is unobservablebecausethe familylabourdevotedto the
plot is chosen by the tenantin an unverifiableway an additionalmoral hazardconstraint
of the choice of If must be added. We are then back to our previousmodel with a slight
variationon the specificationof the disutilityof effort'2.
11. See Eswaranand Kotwal (1985) for alternativefoundationsof similarrelationships.
12. The formulationlIV(e)wouldlead to the sameconditionalpredictionsin Section3.
REVIEWOF ECONOMICSTUDIES
390
If thereis no outsidelabourused and we have constantreturnsto scale the problem
is reducedto our previousformulationif we reasonper unit of land:
max
(a,f3,h,e,lf/h,x,?-
h {(1 - a)g(e'-f, -(1h h
ag(e^-,T
aag---
Rt
--f
h
3) -+r
h
1/ h
h3
,'(e)=0
x
if
0O
--w --r>
h
h
A conclusionof this model is that if there are constant returnsto scale, R' and h
should appearonly as the ratio Rt/h in the explanationof the contractchosen. When a
familyworkson severalcropsthe workingcapitalnormalizedby the total surfacecultivated
shouldbe used.
(iii) Risk aversion-
So far we have neglected risk aversion in our explanationof contracts. Clearly, risk
aversionof the tenantmay have a role in justifyinga smallershareof output for him. As
risk aversionis usually inverselyrelatedto wealth we will test this possibilityby testing
the significanceof wealthin the explanationof the main featuresof the chosen contracts.
This is certainlyis a weak test given the relationshipbetweenwealthand workingcapital.
(iv) Repeated relationships
Gametheoryhas familiarizedus with the idea that repeatedrelationshipsmay solvemoral
hazardproblemsby relyingon appropriatethreatssuch as here threatof non-renewalof
the contract (Johnson (1950)). Financialconsiderationswould explain the form of the
contractand efficiencywould be enforcedby repeatedrelationships'3.We will test this
idea by introducingthe length of the relationshipin the productivityequationsthat we
will estimate.
(v) Family labour constraints
The precedinganalysishas assumedthat sharecroppersand tenantsare not constrained
in theiruse of familylabour.This is particularlydoubtfulfor sharecropperswho may be
financiallyconstrainedin the land they can rentand thereforehaveexcessivefamilylabour
in a world whereunemploymentis widespread.To distinguishthe inefficiencyof family
labourin sharecroppingdue to low effortlevelsand the inefficiencydue to excessivelabour
inputswe will introducea dummyvariablewhichdistinguishes"largesize"familiesfrom
''smallsize" familieswherethe secondeffectshould not appear.
13. See Dutta, Ray and Sengupta (1989).
SHARECROPPINGIN EL OULJA
LAFFONT & MATOUSSI
391
5. ESTIMATIONOF PRODUCTION FUNCTIONS
Our theoreticalanalysissuggeststhat the level of productiondependson the level of the
tenant'sworkingcapital.It is easy to exhibita significantpositivecorrelationbetweenthe
levelof workingcapitalandproductionlevelsbut the economicmeaningof thisdependence
is difficultto ascertaingiventhe high correlationbetweeninputlevelsand workingcapital.
Instead we have chosen to estimate the effect of the contract type on the production
levels'4.For given input levels, the level of workingcapital affects the type of contract
chosen, thereforethe levels of effortand finallythe productionlevels (see Proposition1).
This proceduredoes not raiseeconometricdifficultiesif contracttypes can be considered
as exogeneousin the productionfunction.
First, we considerCobb-Douglas productionfunctionswith inputs, family labour
FL, hired labour HL, and other inputs M, and shift variablesZ1, Z2, Z3 defined as
follows:
ZI = 1 whenthe farmeris the owneror has a rentalcontract
= 0 otherwise
Z2= 1 whenthe farmeris a sharecropper
= 0 otherwise
Z3 = t x Z2 wheret is the lengthof the relationshipbetweenthe landlordand the
farmerfor a sharecroppingcontract(t is measuredin months).
In the followingregressions,Y denotesproductionper hectareand inputsare evaluated per hectare.A two-stageleast-squaresprocedureis used for inputs HL and M. Next
an exogeneitytest on Z1, Z2 and Z3 is carriedout.
For the 1986 survey(170 observations)we obtain (t statisticsin parenthesis):
Log Y= 4 8 Z1+ 4.4 Z2+ 0-009
(8 3)
(7 7)
(5 8)
Z3+
0 20 LogFL+
0 15 LogHL+
(5 6)
(4-4)
0-23 logM
(2 5)
R2=0-42
using as instrumentsdummy variablesindicatingthe type of the crop (tomato, potato,
melon, vegetable),the level of wealth,the numberof active membersin the family.
We test the exogeneityof Z,, Z2 and Z3 as follows.By the probittechniquewe obtain
Z,= 2-7 - 0 5 AGE+ 0-006 (AGE)2+ [-01 logRICH
(0-8) (2-7)
(2.8)
(5 6)
0 47 ACT- 0-6 OWL- 0 0007 R'
(4 8)
(1-8) (2-1)
(5.1)
Z2= 1-09
-
14. An alternativeis to test the role of contractsin the allocationof resourcesby studyingthe dependence
of inputdecisionson contracts.This approachwas followedby Shaban(1987) who testedif differencesin input
intensitiesbetweenrental and sharecroppingcontractswere significant.He considersthat, with monitoring,
marginalproductivitiesof inputsare equatedto prices,while, with no monotoringand sharecropping,prices
are equatedto marginalproductivitiesmultipliedby the farmer'sshare.We believethat the structuralform
representingsharecropping
is more complex.We can only rely on inputdata whenthose inputsare includedin
the contractand presumedobservable.For those (as familylabourin efficiencyunits) that are not observable
it must be taken into accountthat they are chosen by the farmer,but they cannot be used in the estimation.
Indeed,if they wereobservable,they could be monitored.
REVIEWOF ECONOMICSTUDIES
392
and by the least-squaresmethodwe obtain:
Z3= 18-2-5-2 log ACT-00009
(5-5) (-1-6)
(-3-6)
R'+ 0-0012 R'
(5-4)
whereAGE is age, RICH wealth, ACT the numberof workingmembersin the family
OWLowned land, R' the landlord'sworkingcapital.Then the residualspi, p2 and P3 of
these regressionsare introducedin the followingregression:
Log Y=4 7 Z? + 4-3 Z2+ 0009 Z3+ 0 20 log FL+ 0 15 log HL
(7 3)
(2.2)
(3.8)
(5.4)
(8)
/ + 000013 P 3
+ 025 log M-002 p I+ 0 I P2
(0 04)
(2.6)
(-0 14) (0.9)
.R2 =
0-42
As the coefficientsof PI, P2, P3 are not statisticallydifferentfromzero we can accept
the exogeneityof Z,, Z2 and Z3.
These resultsare confirmed'5using the data set from 1988 (136 observations)
Log Y= 5 7 Z, + 5 1 Z2+ 0 009 Z3+ 0 26 log FL+ 0 15 log HL+ 0 09 log M
(3.8)
(1-5)
(4.4)
(5.2)
(8-1)
(8.7)
R2=0 53
We have also explored an alternativeexplanationof these results suggestedby a
referee.More able tenantshave earnedmore in the past, have now more workingcapital
and thereforeare likely to be given rentalcontracts.To eliminatethis effect we restrict
the analysisto young tenants(less than 35 yearsold) and obtain similarresults.
In 1986 (67 observations)
Log Y= 4-6 Z,+ 4.3 Z2+0 006 Z3+ 0 21 log FL+ 0 14 log HL+ 0 25 logM
(2.5)
(1.6)
(4.4)
(2.8)
(3.3)
(4-6)
R2=0-38
In 1988 (54 observations)
Log Y= 4.7 Z, + 4.3 Z2+ 0-005 Z3+ 0O26 log FL + 0 10 log HL + 0O28 log M
(4.7)
(4.6)
(1.4)
(2.3)
(1.4)
(30)
R2=0 43
The significanceof contractsin the explanationof productionis very stable across
thesedifferentregressions.In all the above regressionswe rejectedat the 1%significance
level the hypothesisthat the coefficientsof Z1 and Z2 are equal. The type of contract
mattersin the explanationof productionlevels as predictedby the theory. Using for
referencethe resultsfrom 1986 we see that moving from a sharecroppingcontractto a
rentalcontractincreasesproductionby 50%(comparee48 and e4-4). The effectof the length
of the relationshipbetweenthe landlordand the sharecropperis positiveand significant.A
three-yearcontractof sharecroppingincreasesproductionby 38%.Independentlyof the
15. The exogeneityof the contractvariableswas also testedpositively.
SHARECROPPING IN EL OULJA
LAFFONT & MATOUSSI
393
type of contractthe coefficientof hired labour is 50%less than the coefficientof family
labour.
Thecombinationof a Cobb-Douglasproductionfunctionand themodellingof labour
in efficiencyunits lead to a specificationwhere the effect of the contractis similarto a
Hicks-neutraltechnicalefficiencyeffect. To test the robustnessof our resultswe change
the specificationby assumingthat theremay be a differentelasticityof productionfor the
amount of family labour in the case of rent contractsand in the case of sharecropping
contracts'6.We obtain:
In 1986 (170 observations)
Log Y= 4 2 +0 222 Z,logFL+0
(6.8)
(5.7)
197 Z2logFL+ 0 19 logHL+ 0 28 logM
(5.0)
(5.0)
(2 8)
A2=0 31
In 1988 (n = 136)
Log Y= 4 5 + 0 39Z,logFL+
(6 4) (6.1)
0 32 Z2logFL+
(5-0)
0 20 logHL+ 0 16 logM
(2.3)
(5.0)
A2-0 40
In 1986 (young tenantsn = 67)
Log Y= 3 8 + 0 25 Z, log FL + 0 22 Z2log FL + 0 16 log HL+ 0 34 log M
(3 6) (3.9)
(2.0)
(3-5)
(2.8)
jR2=
0 31
In 1988 (young tenantsn = 54)
Log Y= 3 8 + 0 36 Z,logFL+ 0 31 Z2logFL+ 0 14 logHL+ 0 32 logM
(1 9)
(2-8) (334)
(4 3) (3 3)
f?2
=0-30
With this new specificationwe also find that the coefficientsof familylabourin rent
contracts and sharecroppingcontractsare significantlydifferentat the 1%significance
level.
It may be arguedthat pervasiveunemploymentleads to low efficiencyof sharecropping due to excessiveuse of familylabour.We then introducea dummyvariableZ5which
equals 1 if the numberof familyworkersper hectareis largerthan2-5 and zero otherwise.
The followingresultsuggeststhe existenceof this excessivelaboureffect(0 17 significantly
differentfrom 0- 19 at the 5%level) but also confirms,for familiesof smallsize, the lower
efficiencyof family labour in sharecroppingcontractscomparedto rent contracts(0 19
16. Because of the very high correlation between Z, and Z, log FL (which is 0 96) and the very high
correlation between Z2 and Z2 log FL (which is 0-98) it is not possible to imbed meaningfully the two models
obtained within a single model and test the retrictions to which they correspond. We could engage in non-nested
tests but the purpose here is not to choose the best model, but to check the robustness of our result according
to which contract variables affect productivity.
394
REVIEW OF ECONOMIC STUDIES
significantly different from 0-21 at the 5% level)'7. Using the method of 2SLS we obtain:
In 1986 (n= 170)
Log Y= 4 2 + 0 21 ZlIogFL+
(6.8)
0 17 Z2Z5logFL+
(3.7)
(5.1)
0 19 Z2(1-Z5)logFL
(4 8)
+0 19 logHL+0-28 logM
(5.0)
(2.8)
A2
=0O31
In 1988 (n = 136) we obtain similarresultswith a 1% significancelevel.
Log Y= 4 5 + 0 37 Z, log FL+ 0 30
(4 5)
(6-5) (5 8)
log FL+ 0 33 Z2 (1 -Z5)log FL+
Z2 Z5
(4 9)
+ 0 21 log HL+ 0 16 logM
(2.3)
(4.9)
Rk2=0 40
Similarlyfor the sub-sampleof young tenantswe still get significantdifferencesin the
coefficientsof family labourin rent contractsand sharecroppingcontracts.Howeverthe
excessivelaboureffectdisappearsfor young tenants.
In 1986 (n=67)
Log Y= 3.7 + 0 25 Z, log FL+ 0 21 Z2Z5 log FL+
(3.5)
+ 0 23
(3.8)
Z2 (1-Z5)
(3.4)
log FL+ 0 16 log HL+ 0 35 log M
(2.6)
(3.3)
(2.0)
A2= 0 30
In 1988 (n=54)
Log Y= 3 8 + 0 36 Z logFL+
0 31 Z2Z5logFL+
(2.8)
(4.3) (3.2)
+ 0 31 (1 -Z5)Z2 log FL+ 0-14 log HL+ (0 32) log M
(2-7)
(I19)
A2
(3 3)
=0-38
Finally, we look at an alternativespecificationof the incentiveeffects due to the
length of the relationshipt in sharecroppinglabour and to the share of input fJpaid by
the tenantby introducinga parameterof sharecroppinglabourwhich dependson both t
and fJ(for a given a a high fi means a high productivityplot whichcan supporta high
fundingof inputs; the motivationof introducingfi is the discretenatureof a).
17. Thereis no reasonto test for an excessivelaboureffectin rentalcontractsbecausetenantswith rent
contractsare not financiallyconstrainedand thereforeshould be able to rent enough land for all their family
we arenot interestedin the pervasiveunemployment
labour.Furthermore
effectperse, but ratherin the difference
in theefficiencyof familylabour,stemmingfromdifferencesin effort,betweenrentalandsharecropping
contracts.
Giventhat 0-21 is significantlygreaterthan 0-19 we can expectthe coefficientof Z,(I - Zs) log FL to be even
moredifferentfrom 0 19. So allowingfor the excessivelaboureffectin rentalcontractswould only strengthen
the findings.
LAFFONT & MATOUSSI
SHARECROPPING IN EL OULJA
395
In 1986 (170 observations)
Log Y= 4 8 + 0 21 Z, log FL+ (0 10+0 002t+0 0005f
(8.5) (5.8)
(1.3) (4.8)
(0 5)
Z2
log FL
+ 0 15 log HL+ 0 23 logM
(3.9)
(2.5)
k2=
0-24
In 1988 (n = 136)
Log Y= 5-5 + 0-29 Z, log FL+ (0.07 +0-002t+0.0016f
(8.2) (4.7)
(0.82) (3 3)
(1.6)
Z2
log FL+
+ 0 15 log HL+ 0 12 logM
(3.8)
(1.7)
A2= 0 50
In 1986 (young tenants n = 67)
Log Y= 4 5 + 0 24 Z, log FL + (0. 16 + 0 0012t + 0 0003f3) Z2 log FL
(4.4) (3 9)
+0 13 logHL+0
(2.2)
(1.4)
26 logM
(2.5)
(0.2)
(2.2)
jk2 =0-38
In
1988 (young tenantsn =
54)
Log Y= 4.3 + 0 30 Z, log FL+ (0 05+ 0 002t + 0 004fJZ2 log FL
(4.3) (2.6)
(0.3) (0.2)
(1-6)
+ 0 12 log HL+ 0 31 logM
(1.6)
(3.2)
A2= 042
Again the coefficient of family labour in rent contracts is significantly different at the
1%level (5% level only for young tenants in 1988) from the coefficient in the sharecropping
case (actually the sum of three coefficients computed at the average sample values). Furthermore, with this new specification we again find that the length of the contract significantly affects positively the productivity of sharecropping labour.
6. CHOICE OF CONTRACTS
The previous section has shown the effect of contract type on production. In this section
we test the role of financial constraints and risk aversion in the selection of contracts.
The structural form obtained in Sections 3 and 4 is summarized as an ordered probit
model where the contract type variable, CT takes the values
0
ifa=1/2
1 ifa=2/3
2
if a= 3/4
3 ifa=1
REVIEWOF ECONOMICSTUDIES
396
The underlyingmodelis thenZ = 31+ 32k + f33R'+04tWt+ e with E--,'(0, ca)where
R' (resp.R') is the tenant's(resp.landlord's)workingcapitaland W'is the tenant'swealth
if z,<po
CT=0
1 ifpo<z,<Pl
2 if <z,?<p2
3 if zt>p2
The maximumlikelihood estimatorsof this model are obtained by the Davidson
(1959), Fletcherand Powell (1963) algorithmand the variancecovariancematrixfor the
estimatesis the Berndtet al. (1974) estimatorusing the firstderivatives.
For the 1986 surveywe obtain:
+ 0*0003R'- 00001 R'+ 0 000045 W'
(9 5)
(1.49)
(2 2) (5.1)
with po=0 (normalization).
P2==063
p,= 030
Z=- 036
(3*3)
(4.1)
In 1988, we get:
Z
+ 00005R'-
0019
(0 5)
(3 5)
0 0004 R'+ 0.0001 W'
(2.5)
(-4.4)
with
pi= 08
(3 0)
P2= 03
(4.1)
As predictedby the theory the higher the tenant'sworkingcapital, the closest to a
rentcontractwe are. On the contrarythe higherthe landlord'sworkingcapitalthe higher
his sharein the sharecroppingcontract.The wealtheffectis of the rightsign but not very
significant,suggestingthat financialconstraintsplay a more importantrole than risk
aversionin explainingthe selectionof contracts18.
The orderedprobit model assumeshere that the discretechoice betweenrentaland
sharecroppingis governedby the same model that determineswhethera = 1/2, 2/3 or
a = 3/4. To test this hypothesiswe run a probit of rentalversussharecropping.Since the
varianceof the errortermis not identifiedin sucha probitmodelwe re-scalethe parameters
of the orderedprobitwith the estimateof the standarderrorobtainedabove (6f= O-384).
choice is then made with the model
The rental/sharecropping
Rentalif/31+ 32R'+f3R'+ f4W'+ ? > O
where e is now X(0, 1), insteadof the previousmodel
Rental if
/3I-P2
/32
+-Rt+-
03
/34
+-04 W + ?>O
18. An alternativeexplanationgiven by a refereeuses risk aversion.The more workingcapitala tenant
has, the more crops he plants.The more crops a tenantplants, the more diversifiedhe is, so the less risk he
bears for a given sharingparameterin the contract.However,we did not find any correlationbetweenthe
numberof crops (NP) and the size of workingcapital.
NP=
2-8 -0000084R'
(13-3) (-0 44)
R2= 0 004
LAFFONT & MATOUSSI
SHARECROPPINGIN EL OULJA
397
wherere-scalingis made to have ?/Ca as a A(0, 1) randomvariableso that the estimators
Ij and Pi/cr, i= 2, 3, 4 are two estimatorsof the same value underthe null hypothesisof
no differencebetweenthe choice models.
Noting that f3i/6 is the most efficientestimatorwe can run Hausmantests.
As is often the case in smallsamplesthe differencein the covariancematricesbetween
probit and the re-scaledorderedprobit parametersdid not turn out to be positive semidefinite.Thus to comparethe resultswe simplytest that the coefficientsof R' and W' are
which are 5-66 and 0-43
the same. For the coefficientsR' and W' we obtain X2_statistics
respectivelywhich are below the 1%significancelevel which is 6-63.
We can safely conclude that our assumptionof the same choice model for the four
regimesis not rejected.
Sincethe theoryonly obtainedthe predictionsconcerningthe effectof workingcapital
on contractchoices conditionallyon the level of inputs we also obtainedthe maximum
likelihoodestimatorsfor an enlargedmodel with similarresults.
In 1988 (n= 136)
Z= -1[2 +0-00058R'-0
00032R'+0 00008W'
(2 0)
(2.9)
(-16)
(2.7)
+ 0 0055 FL + 0 0020 HL + 0 00026 M
(0 40)
(2-4)
(0.42)
Po=O
p,u= 086
P2= 1-35
(3 0)
(4.0)
In 1986 (n= 170)
Z=-1
09 + 0 0003 Rt- 0 000l1 R'+ 0 00003 W'
(2.5) (5*3)
(9.01)
(1.0)
+0-00024 FL+0 00047 HL+ 0-001 M
(1.11)
Po=0
(0-3)
p=0-42
(3-3)
(2.3)
P2=067
(4.1)
7. CONCLUSION
We have developeda theory of sharecroppingwhich emphasizesthe dual role of moral
hazardand financialconstraints.The unobservabilityof effortrequiresthe use of incentive
contractsto induce good effort levels. This can easily be achievedwith rental-contracts
which leave to tenants all the proceedsof their effort. However,the tenant'sfinancial
constraintsmake these contractsoften impossible.The poorerthe tenant,the smallerthe
shareof the crop he will retainand thereforethe less efforthe will provide.
Productionfunctionsstressingthe role of effort have been estimated.They support
the theory which predictslower efficiencywhen the tenant's share of output is lower.
However,this inefficiencyis somewhatmitigatedby the lengthof the relationshipbetween
the landlord and the tenant. The working capital of the tenant (and of the landlord)
appearas significantexplanationsof the type of contractchosenby a tenant.Littleempirical evidencewas found for the alternativeexplanationrelatedto risk aversion(assumed
to be decreasingwith wealth).However,the close link betweenwealthand workingcapital
should qualify this last statement.
REVIEW OF ECONOMIC STUDIES
398
APPENDIX
The Data
V
S
FL
HL
M
CT
R'
Rl
t
,B
W'
M
L
Valueof productionon the plot. (in TunisianDinars(T.D.))
Surfaceof the plot (in hectares)
Familylabourin days (per plot)
Hiredlabourin days (per plot)
Cost of inputsotherthan labourin T.D.
Type of contractCT= 3, 2, 1, 0, for a = I; 3/4, 2/3, 1/2
Tenant'sworkingcapital(availablemonetaryliquidities,rentedvalue of variousownedequipments)
Landlord'sworkingcapital(the same)
Lengthof the relationshipin months
Percentageof cost of inputspaid by the farmer
Tenant'swealth(valueof ownedanimals,equipment,and land)
Cost of seeds,ploughing,transportation,water,otherinputs
in front of a variableindicatesthe logarithmof the variable.
TABLE I
Descriptive statistics (1986)
Variable
V
S
FL
HL
M
Rt
R'
t
I?
W'
CT
Mean
5785-0
2-1538
168-21
406-06
1404-0
5510-3
2534-3
68-565
83-229
39274-0
1-8824
Std. Dev.
Minimum
7404 7
280-0
2-4450
156-17
643-87
1761-2
5792-3
6027-6
39-314
20-324
70659-0
1-3667
Maximum
0-4914E+05
0-2000
22-00
1-000
82-00
50 00
1 000
6-000
50 00
501-0
0 0000
12-50
1160-0
3600-0
0-1149E+05
0-3500E+05
0-2950E+05
100 0
100 0
0-4050E+06
3 000
TABLE 2
Descriptive statistics (1988)
Variable
V
S
FL
HL
M
Rt
RI
t
I?
W'
CT
Mean
6913-0
2-0188
185-88
287-21
1640-7
4748-2
1455-1
78-824
87-228
41537-0
2-1985
Std. Dev.
Minimum
7988-4
2-1696
192-75
403 39
2183-4
3996*2
3437 3
33 423
19-861
85324-0
12221
600-0
0-1600
17-00
1.0
109.0
700 0
1 000
6-000
50 00
601-0
0-0000
TABLE 3
Types of contract
CT
1986
1988
2/3
3/4
1
52
13
8
97
170
26
12
7
91
136
a =1/2
Total
Maximum
0-5915E+05
14 50
1715 0
2571-0
0-1709E+05
0-2500E+05
0-1650E+05
100 0
100 0
0-4780E+06
3-000
LAFFONT & MATOUSSI
SHARECROPPING IN EL OULJA
399
AcknowledgementsWe thank the French Ministeryof Foreign Affairsfor financialsupport and the
populationof El Ouljafor its friendlyparticipation.We are gratefulto D. Newbery,J. Reid, Q. Vuong and
threerefereesfor commentsand suggestions.
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