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1Agriculture:Theefficiencyoflanduse•Shareofagricultureinemploymentiscloseto50%fortheworldasawhole(50%inChina,57%inIndia).•Islandusedefficiently?1.0.1Farmsizeandproductivity:observedrela-tionship•Farmsizeproductivitydifferences:seetable.•Profit-Wealthrationandweathervariability(mon-soonoutsetisameasureoftheriskfacedbythefarmer):seefigure—TheProfit-Wealthratioisalwaysgreaterforsmallfarmers—Smallfarmers’profitsarehurtmuchmorebyuncertaintythanlargefarmers’1.0.2Whyisthissurprising?•Argumentsforincreasingreturns(theoppositere-lationship)—Technologywithfixedcosts(tractors,etc..)—Largerfarmershavebetteraccesstocapital—Largerfarmershavebetteraccesstopoliti-callyallocatedinputs(evidencefromAfricainabookbyBates“MarketandstatesintropicalAfrica”).—Thebestfarmerwillhavemoreland...•Mitigatingfactors:—Rentalmarketsinfarmmachinery—Technologicalchangeinnotveryrapid.Savi-nessnotthatimportant.1.0.3Whatcouldbegoingon:Argumentsforde-creasingreturns•—Agencyproblems:largefarmsarecultivatedbyhiredlabor,whichhasfewerincentivetoworkhard.Smallfarmsareownercultivated.⇒Redistributinglandwillcreatemoreownercultivatedlandwhichwillbemoreproductive.—Butwhycannottheownerofthelandnotgivetherightincentivetothefarmers?1.0.4Differentpotentialexplanationsfortheob-servedinverseproductivityrelationship:•Differencesinlandquality•Differencesinfarmercharacteristics•IncentiveProblemsProblemwiththeobservedrelationship:allofthiscouldbegoingon...Howcanweseparatethesedif-ferenteffects.1.0.5Evidence:StudybyBiswangerandRosen-zweig•UsingICRISATdata:verydetailedpanel(repeatedobservationforeveryhousehold)datafromIndia.•Someindividualscultivatebothanowner-operatedplotandarentedplot.•BiswangerandRosenzweigcomparetheinputstheyapplyontheirownplotandtherentedplots,andtheoverallproductivityofbothplots.Πij=α+βRij+ηi+υij,•whereΠijisfarmer’sioutcome(profit,invest-ment)onplotj,andRijindicatewhethertheplotisrented.ηiistheunoberved(butfixed)characteristicsofthefarmers(riskaversion,qual-ity,etc...).WethinkthatηiandRijmaybecorrelated,but,foraminute,notυijandRij.Whatcanwedo?•Controlfortheindividualfixedeffecttocompareplotswithinindividual’s.Soforexample,forallthefarmersthatcultivatetwoplotsofland,wecanruntheregression:Πi2−Πi1=β(Ri2−Ri1)+υi2−υi1,•Theindividualfixedeffectisgone!BiswangerandRosenzweigfindastrongnegativeβ.Whatdoesthissuggest?Whatcouldbetheremainingproblem?1.0.6Moreevidence:Shaban(1987)•Usesthesamedata,butcontrolsinadditionforplotquality.•Hefindsthatindividualwork40%moreontheirownland(controllingforlandsize)andthattheproductivityis15%to30%higheronownlandthanonrentedland(withorwithoutcontrolingforlandquality).•Onbalance,theevidencesuggeststhattheinef-ficiencycomesfromincentiveproblems.AMODELOFSHARE-CROPPINGAMODELOFSHARE-CROPPING2AMODELOFSHARE-CROPPING1.Supposethereisalandlordwhoownsaplotoflandwhichhehimselfcannotcrop.Ineachperiodheemploysexactlyonetenanttocroptheland.Thetenant’soutsideoptionism.AMODELOFSHARE-CROPPING2-AAMODELOFSHARE-CROPPING1.Supposethereisalandlordwhoownsaplotoflandwhichhehimselfcannotcrop.Ineachperiodheemploysexactlyonetenanttocroptheland.Thetenant’soutsideoptionism.2.Supposeineachperiodoutputcantakeontwovalues,YH=1(‘high’or‘success’)andYL=0(‘low’or‘failure’)withprobabilityeand1−erespectively.Thetenantchoosese,(‘effort’),whichcostshimce22.Therealizationsofoutputareindependentovertime.AMODELOFSHARE-CROPPING2-BAMODELOFSHARE-CROPPING1.Supposethereisalandlordwhoownsaplotoflandwhichhehimselfcannotcrop.Ineachperiodheemploysexactlyonetenanttocroptheland.Thetenant’soutsideoptionism.2.Supposeineachperiodoutputcantakeontwovalues,YH=1(‘high’or‘success’)andYL=0(‘low’or‘failure’)withprobabilityeand1−erespectively.Thetenantchoosese,(‘effort’),whichcostshimce22.Therealizationsofoutputareindependentovertime.3.Firstbestmaximizes:e−ce2/2→e=1/cAMODELOFSHARE-CROPPING2-CThekeyassumptionsofthismodelare:AMODELOFSHARE-CROPPING3Thekeyassumptionsofthismodelare:➜Thetenanthasnowealthandcannotsave.Hedoeshoweverhaveanoutsideincomeofw,sothattheleasthecangetpaidinanyperiodis−w.Inotherwords,thelandlordfacesalimitedliabilityconstraint.AMODELOFSHARE-CROPPING3-AThekeyassumptionsofthismodelare:➜Thetenanthasnowealthandcannotsave.Hedoeshoweverhaveanoutsideincomeofw,sothattheleasthecangetpaidinanyperiodis−w.Inotherwords,thelandlordfacesalimitedliabilityconstraint.➜Thetenant’seffortchoiceeisnon-contractible.AMODELOFSHARE-CROPPING3-BThekeyassumptionsofthismodelare:➜Thetenanthasnowealthandcannotsave.Hedoeshoweverhaveanoutsideincomeofw,sothattheleasthecangetpaidinanyperiodis−w.Inotherwords,thelandlordfacesalimitedliabilityconstraint.➜Thetenant’seffortchoiceeisnon-contractible.➜Atfirstassumethatthecontractisone-periodcontract:(h,l).AMODELOFSHARE-CROPPING3-CThekeyassumptionsofthismodelare:➜Thetenanthasnowealthandcannotsave.Hedoeshoweverhaveanoutsideincomeofw,sothattheleasthecangetpaidinanyperiodis−w.Inotherwords,thelandlordfacesalimitedliabilityconstraint.➜Thetenant’seffortchoiceeisnon-contractible.➜Atfirstassumethatthecontractisone-periodcontract:(h,l).➜Whatarepossiblecontracts?AMODELOFSHARE-CROPPING3-DANALYSISOFTH