WPC?` |4&VuI8HX.}7o}@Ō?FdlhA)smв3W`q ܶ麇*@$< ʹpUH q$2;/CPr␋ dfh T<$mh]nA-Y^c!VЉ*0bkavM;㆝' })x`i8NwRʥ'fz{*$a64$2"Agխ <*s;lЎւ(/{K 0~ 0x& 0k 0k 0t 0~ 0 0] 0A 0 0  0 01 0C7 0Vz 0 0 0C 0 0 0f 0! 0 0U4@ %t 0zz 0  0= 0F& 0Pl 1 0O 1( 0-!! 0O%E%r% 0CI((*/*S+ D+6,a, 0 O'- 0?v- A Y-d.P/vd//dIm1T2F 3P3.5W5F 6d5R6N7v7dK8;v;.<d,=|(@v@Ai4Bd*CdDdFvFdkGdMIbKK 0CL AMLCDM hNdUNNdeOvOdO*8P hbPbPbPbPbPbPRR 0UKU3VVY C[f\a\ B *\ B@\@\@\@\@\]\ 1z]1^nXA^ 04____f_a_____w@_4#`#`#`#`#`#`#`#`#`#`7`V& 8Document[8]Document Style0..8` ..` V8Document[4]Document Style.. . V 8Document[6]Document Style8..V 8Document[5]Document Style0..V/8Document[2]Document Style 2A.3  Ԁ   V& 8Document[7]Document Style0..0` ..` zU :Right Par[1]Right-Aligned Paragraph Numbers..2I.3  Ԁ..0..zh :Right Par[2]Right-Aligned Paragraph Numbers..` ..2A.3  Ԁ..0` ..` V?8Document[3]Document Style.. 21.3  Ԁ   z{ :Right Par[3]Right-Aligned Paragraph Numbers..` ..`  ..P 21.3  Ԁ` ..` 0 .. z :Right Par[4]Right-Aligned Paragraph Numbers..` ..`  .. .. 2a.3  Ԁ .. 0..z :Right Par[5]Right-Aligned Paragraph Numbers..` ..`  .. ..h..2(1)3  Ԁ..0h..hz :Right Par[6]Right-Aligned Paragraph Numbers..` ..`  .. ..h..h..2(a)3  Ԁh..h0..z :Right Par[7]Right-Aligned Paragraph Numbers..` ..`  .. ..h..h....2i)3  Ԁ..0..z :Right Par[8]Right-Aligned Paragraph Numbers..` ..`  .. ..h..h....p..2a)3  Ԁ..0p..pVX8Document[1]Document Style  @..^  2I.3  Ԁ     Ԉ l2:Technical[5]Technical Document Style.. 2(1)3  Ԁ. l2:Technical[6]Technical Document Style.. 2(a)3  Ԁ. l/%:Technical[2]Technical Document Style 2A.3  Ԁ   .. l,!:Technical[3]Technical Document Style 21.3  Ԁ   .. l(!:Technical[4]Technical Document Style 2a.3  Ԁ   .. l:0:Technical[1]Technical Document Style  2I.3  Ԁ     .. l1:Technical[7]Technical Document Style.. 2i)3  Ԁ. l1:Technical[8]Technical Document Style.. 2a)3  Ԁ. '\  `TimesRoman&R& 8BibliogrphyBibliography0....fp2Doc InitInitialize Document StyleS !    I. 1. A. a.(1)(a) i) a)S ($0 ($0 0 (($0 0 0   A_ekqwDocumentDocument StyleI.1.A.a.(1)(a)i)a)jo4Tech InitInitialize Technical StyleS #  1 .1 .1 .1 .1 .1 .1 .1 S CuyTechnicalTechnical Document Style11.11.1.11.1.1.11.1.1.1.11.1.1.1.1.11.1.1.1.1.1.11.1.1.1.1.1.1.1x?t2PleadingHeader for numbered pleading paper %  &(   X&&XX?m''*dE*??m''*dE*?\\1\\2\\3\\4\\5\\6\\7\\8\\910111213141516171819202122232425262728  .+('2$ vT!   '    0 .   ($      vT!     Ӏ  1  Lockheedetal.surveyed18studiesbasedontheanalysesof37farmhouseholddatasets.Phillips  supplementeditwith12studiesof22datasets.Theyconcludedthatonaveragefouryearsofschoolingratherthannoneresultedina6.1to7.4percentimprovementinoutput. vT!     Ӏ  2  Singh(1974),Huffman(1977)andRam(1976)hadsomediscussions. % vT!     Ӏ  3  Othermeasuresincludetheeducationofthefarmoperator,theaverageeducationofhousehold  members,theaggregateeducationoffamilymembersandtheaggregateeducationoffarmworkers. I[gamma_k(boldS)-1]{PARTIALgamma_k}over{PARTIALboldS}```<```0``,'dxd Level 1 Level 2 Level 3 Level 4 Level 5('2$ vT!   ($(    )/01.M << deUU&&{V&&{&&A{Y&&{(&&{X&&g{,&&{H&&E{,&&{Z&&{)&&U{P&&{&&[{X&&{PnnJ1X&&{, FV``=``boldY(boldX,`boldH,`boldZ`)boldP``-boldXboldP_X``, l 0#   S S '  1(  1  )    vT!     Ӏ  4  Yang(1994)analyzedtheroleofeducationinothermanagerialdecisions.Sinceempiricallyone  cannotseparateeducation'scontributiontodifferenttypesofdecisionmaking,theanalysispresentedhereissufficienttoillustratethechannelsinwhicheducationaffectsfarmefficiency.^&(*&&=gP&&g,&&gY&&kg(&&gX&&!g,&&qgH&&g,&&EgZ&&g)&&p,&&pXnn]3k&&8&&nnJk&&Pnnk&&S, J{boldPPARTIALY(boldX,`H,`Z)}over{PARTIALX_k}```=```gamma_kP_k``, < 0#   S S ' (2)  vT!     Ӏ  5  Manyexamplesmayrationalizethedivergenceofkfrom1.Forinstance,itmightduetoconsistent  overorundervaluationoftheopportunitycostofinputkbythefarmorthattheexpectedoutputorinput  pricesbecomedivergentfromtheactualprices.Amoreefficientfarmmakesfewermistakesintheseevaluations. }lnV``=``_o`+`_WS_W+`_AOS_AO`+`_MS_M`+`_AlnA`+``_LlnL`+``_KlnK`+``F, MV`=`g(S_M,S_AO)(S_W)^{_L}L^{_L}A^{_A}K^{_K}`. < 0#   S S ' (3)&&CV&&C&&CCV&&C(&&CH&&C(&&CS&&3C,&&CL&&C)&&CC,&&CZ&&C,&&SCg&&C(&&CS&&QC)&&C)&&C, DV``=``V`(boldH(boldS,`boldL`),`boldZ,`boldg(boldS)`)``, l 0#   S S '  1(  4  )  &&/dV&&#&&InnNnnYinnYnn4Y1t&*&&g,&&<gV&&p,&&-pHt&*&&g,&&^gH&& p,&&cpSnn3i&&d&&qSnni&&&&InnNnnYinnYnnY1&*&&g,&&gV&&p,&&pg9&*&&g,&&$ gg&&p,&& pSnnr 3i&& d&& Snnz i&& , dV``=``sumfrom{i=1}to{N}{,V}over{,boldH}`{,boldH}over{,S_i}`dS_i`+`sumfrom{i=1}to{N}{,V}over{,g}`{,g}over{,S_i}`dS_i``, l 0#   S S '  1(  5  )    vT!     Ӏ  6  Forinstance,thedecompositionin(5)mayaccommodatethehypothesisofSchultz(1964,1975)that  educationmayhaveahigherpayoffforfarmersinamodernizingenvironmentthaninatraditionalone.IftheSchultz'shypothesisiscorrect,thesecondtermofallocativeefficiencyismoresignificantinachangingenvironmentthanastaticone.&&H&&(&&L&&K,&&S&&)&&Q&&InnNnn3inn3nnN31&&LnnLi&&Snni&&&&L&&InnQNnn$3innF3nn31&&&1nLnn1i&&DJL&&SnnHi&&~&& L&&z Snn W&&g , rH(boldL,`boldS)`=`sumfrom{i=1}toN`L_i`S_i`=`L`sumfrom{i=1}to{N}{L_i}over{L}`S_i`=`L`S_W``, l 0#   S S '  1(  6  )    vT!     Ӏ  7  Ofcourseotherhumancapitalvariables,suchasexperience,mayalsoaffectmanagerialability.Later  econometricanalyseswillcontrolforotherrelevantvariables. _ vT!     Ӏ  8  AlternativelythesecondhighestschoolingmaybeusedforSAO.Foroursampleusedinthelater  empiricalanalysis,themajorityofhouseholdshavetwoagriculturalworkers.Asaresult,thesetwomeasuresarepracticallythesame.&&[&&Wnnk&&(&&1S&&)&&&&A1&&]&&&g,&&Sgnn*k&&C,&&oCS&&B<&&40&&,&&V&&&&Cg&&(&&Snn<M&&,&&SnnQAO&&)&&AJnnJnnH3Jnn~3nn31&&@H&&(&&L&&p,&&S&&&)nnbBL&&Znno[3JnnWJ&&+ , ZV``=``g(S_M,`S_AO)`PRODfrom{J=1}toJH(boldL,`boldS)^{_L}`Z_J^{_J}~, l 0#   S S '  1(  7  )  &&pV&&p&&pg&&wp(&&pSnn3M&&xp,&&pSnn3AO&&p)&&p(&&-pSnn3W&&p)nn.rL&&pLnn'kL&&pAnn*nA&&pKnn=K&&p.&&pln&&pV&&;p&&pnn;3o&&p&& pnnw3W&&pSnn<3W&&p&&"pnn3AO&&,pSnn3AO&&Ap&&pnn-3M&&pSnn3M&&j p&& pnnR 3A&& plnA&& p&&D pnn 3L&& plnL&& p&&pnn3K&&@plnK&&\p&&pF&&Bp, 0#   S S '  1(  8  )  ݈  Є Level 1 Level 2 Level 3 Level 4 Level 5($     Q0R.A<< c 9 db$  Ӏ  13    WhenSW,SAO,andSMareincludedintheregressionsoneatatime,theestimatedcoefficientsare  allpositive,rangingfrom.045and.056,andhighlysignificant.jj&&CennWnnSYW e^{_WS_W}&&p(&&QpSnn3W&&p)nnRL (S_W)^_L&&CennMnnSYMnnnn7AOnnSAO e^{_MS_M+_AOS_AO}zzzz?z@z@z@z@z@zzK7@z/$@zffffff@zC@zCl{@zQ@z@zHPs?zX2ı.?zb=y?z%C?zQ|a?z[ Ac?TABLE Az  vT!     Ӏ  9  Inastaticmodellandisoftenconsideredasafixedfactor.ThisisparticularlyrelevantfortheChinese  databecauseunderthecurrenthouseholdresponsibilitysystemlandisallocatedtofarmhouseholdsaccordingtothesizeoftheirpopulationand/orthesizeoftheirlaborforce.Localauthoritiesmaynotreallocatelandforatleastfifteenyearsaftertheinitialallocation(Lieberthal1985).(9!2b$ vT!   Ӏ  0   A vT!     Ӏ  10  Twovariablesneedclarification.Theflowofcapitalservices(K)isthesumoftoolreplacementvalue  plusthedepreciationofmajorcapitalequipments.Apersondayisstandardizedtoeightworkinghours. ) vT!     Ӏ  11  ByChineseconvention,apersonisintheworkforceif:(1)15age65formaleand15age60for  female,and(2)Thepersonworkedatleast30daysinthesurveyyear(1990).Thisdefinitionreflectsthefactthatteenagersusuallygraduatefromsecondaryschoolsatage15andtheageofmandatoryretirementis60forfemalesand65formales.Realizethoughthatonfamilyfarmstheseformalageconventionsarelooselyobserved.  vT!     Ӏ  12  Alternativeexperiencemeasures,includingtheaverageexperienceoffarmworkers(EXPA)andthe  highestexperience(EXPM),areallhighlycorrelatedwithEXPW.ThecorrelationcoefficientbetweenEXPW  andEXPAis.795andbetweenEXPWandEXPMis.696,eachwithhighstatisticalsignificance.Inorder h toavoidfurthermulticollinearityproblems,weonlyincludeEXPWintheempiricalfunctions.Theuseof D otherexperiencevariablesdidnotalterourconclusions. dTable_A&0 d d d  db$  Ӏ  14    AlthoughFtestscannotrejectthenullhypothesesthatthecoefficientsforSAOarestatistically  differentfromthecoefficientsofSM.  CRight ParRight-Aligned Paragraph NumbersI.A.1.a.(1)(a)i)a)3|f'\  `TimesRoman&f\  PC&P'\  `TimesRoman]\  PCP( T$   TABLE A EDDD[[ vT!   7uv&&dd7     (#RevisedforForthcomingPpublication:inAmericanJournalofAgriculturalEconomics  L@&EDUCATIONINPRODUCTION:@ MEASURINGLABORQUALITYANDMANAGEMENT(#(#X(#   L@,,*DennisTaoYang*@,January1995@ss'Revised:October1995ABSTRACT:Productionfunctionstudieshaveusedtheeducationoftheheadofthehouseholdortheaverageeducationoffarmworkerstoassessthecontributionofschoolingtofarmefficiency.Thispapercriticallyexaminestheinformationcontentofthesemeasuresbydevelopingateamproductionmodelwhichsuggestsseparateeducationmeasurestoapproximatelaborqualityandmanagerialskills.EmpiricalanalysesbasedonChinesefarmhouseholddatashowthatthenewmeasuresarestatisticallysuperiortotheexistingalternatives.Thereisevidenceofcentralizeddecisionmakingonthefarmswherethehighestschoolingcontributesthemosttoproductionefficiency.ACKNOWLEDGMENT:IwishtothankMarkAn,GaryBecker,WallaceHuffman,D.GaleJohnson,AllenKelley,RobertMarshall,MarjorieMcElroy,TomMroz,SherwinRosen,ananonymousrefereeandseminarparticipantsattheUniversityofChicagoandDukeUniversityforadviceandhelpfulcomments.Theusualdisclaimerapplies.*Address:DepartmentofEconomics,DukeUniversity,Durham,NC277080097.Phone:(919)6601821.EMAIL:yang@econ.duke.edu.̀ 8-(/L Ї I.Introduction   Thecontributionofeducationtoproductionefficiencyhasbeenexaminedinalargenumberofstudiesusingindividualfarmdata.Lockheed,JamisonandLau(1980)andPhillips(1994)presentedampleevidencethatfarmereducationhadapositiveeffectonagriculturalproductivity.* )  1      ׀However,giventhe   consensusinresults,themeasuresoffarmeducationdifferacrossstudies,anissuewhichhasreceivedmuchlessattention.+ )  2      ׀Infact,thetwocommonlyusedvariables,namelytheeducationoftheheadofthe 4   householdandtheaverageeducationoffarmworkers,domeasuredifferentelementsofthefarmeducationstock., )  3      ׀Whataspectsofhumanskillsdoeseducationintendtomeasure?Whatarethemeritsandrationale   ofalternativemeasurements?Andempirically,whichspecificationsprovidemoreexplanatorypower?Thispaperaddressesthesequestions.  SectionIIsketchesateamproductionmodelwhereeducationisallowedtoaffectthequalityofdirectlaborinputsaswellasallocativedecisionmaking.Morespecifically,theroleofeducationinphysicalefficiencyisreflectedinthequalityadjustedlaborunits.Itsroleinmanagementisspecifiedtoaffecttheoptimaluseofvariableinputs.Assumingfullutilizationoffarmresources,thismodelemphasizestheuseofthehighestschoolingtoapproximatemanagerialskillsandaweightededucationschemetoapproximatelaborquality.SectionIIIpresentsempiricalanalysisusingcrosssectiondataofsmallscaleChinesefarms.Themeritsoftheproposedandtheconventionaleducationmeasuresareevaluatedbythegoodnessoffitcriterionandvariousttests.Theresultsshowthattheproposededucationmeasureshavemoreexplanatorypowerthantheexistingalternatives.Thereisevidenceofcentralized X#$ decisionmakingonthefarmswherethehighestschoolingcontributesthemosttoproductionefficiency.BasedonempiricalresultsfromtheChineseagriculture,SectionIVconcludesthepaperbydiscussingtheroleofproductioninunderstandingthedemandforeducationinruralareas. II.TheValueofEducationinTeamProduction    Schultz(1964,1975)arguedthatschoolingmayenhancetheefficiencyofhumanagentstoperceive,tointerpretcorrectly,andtoundertakeactionthatwillappropriatelyreallocatetheirresourcesinresponsetoeconomicdisequilibria.Hehypothesizededucationmayhaveahigherpayoffforfarmersinadynamic,modernizingenvironmentthaninastatic,traditionalone.Morespecifically,educationmaycontributetoproductivitythrougha"workereffect"andan"allocativeeffect"(Welch1970).Theworkereffectreferstoeducation'seffectontechnicalefficiency,thatis,amoreeducatedworker'sabilitytoproducemoreoutputfromagivenbundleofinputs.Theallocativeeffectreferstotheskillsofobtainingandusinginformationformanagerialdecisionsincludingthepurchaseoffactorinputsandthechoiceofproductstoproduce.Empiricalstudies,includingChaudhri(1968),Huffman(1977),Fane(1975)andKhaldi(1975),haveestablishededucation'simportanceinfarmefficiency.  Ontheotherhand,previousstudieshaveimplicitlyassumedasinglepersonproductionstructureinwhichtheeducationofindividualfarmmembersisnotexplicitlydistinguished.Wheneducationalinputoftheproductionunitismeasuredbytheeducationoftheheadofthehouseholdortheaverageeducationoffarmworkers,thesamevariableisassumedtoaffectbothworkerproductivityandallocativedecisionmaking.However,toallowfordifferentialcontributionsofindividualstovariousdimensionsofeducationaloutcomes,itrequiresamultipersonproductionstructure.  Letusconsiderthevalueaddedfunction:2435QA=zx 0 @Xdddddddd@E(*xd' L(*@A (#(#  +,'. whereVdenotesthevalueaddedinfarming; Y isavectorofoutputs; X , H and Z denoteaKvectorof  purchasedinputs X =(X1,...,XK),farmlaborinputsofNworkers H =(H1,...,HN)andaJvectorofquasi h fixedfarmsuppliedinputs Z =(Z1,...,ZJ)respectively; P and PX areoutputandpurchasedinputprices.  p Bydefinition,Vequalsthetotalrevenueoffarmingminusvariablecosts.Thefarm'sshortrun  ( maximizationproblemistochooseasetofpurchasedinputs X tomaximizeV.     Thevalueaddedfunctionisusedbecauseitgivesroomforeducationtoaffectboththeworkerproductivityandthemanagerialefficiency.Ithasbeenwellrecognizedthatalternativefunctionalspecificationsmaylimittheroleofeducationasaproductiveinput.Forinstance,anengineeringproductionfunctionofasingleoutputexcludestheroleofeducationinmanagerialdecisionmaking,andaproductionfunctionofgrosssalesexcludestheroleofeducationinselectingtheappropriatemixofinputs.Incontrast,thevalueaddedproductionfunctionallowseducationtoaffectvariousaspectsoftheproductionprocess,includingtechnicalefficiencyandproductionmanagement.Thereforethisfunctionisanappropriatevehicleforinvestigatingtheeducation'sroleinproduction.  Inteamproduction,itseemsplausiblethatincreasedschoolingofworkersmayenhancetheirlaborquality,whichimpliesproducingmorewithgivenlaborhoursorachievingthesametaskwithlesslaborinputs.Thisworkerproductivityeffectmaybereflectedinequation(1)byspecifying H asefficiencylabor P units.Denotingtheithworker'slabordaysasLiandschoolingasSi,hiseffectivelaborinputHimaybe  X  expressedasHi=H(Li,Si),suchthat,Hi/,Li0and,Hi/,Si0.Noticethateducationisspecifiedhereas !" alaboraugmentingfactor,i.e.,thequalitycomponentoflabordoesnotaffecttheuseofnonlaborinputs.  Inadditiontoincreasinglaborquality,educationmayenhancefarmers'abilitytoacquire,decode,andsortmarketandtechnicalinformationmoreefficientlyformakingmanagerialdecisions.Infarming,typicalallocativedecisionsincludeselectingacombinationofcrops,purchasingamixofvariableinputs,allocatingtheinputsamongalternativeuses,decidingwhentocultivate,plant,waterandharvest,aswellasthesalesoffinalproducts.Foranalyticalconvenience,thispaperfocusesontheroleofeducationin +L'. selectingtheoptimalmixofinputs.6 )  4          Theefficiencyofinputselectionisameaningfulconceptonlyinanenvironmentofimperfectinformation.Withperfectinformation,competitivetheoryrulesoutallocativeabilityasasourceofreturntoeducation.Wheninformationoncostandproductionisincomplete,howeffectivelyafarmequatesthevaluemarginalproductofpurchasedinputstotheirpricessummariesthefarm'smanagerialability.Thisabilitymaybereflectedinthefirstorderconditionsforthefarm'soptimizationprobleminequation(1).Assumingthefarmequatesthevaluemarginalproductofeachfactortoaproportionoftherespectivefactorprice,wehave2879QA=zx 0 @Xdddddddd@EPxd' LP@; (#(#  (#(#wherek=1,...,K,k>0forallk,andPkisthepriceofthekthinput.kindexestheefficiencyofthefarm  inusingtheinput.Ifk>1,theindicationisthatthevaluemarginalproductofXk(VMPXk)exceedsthe p unitinputcost;0<k<1indicatestheopposite;andk=1correspondstotheoptimumuseofXk.The (x closerkisto1,themoreefficientthefarmusesthefactor.: )  5       0   Wheneducationenhancesworkers'abilitytodecipherinformationandrespondtodisequilibrium,  kcanbespecifiedasafunctionofthefarmeducationstock S =(S1,...,SN),satisfying L 2-J=RB>zx p @Xdddddddd@E xd' L @; (#(#  (#(#  wherek>0andkc1.Equation(3)isequivalentto-k( S )>0when0<k<1andk-( S )<0when l#$ k>1,aconditionwhichleadstotheconvergenceofkto1withincreasedfarmeducationstock.      Takingintoaccounttheroleofeducationinselecting X andsolvingforthefarmoptimization h problem,thechoicevariable X isafunctionofefficientlaborunit H ,farmsuppliedinputs Z ,farm  p educationstockg( S ),andinputandoutputprices P and PX .Substitute X *( H , Z ,g( S ), P , PX )andthe  ( efficiencylaborunits H ( S , L )intoVin(1),areducedformvalueaddedfunctionwhichomits P and PX is   givenby2?>@QA=zx 0 @Xdddddddd@ExndVl' L@ (#(#  (#(#whereVisanondecreasingfunctionin H ( S,L )andg( S ),andg-( S )0. d    Theroleofeducationinproductionsummarizedin(4)differsfromtheexistingliteratureintwoways.First,itexplicitlyallowstheeducationofallfamilymemberstoaffectthevalueaddedinfarming.Second,itspecifiestwoseparateeducationvariables:oneaffectsthequalityoflaborandtheotheraffectstheteam'smanagement.Bydifferentiatingequation(4)withrespectto S ,theproductivevalueof 8 educationisdecomposedintotwoprincipleelements:2BACQA=zx 0 @Xdddddddd@Ex d D' L@p (#(#   (#(#wherethefirsttermreferstothegainsfromaugmentingthequalityoflabor,andthesecondtermreferstothegainsfromimprovementsinallocativedecisionmaking.Thenatureofproductionandtheenvironmentinwhichthefarmoperatesmaydeterminetherelativecontributiontoefficiencyfromthesetwosources.D )  6       &,"(   Thedecompositionin(5)providesabasisfordiscussingthemeritsandrationaleofalternativeeducationmeasureswhichaffectfarmperformance.AstraightforwardmeasurementoflaborinefficiencyunitsisobtainedbymultiplyingthenumberofdaysalaboreractuallyworksonthefarmbyhisformalschoolingS.DenotingLiasworkerI'sdaysinfarmingandSihisschooling,hislaborinputinefficiency   unitscanbeexpressedasLiSi.Consequently,thequalityadjustedfarmlaborinputis:   2FEGQA=zx 0 @Xdddddddd@E< xd ' L< @J (#(#  (#(#whereListhetotalworkingdaysofallfarmworkersinagivenproductionperiod,andSWisameasure   ofworkers'educationweightedbytheproportionoftheirfarmlaborparticipation.Thisvariablerepresentsameasurethatreflectsthequalityoflaborindirectproduction.Ifeducationenhanceslaborqualityandthusfarmefficiency,then, H /,SW>0and(,V/, H )(, H /,SW)>0,aconditionwhichisreflected  inthefirsttermofequation(5).  Amongthevariousworkersonafarm,whoseeducationismostrelevantformakingallocativedecisions?Ifschoolingincreasesone'sabilitytoprocessmarketandtechnicalinformationinresponsetoeconomicdisequilibria,thehighestschoolingoffarmworkersseemstobethemostreasonableproxyformanagerialinputs.Considertheaccumulativelearningexperienceofformalschoolingwhichaddsincrementalskillsto"raw"labor.Ifqualityofschoolingisignored,workerswiththesamelevelofeducationpossessthesamesetofallocativeskillsandthosewithmoreschoolinghaveadditionalskills.H )  7      ׀ !" Thisargumentimpliesthatthehighestschoolingcanbesingledouttocontributethemosttomanagerialdecisions.Moreover,educationoffarmmembers,otherthanthemosteducatedworker,mayalsocontributetomanagement.Capturingthepotentiallydifferentroleofeducationfromallmembers,themanagerialinputfunctiongin(4)maydependonSMandSAO,i.e.g(SM,SAO),whereSMdenotesthehighest (#* schoolingandSAOdenotestheaverageschoolingofotherfamilyworkers.I )  8      ׀Ifthehighestschooling  significantlycontributestofarmefficiency,then,g/,SM>0and(,V/,g)(,g/,SM)>0.Iftheeducationof h otherfarmworkersdoesnotsignificantlyimprovefarmdecisions,then,g/,SAO=0and  p (,V/,g)(,g/,SAO)=0.Theseconditionsareembeddedinthesecondtermofequation(5).  (   Basedonthedecompositionin(5),alternativemeasuresoffamilyeducationcanbecomparedtothemeasuresoflaborqualityandmanagementskills.Existingproductionfunctionstudieshavetypicallymeasuredfarmeducationby:(a)theeducationoftheheadofthehousehold,or(b)theaverageeducationoffarmworkers.Measure(a)stressestheroleofdecisionmakingandemphasizestheinputfromtheheadofthehousehold.Tojustifytheuseofthismeasure,onehastoexplainwhythehouseholddoesnotfullyusetheaddedschoolingofthemosteducatedmember.Iffarmsseektomaximizeprofitandeducationenhancesefficiency,familiesoughttousetheideasofthemosteducatedworkers.Heretheutilizationofknowledgedoesnotconflictwiththeauthorityofthehousehold.Whilethemosteducatedmembercontributesideas,thehouseholdheadcanstillmakethefinaldecision.Measure(b)isareasonableproxyforlaborqualitybutitmayleaveoutinformationaboutmanagerialquality.Ifallocativedecisionsareimportant,thisvariablemaynotfullycapturethecontributionofeducation,especiallywhenthereissignificantvariationinworkers'schooling. III.EmpiricalMethodology,DataandFindings  !" Themeritsofthealternativeeducationmeasureswillbeevaluatedempiricallywithfarmhouseholddata.IfirstspecifyaCobbDouglasvalueaddedfunctionwhichincludesproxiesoflaborqualityandmanagerialskillsasexplanatoryvariables.Variantsofthisfunctionwillbeusedtoevaluateothereducationmeasures. & "( A.TheCobbDouglasSpecification  Consideringitscomputationaleaseandextensiveuseinpreviousstudies,theCobbDouglasformisselectedforthevalueaddedfunctionin(4).Assumingthatfarmeducationaffectsmanagementthroughamutualdisplacementparameter,thefunctioniswrittenas:2LKMQA=zx 0 @Xdddddddd@E x[d| ' L @J (#(#  (#(#where Z representsquasifixedinputs,includingland(A)andcapitalservices(K).Substituting H ( L , S ) <  in(6)andwritingoutthefarmsuppliedinputs Z explicitly,wehaveS<NJ:6z \ i/ p @@@E/" VH! ߀   AssumingtheexponentialformSWVJ:6z \ @ p @@@E)F =+߀forSYXG73z X i p @@@EVV)8m ,S[ZG73z X @ p @@@E@))x8 ߀forg(SM,SAO)andtakingnaturallogarithms P ofV,amorespecificCobbDouglasfunctionforestimationis:  2;OPQA=zx 0 @Xdddddddd@EbxPd' Lb@D  (#(#  (#(#wheretheparametersW,AOandMgivethepercentageincreasesinVinresponsetoaunitincreasein  theeducationvariables,andtheparametersA,L,andKgivetheelasticitiesofthevalueaddedwith  respecttothecorrespondingfarmsuppliedfactors.Thestochasticdisturbanceterm addedtoequation : (8)assumesthat onlyaffectstheexplainedvariablebutnottheindependentvariablesintheequation. > Weathervariations,forinstance,arepossiblesourcesofthiserror.  Intheestimationofproductionfunctions,laborandcapitalaresometimesconsideredasendogenousvariableswhichsuggestthattheOLSprocedurewillresultininconsistentestimators.b )  9      ׀  %Z $ However,Zellner,KmentaandDreze(1966)arguedthatsincefirmsweretomaximizeexpectedprofit &"& ratherthanexpostprofit,onecanuseOLStoestimatetheproductionfunction.Thelogicisthatifoneconsidersoutput,laborandcapitalasendogenousvariablesinasimultaneousequationsystem,theoptimalinputsarederivedfromthefirm'sfirstorderconditions.Solvingforthereducedformsfortheendogenousvariables,itisreasonabletoassumethattheerrortermsforcapitalandlaboraredueto"humanerrors"ofmanagerialjudgementandthatforoutputisdueto"actsofnature."Becauseoftheseassumptionscapitalandlaborareindependentoftheerrortermforproduction.HenceOLSestimationgivesconsistentestimatorsfortheparameters  and  . 8    Tochecktheadequacyoftheseassumptions,weperformatestonexogeneity(Hausman1978).Householdpopulationischosenasaninstrumentforagriculturallaborinputandthevalueofdurableconsumptiongoodsischosenasaninstrumentforproductivecapitalinput.Laborandcapitalmeasuresareregressedontheinstrumentsandallotherexogenousvariablesandthentheirpredictedvaluesareinsertedintoequation(8).UsingFtest,anOLSestimationofthisspecificationdoesnotrejectthehypothesisthatthecoefficientsofthepredictedlaborandcapitalvariablesarejointlyzero.Intheabsenceofsimultaneousequationbias,laterempiricalanalysiswilluseOLStofittheempiricalmodel.  Toevaluatethemeritsofcompetingeducationmeasures,functionalformssimilarto(8)willbeused.Iftheeducationoftheheadofthehousehold(SH)isassumedtoaffectfarmefficiency,theterm D WSW+AOSAO+MSMwillbereplacedbyHSH.Iftheaverageeducationoffarmworkers(SA)isassumed L  toaffectfarmefficiency,atermASAwillbeusedin(8).AccordinglytheparametersHandAgivethe !" percentageincreaseinVinresponsetoaunitincreaseintherelevanteducationvariables. l#$   Withalternativeeducationmeasuresimplementedtoexplainfarmefficiency,thecriteriontobeusedforselectingthebestmodelistheusualmethodofmaximummultiplecorrelation(adjustedR2)(Theil &("( 1957).TheproductionmodeldevelopedinSectionIIseparatestheroleofeducationintoitsimprovementsinlaborqualityandmanagerialskills.Thismodelcriticizedtheuseoftheeducationofthehouseholdheadortheaverageeducationtocapturethetrueunderlyingproductionrelationships.Therelativemeritsof +H'. thesealternativetheoreticaldistinctionswillnowbeassessedwithfarmhouseholddata.B.DataDescription h Thedatatobeusedforempiricalanalysisrepresentarandomsampleof102householdsineachofthetwocountiesoftheSichuanprovinceinChina.Duetomissingdata,atotalof197householdsarefeasibleforanalysis.Thesurvey,conductedbyresearchersattheChineseAcademyofSocialSciencesin1991,containsdetailedproduction,income,anddemographicinformationofhouseholdmembersforthe1990agriculturalyear(Yang1994).  SummarystatisticsonfarmproductionandlaborforcecharacteristicsarereportedinTable1.Whilethereareofffarmearnings,farmingisthedominantsourceofincome.Thevalueaddedinfarmingisequaltothegrossvalueofcropsandanimalhusbandryminusthevariablecostsofgrowingcropsandraisinganimals.Thesamplebasicallyrepresentsfamilyfarmingwherelaborhiringisminimal.Noticethatthescaleofoperationissmallforthesample:theaveragefarmlandis1.18acresandtheyearlyaveragefarmlaborsupplyis435persondays.e )  10      ׀ $   ThelowerportionofTable1reportsinformationaboutlaborforcecharacteristics.fF )  11      ׀Onaverage  eachfarmhas2.5workersandtheirageis33.Thedatarevealvariationsintheeducationalattainmentamongtheworkers.Theaverageeducationoftheheadofthehousehold(SH)andtheaveragehighest @  education(SM)arerespectively.4yearsbelowand1.3yearsabovetheaverageeducationofallfarm !" workers(SA).Theaverageeducationofworkersotherthanthehighest(SAO)isonaverage2.6yearslower `#$ thanSM.    Thesmallsizeofthefamilyfarmsposespotentialeconometricdifficultiesinusingdifferenteducationproxiestoseparatelaborqualityandmanagementskills.TheeducationmeasuresinTable1arehighlycorrelatedwithpairwisecorrelationcoefficientsrangingfrom.58to.81.Inparticular,thecorrelationcoefficientbetweenSWandSMis.693andbetweenSWandSAOis.762.Thusaspecification   whichincludesSW,SAOandSMasexplanatoryvariableswouldbeaffectedbymulticollinearity.The <   solutionadoptedhereisthecommonmethodofdroppingvariableapproach(Maddala,1977).Weshallreporttheregressionresultswhichincludeoneeducationvariableatatimeandthenreporttheresultsofincludingcombinationsofvariables.SinceSWservesasaproxyforqualityoflaborwhileSAOandSMare \  proxiesformanagerialskills,separateregressionswillprovideinformationoneducation'scontributionfromdifferentdimensions.Inaddition,theestimationincludingallthreevariablesmaysupplementtheresultsofindividualregressions.C.EstimationResults 4 TheOLSestimatesoftheproductionfunctionin(8)anditsvariantsarereportedinTable2.AllspecificationsincludethecultivatedlandlnA,familylaborlnLandcapitalequipmentlnKasindependent L variables.Theexperienceofaworkerisdefinedasageminusyearsofschoolingminusseven.AweightedexperienceEXPW,whichisthesumofworkers'experienceweightedbytheproportionoftheir !" farmlaborparticipation,isalsoincludedintheempiricalfunctionstoapproximateexperiencerelatedattributes.h )  12      ׀Eachspecification,however,includesdifferenteducationvariables.Theeducationofthehead $%t & ofthehouseholdandtheaverageeducationappearoneatatimein(1)and(2).Function(3)includestheproposedproxiesformanagerialskills(SAO,SM)andforlaborqualitySW.Specifications(4)(6)includeSM d andoneofthethreeeducationvariablesSAO,SAandSH.Forthesespecifications,Fvaluesrangefrom30.0 l to40.1whichrejectthehypothesesthatallcoefficientsotherthantheconstantsarezero.Thecoefficientsfornoneducationvariablesappeartobestableacrossthedifferentfunctions.Thecoefficientsforlandandlaborareallpositiveandhighlysignificant,indicatingthattheyarethemaincontributorstothevalueaddedinfarming.Theestimatedcoefficientforcapitalisrelativelysmall,possiblyreflectingthelimiteduseofmachineriesonthesmallfarms.ThecoefficientsforEXPWarepositiveandstatisticallysignificant   forfiveoutofsixcases.Theysuggestthat,aroundthesamplemean,aoneyearincreaseinEXPWraises \  thevalueaddedinfarmingbyabout1%,implyingthatfarmingexperiencehasfairlystrongpositivereturns.  Column1ofTable2showsthattheeducationoftheheadofthehouseholdisnotsignificantlyassociatedwiththevalueaddedinfarming.Withinthecontextofthetheoryinthispaper,thisresultisatvariancewiththeideathattheheadofthehouseholdislikelytobethedecisionmaker,and/orthathisschoolingmayaffectfarmefficiencyinanimportantway.Theresultin(2)indicatesthattheaverageschoolingSAispositivelyassociatedwithlnV.However,thiscoefficientalonemaynotleadtomeaningful L conclusionsbecausetheeducationregressorsarehighlycorrelatedinoursampleofsmallfarms.T )  13      ׀  T  Specifications(3)and(4)useseparateeducationmeasuresforlaborqualitySWandmanagement(SAO,SM). !" TheinclusionoftheseproposedmeasuresraisestheadjustedR2s(hencereducestheunexplainedvariances) p#$ byabout1percentover(2)andbymorethan2percentover(1),indicatingmoreexplanatorypowerover theconventionalalternatives.Inboth(3)and(4),theestimatedcoefficientsforSMarehighlysignificant &,"( whilethecoefficientsforSWandSAOarenotsignificant.r )  14      ׀TheseresultssuggestthatSMisthemost   importanteducationvariabletoexplainfarmprofitability.  Columns(5)and(6)inTable2presentfurtherevidencetosupporttheimportanceofSM.When l ttestsareperformedonSHandSAtoseewhethertheyexplainlnVaftercontrollingforSM,noneofthe  $ testedcoefficientsisstatisticallysignificant.Inbothspecifications,thecoefficientsforSMremainvery   significant.TheseresultssuggestthatvariationsuniquetotheregressorSMexplainvariationsinlnVwhile D   variationsuniquetoothereducationvariablesdonotpossessmuchexplanatorypower.Themagnitudeofthecoefficientsin(3)(6)suggestthat,aroundthesamplemeans,thevalueaddedinfarmingincreasesby3.9to5.8percentifoneadditionalyearofschoolingisaddedtothemosteducatedmember.  Informationontheattributesofthemosteducatedworkersmayhelptointerprettheaboveempiricalresults.Amongthe197samplehouseholdsusedfortheanalysis,themosthighlyeducatedmembersaremalesin92householdsandfemalesin58households.Fortheremaining42families,atleastonemaleandonefemalehavetheequallyhighestschoolingattainment.Theaverageageandworkexperienceofthemosteducatedworkersarerespectively32.2and17.9yearswhichareslightlylowerthanthesamplemeansof33.2and20.2.Onaverage,theyworked162daysonthefarmsin1990whilethesamplemeanwas174days,andtheysuppliedmorelabortoofffarmwageemployment(Yang1995).Fromtheseinformation,themosteducatedfarmersdoseemtorepresentacomprehensiveratherthanaspecialsubsetoftheworkforceinregardtodemographicandworkcharacteristics.Thisevidenceisconsistentwiththetheoreticalhypothesisthateducationistheunderlyingvariablewhichenhancesfarmefficiency IV.ConcludingRemarks  (#* Productionfunctionanalysesbasedonfarmhouseholddatahavebeenfrequentlyconductedtoassesstheroleofeducationinproduction.Thispaperquestionswhethertheexistingeducationmeasuresareappropriatetorepresentthefarmeducationstock.Theteamproductionmodeldevelopedheresuggeststheuseofseparateeducationvariablestorepresentthemanagerialskillsandthelaborqualityoffarmworkers.Theempiricalanalysesindicatethattheseproposedmeasuresgivebetterfittothedatathantheexistingalternatives.Anovelresultisthatthehighestfarmeducationisthemostimportanteducationvariabletoexplainefficiency.Thisresultgivessupporttothehypothesisthatthereiscentralizeddecisionmakingonthefarmswherethehouseholdsfullyutilizeallavailablehumanresources.Thisresultsuggeststhattheomissionofthehighestleveloffarmschoolingmayleadtospecificationerrorsinproductionfunctionestimatesandthereforeresultinmismeasurementofreturnstoeducation.  BasedonasamplefromsmallscaleChineseagriculture,thisstudyhasshedlightonthereturnstothecompositionofeducationalattainmentwithinthehousehold.Thisinformationonreturnsmayprovideimplicationsonthefarm'sdemandforschooling.Forinstance,theempiricalresultshaveindicatedthatthereisasignificantreturntothehighestfarmeducationbutnottotheeducationofotherhouseholdmembers.Accordingly,farmhouseholdsmaychoosetobettereducateasinglechildwiththeavailablefinancialresourcesratherthanprovideequaleducationtoallchildren.Forthesameproductionorientedconsiderations,farmhouseholdsmaychoosetobettereducatetheirboysbecausetheyaremorelikelytostayandcontributetothefarm.Thespecialfeaturesoffarmproductiondeterminethereturnstoeducationofitsmembers,which,inturn,determinehowthehouseholdsdemandforeducationinvestment.  (*x%, S&&@OOTABLE1.SUMMARYSTATISTICS:HOUSEHOLDMEANSANDSTANDARDDEVIATIONS  *qjk ddd Xdd Xdd X(#(#q,<d ,td ,td ,t +  1ll" @ 1@E E f Variable 0lm!xll 0@~~5~Symbol 0lm!lm 0@CMean 4lml! lm 4@ffM Standard@GGM Deviation Fmll5!x   lml F̀GROSSHOUSEHOLDINCOME(Yuan)̀AgriculturèWageEarnings̀VALUEADDEDINFARMING(Yuan)̀GrossValueofCropOutput̀GrossValueofAnimalHusbandrỳVariableCostofCropProductioǹHiredLabor̀Seeds̀Fertilizers̀Pesticides̀ManurèRentalandFees̀VariableCostofAnimalHusbandrỳFARMSUPPLIEDINPUTS̀CultivatedLand(Acre)̀FlowofAgriculturalCapital(Yuan)̀LaborDaysinFarming(Day)̀LABORFORCECHARACTERISTICS̀NumberofWorkers̀AgèEducationofHouseholdHead p * ЀEducationofWorkers 8!+ ЀWeightedEducation "P, ЀHighestEducation "- ЀEducationofWorkersExcepttheHighest̀NUMBEROFHOUSEHOLDS 2mml!%8!1mll 2@BB8~V@HH8~Z@BB8~A@DD8~K@JJ8~L@7~AGE@,,7~SH p O @--7~SA 8!P @""7~SW "PQ @$$7~SM "R @  7~SAO 2mml!#Smml 2@B2836.2@B2709.5@C568.5@wwA1795.5@B1882.6@C826.9@C412.5@$$D3.0@C67.4@C146.0@C32.0@C125.8@C26.4@C501.5̀@C1.18@C148.6@C435.2̀@$$D2.5@C33.2@C5.6 p q @C6.0 8!r @C5.8 "Ps @C7.3 "t @C4.7 #u @D197̀ 4mmll!%8!xmml 4@N 1615.8@N 1606.8@O 762.1̀@N 1265.4@N 1067.5@O 767.6@O 232.4@O 14.3̀@O 46.8 `  Ѐ@O 105.4 (x @O 47.2@O 99.0@O 51.0@O 376.2̀@ P .69@O 110.4@N 251.3@ P 1.2@O 12.4@  O 3.0 p  @  O 2.8 8! @  O 2.2 "P @  O 4.6 " @  O 2.7 # 1'% %p  0   mmll 1 X,' @Table2.OLSESTIMATESOFPRODUCTIONFUNCTIONS:THEROLEOFEDUCATION*zm{dd<d td td t jk(#(#,Zdd ,Zdd ,Zdd ,Zdd ,Zdd ,Zdd ,Zdd +   @    @+DependentVariable:lnV@@7  4 @ Variable 4*    ?1?4@  7 1 SI(   ?1 ?  @2@S@hh'2 SI(    @2 @  @3@S  3 \R1     @3 @  @4@\ѝ@<E4 SI(    @4 @  @5@S@vvG5 SI(    @5 @  @6@S@ R 6 4*(    @6 @ 4@ Intercept   @RRlnA  \  ̀@ZZlnL d  @TTlnK   @SH d @SA l @SW ! @hhSAO l$ @@SM t' @EXPW  *   !+   4.689**  - (.405).491**  \ 0 (.079).226** d 3 (.072).036**  6 (.018).016(.014).............005(.005)  \"J   4.271**  L (.435).510**  \ O (.078).226** d R (.071).041**  U (.018)....055** l[ (.021)..........010**  g (.005) !h    4.600**  j (.475).520**  \ m (.078).164** d p (.074).036**  s (.018)......̄.016(.038).032(.023).044** t (.023).010*   (.006) !    4.481**   (.387).521**  \  (.078).172** d  (.072).037**   (.018)..........026(.019).039** t (.020).012**   (.005) !  =  4.371**   (.446).511**  \  (.078).193** d  (.072).037**   (.018)....006(.034).......051* t (.027).010**   (.005) !    4.505**   (.402).507**  \  (.077).187** d  (.072).036**   (.018)̄.005(.015)..........058** t (.019).009*   (.005) !  ڧ@Adj.R2 $ Ѐ 8. H%  HPs?.4914HPs?8@w w 7 .4914 [Q,$ HPs?.4914 HPs? X2ı.?.5057X2ı.?[  .5057 dZ5$  X2ı.?.5057 X2ı.? b=y?.5148b=y?d   .5148 dZ5$  b=y?.5148 b=y? %C?.5170%C?d  .5170 [Q,H%  %C?.5170 %C? Q|a?.5119Q|a?[  .5119 dZ5$  Q|a?.5119 Q|a? [ Ac?.5122[ Ac?d  .5122E;9$  [ Ac?.5122  [ Ac? ENote:Thefiguresinparenthesesarethestandarderrorsofestimatedcoefficients.*and**denotestatisticalsignificanceatthe5and1percentagelevel. (*x% TRY3'3' 3' Letter3'T  @-REFERENCES  Chaudhri,D.P.(1968):"EducationandAgriculturalProductivityinIndia,"Ph.D.dissertation,UniversityofDelhi.Fane,George(1975):"EducationandthemanagerialEfficiencyofFarmers,"ReviewofEconomicsand     Statistics,57:45261.  Hausman,J.A.(1978):"SpecificationTestsinEconometrics,"Econometrica,46(6):12511271. ( x ЀHuffman,Wallace(1977):"AllocativeEfficiency:TheRoleofHumanCapital,"QuarterlyJournalofEconomics,      91:5977.Khaldi,Nabil(1975):"EducationandAllocativeEfficiencyinU.S.Agriculture,"AmericanJournalofAgricultural `    Economics,57:65057. (  Lau,LawrenceJ.(1978):"ApplicationsofProfitFunctions",In:M.FussandD.McFaddeneds.Production h    Economics:DualApproachtoTheoryandApplication.NewYork:NorthHolland. 0  Lieberthal,Kenneth(1985):"ThePoliticalImplicationsofDocumentNo.1,1984,"TheChinaQuarterly,    No.104:583613.Lockheed,M.E.,D.JamisonandL.Lau(1980):"FarmerEducationandFarmEfficiency",EconomicDevelopment h   andCulturalChange,29:3776. 0 ЀMaddala,G.S.(1977):Econometrics,NewYork:McGrawHillPublishingCompany. p Phillips,JosephM.(1994):"FarmerEducationandFarmerEfficiency:AMetaAnalysis",EconomicDevelopment P   andCulturalChange,42:149165.  Ram,Rati(1976):"EducationasAQuasifactorofProduction:TheCaseofIndia'sAgriculture,"Ph.D.  dissertation,UniversityofChicago.Singh,Baldev(1974):"ImpactofEducationonFarmProduction,"EconomicandPoliticalWeekly(Sept.):A92A96.   Schultz,TheodoreW.(1964):TransformingTraditionalAgriculture,NewHaven:YaleUniversityPress. @" ______(1975):"TheValueofAbilitytoDealwithDisequilibria",JournalofEconomicLiterature,13:  $   82746.Welch,Finis(1970):"EducationinProduction",JournalofPoliticalEconomy,38:3559. (#x' Yang,DennisT.(1994):KnowledgeSpilloversandtheLaborAssignmentsoftheFarmHousehold,Ph.D. $ )   dissertation,TheUniversityofChicago.______: EducationandOffFarmWork,EconomicDevelopmentandCulturalChange,forthcoming. '`", Zellner,A.,J.KmentaandJ.Dreze(1966):"SpecificationandEstimationofCobbDouglasProduction  FunctionModels,"Econometrica,34(4):784795. h)$/