WPCj \X@_/b(<G|ya)'yܐNϱ|q{@J`2۟申ԃqs)_j_Aa%뫡Qi WE=2e '%PLZI.3FKX ȥF@'B7WCJu  tpqtIOm? jG"Bk:{í$L zyRM ֙?*:yNx…(R sfnC,"[HۊYĄk6`q̴*9 y>!,TRF9 Бjba2cRn GR']Zj&J|o੼a֝9*L꠸א s{m2_C2g 7 ;$g\pMʑqw:#`eFSK@:m Gi"ۛP 0}& 0x 0j 0j 0 0} 0 0 0 0] 0 S 0\ 00y 0B 0U 0@ 0 0 0V 0 0 0 0e 0U0 % 0y 0Z J 0=[ 0F 0P 1. 0 1 0!Z" 0O%EF& 0DH&& 0y(Q(RL*+,J/ D+01 0O1 0 ?$2 A Yc2d2hC4F4d4~7F08dv8'?F8@~@BqB GId4JT-LyLd<Ls6OyO"PdMSq Vdn{VXvoYd}Y;b[v[\ 0C\ AM]di]cw__dU_deL``d`>add&bdve$edfiSjd`jT?lGll9~m$oqr&Su yvvd8w{|~ Cfa BH* Bf7a9fMaOfcaey 04dr/ 0P AOE 0DZ D/ B̓d<dPdn hXw@+4k hc h hœV& 8Document[8]Document Style0..8` ..` V8Document[4]Document Style.. . V 8Document[6]Document Style8..V 8Document[5]Document Style0..V/8Document[2]Document Style 2A.3  Ԁ   V& 8Document[7]Document Style0..0` ..` zU :Right Par[1]Right-Aligned Paragraph Numbers..2I.3  Ԁ..0..zh :Right Par[2]Right-Aligned Paragraph Numbers..` ..2A.3  Ԁ..0` ..` V? 8Document[3]Document Style.. 21.3  Ԁ   z{ :Right Par[3]Right-Aligned Paragraph Numbers..` ..`  ..P 21.3  Ԁ` ..` 0 .. z :Right Par[4]Right-Aligned Paragraph Numbers..` ..`  .. .. 2a.3  Ԁ .. 0..z :Right Par[5]Right-Aligned Paragraph Numbers..` ..`  .. ..h..2(1)3  Ԁ..0h..hz :Right Par[6]Right-Aligned Paragraph Numbers..` ..`  .. ..h..h..2(a)3  Ԁh..h0..z :Right Par[7]Right-Aligned Paragraph Numbers..` ..`  .. ..h..h....2i)3  Ԁ..0..z :Right Par[8]Right-Aligned Paragraph Numbers..` ..`  .. ..h..h....p..2a)3  Ԁ..0p..pVX8Document[1]Document Style  @..^  2I.3  Ԁ     Ԉ l2:Technical[5]Technical Document Style.. 2(1)3  Ԁ. l2:Technical[6]Technical Document Style.. 2(a)3  Ԁ. l/$: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:/: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. ) `CG Times&R& 8BibliogrphyBibliography0` ..` ..fp2Doc InitInitialize Document Style  S !    I. 1. A. a.(1)(a) i) a)S ($0 ($0 0 (($0 0 0   A_ekqwDocumentDocument StyleI.1.A.a.(1)(a)i)a)jo4Tech InitInitialize Technical StyleS #  1 .1 .1 .1 .1 .1 .1 .1 SCuyTechnicalTechnical Document Style11.11.1.11.1.1.11.1.1.1.11.1.1.1.1.11.1.1.1.1.1.11.1.1.1.1.1.1.1x?t2PleadingHeader for numbered pleading paper %  &(  XX6w''*d66w''*d6dl&1dl&2dl&3dl&4dl&5dl&6dl&7dl&8dl&9&10&11&12&13&14&15&16&17&18&19&20&21&22&23&24&25&26&27&28  .+('28W$ U!   (#$  0    *g$  Ӏ  1    Kimhi(1989)reportedthatroughlyonethirdoffarmersindevelopedeconomieswereengagedinoff  farmemployment.Indevelopingcountries,approximatelyaquarteroftherurallaborforcewereengagedinnonagriculturalproduction(AndersonandLeiserson1980).Thenonfarmsectorisanimportantsourceoflabordemandandasignificantcontributoroffarmearnings.(9!2g$ U!   Ӏ  0   G *g$  Ӏ  2    Thispaperprimarilyconcernsparttimefarmingwherehouseholdmembersresideintheirruralhomes.  Seasonalandpermanentoutmigrationfromruralareasisarelatedtopicwhichisnotsystematicallystudiedhere. H *g$  Ӏ  3    Therehavebeenindirectanalyses.PapersbyHuffman(1976)and(1980)canbeviewedtogetherto  seehowwageratesforofffarmworkandvalueofmarginalproductoffarmlaborforfarmoperators(andwives)compare. *g$  Ӏ  4    ModelsalongthislineincludeHuffman(1980),Rosenzweig(1980),Singhetal.(1986)andHuffman  andLange(1989).  *g$  Ӏ  5    Thesestandardtheoreticalconditionsare,byandlarge,consistentwiththeChineseempiricalsetting.  Whenthedatawerecollectedin1990,individualhouseholdswereresponsiblefortheirownproductionandconsumptiondecisions.Exceptthathouseholdshadtofulfillasmallquotaatprocurementprices,whichwasineffectafixedagriculturaltax,farmsoperatedinrathercompetitiveinputandoutputmarkets.Thiswasaresultofeconomicreformswhichstartedin1978.Therestillwasnotalandmarket,anaspectwhichwillbeelaboratedinthelaterempiricalanalysis.  *g$  Ӏ  6    Thisrelatedsubjectrequiresaratherdifferenttheoreticalframework,whichliesbeyondthescopeof  thecurrentpaper.Inaddition,thedatatobeuseddonotcontainanyinformationonmigrants'employmentandincomes,althoughthereisrichinformationonthosewholiveruralhomes.'dxd Level 1 Level 2 Level 3 Level 4 Level 5('28W$ U!   ($(    )1230M << deUU &&{V&&{&&i{Pnn1A&&({Y&&{(&&{X&&D{,&&{Z&&{,&&|{Tnn1f&&{,&&{S&&{,&&I{E&&{;&&'{M&&{)&&{&&{Pnn 1X&&Z {X&& {. ^V```=```P_AY(boldX,``boldZ,``boldT_f,``boldS,``boldE;``varphi)``-``boldP_XboldX``. < 28W#   o(1) &&pWnn3i&&p&&pW&&Rp(&&pSnn3i&&%p,&&apEnn3i&& p,&&\p2&&p)&&@p,&&pwhere&&-pSnn3i&&p&& p0&&z p,&& pEnn{ 3i&& p>&&S p0&& p,&&; p,&& pW&&+ p/&&g p,&& pEnn43i&&Vp>&& p0&&pand&&p,&&tpW&& p/&&Hp,&&pSnn3i&&#p>&&p0&&5p. tW_i```=```W(S_i`,E_i`,`OMEGA``),~~where~S_i>=0,~E_i>0,~PARTIALW/PARTIALE_i>0~\and~PARTIALW/PARTIALS_i>0. < 28W#   o(2) &&(&&Qa&&)&&9If&&W&&(&&Snn,i&&N)&&&& W&&(&&SnnUj&&w)&&>&&VMP&&1(&&mSnni&&)&&@ && VMP&&: (&&v Snn j&& )&&5 ,&& i&& first&&works&& for&&.wages&&;&&82(&&t2b&&2)&&\2If&&2W&&2(&&2SnnOi&&q2)&&2&&C2W&&2(&&2Snnxj&&2)&&2&&2VMP&& 2(&&H2Snni&&2)&& 2&& 2VMP&& 2(&&Q 2Snn j&& 2)&& 2,&& 2i&&o 2or&&a2j&&2works&&2for&& 2wages&&2;&&o(&&Voc&&o)&&4oIf&&oW&&o(&&oSnn'2i&&Io)&&o&&oW&&o(&&oSnnP2j&&ro)&&o<&&oVMP&&,o(&&hoSnn2i&&o)&&; o&& oVMP&&5 o(&&q oSnn 2j&& o)&&0 o,&& oj&& ofirst&&oworks&&ofor&&)owages&&o. linespace200stack{(a)~If~W(S_i)`-`W(S_j)``>``VMP(S_i)`-`VMP(S_j),~~i~first~works~for~wages;#(b)~If~W(S_i)`-`W(S_j)``=``VMP(S_i)`-`VMP(S_j),~~i~\or~j~works~for~wages;#(c)~If~W(S_i)`-`W(S_j)``<``VMP(S_i)`-`VMP(S_j),~~j~first~works~for~wages.} < 28W#   o(3)  *g$  Ӏ  7    Theseresultsarebasedontheassumptionthatfactorsofcompensatingdifferentials,suchaswork  environment,commutingandnonpecuniarybenefits,donotsignificantlyaffecttimeallocation.Iftheassumptiondoesnothold,thetheoreticalimplicationsshouldbeadjustedaccordingly. y *g$  Ӏ  8    SeeWillis(1986)forasurvey. g *g$  Ӏ  9    Inthesummerof1990IvisitedafamilyfarminthesuburbofBeijing.Thefarmconsistedofthree  adultmembers:awomenoperatorandherson,whotookcareofthefarm,andherhusbandwhoworkedfulltimeinalocalrailwaystation.Thehouseholdresponsibilitysystemhadbeenadoptedinthevillagesothatthehouseholdhadfreedominchoosingacombinationofcrops.Theyearbeforeourvisit,afewvillagefolksstartedplantingwaxgourdandobtainedhandsomeprofits.Inthefollowingsummermorepeoplestartedgrowingthevegetable.Thefamilyalsoconsidereditbutfinallydecidednottodoso.Iaskedthewomenoperator:"Whodecidewhethertoplantitonthefarm?"Shereplied:"Wetalkedaboutitathome...myhusbandwasverycautious.Hewantedtoseewhethertheotherswillstillmakemoneythisyear."Ididnotaskwhoseeducationwashigher.Butthenotionthatapersonwhoworksofffarmmaystillcontributehissuggestionstofarmactivitiesisexemplifiedbyherstory.  *g$  Ӏ  10    Table3describesthefrequencydistributionoffarmersaccordingtotheirfarmandofffarmlabor  supply.Onlyabout3percentofthefarmersworkentirelyofffarmwhiletheotherstakecombinationsofworkandliveintheirruralhomes.Thesetimearrangementsallowmanywaysofexchangingideas.Forinstance,constructivediscussionsmaytakeplaceatworkoracrossdinnertablesonadailybasis.  *g$  Ӏ  11    Onemayalsousedaysofofffarmemploymenttoindicatetheabsenceofthemosteducatedmember  workingonthefarm.Empiricallytheyofferthesameresults. &&pV&&p&&CpV&&p(&&pZ&&_p,&&pH&&3p(&&opTnn3f&&p,&&^pS&&p)&&p,&&PpM&&p(&&$pSnn3M&&p,&&%pSnn3AO&&&p,&&bpOPnnV 3SM&& p)&&2 p,&& pE&& p;&&B pM&& p)&& p. JV``=``V(boldZ,`H(boldT_f,`boldS),`M(S_M,S_AO,OP_{SM}),`E;`M)``. o 28W#   o 3(  4  )   &&V&&&&Cg&&(&&M&&s(&&SnnM&&t,&&Snn%AO&&,&&OPnn SM&&)&&)&&5JnnJnnF3jnnh3nn31&&4H&&(&&Tnni f&& ,&& S&&I )nn B T&& Znn [ 3jnnz j&&@ , iV``=``g(M(S_M,`S_AO,`OP_{SM}))`PRODfrom{j=1}toJH(boldT_f,`boldS)̀^{_T}`Z_j^{_j}~, o 28W#   o 3(  5  )    *g$  Ӏ  12    Amoregeneraltranslogfunctionintheformof  4KJVFBz Xx 0 @Xdddddddd@ExdJ6L&@    where Z includesland,capitalandlabor,istestedinreferencetotheCobbDouglasform.AFtestis  carriedouttoexaminethenullhypothesisthatallii=0andallij=0,wheretherejectionofthenullfavors d thetranslogspecification.Usingthesampledata,thecomputedF(6,188)equals.82,whilethecriticalFvalue @  atthefivepercentsignificancelevelis2.10.ThisresultdoesnotrejecttheCobbDouglastypeastheappropriatefunctionform. &&plnV&&p&&pnn3o&&;p&&<I&&pnn53i&&WplnZnnP3i&&p&&<I&&pnnh3ii&&p(&&plnZnn3i&& p)nn? 2&& p&& <I&& pnns 3ij&& p(&& plnZnn 3i&& p)&&J p(&& plnZnn3j&&p)&&p&&spFnn3i&&p, glnV=_o`+`sum`_ilnZ_i`+`sum_ii(lnZ_i)^{2}`+`sum_ij(lnZ_i)(lnZ_j)`+`F_i`, &&H&&(&&TnnPf&&z,&&S&&0)&&&&Inn>NnnYinn3Ynn}Y1&&Tnn{fi&&Snn4i&&j&&TnnWf&&InnNnnYinnYnnY1L&*&&TnnWfi&&pTnn%3f&&Snni&& && Tnn f&&; Snn W&&( , |H(boldT_f,`boldS)`=`sumfrom{i=1}toN`T_fi`S_i`=`T_f`sumfrom{i=1}to{N}{T_fi}over{T_f}`S_i`=`T_f`S_W``, l 28W#   o 3(  6  )   &&pM&&p(&&pSnnJ3M&&p,&&pSnn_3AO&&p,&&OpOPnnH3SM&&p)&&Lp&&pSnnC3AO&&p&&ypSnn3M&&Rp&&pSnn5 3M&& pOPnn 3SM&&n p, 1M(S_M,`S_AO,`OP_SM)``=``S_AO`+`S_M`+`S_M`OP_SM``, l 28W#   o 3(  7  )  ݄ Level 1 Level 2 Level 3 Level 4 Level 5($     R2S0A<< c &&pV&&p&&pg&&wp(&&pSnn3AO&&p&&"pSnn3M&&p&&UpSnn3M&&.pOPnn'3SM&&p)&&p(&&?pSnn3W&&p)nn@T&&pTnn9 } Tnn! @f&& pAnn<  A&& pKnnO  K&& p. YV`=`g(S_AO+S_M+S_M`OP_SM)(S_W)^{_T}T_f^{_T}A^{_A}K^{_K}`. e^{_WS_W} &&CennWnnSYW &&p(&&QpSnn3W&&p)nnRT (S_W)^_T &&CennAOnnFSAOnnnnKMnnS MnnlnnOPnnxSMnnOPSM 4e^{_AOS_AO+_MS_M+_OPS_MOP_SM} &&pV&&p&&Cpenn(nn"WnnnSWnnnn_AOnn!SbAOnnnn@MnnSMnnnnn OPnnSMnnOPSMnn@ )&&| pTnn C Tnn @f&& pAnn Z A&& pKnn=  K&& p. V``=``e^{(_WS_W`+`_AOS_AO`+`_MS_M`+`_OPS_MOP_SM`)}̀`T_f^{_T}`A^{_A}`K^{_K}~. l 28W#   o 3(  8  )    *g$  Ӏ  13    SeesurveysbyLockheed,JamisonandLau(1980)andPhillips(1994)whichreported30production  functionstudiesbasedontheanalysesof59farmhouseholddatasets. &&pln&&pV&&;p&&pnn;3o&&p&& pnnw3W&&pSnn<3W&&p&&pnnx3AO&&pSnny3AO&&p&&pnn3M&&}pSnn3M&&V p&& pnn. 3OP&& pSnn/ 3M&& pOPnn 3SM&&@ p&& pnn(3A&&rplnA&&p&&pnn3T&&plnTnn3f&&p&&pnn3K&&=plnK&&Yp&&pF&&?p, lnV``=``_o`+`_WS_W+_AOS_AO+``_MS_M`+_OPS_M  OP_SM`+`_AlnA`+  ``_TlnT_f`+``_KlnK`+``F, 28W#   o 3(  9  )  ݈   &&plnW&&wp&&!pnn3o&&p&&Ypnn3S&&pS&&p&&pnng31&&pE&&)p&&pnn32&&OpEnn2&&.p&&pFnn 3w&&x p, JlnW```=```_o`+`_S`S`+`_1E`+`_2E^2`+`F_w``, = 28W#   ??o(10) *g$  Ӏ  14    Yang(1994)hasdescribedthedatasetandvariablesindetail. / *g$  Ӏ  15    ByChineseconvention,apersonisintheworkforceif:(1)15age65formaleand15age60for  female,and(2)Thepersonworkedatleast30daysinthesurveyyear(1990).Thisdefinitionreflectsthefactthatteenagersusuallygraduatefromsecondaryschoolsatage15andtheageofmandatoryretirementis60forfemalesand65formales.Realizethoughthatonfamilyfarmstheseformalageconventionsarelooselyobserved.  *g$  Ӏ  16    TheadjustedR2soffittingequation(9)anditsvariantsreportedinTable(4)areabout.54,whichis  smallerthantheaboveintervariablecorrelations,indicatingtheconcernofmulticollinearity(Greene1993).Itshouldbenotedthatothervariablesalsohavehighintervariablecorrelations.Forinstance,thecorrelationoflnAandlnTisabout.69andbetweenlnVandlnAis.71. *g$  Ӏ  17    TheR2oftheOLSregressionis.67andthenumberofworkersishighlycorrelatedwithTf.  *g$  Ӏ  18    Previousproductionfunctionstudieshaveusedothereducationmeasures,includingtheeducationof  theheadofthehousehold,theaverageeducationofthefamilymembers,ortheaverageeducationoffarmworkers,toassessthecontributionofschoolingtofarmefficiency.Yang(1995a)evaluatedthestatisticalmeritofalternativemeasuresandconcludedthatspecifyingtheroleofeducationintoitsimprovementsinlaborqualityandmanagementcapturesthemostinformationthateducationcarries.Thispaperutilizesandbuildsonthisresult.  *g$  Ӏ  19    OnemayalsoaddquadratictermstobothEWandEM.Noneofthesealternativespecifications  significantlyaffecttheestimatesofothervariables.   *g$  Ӏ  20    SeeYang(1995a)formorestatisticalanalyseswhichconcludedthatthehighestschoolingwasthe  mostimportanthumancapitalvariabletoexplainfarmefficiency. &&;lnW&&;;&&;1&&;.&&U;248&&;&&';.&&c;408&&w;DnnT&&j;&&;.&&<;298&&P;DnnG&&C ;&& ;.&& ;023&& ;S&& ;&& ;.&&W ;025&& ;E&&;&&;.&&;0004&&;Enn"2&&`;,&&=;Adjusted&& ;Rnn2&&;&&F;.&&;319&&;,&&";Sample&&>;&&;131&&;,&&mC(&&C.&&C150&&C)&&&C(&&bC.&&C067&&C)&&C(&&C.&&WC091&&kC)&& C(&& C.&& C013&&$ C)&& C(&&= C.&&y C010&& C)&&jC(&&C.&&C0002&&RC) linespace100stackalign{lnW=&`1.248````.408D_T``-``.298D_G`+`.023S`+``  .025`E``-```.0004``E^2,~~Adjusted~R^2=.319,~Sample=131,#(&.150)~~~(.067)~~~(.091)~~~(.013)~~(.010)~~(.0002)}  *g$  Ӏ  21    Sincedataonaworker'sactualfarmingexperiencewasnotreported,atransformation,E=AgeS7,  isusedasaproxy.7reflectsthepopularageofstartingelementaryschoolinChina.Moreover,thedatadidnotdirectlyprovidewageratesfornonfarmworkers.However,individualannualnonfarmworkingdaysandincomewerereported.Iuseincomedividedbyworkingdaysasaperson'seffectivewagerate. *g$  Ӏ  22    Separateregressionsformenandwomenarenotfeasiblebecausethereareonly21observationsfor  women. dTable_A&0 d d dTable_BTable_CTable_D3|mC( U$   hV``=``g(M(S_M,`S_AO,`OP_{SM}))`PRODfrom{j=1}toJH(boldT_f,`boldS)̀^{_T}`Z_j^{_j}~,Level 1Level 2Level 3Level 4Level 5((3$ U!   2C<< CLevel 1Level 2Level 3Level 4Level 5($$   1  ' dxdP PdLevel 1Level 2Level 3Level 4Level 5 &&V&&&&.g&&(&&M&&^(&&SnnM&&_,&&SnnAO&&,&&OPnnSM&&)&&)&& JnnkJnn13jnnS3nn31&&H&&(&&TnnT f&&~ ,&& S&&4 )nnp B T&& Znn} [ 3jnne j&&+ , Z 28W#   3(  5  )   H(boldT_f,`boldS)`=`sumfrom{i=1}toN`T_fi`S_i`  =`T_f`sumfrom{i=1}to{N}{T_fi}over{T_f}`S_i`=`T_f`S_W``, &&H&&(&&Tnn;f&&e,&&S&&)&&k&&Inn)Nnn_inn_nnh_1&&Tnnffi&&Snni&&U&&TnnBf&&xInnNnn_inn_nn_1L&'&&TnnSfi&&{Tnn1f&&lSnni&& && Tnn f&&& Snn W&& ,t ttttttt@t33333?@Table_At 9:U;=>?@ABC[x$xxxxxxx?xxxxxxX9v?x?xxxxx'1Z?xK7?x?xxxxRQxlڿxܿx?xxxtVxV-ҿx)\(ܿxDl?x?Table_Bxz3zzzzzzzzzzzzN@z^@zf@zn@zr@zzzzzzzzzzzzzzz ףp= @zHzG?z\(\ @zzzzzzzzzz ףp= @zQ@zq= ףp@z333333@z ףp= @zHzG@zzG@zRQ@Table_Cz||||||||?|@|@|@|@|"~j?|V-?|rh|?|+?Table_D| U!   7&&dd7  FF(#Forthcoming:EconomicDevelopmentandCulturalChange  L@ !EDUCATIONANDOFFFARMWORKL@,,&DennisTaoYang*ABSTRACT:Ahouseholdtimeallocationmodelisdevelopedtoexplaintheempiricalregularitythatthebettereducatedfarmmembersareusuallythefirsttoparticipateinnonfarmemployment.Centraltothemodelisthecomparativeadvantageprincipleandaknowledgespilloverhypothesisthatworkerswhoparticipateinofffarmworkmaystillcontributeknowledgetofarmmanagement.UsingChinesefarmdata,itisfoundthat(a)schoolingdoesnotcontributetophysicalefficiencyinfarming,(b)thehighesthouseholdschoolingcontributesthemosttoallocativeefficiencyandyetthecontributionisnotaffectedbyofffarmparticipation,and(c)educationraisesofffarmwages.Themodel'simplicationsfromtheseresultsareconsistentwiththeobservedpatternsoftimeallocation.ACKNOWLEDGEMENT:IwishtothankMarkAn,GaryBecker,WallaceHuffman,D.GaleJohnson,AllenKelley,MarjorieMcElroy,SherwinRosen,GeorgeTolley,ananonymousrefereeandseminarparticipantsattheUniversityofChicagoandDukeUniversityforhelpfulcomments.Theusualdisclaimerapplies.*ADDRESS:DepartmentofEconomics,DukeUniversity,Durham,NC277080097.Phone:(919)6601821.EMAIL:yang@lewis.econ.duke.edu. y-(/ Ї@ii!EducationandOffFarmWork̀ I.Introduction  > Inruralareashouseholdsallocatethetimeoftheirmemberstosomecombinationoffarmandnonfarmjobs.) (#  1      ׀Asalientfeatureofthisdualemploymentchoiceistheeducationalselectivityofworkers.Schultz   (1988)documentedinasurveythatfarmerswithmoreschoolingoftenfirstsuppliedfamilylaborofffarm.+ (#  2      ׀ Z   Therewerealsoeconometricevidenceforthisregularity.Gisser(1965)andHuffman(1980)foundthateducationincreasedthewageworkoffarmoperators.Instudiesofthejointdecisionsoffarmspouses,HuffmanandLange(1989)andGouldandSoupe(1989)foundthatahusbandorawifewhohadmoreschoolinghadasignificantlygreaterprobabilityofnonfarmwork.  Despiteoftheconsistentempiricalevidence,existingstudieshaveagreedwiththeapriori,ambiguouseffectofmoreschoolingonofffarmwork.Thisresultisbasedonthestandardlaborsupplymodelwhereanindividual'sallocationoftimebetweenhomeactivities,farmworkandmarketworkareassumedtoadjustsothatthemarginalvaluesoftimeinallusesareequal(Sumner1982).Sinceeducationmayenhancelaborproductivityinfarmandnonfarmwork,selectivitydependsonrelativereturns,anditmaygoineitherdirection.Empirically,however,previousstudieshavenotactuallycomputedthesectoralreturnstoschooling.,(  (#  3      ׀Insteadresearchershavespecifiededucationinofffarmlaborsupplyorparticipation f functionsandinterpretedtheestimatedcoefficients.Whilepositivecorrelationswerefound,causalitywasnotexplored.  Thispaperinvestigatesthedeterminantsofeducationalselectivityinaframeworkwhichemphasizesthecoordinationofhouseholdmembers.Sectoraltimeallocationisbasedonmembers'comparativeadvantagewhichinturndependsontheutilizationandreturnstoschoolinginthetwosectors.Centraltothemodelisaknowledgespilloverhypothesisthatworkerswhoparticipateinofffarmworkmaystillcontributeknowledgetofarmmanagement.Contributingknowledgetofarmingwhileparticipatinginofffarmemploymentgivesthemoreeducatedmemberscomparativeadvantageinofffarmwork,allowingthemtocapturereturnstoeducationinbothfarmandnonfarmsectors.  EstimationofthemodelisbasedoncrosssectionalChinesefarmhouseholddata.Anovelfindingisthatthehighesthouseholdschoolingcontributesthemosttofarmallocativeefficiencyandyetthecontributionisnotsensitivetotheperson'sofffarmparticipation.Thereisalsoevidencethatschoolingdoesnotcontributetophysicalefficiencyinfarmingbutraisesofffarmwages.Theimplicationsofthemodelwiththeseresultsareconsistentwiththesampleobservationthatthebettereducatedfarmersworkinnonfarmactivities. II.AModelofTimeAllocation  @  Thetypicalfarmhouseholdmodeladoptsastaticframeworkwherethehouseholdmaximizesaoneperiodutilityfunctionoveranaggregateconsumptiongoodandleisureofitsmembers.- (#  4      ׀Beforeeachproduction X#$ cycle,thehouseholdisassumedtochooseconsumption,selectpurchasedagriculturalinputs,determinemembers'laborsupplytofarmandofffarmwork,subjecttoanagriculturaltechnologyandtheendowedtimeofhouseholdmembers.Farmownedassets,suchasland,equipments,members'schoolingand t(#* experience,areassumedtobefixedintheshortrun.Theirinvestmentdecisionsaremadeinlongtermplanning.Inaddition,competitivemarketsexistforvariableinputs,labor,theconsumptiongoodandagriculturalproducts.. (#  5      ׀ h   Foralandholdinghousehold,memberstypicallyallocatetheirtimeamonghomeactivities,workonthefarmandworkoffthefarm.Dependingoncircumstances,offfarmworkmaybelocalormaytakeplaceincitiesfarawayfromruralareas.Inregionswithhighpopulationdensity,suchasEastAsia,localnonfarmindustriesemployasignificantshareoftherurallaborforce(AndersonandLeiserson1980).InregionssuchasAfrica,however,nonfarmjobsareoftennotlocal.Thecurrentpaperfocusesonworkassignmentstolocaljobs.Itdoesnotexaminetheeffectofeducationonseasonalorpermanentmigrationdecisions./ (#  6       T   Theincomeofthehouseholdmaycomefromfarmingandnonfarmemployment.Thehouseholdcarriesoutfarmproductionbyutilizingfarmsuppliedquasifixedfactors Z =(Z1,...,ZK),members'farm l laborsupply Tf =(T1f,...,TNf)andpurchasedinputs X =(X1,...,XJ).Theproductionalsodependsonthe $t schoolingoffamilymembers S =(S1,...,SN),theirexperience E =(E1,...,EN)andotherfarmspecific , characteristicsM,suchasfarmsizeandweather.DenotingYasanagriculturalproductionfunction,PA  astheoutputpriceandPXasavectorofpurchasedinputprices,thevalueaddedVinfarmingcanbe L representedas !" #4657QA=zx 0 @Xdddddddd@Ex d' L@##4657TD@zx 0 z@Xdddddddd@ExdK oL@A (#(#  (#(##Thisagriculturalincomeconsistsofreturnstothefarmsuppliedinputs,familiallaborandtheirhumancapital.  Familymemberscouldalsooffertheirlaborservicestotheofffarmwagemarketwhichisassumedtocompensateworkersaccordingtotheirschooling,experienceandotherpersonalandlocallabormarketcharacteristics2.Followingthestandardpractice,individualwagerateisconsideredtobeindependent 8  ofhoursofwork.Themarketwageforworkeriiswrittenas   "498:VFBz Xx 0 @Xdddddddd@EPx d' L@j"$"498:\LHz Xx 0 % @Xdddddddd@EPxjqdL@j"$$498:\LHz Xx 0 %z@Xdddddddd@ETxdoL@$ T  If W =(W1,...,WN)representsthemarketwagesforfamilymembersand To =(T1o,...,TNo)forofffarm d labordays,thehouseholdwageincomeis WTo .Inconjunctionwithagriculturalearnings,thetotal  householdcashincomeis WTo +(PAY PXX ).󀀀    Assumingutilitymaximizationoverconsumptiongoodsandleisureofhouseholdmembers,thefarm'sdecisionsmaybesolvedthroughthestandardLagrangianproblem.Attheoptimum,themarginalutilityofconsumptionequatesthecommodityprice.Thevaluesofmarginalproductofvariableinputs X   reflecttheirmarginalcosts.Thetimeallocationforhouseholdmembersisguidedbytheirmarginalvalueofhometime,thevaluemarginalproductinfarmingandthewagerateinofffarmwork.Onemayspecializeinofffarmworkifhiscompensationconsistentlyexceedsthereturnsfromfarming,orviceversa.Onemayalsosplitthetimeacrossthetwoactivities,equatingalternativemarginalearnings.Thereareoptimalconditionsoftimeallocationforeachmemberofthehousehold.  Thesestandardsolutions,astheystand,donotsuggestanydeterministiceffectsofaccumulatedschoolingonfarmversusofffarmwork.Addedschoolingmayraiseanindividual'sofffarmwage,butatthesametimeitmayraiseone'sproductivityinfarming.Toexplaintheaccruedempiricalevidencethat H,', thebettereducatedfarmersfirstsupplytheirfamilylaborofffarm,additionalanalysisisneeded.  Underutilitymaximization,optimallaborassignmentsofthehouseholddependonmember'srelativeproductivityinwageandfarmactivities.Inthecurrentmodel,familymembers'schoolingmayaffecttheirproductivitydifferentialsinthedualsectorsbecauseindividualschoolingdirectlyentersfarmproductionandwagefunctions.Householdandlabormarketvariables,suchasthelabormarketcharacteristics2in(2)andthefarmownedandpurchasedinputsinfarming,arenotlikelytoaffect 4   members'relativeproductivitybecausetheyarethesameforallmembers.Otherhumancapitalvariables,suchasgenderandexperience,mayalsodetermineamember'srelativeproductivity.Buttofocusontheroleofformalschooling,theanalysisofthesevariablesaredelayedtotheempiricalsection.  Morespecifically,considerlaborproductivityoftwomembersiandj.Sincethewageemploymentcondition2isthesameforthem,thereducedformoftheirwagefunctionscanbewrittenasW(Si)and  W(Sj).Infarmproduction,valuemarginalproduct(VMP)ofamemberisdefinedbypartially p differentiatingthefarmvalueaddedfunctionV=PAY( X , Z , Tf , S , E ;M) PXX withrespecttohislaborinput (x Tf,VMP=,PAY( X , Z , Tf , S , E ;M)/,Tf.Atagivenlevelofinputs,thereducedformofiandj'sVMPmay 0 bewrittenasVMP(Si)andVMP(Sj).Whenschoolingofiandjaredifferent,theirVMPsandWsare  expectedtodiffer.  Nowconsiderthejobassignmentofiandjinagricultureandwageactivity.Forsimplicityofexposition,assumeSi>Sj.Giventhecurrentinputsinfarming( X , Z , Tf , S , E ;M)andlabormarket !" condition2,theprincipleofcomparativeadvantagesuggeststhefollowingtimeallocationbasedonrelative p#$ marginalproductivity:%4<;=QA=zx 0 @Xdddddddd@E&x d' L&@%%4<;=TD@zx 0 z@Xdddddddd@E&xedIEoL&@ (#(#    +D'. %  Theutilitymaximizinghouseholdfollowstheserulestodecidethetimeallocationforfamilymembers.WhenVMP(Si)>W(Si)andVMP(Sj)>W(Sj)orwhenVMP(Si) (#  7      ׀Whenthefamilysupplieslabortobothsectors,the l questionofeducationalselectivityrises.Considercase(a).Thehouseholdwillfirstassigniforwagessothatimaysplithisworktimeintwojobswhilejworksfulltimeonthefarm.Onemayalsoobservethatiworksfulltimeofffarmwhilejsplitshistime.Thecasethatiworksonthefarmwhilejworksforwageswillnotoccurbecauseitviolatesthetheoryofcomparativeadvantage.Switchingworkdutiesmayincreasefamilyincome.Theworkassignmentsforworkersiandjarereversedincase(c).When(b)isthecase,thehouseholdisindifferenttoassignitsmemberstoeithersectorbecausenobodyhassectoralcomparativeadvantage.  Thetimeallocationrulesin(3)suggestasetofsufficientconditionsforeducationalselectivity.Inparticular,ifschoolingdifferencesresultinalargerproductivitydisparityinwageemploymentthaninfarming,thefamilieswillassignthebettereducatedtoworkofffarm.Whyworkersofdifferentschoolingmayhavesmallerproductivitydifferentialsinfarming?Theanswerispreciselythecauseofeducationalselectivity.  Itisarguedherethattheutilizationandreturnstoeducationinfarmingmaybesystematicallydifferentfromwageactivities.Alargebodyofresearchhasstudiedreturnstoschoolinginwageactivities.ThewidelyusedempiricalwagefunctionpioneeredbyMincer(1974)specifyschoolingandexperienceasdeterminantsofindividuallaborincomes.Aconsistentpositiverelationshipbetweenschoolingandwageratehasbeenfoundregardlessoftime,placeandthenatureofthedatasets.? (#  8      ׀Inagriculture,educationwas %` & hypothesizedtoenhanceaworker'sphysicalproductivityandtheefficiencyofmakingallocativedecisions(Welch1970).Empiricalstudies,includingChaudhri(1968),Huffman(1977),Fane(1975)andKhaldi(1975),proceededtodecomposetheproductivitygainsofmoreeducatedfarmersintolaborefficiencyandallocativeeffects.Inateamproductionmodel,Yang(1995a)usedthehighestschoolingoffarmmemberstoapproximatemanagerialskillsandaweightededucationschemetoapproximatelaborquality.Hefoundthatthehighestfarmschoolingisthemostimportanteducationvariabletoexplainfarmefficiency.  BuildingonYang'sanalysis,thispaperadvancestheideathatofffarmemploymentofthebettereducatedmembersmaynotaffecttheeffectivenessofcontributingknowledgetofarmdecisions.Itiswellknownthatinfarming,typicalallocativedecisionsincludeselectingacombinationofcrops,purchasingamixofvariableinputs,allocatingtheinputsamongalternativeuses,decidingwhentocultivate,plant,waterandharvest,aswellasthesalesoffinalproducts.Thesedecisionsusuallydonotrequireinstantjudgementattheworksites.Sincethemoreeducatedmembersresideintheirruralhomes,itisexpectedthattheycommunicatewithotherfamilymembersandcontributetodecisionmakingregardlesswheretheywork.@ (#  9       $   Inregardtotheassignmentconditionsinequation(3),itisarguedthatcentralizedallocativedecisionmakingmaybeimportantinfarmingwherethebettereducatedmemberstakeprimaryresponsibilities.Theymaycontributeknowledgetoproductiondespiteofparticipationinofffarmworkbecausemanyofthemstillworkandliveonthefarms.Thesecloseinvolvementsallowcommunication !" withotherfamilymembers.A (#  10      ׀Thishypothesissuggeststhatthereturnstoeducationinallocativedecision  makingarerealizedatthefamilylevel.Ontheotherhand,thereturnstoindividualeducationarelikelyreflectedinthequalityoflaborinputsincarryingoutroutinetasks,suchasdrivingatractororwateringplants.Ifthereturnstoschoolingarelowinthesemanualactivities,laborinputsofdifferentschoolingareclosesubstitutes.Consequently,thebettereducatedmembersmayhavecomparativeadvantageinwageemployment.  Theeffectofschoolingonlaborqualityandmanagerialskillscanbemodeledmoreexplicitlyinthefarmproblem.Let X *( Z , Tf , S , E ;PA, PX ,M)representstheoptimaluseofvariableinputs.Substitute X *   into(1),thevalueaddedfunctionmaybeexpressedasV=V( Z , Tf , S , E ;PA, PX ,M).Toclarifymoreclearly T  theroleofschoolinginproduction,twotermsaredefined.FirstdefineaqualityadjustedlaborunitH( Tf , S ),where Tf representsworkers'labordaysand S theirschooling,suchthat,H/,Tf0and,H/,Si0.  AlsodefineafunctionMforthefarm'smanagerialabilitywhichdependsonthehighestschoolingSM,the x averageschoolingoffarmmembersotherthanthemosteducatedworkerSAOandanofffarmwork 0 participationvariableforthemosteducatedworkerOPSM.OPSM=1ifthemosteducatedworker 8 participatesinofffarmemploymentandOPSM=0otherwise.B (#  11      ׀Wehypothesizethatthe"mosteducated"  workeristheleadingcandidateformanager.Whileanyeducationconceptuallycontributestomanagerialskills,theaddedschoolingofthemosteducatedworkersmaycontributethemostinmakingallocativedecisions.SAOreflectsthepotentialcontributionofotherfamilyworkers.TheinclusionofOPSMisto !" capturetheinteractiverelationshipbetweenthehighesteducationandhisofffarmparticipation.Denoting x#$ themanagerialfunctionasM(SM,SAO,OPSM)andomittingthefarmcharacteristicsMandcompetitiveprices  PAand PX forsimplicityofexposition,areducedformvalueaddedfunctionmaybeexpressedas h 4DCETD@zx 0 z@Xdddddddd@E xdk oL @D (#(#  (#(#Inadditiontoeducation,experienceandgenderofthemosteducatedworkermayalsoaffectmanagerialquality.Withoutspecifyingthefunctionaldetailshere,laterempiricalanalysiswillaccesstheroleofotherhumancapitalvariables.  Equation(4)providesaframeworktoassessthereturnstoindividualhumancapitalonthefarm.ThemanagerialfunctionM(SM,SAO,OPSM)allowsthebettereducatedworkertomakefarmdecisionsand X  permitsatestforsharingknowledgewithhisofffarmparticipation.TheefficiencylaborunitH( Tf , S )sets ` abasistoestimatethereturnstoschoolingthroughdirectlaborservicesofcarryingoutspecifictasks.Theseinformationarecrucialtounderstandtherelativeproductivityofworkerswithdifferentschoolinginfarming.Whenthereturnstoschoolinginwageactivitiesarealsoestimated,implicationsoflaborassignmentsmaybederivedformthecomparativeadvantageprinciplesin(3).Consequentlythevalidityofthetheoreticalimplicationsmaybejudgedinlightoftheobservededucationalselectivity. 11III.EmpiricalHypothesesandSpecifications  !" 0Consideringitscomputationaleaseandextensiveuseinpreviousstudies,theCobbDouglasformisselectedforthevalueaddedfunctionin(4).AssumethatthemanagerialvariableM(SM,SAO,OPSM)affects060 %l & 067 %l & 70efficiencythroughamutualdisplacementfunctiong,Viswrittenas:02q4GFH^NJzx ^x 0 z@Xdddddddd@q282r4mH_OKzx ^x p z@Xdddddddd@r28984mH_OKzx ^x p z@Xdddddddd@E(x ddpoFb(@89: &$"( :=;c4-` 0  `E(x<( kc;==n46&"p 0  `zE(xd o( n (#(#   +D'. =where Z representsfarmsuppliedquasifixedinputs,includingcultivatedlandAandcapitalservicesK.I (#  12       d   ForestimationitisnecessarytospecifythefunctionalformsofM(SM,SAO,OPSM)andH( Tf , S ).A l straightforwardmeasurementoflaborinefficiencyunitsisobtainedbymultiplyingaworker'sformalschoolingbythedaysofhisfarmwork.DenoteTfitobeworkeri'stotalfarmingdaysandSihisschooling.   HislaborinputinefficiencyunitscanbeexpressedasTfiSi.Consequently,thequalityadjustedfarmlabor @   inputis:>4MLNQA=zx 0 @Xdddddddd@Ex d' L@>?>4NRB>zx p @Xdddddddd@Ex d' L@>??4NUEAzx p z@Xdddddddd@Ex>do 7oL@c (#(#  (#(#?whereTfdenotesthetotalworkingdaysofallfarmworkersinagivenproductionperiod,andSWisa d measureofworker'seducationweightedbytheproportionoftheirfarmlaborparticipation.Thisvariablerepresentsameasurewhichreflectsthequalityoflaborindirectproduction.  Themanagementvariableisspecifiedas:@4POQQA=zx 0 @Xdddddddd@Ex d' L@@@4POQTD@zx 0 z@Xdddddddd@Exd oL@D (#(#  (#(#@wherethehighestschooling(SM)andtheaverageschoolingofotherworkers(SAO)approximatethe P managerialcapacityofthefarm.TheproductofSMandOPSMreflectstheconcernthatthecontribution  X  ofknowledgebythemosteducatedworkermaybeaffectedbyhisofffarmparticipation.Iftheinteractivetermisinsignificantempirically,itsupportstheknowledgesharinghypothesis. t#$   Substitutingthespecifications(6)and(7)into(5)andexplicatingthefarmsuppliedinputs Z ,we  haveTVUG73z X d p @@@EBh4 o4 oz ߀AssumingtheexponentialformTWXG73z X = p @@@Ev))JforTZYG73z X d p @@@EBVVzm ߀and h T\[G73z X = p @@@ED 9)9)| ߀forg(SAO+SM+SMOPSM),amorespecificCobbDouglasfunctionbecomes: D  A4^]_QA=zx 0 @Xdddddddd@E x d' L @ AA4^]_^ NJzx 7x 0 z@Xdddddddd@E x7Fd^ ooF @  (#(#  (#(#AOLSestimationof(8)iswidelyusedintheliteraturewhichaddsastochasticdisturbanceterm tothe L  humancapitalvariablesintheparenthesis.` (#  13      ׀Itisoftenassumedthat onlyaffectsthedependentvariable   butnottheindependentvariablesintheequation(Mundlak1961,MundlakandHoch1965).Exampleswhichjustifytheuseof includeweathervariationsandunexpectedchangesininputandoutputprices. h When isindependentoftheproductiveinputs,OLSestimationisunbiased.    However,Tfin(8)isapotentiallyendogenousvariable,whichmaybeaffectedbytheeducation  ofhouseholdmembers,theirofffarmworkopportunitiesandothervariables.ConsequentlyOLSestimationofthefunctionmaybesubjecttosimultaneousequationbiaswheretheunobservedfactorsintheerrortermmayaffectbothTfandV.Todealwiththeendogeneity,aninstrumentalvariableapproach  willbepresented.ThenumberoffamilyworkerswillbechosenasaninstrumentforTfbecauseitis \ expectedtobecorrelatedwithfamilylaborinputsinfarmingbutuncorrelatedwiththevalueaddedofcurrentfarmoperations.Tfwillberegressedonthenumberoffamilialworkersandallotherexogenous !  variablesintheVfunction.ThenthepredictedvalueofTfwillbeusedforfitting(8).Theresultsof #" instrumentalvariableestimationwillbeinterpretedandcomparedwiththeOLSestimates.  Thespecificationoflandasanexogenousvariablealsoneedsexplanation.Itisoftenobservedthatfarmerswithmoreschoolingpossessmoreland,suggestingthatAmayalsobeanendogenousvariable (#( whichrequireseconometriccorrection.ThisconcernisnotnecessaryinChina,however,becausethedistributionoflandisindependentoffarmers'schoolingattainment.UndertheChineseHouseholdResponsibilitySystem,collectiveorganizationsallocatelandtohouseholdsaccordingtopopulation,sizeoflaborforce,orbothpopulationandlaborsize(Yang1995b).Thedurationoflandcontractsareoftenmorethan15years(Lieberthal1985).Inaddition,landrentalsareoftenprohibitedorverylimited.Amongthesampleof204householdsusedforthispaper,onlythreehouseholdsrentedlandfromotherfamiliesin1989whileonlyfourhouseholdsleasedoutland.Theseinformationprovidesjustificationfortreatinglandasanexogenousvariable.  Takingnaturallogarithmsof(8),thebasicfunctionalformforestimationis:B4bacR B>zx p @Xdddddddd@Ex d' L@ BB4bacU EAzx p z@Xdddddddd@Ex-doL@D  (#(#  (#(#BwherelnVisthedependentvariable;SW,SAO,SM,OPSM,lnA,lnTfandlnKareindependentvariables;and l   and  areparameterstobeestimated.StandardtotheCobbDouglasform,theparametersW,AOand $t MgivethepercentageincreasesinVinresponsetoaunitincreaseintheeducationvariables.The , parametersA,TandKgivetheelasticitiesofthevalueaddedwithrespecttothefarmsuppliedfactors.    Hypothesesconcerningtheroleofeducationinfarmproductioncanbebrieflysummarized.Schoolingmayimprovequalityoflaborthroughcarryingoutroutinetasks.Symbolicallythisimplies,V/,SW>0orW>0.Thenullhypothesisis,V/,SW=0orW=0,indicatingthateducationdoesnotaffect !" physicalefficiency.Whentheschoolingofthemosteducatedmemberimprovesfarmmanagement,weexpect,V/,SM>0orM>0.ThenullhypothesisthatSMdoesnotaffectefficiencyimplies,V/,SM=0or  %p & M=0.ThesameinterpretationappliestotheeducationofotherfamilyworkersSAOanditscoefficientAO. &("( Thehypothesisthatknowledgecontributionbythemosteducatedworkerisnotnegativelyaffectedbyhisparticipationinofffarmworkisconsistentwith,V/,SM,OPSM=0orOP=0.Ifparticipationreducesthe D*%, effectivenessofknowledgesharingweexpectthat,V/,SM,OPSM<0orOP<0. +L'.   Theestimationof(9)willprovideinformationonreturnstoeducationinfarming.Todrawimplicationsonsectorallaborassignments,however,onehastoestimatereturnstoschoolinginofffarmearnings.Thestandardhumancapitalearningsfunctionwillbefittedtoallobservationswithreportedwagework:C4edfQA=zx 0 @Xdddddddd@E x d' L @ CC4edfT D@zx 0 z@Xdddddddd@E x d 6oL @b  (#(#  (#(#CwhereWisthewagerateforanonfarmworker.Theschoolingcoefficient,S,providesanestimatefor 8  therateofreturntoeducationwhichisassumedtobeaconstantparameter.Thequadraticexperienceterms,EandE2,allowconcavewageprofiles. P    Whenthereturnstoeducationinfarmandofffarmactivitiesareestimated,thecomparativeadvantageprinciplesin(3)willofferspecificimplicationsonlaborassignmentsbyschooling.Forinstance,supposeeducationdoesnotimprovephysicalefficiencybutenhancesdecisionskills.Ifknowledgespilloverstakeplaceinfarming,anypositivereturnstoeducationinnonfarmactivitieswouldgivethebettereducatedmemberscomparativeadvantageinthatsectorandgivethefarmhouseholdincentivestoassignthemtowagework.Onemayfurtherexaminewhetherthisimplicationconfirmswiththeobservedpatternsoflaborassignments. IV.DataandResults  !" Thedataforthisstudyconsistofa1990crosssectionof204Chinesefarmhouseholds,whichwererandomlyselectedfromSichuanprovince.SichuanisthemostpopulatedprovincelocatedinthecentralpartofChina.Thelevelofitspercapitaincomeisslightlybelowthenationalaverage.Themainagriculturalproductsarewheat,vegetables,sweatpotatoesandanimalhusbandry.Themainnonagriculturaljobsinthesampledregionsareinfoodprocessing,liquorfactories,manufacturing,constructionandretails. +0'. SummaryStatistics d InformationonfarmaverageproductionandincomeisreportedinTable1.Farmgrossincomeconsistsoftotalvalueofagriculturalproducepluslaborearningsofwageemployment.Itisevidentthatagricultureisthemajorsourceoffarmincomes.Thevalueaddedinfarmingisequaltothegrossvalueofcropsandanimalhusbandryminusthevariablecostsofcropsandraisinganimals.Variablecostsofcropsincludeexpendituresonhiredlabor,seeds,fertilizer,pesticide,manure,equipmentrentalsandmiscellaneousfees.Thecostsoffertilizerandmanureaccountthebiggestsharesamongthevariablecosts.Theexpensesonhiredlaborisverylimited.Inregardtothevariablecostofraisinganimals,feedcostisthemajoritem.Noticethatthevalueaddedinfarmingconsistsofreturnstothefarmsuppliedinputs,includingland,capital,familylaborservicesandhumancapital.g (#  14          Table1alsorevealsthatthesamplefarmsaresmall.Theaveragefarmcultivatedlandisonly1.18acres.Theaveragereplacementvalueoffarmequipmentsis480.1yuan,whichisaboutonesixthofthefarmannualgrossincome.Theaveragefarmlaborinputisroughlyequaltooneandahalffulltimeannuallabor.Alabordayisdefinedonaneighthourbasis.  Thedemographiccharacteristicsoffarmworkerscanbebrieflydescribed.Theaveragenumberoffamilialworkersis2.5forthesampledhouseholds.hj (#  15      ׀Theaverageageis33.2whiletheaverageyears @  ofschoolingis6.0.Noticethatthestandarddeviationforschoolingis2.8,indicatingvariationsintheattainmentofeducation.Informationontheaveragehighestschooling(SM)andtheschoolingofother X#$ familymembers(SAO)isanalternativeindicatorforintrahouseholdschoolingdifferences.SM=7.3and  SAO=4.7yearsofschoolingareroughlymatchedwiththeattainmentofjuniorhighandelementaryschool h graduates.Thisdifferencecanbeimportantinaffectingproductionefficiency.  Thesmallnumberofworkersonindividualfarmsmaycauseeconometricdifficultiestoincludevarioushumancapitalmeasuresinanempiricalfunctionbecauseofpossibleintervariablemulticollinearity.Table2reportsacorrelationmatrixofhumancapitalvariables,includingthehighestschoolingSM,theaverageschoolingofothermembersSAO,schoolingweightedbyfarmparticipation @  definedin(6)SW,experienceweightedbyfarmparticipationEWandthehighestexperienceEM.Rather   highcorrelationsarefoundamongtheschoolingvariablesandbetweentheexperiencevariables.i (#  16      ׀Inlater `  regressionanalysis,thesefactswillbeusedtoguideempiricalspecificationsandtointerpretresults.  Table3crosstabulatesthepercentagefrequencydistributionandtheeducationoffarmersaccordingtotheirtimeallocationbetweenfarmandofffarmactivities.Inthefirstpartofthetable,eachcellcorrespondstoaspecificcombinationofonfarmandofffarmworkdays.Thepercentagefiguresrevealsometendencyforspecialization.Farmerswhoprimarilyengageinoneoccupationandonlyworklessthan60daysinanotheroccupationcountformorethan87percentofthetotalworkforce.Onlyabout13percentoftheworkforceratherevenlyallocatetheirworkinthetwosectors.Anotherwaytoseethetendencyforspecializationistotracealongthebottomleftversustoprightdiagonalcellswhichhavethesametotallaborsupplyinfarmandnonfarmactivities.Thefrequencydistributionstendtoincreasetowardsthetwoends,indicatingsectoralworkspecialization.  ThesecondpartofTable3reportstheaverageschoolingofworkersconditionalonofffarmlaborsupply.Theaverageschoolingofthosewhodidnotworkofffarm(D=0)is5.51years.Thosewho & "( workedmorethan300daysofffarmhaveonaverage7.47yearsofschooling.Generally,theaverageschoolingincreasesconsistentlywiththeextentofofffarmemployment.  Inshort,thedatahaverevealedtwopatternsoflaborsupplyandschoolingoffarmers:(1)thereisatendencyforspecializationinoneworklocation,and(2)bettereducatedfarmersallocatemoretimeinthewagesector.AssessingtheroleofeducationinfarmingandwageactivitiesandexplainingtherevealededucationalselectivityarethetaskstowhichInowturn.EstimationResults   Table4reportstheresultsofinstrumentalvariable(IV)estimationaftercorrectingforthepotentialendogeneityoffamilylaborsupplyTf.Thenumberofhouseholdlaborforceisusedastheinstrument. T FirstTfisregressedontheinstrumentandallotherexplanatoryvariablesin(1)ofTable4.j (#  17      ׀Thenthe   predictedvaluesofTfisusedfortheregressions.IncomparisonwithOLSresults,theIVapproach t supportsthesamebasicconclusions.Aftercorrection,however,thecoefficientsoflnTfhavegenerally ,| increasedinsizeandtheexperiencevariables,EWandEW2,havebecomestatisticallymoresignificant. 4 Overall,theIVapproachprovidesbetterfitfortheregressions,raisingtheadjustedR2sbyabout2to3  percentforeachspecification.Duetotheseimprovements,onlytheIVresultsarepresentedandinterpreted.  Amongthe204householdsinthesample,6aredroppedintheregressionsbecauseofnorecordsofagriculturalproduction,zeroornegativevalueaddedinfarmingornofamilymembersinthelaborforce.ThedependentvariableoftheregressionsisthelogarithmofthevalueaddedinfarminglnV. $%t &  Regression(1)isthebasicCobbDouglasproductionfunctionspecifiedin(9)withlaborquality &,"( approximatedbySWandmanagementapproximatedbySMandSAO.k (#  18      ׀Theexperiencevariableweighted   byfarmparticipationEWanditsquadratictermEW2arealsoincludedintheregression.Analternative h specificationmayincludeEWandthehighestexperienceEMasexplanatoryvariables.However,Table2  p indicatesthatthecorrelationcoefficientbetweenthetwovariablesis.677.Sincetheircorrelationmayintroducemulticollinearityproblemsinadditiontotheschoolingmeasures,wedonotsystematicallyanalyzethisspecification.l (#  19       @     Regression(1)showsthecontributionoffarmsuppliedinputstothevalueaddedinfarming.Land(A)contributesalionsharewhichreflectsitsscarcityintheChineseagriculture.Labor's(Tf)contribution   isthesecondhighestamonghouseholdresources.Theflowofcapitalservices(K)isthesumoftool `  replacementvalueplusthedepreciationofmajormachineriesadjustedbytheireffectivedaysofuseinagriculture(Yang1994).Itscontributionispositivelysignificant,yetquitesmall.Theseshareestimatesaresimilarwithotherproductionstudiesofsmallscalefarming,suchasLauandYotoupolas(1971).Theimpliedmarginalproductivityofthesefarmsuppliedinputsarerespectively781yuan/acreforland,1yuan/dayforlaborand.12yuan/yuanforcapital.TheseresultssuggestthatlandhasrelativehighreturnsinChineseagriculture,thatlabormarginalproductivityinfarmingismuchbelowwageratesinnonfarmwork(seeresultsonpage19),andthatagriculturalcapitalhasapproximately12percentofannualreturns.  In(1)thecoefficientoftheweightedschoolingSW,whichapproximateslaborqualityindirect  T  production,hasaninsignificanttvalue.Theimplicationisthatanincreaseinworkers'schoolingimproves ! " positivelybutnotsignificantlytheiroperationalskills.ThecoefficientofSMispositiveandsignificant,  givingsupporttothehypothesisthatthehighesteducationimprovesallocativedecisionmaking.Thiscoefficientimpliesthatifoneadditionalyearofschoolingisaddedtothemosthighlyeducatedmemberabovethesamplemean,thefarmvalueaddedwillincreaseby3.3percent.SimilartoSw,thecoefficient   ofSAOhasapositivebutinsignificantcoefficient.Theestimatesfortheexperiencevariablesarealso   consistentwithexpectation.Thepositiveexperiencecoefficientandthesmallerandnegativequadraticcoefficientindicateastandardconcaveprofilethatexperienceenhancesfarmefficiencyatadecreasingrate.  Specifications(2)(4)presentinteractionsofthehighestschoolingwiththeperson'sgender,experienceandofffarmparticipationstatus.Thelastinteractionisofparticularimportancebecauseitteststheknowledgesharinghypothesiswithinthehousehold.Anotherchangeisthatequation(2)(4)omitschoolingvariablesSWandSAO.Table2reportedthatthecorrelationcoefficientbetweenSMandSWis.702 x andbetweenSMandSAOis.673,whicharebothhighrelativetotheadjustedR2inthefirstregression.To 0 avoidmulticollinearity,equations(2)(4)onlyincludeschoolingvariableSM,whichhasthehighest 8 statisticalsignificancein(1).n (#  20          Regressions(2)(4)revealthatthereturnstoland(A),familiallabor(Tf),capital(K)andexperience T (E,E2)arequitestablewithalternativespecifications.ThecoefficientsofSMareallpositiveandhighly  \  significant,indicatingthatthehighestschoolingenhancesallocativedecisionmaking.Inthesample,thehighesteducatedmembersin63householdsarefemales.Theinteractionofagenderdummy(female=1,male=0)withSMin(2)hasaninsignificantcoefficient,whichimpliesthatgenderdoesnotaffectthequality ,%| & ofdecisionmaking.In(3)thecoefficientofinteractionbetweenSMandtheexperienceofthemost &4"( educatedmember(ESM)alsohasalowtvalue,whichimpliesthatincreasedexperiencedoesnot (#* significantlycomplementsschooling.Inaddition,theinteractivetermSM*OPSMin(4)hasanstatistically  insignificantcoefficient.Thisresultsuggeststhattheparticipationofofffarmwageearningsbythehighesteducatedworkerdoesnotaffectthequalityofhisdecisionmakingonthefarm.Inthesample,workerswiththehighestschoolingonaverageworked76.3days(std=108.5days)offfarm.Theirknowledgecontributionremainedtobeimportantinfarming,anevidencewhichgivessupporttotheknowledgespilloverhypothesis.  TheestimatesonreturnstoeducationinofffarmemploymentbyfittingOLStoequation(10)are:4po\LHzx Bx p @Xdddddddd@E:x3d@ (#(#   (#(#wherefiguresinparenthesisarestandarderrors,DTisatownshipdummy,andDGisagenderdummy   variable:DG=1forfemalesandDG=0formales.q (#  21      ׀Theestimatedcoefficientsofthehumancapital t variablesareallstatisticallysignificant.Theresultsindicatethatwomenearnlessthanmen.r (#  22      ׀Therate ,| ofreturntoeducationis2.3percentinwageearningswithasampleaveragedailyrateat4.65Yuan.Thisrateisrelativelylowcomparedwithotherdevelopingcountries(Psacharopoulos1973).WidelyadoptedwagecontrolsinChinamaydepressthereturnstoeducationandresultinthelowrate.Thecoefficientsforexperienceandexperiencesquaredare0.025and.0004,implyingthatwagegrowthisabout2.5percentatbeginningofone'sworkinglifeandwageincreasesatadecreasingratewithmoreexperience.Wageismaximizedataboutfiftysixyearsofexperience.Theseresultsrevealfairlystandardeffectsof d#$ experienceonlnW.  Ѐ  Inshort,theaboveresultshaveindicatedthreeempiricalfactsconcerninglaborproductivityand h returnstoschoolingforthesample.First,laborproductivityofcarryingoutroutinetasksarethesameforhouseholdmemberswithdifferentschooling.Second,thebettereducatedmembersmaycontributetoagriculturalmanagementwhileparticipatinginofffarmwageactivities.Andthird,schoolingincreasesofffarmwagerates.Giventheseresults,equation(12)suggeststhatthebettereducatedworkershavecomparativeadvantageinofffarmworkandthecorrespondingselectiveassignmentsbyeducationmaximizethehouseholdincome.Ifthehouseholdviolatesthecomparativeadvantageprinciplesbyassigninglesseducatedmembersforwagesandbettereducatedmembersworkingonthefarm,thehouseholdwouldnotrealizethepotentialgainofknowledgespilloversthewagedifferencebetweenmembersofdifferentschoolinginnonfarmemployment.  Theobservedpatternsoftimeallocationareconsistentwiththeimplicationsofoptimalassignments.Table3hasshownthatruralworkerstendtospecializeinonesectorandTable4hasshownthatofffarmworkersaregenerallybettereducatedthanfarmworkers.Theseobservationsconfirmthatfarmhouseholdsbehaveaccordingtocomparativeadvantageprinciplesandrespondtolocalproductionandlabormarketconditions. IV.SummaryandFurtherImplications  !" Asabasiceconomicunitthefarmhouseholdtypicallysharesallproductiveresources.Formalschoolingofhouseholdmembersisanassetbywhichthehouseholdwouldliketocaptureitsmaximumreturns.Thispaperhasinvestigatedthepossibilitythatknowledgesharingwithinahouseholdisacauseofeducationalselectivityofofffarmfamilylaborsupply.Ifthemosteducatedworkercouldmakemanagerialdecisionswhileworkingofffarm,assigninghimtowageearningswouldenablethehouseholdtorealizethereturnstohiseducationinthetwosectors.Thisselectivearrangementbyeducationmaximizeshouseholdincome. +0'.   DatafromChinesefarmhouseholdsrevealworkspecializationandtheselectionofbettereducatedworkersinofffarmactivities.Theseobservationsareconsistentwiththecomparativeadvantageimplicationsderivedfromthereturnstoeducationconditionsestimatedforthesample.Itisfoundthatschoolingdoesnotenhancelaborproductivityofcarryingoutroutinetasks,thatthecontributiontofarmefficiencybythemosteducatedmembersisnotsensitivelyaffectedbytheirnonfarmparticipation,andthatschoolingincreaseslabormarketwagerates.Theseempiricalresultsgivecomparativeadvantagetothebettereducatedfarmerstoworkofffarm.  Indevelopingcountries,nonfarmactivitiesinruralareashavebecomeincreasinglyimportant.Existingstudiesofeducationanddevelopmentpolicieshavetypicallyexaminedthereturnstoindividualschoolingataparticularjob.Thecurrentstudyhasindicatedthatreturnstoeducationmaynotbelimitedtoindividualsandtothesectoroftheirwork.Knowledgemayspillovertootherhouseholdmemberscreatingadditionalreturns.Thisresultcallsforareassessmentoftheroleofeducationingeneratingfarmearningsandthefarmhouseholdbehavior.0&&   @OO TABLE1.SUMMARYSTATISTICS:HOUSEHOLDMEANSANDSTANDARDDEVIATIONS*qtu ddd Xdd Xdd X(#(#q,<d ,td ,td ,t +  1vv" @ 1@E E f Variable 0vw!xvv 0@~~1~Symbol 0vw!vw 0@>Mean 4vwv! vw 4@ffH Standard@GGH Deviation Fwvv5!x   vwv hF̀GROSSHOUSEHOLDINCOME(Yuan)̀AgriculturèWageEarning̀VALUEADDEDINFARMING(Yuan)̀GrossValueofCropOutput̀GrossValueofAnimalHusbandrỳVariableCostofCropProductioǹHiredLabor̀Seeds̀Fertilizers̀Pesticides̀ManurèRentalandFees̀VariableCostofAnimalHusbandrỳFARMSUPPLIEDINPUTS̀CultivatedLand(Acre)̀ReplacementValueofFarmingCapital(Yuan)̀LaborDaysinFarming(Day)̀HUMANCAPITALVARIABLES(Average)̀WorkersperHousehold̀AgèWeightedExperience p * ЀHighestExperience 8!+ ЀEducationofWorkers "P, ЀWeightedEducation "- ЀHighestEducation #. ЀEducationofWorkersExcepttheHighest X$/ ̀NUMBEROFHOUSEHOLDS 2wwv!&"2wvv 2@BB4~V@HH4~Z@BB4~A@DD4~K@993~Tf J @3~AGE@3~EW p P @3~EM 8!Q @--3~SA "PR @""3~SW "S @$$3~SM #T @  3~SAO 2wwv!X$Uwwv 2@=3278.0@=2709.5@>568.5@ww<1795.5@=1882.6@>826.9@>412.5@$$?3.0@>67.4@>146.0@>32.0@>125.8@>26.4@>501.5̀@>1.18@>480.1@>435.2̀@$$?2.5@>33.2@>20.7 p s @>28.1 8!t @>6.0 "Pu @>5.8 "v @>7.3 #w @>4.77 X$x @?198̀ 4wwvv!&"{wwv 4@I 1615.8@I 1606.8@J 762.1̀@I 1265.4@I 1067.5@J 767.6@J 232.4@J 14.3̀@J 46.8 `  Ѐ@J 105.4 (x @J 47.2@J 99.0@J 51.0@J 376.2̀@ K .69@J 519.0@J 251.3@ K 1.2@J 12.4@  J 9.5 p  @J 13.1 8! @  J 2.8 "P @  J 2.2 " @  J 4.6 # @  J 2.7 X$ 1'%%8! 0 h  wwvv 1  *P% @ Table2.CORRELATIONMATRIXOFHUMANCAPITALVARIABLES*xy dd<d td td t tu(#(#,d ,td ,td ,td ,td ,t +  1vv"  @ 1 0vw!  vv 0@V V V @  V Weighted@  V Education@ V (SW) 0vw! @ vw 0@hh%jHighest@$jEducation@&j(SM) 0vw! @ vw 0@bb1~Average@/~EduExcept@||1~Highest@2~(SAO) 0vw! @ vw 0@QQ<Weighted@;Experience@>(EW) 4vwv! @ vw 4@I Highest@G Experience@J (EM)  @   Hwv9!   vwv H@RSW    0ww!` "wv 0@ V 1.000@ V (.000) 0ww! %ww 0@'j... 0ww! 'ww 0@**3~... 0ww! )ww 0@>>?... 4wwv! +ww 4@: : K ... Hwv9! -  wwv H@RSM x/  0ww!X1wv 0@ V .702@ V (.000) 0ww!@4ww 0@&j1.000@%j(.000) 0ww!@7ww 0@**3~... 0ww!x9ww 0@>>?... 4wwv!x;ww 4@: : K ... Hwv9!x=  wwv H@RSAO  p?  0ww!Awv 0@ V .761@ V (.000) 0ww!8Dww 0@&j.673@%j(.000) 0ww!8Gww 0@2~1.000@1~(.000) 0ww!8Jww 0@>>?... 4wwv! pLww 4@: : K ... Hwv9! pN  wwv H@REW P  0ww!XRwv 0@ V .510@ V (.000) 0ww!Uww 0@&j.421@%j(.000) 0ww!Xww 0@2~.450@1~(.000) 0ww![ww 0@>1.000@=(.000) 4wwv!^ww 4@: : K ... Fwvv5!`  wwv F@REM pb  2wwv!!Pdwvv 2@ V .573@ V (.000) 2wwv!8 gwwv 2@&j.284@%j(.000) 2wwv!8 jwwv 2@2~.440@1~(.000) 2wwv!8 mwwv 2@>.677@=(.000) 4wwvv!8 pwwv 4@J 1.000@I (.000)1'%8 s 0   wwvv 1@##Note:Numbersinparenthesesaretheprobabilitiesthatthenullhypotheses(coefficient=0)cannotberejected.  )P$| @TABLE3:FREQUENCYDISTRIBUTIONANDEDUCATIONOFFARMERS:@H H FARMVERSUSOFFFARMLABORSUPPLY*z{ ddd td td td td t xy(#(#,d , td , td , td , td , td , td , td , t +  7vv& `  7@Variables@aa ofInterest Ivwv6'( x 0HHvv I@oo'OfffarmLaborSupply(D=Day) A7$   vwv HA &ww `  &@V V V @ V D=0 0ww! ww 0@#b0<300 0ww! ww 0@ED300 4wwv! ww 4 Hwv9! 8 H wwv H 8wwv%0 wv 8@gg&PERCENTAGEFREQUENCYDISTRIBUTION Kwv<$ !  wwv `K@[[ FarmLaborDays:@$$D=0@vv0 Chaudhri,D.P.(1968):"EducationandAgriculturalProductivityinIndia,"Ph.D.dissertation,  UniversityofDelhi.Fane,George(1975):"EducationandthemanagerialEfficiencyofFarmers,"ReviewofEconomicsand     Statistics,57:45261. ^   Gisser,Micha(1965):"SchoolingandtheFarmProblem",Econometrica,33:58292. d  Gould,BrianW.andWillaimE.Saupe(1989):"OffFarmLaborMarketEntryandExit",American     JournalofAgriculturalEconomics,November:672683.   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