Accounting for Fertility Decline during the transition to growth

8/12/2019 Accounting for Fertility Decline during the transition to growth

1/38

Accounting for Fertility Decline during the Transition to GrowthAuthor(s): Matthias DoepkeReviewed work(s):Source: Journal of Economic Growth, Vol. 9, No. 3 (Sep., 2004), pp. 347-383Published by: SpringerStable URL: http://www.jstor.org/stable/40215875.

Accessed: 06/12/2012 12:16

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at.http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of

content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms

of scholarship. For more information about JSTOR, please contact [email protected].

.

Springeris collaborating with JSTOR to digitize, preserve and extend access toJournal of Economic Growth.

http://www.jstor.org

This content downloaded by the authorized user from 192.168.72.221 on Thu, 6 Dec 2012 12:16:13 PMAll use subject to JSTOR Terms and Conditions
http://www.jstor.org/action/showPublisher?publisherCode=springerhttp://www.jstor.org/stable/40215875?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/stable/40215875?origin=JSTOR-pdfhttp://www.jstor.org/action/showPublisher?publisherCode=springer


2/38

& JournalfEconomic rowth,, 347-383, 004W 2004 Kluwer cademic ublishers. anufacturedn The Netherlands.

AccountingorFertilityeclineDuring heTransitionoGrowthMATTHIAS DOEPKE [email protected], CLA, osAngeles,A90095J77,USACentreorEconomicolicy esearch,0-98 Goswell oad, ondon C V 7RR,United ingdomIn every eveloped ountry,he conomic ransitionrom re-industrialtagnationo modem rowth asaccompaniedy demographicransitionromigho owfertility.ven houghhe verall atternsrepeated,therere arge ross-countryariationsnthe imingnd peed f he emographicransition.hat ccountsorfallingertilityuringhe ransitionogrowth?o answerhis uestion,his aper evelops unifiedrowthmodel hat elivers transitionromtagnationogrowth,ccompaniedydecliningertility.hemodel s usedto determinehetherovernmentolicies hat ffecthe pportunityostofeducationanaccount or ross-countryariationsnfertilityecline. monghe oliciesonsidered,ducationubsidiesrefoundohave nlyminorffects,hile ccountingor hild abor egulations crucial. part romnfluencingertility,he oliciesalso determinehe volutionf the ncome istributionn the ourse fdevelopment.Keywords:rowth,ertility,ducation,hildabor,nequalityJELclassification:20,J13, 14,O40

1. IntroductionFertilityecline s a universaleaturefdevelopment.veryndustrializedountryasexperienceddemographicransitionrom igh o owfertility,ccompaniedy largerise n ife xpectancy.ostdevelopingountriesre n themidst f their emographictransitionoday.Until short ime go, economic nddemographichangeduringdevelopmentere tudiedn solation: esearcherstudyingconomic rowthended oabstractromopulationynamics,hile emographersoncentratednexplanationsorthe emographicransition.ore ecently,conomistsave tartedorecognizemportantinteractionsetweenemographicnd economichange,ndrespondedydevelopingunified odelswhichncompassoth he conomicakeoffromtagnationogrowthndthe emographicransitionrom igh o owfertility.Accountingor ertilityehaviors an mportanthallengeor heoriesfdevelopmentbecause emographichangeffectshe conomicerformancef countryna numberofways.The most amiliaroncerns that igh opulationrowthilutes he tock fphysicalapital,nd hereforexertsnegativeffectn ncomeer apita. n venmoreimportanthannel orkshroughhe ccumulationfhumanapital.High ertilityatestend o be associated ith oweducation;ountries ith high ertilityate hereforeaccumulateesshumanapital. thirdhannelromhe emographicransitionogrowthworkshroughhangesn he gestructuref he opulation.apid ertilityeclineowersthedependencyatio ince nitiallyoth heold-age ndchild-ageohorts re small

http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp


3/38

348 MATTHIASDOEPKE6.5 |-n^- r- , , 1 i =r\\ ^v. - Brazil60 - v """^-^^^ England\ s^ Korea55 \ * - ^. Nv5.0- \^ " * ^ - .^ ^s.

* 45 \ -V \.4.0 - xv^ \ \3.5- s \3.0- %V \ -2.5 -2.0Lj 1 . . 1 11,000 1,500 2,000 2,500 3,000 3,500 4,000GDPper apita

Figure . Fertilityecline romeak elativeoGDPper apitanBrazil, orea,ndEngland.hegraphoversapproximatelyheperiods 820-1914 orEngland, 945-1980 orBrazil, nd 1960-1985 orKorea.Datasources:Korean ndBrazil: ertilityrom hesnais1992),GDPper apita romermWorld ables. ngland:Fertilityromhesnais1992)andLee andSchofield1981),GDPper apita romMaddison1991).relative to the working-age opulation.Hence, countries hatundergoa fastfertilitytransitionxperience sizable, if temporary,oost to their evel of outputper capita,because the size ofthe abor force ncreasesfaster han hepopulation s a whole.1The focus of thispaper is to understandwhydifferentountries ndergodifferentdemographicransitions.espitethefact hat heoverallpatternsrepeated, he peedandthe imingffertilityeclineduringhe ransitionromtagnationogrowthiffers idelyacross countries.An examplethatwill be used repeatedly hroughouthepaper is thecontrast etweenBrazil and SouthKorea (referredo as Koreathroughoutest fpaper).Fromthe 1950s to the 1980s,thetwo countrieshad a verysimilargrowth xperience.Substantial rowthnincomeper capitastarted t the sametime, ndthroughouthe ate1960s and 1970sboth ountrieswere onsidered o be "miracleeconomies,"with rowthratesofoutput er capita exceeding5 percent er year. nitially, ertilityas similar swell, with a totalfertilityateof 6.0 in both countriesn 1960. After1960, however,fertilitytarted odropfast nKorea,whilefertilityeclinewas much slowerand morespreadout nBrazil.Figure1plots he otal ertilityate elative o GDP percapita n the wocountries. s abenchmark, ata fromEngland,the first ountry o experiencethe transition rom1 Bloom nd Williamson1998)argue hathis ohort ffectccountsor large roportionfEast Asia's"economicmiracle" etween 960 nd 1990.



4/38

ACCOUNTINGOR FERTILITY DECLINE DURINGTHETRANSITIONTO GROWTH 349

stagnationogrowth,s also included n thegraph.Relative o incomeper capita,fertilityfellmuchfaster n Korea than t had inEngland,whereas hedecline was much lower nBrazil. Throughoutmost of thetransition,or a given level of incomeper capita thefertilityifferentialetweenBrazil and Korea exceeds twochildren er family.2imilarvariationsnthespeedoffertilityeclinecan be observed crossmanyother ountries.The transitionwas especially rapid in the East Asian *'miracle" economies such asTaiwan,Hong Kong, and Singapore. Examples of a slow transitionncludeMalaysia,Turkey,Mexico,and Costa Rica.Whydid thedemographicransitionroceedso much faster n Korea than n Brazil?The aim of thispaper is to explore the abilityof one specific explanation,namelydifferencesn educational nd child aborpolicies,toexplain cross-countryariationsnthe peedoffertilityecline.3Themotivationor his xplanations twofold. irst,mosteconomic models offertilityhoice are builton the notion f a quantity-qualityradeoffbetween he number f children nd educationperchild (see Beckerand Barro,1 88;Becker et al., 1990). If fertilitynd educationare indeed oint decisions,governmentpolicies that ffect heopportunityost of education hould have a first-orderffect nfertility.Second,we do in factobserve argevariations n educational nd child aborpoliciesacross countries uring hetransitionogrowth.Most countries ntroduce ducation ndchild abor reformst somepointduring heir evelopment, ut the extent ndtiming fthesereforms arieswidely.Brazil and Korea are onceagaindrastic xamples.Startingnthemid-1950s after he Koreanwar),the two countrieswerepolar opposites n terms ftheir ducational nd child laborpolicies. In Korea,child labor was almostcompletelyeradicatedby 1960, and largeamounts f resourceswere devoted to building publiceducationsystem. n termsof educationaloutcomes enrollment ates, iteracy ates,average schooling)Korea was far ahead of othercountries t a comparable evel ofdevelopment. razil,on the otherhand,spent relativelyittleon basic education, ndlagged far behindcomparable ountriesn terms f educationaloutcomes. Child laborlaws were ax and oosely nforced,nd as a consequence hild aborwaswidespreadwellintothe1990s.4

In order o examine the role of educationalpolicies during hefertilityransition,developa growthmodel thatgenerates phase of Malthusian tagnationombinedwithhighfertility,ollowedbya transitionoa growth egime nd low fertility.he model s

2 Thefigure ould ookqualitativelyimilarf we consideredhenumberfsurvivinghildrensay, oage5) instead f thenumberf ive birthsthefertilityate). nEngland,hefractionf childrenyinguntil ge 5 was 27 percentn1861, nd then ell o 19percent y1911 Preston,eyfitz,ndSchoen,1972). n Brazil ndKorea,18versus 2percentfchildren oulddiebyage5 in 1960, ndby1980these umbers ad declined o 8 versus percentWorld evelopmentndicators000).Therankingfthethree ransitionstays ntact,lthoughnglands closer o Korea n terms f survivinghildrenbecause fhigherhildmortality.3 Inconcentratingn the ole fpolitical ariables,abstractrom ther actorshat ould lso affecthefertilityransition.he aim here s to derive he mplicationsfdifferentducationalolicies n thefertilityransitionn solation;he nalysis oesnot ule ut hat ther actorsould lsomatter.4 See Section for descriptionf ducationalolicies ndoutcomesn Brazil ndKorea.



5/38


6/38

ACCOUNTINGOR FERTILITYDECLINE DURINGTHETRANSITIONTOGROWTH 35 1This research dds to an emergingiteraturen long-run rowthnd populationdynamics.alor ndWeil 2000),Kogel ndPrskawetz2001),Jones2001),HansenndPrescott2002), ndTamura2002) lldevelopmodelshat eneratetransitionromre-industrialtagnationomodernrowth,ccompaniedy demographicransition.o theextenthat ertilitys endogenous,hesemodels lso havethefeaturehat rise nthereturnohumanapitalsthe rivingorce ehindertilityecline. lternativeheoriesffertilityecline re basedonchangesngenderoles Galor ndWeil,1996;Lagerlof2003),theold-age ecurity otiveMorand, 999),and changesn childmortality(Kalemli-Oczan,002).6Our mphasisn child abor s shared ith azan ndBerdugo(2002),whoemphasize risingwagedifferentialetween hildrenndadults s thedriving orceforfertilityecline.While the existingiteratureenerally as notconcentratedncross-countryifferencesnfertilityecline, hemechanismsnthesepapers uggest numberf alternativexplanationsor uchdifferences.orexample,cross-countryariationnpreferencesor hild uality,hecostofchildren,he kill-intensityfproductionechnologies,r he roductionunctionor umanapitalould llhave omempactnfertilityuringhe ransition.ome f hese actorsre ndogenizedinGalor nd Moav 2002),whodevelop nevolutionaryccount f thedistributionfpreferencesor hild ualityna population,nd n Galor ndMountford2003),whoconcentraten the nteractionf nternationalrade,hedemand or killedabor, ndpopulationrowth.Therest fthepaper s organizeds follows. hefollowingection ntroduceshemodel. ection derives numberftheoreticalropertiesfthemodel, ndSectiondiscusses he ehaviorf hemodel ntheMalthusianegime,he rowthegime,nd hetransitionetweenhe wo.nSection,1discuss he alibrationrocedure,nd ectionuses he alibrated odel o ssess he ffectfgovernmentolicies uringhe ransition.Section concludes.

2. TheModelThe conomyspopulatedy verlappingenerationsfpeoplewho ivefor wo eriods,childhoodnd dulthood.hildreneceive ducationrwork,o not njoy ny tility,nddonot et odecide nything.dults anbe eitherkilled runskilled,ependingntheireducation.neachperiodheres a continuumf dults f ach ype; s s themeasurefskilled dults, ndNv is the measure f unskilleddults.Adultsdecideon theirconsumption,abor upply,ndon thenumberndthe ducationftheir hildren.

link ertilityifferentialsithincountryo economic rowth.nteractionsetweenertilityifferentialsand nequalityre also thefocus fDahan nd Tsiddon1998),KremerndChen 2002),and Veloso(1999).6 Otherrecent tudieswhich use quantitativeheory o evaluategrowthmodels withendogenouspopulationnclude Fernandez-illaverde2001) on the role of capital-skill omplementarityorexplainingertilityecline, reenwoodndSeshadri2002)on theUS demographicransition,ndNgai(2000)on barriersotechnologydoption.



7/38

352 MATTHIASDOEPKE

2.1. TechnologyThe single consumption ood in this economycan be producedwith two differentmethods.There s an agricultural echnologyhat ses skilled abor,unskilledabor, ndland as inputs, nd an industrial echnology hatonly uses the two typesof labor.Production n each sector s carried out by competitive irms. he main task of thetechnology etupis to deliveran industrial evolution rom tagnation o growth: hetakeoffakesplace once the ndustrialechnology ecomessufficientlyroductiveo beintroducedlongside agriculture.The firm-levelndustrial roduction unction xhibits onstant eturns o scale, and isgiven by:

y, A>(is?-"(ivr, (i)whereyt soutput/stands orndustry), j is a productivityarameter,s and v are nputsof skilled ndunskilledabor, nd theparameter satisfies < a < 1. Since there re noexternalities,ggregatendustrialutputs YI = Aj (LIS)1 a (L/t/)a, here ISandLw aretheaggregate mounts f skilled and unskilled aboremployed n the ndustrial ector.Since I want o abstract rom equests, here s nocapital ntheproductionunction.hesetupis equivalent,however,to a model withcapital under the small-open-economyassumption,which s theapproach akenbyGalorand Weil (2000).7The agriculturalectoruses thetwotypes f abor and and.The aggregate griculturalproductionunctions given by:

YF =AF {LFSf> (LFU)0" (Z)1-*-"". (2)HereYF s agriculturalutputF stands orFarm),AFis a productivityarameter,FSandLFUare the ggregatemounts f skilled nd unskilled aboremployednthe griculturalsector, nd Z is the total mount f land. assume that heparameters atisfy s,6u>0and^-f 0/--)/i-ijwhich s (1) by setting , =B(1/1~a)(a/r)(a/1~fl).he same argumentppliesto the agriculturalproductionunction.



8/38

ACCOUNTING ORFERTILITYDECLINEDURINGTHETRANSITIONTO GROWTH 353where

AF=AF [(LFS)\LFV)9]-i^ (Z)1-^-"".Thus he otal mount f abor mployedasa negativeffectn theproductivityfanindividualirm.he pecificormf he xternalffect as hosen uch hat he ndividualproductionunctions3) aggregateo 2) above.As far s the nalysisnthis aper sconcerned,hemain eaturef he griculturalroductionunctionsdecreasingeturnsolabor. heassumptionfdecreasingeturnss essential or eneratingheMalthusianregime.8assume hat he ndustrialectors more kill-intensivehan he griculturalsector:Assumption The industrialector s more kill-intensive,hat s, theproductionfunctionarametersatisfyx 9S.This ssumptionillbeimportantor eneratingertilityecline uringhe ransitionothegrowth egime. heproductivitiesfboth echnologiesrow t constant,houghpossiblyifferent,ates:

A'F= yFAF, A't=yiAh (4)where F,y7 1. The simplifyingssumptionfexogenousnd constantroductivitygrowths made oemphasizehat he pecificource fproductivitymprovementsoesnotmatteror he ualitativeeaturesfthemodel;t s only ecessaryhat roductivitygrowthakesplace at all. Neithers itnecessaryo assume changen the rateofproductivityrowthoexplainhe witch romtagnationogrowth. hile roductivityshould ltimatelye thoughtf as anendogenousariable,he conomicmechanismsexplorednthis aper o not ependn a particularngine ftechnologicalrogress.Thestate ector in this conomyonsists fthe roductivityevelsAFandAj intheagriculturalnd ndustrialectors,ndthemeasures s andNyof skilledndunskilledadults: = {AF,AhNSiNy}.Theonly estrictionnthe tate ectors thatthastoconsistofnonnegativeumbers.hereforehe tatepaceXfor his conomysgiven yX= R+.Inequilibrium,ages re functionf he tate.twill e shownnPropositionbelowthat irms ill lways eoperatingnthe griculturalector, hile he ndustrialectorsonly peratedfthewages atisfyhe ondition sC*)1*wu(x)a At (1 -a)1"'^.Theproblemf a firmnsector ,where e F, /}, s to maximizerofitsubjecto theproductionunction,aking ages sgiven. rofit aximizationmplieshatwages qualmarginalroductsneach ector.Writingabor emand s a functionf he tate, or heagriculturalectorweget he ollowingonditions:8 Theassumptionf an externalffect romabor, n the ther and,s not ssential,nd s usedonly oabstract rom andownership.he model s equivalento a setup n which ll land is ownedbyforeignersr a separateand-owninglass.



9/38

354 MATTHIASDOEPKE

^~*>Kki^z'--"- (5)Notice hat hesewages redecreasingntotal abor upplyifLFU ndLFS revaried nproportion)inceQv+ 0S 1. Ifthe ndustrialectors operating,ageshavetoequalmarginalroductss well:

ws(x)=A,(l-z)(^Qy if Lls{x),Lw{x)0, (7)Wu(x)=A,x(j^y

" if Lls(x),Llu(x)>0. (8)Inthis ector, ages nly epend n the atio fskilledndunskilledabor upplyincethe fixed actorand does notenter.nstead fwritingutthe firms' roblemn thedefinitionfanequilibriumelow, will mpose5)-(8) as equilibriumonditions.

2.2. Preferencesnd PoliciesI willnow urn o the ecision roblemfthe dults. dultsare bout onsumptionndthenumberndutilityf heirhildren.hepreferencetructures anextensionfBeckerand Barro 1988)tothe ase ofdifferentypes f children.hemain bjective f thepreferenceetups togeneratequantity-qualityradeoffetweenhe umberf hildrenand ducationer hild. his radeoffs essential or ducationalnd hildabor oliciesto have n effect.Adults iscounthe tilityf heirhildren,nd he iscountactorsdecreasingnthenumberfchildren.nother ords,hemore hildrennadult lready as, he mallersthe dditionaltilityromnotherhild. heutilityf anadultwho onsumes units fthe onsumptionood ndhasnsskilledndnvunskilledhildrensgiven y:and assume < ft 1,0 < a < 1,and0 < s < 1.V's sthe tilitykilledhildren illenjoy s adults,ndVy s theutilityfunskilledhildren,oth oreseenerfectlyy heparent.heparameterdetermineshe lasticityfutility ith espectoconsumption,is the eneralevel f ltruism,nd is the lasticityf ltruismithespecto he umberofchildren.he utilities 's ndVvareoutside f he ontrolfparentsnd re hereforetaken s given. heutilityfchildrenependsn the ggregatetate ectorn thenextperiod,nd ince heres a continuumfpeople, ggregatesannot einfluencedy nyfinite umberfpeople.Adultsre ndowed ith neunit f ime,nd heyllocateheirime etween orkingand hild-raising.hildrenre ostly,othntermsfgoods nd n ermsf ime. aising



10/38

ACCOUNTING FOR FERTILITY DECLINE DURING THE TRANSITION TO GROWTH 355

each child akesp > 0 units fthe onsumptionoodand a fractionj> 0 ofthe otal imeavailable to an adult. Adults also have to decide on the education of their hildren.Children eed a skilled eacher o become skilled. t takes fractionj>s f a skilled dult'stime o teachone child.Therefore,fparentswant killed hildren,heyhave to send theirchildren o school and pay the skilled teacher.Childrenwho do notgo to school stayunskilled nd workduring hildhood.Children an perform nlytheunskilled ask, ndoneworkinghildsupplies j)vunits f unskilled abor.Theparameterj>ys smaller hanone since children o notworkfrom irthnward,ndsincethey re not s productivesadults. also assume, o that venafterccountingor hild abor heres still netcost associatedwithhavingunskilled hildren.There are two government olicies in the model: a child labor restrictionnd aneducation ubsidy.With hesepolicies,thegovernmentan influence oth omponents ftheopportunityostof education or child: thevalue of a child's time n terms f childlabor,and the direct choolingcost. A child laborrestrictionmounts o lowering heparametert>u. he governmenthooses a function^( ) whichdetermines ow muchtimechildrenwork,depending n the state.Since restrictionsan only ower the egalamount f child abor, require hat < u(x) vor ll x? The governmentlso hastheoptionofsubsidizing fixed mount ftheschooling ostfor ll children t school.This expenditures financedwith flat ncometax,and budgetbalance is observed neveryperiod.The governmenthooses a function thatdetermines he fraction f theschooling ost to be paid bythegovernment, here < S(x) < 1 for ll x. Contingentnthisfunction,he flat ax t is chosen to observebudget alance.With axes and thesubsidy, hebudget onstraintf an adultoftype/ s givenby:

c + p (ns+ nv) + (1 - S(x)) uo "Y/to/] (9)The right-handide is the after-taxncome of the adultplus the income from endingunskilled hildren o work.Notice that he ime ost or ach child has to be subtractedfrom he ime ndowment ocomputeabor upply. n the eft-handide areconsumption,thegoodscostfor achchild, nd thepart f the ducation ost for he killed hildren hatispaidbytheparents. orsimplicity,dults renot estrictedochoose nteger umbers fchildren. lso notice hat here s nouncertaintynthismodel. Whether child becomesskilleddoes notdependon chanceorunobservedbilities, ut s under ull ontrol ftheparent.In equilibrium,hewagesand theutilities f skilled nd unskilled eople arefunctionsofthe statevector.The maximization roblem f an adultoftype/,where e {5, U}, isdescribed ythefollowing ellmanequation:

Vt(x) max cff fi(ns nv) *[nsVstf) %W)]}c,nu,ns>}jsubject o thebudget onstraint9) andtheequilibriumaw ofmotion = g(x).9 In theapplicationsbelow, will consider one-time hange n child aborpolicy.



11/38

356 MATTHIASDOEPKE

For he roblemf parentobealwayswell efined,e have oplace oint estrictionon the arametershat nsureshat he ffectiveiscountactors nothigherhan ne. nother ords,dultsannotlacehigher eightn the tilityf heirhildrenhan ntheirownutility.ince thediscount actor epends n thenumberfchildren, e have toconsiderhehighest ossible umberfchildren,hich sreachedy n unskilleddultwho pendsll income n children.heresultingumberfchildrens 1/(0- u).Assumption2 Theparameters t, , a, (f>,f>Ufnd yt atisfy:

r(jh;)'"


12/38

ACCOUNTING ORFERTILITY DECLINEDURINGTHE TRANSITION OGROWTH 357

3. Analytical esultsThis ection erives numberftheoreticalesultshatwillbe useful or escribingheequilibriumehaviorfthemodel. irst,analyzehe wo roductionectors,nd henturn o thedecision roblemf anadultn the conomy. llproofsrecontainedntheAppendix.Onthe echnologyide, hemain esults thatwhile he griculturalectors alwaysoperating,ndustrialirmsroduce nly f industrialroductivitys sufficientlyighrelativeowages.Thefollowingropositionserive he onditionshat renecessaryorproductionn ndustrynd griculture.Proposition Firmswillbe operatingnthe ndustrialector nly fthe killed ndunskilledagesws(x) ndwv(x)satisfyhe ondition:

wsto1"*(*)"


13/38

358 MATTHIAS OEPKE

and u = (j)w ^>(jWv p.We lways ave/?5 pv\ killedhildrenremorexpensivethan nskilledhildren.We can nowwrite hemaximizationroblemfan adult s:ma*J(w "Psns PunuY P(ns nu) B[nsvsnuvu\}- 02)An alternativeayofformulatinghis roblems to maginehe dultss choosinghetotal ducationost they pend nraisinghildrennd he raction/ofhis ost hatheyspend n skilled hildren. he numberf childrens thengivenbyns=fE/ps andnv- (1 -f)Elpu. Inthis quivalentormulation,hemaximizationroblemf he dultis:o


14/38

ACCOUNTINGORFERTILITYDECLINE DURINGTHETRANSITIONTO GROWTH 359If n adult s ndifferentetweenkilled ndunskilledhildren,he otalxpenditurenchildrenoes notdepend n the ype fthe hildren.

Proposition An dult s ndifferentetweenkilled ndunskilledhildrenf ndonly fthe osts nd utilitiesfchildrenatisfy:Vs ... Vv (15)(PS)'"8"...W-" (15)

If n adult s indifferent,he otal xpendituren childrenoesnot ependn the ype fchildrenhat s chosen.Propositionsand3 have mplicationsor ntergenerationalobilityn themodel.Propositionstates hat or iven tilitiesf killed ndunskilledhildrenhe atio f heprices f killed ndunskilledhildrenetermineshetherarentsend heir hildrenoschool.As long s thewagefor killed abor s higherhan heunskilled age, killedchildrenrerelativelyheaperor killed arents,incews> wv mplies:


15/38

360 MATTHIAS OEPKE Apositiveractionfskilled dultshas skilled hildren,nd a positiveractionfunskilleddults as unskilledhildren:

*s-s(*Mi/->/to>0. Just netype f dult an be indifferentetweenhe wo ypes fchildren:*s-c/M > implies u^s{x) = 0,A(/_5(jc) 0 implies s^u(x) = 0.

Specifically,s^v(x) > implies:(d>ws(x)+


16/38

ACCOUNTINGORFERTILITYDECLINE DURINGTHETRANSITION O GROWTH 361

systemof steady-state quations under the assumptionthat only the agriculturaltechnologys used. For a wide rangeof parameterhoices,there s a solution o thesteady-statequations nwhichbothwagesand theratio f skilled ounskilled dults reconstant.11n thesteady tate, veragefertilitys higher orunskilled dults.While allskilled dults endtheir hildrenoschool, here resome unskilled arentswith nskilledchildren nd otherswith killed hildren.Wages dependonpreferencearametersnd thegrowth ateofagricultural roductivity,ut are independentf the evel ofproductivity,sinceproductivityrowths exactlyoffset ypopulation rowth.Eventhough nly he griculturalroductionunctions used n theMalthusian egime,the productivityf the industrial echnology ncreases over time. At some point,productivitynindustryeaches a level atwhich ndustrialroductions profitablet thewagesthat revail ntheMalthusian egime. rom hat ime n,the ndustrialechnologywill be used alongsidethe agricultural echnology. ince populationgrowth oes notdepresswagesinindustry, ages and incomepercapitastartogrowwithproductivitynthe ndustrial ector.While the model assumes that hegrowth ate of productivitynindustrys constant ven beforethe technologys used, all that s necessary s thatproductivityrowthnindustrys bounded wayfrom ero. This is a natural ssumptionsince echnologyn ndustryndagriculturescomplementary,nthe ense thatnventionswhichare useful foragriculturelso have industrial ses. For example,James Watt'scontributionso thedesignof steam ngineswould nothavebeenpossiblewithout riordiscoveries n mechanics and metallurgyhat were originally imed at improvingagriculturalandperhapsmilitary) echnology.The evolution ffertilitynd the ncomedistributionnce thetransitiontarts ependson the specificproperties f the industrial roduction unction.Given Assumption1(production n industrys more skill-intensive hanproduction n agriculture), heintroductionf the ndustrialechnologyncreases hewage premium or killed abor.This increases he returns o education, nd more unskilled dultswill choose to haveskilledchildren, esultingn higher ocial mobility. he overall effect n fertilitysuncertain. he increaseddemand forexpensiveskilled childrenwould tendto lowerfertility,utthen incewages start ogrow, heutilityf children elative o their arentsincreases,which tends to increasefertility.he transition an be influenced y publicpolicy.Both an education ubsidy nd child abor restrictionsower therelative ost ofskilledchildren,nd as a resultbothpolicieshave a positiveeffect n thenumber fchildren oingto school.The effects n fertility,owever, re different.ince a subsidylowers he costofchildren,n education ubsidy ncreasesfertilitymong parentswhowouldhavesent heir hildreno school even without he ubsidy.At the ametime,moreparents end their hildren o school,whichwould tend o lowerfertilitys longas theopportunityost of education s not zero. The neteffects generally mbiguous;eventhough,n all computed xperiments ertilityises n response o an education ubsidy.

11 If the choolingost s very igh,t s possible hat o solutionxists nd thefractionf skilled dultsconvergesozero.Also, fproductivityrowthndthe ostof childrenrevery ight s possible hatpopulationrowths nothigh nougho offsetroductivityrowth.eitherase arisesnthe alibratedmodel.



17/38

362 MATTHIAS OEPKEChild laborrestrictions,n theotherhand,unambiguouslyncrease he cost ofchildren,and thereforeead to owerfertility.he quantitativemportancefpublicpolicies duringthe transition illbe assessed below.Ifproductivityrowthn ndustrys sufficientlyigh, hefractionfoutput roducednindustrywill increase over time, until the agricultural ector ultimatelybecomesnegligible. he economywill then each balancedgrowth ath: hegrowth egime.Herethe model will behavelike one in whichthere s the ndustrialechnologynly, nd allvariables can be computedby solvinga system fbalanced-growthquations.Whetherfertilitys highern thegrowthegime han n theMalthusian egimes determinedytherelativeimportance f skill in the two technologies. f the industrial echnology ssufficientlykill-intensive,n thegrowth egimemost childrenwill go to school. Sinceschooling s costly, hiswill tendto lowerfertilityndpopulation rowth. n the otherhand, s wages grow, hephysical ostp ofchildren ltimatelyecomesnegligible. hiseffectmakes children elatively heaper nthegrowth egime,whichwill tend o increasefertility.nless theschoolingcost is very high,the ratio of skilled to unskilled dultsreaches a fixednumber n the growthregime.12 opulationgrowth nd fertilityreconstant, nd wages and consumption rowat the rate of technicalprogress.Averagefertilitys lower for skilledthan for unskilledadults.This would be true even if theschooling ost werezeroand iftherewereno child abor, incethen heonlyremainingcost of childrenwouldbe a time ost. t was shown nSection3 that fthere s a pure imecost forhaving hildren, agesandfertilityrenegativelyelated.With ositive choolingcost and child abor herelative ost of skilled hildrenncreases,nd sincerelativelymoreskilled adults have skilledchildren, hiswill furtherncreasethe fertilityifferentialbetween he twotypesofadults.Given thatfertilitys higher orunskilled dults n thebalancedgrowth ath,thas to be the ase that ome unskilleddultshave skilled hildren.Otherwise he fraction f unskilled dultswouldincreaseovertime.Therefore nskilledadults are ust indifferentetween he twotypesofchildren.Inthe imit-economyithoutgriculture, agesaredeterminedythe atio fskilled ounskilled aborsupply. he onlyrequired tatevariables re thereforeheratioof skilledand unskilledadults and theproductivityevel in industry. he setupcan further esimplifiedynoting hat heperiodutility unctions of theconstant-elasticityorm,ndthatwages are linear n theproductivityevel. This results n value functionshat rehomogeneousn the ndustrialroductivityevel:

This reduces hegrowth egime ssentially o a one-dimensionalystem,with heratio fskilledto unskilled dults s the statevariable.I will now turn o the uestion f whetherublicpolicy an have arge ffectsuringhetransition.n thefollowing ections, calibrate he modelparameters,nd simulate hemodel underdifferentssumptionsn policies.12 Ifthe choolingost s toohigh,henumberf killed dults onvergesozero ver ime.



18/38

ACCOUNTING ORFERTILITYDECLINE DURINGTHETRANSITION O GROWTH 3635. CalibrationIn this ection describehe rocedureor alibratinghemodel arameters.ince usethemodelo xamine hetherolicy ifferencescross ountriesan ccount or ifferenttransitionxperiences,twouldbe counterproductiveo chooseparameterso closelymatch ata romne pecificountry.ather,choose arametersuch hatnthe rowthregimehemodelmatchesertaineaturesfmodernndustrializedountries,hilen heMalthusianegimehemodel esemblespre-modernconomy.or he rowthegime,usecurrentS data,while or he re-modernconomyrelymostlynEngland, herethe vailable ata s ofrelativelyigh uality.ince he alibrationrocedureinsdownonly he wo nds f he imeine,we can use the ransitioneriod or estinghemodel.I startydescribinghe arameterhoices hat redeterminedyfeaturesf he rowthregime. heparameterhthe rateoftechnologicalrogressn the ndustrialector,determineshe rowthate fper-capitautputn he rowthegime.ntheUnitedtates,realGDPper apitancreasednaverage y1.9percenteryearnthe eriod rom960to1992. thereforehose heyearly rowthate fproductivitynthe ndustrialector obe 2 percent.ince model eriods 25years,his ives valuefor yf 1.64.Given hatherere trictompulsorychoolingaws nd hild abor estrictionsntheUnited tates he arametersor hegrowthegimerecalibratednder he ssumptionthat hild abor s ruled ut.Theschoolingostparameter/)setermineshenumberfteachersndthe tudent-teacheratio n thegrowthegime. ccordingo theDigest fEducationtatisticsUSDepartmentfEducation,998),n heUnited tates eachersnall levels f education akeup 1.5percentf theAmericanopulation,nd there reabout 6 studentser eacher.ince,unlikenthemodel,nthe ealworld achteacherteachesmore han negenerationfstudents,e cannotmatch oth alues t the ametime.fthe atio f eachersopopulationsmatched,lass izeswould e toobig, nd fclass ize smatched,here ould e toomanyeachers. s a compromise,chose />sobe0.04,which esultsn a class size of21,and 1.7percentfthe opulationre eachers.13Thetime ost t> asthen hosen omatch he otal xpenditurenchildrenntheUnitedStates,stimatedor 992byHaveman ndWolfe1995).Accordingo theirstimates,parentaler-childxpendituresere 9,200 r bout 8percentfper apitaGDP. choseobe0.155,whicheads othe ame atio fper-childxpenditureso GDPper apita.Knowles1999)calibrateshe ameparametero other stimatesf the ostofchildrenand rrivest a similar alueof0.15.Using ata rom975,Jones1982)findshatn Britainhe ifferencentotal ertilitybetween omen ith lementaryducationr essandwomenwithecondaryrhighereducations about .4,andthe orrespondingaluefor heUnited tatess about .5.1chose he referencearametersx, nd/? o be consistentith fertilityifferentialf0.5 betweenkilled arentsndunskilledarents hohaveunskilledhildren,nd totalfertilityate f2.0,whichmatches urrentertilityn theUnited tates. hechoicesc = 0.5,e= 0.5,and 8 0.132 areconsistent ith hese bservations.AccordingheDigest fEducationtatistics,n1994 otal xpendituresn education13 Variationsf themodelwhichmatch ithertatisticxactlyead toessentiallyhe ameoutcomes.



19/38

364 MATTHIAS OEPKEwere7.3 percent fGDP,whilepublic xpenditures ere4.8 percent,rroughlywothirdsof the total.These numbers xcludeexpendituresy parents ndstudents,ike textbooksand transportation.he government herefore ays for less than two thirdsof alleducational xpenditures.n themodel, chose thefraction of education ostpaidbythegovernmento be 0.5.The technology arameter, the share of unskilled abor in the ndustrialroductionfunction, ainly eterminesheratio f skilled o unskilled eople nthegrowth egime.tis hard to match his ratiotodata,since there remore than wo skill evels in the realworld. fwe define kill tomeancompletedhighschool,skilledpeople wouldmakeupmost of thepopulation, ince alreadytodayalmost90 percent f recent chool cohortssatisfyhis riterion. n theother and, f skilledmeanscompleted ollegeeducation,henumber f skilledpeoplewoulddropbelow 30 percent. ince collegeeducations rare nsome of thecountries nd timeperiods hat am interestedn, chose a compromisewithhigherweight nhigh chool. Theparameter was chosen tobe 0.22,which esultsn75percent fthepopulationn thegrowth egime o be skilled.I now turn o the Malthusianregime.Most parameters re identicalto thegrowthregime we only need to calibratethe agricultural echnology nd the child laborparameter.he fixed ost for hildren is a scaleparameterndcan be chosen rbitrarily.chosep = 0.001. The parameter F, he rate oftechnological rogressntheagriculturalsector, eterminesertilityn theMalthusian egime. n Britain hetotalfertilityatewasabout 4.0 in 1700, and values in otherEuropean countrieswere similar.The valueyF= 1.32yieldsthisfertilityate ntheMalthusian egime.Notice that argetingertilitywhileabstractingrom hildmortalityeads toa counterfactualrediction:n themodel,population rowths veryhigh ntheMalthusian hase,while ctualpopulation rowthnmostcountrieswas ratherow before he onsetof the ndustrial evolution. nlesschildmortalitys integratednthemodel, t s notpossibletomatch oth ertilityndpopulationgrowthn thepre-industrialhase.While such an extensionwouldbe possible, he mainfocushere s thetransition,ot theMalthusian hase.Therefore,he calibrationmatchesconditionst theonsetoffertilityecline,whenpopulation rowth adalreadyncreasedsubstantially. ur key requirementsre thatfertilitys highand incomeper capita isroughly onstant efore he onsetof thetransition. lso noticethatwhile thecalibratedvalue foryF s smaller hanyl9 hisfeatures notnecessary or he ransitiono takeplace:y7 0 is all that s needed.The child aborparameterv ishard o calibrate ince theres only imited videnceonthe extent f child aborbefore he ndustrial evolution. owever,4>vhas to be chosensufficientlyarge o allowa Malthusian egime.fu s notunrealisticallylarge.From theperspective f theparent, hekey question s how muchof household



20/38

ACCOUNTINGORFERTILITYDECLINE DURINGTHETRANSITION O GROWTH 365incomes contributedy hildren. orrellndHumphries1995)find hatn a sample fworking-classamiliesnEnglandround ,800 hildrenontributedetween 7 and32percentf householdncome, hereasnthemodel ncome rom hild abormakes ponly 5percentf ncomen families ithworkinghildren.For he arametersf he griculturalechnology,chose S= 0.1andQy= 0.5. Withthesehoices,he hare foutputoing o and entss 40percent,nd killed dultsmakeupabout percentf he opulationntheMalthusianegime. lower ound n the andshare anbederived rom heEnglishNational ccountsor1688 n Deane andCole(1969).Atthat ime entsmadeup27percentf nationalncome. ince ome fthe 4percentfnationalncome oing onon-rentropertyncome ndprofitsre lsoderivedfromand, 0percentsa reasonableower ound or he hare f and.Onthe ther and,share-croppingontractsypicallyllocated 0percentfoutputothe and wner. incenot ll ofnationalncome asderived romgriculture,0percents then nupper oundfor he and hare.Mychoice ies nthemiddle etweenhese ounds.6. ComputationalxperimentsThis ection ses he alibrated odel odeterminehetherolicy hangesanhave argeeffectsuringhe ransition.simulatehemodelunderhree ifferentssumptionsngovernmentolicies, oughlyorrespondingo the asesofBrazil,Korea ndEnglandmentionedarlier. startydescribinghese oliciesnmore etail.6.1. Actual olicies nd ModelPoliciesKorea ndBrazil repolar ases nterms feducationalndchild abor olicies.Koreainstitutedsystemffree,ompulsoryducationromhe ges f6-12 n1949, ightfterindependence.fterheKoreanwar hegovernmentnstitutedCompulsoryducationAccomplishmentlan, ndby 1959theprimarynrollmentatereached 6 percent.Strictlynforcedompulsoryducationerved s aneffectiveonstraintnchildabornaddition o direct hild labor restrictions.ccording o the InternationalaborOrganizationILO), n1960only .1percentfthe hildrenromero o 15yearswereeconomicallyctive,ndby1985 nly .3percentf he hildrenetweenges10 and 14participatednthe abormarket.InBrazil, y he etterf heawfree nd ompulsoryducation as ntroducedlreadyin1930. npractice,owever,rimarychooling as not vailablenmany uralreas,and othe resentay he vailable chools reoften fpoor uality.n1965 he rimaryenrollmentatewas till elow 0percentnruralreas. heneglectfprimaryducationin Brazil analso begauged rom ducation inances.n 1960, ess than 0percentfpublic pendingn education asdirectedothe rimaryector, hile he orrespondingfigure as about 0percentorKorea.Child abor egulations lessrestrictivenBrazilthannKorea.WhileKorea ignedn ILO conventionhat ules utchild aborunderthe geof14,Brazil idnot. heminimumgeformploymentnBrazil snow12, ndeven his imits not lways nforced.n 198518.7percentf he hildrenetweenges



21/38


22/38

ACCOUNTINGORFERTILITYDECLINE DURINGTHETRANSITIONTO GROWTH 367

percentf he ducationost or killedhildren,nd hild abor s ruled ut.While n heKoreanpolicy hereformakesplace immediatelynce the ndustrialechnologysintroduced,nthe tylizednglisholicy he ame eformsre arriedutwith delay fthreeeriodsor75years) fter he eginningf the ransition.hepolicies sed n thesimulationsrenotntendedobe exact opies f he eal-worldolicies, ut obestylizedversionshatmphasizehe ifferenceetweenhe olicy egimes.speciallyor razil,thepolicydescriptionn themodel s not "fair" formore ecent ears: upportoreducation as ncreasedn the astdecadesandfertilityas beenfallingaster).All economies tart rom dentical onditions.he initial alues foragriculturalproductivityndthenumberf skilled nd unskilled dults re chosen o start heeconomiesntheMalthusianteadytate. heproductivityn ndustrys chosen uch hatthe ransitiontartswoperiodsfterhe tart fthe imulation.part romhe ifferenttimingfpolicy eformsnoreformnderheBrazilian olicy,mmediateeformndertheKorean olicy, elayedeformnder he nglish olicy),llsimulationsre dentical.6.2. EffectsnFertilityndGrowthThe outcomes fthe imulationsan be summarizeds follows. hetimingfpolicyreformsas a major mpactn the imingnd peed fthefertilityransition.ithoutpolicy eform,hedecreasenfertilityuringhe ransitionogrowths small.Whenreforms introduced,t causes an immediaterop n fertility,nd the transitionoreplacementertilitys completed ithinwogenerationsfter hereform.n addition,loweringhe pportunityost feducationncreasesrowthnGDPper apita ince hefractionf killedworkersn he opulationncreases. ut f he wo olicies onsidered,child abor estrictionsccount or hebulk fthe esults, hile he ffectsfeducationsubsidiesre omparativelymall. he samepolicy eformslso have majormpactnthe volutionf he ncome istribution.s long s nopolicies re ntroduced,nequalityrises uringhe ransition,ince he kill remiumoesup.Once he olicy eformowersthe pportunityost f ducation,owever,he ractionf killedworkersncreasesvertime,whichowershe kill remiumndoverallnequality.Figure shows he imulatedath orGDPper apita ndthe otal ertilityate nderthedifferentolicies.n thegraphs or heKorean ndEnglish olicies, heBrazilianoutcomesre ncludedwith ashedines) s the enchmarkasetofacilitateomparisons.The ime xis s abeled uch hat achmodel eriod orrespondso25years,nd he tartof the ransitionothegrowthegimes placed n theyear1950 for heBrazilian ndKorean olicies,nd n1800for he nglish olicy. DP per apita s initiallyonstant,since he imulationtartsntheMalthusianegime herewages reconstant.nce heindustrialechnologys introduced,ncomes tart ogrow.The total ertilityate ncreaseslightlyeforehe tart f thetransition,ndthendeclinesn all simulations.hespeedandtimingffertilityecline, owever,ariesacross he imulations. ith oreform,ertilityecreasesnly lowly o a total ertilityrate f bout . With n mmediateeform,he otal ertilityate rops elow alreadytthe tartf he ransition,nd eplacementertilitys reachedn essthan wogenerationsafter he ake-off.he maximumifferencenfertilitycross heBrazilian nd Korean



23/38

368 MATTHIAS OEPKE

Noreform"Brazi Noreform"Brazil"8f ' ' | I ' '

0' ""r ' 1 1 1900 1950 2000 2050 1900 1950 2000 2050Immediateeform"Korea" Immediateeform-Korea"

6 / '^ \ ~~ ^ "^I4 ^


24/38

ACCOUNTINGORFERTILITYDECLINE DURINGTHETRANSITIONTOGROWTH 369whichompareso growthate f nly .3percentnderhe razilianolicy.nthe ata,we also observe hat orea, s well s otherountries ith fast emographicransition,experiencedasterrowthnGDP percapita han low-transitionountriesikeBrazil.Accordingothe ennWorld ables, he verage rowthatenGDPper apita etween1960and1990was6.7 percentnKorea, ndonly2.8 percentnBrazil.Even fweconsiderhe hortereriod rom 960 o1980 whichxcludesheLatinAmericanebtcrisisnthe 980s),verage rowthas6.2percentnKoreaversus .4percentnBrazil.Thegrowthate ifferentialnthe ata s largerhan he ifferentialn themodel,whichsuggestshat ocialpoliciesnd ducationecisionsrenot he nly actorxplainingherelativeerformancefBrazil ndKorea.Given hat he wo ountriesredifferentlonga numberfdimensions,twould nfact everyurprisingf he olicies onsiderederewere hemain xplanationor ifferencesn economic erformance.evertheless,heresultsuggesthat he oliciesnd heirffectsnfertilitynd ducationecisionsre nimportantart f he verall xplanation.Thereason or he rowth-rateifferentialnthemodel s thatwith ducationubsidiesand child abor estrictions,he killed ractionf thepopulationncreasesast,whichraises utputince hendustrialechnologys skill-intensive.15nder heKorean olicy,the ractionf killed dultsnthe opulationncreasesrom percentn 1 50toalmost70percentn2000.Underhe razilianolicy,he ncreases frompercentoonlybout33percent.nthe ata,we observearge ifferencesnaveragekill etween orea ndBrazil s well. nKorea, verage ears f choolingfthepopulationged25 andoverincreasedrom .2 n1960 o7.8 n1985. nBrazil, he ncrease as from .6 n1960 oonly .5 in 1985.Notice hat f the hree hannelshroughhich he peed ffertilitydeclineffectsDP per apita nly hehuman-capitalhannels presentn themodel.This hannelaptureshat ecause f the uantity-qualityradeoff,arentsncrease heeducation f their hildren hen ertilityalls.Themodel bstractsrom he apital-dilutionhannellower opulationrowthncreaseshe apital tock erworker)nd hecohort-sizehannelrapid ertilityecline owers hedependencyatio).f weextendedthemodel o apturehese ffectsswell, he redictedrowthifferentialould e evenlarger.6.3. Effectsn the ncomeDistributionApart romnfluencingertilitynd output, olicychanges lso affect he ncomedistribution.hegraphsnthe eft-handideofFigure shows ncome ini oefficientsfor he imulations.nthemodel,nequalitys determinedy he kill remium,hichnturn ependsn therelativeupply f skilled nd unskilledabor.The Korean olicyincreaseshe elative umberf skilleddults,which ffsetshe ncreased emand orskilledaborn he ndustrialector.herefore,n he imulationith n mmediateolicyreformnequalitysgenerallyow nddecreaseslightlyuringhe ransition.he nitial15 Becauseproductivityrowths exogenous,he effect n growthates s transitory,ut there s apermanentevel ffects long s policies iffer.



25/38

370 MATTHIAS DOEPKE

Figure 3. Gini coefficientsnd fertilityifferentials.

increasentheGini t he ime f he olicy eformccursince he emandor ducationsuddenlyncreases. his emporarilyaises he kill remiumecause eachersre killed.In theBrazilian imulationnskilleddults ontinue omakeup themajorityf thepopulation.he increased emand or kill n the ndustryranslatesnto n increasedwagepremium,o thatnequalityncreasesuringhe ransition.ith delayed olicyreform,nequalityirstncreases,hen ecreases uringhe ransition.Thusonlywith heEnglish olicy o we observe hepronouncednverse-U-shapedrelationshipetweenncomend nequalitynowns theKuznets urve.n the ealworld,this atternf nequalityver he oursefdevelopmentasobservedn he ountrieshatindustrializedirstKuznets,955, ooked tEngland, ermany,ndtheUnited tates),butfor ountrieshat tartedogrowmore ecentlyhe vidence smixed. pecifically,neither oreanorBrazil xhibit Kuznets urve.n Korea nequalityasgenerallyow,and here as ittlehangenthencome istributionver ime. etween 955 nd1985,theGini oefficientaries etween.3 and .4. nBrazil,nequalityas lways igh, ith

Noreform"Brazi" Noreform"Brazil"0.6

' 4" * "*-^^ 3

5 / 2 j- - Unskilledol , . 1 o> 11900 1950 2000 2050 1900 1950 2000 2050

Immediateeform"Korea" Immediateeform"Korea"0.6 4 Xx*5 .4 vL ** .. ^5 2 L... :...^^ ^

\s,. - - UnskilledOl . I 0' " 11900 1950 2000 2050 1900 1950 2000 2050Delayed eform"England" Delayed eform"England"0.6 I 4f" ~v> :

S 0.4 / """"""X *i 0.4 // """"""X\ 2 - -- - Unskilledol . . 1 ol . J1750 1800 1850 1900 1750 1800 1850 1900



26/38

ACCXDUNTINGORFERTILITYDECLINE DURINGTHETRANSITION O GROWTH 37 1a Ginibetween .5 and 0.6 (see Deininger ndSquire,1996). The income sharegoingtothepoorest 0 percent f theKoreanpopulations about he ame as the haregoing o thepoorest 0 percentn Brazil.Evenconsideringhat hemodel abstracts rom omefeatureswhich are relevant orexplaining he incomedistribution,16heresultsdo show thatinteractionsfpublicpolicieswith ertilityecisions an have arge ffects n thegrowth-inequality elationship.hismayprovide n explanationwhyKuznets urves howup insomecountries,utnot nothers.A moredirect est f the distributionalmplicationsfthemodel would look atwageinequality, speciallythe premiumfor skilled labor, since the skill premium s thedriving orcebehind hanges n inequalityn the model. The skillpremium eacts o thepolicies throughhegeneral-equilibriumffect feducation ndfertilityecisionson therelative upply f skilledandunskilled abor.Clearly, hisgeneral quilibriumffect scentral o the results: ertilityalls fast n the Korean simulation reciselybecause thepoliciesdeliver low skillpremium,whichmeans that ducation s affordable ven forunskilledparents. ark et al. (1996) comparewage inequality n Brazil and Korea in1976and 1986.Consistent ith hepredictionsf themodel,they indmuchhigher killpremia in Brazil than in Korea. Moreover,there s a substantialdecline in wageinequalitynKorea between 1976 and 1986. Specifically, arket al. estimate standardearnings quation, hat s, the ogarithmfearningss regressed n education nd workexperience. n 1976, high school graduates n Brazil earned a 60 percentpremiumrelative o workerswhofinishedrimarychool,whilethepremiumwas only35 percentin Korea. Foruniversity raduates, hepremiumrelative o primarychool) was 201percentn Brazilversus121percentn Korea. In 1986,the differences ere even morepronounced.n Brazil,thepremiaforhigh choolanduniversity raduateswerestill55and 188percent, espectively,hile nKorea thepremiahad fallen o ust 10percent nd76 percent.In themodel, hanges noverallfertilityre driven ydifferencesnfertilityetweenskilled nd unskilled arents. hegraphs n theright-handide ofFigure breakdownthetotalfertilityate neach simulation ythetype f theparent.n theBrazilian imulationthere re no education ubsidiesorchild aborrestrictions.nskilled hildren recheaprelative o skilled hildren,ndthereforenskilled arentsontinueohavemany hildrenthroughouthe transition.nitially,verage fertilityncreasesforbothgroupsofparents,and theaggregate otalfertilityate fallsonlybecause skilled dultsbeginto makeup alarger raction f thepopulation. he fertilityifferentialetween killed and unskilledparents tays arge.Under the Koreanpolicy,thefertilityifferentialetweenthetwotypes fparents eclinesrapidly fter hepolicy change.The abolition f child abor andeducation ubsidies mplythat skilled children re only slightlymoreexpensivethanunskilledchildren,which results n a small fertilityifferential etween skilled and

16 For he omparisonf Brazil ndKorea, he oleof andownerships essential. fter landreformtthe ndofJapaneseccupation,and wnershipasdispersednKorea, ut lwayshighlyoncentratedin Brazil. ndeed,f concentratedandownerships introduced,hemodel eneratesigh nequalityithalmost o timerendnder heBrazilian olicy.



27/38

372 MATTHIASDOEPKE

Figure . Outcome ith solated olicies.

unskilled arents. he same effect ccurs n theEnglish imulation fter henewpoliciesare introduced.In thedata, in line withthepredictions,he available evidence showssmall fertilitydifferentialsn Korea and large differentialsn Brazil. Accordingto United Nations(1995), in 1986Brazilian womenwithout ormal ducationhad a totalfertilityateof6.7,while for women with seven or moreyearsof educationthe number s 2.4. Thus thefertilityifferentialmounts o more han our hildren. lamandCasterline1984) reportthat n 1974 thetotalfertilityate forKorean womenwithout ormal ducationwas 5.7,whileforwomenwith evenor moreyears feducation herate s 3.4. Thisgivesa fertilitydifferentialf 2.3, roughly alf of the differentialn Brazil.17England, s well as otherindustrializedountries, as small fertilityifferentials ithin hepopulation oday ncomparison odeveloping ountries.In summary, e see that hepoliciesconsideredhave largeeffects n fertilityeclineduring he transition o growth. hese differencesranslatentofurthermplications orGDP per capita, average education levels, fertility ifferentials,nd the incomedistribution hich ine up well with the evidencefor our examplesBrazil and Korea.So far heanalysisofpublic policywas restrictedo a combination ftwopolicies,aneducation ubsidy nd child abor estrictions. natural uestion o ask s which fthe wopoliciesis more mportantorgeneratingheresults escribed bove. It turns utthat hechild labor restriction as a muchbigger mpactthanthe educationsubsidy.Figure4

17 Unfortunately,heres no datafor razil nd Korea or he ameyear.However,iven he verall all nfertility,t seems ikelyhat he ertilityifferentialyeducationn Koreawas even owern 1986 hanin 1974.

Child Labor estrictionnly Child Labor estrictionnly

0' ~r^ . 1 I 1900 1950 2000 2050 1900 1950 2000 2050Educationubsidynly EducationubsidynlyI' /^ eiM ^y i \1900 1950 2000 2050 1900 1950 2000 2050



28/38

ACCOUNTING ORFERTILITYDECLINEDURINGTHETRANSITION O GROWTH 373showsoutcomes orGDP per apita ndfertilityf ither ducation ubsidies r child aborrestrictionsre introducedn isolation. fonlya child abor restrictions introduced,heevolution f incomeper capitaand fertilitys similar o theKorean simulation,whichintroduces othpolicies.With child aborrestrictionhere s anunambiguousncrease nthe cost of unskilled hildren,whichreducesfertilityven faster ompared o the casewhen bothpoliciesare combined. n contrast, hen there s onlyan education ubsidy,fertilityctuallyncreasesnitially,nd the ubsequent ecline smuch maller han ntheKorean simulation. hereason s that heeducation ubsidyworks ntwo differentays.Since skilled children ecomecheaper,moreunskilledparents ecide to educate theirchildren,which owersfertility.t the same time,however,fertilityncreases for theskilled arentswho wouldhave decided oeducate heir hildren venwithouthe ubsidy.The two effects re partially ffsetting,nd the overall impact s small. These resultsunderline he mportancef including he cost of the children's ime n theopportunitycost ofeducation.nfact,fwe did not ccountfor he ost ofthe hildren's ime,t wouldbe ratherurprisinghat nEnglandfertilityell fastestustat the timewhen freepubliceducationwas introduced.A welfare nalysis f thepolicies s made difficultythefact hat killed ndunskilledpeoplehaveopposing nterests. herefore hepoliciescannotbe ranked singthe Paretocriterion. he education ubsidy,however, s beneficial or dults of both skills in theperiodwhen thesubsidy s introduced. uture enerationsf skilledpeoplehave lowerutilitywith hepolicybecause of a lower skillpremium.A child abor restrictionlonehurtsboth skills in theperiodwhen it is introduced,ince the unskilledparents oseincome, nd theutilityf skilled hildren alls.However,future enerationsf unskilledpeoplebenefit rom hild abor restrictions. combination f the twopolicies yieldsthehighest rowth athforGDP per capita,but future killedgenerationsre stillbetter ffwithout hepolicies.

7. ConclusionsThispaperdevelops theoryhat s consistent ith phaseofstagnation uringwhich heeconomy xhibitsMalthusian eatures,ollowedbya transitiono a growth egime.Theeconomictransitionogrowths accompaniedbya demographicransition rom ightolow fertility.he model is used to assess whether hild aborrestrictionsndeducationsubsidies an have arge mpacts n thefertilityeclinethat ccompanies he ransitionogrowth.Thepossibilityfchild abor mplies hat hevalue of a child's timebecomespart ftheopportunityost ofeducation.18Withoutccounting or hevalue of the hildren's ime,twould be verypuzzling hat nmany ountries ertilityell fastestustat the time whenfree ubliceducationwas introduced.When theres no alternative se for child'stime,18 The role f childaborndeterminingertilityas been nalyzed yRosenzweigndEvenson1977). nlinewith he esultsere,hey ind hat he conomic ontributionsfchildrenhroughhild abor re nimportanteterminantor ertilityates.



29/38

374 MATTHIASDOEPKEfree ducation owersthecost of children ndthereforehould ead tohigher ertility.ncontrast,nce we account forthefullopportunityost of education ncluding otentialchild abor ncome, ducating child s costly ven fschoolsare free.A steepdecline nfertilityightftermajor ducation eformss thereforeustwhatwe should xpect o see.Indeed,we find hat ducation nd child aborpolicieshavelarge ffects nthefertilitytransition. he policies also determine he evolution of income per capita, averageeducation, nd the ncomedistributionf a country uring he ransitionogrowth.Whencomparinghe twopolicies,the effects f education ubsidies rerelativelymall,whileaccounting or hild aborregulationss crucial.The results how that ccounting orpolicychanges s importantorunderstandingheexperience f differentountries uring he transitionrom tagnation o growth. hisfinding oes not rule out thatotherfactors ould play an importantole as well. Forexample,the model abstracts rom hangesin mortalityates,even thoughdecliningmortalitys an equally important spect of the demographic ransition s decliningfertility. s a simple extension to the model, changes in child mortality an beincorporated y introducing probabilityf survivaluntil dulthood. n the calibratedmodel,for small increases n child mortalityhenumber f births ncreases,but thenumber f surviving hildrendeclines.Feedingrealistic urvivalratesinto the modelmakes tpossibletomatch ctualfertilityumbersmore losely,buttheeffects fpolicychanges re still he ameand dominate he ffectsfchanging hildmortality.19n orderto ncorporatedultmortality,heframework ouldhaveto be extended oallow formorethan woperiodsof life.Another pen question s how the tylized olicies n themodelareimplementedn thereal world.Child aborregulationsresubject o an obviousenforcementroblem,whichis severegiven hatmuch hild abor akesplaceinagriculture,here irect upervisionsdifficult. number f studieshave found hat fficial hild aborrestrictionso little oconstrain hild abor. n practice, ompulsorychooling aws often ppearto be a moreeffectiveonstraintnchild abor han irect egulation.20rom nadministrativeoint fview, t s easier tocheck that hildrenhowup ina givenclassroom t a certain ime, sopposedtoascertaininghat hey o notengage n llegalwork tanytime ndany place.Therefore,ven though hepolicies can be used separatelyn themodel,they re bestthoughtf as a jointpolicy npractice.A question eyond he copeof thispaper s howthegovernmentoliciesthat re takenas exogenoushere reultimatelyetermined.wo recent aperswhichtry o understandthepolitical conomyof such reformsreAcemogluand Robinson 2001), where richelite introduces eforms o reducea threat f revolution,nd Galor and Moav (2003),where the elite creates social institutionsoluntarilyn orderto reap humancapitalexternalities.n thetheory f Galor andMoav, thetiming feducationreforms eflects

19 Within hedynastic tilityramework,hangesn childmortalityateshaveonlyminor ffectsnfertilityven f stochasticurvivalndsequentialertilityhoice re taken nto ccount,ee Doepke(2004).20 For xample, singUS data,Margo ndFinegan1996)find hat hild abor estrictionsreespeciallyeffectivef ombined ithompulsorychoolingaws.



30/38

ACCOUNTING OR FERTILITY DECLINEDURINGTHETRANSITIONTO GROWTH 375

changesn the emand or kill. rom his erspective,he xpansionfeducationn thelatenineteenthenturyn Britain ayhavebeen ausedby n ncreasedolefor killedlabornproductionn the ameperiod. imilarly,oepke ndZilibotti2004)argue hataftern ncreasedemand orkilledgrowingumberfparentso end heirhildrenoschool,hose arents ill upporthe ntroductionf hildaboraws, ince hey o ongerdepend n child abor ncome. hus,while his aper oncentratesnthe volutionffertilityor iven overnmentolicies,or utureorkhereppearsobe some cope orunified heories hatexplainchanging overnmentolicies alongside ertilityndgrowth.21In thediscussion f the ransitionromtagnationogrowthconcentratedn cross-countryifferencesnfertilityecline. differenthallenges to xplainwhyhe ake-offoccurs at differentimes n differentountries. learly, hegovernmentoliciesconsidered ere annotxplainwhy urope ook ff irst,iven hat conomic rowthstartedongbefore he ntroductionfbroad ducationnd hild aboregislation. hencomparingcross evelopingountries,he olicies ave he otentialocause delaynthetake-offf about10 to 20 years,whichs still oo little oexplain heobserveddifferences.norderomake rogresslong hisine,twillbenecessaryomove eyondthe ssumptionf xogenous roductivityrowthnd ntroducetheoryf echnologicalprogress.heresultsnthispaperdo notdependn any wayon the ssumptionhatproductivityrowthsexogenous. s a firsttep eyondxogenous rowth,t spossibleto ink he ate ftechnologicalrogresso thenumberf killed eoplen the conomy.Such model anexplainwhyhe ate f conomicrowthncreaseduringhe ndustrialrevolution,nstead f umpingo thegrowth-regimeevelrightway.The effects fgovernmentolicies ngrowth ould eamplified.

Appendix . Definitionf n EquilibriumThis section ntroduces he remaining quilibriumonditions,tarting ith thedeterminationf labor upply. killed dultsdistributeheir imebetweenworking,raisingndteachingheir wnchildren,ndteachinghildrenf unskilled arents.Thereforehe otal upplyf skilledabor s isgiven y:

**(*) =[ -(* + 05) is^sW s(S,x) - s^u(x) nvfrx)]Ns-tslu^sWnsiU^Nu. (16)Unskilledabor v issupplied yunskilleddults ndby hildren ho o not oto chool:21 ConcerninghecontrastfKorea ndBrazil, n additional actor hat s likely o be importants theinitial istributionfwealth. his hould eespeciallyelevantor olicies,uch s the nesconsideredhere,hat ave large mpactn the volutionf nequalityna country.istorically,razil lways ada high oncentrationf wealthngeneralndof andownershipnparticular,hereas orea arried uta landreformfterndependencehat eveled hedistributionf wealth. ee Galor,Moav, nd Vollrath(2003)for omework nthe ole f andnequalityndevelopment.



31/38

376 MATTHIASDOEPKE

+ uofo-c/to M *s+ *(/-(/o Mtf>*)y/]. (17)Inequilibrium,aborupply as o qual abor emand or ach ypef abor. assume hatskilled dults anperformoth he killed nd he nskilled ork, hile nskilleddultscando unskilled orknly. nder his ssumption,he killed age annotall elow heunskilled age:

"sM > Hfc(*). (18)Themarket-clearingonditionsor he abormarketre:

LFS(x)+ LIS(x)< Ls(x), = ifws(x)> w^x), (19)LFU(x)+Llu(x)=Lu(x) + [Ls(x)-LFS{x)-Lls(x)]. (20)The flat axt which inanceshe ducationubsidy as to be chosen o observe udgetbalance.The correctax rate s givenby dividinghe otal xpendituren schoolingsubsidiesytotalwage ncome:

TW Ls(x)ws(x)+Lu(x)wu(x)sN'sWs(xr [ >where 's s the otal umberf killed hildren. otice hat or he omputationftotallabor ncomewe have oaddthencomef he eachersothewage f he sualworkers.Teachers eceivewagesfor heirwork nd are taxed ike ll other dultsnthemodeleconomy.The final quilibriumonditions the awofmotion or opulation.ince abstractfrom hildmortality,henumberf adults f a given ype omorrows givenbythenumberf childrenfthatype oday:

**s ^sto ns(S,x)Ns+ A^jc) ns{U,x)Nv, (22)K = ^s- i/to i/(M Ns+ kv^v(x) nv(U9x)Nv. (23)We nowhave ll the ngredientst hand hatreneeded o definenequilibrium.Definition (RecursiveCompetitive quilibrium) Givena governmentolicy{uid}> recursiveompetitivequilibriumonsistsf tax unction,value unctionsVsandVUtabor upplyunctionss andLUfabordemandunctionsFS, FU, IS, ndLiu,wage unctionssandwUfmobilityunctionss_>s, .s_>u,y^s*and^u^>u>a^mapping intoR+,policyunctionss ndnvmapping5, U} x X into +,and lawofmotion mapping intotself,uch hat:

i. Thevalue unctionsatisfyhe ollowingunctionalquationor e {5,U}:Vk(x) ma* {c" + P(ns+ ) -[s^(^) + t/^(x')]}. (24)subjecto the udgetonstraint9) and the awofmotion f g(x).



32/38

ACCOUNTING ORFERTILITYDECLINE DURINGTHETRANSITIONTO GROWTH 377ii. For ,j e {5, U}, ifAj_>j(x) 0,tij(i,x) ttains hemaximumn 24).ill. The ax unctionsatisfieshe overnmentudgetonstraint21)iv. Thewagesws ndWynd abor emandFS, FU, IS, ndLw satisfy5)-(8) and(18).v. Labor upplys andLv satisfies16) and 17).vi. Labor upplys andLv and abordemandFS, FU, IS, ndLw satisfy19) and(20).vii. Themobilityunctions.s_>s,.s_>Uty _>s,nd^u^u satisfy10).viii. The awofmotionfor he tate ariable isgiven y 4), (22),and 23).

Theequilibriumonditionso not nclude market-clearingonstraintor hegoodsmarket,ecause t holds utomaticallyyWalras'Law. In conditionii) above, t isunderstoodhat arentshooseonly netype fchildren.n otherwords,aying hatns(S,x) attains he maximumn (24) means that ns= ns(S,x)1nu 0} and theconsumptionthat esults rom hebudgetonstraint aximize tility. aximizationsonly equiredfa positive umberfparentshoose he ype f childrennquestion.Conditioniii) is thegovernmentudgetonstraint.onditioniv) requireshatwagesequalmarginalroductsnd hat he killedwagedoesnot all elow he nskilled age,conditionv) links abor upplyopopulationnd educationime, onditionvi) is themarket-clearingonditionor he abormarket,onditionvii)requireshat or ach ypeof dult he ractionsavingkilledndunskilledhildrenum oone, nd onditionviii)defineshe aw ofmotion.

Appendix . Proofs or ll PropositionsProof fProposition. Theprofit-maximizationroblemf firmnthe ndustrialectorisgiven y:

maxU (ls)1 a (/)" ws(x) s- wv(x) }. (25)The first-orderonditionor maximum ith especto vgives:

{ls} =- IT* Plugginghis xpressionack nto25) yields formulationf theprofit aximizationproblems a functionfunskilledabor nly:



33/38

378 MATTHIAS OEPKE

maxj^Mh_^y1'1"'*/,,Wu(x)/f,J. (26)Since thisexpressions linear n lUy roductionnthe ndustrialectorwill be profitableonly f we have:

whichcan be rearrangedoget:

which s (11).The first-orderecessary onditions or maximum f theprofit-maximizationroblemofa firm nagricultureregiven bythewage conditions5) and (6):^-Awa-.z'-'-'-- (27)Since theobjectivefunctions concave,the first-orderonditionsre also sufficientormaximum. t is therefore ufficiento show thatforanyws(x),wu(x) > 0 we can findvalues for skilled and unskilled aborsupplyLFS and LFU such that 27) and (28) aresatisfied. he required alues are givenby:

/ A \O/l-0s-0max


34/38

ACCOUNTINGORFERTILITYDECLINE DURINGTHE TRANSITION O GROWTH 379

continuouslyifferentiablen/, ftherewere n interiorolution,heoptimal wouldhavetosatisfy irst-nd second-orderonditions or maximum. solve for heunique/whichsolves the first-orderondition,nd showthat his/ does not satisfy he second-ordercondition. hisproves hat here reonlycomer solutions.I willnamethemaximandU( ). The firstnd secondderivatives fU with espect o/are: 8/ .-.L.(I_V/+ V)~Y/ k+iWEi)[ \Ps PuJ Ps PuJ \Ps Pu J/ [ \Ps PuJ Ps PuJ \Ps Pu J\Ps PuJ \Ps PuJl

9/2 \Ps PuJ Ps PuJ[(1+^i_v/+iz/yY^+(w)^)_2^_M'.uJ\Ps J J\Ps PuJ\Ps Pu J \Ps Pu J \Pu PsJ_Inthefirsterivative,or < / < 1 thefirstermwithin he uter racketsspositive. oran interior olution o be possible, t has to be the case thatVs/ps Vy/py,becauseotherwisehe econdterm s also positive nd thefirst-orderondition annotbe satisfied.ThereforefVs/ps> Vy/py,we are done. For the case thatVs/ps< Vy/pv, ettinghefirst erivative qual to zeroand solvingfor/yields:

r_ \PS Pu) \PS PuJv1 cwuyPs uJ\Ps v)I will now plug this value for/ into the second derivative o verify hat the secondderivatives positive,o that he ritical oint s not maximum. he secondderivativespositive f thefollowing nequality olds:

\Ps PuJ \Ps Pu J \Ps Pu J \Ps PuJPluggingnour value for yields after omealgebra:

Pu \Ps PuJ Pu I \Ps PuJ \Ps PuJl Pu \Ps PuJ

Pu\Ps PuJ Pu\Ps PuJ'Vu Vythe econd-orderondition or maximum s not atisfied,nd therefore



35/38

380 MATTHIASDOEPKEthere sno interiormaximum. onversely,fVswere maller hanV\j, herewouldbe onlyunskilled hildren or ure, incethey recheaper o educate.Thus onceagainwe obtaincorner olution.Thus in everycase there reonlycorner olutions. amilies have eitherunskilled r skilledchildren, uttheydo not mix. ProofofProposition . It is helpful o consider he formulationf theproblemn whichadults choose the total education ostE, so that henumber f children quals //?, oradults who choose to have children of type i. The maximizationproblemin thisformulations:

max (w- Ef + p(E/Pi)1V,l (29)O


36/38

ACCOUNTINGORFERTILITYDECLINE DURINGTHETRANSITION O GROWTH 381

Appendix . Notes nComputationWithinheMalthusianegimend thegrowthegime,hemodel anbe computediastandardalue unctionterationn discretizedtatepace.The nitialuess or he aluefunctionsscomputedy ettinghenumberf hildreno ero, o that tilitytemsromconsumptionnly. uringheterations,or giventate ,the lgorithminds state nthenext erioduch hat he esultingertilityecisions f dultsre onsistentith tatey. Afterhe terationsonverge,he quilibriumaw of motion anbe used ocomputesteady-statealues.Alternatively,he teadytateanbecomputedy olving systemfequationshat efineshe teadytate.Inprinciplet spossible ocomputehe ntiremodel, ncompassingheMalthusianregime,he ransition,nd thegrowthegime, ith he amemethod escribedbove.However,ince he tate ectorsfour-dimensional,omputationsould itherake erylong r would e imprecise.hereforeuse a shootinglgorithmhat irectlyomputesthe quilibriumath verT periods romny tartingaluex0for he tate ector. hecomputationsre started numberfperiods eforehe ndustrialechnologyecomescompetitive.he numberfperiods tobecomputedas tobe chosenufficientlyargesuch hat he conomyscloseto the alanced rowthath t T. Whetherhis s the asecanbecheckedy omputinghe rowthegimes describedbove eforeomputinghetransition.healgorithms not uaranteedoconverge,ut t workswell npractice.AcknowledgmentsThispapers basedonmyPh.D. dissertationttheUniversityfChicago2000). amgratefuloGary ecker,dward rescott,obertownsend,nd specially obertucasfor heiruidancend ncouragement.orkshoparticipantstChicago,he ED annualmeetings,he Max Planck nstituteorDemography,he FederalReserveBankofMinneapolis,Wharton,ennsylvania,ostonUniversity, estern ntario,UCLA,Stanford,ochester,irginia, CL, Cambridge,IES, Illinois,Minnesota, SC, UCRiverside, uke, ndBrown rovidedmany elpfulomments.also benefitedromsuggestionsySylvain essy, dedGalor, irkKrueger,eeOhanian,anaZakharova,Rui Zhao, and an anonymouseferee. inancial upport y the National cienceFoundationgrantES-02 7051) sgratefullycknowledged.ReferencesAcemoglu,., and J.A. Robinson.2001)."A Theoryf Political ransitions,"mericanconomic eview91(4),938-963.Alam, ., andJ.B. Casterline.1984).Socio-Economicifferentialsn Recent ertility.orld ertilityurveyComparativetudies o.33,Voorburg,etherlands:nternationaltatisticalnstitute.Barro, .J., ndJ.W.Lee. 1993). InternationalomparisonsfEducationalttainment,"ournalfMonetaryEconomics2,363-394.Barro, .J., ndJ.W.Lee. 2001)."Schooling ualityn a Cross ection fCountries,"conomica8(272),465-488.



37/38

382 MATTHIASDOEPKEBecker, .S.,andR. J.Bamo.1988).A "Reformulationf he conomicheoryfFertility,"uarterlyournalofEconomics3(1),1-25.Becker, .S.,K. M.Murphy,ndR. Tamura. 990. Human apital, ertility,ndEconomic rowth,"ournalofPolitical conomy8, 12-37.Bloom,D. E., and J.G. Williamson.1998). "DemographicransitionsndEconomicMiraclesnEmergingAsia,"Worldank conomic eview 2(3),419-455.de aCroix, .,andM.Doepke.2003)."InequalityndGrowth: hy ifferentialertilityatters,"mericanEconomic eview3(4),1091-1 13.Chesnais, .C. (1992).TheDemographicransition.xford: xford niversityress.Dahan,M.,andD. Tsiddon.1998)."Demographicransition,ncome istribution,ndEconomic rowth,"JournalfEconomic rowth,29-52.Deane,P.,and W.A. Cole. 1969).British conomic rowth688-1959.Cambridge: ambridge niversity

Press.Deininger,.,andL. Squire.1996)."A New Data SetMeasuringncomenequality," orld ank conomicReview 0(3),565-591.Doepke,M. (2004). "ChildMortalityndFertilityecline:Does theBarro-Beckerodel Fit theFacts?"JournalfPopulationconomicsforthcoming).Doepke,M., ndF. Zilibotti.2004).TheMacroeconomicsfChild aborRegulation.npublished anuscript,UCLA and DES.Fernandez-illaverde,. 2001).WasMalthus ight?conomic rowthndPopulationynamics. npublishedManuscript,niversityfPennsylvania.Galor, .,andO.Moav. 2002)."Natural electionnd heOriginfEconomic rowth,"uarterlyournalfEconomics17(4),1133-1 92.Galor, .,andO. Moav. 2003).Das Human apital: Theoryf he emise f he lassStructure.npublishedManuscript,rown niversityndHebrew niversity.Galor, .,O.Moav, ndD. Voilrath.2003).Land nequalitynd heOriginfDivergencendOvertakingn heGrowthrocess: heoryndEvidence. npublishedanuscript,rown niversityndHebrew niversity.Galor,O., andA. Mountford.2003).Trading opulationorProductivity.npublished anuscript,rownUniversityndHebrew niversity.Galor, .,andD. N. Weil.1996)."TheGender ap,Fertility,ndGrowth,"mericanconomic eview6(3),375-387.Galor, ., andD. N.Weil. 2000)."Population, echnology,ndGrowth:romMalthusiantagnationotheDemographicransitionndBeyond," mericanconomic eview0(4),806-828.Greenwood,., ndA. Seshadri.2002). The USDemographicransition,"mericanconomic eviewapersandProceedings2(2),153-159.Hansen, .D., andE. C. Prescott.2002)."MalthusoSolow,"Americanconomic eview2(4),1205-1217.

Haveman, .,andB. Wolfe.1995)."The Determinantsf Children's ttainments:Review fMethodsndFindings,"ournalfEconomic iterature3,1829-1878.Hazan,M.,andB. Berdugo.2002)."ChildLabor, ertility,ndEconomic rowth,"heEconomic ournal112(482), 10-828.Horrell,.,andJ.Humphries.1995). TheExploitationfLittle hildren:hild abor nd he amily conomyinthe ndustrialevolution,"xplorationsn Economic istory2,485-516.InternationalaborOrganizationILO). YearBookofLabour tatistics,ariousditions. eneva:LO.Jones, . I. (2001)."Was an Industrialevolutionnevitable?conomic rowthver heVery ongRun,"AdvancesnMacroeconomics(2),Article .Jones, . F. (1982).Socio-Economicifferentialsn Achievedertility. orld ertilityurvey omparativeStudies o.21,Voorburg,etherlands:nternationaltatisticalnstitute.Kalemli-Ozcan,. (2002)."Does theMortalityeclinePromoteconomic rowth?" ournalfEconomicGrowth(4),411-439.Kogel,T, andA. Prskawetz.2001)."AgriculturalroductivityrowthndtheEscapefrom heMalthusianTrap,"JournalfEconomic rowth,337-357.Knowles, . 1999).Can Parental ecisionsExplainUS Income nequality? orking aper,UniversityfPennsylvania.



38/38

ACCOUNTING ORFERTILITY DECLINE DURINGTHETRANSITION O GROWTH 383Kremer, ., and D. Chen. 2002). "IncomeDistributionynamics ith ndogenous ertility,"ournalfEconomic rowth(3),227-258.Kuznets,. (1955)."EconomicGrowthnd ncomenequality,"mericanconomic eview5,1-28.Lagerlof,.-P.2003)."Gender qualityndLong-Runrowth,"ournalfEconomic rowth(4),403-426.Lee,R. D., andR. S. Schofield.1981)."British opulationn theEighteenthentury,"nFloud,R.,andD.McCloskeyeds.),TheEconomic istoryfBritainince 700.Cambridge:ambridge niversityress.Maddison, . (1991).Dynamic orces nCapitalist evelopment: Long-Run omparativeiew.Oxford:Oxford niversityress.Margo, .A., ndT. A.Finegan.1996)."Compulsorychooling egislationnd choolAttendancenTurn-of-the-Centurymerica: 'Natural xperiment'pproach,"conomics etters3,103-110.Moav,O. (2005)."CheapChildrenndthe ersistencefPoverty,"heEconomic ournalforthcoming).Morand,. F. 1999)."Endogenousertility,ncome istribution,ndGrowth,"ournalfEconomic rowth4(3),331-349.Nardinelli,. (1980)."ChildLabor nd he actorycts,"JournalfEconomic istory0(4),739-755.Ngai,L. R. (2000).Barriersnd theTransitiono Modern rowth. npublished anuscript,niversityfPennsylvania.Park, .-B.,D. R.Ross, ndR. H. Sabot.1996). Educationalxpansionnd henequalityfPay nBrazil ndKorea," nBirdsall, .,andR. H. Sabot eds.),Opportunityorgone: ducationn Brazil. nter-AmericanDevelopmentank:Washington,.C.Preston,. H.,N.Keyfitz,ndR. Schoen.1972).CausesofDeath:LifeTables orNational opulations.ewYork: eminarress.Rosenzweig,.R., ndR. Evenson.1977)."Fertility,chooling,nd he conomic ontributionfChildrenn

Accounting for Fertility Decline during the transition to growth

Documents