NBER WORKING PAPER SERIES INTERGENERATIONAL TRANSFER, HUMAN CAPITAL AND LONG-TERM GROWTH IN CHINA UNDER THE ONE CHILD POLICY

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1 NBER WORKING PAPER SERIES INTERGENERATIONAL TRANSFER, HUMAN CAPITAL AND LONG-TERM GROWTH IN CHINA UNDER THE ONE CHILD POLICY Xi Zhu John Whalley Xiliang Zhao Working Paper hp:// NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachuses Avenue Cambridge, MA June 2013 We are graeful o he Onario Research Fund (ORF), he Naional Naural Science Foundaion of China ( , , ), and Shanghai Pujiang Program (12PJC067) for financial suppor, and o a seminar group a Wesern Universiy for commens. The views expressed herein are hose of he auhors and do no necessarily reflec he views of he Naional Bureau of Economic Research. NBER working papers are circulaed for discussion and commen purposes. They have no been peerreviewed or been subjec o he review by he NBER Board of Direcors ha accompanies official NBER publicaions by Xi Zhu, John Whalley, and Xiliang Zhao. All righs reserved. Shor secions of ex, no o exceed wo paragraphs, may be quoed wihou explici permission provided ha full credi, including noice, is given o he source.

2 Inergeneraional Transfer, Human Capial and Long-erm Growh in China under he One Child Policy Xi Zhu, John Whalley, and Xiliang Zhao NBER Working Paper No June 2013 JEL No. J13,O11,O53 ABSTRACT We argue ha he demographic changes caused by he one child policy (OCP) may no harm China s long-erm growh. This aribues o he higher human capial induced by he inergeneraional ransfer arrangemen under China s poor-funcioning formal social securiy sysem. Parens raise heir children and depend on hem for suppor when hey reach an advanced age. The decrease in he number of children promped by he OCP resuled in parens invesing more in heir children s educaions o ensure reiremen consumpion. In addiion, decreased childcare coss srenghen educaional invesmen hrough an income effec. Using a calibraed model, a benchmark wih he OCP is compared o hree counerfacual experimens wihou he OCP. The oupu under he OCP is expeced o be abou 4 percen higher han i would be wihou he OCP in 2025 under moderae esimaes. The oupu gain comes from a grealy increased educaional invesmen driven by fewer children (11.4 years of schooling raher han 8.1). Our model sheds new ligh on he prospecs of China s long-erm growh by emphasizing he OCP s growh enhancing role hrough human capial formaion under he inergeneraional ransfer arrangemen. Xi Zhu Anai College of Economics & Managemen Shanghai Jiao Tong Universiy Anai Building 535 Fahuazhen Road, Shanghai, China zhuxi97@gmail.com Xiliang Zhao Deparmen of Economics Xiamen Universiy zhaoxiliang@singhua.org.cn John Whalley Deparmen of Economics Social Science Cenre Universiy of Wesern Onario London, ON N6A 5C2 CANADA and NBER jwhalley@uwo.ca

3 Inergeneraional Transfer, Human Capial and Long-erm Growh in China under he One Child Policy Absrac We argue ha he demographic changes caused by he one child policy (OCP) may no harm China s long-erm growh. This aribues o he higher human capial induced by he inergeneraional ransfer arrangemen under China s poor-funcioning formal social securiy sysem. Parens raise heir children and depend on hem for suppor when hey reach an advanced age. The decrease in he number of children promped by he OCP resuled in parens invesing more in heir children s educaions o ensure reiremen consumpion. In addiion, decreased childcare coss srenghen educaional invesmen hrough an income effec. Using a calibraed model, a benchmark wih he OCP is compared o hree counerfacual experimens wihou he OCP. The oupu under he OCP is expeced o be abou 4 percen higher han i would be wihou he OCP in 2025 under moderae esimaes. The oupu gain comes from a grealy increased educaional invesmen driven by fewer children (11.4 years of schooling raher han 8.1). Our model sheds new ligh on he prospecs of China s long-erm growh by emphasizing he OCP s growh enhancing role hrough human capial formaion under he inergeneraional ransfer arrangemen. Keywords: inergeneraional ransfer, human capial, growh, demographic ransiion JEL Classificaion: J13, O11, O53 1. Inroducion China s governmen inroduced he one child policy (OCP) in 1979 wih he aim of conrolling rapid populaion growh. As a resul, China experienced a grea demographic ransiion from high o low raes of feriliy and moraliy in he wenieh cenury (McElroy and Yang, 2000). According o UN world populaion 2

4 prospecs, here will be an increase in he populaion of young aduls (and is share of he oal populaion) before he 2020s, a decrease in he childhood populaion afer he 1990s and a coninuous increase in he elderly populaion afer In he demographic ransiion, he elderly populaion is expeced o exceed he working-age populaion by (See figure 1) Inser figure 1 here How he OCP would affec China s fuure growh has become one of mos widely considered quesions regarding China s fuure growh. We firs analyze he relaionship beween populaion and economic growh. There have been debaes on his opic for hundreds of years. In his mos influenial book, Malhus (1798) assers ha given limied resources, populaion growh hampers economic growh. Boserup (1981) is more opimisic. He argues ha populaion may have a scale effec ha is beneficial o economic growh. The Malhusian model reas echnological progress as exogenous, which has also been challenged in more recen sudies. Romer (1986, 1990) and Jones (1999) emphasize ha he role of populaion in economic growh becomes neural or even posiive when allowing echnological progress o be endogenous. Thus, hese heories offer no consensus abou he OCP s impac. Oher economiss have ried o conduc empirical invesigaions on his opic. Li and Zhang (2007) show ha he birh rae has had a negaive influence on economic growh, also suggesing ha he OCP is growh enhancing. Bloom and Williamson (1998) highligh he role of he working-age populaion. According o heir sudies on Eas Asia, he OCP would firs enhance economic growh hrough a fas increase in 1 In our calibraed model, we define he generaional groups as childhood (0-24 years), young adulhood (25-49 years) and elderly (50 or more years). Typical definiions place childhood from 0 o 14 years, youh a 15 o 64 years and old age a 65 or more years, bu he rend of China s demographic ransiion is robus o differen definiions. 3

5 he working-age populaion, which is called a demographic gif. However, his demographic gif would dissipae wih he rising volume of elderly individuals in he near fuure, as depiced in Figure 1. The idea of a disappearing demographic gif in China has become increasingly popular in he pas several years, paricularly in ligh of he labor shorages experienced in some coasal provinces. Cai (2010) and Zhang e al. (2011) view i as a sign ha he Lewis Turning Poin has been reached and express concern over he challenges o China s fuure growh. We argue ha he demographic changes caused by he OCP may no harm China s long-erm growh as convenionally believed, given parens behavior response as refleced in heir children s educaional invesmen in he OCP under China s inergeneraional ransfer arrangemen. Wihin a poorly funcioning formal social securiy sysem, Chinese parens raise heir children and depend on hem for suppor once hey have reached an advanced age. Thus, he decrease in he number of children promped by he OCP resuls in parens invesing more in heir children s educaion o ensure reiremen consumpion. In addiion, he decreased childcare coss srenghen he educaional invesmen hrough an income effec. Using a calibraed model, we compare a benchmark wih he OCP o a counerfacual experimen wihou he OCP. The model sheds new ligh on he prospecs for China s long-erm growh. The framework is a hree-period overlapping generaion economy under he OCP. In he model, only he parens work for wage income and hey ake care of he children and he elderly. The children depend on heir parens for suppor. As a reward, he parens hen depend on heir children upon reaching an elderly sae. We assume ha he parens ask for a share of heir children s fuure wage income in he inernal agreemen. The parens make decisions and supply labor o he producion secor. Childcare coss are fixed, so hey choose heir own consumpion and he level 4

6 of he children s educaion. The parens have an incenive o inves in heir children s educaion because i can increase heir children s fuure wage income, which will be shared by parens who have reired in ha period. By plugging China s demographic srucure as shaped by he OCP ino he model, we calibrae he main parameers of he model using daa from 1975 o We hen conduc hree counerfacual experimens wihou he OCP. Under moderae esimaes, we find ha he oupu in 2025 would decrease by 4.1 percen wihou he OCP despie an increase in he working populaion of 28.2 percen wihou he policy. Our model conribues o he lieraure in several respecs. Firs and mos imporanly, i shows ha he OCP is growh enhancing in he long erm under he inergeneraional ransfer arrangemen. I is a well-known fac ha Chinese parens depend on heir children for reiremen consumpion under a poorly funcioning social securiy sysem (Banejee e al., 2010). However, here has been lile aenion paid o he implicaion for China s human capial and growh. Unlike oher sudies, our model reas children s educaion as an invesmen raher han a consumpion good. This implies ha he inergeneraional ransfer arrangemen would urge parens o inves more in heir children s educaion wih he OCP in effec, which could by and large offse he adverse effecs of he disappearing demographic gif. Our resuls are consisen wih hose of Li and Zhang (2007), which suppor he neo-malhusian school of hough. Second, we provide an explanaion of Chinese parens sronger preference for more educaed children compared o oher counries. Li e al. (2008) and Rosenzweig and Zhang (2009) find ha family size has a negaive effec for average child qualiy(educaion). This is usually inerpreed as a quaniy-qualiy radeoff originaed 2 The ime period in he model is 25 years. 5

7 by Becker and Lewis (1973), which assumes ha boh he number and educaion of children can increase parens uiliy. Ye i does no explain why Chinese parens prefer educaion o a greaer degree han parens from many oher counries. We sae ha under he inergeneraional ransfer arrangemen, parens share he reurn of educaion invesmen in children, hus hey have a sronger invesmen incenive o ensure heir reiremen consumpion when feriliy is consrained by he OCP. I also parly explains he grea increase in he educaion of he Chinese working-age populaion since he 1990s. Three recen papers are mos relaed o our sudy, and our sudy supplemens he lieraure. Liao (2012) uses a calibraed general equilibrium model and finds ha he OCP promoes human capial and increase per capia oupu. In her model, he incenives for invesing in children s educaion come from he price effec (general equilibrium) and parens preference (quaniy-qualiy radeoff). Wei and Zhang (2011) sudy he compeiive saving moive (for a son s relaive araciveness in he marriage marke) creaed by he rising sex raio caused by he OCP. They show ha he compeiive saving moive explains much of China s high savings rae. Neiher of hese sudies akes he inergeneraional ransfer ino accoun. Banejee e al. (2010) noes he populariy of parens dependence on heir children and inroduces i ino a life cycle model o explain Chinese households savings behavior. Their focus is on he OCP s impac on savings, however, and hey do no consider is influence on educaion or he long-erm growh effecs. The remainder of his paper is organized as follows. In Secion 2 we provide some background. We summarize he OCP and is impac on demographic srucure and provide evidence of parens dependence on heir children. In Secion 3 we describe he model. In Secion 4 we discuss he calibraion. The experimens and resuls are 6

8 provided in Secion 5 and Secion 6 concludes he paper. 2. Background 1. The One Child Policy and China s Demographic Srucure China s OCP was formally inroduced as a family planning policy ha was inroduced in 1978 and iniially applied o firs-born children beginning in I officially resriced married urban couples o having only one child, while allowing exempions in several cases including wins, ehnic minoriies, rural couples and parens wihou any siblings hemselves. I was creaed by he governmen o alleviae economic, social and environmenal problems in China. The policy has been srongly enforced mainly hrough fines ha are imposed based on family income and oher facors 3, bu he implemenaion varies from locaion o locaion. As menioned above, he majoriy of provinces now permi wo parens who were only children hemselves o have wo children. All non-han ehnic groups are usually allowed o have wo or more children. Han Chinese living in rural areas are also permied o have wo children if heir firs child is female. Afer he inroducion of he OCP, he feriliy rae in China fell from 2.63 birhs per woman in 1980 o 1.61 in According o auhoriies claims, he policy has prevened abou 400 million birhs in 30 years 4, which proved he policy o be remarkably effecive. There has been some debae regarding wheher here had already been a sharp reducion in he feriliy rae in he early 1970s (five birhs per woman) in China. Thus, he policy is probably only parially responsible for he 3 There are also some benefis and financial rewards for single-child families including a small amoun of child allowance ha coninues unil he child reaches age 14 and prioriy access o schools and healh care million birhs prevened by one-child policy, Ocober 28, 2011, People s Daily. 7

9 reducion. However, i has played an imporan role in shaping China s demographic srucure since he end of he 1970s. Inser figure 2 here As figure 2 shows, he proporion of he group aged 24 years and below in he oal populaion has declined since 1975, from 58.42% in 1975 o 40.53% in According o he medium esimaes of he world populaion prospecs 5, his rend will coninue, declining o 26.80% in 2025, and 21.42% in Meanwhile, he proporion of he group aged 49 years and above has coninued o increase since 1975, from 27.48% in 1975 o 38.02% in I is expeced o reach 52.01% in This demographic srucure has srong implicaions for China s fuure growh. 2. Inergeneraional Transfer Arrangemen There is a widely held belief ha Chinese parens view heir children as a form of pension for when hey are elderly. Alhough China has made a grea deal of effor in pension reform, Herd, Hu and Koen (2010) poin ou ha under curren rules, effecive replacemen raes are fairly low and projeced o decline furher, boh for rural and urban residens, which may be difficul o susain wih he elderly living increasingly less frequenly wih heir descendans. Furhermore, as he counryside ages, he problems can become even worse. A recen survey in China confirms he inefficiency of he pension sysem. Unil 2010, only 24.1% of he elderly relied mainly on a pension while 40.7% depended on 5 The fuure populaion of each counry is projeced saring wih an esimaed populaion for July 1, To projec fuure populaion, he UN Populaion Division uses assumpions regarding fuure rends in feriliy, moraliy and inernaional migraion. Because fuure rends canno be known wih cerainy, a number of projecion varians are produced. We use he medium feriliy projecion varian. For furher deails, refer o "Assumpions Underlying he 2010 Revision." (hp://esa.un.org/wpp/documenaion/pdf/wpp2010_assumptions_and_vari ANTS.pdf) 8

10 heir family members for suppor. 6 Using daa from he China Household Reiremen Longiudinal Survey (CHRLS), Benerjee e al. (2010) find ha as expeced, more han half of he surveyed elderly live wih heir children and parens are more likely o live wih heir children if one of he parens is in poor healh, which is consisen wih he belief ha children ake care of heir parens when he laer are elderly. The advanage of having many children is consisen wih he observaion ha he fracion of parens living wih a leas one adul child increases from 56% for parens wih only one child o over 70% for hose wih seven or eigh children Educaional Transformaion While he educaional saus of he working-age populaion has coninued o rise in he pas six decades, is srucure has undergone major change since he 1990s. Figure 3 shows he average years of primary, secondary and eriary schooling for he working-age populaion based on Barro and Lee (2010). I is clear ha eriary educaion gains much higher growh and conribues mos o he rise in educaional aainmen in he pas wo decades. This is also documened in Li e al. (2011). Furhermore, China sill exhibis grea poenial in increasing heir human capial compared o he US, especially in eriary educaion (see figure 4). Inser figure 3 and 4 here As he World Bank (2012) repors, hundreds of millions of unskilled Chinese workers joined he global labor force as par of China s opening up sraegy in he 1980s and 1990s. Now, ens of millions of eriary-educaed Chinese workers will join 6 Over 20% of China s elderly rely on pension, CRI, Oc 23, 2012, hp:// 7 The CHRLES is a survey a he household level ha only samples he elderly. Benerjee e al. (2010) resric he sample o hose who had heir firs child during he 1970s and early 1980s. 9

11 he global workforce o significanly expand he global supply of skill-inensive producs. The number of college graduaes could swell by 200 million over he nex wo decades more han he enire labor force of he Unied Saes. 3. The Model We imagine a simple life cycle divided ino hree periods: childhood, young adulhood (parens), and old adulhood (reired). I is assumed ha children will no work, bu raher ha hey will depend on heir parens for suppor, including subsisence consumpion (childcare coss) and educaional invesmen. As a reward, hey agree o provide par of heir fuure wage income o heir parens reiremen consumpion when hey ener he workforce in he nex period. The parens supply labor o gain wage income and make decisions. They are responsible for heir children s subsisence consumpion and for heir parens reiremen consumpion. They independenly choose heir own consumpion and heir children s educaional invesmen. Educaional invesmen coss money, bu will increase children s wage in he nex period. We assume ha feriliy is exogenously deermined under he OCP. Tha is, parens ake he number of children as given. 1. The Basic Model Define L e as he populaion and educaional aainmen of generaion z, when z z z cy o represens children, young aduls and old aduls. The survival rae of children and he life expecancy of old aduls migh change over ime, so we allow L L L This is easy o check using Table 1. 8 We assume ha he educaion c y o Because our period is 25 years, he quaniy of survival rae and life expecancy is a lile differen compared o he regular concep. 10

12 c y level remains consan as children grow up ino young aduls, i.e. e e 1 y o The lifeime uiliy funcion of young aduls a is U c c 1, where c z is generaion z s consumpion in period. We do no add childhood s subsisence consumpion here, because i is assumed o be he same for everyone and provided by parens. We also assume ha neiher children s nor heir own educaion level eners an agen s uiliy funcion. I is no uncommon for children s educaion o ener he parens preference, given Becker and Lewis (1973), bu here we ignore i o focus on he effec of inergeneraional ransfers. We assume a consan reurn o scale (CRS) Cobb-Douglas producion funcion: y 1 Y AK H y y AK L exp( e ) 1 where oupu is deermined by echnology A capial sock K and human capial y H. For human capial, we follow he growh lieraure (e.g. Hall and Jones, 1999; Bils and Klenow, 2000) by seing H y L y exp( e y ). This specificaion is consisen wih he common Mincer (1974) equaion, which implies ha he log of he individual s wage is linearly relaed o ha individual s years of schooling. I could also be inerpreed ha an addiional year of schooling raises a worker s efficiency proporionally by. Choosing he exponenial form could allow us o draw on he large volume of micro evidence on o quanify he impac of schooling on human capial and growh. Assume ha capial accumulaion and echnology progress are exogenous, and he y only income ha a young adul earns is his wage income wl 1 Y As discussed above, a young adul would suppor heir reired parens and children. To simplify he model, we assume ha hey would share a fixed proporion of heir wage 11

13 income ( ) wih heir parens and pay a consan childcare cos ( c sub ) for each of heir children. The remaining par is allocaed beween heir own consumpion and he children s educaional invesmen. We assume ha he educaional cos for each child s addiional years of schooling is p, and parens make an equal invesmen for each child. Thus, he young aduls maximize uiliy subjec o he budge consrain. maxu c y c c e y c o 1 y c c c sub s c pexp e L 1 1 Y Lc (1) o y y exp( 1) 1 c A K e L Here, educaional cos is p exp e c, which includes uiion and oher coss (such as ime and effor). As Bils and Klenow (2000) sugges, we assume ha uiion coss increase wih he opporuniy cos (wage) of schooling because in realiy, uiion rises wih he level of educaion. We assume ha preferences are CRRA; ha is, y o 1 y 1 o U c c 1 c c where is he subjecive discoun facor wih respec o he uiliy of consumpion and 1 denoes he elasiciy of iner-emporal subsiuion. The firs order condiion wih respec o he young aduls own consumpion and heir children s educaional invesmen implies he following condiion o c 1 c y 1 A K exp 1 e L 1 y c pexpe c where he lef is he marginal benefi of increasing children s educaional aainmen 12

14 and he righ is is marginal cos. The marginal benefi consiss of a discouned facor, marginal oupu of educaion and survival rae of children 1 (which equals L y 1 L ). The parens sacrifice heir curren consumpion and spend i on heir c children s educaion o enjoy more reiremen consumpion from he higher fuure o y wage income earned by more highly educaed children. Expressing c 1 by e 1 (or c e ) in his equaion resuls in y c 1 y c 1 A 1K 1 1 L 1 L p c y e L1 (2) exp Parens dependence on children for reiremen consumpion does influence children s educaion. When (proporion of shared wage income) increases, children s educaional level increases. 2. The OCP s Impac on Educaion and Growh Now consider he impac of he OCP. From he budge consrain (1) and firs-order condiion (2), i is clear ha under saionary populaion growh ( L c L y L o ), he educaional invesmen would also be saionary. The enforcemen of he OCP decreases he number of L c, which have wo channels hrough which o affec children s educaion: (1) income effec. Tha is, here would be fewer mouhs o feed (he childcare cos, Lc c sub, decreases) and he parens real income increases; (2) subsiuion effec. Tha is, wih fewer children, he parens would increase heir children s educaional invesmen o ensure shared wage income during reiremen. This is a maerialisic moive for he well-known quaniy-qualiy radeoff. For simpliciy, he changes of echnology, capial, cos of educaion and childcare, 13

15 survival rae are assumed o be consan. Then i is easy o show ha 9 sub Proposiion 1. When AK pc 1 remain consan, he enforcemen of he OCP (1) increases each child s educaional level, and (2) even increases oupu. I is a lile surprising ha he oupu would increase under he OCP. Why he response in he human capial can over compensae? Inuiively, his is caused by he income effec (higher real income and less childcare cos) besides he subsiuion effec (quaniy-qualiy rade-off). Thus, he dependence on children will make parens make srong response o he demographic change caused by he OCP, which will offse he negaive effec on economic oupu caused by a decreasing labor force. The proposiion has srong implicaions for China s long-erm growh. I predics an relaively opimisic fuure. Proposiion 1 depends on he assumpion ha parameer in uiion cos, p, is consan. In realiy, p migh increase very fas when he educaional aainmen reaches a cerain level. In ha case, OCP s impac on growh could urn o be moderae or even negaive. However, since China s curren educaional aainmen is relaively low compared o he developed counries, he posiive impac could sill dominae in he near fuure. 3. Discussion of he Model Sharing Rule We assume a linear sharing rule on wage income o describe he inergeneraional ransfer arrangemen beween young aduls and heir reired parens. Alhough we hink i reasonable based on wha happens in China, here could be alernaive choices. 9 Proof is provided in Appendix. 14

16 One alernaive is a linear sharing rule on wage. Tha is, young aduls promise he elderly an average reiremen consumpion of w.(replacemen raio) The model becomes maxu c y c c e y c o 1 sc pexp e L 1 Yc Lc y c c o c sub 1 c 1 A K L e L L o y1 c1 o y This model is similar o our basic model when populaion growh is saionary L L y o 1 1. However, he enforcemen of he OCP will make L L. Thus, i has c y he advanage of underlining he burden of he increasing elderly populaion caused by he OCP. When he elderly populaion increases, educaion will increase reflecing is high reurn. Anoher alernaive is ha young aduls promise a fixed amoun of reiremen consumpion c old for each paren. The model becomes maxu c y c c e y c o y c c y y 1 c sub sc pel AK el Lc c c L o old o 1 In his case, he young aduls would have no incenive o inves in children s educaion because heir reiremen consumpion is ensured. This model makes sense if we apply some revisions and le children make decisions on heir consumpion and educaion and pay back heir educaion coss as a loan o parens. The elderly s reiremen consumpion seems like a lump sum ax o hem, which would give hem more incenive o gain a higher educaion. We assume ha he parens deermine children s invesmen. Educaional Credi Consrains We assume ha households face a credi consrain on educaional invesmen, such 15

17 ha parens mus cover all of he coss in he curren period. While credi for educaion in China has grown in recen years, i sill amouns o a small fracion. Mos children s uiions and oher educaional coss are paid by heir parens. Incenive for Educaional Invesmen The sandard model of human capial invesmens, such as ha provided by Ben-Porah (1967), assumes ha he individual chooses he invesmen (in erms of ime) under perfec capial marke condiions, and ha he only margin of choice is beween marke work and schooling. Bils and Klenow (2000) use i o examine he relaionship beween schooling and growh. Things are differen in China. Parens ypically make decisions abou children s educaional invesmen under binding credi consrains. Parens inves in heir children, parially from alruisic parenal love and parially in he ineres of an ensured reiremen consumpion. I is difficul o differeniae one from he oher bu due o China s poor social securiy sysem, he laer could be more imporan, so we emphasize i. Measuremen of Human Capial There are various approaches o measuring human capial in he lieraure. Mankiw e al. (1992) assume a human capial producion echnology idenical o ha of physical capial and use he proporion of he adul populaion enrolled in secondary school as a proxy for human capial invesmen. However, he school enrollmen does no adequaely measure he aggregae sock of human capial available conemporaneously as an inpu in producion. I seems inappropriae o use i as a sock variable. More recen sudies (e.g. Hall and Jones, 1999; Bils and Klenow, 2000) define y e human capial as H exp y i L i, where y i reflecs he efficiency of a uni of 16

18 labor wih e years of schooling relaive o one wih no schooling ( ). The y i 0 0 derivaive y e i is he reurn o schooling esimaed in a Mincerian wage regression (Mincer, 1974). We ake he more recen approach o measure human capial because i ensures ha our esimaes of human capial are consisen wih he privae reurn o schooling seen in he micro daa. Our definiion is similar o ha of Young (2003) and Wang and Yao (2003) in ha i akes boh he quaniy and he qualiy of he labor force ino consideraion. 4. Calibraion 1. Daa and Measuremen Issues In our model, a period is 25 years. To accoun for he effec of he OCP, we mus cover he periods boh before and afer is enforcemen. The model is calibraed o Chinese daa from 1975 o In 1975, he OCP had no ye been inroduced. In 2000, he OCP s impac on demographic srucure emerges. The main parameers can be calibraed based on he wo periods. To explore he effec of he OCP, we compare i o a counerfacual experimen wihou he OCP. We also discuss he model s implicaion for China s long-erm growh in 2025 and Demographic Srucure Our daa cover hree periods (1975, 2000, 2025) of China s demographic srucure gahered from World Populaion Prospecs: The 2010 Revision (Unied Naions, Deparmen of Economic and Social Affairs, Populaion Division, 2011), which provides deailed populaion disribuion by 5-year age groups in 5-year inervals ( ). I also gives he populaion prospecs from 2010 o We define 17

19 children as aged 24 years and below, young aduls as aged 25 o 49 years and he elderly as aged 50 years and above. The resuls are in Table 1. For 2025, we use he esimaed populaion under medium-feriliy varian. Physical Capial Sock Many papers have repored esimaes of he capial sock in he course of esimaing produciviy growh in China (e.g. Chow and Li, 2002; Huang e al., 2002; Young, 2003). The esimaes of Bai e al. (2006) regarding he capial sock in China differ from hese earlier esimaes in wo principal ways. Firs, hey make use of he updaed daa repored by China s Naional Bureau of Saisics (NBS) afer he 2004 census. Second, hey calculae he capial sock in marke prices raher han in consan prices. 10 We follow he mehod of Bai e al. (2006) and use heir updaed esimaes of he capial sock. We ake 1978 as he base year o generae real capial sock. Human Capial Sock In our model, human capial is measured as a funcion of years of schooling and curren labor force. The curren labor force is he populaion aged 25 o 49 years in he curren period. The daa on years of schooling are calculaed from Barro and Lee (2000, 2010). Their esimaion procedure is a perpeual invenory mehod ha uses he census/survey observaions on aainmen as benchmark socks and new school enrans as flows ha are added o he socks wih an appropriae ime lag. They provide a deailed daa se on educaional aainmen by 5-year age groups over 5-year inervals ( ). Using heir daa, we consruc he number of years of schooling for aged 25 o 49, y e, as e 5 y a a l e a1 10 We hank he auhors and Zhenjie Qian, heir RA, for providing he updaed daa. 18

20 where a l is he populaion share of group a in he populaion aged 25 o 49 and a e is he number of years of schooling for he age group a ( a age group, a age group,..., a ). The number of years of schooling for he age group a in ime is e h Dur a a a j j j1 where a h j is he fracion of group who have aained he educaional level j prisecer (coresponding o primary, secondary and eriary educaion, respecively) and Dur indicaes he corresponding duraion in years. The grea increase in educaional aainmen of China s labor force can be seen in Figure 3. Oupu The oupu daa come from he China Saisics Yearbook (CSY). We ake 1978 as he base year o generae real GDP. 2. Calibraion Sraegy Our basic sraegy is o calibrae he parameers such ha he following wo equaions hold. y c 1 y c 1 A 1K 1 1 L 1 L p c y e L1 (3) exp y c c c sub c p exp e L 1 1 Y Lc (4) Specifically, he seps of calibraion are conduced as follows: 1. (Before he OCP) Using he oupu daa and children s educaion in 1975 and 2000, 11 we calibrae p 1975 Noe ha c 1975 and p 1995 are 11 Children s educaion in 1975 is no direcly observable in he curren year, bu i equals he young aduls educaion in

21 simulaneously calibraed. y 2. (Benchmark) Assume ha e , 12 and TFP and capial sock s growh in keep he same as , we calibrae p 2000 o fi he model. 3. (Cases I, II and III) We hen conduc hree counerfacual experimens based on hree differen esimaes (from high o low) of he OCP s impac on China s demographic srucure. We use he calibraed model o simulae he possible impac of he OCP on educaion and oupu under hese counerfacual scenarios. Sep I corresponds o he period before he OCP, which is calibraed o show how he model fis he daa. I capures a prior belief. Sep II provides he basic benchmark under he OCP. Sep III conducs hree counerfacual experimens o evaluae he impac of he OCP on educaional oupu, based on he hree esimaes of counerfacual demographic srucure. Noe ha his sudy focuses on how OCP s impac under differen scenarios y designed in Sep III. Alhough he number of e 2025 in sep II is se by a linear predicion here, i won change our main resuls. 3. The Three Esimaes of Demographic Srucure There is no consensus on he OCP s influence over China s demographic srucure. The official claim is ha he OCP prevened 400 million birhs in China from 1978 o Alhough his is ofen cied by he governmen, i is holy debaed. A common criique is ha he feriliy rae usually decreases when an economy grows, according 12 We ge he number by assuming he young aduls years of schooling grows from 2000 o 2025 a he same speed as from 1975 o

22 o he experiences of oher indusrialized counries. Thus, he effec could be exaggeraed. Thus, we ake he officially repored number as a high esimae and also consider moderae and low esimaes (200 and 100 million). The esimaes are adjused according o he ime period for our model. 13 The hree esimaes are presened in Table Parameers Table 2 summarizes he parameers in he calibraion. Following Liao (2012), we choose a CRRA preference wih a risk-aversion parameer of 05 and he subjecive discoun facor I is also assumed ha hese preference parameers are consan over ime. For he echnology parameer, we firs ake K from Bai e al. (2010). Because he labor share has been approximaed a 50 percen in China (Wang and Yao, 2003; Brand and Zhu, 2010), we se 05. According o Heckman and Li (2004) and Zhang e al. (2005), he reurn o years of schooling is abou percen for he lae wenieh cenury in China. We hen se 010. The oher parameers of exogenous driving force include c sub p The average cos of rasing a child (excluding educaion coss) is 22.7 percen of a family s income, which follows Liao s (2012) calculaions based on Ye and Ding s (1998) survey. 14 So sub c is calculaed from our daa on family income and he childhood populaion. We 13 Take he high esimae for example. Because our period is , we compue c c he populaion aged 24 and below as L2000n L We also projec i ino 2025 as populaion aged 25-49, using a same survival rae as he rae under he OCP. 14 Ye and Ding (1998) compare he cos of child care in Xiamen o ha in Beijing. In Xiamen, a child s care cos abou 29 percen of a family s annual income in The percenage was 16.4 percen in Beijing. Thus, he average cos of child care is 22.7 percen. 21

23 se he share of young aduls wage income ransferred o heir elderly parens as 015. The parameer for educaional cos p is calibraed as discussed in he calibraion sraegy. 5. The Effecs of he OCP 1. Resuls for 1975 Table 4 shows he calibraion resuls for each generaion s expendiure (consumpion and educaion) in The daa in he firs row give he share of expendiure by each group while hose in he second row give he oal expendiure and hose in he hird row give per capia expendiure. We se he parameers of he share of expendiure on child care and reired aduls as 23 and 15 percen, respecively. The young aduls would spend 30 percen on heir own consumpion and 32 percen on heir children s educaional invesmen. The average consumpion of young aduls and reired aduls is close. These resuls provide confidence for our furher analysis. 2. The OCP s Influence: Three Counerfacual Experimens Panel (a) of Table 5 shows he calibraion resuls of each generaion s expendiures (consumpion and educaion) in If we believe ha he young aduls years of schooling reach 11.4 in 2025, hen he oupu becomes 207, Thus, he growh rae could reach 8.4 percen from 2000 o 2025, whereas i remains a 7.0 percen from 2010 o The young aduls would spend 33 percen on heir own consumpion and 29 percen on heir children s educaion. We hen urn o our main resuls on he OCP s influence by conducing hree counerfacual experimens assuming ha here was no OCP in

24 Under high esimaes (Case I shown in Panel (b)), which assume ha he number of children increases by 56.4 percen wihou he OCP, he young aduls years of schooling would decrease o 5.12 in The young aduls would spend 25 percen of heir income on heir own consumpion and 24 percen on heir children s educaion. As a conras, hey mus spend 35 percen of heir income on child care because here are many more children o feed. Under moderae esimaes (Case II shown in Panel (c)), which assume ha he number of children increases by 28.2 percen wihou he OCP, he young aduls years of schooling would decrease less, reaching The young aduls would spend 29 percen of heir income on heir own consumpion and 27 percen on heir children s educaion. The child care coss would decrease o 29 percen because he number of children would no be as big as in Case I. Under low esimaes (Case III shown in Panel (d)), which assume ha he number of children increases by 28.2 percen wihou he OCP, he young aduls years of schooling would decrease o 9.67, which would be higher han in Case II. The young aduls would spend 31 percen of heir income on heir own consumpion and 28 percen on heir children s educaion. The child care coss would decrease o 26 percen. Taken ogeher, he resuls indicae ha young aduls will increase he invesmen in heir children s educaion when he OCP comes ino effec. To ensure heir reiremen consumpion, he more sricly he policy is implemened, he fewer children young aduls will have and he more hey will inves in heir children s educaion. The behavioral response of subsiuing quaniy wih qualiy (educaion) will offse he OCP s negaive influence on oupu. Because he presence of fewer children subsanially reduces he child care coss, he oupu under he OCP will be 23

25 higher han ha wihou he OCP due o he income effec. Taking moderae esimaes as an example, he oupu would be wihou he OCP, which is 4.2 percen lower han he oupu under he OCP. 6. Conclusion We claim ha he demographic changes caused by he one child policy (OCP) may no harm China s long-erm growh. This aribues o he higher human capial induced by he inergeneraional ransfer arrangemen under China s poor social securiy sysem. Parens raise heir children and depend on hem for suppor once hey have reached an advanced age. Thus, he decrease in he number of children promped by he OCP resuls in he parens invesing more in heir children s educaion o ensure heir reiremen consumpion. In addiion, he decreased child care coss srenghen he educaional invesmen hrough he income effec. Our numerical simulaion proves hese insighs. Using a calibraed model, we compare a benchmark wih he OCP o hree counerfacual scenarios wihou he OCP. The oupu under he OCP is abou 4 percen higher han wihou he OCP in 2025 under moderae esimaes. The oupu gain comes from he grealy increased educaional invesmen in fewer children (years of schooling 11.4 raher han 8.1). Our model sheds new ligh on he prospecs of China s long-erm growh by emphasizing he OCP s growh enhancing role hrough human capial under he inergeneraional ransfer arrangemen, which also provides a moive for he popular quaniy-qualiy radeoff heory. Human capial could sill play an imporan role in China. We assume ha he average years of schooling will reach 11.4 in Compared o 13.4 years of schooling in he US in 2010, here is sill some poenial for China o mainain is high 24

26 growh in he fuure. Thus, we hink ha he disappearing demographic gif will no hur China s growh in he nex several decades. 7. Appendix: Proof for Proposiion 1. Proof. Proposiion 1 is proven by conradicion. Rewrie he firs-order equaion (2) as c y e L1 c sub c c 1 1 Y Lc p expe L exp A K p Simplify i by assumpion, where ab are consan. c c exp e L c sub c c alc p exp e L b (1) Assume ha e c decreases when L c decreases. Then in he lef par of he equaion he numeraor increases while he denominaor decreases. This conradics he consan in he righ par. c c (2) Assume ha exp e L decreases (wih an increased c e ) when c L decreases. Then, in he lef par of he equaion he numeraor increases while he denominaor c c decreases. This conradics he consan in he righ par. So exp e L increases when c L decreases, which leads o an increase in oupu. QED. 25

27 References [1] Bai, C.; Hsieh, C. & Qian, Y. The Reurn o Capial in China, Brookings Papers on Economic Aciviy, Brookings Insiuion Press, 2006, [2] Banerjee, A.; Meng, X. & Qian, N. The Life Cycle Model and Household Savings: Micro Evidence from Urban China mimeo, Yale Universiy, [3] Barro, R. & Lee, J. Inernaional daa on educaional aainmen updaes and implicaions Naional Bureau of Economic Research, [4] Barro, R. & Lee, J. A new daa se of educaional aainmen in he world, Naional Bureau of Economic Research, [5] Becker, G. & Lewis, H. On he Ineracion beween he Quaniy and Qualiy of Children, The Journal of Poliical Economy, 1973, [6] Ben-Porah, Y. The producion of human capial and he life cycle of earnings, The Journal of Poliical Economy, 1967, 75, [7] Bils, M. & Klenow, P. Does schooling cause growh? American Economic Review, 2000, [8] Bloom, D. & Williamson, J. Demographic ransiions and economic miracles in emerging Asia The World Bank Economic Review, World Bank, 1998, 12, [9] Boserup, E. Populaion and Technical Change: A Sudy of Long-Term Trends, Chicago: Universiy of Chicago Press, [10] Brand, L. & Zhu, X. Accouning for China s growh, IZA Discussion Paper, [11] Cai, F. Demographic Transiion, Demographic Dividend, and Lewis Turning Poin in China, Economic Research Journal, 2010, 4, 002. [12] Chow, G. & Li, K. China s Economic Growh: , Economic Developmen and Culural Change, 2002, 51, [13] Hall, R. & Jones, C. Why Do Some Counries Produce So Much More Oupu Per Worker Than Ohers? The Quarerly Journal of Economics, 1999, 114, [14] Heckman, L. Heerogeneiy, Selecion Bias and he Reurn o Educaion: A Empirical Analysis Based on Chinese Micro-Daa, Economic Research Journal, 2004, 4, 9. [15] Herd, R.; Hu, H. & Koen, V. Providing greaer old-age securiy in China OECD Publishing,

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29 Raios and Savings Raes in China, Journal of Poliical Economy, 2011, 119, [31] Ye, W. Z. & Ding, Y. The Cos of Child Care in Xiamen Special Economic Zone, China Populaion and Economics (in Chinese), 1998, 6, [32] Young, A. Gold ino Base Meals: Produciviy Growh in he People s Republic of China during he Reform Period, Journal of Poliical Economy, 2003, 111, [33] Zhang, X.; Yang, J. & Wang, S. China has reached he Lewis urning poin, China Economic Review, 2011, 22, Figure 1: Populaion by age group

30 Figure 2: Demographic Srucure of China: Figure 3: Educaional Aainmen in China:

31 Figure 4: Educaion: China and US Table 1. Age Srucure (UN) year pop pop0024 pop2549 pop5099 child/pop labor/pop old/pop Source: Unied Naions, Deparmen of Economic and Social Affairs, Populaion Division (2011). World Populaion Prospecs: The 2010 Revision, CD-ROM Ediion. Table 2. Parameers for Calibraion Targe/Mehod Preference Liao (2012) 30

32 Liao (2012) Brand and Zhu (2010) Technology A by caculaion K Bai e al (2006) Heckman and Li (2005) Exogenous Driving Force sub c by calculaion by calculaion Calibraed Parameer p calibraed Table 3. Demographic Srucure under Differen Predicions pop0024 pop2549 pop5099 Benchmark Wih OCP Case I NO OCP: HIGH Case II NO OCP: MOD

33 Case III NO OCP: LOW Table 4. Calibraion Resuls in 1975 Before he OCP (1) worker (2) child care (3) educaion (4) old Share(%) To. Expend Avg. Expend Table 5. Impac of OCP in 2000 Panel (a) Benchmark Wih OCP oupu2025 edu (1) worker (2) child care (3) educaion (4) old Share(%)

34 To. Expend Avg. Expend Panel (b) Case I NO OCP: HIGH oupu2025 edu (1) worker (2) child care (3) educaion (4) old Share(%) To. Expend Avg. Expend Panel (c) Case II NO OCP: MOD oupu2025 edu (1) worker (2) child care (3) educaion (4) old Share(%) To. Expend Avg. Expend Panel (d) Case III NO OCP: LOW oupu2025 edu (1) worker (2) child care (3) educaion (4) old Share(%) To. Expend Avg. Expend