Health, Demographic Transition and Economic Growth

Transcription

1 Public Disclosure Auhorized Public Disclosure Auhorized Public Disclosure Auhorized Public Disclosure Auhorized Policy Research Working Paper 5304 Healh, Demographic Transiion and Economic Growh The World Bank Lain American and Caribbean Region Economic Policy Secor May 200 Ole Hagen Jorgensen WPS5304

2 Policy Research Working Paper 5304 Absrac This paper develops a link beween four cenral componens of he demographic ransiion: survival raes; feriliy decisions; alruisic inergeneraional ransfers from workers oward heir parens; and economic growh. An increase in child survival is found o reduce he feriliy rae and alruisic ransfers, and hereby increase he savings rae and he produciviy growh rae. The analysis illusraes he key role of child healh in he demographic ransiion. This paper a produc of he Economic Policy Secor, Povery Reducion and Economic Managemen in Lain American and Caribbean Region is par of a larger effor in he deparmen o undersand he economic implicaions of populaion dynamics in less developed economies. Policy Research Working Papers are also posed on he Web a hp://econ.worldbank. org. The auhor may be conaced a ojorgensen@worldbank.org. The Policy Research Working Paper Series disseminaes he findings of work in progress o encourage he exchange of ideas abou developmen issues. An objecive of he series is o ge he findings ou quickly, even if he presenaions are less han fully polished. The papers carry he names of he auhors and should be cied accordingly. The findings, inerpreaions, and conclusions expressed in his paper are enirely hose of he auhors. They do no necessarily represen he views of he Inernaional Bank for Reconsrucion and Developmen/World Bank and is affiliaed organizaions, or hose of he Execuive Direcors of he World Bank or he governmens hey represen. Produced by he Research Suppor Team

3 HEALTH, DEMOGRAPHIC TRANSITION AND ECONOMIC GROWTH Ole Hagen Jorgensen 2 LCSPE JEL Classificaion: H55, I8, J3, O, O6, O4 Keywords: Healh, Moraliy, Endogenous Feriliy, Demographic Transiion, Endogenous Economic Growh I am graeful o Jocelyn Finlay and Svend E. Hougaard Jensen for excellen commens and valuable discussions. Furhermore, I hank Michele Gragnolai, Jan Walliser, Tio Cordella, Makhar Diop, Rodrigo Chaves, Dino Meroo, Oded Galor, David Bloom, and David Canning for helpful commens. 2 The World Bank, Povery Reducion and Economic Managemen, LCSPE, 88 H Sree, N.W., Washingon, D.C., 20433, USA, ojorgensen@worldbank.org, Tel.: , Fax.:

4 . Inroducion Mos counries have seen child and adul survival raes increase during he firs sage of heir demographic ransiion. This has usually been followed by a decline in feriliy in he second sage and, hus, srongly decreasing dependency raios. As a resul, he demographic ransiion provides a window of opporuniy for economic growh by releasing resources for capial savings and human capial formaion. According o Bloom and Williamson (998) approximaely one-hird of he increase in economic growh for he Eas-Asian igers can be explained by purely demographic facors, i.e. he declines in moraliy and feriliy. This demographic dividend herefore enails a real chance o reduce povery. This paper considers an increase in survival raes for boh children and aduls, and races he effecs hrough he key mechanisms in he economies of less developed counries (LDCs): feriliy decisions, alruisic inergeneraional ransfers and capial savings. These mechanisms ranslae a change in healh condiions ino prospecs for economic growh. The exising lieraure has already analyzed some of hese componens ogeher, bu has failed o include hem all ino one unified framework. I would be oo simplisic, in he conex of LDCs, no o incorporae one or more of hese cenral mechanisms when analyzing he firs sage of he demographic ransiion wih reducions in (child) moraliy. The presen analysis feaures, herefore, one possible channel for he rade-off beween children and capial as savings mechanisms when child survival increases. To our knowledge, his has no been aemped before. Capial savings are a key variable in an economy s demographic ransiion owards susained economic growh. 3 In a model wih exogenous feriliy and wihou he care by workers for he subsisence of heir parens, Chakrabory (2004) finds ha a higher adul survival rae will increase he capial sock and per capia income. The reason is ha capial savings increase when people expec a longer reiremen period. 4 However, in LDCs, children can also be considered a form of savings because hey end o care for heir parens in old age, i.e. he higher number of children per household he more alruisic ransfers can be expeced in old age (Ehrlich and Lui, 99). In order o race he effecs on capial savings, hese mechanisms should be accouned for in he analyical framework. We accomplish his by endogenizing feriliy and alruisic inergeneraional ransfers. Consequenly, he ne effec on capial savings may no necessarily be an increase, because workers may choose o save hrough having more children and, in urn, dis-save hrough capial. The resul in Chakrabory (2004), ha improved healh condiions will increase capial savings and economic growh, may herefore no hold when he economy is modeled wih endogenous feriliy decisions and alruisic ransfers in accordance he empirical observaions in LDCs (see, e.g., Caldwell, 982). 3 Increased capial savings will produce a higher capial-labor raio and, in line wih sandard growh heory (see, e.g., Diamond, 965), also he poenial for higher per capia oupu. 4 In Chakrabory s model, invesmens in healh increase proporionally o he increasing income, which in urn leads o a longer life span. So he economy eners a posiive spiral of beer healh, longer lives, more capial savings, and higher per capia income. 2

5 In addiion o our personal joy of having children, o which we seem o be more or less geneically programmed (Dasgupa, 993; p. 356), he moivaion for having children can indeed be considered an economic one. Children can provide labor ha will benefi he household; hey can provide care for parens in old age; and hey may be an insrumen of alruism from paren o child (Barro and Becker, 989). Anoher moivaion for having children is he expecaion of receiving alruisic inergeneraional ransfers from one s children afer reiremen (Ehrlich and Lui, 99; Wigger, 2002). Higher capial savings would subsiue hese inergeneraional ransfers o he effec of lowering he ransfer rae and furher reducing he need for having children as an old age securiy device. 5 Concurren wih he child survival response, parens also face he quaniy/ qualiy rade-off (Galor and Weil, 996, 2000). Wih a fixed amoun of resources available o devoe o he children of he household, parens make he decision o have many (few) children and inves lile (more) in each. The incenive for he laer will grow as he reurn o human capial increases parallel o he echnological developmen. In his paper, we absrac from human capial invesmens since he effecs hereof are well esablished. Improved adul healh (proxied in he lieraure by higher life expecancy; longer reiremen period) is generally found o have an increasing effec on oupu per capia (see, e.g., Bloom e al., 2007, Chakrabory, 2004, Jensen and Jorgensen, 2008, Jorgensen and Jensen, 2009). In he presence of perfec capial markes and no social securiy arrangemen, we would envision longer life expecancy o have no effec on he savings rae as he exension of working life is proporional o he exension of life expecancy. However, in he presence of social securiy arrangemens, where he reiremen age is fixed, an increase in life expecancy increases he years of reiremen disproporionaely o he working years. This is a case where he ineremporal prices of consumpion in he firs relaive o he second period change, and if hey do no change in equal proporions hen he savings rae will be affeced (Chang, 990; Jensen and Jorgensen, 2008, Jorgensen and Jensen, 2009). 6 Higher adul survival can also have incenive effecs ha may be imporan for capial savings: invesmens in human capial will be encouraged as he ime horizon over which reurns o invesmen can be earned is exended (Weil, 2007; Finlay, 2006). Adul survival may also represen a proxy for experience: he longer one is alive he larger he work experience. Alhough his heory is dispelled by Bloom e al. (2004), who conrol for labor marke experience, hey found ha increased adul survival 5 The choice of how many children o have is, o a large exen, a funcion of child survival (Priche, 994; Barro and Becker, 989) and of access o family planning (Bongaars, 990, 994). A family plan o have heir desired number of (live) children, and in an environmen of high child moraliy he differenial beween he number of desired children and birhs widens (Fink, 2007). As he child survival rae improves, families need fewer birhs o achieve heir desired number of children. 6 The reiremen age as a policy insrumen could be adjused o offse his effec (Jensen and Jorgensen, 2008, and Jorgensen and Jensen, 2009). Bloom e al. (2005) show, however, ha his life-cycle savings model is incomplee, and ha an increase in life expecancy can acually have a negaive effec on he savings rae. They argue ha if he reiremen age is endogenously deermined, hen a rise in life expecancy may lead o a more or less han proporional rise in he reiremen age so he effec on he savings rae is ambiguous. This resul is driven by a wealh effec of he longer working life. Jorgensen and Jensen (2009) finds a similar resul in a model wih endogenous labor supply, where he wealh effec due o disorionary axaion more han ouweighs he sum of subsiuion and income effecs when life expecancy increases. 3

6 had a posiive effec on savings and economic growh. Alernaively, if adul survival is considered a proxy for healh, hen beer healh can lead o higher worker produciviy and promoe economic growh (Barro and Lee, 994; Bloom e al., 2004; Zhang and Zhang, 2005; Finlay, 2006). While exising lieraure mainly sudies changes in adul survival as a proxy for life expecancy, his paper separaes he effecs from higher child survival and adul survival, respecively. Thereby, we can isolae he unique effecs from each survival rae on variables cenral o he demographic ransiion. The economic implicaions of changes in child survival have been explored o a much lesser exen han adul survival in he heoreical lieraure. To accoun for his shorcoming, his paper illusraes a channel of dynamics ha can unfold, in which he moivaion for having children will shape he resource allocaion hrough endogenous feriliy decisions. The child and adul survival raes are incorporaed ino he working and reiremen periods, respecively, as implici prices on consumpion. This framework is combined wih alruisic ransfers from working age members of he household o heir reired parens. While ohers have modeled endogenous feriliy decisions ogeher wih boh one-sided and wosided alruisic inergeneraional ransfers (see, e.g., Blackburn and Cipriani, 2005), nobody has incorporaed survival raes in he conex of boh endogenous feriliy decisions and alruisic ransfers. Adul survival raes have frequenly been incorporaed ino life-cycle models (see, e.g., Blackburn and Cipriani, 998, 2002; Bohn, 200; Chakrabory, 2004; Jorgensen and Jensen, 2009) bu have no been analyzed in conjuncion wih alruisic ransfers. This paper brings ogeher his lieraure by combining hese elemens ino a unified endogenous growh model. Having explored he heoreical benefis of improved survival raes, we hen ake his a sep furher and ask: Can economic policy be argeed a healh inervenions in order o provide incenives for having fewer children, and could such a feriliy decline poenially promoe higher per capia economic growh? Assuming ha beer healh is he cause of increasing survival raes, we race increases in he child survival rae, as well as he adul survival rae, o heir impacs upon feriliy, alruisic ransfers, capial savings and economic growh, respecively. We nex consider how public pay-as-you-go pensions can poenially reduce he need for children as an old age securiy device, and hrough hese dynamics increase capial savings and economic growh. I is well known ha pensions crowd ou he physical capial sock, bu in a seup wih children as a savings mechanism he reducion in household savings may be direced owards children raher han owards capial. As a resul, if feriliy is high hen capial accumulaion may also be higher han previously believed because alruisic inergeneraional ransfers are operaive a low levels of developmen. This issue was also addressed by Wigger (2002), bu he does no incorporae survival raes ino his model and is herefore no in a posiion o sudy he demographic ransiion (riggered by low child moraliy) and he implicaions for susained growh i enails. The paper is srucured as follows: in secion 2 he model is oulined, and in secion 3 here is solved for he compeiive equilibrium. Comparaive saics are hen conduced in secion 4, where exogenous increases are imposed in, firs, he child survival rae and, second, he adul survival rae. Nex, he experimen wih a composie increase in he child and adul survival raes is performed. 4

7 Finally, secion 5 provides perspecives on he poenial of public pensions o promoe he dynamics of he demographic ransiion, discusses some model limiaions, and provides suggesions for fuure research. Secion 6 concludes. 2. The Model The overlapping generaions (OLG) model is oulined in his secion. We owe he basic srucure of he model o Wigger (2002), who incorporaes alruism and endogenous feriliy decisions ino an OLG model, ad modum Diamond (965), which leads o an old age securiy moive for having children. 7 Our model exends his srucure by incorporaing child and adul survival raes, respecively. We assume ha improved healh condiions generae higher survival raes. 8 We follow Jorgensen and Jensen (2009) in heir incorporaion of he survival raes in order o analyze heir impac on savings, feriliy and economic growh. The model consiss of differen building blocks: demographics, budge consrains, household behavior and echnology. We presen hese in urn, before oulining he soluion mehod in secion Demographics Individuals are assumed o live, as shown in Figure, for hree periods: as children, as working age aduls, and as reired aduls. Figure. Child and Adul Survival Raes Childhood Working age Reiremen μ Child survival rae μ2 Adul survival rae Parens are assumed o make economic decisions on behalf of heir children. The child survival rae, 0<μ, is assumed o denoe he survival of children immediaely before hey ener he labor force as adul workers. In ha way, a higher μ ranslaes ino a larger labor force. A higher adul survival rae, 0<μ2, is incorporaed such ha more workers survive ino reiremen. Labor is inelasically supplied by workers, N, and is assumed o grow by +n-= N/(μN-), where n>- is he growh rae. If child survival or feriliy increases hen he labor force will grow a a higher rae. 7 Blackburn and Cipriani (2005) also invesigae he dynamics of feriliy and alruisic inergeneraional ransfers in he conex of he demographic ransiion. Neiher hey nor Wigger (2002) incorporae survival raes (or lengh of life) ino heir models. As a resul, hey are unable o invesigae he role of child moraliy in he firs phase of he demographic ransiion. This is exacly he link ha his paper provides. 8 We do no, however, incorporae a governmen healh secor or privae invesmens in healh. Higher healh invesmens would oherwise be expeced o increase survival raes in line wih Chakrabory (2004), bu since we are ineresed in a closed form soluion for key variables, which Chakrabory does no provide, a framework wih endogenous healh expendiure ha endogenously affecs survival raes will remain an issue for our fuure research. 5

8 2.2 Budge consrains Workers earn wages, w, and choose savings, S, in accordance wih (). ( ) S z n w c () Differen coss mus be serviced by workers: firs, here exiss a pay-as-you-go (PAYG) pension sysem wih a conribuion rae, θ. 9 Secondly, he cos of raising (+n) number of children is denoed by κw, where κ is he share of income ha covers he coss per child. Consequenly, if eiher he number of children per household increases, if he cos of rearing a child increases, or if pension conribuions increase, here will be less income available for firs period consumpion, c, and savings. Workers are assumed o be alruisic owards he subsisence of heir reired parens, o whom hey have he opion of ransferring income (gifs). If, however, reirees already have enough consumpion, and hus adequae uiliy, workers will reduce he gif rae, z, o whichever level heir degree of alruism suppors. Second period consumpion, c2+, is deermined in (2) by las period s savings ha yield a gross reurn of R=+r. R c S ( n ) z w (2) 2 2 An increase in μ2 would force more reired members of he household o spend heir savings a a lower rae, /μ2. Reirees may receive alruisic ransfers from heir working age children, depending on he number of children hey have and he wage rae. Consequenly, he more children you have o suppor you in old age, he more alruisic ransfers you will probably receive. An addiional child will provide you wih more inergeneraional gifs in old age, bu you also have o suppor hem whils working, implying less consumpion and capial savings. The rade-off herefore (also) depends upon he fac ha children possess he same degree of alruism as you, so ha you can be cerain o receive in old age wha you expeced when deciding on your number of children. 0 Finally, reirees receive variable pension benefis in accordance wih he PAYG sysem in (3) 2wN wn (3) where he fixed conribuion rae is scaled by he relaive survival raes in (4). n 2 ( ) (4) In case reirees face a higher survival rae hey are forced o spend heir benefis a a lower rae. When children, on he oher hand, face a higher survival rae, he labor force increases and more workers will pay fixed conribuions o he PAYG sysem. This will allow heir reired parens o spend pension benefis a a higher rae. Equivalenly, if workers decide o have more children, hey can also expec higher pension benefis in old age. 9 A very small conribuion rae is assumed in line wih he feaures of pension schemes in developing economies. 0 This is in principle a game-heoreic issue as analyzed by, e.g., Zhang and Nishimura (993) and Nishimura and Zhang (995). In his paper i is assumed ha all generaions are equally alruisic. The PAYG sysem does no necessarily need o be characerized by fixed conribuions. I could also be a fixed benefis sysem, where he conribuion rae is flexible. The PAYG sysem would hen be re-saed as 2 ( n ). This would imply ha if workers had more children, or if he child survival rae decreased, hey 6

9 2.3 Household behavior The uiliy of individuals in (5) is assumed o, firs, be composed of c and c2+, where ρ>- is he discoun rae: u ln c ln( n) 2ln c2 (5) Secondly, workers are assumed o be geneically programmed o value children (Dasgupa, 993, p. 356), where φ>0 is he weigh on children in uiliy. Children are herefore (also) considered o be consumpion equivalen goods. The idea o incorporae survival raes ino he uiliy funcion is inspired by Jorgensen and Jensen (2009), such ha if μ (μ2) increases, more workers (reirees) will survive o enjoy consumpion and children. The alruisic elemen in (6) is capured by U u u (6) where χ measures he degree of alruism from workers owards heir reired parens, by weighing your parens uiliy relaive o your own. The number of children is herefore deermined by wo feriliy moives: he geneic moive and he savings moive, where he former is incorporaed in he posiive effec of children in uiliy (5), while he laer arises hrough (6) because parens are assumed o be cerain ha heir children will suppor hem in old age Technology The producion srucure is also based on Wigger (2002) and assumes he endogenous growh se-up inspired by Arrow (962) and Romer (986). Idenical firms are assumed o employ labor and capial, K, in order o produce oupu, Y, in accordance wih a sandard producion: Y F( K, AN ), which is assumed o have consan reurns o scale. Labor produciviy, A, is endogenized by assuming a linear relaionship in (7) beween produciviy and capial per worker due o a posiive spill-over exernaliy from invesmens on produciviy K A (7) an where 0 is a posiive echnology parameer. This means ha f ( k ) F( k,), and ha he capial sock in efficiency unis is k K / AN, such ha he ineres rae is r f '( k ), and he wage rae is w A f( k ) k f '( k ). This Arrow-Romer approach implies ha he ineres rae is consan, and ha he wage rae is deermined by K w Af( ) f '( ) (8) N where f f ( ) '( ) / is he exernal reurn on capial caused by he spill-over of cumulaed invesmen upon labor produciviy (see Wigger, 2002). Consequenly, if N rises he capial-labor would no receive more in pension benefis anyway, since he rae, λ, would be fixed. Therefore, here would be no need o have more children for ha reason, so feriliy migh fall. This is an issue for our fuure research. 2 This is in erms of volunary inergeneraional gifs and sauory fixed pension conribuions. 7

10 raio will fall and he economy-wide level of echnology will decrease: hen A falls and k will remain consan. Produciviy growh in (9) is linked o he growh in he wage rae w K N g (9) w K N and is deermined by he growh in endogenous producion facors. The capial marke equilibrium condiion in (0) complees our model: K NS (0) 2.5 The compeiive equilibrium In his secion we derive and inerpre he firs order condiions of he individual opimizaion problem. We furhermore ransform he model ino a reduced form sysem of equaions, in erms of he variables we are ineresed in, which fully describes he dynamic pah of he economy. Our resuls are similar o hose of Wigger (2002), on which we build our formal analysis, bu all expressions are now adjused for he child and adul survival raes. To our knowledge, his exension is unique. By combining (5) and (6), individuals face he following opimizaion problem where aggregae uiliy in () is maximized subjec o he ineremporal budge consrain in (2): max U ln cln n 2ln c2 2ln c2 () c c w z w n z w Subjec o R R R Assuming an inernal soluion he firs order condiions hold wih equaliy. The firs opimaliy condiion is he Euler equaion ha opimally allocaes firs and second period consumpion ineremporally: c c 2 The second opimaliy condiion is more complicaed: (2) R (3) u w u z w u (4) 2 3 The fracion uφw in (4) deermines he opporuniy cos of having an addiional child, measured in erms of he marginal value of he los firs period consumpion. The righ-hand side shows he sum of wo componens: he marginal value of he gifs ha curren workers will receive from heir children in he nex period, and he marginal value of having anoher child. Alogeher (4) shows he benefis and losses of having anoher child in erms of marginal uiliies u, u2 and u3. By subsiuing hese, we find a posiive correlaion beween feriliy and firs period consumpion in (5) w z w (5) 2 c c2 n 8

11 and hus an inverse relaionship beween feriliy and savings. The hird opimaliy condiion (6) describes your rade-off beween consuming an addiional uni yourself and ransferring ha uni for your parens o consume. 3 c c 2 2 n (6) A higher degree of alruism, χ, and a larger adul survival rae (an increase in μ2) induce workers o value heir parens marginal uiliy of consumpion o a greaer exen. If you have many siblings (+n-) is large) who cooperae in supporing your parens, less of your income is needed o suppor hem, and hey consequenly become cheaper o care for. This means ha he price of supporing your parens goes down, and you choose o shif consumpion from yourself o your parens. In his paper we are mainly ineresed in inerpreing he effecs of changes in survival raes on he variables: feriliy rae, n, produciviy growh rae, g, savings rae, s, and he alruisic gif rae, z. The Arrow-Romer producion srucure allows us o derive he savings rae in (7) by combining (0) wih (7) s g n (7) For developing counries we would be ineresed in seeing an increase in capial savings. The direc posiive effec on he savings rae of a change in child survival is eviden from (7), bu he ne effecs on he savings level will become clear in our laer derivaions in general equilibrium. We herefore solve he model by reducing i o a sysem of equaions in he variables g, n and z: subsiue ino he opimaliy condiions (3) (6) he consrains () and (2), he wage rae (8) and he consan ineres rae, he pension benefi rae (4) and, finally, he capial marke equilibrium condiion in (0). Noe, ha he resuling expressions in (8), (9), and (20) incorporae he child and adul survival raes: r z n n g r z n g n r z n g r z n g 2 (8) (9) r z z n n g (20) 3 The hird opimaliy condiion in (6) is derived by lagging c2+ o be c2 and subsequenly combining he resuling expression wih IBC in (2) over zw. 9

12 n, g, z : feriliy, This procedure has defined he compeiive equilibrium as a sequence of only 0 produciviy growh and alruisic gifs. I is our aim, in he following secion, o analyze he effecs of he higher survival raes on hese hree key variables. 3. Comparaive Saics The purpose of his secion is o apply our model o sudy he effecs of higher child and adul survival raes on feriliy, produciviy growh and alruisic inergeneraional ransfers. We firs derive a closed form soluion for hose variables. 3. Feriliy, produciviy growh and alruisic ransfers To derive a closed form soluion for he hree key variables (z, g and n) in order o perform comparaive saics on he balanced growh pah, we employ he seady sae versions of (8), (9) and (20). 4 I is clear ha he survival raes (μ and μ2) affec heir seady sae pahs. 5 The expressions are idenical o hose in Wigger (2002), wih he excepion ha ours are adjused for he child and adul survival raes, respecively: 2 z, g 2 w r r 2 r 2 z, , r (2) (22) n, z, (23) The purpose of he following hree subsecions is o inerpre hese relaionships boh heoreically and numerically. The aim is hen o employ hem in policy reflecions on savings, feriliy and economic growh. This involves calibraing he model using wha is believed o be realisic parameer values in Table. We iniially calibrae he child and adul survival raes by μ= and μ2=, bu in he simulaions experimens are conduced wih increases in hese raes. In secion 4.2 we sudy increases in only he child survival rae, while in secion 4.3 only he adul survival rae is assumed o increase. Ulimaely, a composie increase in boh survival raes is sudied in secion To obain he seady sae version of (20), divide (8) by (20) such ha he resuling expression, χμ2(+n)(+g)= (+r), relaes he reurn o savings o he economy s growh facor in seady sae, (+n)(+g), scaled by he degree of alruism and he adul survival rae. 5 To derive z in (2), inser he seady sae version of (9) and (20) ino he seady sae version of (8) and isolae z. The produciviy growh rae, g, in (22) is found by isolaing g in he seady sae version of (8). By combining (22) wih he seady sae version of (20) we arrive a he expression for feriliy in (23). 0

13 Table. Calibraion of he Model Parameer Calibraion Inerpreaion 0.9 Degree of alruism Child survival rae Adul survival rae Consumpion discoun rae 0.4 Weigh on children in uiliy r 4 Ineres rae 0. PAYG conribuion rae 0. Cos of rearing a child 20 Exernal reurn on capial 3.2 Child healh In his secion we simulae he impac of an increase in he child survival rae, μ, on four variables: he produciviy growh rae, g, he feriliy rae, n, he alruisic gif rae, z, and he savings rae, s. The impac on hese four variables is illusraed in Figures 2 hrough 5. We idenify hree key effecs ha govern he dynamics of he model when μ increases: firs, when more members of he household survive, consumpion mus also be divided among hose addiional members. This yields less individual firs period consumpion, and consequenly renders second period consumpion more aracive in comparison. Equivalenly, he relaive price of firs o second period consumpion increases a he same rae as μ increases (see he ineremporal budge consrain in (2). Therefore, he savings rae in (7) increases proporionally o he increase in μ (Figure 2). Figure 2. Child Survival & Saving Rae s Figure 3. Child Survival & Produciviy g μ μ Second, he coss of using children as an indirec savings mechanism (raher han saving hrough capial invesmens) will increase because he savings rae and hus wages and produciviy increase. This increases he opporuniy cos of rearing children, and hus renders children less aracive as an old age savings mechanism, given he consan reurn on capial savings. Third, individuals gain higher uiliy in heir working period by surviving a a higher rae. This increases he marginal uiliy

14 for firs period consumpion so savings fall. These hree key effecs yield an ambiguous ne resul on savings, bu our simulaions show ha he wo posiive effecs ouweigh he single negaive effec. A larger seady sae capial sock generaes knowledge spillovers and increases labor produciviy in Figure 3, in accordance wih (22). There is an offseing effec, however, because he size of he labor force also increases when more children survive ino he working age. This reduces, bu does no dominae, he effec on wages and he produciviy growh rae. Since i is cosly o rear children for he purpose of providing for old age consumpion, he need for children as a savings device falls when savings, and hus second period income, increase. This exers downward pressure on feriliy, (+n) (Figure 4). For he same reason he alruisic gif rae also decreases (Figure 5). Figure 4. Child Survival & Feriliy n Figure 5. Child Survival & Transfers z μ μ There are consequenly feedback mechanisms hrough savings and feriliy: he more μ increases, he more he savings rae and produciviy growh will increase, and he more feriliy and alruisic gifs decrease. When feriliy falls, more resources are released for consumpion and savings, so he capial sock increases and furher enhances produciviy growh. An addiional mechanism hrough which second period income increases is he PAYG sysem. In accordance wih (4), he more μ increases, he higher will be he number of workers who pay fixed pension conribuions leading o higher benefis per reiree. This increases second period income, and reduces he alruisic ransfers hrough less need for cosly children as a savings mechanism. In his case where pension conribuions are fixed, curren workers know ha he more children hey have, he higher will be he number of fuure workers o pay fixed conribuions o hem generaing more reiremen benefis. This effec is an addiional elemen ha causes high feriliy, bu even hough a sysem wih fixed conribuions is included in Wigger (2002), Wigger does no analyze his link, and so leaves ou he imporance of he incenives for high feriliy caused by he fixed conribuions and he poenial gains of swiching regime o a fixed benefis PAYG sysem. 6 6 The laer argumen implies ha, no maer how many children workers have, he old age pension benefis will remain he same. Incorporaing such a sysem will lead o wo imporan effecs: firs, he feriliy incenive of pension benefis is removed so feriliy (and herefore also alruisic gifs) can be expeced o fall and produciviy growh can be expeced o increase. Second, if workers need fewer children o finance old age consumpion, hey will finance his hrough he oher available channel: capial savings. More savings lead o a higher capial sock 2

15 3.3 Adul healh This secion provides he oher leg of inerpreing healh improvemens in he demographic ransiion by analyzing an increase in adul survival. There is again an effec on he savings rae originaing from he ineremporal price srucure of consumpion: he prices are seen o depend direcly on μ and μ2 in he ineremporal budge consrain (2). Consequenly, when heir raio changes so will he opimal ineremporal smoohing of resources for consumpion (i.e. he savings rae). As such, he increasing price (μ 2 /R) of second period consumpion produces a decline in he savings rae (Figure 6). A couneracing effec is presen when μ 2 increases, however, because he marginal uiliy of second period consumpion increases, exering upward pressure on savings. 7 Figure 6. Adul Survival & Saving Rae s Figure 7. Adul Survival & Feriliy n μ2 μ2 The ne impac upon feriliy when μ2 increases is illusraed in Figure 7. The increase in he price of second period consumpion auomaically reduces he relaive price on children, (κw-z+w+μ2/r+), which increases he feriliy rae. When he increase in μ2 is small, feriliy will iniially fall, and will hen, due o he quadraic erms in μ2 in n(μ, μ2) in (23), increase he larger μ2 is. Since he savings rae iniially fell, he wage rae will also fall, providing households wih less income for all ypes of goods: c, c2 and (+n). This will iniially reduce feriliy, bu he more μ2 increases, he less income is available in old age and he savings moive for having children exers upward pressure on alruisic gifs and hus feriliy. As a sraegy o finance old age consumpion, workers herefore increase feriliy because children now become relaively cheaper han capial savings. An amplifying impac on feriliy and savings again originaes from he PAYG sysem. There is a couneracing effec on pension benefis, hough: here will be more reirees per household, for any given number of children, and his will generae fewer benefis o be disribued among reirees. The ne effec on benefis is ambiguous, bu he effec on feriliy, o a leas keep benefis unchanged, is clearly posiive and increasing in he size of μ2. and a higher produciviy growh rae. These dynamics can be elaboraed on analyically by reformulaing he PAYG sysem in erms of fixed benefis, bu his is ouside he scope of his paper o consider. 7 This is he mos well-known effec on savings, which is analogous o he resul from he lieraure on ageing, where workers save more o finance a longer reiremen period (see Chakrabory, 2004; and Finlay, 2006; Jensen and Jorgensen, 2008). 3

16 Since he ne effec on savings is negaive due o he presence of alruisic ransfers and endogenous feriliy he produciviy exernaliy on he wage rae diminishes, and consequenly produciviy growh will decrease (Figure 8). The fall in second period income, due o lower ne reurns o he declining capial sock, will render alruisic gifs relaively more imporan as a means of financing old age consumpion. As a resul, he gif rae in Figure 9 increases. Figure 8. Adul Survival & Produciviy g Figure 9. Adul Survival & Transfers z μ2 μ2 Increases in, for insance, governmen healh spending or general exogenous improvemens in living condiions are likely o improve healh, bu i is no clear ha such developmens only cause higher survival raes for children and no for aduls or he reverse. I is more reasonable o assume ha boh survival raes increase when healh invesmens increase. Having idenified, and analyzed in isolaion, he key dynamics of changes in child and adul survival raes on economic variables, we move on o sudy a composie change where boh child survival and adul survival raes increase simulaneously. 3.4 Child and adul healh The simulaneous and equi-proporional increase in child and adul survival will produce a combinaion of he effecs analyzed above. An increase in μ (μ2) led o a higher (lower) savings rae hus he composie shock enails perfecly offseing effecs on he savings rae (Figure 0). This is because he raio of he implici prices on firs and second period consumpion remains unchanged. We have idenified hree effecs on savings following an increase in child survival, μ. Since he effec from ineremporal prices is absen for a composie increase in survival raes, he posiive effec on savings is due o he effec from a lower price of children being larger han he effec from a higher marginal uiliy of firs period consumpion. The ne effec of μ2 on savings, on he oher hand, was negaive and dominaed by he fac ha children could be used as an old age savings mechanism. Savings also ended o rise because an increase in μ2 would increase he marginal uiliy of second period consumpion. The ne increase in savings for a composie increase in survival raes will, for hose reasons, generae similar effecs on feriliy, produciviy growh and alruisic gifs as sudied in 4

17 secion 4.2 for μ, albei a a lower scale because he effecs on hese economic variables are couneraced by he impacs of μ2. Figure 0. Composie Shock & Saving Rae s Figure. Composie Shock & Feriliy n μ,2 μ,2 The sum of effecs on feriliy is a clear decline (Figure ), due o increased savings, which leads o more capial per worker, more second period income, and less need for children as a mechanism for old age consumpion. In addiion, children become relaively cheaper when μ2 increases (see he price of children: κw-z+w+μ2/r+, so feriliy falls even furher (hence, alruisic gifs also fall; Figure 2). Regarding produciviy growh, he increased knowledge spillovers on he wage rae will yield a higher rae of produciviy growh (Figure 3). Figure 2. Composie Shock & Transfers z Figure 3. Composie Shock & Produciviy g μ,2 μ,2 The resuls above res upon he assumpion ha μ and μ2 increase in equal proporions such ha all effecs on he savings rae ne ou. In a case where he increase in μ is larger (smaller) han he increase in μ2, he increases in feriliy and produciviy growh will also be larger (smaller). 5

18 4. Discussion An increase in he child survival rae increases he number of dependens and reduces household resources. Furhermore, an increase in adul survival encourages savings, as we expec o live longer. This implies ha improvemens in child survival should have negaive effecs on economic oucomes, while improvemens in adul survival should have posiive effecs. However, once we ake hree aspecs ino accoun: firs, he negaive feriliy response o child survival, second, he possibiliy of inergeneraional ransfers and, hird, he compounding effec on capial savings from adul survival due o subsiuion for less expensive children as a savings mechanism, hen we observe ha child survival has a ne posiive effec on economic oucomes compared o he negaive effec on savings from adul survival. Exising lieraure only capures he posiive effec of adul survival on capial savings, which is usually modeled in erms of increasing life expecancy. In our model, when feriliy has declined o a cerain level, here will be no alruisic ransfers as reirees obain more and more income hrough capial savings. As a resul, he savings moive for having children, faciliaed by alruisic ransfers, gradually disappears and workers only have children based on he geneic moive. The model will hen collapse o feaure a sandard OLG model wih endogenous feriliy however, sill wih survival raes incorporaed. When adul survival hen increases furher, he impac upon capial savings will be posiive, in line wih exising lieraure (e.g. Chakrabory, 2004; Jorgensen and Jensen, 2009). The exising lieraure, herefore, is mainly argeed a developed counries, since i does no ake ino accoun he developing counry feaure of children as an old age securiy device. In he model, we have incorporaed he child and adul survival raes (in line wih Jorgensen and Jensen, 2009) ino he basic seup in Wigger (2004). Wigger s key argumen is ha an increase in public pensions will reduce feriliy and increase produciviy growh. He canno sudy hese dynamics in he conex of he demographic ransiion wih increasing survival raes. However, based on he resuls repored in his paper we can show ha his argumen sill holds: we examine he resuls from our simulaneous and equi-proporional increase in child and adul survival raes (from secion 4.4) for an increasing pension conribuion rae, θ. We find ha he feriliy pah (Figure 4) and produciviy growh pah (Figure 5) will move in favorable direcions: he pah for feriliy (produciviy growh) decline will shif downwards (upwards). This finding is in line wih empirical research ha shows a srong correlaion of feriliy reducion wih governmen provided pensions hrough children s care for reired parens via old age ransfers (see, e.g., Boldrin e al., 2005). These dynamics occur because increasing pension benefis o reirees will reduce heir need for alruisic ransfers. Thus, hey can save resources on child rearing, and make hese available for consumpion and capial savings. This suggess ha increasing public pensions will increase produciviy growh, which is a conroversial asserion. 6

19 Figure 4. Feriliy and Pensions n Figure 5. Produciviy and Pensions g μ,2 ax=0. ax=0.2 ax=0.5 μ,2 ax=0. ax=0.2 ax=0.5 The key dynamics o ake ino accoun is he presence of alruisic ransfers and endogenous feriliy. When he economy reaches he poin in he demographic ransiion where feriliy has declined so much ha he only moive for having children is he geneic moive, parens realize ha hey can no longer save child-rearing resources by swiching o capial savings and away from having children as an old age savings mechanism. Afer his poin, an increase in public pensions will reduce he seady sae capial sock in line wih convenional wisdom. However, while alruisic ransfers are sill operaive, a rise in public pensions increases produciviy growh and reduces feriliy and herefore speeds up he process by which a counry will go hrough he demographic ransiion. We have argued in his paper ha a shif from a fixed conribuions PAYG sysem owards a fixed benefis sysem would even furher reduce feriliy and increase produciviy growh. This will happen as parens realize ha having more children will no provide hem wih more pension benefis, bu only draw down on heir resources. While his is an issue for our fuure research, we expec ha he feriliy pahs would shif down (up) even furher han in Figure 4 (5). The model incorporaes perfec capial markes, which is a limiaion ha should be addressed in fuure work on his opic. We would expec ha if capial markes were imperfec, he reurn on capial savings would fall and children be rendered more aracive as a savings mechanism. 8 Over he course of economic developmen capial markes would develop, and he relaive reurn on capial savings would increase depressing furher he savings moive for having children, as illusraed in his paper. In our model we chose o absrac from educaion. The effecs of educaion in an ineremporal seing are well undersood: he qualiy/quaniy rade-off informs us ha an increase in child survival will lower feriliy and hus increase he resources (for educaion) devoed o each child. In his conex, an issue for our fuure research is o incorporae human capial formaion alongside a wosided alruism formulaion of uiliy (modifying (6) such ha U= πu-+u+π2u+). This would allow us 8 In mos developing counries an enormous problem is access o credi (very high ineres rae), savings, insurance and oher capial marke insrumens especially in rural areas, where microfinance is ofen he only opion for small-scale credis. 7

20 o race he effecs of beer healh in he demographic ransiion hrough a framework wih wo-sided alruism, wo feriliy moives and human capial formaion as an addiional feaure of endogenous economic growh. 5. Conclusion Developed counries have all gone hrough he demographic ransiion a some poin in hisory. However, several developing counries have no even passed hrough he firs sage of low moraliy, and many oher counries have sill no enered he second sage of low feriliy. As a resul, hese counries are resrained from he enormous poenial for economic gains ha are associaed wih lower dependency raios. In order o reduce povery, i is essenial for hese counries o obain high survival raes in order o quickly reduce feriliy raes. In his paper, we find ha a policy rule of child healh will aid counries in achieving his objecive. An addiional key finding is ha by increasing (or modifying) public pensions here is scope for reaching even more favorable pahs for feriliy reducions and produciviy growh. Life expecancy is a measure ha conains informaion abou he age specific survival raes: a rise in child survival will increase life expecancy, as will an increase in adul survival. Our decomposiion of life expecancy ino child and adul survival, respecively, is unique relaive o he exising lieraure on his opic, where only adul survival (as a proxy for life expecancy) is modeled. We derive our resuls by reflecing on wo moives for having children: he savings moive and he geneic moive, respecively, and faciliae he former by incorporaing, ino an OLG model wih endogenous feriliy, he possibiliy for alruisic ransfers from workers o heir reired parens. If eiher he relaive opporuniy cos of having children or he relaive reurn on capial savings falls, we find a decline in capial savings and an increase in feriliy hrough he savings moive for having children. Such relaive price changes occur when child and adul survival raes change disproporionaely, and we find a posiive (negaive) ne effec on capial savings when child (adul) survival increases. In he case where boh child and adul survival raes increase simulaneously, and in equal proporions, we find no change in he savings rae, due o our modeling of survival raes as implici ineremporal prices. Our model consequenly provides us wih imporan insighs ino he savings behavior ha evolves as a counry goes hrough he demographic ransiion. This seup leads us o conclude ha an increase in child survival will promoe capial savings and discourage savings hrough children as an old age securiy device. Such dynamics will ulimaely lead o lower feriliy and higher produciviy growh. In conras o convenional wisdom, we find ha as long as alruisic inergeneraional ransfers are operaive, an increase in adul survival is likely o be derimenal o produciviy growh. The exising lieraure indicaes ha increases in he adul survival rae will increase capial savings and hereby economic growh, bu his resul is modified in he sages of economic developmen where he subsisence of reired parens o some degree depends upon financing by heir working-age children: increasing adul survival (life expecancy) will no unambiguously lead o 8

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