WORKING PAPER. Inflation and human capital formation : theory and panel data evidence

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1 FACULTEIT ECONOMIE EN BEDRIJFSKUNDE HOVENIERSBERG 24 B-9000 GENT Tel. : 32 - (0) Fax. : 32 - (0) WORKING PAPER Inflaion and human capial formaion : heory and panel daa evidence Freddy Heylen Arne Schollaer Gerdie Everaer Lorenzo Pozzi SHERPPA, Ghen Universiy, Belgium April /174 Correspondence o: Freddy Heylen, SHERPPA (Sudy Hive for Economic Research and Public Policy Analysis), Ghen Universiy, Hoveniersberg 24, B-9000 Ghen, Belgium, phone , fax , e- mail: Acknowledgemens: This paper builds on earlier work by Heylen, Schollaer and Dobbelaere (2001), who obain similar conclusions. The heoreical model and he panel daa resuls in he curren paper are new conribuions. We are graeful o Dirk Van de gaer, Ferre De Graeve, Rafael Doménech, Ger Peersman, Glenn Rayp and seminar paricipans in Maasrich for mos helpful commens. Any remaining errors are ours. D/2003/7012/12

2 Absrac Exising moneary growh heories predic eiher negaive or neural effecs from inflaion on human capial. In his paper we develop a simple alernaive model, which can generae posiive effecs. Our empirical analysis for 93 counries in ends o confirm hese posiive effecs. Using recen GMM panel daa procedures, we find ha rising inflaion basically simulaes human capial. A robus negaive effec can be observed only a exremely high inflaion raes. A represenaive hreshold may be 100%. For inflaion raes below 15%, he effec of rising inflaion seems insignifican. The laer resul can also be raionalized from our model. JEL Classificaion: E31, J24, O40 Keywords: Human capial, educaion, inflaion, moneary growh models, panel daa

3 1 1. Inroducion Since he early 1980s, achieving very low and sable inflaion has become he primary goal of moneary policy makers in many counries, especially in Europe. To some exen, his is surprising. Firs of all, here is no unambiguous heoreical jusificaion for his policy (Orphanides and Solow, 1990; Temple, 2000). Second, he only robus resul from many recen empirical sudies on inflaion and economic growh, is ha high inflaion is bad for growh. For low inflaion raes, say inflaion raes below 10 or 15%, here is no such consensus, on he conrary. In mos sudies, low inflaion exers no significan negaive influence on growh (see e.g., Sarel, 1996; Barro, 1997; Clark, 1997; Bruno and Easerly, 1998; Ghosh and Phillips, 1998; Judson and Orphanides, 1999; Ahmed and Rogers, 2000). 1 Afer an exensive survey of he lieraure, Temple (2000, p. 420) concludes ha "any case for price sabiliy which relies on a posiive growh effec should coninue o be regarded wih considerable scepicism". Among recen sudies, only Andrés and Hernando (1999) and - arguably - Bassanini e al. (2001) sugges oherwise. This paper is moivaed by a double observaion. The firs relaes o he significance of human capial for growh. Theoreically, his has been esablished clearly in a wide range of recen models, beginning wih Romer (1986) and Lucas (1988). Empirically, alhough here are dissonan voices (e.g., Islam, 1995; Caselli e al., 1996; Klenow and Rodríguez-Clare, 1997; Kalaizidakis e al., 2001), he balance of recen evidence suppors he hypohesis ha having or accumulaing more human capial, especially a he secondary and eriary level, simulaes per capia income growh (e.g., Mankiw e al., 1992; Benhabib and Spiegel, 1994; Engelbrech, 1997; Barro, 1999; de la Fuene and Doménech, 2001; Bassanini and Scarpea, 2001; Caselló and Doménech, 2001; Temple, 2001). The second observaion is ha exising work on he effecs of inflaion on human capial sill is raher limied, especially empirical work. We know of no empirical sudy. Valuable heoreical work has been done by, among ohers, Wang and Yip (1992), Gomme (1993), Jones and Manuelli (1995), Pecorino (1995), Mino (1997), Gillman and Kejak (2001) and Chang (2002), who develop moneary growh models wih endogenous human capial. In general, hese models predic eiher neural or negaive inflaion effecs on human capial. The srucure of his paper is as follows. In Secion 2 we firs briefly discuss exising moneary growh models wih endogenous human capial. Then, we presen a simple 1 For he sake of correcness, i should be menioned ha mos of hese sudies invesigae he effec of inflaion in growh regressions, conrolling for physical capial accumulaion. Sarel (1996) is an excepion. Consequenly, he esimaed coefficien for inflaion in hese sudies capures only effecs on produciviy and no on physical capial formaion. Does his lead o any underesimae? No necessarily. Considering Barro's (1997) resul ha he effec of moderae inflaion on fixed invesmen is also insignifican, here is no need o change he conclusions.

4 2 alernaive model, which can generae posiive effecs of inflaion on human capial. Inuiively, a crucial idea is ha inflaion undermines he producive capaciy of he economy, which makes working less aracive. To he exen ha young agens expec high inflaion o be emporary, hey will sudy now and work laer, wih more human capial and under beer expeced aggregae condiions. Secion 3 goes ino he empirical relaionship beween inflaion and human capial. We esimae various equaions using recen GMM panel daa echniques, which pay paricular aenion o he issues of simulaneiy and counry heerogeneiy. Our empirical resuls reveal ha rising inflaion basically simulaes human capial. A robus negaive effec can be observed only a very high inflaion raes. A represenaive hreshold may be 100%. For inflaion raes below 15%, he effec of rising inflaion on human capial seems o be insignifican. These resuls largely confirm he predicions of our alernaive heoreical model. Wih respec o oher deerminans of invesmen in human capial, we find a significan role for governmen spending on educaion. Secion 4 concludes and discusses some policy implicaions of our findings. 2. Inflaion and human capial formaion : heory Recen models of growh, beginning wih Romer (1986) and Lucas (1988), as well as he balance of empirical work (see Secion 1) emphasize ha human capial invesmen is an imporan facor ha conribues o long-run growh. I hen comes as no surprise ha models on inflaion and growh have gradually aken ino accoun human capial as an endogenous variable. In general, hese moneary growh models predic eiher neural or negaive effecs from inflaion on human capial invesmen. We briefly discuss hese models characerisics in secion 2.1. In Secion 2.2. we develop an alernaive model. Our aim is o demonsrae ha under cerain condiions inflaion can generae posiive effecs on human capial Exising heoreical models Wang and Yip (1992) and Pecorino (1995) specify wo-secor models where money eners as a facor of producion in he final goods secor, i.e. he secor ha produces consumer and physical capial goods. Money does no ener in he "educaion indusry", i.e. he secor where new human capial is being produced. In boh models, oal labor supply is exogenous. There is no labor-leisure choice. Wang and Yip (1992) obain neural effecs from money growh and inflaion on human capial and oupu growh. A crucial elemen is heir Lucas-Uzawa assumpion ha he producion of human capial does no require physical capial as an inpu. Pecorino (1995) follows King and Rebelo (1990) and includes physical capial in he human capial producion funcion. Higher money growh and inflaion now undermine oupu

5 3 growh and human capial. The reason is ha higher inflaion discourages he use of money, which reduces he marginal produc and he oupu of physical capial. A smaller physical capial sock has negaive consequences for he reurn and oupu in he human capial secor. Exending Wang and Yip (1992), Chang (2002) obains negaive effecs from inflaion and money growh by including real money as an inpu ino human capial producion. Several auhors inroduce money via a cash-in-advance consrain (e.g., Gomme, 1993; Jones and Manuelli, 1995; Mino, 1997). Neural effecs of inflaion on human capial and growh can be obained in hese models if he cash-in-advance consrain only applies o consumer goods and if labor supply is exogenous. Oherwise, inflaion effecs are ypically negaive. For example, Gomme (1993) makes he firs assumpion, bu endogenizes labor supply, as well as he allocaion of labor. Labor can be employed eiher in he producion of goods in profi-maximizing firms or in new human capial producion ouside he marke. Inflaion reduces he effecive reurn o working since - due o he cash-in-advance consrain - income earned in he curren period canno be spen unil he nex one. This makes households subsiue leisure for labor. Boh goods producion and human capial producion will fall. Mino (1997) obains negaive effecs from inflaion wih fixed labor supply, bu he assumes a cash-in-advance consrain on invesmen spending. As in King and Rebelo (1990) and Pecorino (1995), here are wo secors, boh employing physical and human capial. Under a cash-in-advance consrain applying o invesmen in one of hese secors, higher money growh produces a direc negaive inflaion ax effec on he rae of reurn o capial, discouraging capial formaion. Anoher srand of recen lieraure relevan o he inflaion/human capial relaionship, pus he effec of inflaion on he allocaion of human capial a he cener. Referring o among ohers De Gregorio (1992), Temple (2000) noes ha a imes of (very) high inflaion, alened individuals may be divered o aciviies in he financial secor and away from eaching 2. This may undermine he produciviy of schooling for youngsers and as a consequence he ime hey allocae o building human capial. Insead of educaion, hese youngsers migh prefer financially moivaed aciviies hemselves An alernaive heoreical approach In his secion we develop a simple alernaive model. Firs, we give up he infiniely lived agen assumpion ha underlies he above-described moneary growh lieraure. Second, 2 Aiyagari e al. (1998) provide an ineresing empirical illusraion of his argumen. Alhough heir focus is differen, hese auhors show for high inflaion counries (Argenina, Brazil, Israel) ha here is a srong posiive relaionship beween he employmen share in he banking secor and consumer price inflaion. English (1999) also finds ha he size of a naion s financial secor is srongly affeced by is inflaion rae.

6 4 insead of direcly inroducing money growh and inflaion ino he model, we build on sandard resuls from he lieraure on he real effecs of inflaion (see Temple, 2000, for a survey). An imporan resul is ha inflaion may undermine oal facor produciviy in producion, e.g. by forcing economic agens o economize on he use of money or by disruping he crucial role of he price mechanism in he efficien allocaion of resources. Basic assumpions Our analyical framework consiss of a simple wo-period OLG model for a small open economy. We assume perfec inernaional mobiliy of physical capial, bu immobile labor and human capial 3. We consider wo generaions, he young and he old. In each period of life people are endowed wih one uni of (non-leisure) ime. Young people can choose eiher o work and generae labor income, or o sudy and build human capial (a non-marke aciviy). Labor income is parly allocaed o he consumpion of a single commodiy and parly o savings. Old people do no sudy anymore, hey only work and consume. They leave neiher bequess nor debs. Economy-wide savings in a paricular period (i.e. he savings by he young) generae he sock of non-human wealh in he nex period. Non-human wealh is held as physical capial employed in domesic or foreign firms. The rae of reurn on nonhuman wealh is he (given) world real ineres rae, which equals he ne marginal produc of world physical capial. Wihou loss of generaliy we assume he world ineres rae o be consan over ime. Furhermore, firms are assumed o ac compeiively. They employ physical capial ogeher wih exising echnology and he labor provided by he young and he old. A final imporan assumpion is ha, following Azariadis and Drazen (1990), educaion generaes a posiive exernaliy in ha he average level of human capial of a generaion is inheried by he nex generaion. In wha follows, we concenrae on he core elemens of he model: he ime allocaion decision of young people, he behavior of domesic firms and he deerminaion of aggregae oupu and wages. These allow us o assess he poenial influence of inflaion. Since populaion growh is irrelevan o our argumen, we assume ha all generaions are of equal size (N). Populaion is consan. Individuals The preferences of an individual born in are represened by a log-linear uiliy funcion of he form: 3 Seminal work in his radiion has been done by Diamond (1965), using earlier insighs of Samuelson (1958). Early open economy versions of he model puing human capial formaion a he cener, have been developed by Buier and Klezer (1993, 1995) and Nielsen and Sørensen (1997).

7 5 u = ln c + φ ln c (1) 1 2 where he superscrip indicaes he period of birh/youh. Lifeime uiliy is defined over consumpion when young ( c 1 ) and consumpion when old ( c 2 ). Second period uiliy is discouned for he rae of ime preference ρ, wih φ = 1/(1+ρ). Individuals will maximize Equaion (1), subjec o he consrains described in (2) and (3). c 1 s1 = w (1 e ) h1 + (2) c = w + h + s (1 r ) (3) wih : h + 2 = (1 g( e )) h1 In hese equaions, w and w +1 sand for he real wage per uni of effecive labor in periods and +1. The effeciveness of a full-ime young worker born in equals his human capial inheried from he old generaion. Since young workers allocae a fracion educaion, hey earn a real wage and w + supply 2 (1 g( e )) h1 h 1, e of heir ime o w (1 e ) h1. In +1, when hey are old, hey work full-ime h = + unis of effecive labor, yielding a real wage + 1(1 g( e )) h1. The funcion g( e ) describes he reurn on invesmen in educaion. We assume ha g(0)=0, g' >0, lim e 0 g'= and g"<0 4. A funcion saisfying hese condiions α.e γ is g ( e ) =, wih 0<γ<1 and α>0. In his funcion, α is he main deerminan of he γ produciviy of schooling. The educaion exernaliy described above implies ha he young in he nex period (+1) also benefi from he educaion invesmen of he young in. Algebraically, h = h2 = (1 g( e )) h1. Equaion (2) describes he consrain ha young people face while sharing heir ime beween working (fracion income from work 1 e ) and invesing in human capial (fracion e ) and heir w (1 e ) h1 beween consumpion 1 c and savings s 1. If young individuals decide o sudy, hey will earn less when young, bu hey will develop skills which raise heir effecive labor and income when old. If hey choose o work, hey will earn income immediaely which enables hem o consume and o build non-human wealh, also generaing more income in he fuure. The rae of reurn on non-human wealh is he world real ineres 4 lim e 0 g'= implies ha young individuals will allocae a posiive fracion of heir ime o schooling. Similarly, he logarihmic uiliy funcion implies ha individuals will choose posiive consumpion levels in each period ( ci > 0 ).

8 6 rae r, which is exogenous and assumed o be consan over ime. Noe ha Equaion (3) incorporaes he assumpion ha old people leave neiher bequess nor debs. They consume heir oal labor income and accumulaed non-human wealh. Subsiuing Equaions (2) and (3) ino (1), lifeime uiliy of a person who is young in can be rewrien as : u ( w (1 e )h s ) + ln( w (1 + g( e ))h + s (1 + r )) = ln φ + (4) Maximizing wih respec o s 1 and of simpliciy, we drop he superscrip. 1 c 2 e yields he following firs order condiions. For he sake r = φ (5) c w h1 w + 1g' ( e )h1 = φ (6) c1 c2 Equaion (5) is he familiar condiion equaing he marginal uiliy of consumpion when young o he discouned marginal uiliy when old of he consumpion allowed by savings. Equaion (6) imposes ha he marginal uiliy gain from working when young (LHS) should equal he marginal uiliy gain from invesing in human capial (RHS). The laer reflecs he discouned marginal uiliy from consuming he addiional income due o higher labor effeciveness. Subsiuing (5) ino (6), we obain ha he opimal fracion of ime allocaed o sudying should saisfy g' ( e ) w = (1 + r ) (7) w + 1 Since g " < 0, i follows ha young people will sudy more (and work less) when he real ineres rae and he raio of curren o fuure real wages are lower. Assuming, as menioned above, ha γ α.e g ( e ) =, wih 0<γ<1 and α>0, i can be derived ha : γ 1 α w γ e = 1 + r w (7') Nex o he real ineres rae and he relaive real wage, his equaion emphasizes he major role of α, he produciviy of schooling. If sudying resuls in a sronger increase in human capial and fuure labor effeciveness, young people may wish o inves more in educaion.

9 7 This is a well-known resul from he lieraure (e.g., Becker, 1964; Williams, 1979; Lucas, 1988). One obvious deerminan of α would be governmen educaion spending. More and beer eachers, beer books, ec., should raise he produciviy of schooling and make invesmen in educaion more aracive (e.g., Capolupo, 2000; Glomm and Ravikumar, 2001). Domesic firms, oupu and facor prices Firms ac compeiively on oupu and inpu markes and maximize profis. All firms are idenical. Toal domesic oupu is described by he producion funcion (8) which exhibis consan reurns o scale in aggregae physical capial (K ) and effecive labor (H ). Equaion (9) describes oal effecive labor supplied by young and old workers. Noe our assumpion ha boh generaions have equal size (N) and ha young workers inheri he human capial of 1 he old ( h 1 = h ). Toal facor produciviy (A ) is assumed o be counry-specific and given, 2 a leas for he momen 5. Compeiive behavior implies in Equaion (10) ha firms will carry physical capial o he poin where is marginal produc ne of depreciaion equals he world real ineres rae. The depreciaion rae is indicaed as δ. The real ineres rae being given, firms will insall more capial when oal facor produciviy improves or when he amoun of effecive labor increases. Furhermore, perfec compeiion implies equaliy beween he real wage and he marginal produc of effecive labor (Equaion 11). Higher real wages follow from an increase in physical capial per uni of effecive labor or an improvemen of oal facor produciviy. Y = A K H 0 < β < 1 (8) β 1 β H = N(1 e )h1 + Nh1 = N( 2 e ) h1 (9) = βa r δ 0 δ 1 (10) β ( K / H ) 1 β K β w = (1 )A (11) H Rewriing (8) as ha Y K A β H = H, and subsiuing (9) and (10) for H and K, we obain H Y = A 1 /( 1 β ) β r + δ β /( 1 β ) N( 2 e ) h 1 (8 ) 5 We give up he assumpion ha A is given on he nex page, where we allow for he effec of inflaion shocks.

10 For given srucural parameers (α, γ, β, δ) and assuming consan N, r, and A, we obain he long-run (per capia) growh rae of he economy as 8 1 Y h h 1 2 α.e ln ln ln = ln(1 + g( e )) = ln( Y = = 1 h 1 h 1 γ γ ) (12) where i is aken ino accoun ha e will be consan over generaions. In line wih some earlier models (e.g., Lucas, 1988; Azariadis and Drazen, 1990; Buier and Klezer, 1993), he long-run (per capia) growh rae is posiively relaed o he produciviy of schooling (α) and o he fracion of ime ha young people allocae o educaion (e). The real effecs of inflaion Our aim is now o demonsrae ha under cerain condiions inflaion can simulae (long-run) human capial and oupu. Mainly, i has o be assumed ha he young generaion in -1 did no anicipae high inflaion in, and ha he young generaion in does no expec i o persis unil +1. Considering ha generaions consis of 20 o 25 years, his assumpion seems no unreasonable. All we furher need is he sandard argumen ha inflaion during a period undermines he efficien allocaion of facors of producion in ha period (Temple, 2000; Issing, 2001). In our model his is refleced by a drop in oal facor produciviy A. Since his negaively affecs he marginal producs of capial and labor, inflaion will also bring down he physical capial sock (K ) and he real wage (w ). Only invesmen in educaion ( e ) may benefi. Assuming ha i is no expeced o persis over generaions, high inflaion in will reduce individuals' percepion of he relaive wage w /w +1. The fall in w for given w +1 will make working less, and sudying more aracive (see Equaion (7)). Human capial will rise 6. Figure 1 illusraes hese effecs of emporary high inflaion, as well as is long-run consequences. We assume ha due o high inflaion in period 1 oal facor produciviy in ha period falls by 10%. This fall was no anicipaed and once i occurs i is no expeced o persis. Individuals consider high inflaion o be limied o one generaion. We impose he following parameer values and benchmark levels for he main variables in period zero: α=0.75, β=0.5, γ=0.25, e=25%, A=N=h 1 =1, H=1.75, K=0.13, Y=0.48 and w= The iniial values for A and w are also he expeced ones for laer periods. The level of e and he chosen parameer values for α, β and γ deermine he benchmark evoluion of h 1, H, K and Y. 6 Obviously, if young individuals in expec high inflaion (and low real wages) o persis, hey canno benefi from sudying more. Noe also he imporance of our assumpion ha high inflaion was no anicipaed in -1. If i were, he young generaion in -1 would expec a high relaive real wage (w -1 /w ) and would sudy less. So e -1 would fall, compensaing he rise in e. 7 Underlying values for he real ineres rae (r) and he depreciaion rae (δ ) are and Assuming ha a period conains 25 years, hese values correspond o annual ineres and depreciaion raes of 3% and 5%.

11 9 Boh pars of figure 1 show he deviaions from his benchmark caused by high inflaion (low oal facor produciviy) in period 1. The precise numbers in his figure are of limied imporance. Wha maers is he direcion of change of he main variables, which is robus o changes in α, β and γ. The firs par shows he evoluion of he ime allocaion of young individuals, as well as he inheried human capial sock of young generaions in laer periods. As can be seen, here is a emporary rise in he fracion of ime allocaed o schooling in period 1. Due o he inergeneraional educaion exernaliy, his has permanen effecs on he human capial sock of laer young generaions. The increased schooling effor of young people in period 1 explains he fall in employed effecive labor (H) in ha period. In laer periods employed effecive labor benefis from he rise in he human capial of all young and old workers. Lower oal facor produciviy and lower employed effecive labor in period 1 cause a drasic fall in he marginal produc of physical capial in ha period. Firms respond by reducing he amoun of capial (K) insalled. In laer periods he physical capial sock will be higher han ever before, due o he permanen increase in effecive labor. The laer pushes he marginal produc of physical capial above he world ineres rae, causing an inflow of capial. The evoluion of real oupu reflecs he evoluion of is underlying deerminans (A, K, H) according o Equaion (8). During high inflaion, oupu suffers. In he long-run, however, our model predics a posiive oupu effec. Finally, he real wage per uni of effecive labor (w) decreases wih he fall in boh oal facor produciviy and he raio of physical capial o effecive labor in period 1. Laer, here is no influence on he real wage anymore since boh A and K/H reurn o heir iniial (benchmark) levels. Figure 1. Simulaed effecs of (emporary) inflaion: an illusraion 10% 8% 6% 4% 2% 0% -2% Generaion fracion of educaion ime (e, deviaion in %-poins) inheried human capial (h, deviaion in %) 10% 5% 0% -5% -10% -15% -20% -25% -30% Generaion Effecive labor (H, deviaion in %) Capial (K) and oupu (Y, deviaions in %) Real wage (w, deviaion in %) Noe: The daa show deviaions from a benchmark simulaion wihou high inflaion (i.e. wihou a 10% fall in oal facor produciviy (A )) in period 1. Several exensions of our model are possible. Inflaion is ofen blamed, no only for undermining (expeced) efficiency in producion, bu also for creaing uncerainy abou real

12 10 coss and revenues in producion. Furhermore, as emphasized by Feldsein (1983), due o shorcomings in he ax sysem mainly he fac ha only he hisorical cos of an asse can be wrien off inflaion de faco raises he real depreciaion rae of physical capial and undermines is ne reurn. A furher reducion of he physical capial sock and he real wage in are he resuls. These exensions provide addiional argumens why inflaion may make working less aracive, and sudying and human capial formaion more aracive. 3. Inflaion and human capial formaion : he empirical relaionship 3.1. Some preliminary resuls Despie he generally acknowledged imporance of human capial for economic growh, empirical sudies on he effecs of inflaion on growh have disregarded human capial. Everyone seems o assume ha he expeced (and ofen observed) negaive effecs of inflaion on physical capial 8 also apply o human capial. Exising moneary growh models wih endogenous human capial jusify his assumpion. So may Figure 2. This figure relaes a proxy for he human capial sock in 89 developed and developing counries in 1980, 1990 and 2000 o average annual consumer price inflaion in he preceding decade. Human capial is measured as average years of oal schooling in he populaion of age 15 and older (Barro and Lee, 2000). As can be seen, a negaive relaionship becomes apparen. Correlaion equals Figure 2. Inflaion and human capial (a) in 89 counries in 1980, 1990 and 2000 (b) Human capial N.Obs. 248, R = -0,27 a Human capial is measured as average years of oal schooling in he populaion of age 15 and older. Inflaion is consumer price inflaion. b Daa sources: Human capial: Barro and Lee (2000); inflaion: World Bank (2001). For furher deails, see Appendix 1. 8 Recall ha our model in he previous secion also predics negaive effecs on physical capial during periods of rising (high) inflaion Inflaion (log, preceding decade)

13 11 Figure 2 nowihsanding, his secion will challenge he view ha physical and human capial are equal wih respec o heir response o inflaion. In line wih our model, we presen economeric resuls indicaing ha rising inflaion simulaes human capial formaion, excep a exremely high and (in some regressions) very low levels. A firs sep is o noe ha he negaive relaionship in Figure 2 is no robus. Table 1 conains a number of illusraive regressions. The firs of hese describes he regression line in Figure 2. As can be seen in he second regression, as soon as one conrols for lagged human capial (i.e. he human capial sock en years earlier), he negaive effec from log inflaion (lnπ i,dec ) becomes insignifican 9. Also including seven regional dummies in regression (3) yields an insignifican posiive effec from inflaion. For deails abou hese dummies we refer o he noe below he able. Regression (4) specifies anoher funcional form for he inflaion effec. Insead of log inflaion, i includes boh he inflaion level and is square. The former geing a posiive sign and he laer a negaive one, his equaion shows for he firs ime he invered U-shaped relaionship ha will become imporan in he remaining par of his secion. Table 1. Inflaion and human capial: some simple regressions (a) (1) H i, = ln(π i,dec ) (16.4) (4.44) (2) H i, = H i, ln(π i,dec ) (7.52) (54.3) (0.93) (3) H i, = H i, ln(π i,dec ) + regional dummies (4.57) (33.7) (0.27) (4) H i, = H i, π i,dec 0.97 π² i,dec / regional dummies (4.71) (34.0) (0.30) (0.28) R²(adj) N.obs a The esimaion mehod is pooled OLS. Absolue -values based on Whie heeroskedasiciyconsisen sandard errors in parenheses. The subscrip i refers o 89 counries, he years concern 1980, 1990 and H i, sands for average years of oal schooling in he populaion of age 15 and older in counry i and year ; π i,dec is he average consumer price inflaion rae in counry i in he decade before. Regressions (3) and (4) conain regional dummies for he OECD, Norh Africa and he Middle Eas, Sub-Saharan Africa, Souh Asia, Eas Asia and he Pacific, Lain America and he European economies currenly in ransiion Basic economeric framework and consideraions This Secion and he nex conain more rigorous empirical work. From he beginning i has o be made clear ha choosing average years of schooling as an empirical proxy for human capial, implies some small deviaions from he heory discussed in he Secion 2.2. On he 9 Noe ha he esimaed long-run effec of log inflaion in his regression is also insignifican. The long-run coefficien equals 0.82, which is comparable o he resul in Regression (1). The corresponding -value is 1.02.

14 12 one hand, hings become more simple because changes in years of schooling direcly reveal he fracion of ime invesed in educaion e, which is cenral in our heory. For example, a an individual level, when years of schooling beween and -5 rise by 1, i will be clear ha his individual has allocaed 20% of his ime o educaion. As a consequence, wih daa on years of schooling, esing hypoheses on he deerminans of e is relaively easy. On he oher hand, his proxy also inroduces a complicaion. If knowledge can be mainained over generaions, even wihou invesmen in educaion by he young, human capial will show a uni roo. This is he inergeneraional exernaliy assumpion from Secion 2.2. Wih average years of schooling as a proxy, however, here can be no uni roo. If he young do no sudy, average years of schooling will gradually fall since every period educaed older people will die. Empirically, his idea of depreciaion of (our proxy for) human capial will have o be aken ino accoun. Equaion (13) pus our hypoheses ino a workable economeric framework. In his equaion, H i, H i,-5 sands for he change in he human capial sock in counry i beween years and -5. The human capial sock is - as in Figure 2 and Table 1 - defined as average years of oal schooling for he populaion of age 15 and older. The years ha we consider are 1975, 1980, 1985, 1990 and 1995, he maximum number of counries is Our choice for daa a 5-year inervals is mainly inspired by daa availabiliy, especially in he high inflaion ranges. Consrucing daa a 5-year inervals yields 414 observaions. Inflaion exceeds 20% in 80 cases, 30% in 55 cases, 50% in 27 cases and 100% in 11 cases. By comparison, a 10-year inervals here are only 15 observaions wih an inflaion rae higher han 50% and 6 observaions wih inflaion higher han 100%. H 2 i, H i, 5 = a0 + a1h i, 5 + a2 i,5 y + a3π i,5 y + a4 GE) i, 5 y π ln( + α + ε (13) i i wih : α i an unobserved counry-specific fixed effec, and ε i he error erm. Building on he heory described in he previous secions, i will be our hypohesis ha average per capia invesmen of ime in educaion and herefore he change in average years of schooling - is mainly influenced by wo variables: per capia governmen spending on educaion and inflaion. Higher governmen spending on educaion may raise he produciviy of schooling and make invesmen in educaion more aracive. Inflaion is included as a deerminan of he efficiency wih which labor and capial can be employed in producion. Included explanaory variables are average annual consumer price inflaion in he period of 10 The numbers of counries i and years are limied by daa availabiliy for inflaion and especially governmen spending on educaion (see Appendix 1 for deails). For human capial five yearly daa since 1960 are available for mos counries.

15 13 five years from -5 o -1 (π i,5y ), he square of average annual inflaion and he log of average annual real per capia governmen spending on educaion in US dollar (PPP) during ha same period of five years (lnge i,5y ). As o inflaion, Secion 2 has shown ha boh posiive and negaive signs can be jusified. Including inflaion and is square allows for a broad range of empirical possibiliies. From our model in secion 2.2. we would expec a 2 o be posiive. Exising moneary growh models, however, sugges a 2 o be zero or negaive. The idea menioned above of an invered U-shape beween inflaion and human capial would require a 2 o be posiive and a 3 o be negaive. The logarihmic specificaion for GE reflecs he idea of decreasing reurns. Our expecaion is ha a 4 is posiive. Finally, we also include H i,-5 a he RHS of Equaion (13). We expec a 1 o have a negaive sign, mainly capuring he idea of depreciaion when educaed old people leave he populaion. Furhermore, one would expec a 1 o be negaive if invesmen in educaion gradually becomes less aracive or more difficul a high levels of schooling. A jusificaion for he former would be diminishing reurns o educaion, a jusificaion for he laer he simple fac ha he supply of formal educaion is limied in pracice. Rewriing equaion (13), generaes a sandard dynamic panel daa specificaion. H 2 i, = a0 + a11h i, 5 + a2 i,5 y + a3π i,5 y + a4 GE) i, 5 y π ln( + α + ε (14) i i wih: a 11 =1+a 1. The following economeric issues have o be deal wih (see also Verbeek, 2000; Loayza e al., 2000; Bond, 2002). Firs, given he dynamic specificaion of equaion (14) wih a lagged dependen variable a he RHS, he sandard fixed effecs esimaor for panel daa will be biased and inconsisen in realisic samples where he number of ime periods is limied (Verbeek, 2000). An appropriae way o deal wih his problem is he use of GMM afer firsdifferencing equaion (14). Assuming absence of auocorrelaion in he error erm ε i, wice and hree imes lagged observaions for H i (i.e. H i-10 and H i-15 ) would be reliable insrumens. As o he oher explanaory variables, we assume ha hey are sricly exogenous. Their curren levels can hen be used as insrumens in he regression 11. Obviously, we can saisically examine he validiy of his assumpion hrough appropriae specificaion ess. The firs-difference GMM esimaor also has is shorcomings, however. Firs, aking firs-differences eliminaes he cross-counry variaion beween human capial and is 11 These assumpions imply he following momen condiions: E[ ( ε i ε i, 5 ) H i, 10 ] = 0, E[ ( ε i ε i, 5 ) H i, 15 ] = 0, E[ ( ε i ε i, 5 ) X i ] = 0 for X = π, π² and ln(ge). Given ha daa availabiliy for X is limied in mos counries o being 1975, 1980, 1985, 1990 and 1995, we can esimae equaion (14) in firs-differenced form beginning wih =1980. The number of momen condiions will be 19.

16 14 deerminans. Only he effec of changes over ime wihin counries can be sudied. Second, as shown by Bond (2002), when he explanaory variables are persisen over ime, lagged levels of hese variables are weak insrumens for he regression equaion in differences. As o our model, (lagged) human capial and governmen educaion spending may be such persisen explanaory variables. An alernaive GMM sysem esimaor may hen be more appropriae. This alernaive esimaor combines in a sysem he regression in firs-differences wih he regression in levels. The insrumens for he regression in firs-differences are he same as menioned above, i.e. wice and hree imes lagged levels of human capial and curren levels of he oher explanaory variables. For he second par of he sysem, he regression in levels, once-lagged differences of he explanaory variables would be appropriae insrumens Empirical resuls Table 2 presens our main resuls. The resuls in he firs and he second column have been obained using he firs-difference GMM mehod. The resuls in he hird and he fourh column follow from using he alernaive GMM sysem esimaor. Noe ha in he second and he fourh regression ime dummies have been included o capure he ime-specific effecs in each period, common o all counries. Finally, he larger number of observaions in he GMM sysem esimaions is due o he fac ha he levels regression can also be run for =1975. The firs difference regressions can be run only from =1980 onwards. As shown by Hansen (1982), he opimal GMM esimaor is obained in wo seps. In our discussion, we focus on he second-sep resuls 13. On he whole, he specificaion ess in able 2 (Sargan es for overidenifying resricions and ess for firs order and second order serial correlaion) do no show evidence agains our esimaes. The absence of significan second order serial correlaion jusifies our use of wice lagged inernal insrumens. The Sargan es does no rejec heir join validiy. Observing he specific resuls of he specificaion ess in he four models, one may conclude ha he models wih ime dummies and hose wih he GMM sysem esimaor perform beer. The resuls are supporive o our hypoheses. Firs, lagged human capial (H -5 ) has he expeced posiive coefficien below one. Is size reveals a large degree of persisence, which 12 In pracice his implies four addiional momen condiions [ a )( H H )] 0, ( i + i i, 5 i, 10 = E ε wih =1980, 1985, 1990, Only he mos recen difference is used as an insrumen. Using more lags, or firsdifferences of he exogenous explanaory variables would resul in redundan momen condiions (see Loayza e al., 2000, for furher references). 13 Bond (2002) argues ha he asympoic sandard errors of he wo-sep GMM esimaes may be a poor guide for hypohesis esing in some cases. As noed by Bond and Windmeijer (2002) his problem is especially relevan when he number of insrumens grows rapidly wih he ime dimension, which is no he case here since we choose a fixed number of insrumens per ime period. We neverheless repor boh he firs and second sep resuls.

17 15 Table 2. Esimaion resuls for equaion (14), alernaive esimaors a, d One-sep esimaes wih heeroskedasiciy consisen sandard errors Variable (GMM-diff) (GMM-diff) (GMM-sysem) (GMM-sysem) H (20.2) (3.45) (24.5) (10.9) π 5y (1.52) (2.05) (1.77) (1.20) π 2 5y (1.33) (1.64) (1.10) (1.08) ln(ge) 5y (0.12) (1.49) (5.76) (1.18) ime dummies no yes no yes Two-sep GMM esimaes Variable (GMM-diff) (GMM-diff) (GMM-sysem) (GMM-sysem) H (28.0) (4.33) (37.4) (15.6) π 5y (1.46) (2.68) (1.78) (2.49) π 2 5y (1.34) (2.20) (1.07) (2.07) ln(ge) 5y (0.41) (1.94) (6.59) (2.02) ime dummies no yes no yes N. Obs. (counries) 321 (93) 321 (93) 414 (93) 414 (93) Sargan (p-value) (b) (df) Tes for firs order serial correlaion (p-value) (c) Tes second order serial correlaion (p-value) (c) Inflaion a op of invered 162% 167% 245% 164% U-shape Effec on H when inflaion goes from 0 o 100% Noes: a Absolue -saisics in parenheses; b Sargan is Sargan es of overidenifying resricions. The null hypohesis is ha he overidenifying resricions are correc; c The null hypohesis is ha here is no firs (second) order serial correlaion in he error erm; d Daa sources: see Appendix 1. may jusify he use of he GMM sysem esimaor. Second, excep when we employ he firsdifference GMM mehod and include no ime dummies in he regression, we find ha a susained increase in per capia governmen spending on educaion (GE) has a significan and posiive effec on he average years of schooling of he populaion. Third, and mos imporan, rising inflaion ends o simulae human capial formaion as long as inflaion is no very high. Concenraing on he wo models wih ime dummies, he esimaed coefficien for π is always posiive and saisically significan a 2%, he esimaed coefficien for π² is negaive and saisically significan a 5%. An invered U-shape emerges. The resuls for inflaion are somewha weaker when no ime dummies are included. There is no change of signs, bu saisical significance is lower, especially for he firs-difference GMM mehod. As indicaed a he boom of Table 2, he op of he invered U-shape is siuaed a very high inflaion raes of abou 160%. In he hird regression ha is even more han 240%. Clearly, given he very

18 16 small number of observaions for inflaion above 100%, hese numbers have limied significance. Wha is imporan, is he observaion of a significan posiive effec from inflaion below 100%. This clearly suppors our heoreical model in Secion 2.2. If he moneary growh models are relevan, hey only seem o be when inflaion is exreme. A final resul a he boom of able 2 concerns he hypoheical effec over a period of 5 years on he human capial sock when inflaion were o rise from 0 o 100%. Concenraing on he beer models, his effec is esimaed beween abou 0.4 and 0.6 years of schooling (all oher hings equal). We discuss he implicaions of hese resuls in Secion Robusness checks We perform four robusness ess. These concern wo alernaive approaches o capure he effecs of inflaion, anoher dependen variable and a change o daa wih a longer ime inerval (10 years). Tables 3, 4 and 5 show he resuls. Noe ha we only repor he regressions including ime dummies. A firs pair of regressions in Table 3 follow from an alernaive approach o es he invered U-shape hypohesis. More precisely, we esimae a linear spline regression. This is a piecewise linear relaionship beween inflaion and human capial wih he line segmens joining one anoher a he specified breakpoins. We allow differen slopes and inerceps for inflaion below 15%, inflaion beween 15% and 100%, and inflaion over and above 100%. The choice of 15% is inspired by he resul in many empirical sudies ha he ne effec of inflaion on long-run growh may be insignifican for inflaion raes below 15% (see Secion 1). The resuls in Table 3 are ineresing. For inflaion below 15%, he effec of rising inflaion on human capial is negaive bu highly insignifican. For inflaion raes beween 15 and 100% a posiive and saisically significan slope shows up. Over and above 100% he effec of increasing inflaion is again insignificanly negaive. Considering hese resuls, i is clear ha he invered U-shape beween inflaion and human capial survives. In line wih some of he esimaes in Table 2, going from 0 o 100% of inflaion raises he human capial sock by approximaely 0.40 years of schooling (all oher hings being equal). The insignifican negaive effec from exreme inflaion can, as we have argued before, be explained from he moneary growh lieraure. The insignifican effec from inflaion below 15%, however, is a new resul. Maybe surprisingly, i is no inconsisen wih our model. This empirical resul simply suggess ha he negaive effecs of inflaion on efficiency in producion, which are cenral in our model, may be inexisen a low raes. Considering he many sudies ha find no significan negaive effec of inflaion on economic growh when inflaion is below 15% (see Secion 1), his is exacly wha one should expec. Addiional linear spline regressions (no shown, bu available upon reques) confirm hese resuls. For example, when we specify breakpoins a inflaion raes of 5%, 10%, 15%,

19 17 50% and 100%, he GMM sysem esimaor wih ime dummies reveals insignifican inflaion effecs on human capial as long as inflaion remains below 15%. The slopes of he firs wo segmens (0-5% and 5-10%) are posiive, he slope of he hird segmen (10-15%) is negaive. Beween 15% and 50%, as well as beween 50% and 100%, he effecs of rising inflaion are posiive and significan. Over and above 100%, he effec of inflaion is again oally insignifican. The ne effec on human capial of going from 0 o 100% of inflaion is esimaed o be 0.45 years of schooling. Table 3. Inflaion and human capial: alernaive inflaion measures a,d One-sep esimaes wih heeroskedasiciy consisen sandard errors Variable (GMM-diff) (GMM-sysem) (GMM-diff) (GMM-sysem) H (3.32) (10.4) (3.60) (6.70) π 5y (wih π 15) (0.74) (0.70) - - π 5y (wih 15<π 100) (2.11) (1.49) - - π 5y (wih 100< π ) (0.36) (0.25) - - sdπ 5y (2.21) (2.25) ln(ge) 5y (0.90) (0.88) (1.41) (1.91) ime dummies yes yes yes yes Two-sep GMM esimaes Variable (GMM-diff) (GMM-sysem) (GMM-diff) (GMM-sysem) H (4.79) (15.0) (4.40) (9.48) π 5y (wih π 15) (0.80) (0.33) - - π 5y (wih 15<π 100) (6.26) (7.03) - - π 5y (wih 100< π ) (1.03) (0.49) - - sdπ 5y (2.19) (2.84) ln(ge) 5y (1.23) (2.10) (1.95) (2.67) ime dummies yes yes yes yes N. Obs. (counries) 321 (93) 414 (93) 321 (93) 414 (93) Sargan (p-value) (b) (df) Tes for firs order serial correlaion (p-value) (c) Tes second order serial correlaion (p-value) (c) Inflaion a op of invered 100% 100% - - U-shape Effec on H when inflaion goes from 0 o 100% Noes: a Absolue -saisics in parenheses; b Sargan is Sargan es of overidenifying resricions. The null hypohesis is ha he overidenifying resricions are correc; c The null hypohesis is ha here is no firs (second) order serial correlaion in he error erm; d Daa sources: see Appendix 1.

20 18 A second pair of regressions in Table 3 re-esimae equaion (14) wih he sandard deviaion of inflaion over he preceding period of five years (sπ 5y ) as an explanaory variable, raher han average inflaion (π 5y ). To he exen ha he main effecs of inflaion are relaed o uncerainy, he variabiliy of inflaion may be a beer variable o include in he regression. Including sπ 5y as well as is square led o highly insignifican resuls for boh. Dropping he squared sandard deviaion as an explanaory variable, makes sπ 5y saisically significan a less han 5%. In line wih he previous resuls, i has a posiive sign. Finally, including boh average inflaion and is sandard deviaion as explanaory variables makes he laer oally insignifican. Mos likely, his is due o mulicollineariy. Correlaion beween π and sπ exceeds 0.8. We can conclude ha when we assess he effecs of inflaion on human capial by including he sandard deviaion of inflaion, he invered U-shape may no survive. The posiive effecs from higher inflaion (inflaion variabiliy) do, however. As o he esimaed effec of governmen educaion spending in Table 3, we observe ha his is always posiive. In hree regressions (wo-sep esimaes) i is also saisically significan. The resuls in Table 4 involve a change in he dependen variable. Raher han average years of schooling, H is now defined as he percenage of he populaion of age 15 and older ha aained secondary or higher educaion. Educaion a hese levels does no have o be compleed. The daa are from Barro and Lee (2000). Underlying he use of his alernaive variable is Barro s (1999) resul ha in growh regressions only schooling a he secondary and higher level occurs o be significan. To successfully absorb and develop new echnologies, which are imporan for growh, (a leas) educaion a he secondary level seems necessary. As can be seen, he resuls wih his alernaive dependen variable confirm he previous ones. The esimaed coefficien for π is again posiive and significan (a 8% or beer), he esimaed coefficien for π² is again negaive. Is saisical significance is a lile weaker. The calculaed op of he invered U-shape is comparable o he resuls in Table A final robusness check is presened in Table 5. Using daa a an inerval of five years - as we have done unil now - has he obvious advanage ha more daa poins are available. There may also be a cos, however. When one considers shorer periods, i may become harder for he esimaed coefficiens o pick up he long-run effecs ha we are ineresed in. A facor reinforcing his problem is ha daa averages over five years only, e.g. for inflaion, are more vulnerable o business cycle effecs or oher emporary disurbances (Temple, 2000). In Table 5 we use daa wih a longer ime inerval. The underlying specificaion is: 14 For a proper comparison of he esimaed coefficiens in Table 4 wih hose in previous ables, noe ha he percenage of he populaion wih secondary or higher educaion varies from abou 1 o 90 (percen). This range is much wider han for average years of schooling, which varies from abou 0.5 o almos 12 (years).

21 19 Table 4. Esimaion resuls for equaion (14), alernaive dependen variable a,d One-sep esimaes wih heeroskedasiciy consisen sandard errors Variable (GMM-diff) (GMM-sysem) H (3.57) (6.75) π 5y (1.78) (1.79) π 2 5y (1.63) (1.54) ln(ge) 5y (1.44) (2.11) ime dummies yes yes Two-sep GMM esimaes Variable (GMM-diff) (GMM-sysem) H (6.31) (9.73) π 5y (1.73) (2.21) π 2 5y (1.47) (1.83) ln(ge) 5y (1.24) (2.12) ime dummies yes yes N. Obs. (counries) 321 (93) 414 (93) Sargan (p-value) (b) (df) Tes for firs order serial correlaion (p-value) (c) Tes second order serial correlaion (p-value) (c) Inflaion a op of invered 172% 174% U-shape Effec on H when inflaion goes from 0 o 100% Noes: a Absolue -saisics in parenheses; b Sargan is Sargan es of overidenifying resricions. The null hypohesis is ha he overidenifying resricions are correc; c The null hypohesis is ha here is no firs (second) order serial correlaion in he error erm; d The dependen variable H in hese regressions is he percenage of he populaion wih secondary or higher educaion. H 2 i, = a0 + a11h i, 10 + a2 i, dec + a3π i, dec + a4 GE) i, dec π ln( + α + ε (15) i i Lagged human capial now refers o -10. In line wih his, he explanaory variables GE dec and π dec are averages over he decade from -10 o -1 (see Appendix 1 for deails). Daa are available for mos counries for = 1980, 1990 and Equaion (15) is esimaed wih he firs-difference GMM mehod, as well as wih he GMM sysem esimaor. Noe also ha we include wo alernaive variables for he human capial sock: average years of schooling and he percenage of he populaion wih secondary or higher educaion. The new resuls in Table 5 broadly confirm he previous ones. Excep for he fourh regression where he Sargan es saisic is problemaic, he available specificaion ess do no show evidence agains our empirical approach. Again concenraing on he wo-sep

22 20 esimaes, we sill observe a significan invered U-shaped relaionship beween inflaion and human capial. Ineresingly, he op of his invered U-shape is now siuaed a abou 90%. This resul clearly suppors he idea of being cauious abou he repored exreme numbers (±165%) in Tables 2 and 4. I would raher sugges 100% o be a represenaive hreshold level. The esimaed posiive and generally significan effecs from governmen spending on educaion in Table 5, also confirm our previous findings. As o he esimaed coefficiens on lagged human capial, we again observe posiive coefficiens below 1. No unexpecedly, hese are lower han in he case of 5 year daa inervals. The esimaed coefficiens on H -10 also end o confirm he need for using he GMM sysem esimaor when highly persisen explanaory variables are included. As shown by Bond (2002), he firs-difference GMM esimaor may hen induce a downward bias, which clearly seems o show up in our resuls. Table 5. Esimaion resuls for equaion (15), alernaive dependen variables a, d Average years of schooling Percenage of populaion wih secondary or higher educaion One-sep esimaes wih heeroskedasiciy consisen sandard errors Variable (GMM-diff) (GMM-sysem) (GMM-diff) (GMM-sysem) H (1.06) (2.65) (0.39) (3.32) π dec (1.81) (1.15) (2.18) (1.80) π 2 dec (1.60) (1.07) (2.06) (1.69) ln(ge) dec (2.17) (1.14) (1.85) (1.80) ime dummies yes yes yes yes Two-sep GMM esimaes Variable (GMM-diff) (GMM-sysem) (GMM-diff) (GMM-sysem) H (1.53) (2.65) (1.03) (5.61) π dec (2.12) (2.50) (2.16) (2.85) π 2 dec (1.79) (2.16) (1.94) (2.48) ln(ge) dec (2.18) (2.69) (1.68) (2.61) ime dummies yes yes yes yes N. Obs. (counries) 155 (84) 239 (84) 155 (84) 239 (84) Sargan (p-value) (b) (df) Tes for firs order serial correlaion (p-value) (c) Inflaion a op of invered 89% 90% 85% 89% U-shape Effec on H when inflaion goes from 0 o 100% Noes: a Absolue -saisics in parenheses; b Sargan is Sargan es of overidenifying resricions. The null hypohesis is ha he overidenifying resricions are correc; c The null hypohesis is ha here is no firs order serial correlaion in he error erm. Noe ha, in conras o previous ables, esing for second order serial correlaion is no possible here due o insufficien daa along he ime dimension; d Daa sources: see Appendix 1.

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