Do cognitive skills Impact Growth or Levels of GDP per Capita?

Transcription

1 Do cogniive skills Impac Growh or Levels of GDP per Capia? Zvi Ecksein, Assaf Sarid,andYuli(Yael)Tamir June 1, 2016 Absrac Incredible policy aenion has been given o he claim ha an increase in he qualiy of educaion as measured by inernaional ess (e.g. PISA ess) has a significan impac on he GDP long-run growh rae (Hanushek and Woessmann, 2015). This sudy is based mosly on aggregae daa from he second half of he cenury, and never addresses he quesion of he curren paper, which is wheher he impac of he qualiy of cogniive skills a ecs he level of GDP per capia or he long run growh rae. Focusing on his quesion, we consruc a varian sandard growh model in which cogniive skills have heoreically boh a level and growh rae e ecs by assumpion. Esimaing his model using sandard cross-counry daa and panel daa, cogniive skills measured by he mehodology of HW have a significan level e ec on GDP bu no a growh e ec. Therefore, he cogniive skills improvemen impac economic growh is bounded. JEL Clasificaion: I25, O47, O15, I20 Keywords: Educaion and Economic Developmen, Empirical Sudies of Economic Growh, Human Capial This research was suppored by THE ISRAEL SCIENCE FOUNDATION (Gran No. 110/15) The Inerdisciplinary Cener (IDC), Israel Deparmen of Economics, The Universiy of Haifa Shenkar College, Israel 1

2 1 Inroducion This paper reconsiders he impac of invesmen in human capial on long-run economic growh. In order o analyze his quesion, we sar from an aggregae producion funcion, and generae a growh equaion, which we esimae wih cross counry and panel daa, as acceped in he lieraure (Durlauf e al., 2005). An imporan feaure of our paper is ha we use a proxy for he qualiy of human capial, which is based on he average achievemen in inernaional ess in mah and sciences, as in Hanushek and Woessmann (2015) (HW). HW used cross counry daa and concluded ha: 1 A rise of one sandard deviaion in cogniive skills of a counry s workforce is associaed wih approximaely wo percenage poins higher annual growh in per-capia GDP. In his paper we es if his argumen is rue. The lieraure on he impac of invesmen in human capial on economic growh is vas, and so are he variey of measures used o proxy human capial. Some measures consis on he quaniy of human capial, such as lieracy raes (e.g., Mankiw e al. (1992)) or average years of schooling (e.g. Cohen and Soo (2007) and Barro and Lee (2013)). While hese measures find a posiive correlaion beween human capial and growh, hey do no include any informaion on he qualiy of human capial, and as such heir resul may be biased. Recenly, a new proxy for human capial which consiss on qualiy raher han quaniy has been developed in Hanushek and Kimko (2000), and is used in HW. They aemp o proxy cogniive skills using he average achievemen of sudens in inernaional ess in mah and sciences. The conribuion of his measure is imporan for undersanding di erences in income levels, as indeed, as HW argue, his measure is more correlaed wih he average annual growh rae of di eren economies around he globe. As a resul, HW argue ha improvemen in he average achievemen in hese ess is crucial for long-run growh. I is hard o emphasize he imporance of he HW resuls, as hey have been adoped by he PISA (Programme for Inernaional Suden Assessmen) analyss, as well as by The World Bank and OECD expers as a jusificaion for imposing a esing policy conesed by mos educaional expers. In an age ha sees educaion hrough economic prism his seems o be a very convincing argumen. Indeed, nowadays he World Bank uses hese ess as a policy device o simulae economic growh. 2 As a resul, 1 This argumen was firs presened in Hanushek and Kimko (2000), and was also repeaed in Hanushek and Woessmann (2012) & Hanushek e al. (2013). 2 François Bourguigono, World Bank s Senior Vice Presiden (2007) wroe in a World Bank research publicaion wrien 2

3 he number of paricipaing counries in hese exams has risen in he pas wo decades from slighly less han 30 o approximaely 100 counries around he globe, and educaional reforms have aken place in an aemp o succeed in hese ess a he expense of oher educaional goals. Neverheless, hese policies are conesed by many educaional expers, who claim ha he esing regime demeans educaion and harms he lives of hundreds of millions of children. 3 The consequences are far beyond he scope of an academic debae. A key aspec in he analysis of HW is ha cogniive skills have a causal impac on long run growh raes. 4 Indeed, HW menion hree views in he lieraure ha suppor he noion ha human capial is vial o growh. Firs, in a neoclassical growh model, human capial is a facor of producion; invesmen in educaion increases he human capial of he labor force, and hus shifs he economy from one seady sae o a higher one. Noe ha according his view, invesmen in educaion a ecs he level of oupu per capia, bu no is long run growh. The second argumen raised by HW comes from he endogenous growh lieraure, namely ha growh is driven mainly by innovaion, and he laer depends on he cogniive skills of enrepreneurs. As such, invesmen in educaion, which raises he cogniive skills of enrepreneurs, a ecs he long-run growh rae of he economy. Las bu no leas, according o a hird view, invesmen in educaion assiss he economy in absorbing new echnologies. 5 Referring o hese hree views, HW argue ha: All hese approaches have in common a view of human capial as an ingredien vial o growh. The laer wo sress is impac on long-run growh rajecories. This is he noion we build on. We quesion if his is correc, or wheher cogniive skills have a level e ec. Figure 1 illusraes he quesion a sake. Le us consider he following exercise, similar o he one presened in Hanushek e al. (2013) (HPW) and in HW: Suppose ha a counry is on is seady sae growh pah. A period T he economy experiences an educaional reform ha increases is cogniive skills level, and hence oupu per capia grows a a higher rae for a cerain period (beween period T and ). If invesmen in cogniive skills has a growh e ec, his economy will experience his high growh rae for all fuure periods, as he by Hanushek and Woessmann, ha The Bank will conribue o ensuring ha he measuremen of learning achievemens is underaken in a more sysemaic way and is properly aken ino accoun in he Bank s dialogue wih parner counries, [World Bank, 2007]. 3 See, Ravich (2013), and OECD and PISA Tess are Damaging Children Worldwide, An Open Leer o Dr. Andreas Schleicher, he Guardian 6 may HW explain in deail he idenificaion sraegy hey use o esablish a causal e ec of cogniive skills on growh (See chaper 4). Consequenly, we do no focus on esablishing such a causal connecion, bu raher on he naure of his connecion. 5 This idea was highlighed by Nelson and Phelps (1966). 3

4 lef par of he figure shows. This is also he inerpreaion of HW. If, on he oher hand, invesmen in cogniive skills has a level e ec, hen he spike in he growh rae is emporary; i will decline evenually o is original rae of growh, and he impac of such a reform on oupu per capia will be subsanially lower, as shown in he righ par of he figure. ln y ln y ln y ln y ln y T ln y T T τ T τ a. A growh rae effec caused by an b. A level effec cause by an educaional educaional reform a ime. reform a ime. Figure 1: A growh rae e ec (lef) and a level e ec (righ) of an educaional reform To answer his quesion, we consruc a neoclassical growh model in which invesmen in cogniive skills has a level e ec by assumpion. We use a common mehodology in he lieraure o generae our firs esimaed equaion. We esimae our model using daa from Penn World Tables (Feensra e al., 2015) and from HW. Our firs specificaion replicaes he main specificaion of HW, and indeed, our resuls are very similar o heirs. Ye since in our case his specificaion springs from a model in which cogniive skills have a level e ec by assumpion, we quesion wheher HW really capure a growh e ec. In our second specificaion we add o he model oher componens ha according o he growh heory and our model may have an impac on oupu per worker in he long run, such as he average growh rae of populaion and he average invesmen rae in physical capial. As a resul, he coe cien of he invesmen in cogniive skills declines, suggesing ha no only do he resuls of HW capure only a level e ec, bu also ha heir coe ciens are biased upwards. Finally, we show ha he coe cien of invesmen in cogniive skills is saisically significan only when iniial oupu per worker is one of he regressors, suggesing ha he posiive e ec documened in HW is significan condiional on he iniial oupu per capia level. This is consisen wih he condiional convergence hypohesis, according o which invesmen in human capial has a level e ec. We conclude from his resul, and from he fac ha in his model cogniive skills have a level a ec by assumpion, ha invesmen in cogniive skills has a level e ec, as par of he condiional convergence hypohesis. We hen show he quaniaive di erences of our resuls and hose repored in HW. We show ha 4

5 while HW argue ha 90 years afer an educaional reform, oupu per capia will be 26% higher han is no-reform counerpar, our esimaions sugges ha afer 90 years, oupu per capia will exceed is no-reform level by abou 10%. Furhermore, he di erence beween he resuls of HW and ours increases over ime. These resuls call for a new consideraion of he educaional reforms hroughou he world. As a robusness check, we exend he model and allow invesmen in cogniive skills o have a growh e ec. In his model, each counry converges o a globally sable seady sae. Ye, unlike our basic model, in his model, even in he seady sae counries may di er in heir growh raes, since he growh rae of each economy depends on is level of cogniive skills. We esimae his model, and show ha he model does no fi he daa, suggesing ha he daa do no suppor he growh e ec hypohesis. So far, our analysis relied on cross counry daa. A more powerful approach is o use panel daa, because such daa follow an economy for a long period of ime, and hence hey enable a beer idenificaion of he level and growh e ecs. Furhermore, panel daa allow o idenify counry specific fixed e ecs, and his way o disenangle he poenial bias caused by some omied variables ha are counry specific. We use daa for 13 OECD counries, which paricipaed in he inernaional ess since hey iniiaed. We follow he mehodology of HW and consruc he measure of cogniive skills for hese counries since he onse of he inernaional ess. The consrucion of he level of cogniive skills over ime reveals ha none of he counries has experienced a sharp increase in he average achievemens of i sudens in he inernaional ess. These findings raise wo quesions: firs, wheher he level of cogniive skills is bounded from above, and as such so is is impac on he level of GDP per worker. Second, wheher he counries in he sample ha experienced a higher growh rae of cogniive skills indeed experienced a higher growh rae of GDP per capia as well. In order o answer hese quesions, we consruc a model based on a sandard producion funcion, in which he level of human capial a ecs boh he level of oupu per worker. We also assume ha he level of human capial a ecs he growh rae of echnology. Hence, he model includes boh he level e ec and he growh e ec. We develop from he producion funcion he growh rae of oupu per worker, which in urn depends on boh he level and he change of cogniive skills, capuring boh he growh e ec and he level e ec, respecively. We esimae he model described above, using daa from PWT and our calculaions of cogniive skills. Since mos of he inernaional ess are aken a he age of 14, we use in our esimaions a five year lag of he cogniive skills level. As menioned above, if cogniive skills have a growh e ec, hen heir level 5

6 should be posiively correlaed wih he growh of GDP per capia, while if hey have a level e ec hen heir change should be correlaed wih he growh rae of GDP per capia. We firs measure he model assuming ha cogniive skills have a growh e ec alone. The coe cien of he level of cogniive skills on GDP per worker growh rae is no saisically significan. We hen es he hypohesis of he level e ec alone (assuming ha here is no growh e ec of cogniive skills on growh), and indeed he coe cien of he change in cogniive skills is posiive and saisically significan. Finally, we do no resric he model, and allow boh level e ec and growh e ec play a role. Consisen wih our previous resuls, he level of cogniive skills is no correlaed wih he growh rae of oupu per worker, whereas he change in he level of cogniive skills (which capures he level e ec) is posiive and saisically significan. We conclude from his analysis ha consisen wih he cross counry analysis, he panel daa suppor he level e ec hypohesis, raher han he growh e ec hypohesis. The res of he paper is consruced as follows: Secion 2 presens our baseline model, where he accumulaion of cogniive skills and physical capial are deermined endogenously, and echnology advances in an exogenously given rae. In secion 3 we describe he daa we use; In Secion 4 we presen he resuls of esimaing our baseline model. In Secion 5 we discuss he quaniaive di erence beween our resuls and he resuls obained by HW, and in Secion 6 we relax our assumpion of exogenous echnical change. Secion 7 presens our panel daa resuls, and Secion 8 concludes. 2 A Baseline Model In his secion we consruc a simple model in which cogniive skills have a level e ec by assumpion. The model is a sandard neoclassical growh model, in which he accumulaion of physical capial and cogniive skills are deermined endogenously, while he rae of echnical change is exogenously given. Consider a closed economy, in which he producion funcion of a single homogenous good is of he form: Y i = K i A i h i L i 1, (1) where Y i is he oupu a period in counry i, A i is he (labor augmening) echnology level in counry i a period, K i is he capial employed in producion in counry i a period, h i is he average cogniive skills of a worker in counry i a period and L i is he raw labor employed in producion in counry i a period ; 0 < <1. This is a sandard producion funcion, used in many empirical growh sudies (e.g., Fernald and Jones (2014)). 6

7 2.1 The Dynamics of he Model We assume ha he echnological parameer, A i, increases in an exogenously given consan rae,. This assumpion is common in he neoclassical growh lieraure (e.g., (Mankiw e al., 1992)). 6 We also assume ha he populaion grows a a consan rae, n i. The physical capial formaion follows a usual law of moion, which implies ha he physical capial sock a he nex period equals he sock of capial ha is lef from he presen period (afer depreciaion) plus he invesmen in physical capial: K i +1 =(1 )K i + s i KY i, (2) where is he depreciaion rae and s i K is he invesmen rae in physical capial in counry i, boh assumed o be consan over ime. We assume ha he cogniive skills evolve due o he invesmen rae in cogniive skills, s i H, according o he following equaion: h i +1 = h i + s i H h i, (3) where h i is a measure of ime-invarian level of cogniive skills (bu perhaps counry-specific), which does no require invesmen in cogniive skills. The invesmen rae, s i H, which yields he increase in cogniive skills over ime, may be a consequence of public expendiures on educaion, parenal invesmen in educaion (eiher ime dedicaed o educaion or privae moneary expendiures), or he qualiy of he educaion sysem. Noe ha his dynamic equaion is di eren from he one used in Mankiw e al. (1992), bu shares imporan properies for our purpose. Wih 0 <s i H < 1, he dynamic equaion converges ino a unique seady sae, wih a declining growh rae of cogniive skills. 7 This, in urn, generaes a model in which invesmen in cogniive skills, as capured by s i H has a level e ec, and no a growh e ec, by assumpion. 2.2 Seady Sae A seady sae in his economy is a sae in which oupu per worker, y i, Y i, /L i, grows a a consan rae. In order o find he seady sae, we develop he dynamic equaion of capial per e ecive labor, k i, K i, A i, L i,, and find is seady sae level, k i. Finally, we find he consan rae a which oupu per 6 As discussed above, we relax his assumpion below. 7 Anoher way of modeling he dynamic equaion of cogniive skills accumulaion could be h i +1 = h i (h i ) si H.Noeha his funcion shares he same characerisics of declining growh raes over ime if 0 <s i H < 1. We prefer a more racable funcional form. 7

8 worker grows. h i = For k i o be consan, he average level of cogniive skills has o be consan as well. Tha is, h i 1 s Hi. Consequenly, k i becomes: 8 k i s Ki = n i h i. (4) Characerisics of he Seady Sae Capial per worker is given by: k i, = A i, k i = A i, s Ki n i h i. (5) I is sraighforward ha capial per worker grows a a consan rae and so does oupu per worker. Noe ha counries wih higher h i, or wih a higher invesmen rae in cogniive skills have higher levels of k i and levels of oupu per worker, ye hey share he same GDP per worker growh rae. 2.3 Generaing Average Growh Raes Our las sep owards esimaing he relaion beween he level of cogniive skills and oupu growh rae is o generae he growh rae owards he seady sae. We follow he mehodology of Durlauf e al. (2005), and plug (5) in he producion funcion of oupu per worker, ake logs and subrac oupu per worker a a base year (in logarihmic scale) from boh sides of he equaion. This yields he following equaion: 9 g y i = + ln Ai 0 + ln si K ln(ni + + ) + ln(hi, ) ln y0 i, (6) where g y i is he growh rae of oupu per worker in he ime span beween period 0 and. Hence, according o he model, he growh rae of oupu per worker is an increasing funcion of he exogenous echnical change, he iniial level of echnology, he invesmen rae in physical capial as well as in cogniive skills; i is a decreasing funcion of he growh rae of populaion and of he iniial level of oupu per worker. One would be emped o conclude from his specificaion ha he invesmen rae in cogniive skills a ecs he long-run growh rae of oupu per worker. This is, in fac, he inerpreaion in HW. However, his inerpreaion is no consisen wih he model described above. To see his, noe ha as converges 8 The developmen of his equaion is deailed in Appendix A. 9 The mahemaical procedure is deailed in Appendix B. 8

9 o infiniy, and he economy converges o is seady sae, he only elemen ha a ecs he growh rae of he economy is he exogenous echnical change. This is, in fac, he only elemen in neoclassical model ha has a growh e ec, whereas all oher economic variables, including cogniive skills invesmen have a level e ec. As suggesed below, his model generaes an idenical specificaion analyzed in HW, and hence i raises he quesion wheher HW indeed capure a growh e ec, as hey argue. 2.4 The Esimaed Equaion We esimae equaion (6), under he assumpions ha he exogenous growh rae of echnology,, is common o all counries; we also assume, as in Mankiw e al. (1992) ha A 0 N(A 0, 2 ). Hence, we esimae he following equaion: g y i = + ln Ai 0 + ln si K ln(ni + + ) + ln(hi, ) ln y i 0 + i. (7) where i is he random residual from he disribuion of A 0. Noe ha he consan includes boh he average level of iniial echnology and he exogenous growh rae of echnology,. Noe ha his equaion is similar o he one in Mankiw e al. (1992) or Durlauf e al. (2005) (in Secions 3 and 4). HW esimae a similar equaion, bu hey exclude he impac of invesmen in physical capial as well as he impac of populaion growh rae on oupu per capia growh rae. This specificaion is vulnerable o idenificaion problems, as omied variables may a ec boh growh and cogniive skills. To overcome hese problems, Hanushek and Woessmann (2012) implemen an insrumenal variable approach: They use insiuional characerisics of he school sysem (such as he percenage of privae schools, he exisence of exernal exi exam sysems ec.) and show ha heir resuls are no a eced by hese insrumens. HW also argue ha he problem of reverse causaliy is absen in heir sudy, as hey show ha if hey focus on ess ha ook place before he period sudied, he coe cien of he level of cogniive skills increases, raher han declines, as one would expec if he problem of reverse causaliy exised in he daa. 3 Daa We use daa on GDP per capia and populaion size from 1960 o 2010 for 54 counries from Penn World Tables version 8.1 (PWT) (Feensra e al., 2015). All hese counries did no belong previously o he Sovie bloc. We calculae he real GDP (on aggregae level) for hese counries in hese years, and hen 9

10 use daa on he number of workers in hese years from PWT as well o calculae oupu per worker in each year in he period , and is growh rae. We use daa also from PWT o compue he average invesmen rae in physical capial for his period as he invesmen as a percenage of GDP. We assume ha he exogenous growh rae of echnology is 2% (as in Mankiw e al. (1992)), and ha he depreciaion rae is 4% (as suggesed in he PWT (Inklaar and Timmer, 2013)). From he populaion in he ages of labor we compue for each counry is average annual growh rae of he labor force, n i. Finally, we use he measure of cogniive skills from HW as our cogniive skills measure. Table 1 summarizes he saisics of he variables we use for our esimaions. All variables excep he cogniive skills level are in percenage poins. Table 1: Summary saisics Variable Mean Sd. Dev. Min. Max. N Oupu per worker growh rae, Invesmen Rae n Cogniive Skills level Resuls Table 2 presens he resuls of esimaing equaion (7). Column (1) includes only iniial oupu per worker as a conrol variable. This regression is idenical o he one repored in HW, and our resuls are very similar o he ones repored in heir sudy. In heir esimaion, he coe cien of cogniive skills is close o 2, and he coe cien of iniial oupu per capia is close o However, HW argue ha heir resuls capure a growh e ec, whereas our esimaed equaion springs from a model in which invesmen in cogniive skills has merely a level e ec. This by iself raises a concern wheher heir analysis idenifies a growh e ec. Furhermore, noe ha boh in our esimaion and in heir esimaion, he coe cien of iniial oupu per worker is negaive, supporing he condiional convergence hypohesis, according o which economies wih similar characerisics converge o he same seady sae. 11 This heory suppors our hypohesis ha invesmen in cogniive skills has a level e ec. Column (2) includes in addiion he average invesmen rae in physical capial and he average 10 The quaniaive di erence beween our resuls and heirs springs from he fac ha we use oupu per worker, whereas hey use oupu per capia. 11 For more deails on condiional convergence see, for example, Barro and Sala-i Marin (1992) and Durlauf e al. (2005). 10

11 populaion rae as independen variables. Their coe ciens are posiive and negaive, respecively, exacly like he heory suggess. Noe ha once hese variables are aken ino accoun, he coe cien of invesmen in cogniive skills declines from 1.62 o 1.04, reducing furher more he impac of invesmen in cogniive skills on economic growh. Noe ha his coe cien fis he model, according o which his coe cien is supposed o equal 1. This suggess ha he coe ciens repored in HW include also he complemenariy beween invesmen in physical capial and invesmen in cogniive skills, and he ineracion beween populaion growh and invesmen in cogniive skills. Column (3) includes a resricion ha he coe ciens of s i K and ni + + are equal wih opposie sign, as he model suggess. This resricion yields hree ineresing resuls. Firs, he coe cien of he iniial oupu level keeps a similar magniude as in he previous esimaions, suggesing ha indeed iniial oupu per worker has an exogenous impac on he growh rae. Second, he coe cien of he resricion is posiive and equals This suggess ha marginal produciviy of labor diminishes a a high rae (recall ha his coe cien represens from he producion funcion). Third, he coe cien of invesmen in cogniive skills is 1.289, slighly more han one sandard deviaion from 1 (as he model suggess). As described above, he negaive coe cien of iniial oupu per worker suppors he condiional convergence hypohesis. According o his hypohesis, invesmen in cogniive skills has a level e ec, and no a growh e ec, as HW argue. Hence, in order o rule ou he level e ec hypohesis, he coe cien of he cogniive skills level should be posiive and saisically significan even if iniial condiions are no used as explanaory variables. This is he regression analyzed in column (4). Ineresingly, he coe cien of he cogniive skills measure ceases o be saisically significan. This suggess ha invesmen in cogniive skills a ecs economic growh condiional on he iniial level of oupu per capia. This is consisen wih he condiional convergence hypohesis, according o which invesmen in cogniive skills has merely a level e ec, and no a growh e ec, as HW argue. 5 Discussion In his secion we would like o highligh he quaniaive di erences beween our resuls, as presened in Table 2 o he ones presened in HW. Figure 2 represens he impac of an educaional reform, as presened in HW. The horizonal axis represens ime from he beginning of he educaional reform, while he verical axis represens he raio of GDP per capia afer he reform, relaive o a scenario of no 11

12 Table 2: Growh and Invesmen in Human capial and Physical Capial Oupu per Worker Growh, (1) (2) (3) (4) h i, 1.62*** 1.04*** 1.29*** 0.44 (0.25) (0.25) (0.24) (0.30) y1960 i -0.71*** -0.69*** -0.62*** (0.13) (0.11) (0.11) n i *** (0.14) (0.18) s i K 0.07*** 0.09*** (0.02) (0.02) s i K (n i + + ) 0.07*** (0.02) Adjused-R Observaions Noes: Sandard error esimaes are repored in parenheses; All regressions include a consan; *** denoes saisical significance a he 1% level, ** a he 5% level, and * a he 10% level, all for wo-sided hypohesis ess. reform. In his scenario, we follow HW and assume ha he economy grows a a consan rae of 1.5%. The reform has four sages: 12 In he firs sage, he educaional reform iniiaes, and he cogniive skills of sudens increase gradually, unil he reform is fully enaced, afer 20 years. Only hen sudens begin o enjoy he highes level of cogniive skills. During he second sage, which lass also 20 years, sudens who, due o he firs sage of he reform, have slighly higher cogniive skills han presen workers replace he workers in he labor force. In he hird sage, new workers replace he old workers who were he firs o enjoy he educaional reform, and as such, do no have he highes cogniive skills available (recall ha i ook he reform weny years o be enaced fully). Finally, afer weny years of he hird sage, he economy reaches he fourh sage of he reform, in which all he labor force has he high cogniive skills. HW inerpre heir resul as an impac on he long run growh rae, and heir esimaion is depiced by he upper curve. Our simulaion is based on he resuls above in Table 2, and hey di er from he simulaion of he resuls of HW in wo aspecs. Firs, he coe cien of he impac of such a reform on he change in he (shor-run) growh rae is 1.04, raher han 2, as used by HW. Second, unlike HW, we assume ha he growh rae of GDP per capia converges owards 1.5%. Furhermore, we assume ha he convergence rae is 2%, as in Barro and Sala-i Marin (1992) and Mankiw e al. (1992). 12 For more informaion, see Chaper 7 in HW. 12

13 A he firs sage of he reform, our resul are very similar o he ones of HW. However, as he second sage of he reform iniiaes, di erences beween he wo simulaions emerge, and heir curve becomes seeper han ours. Noe ha as he years go by, while he simulaion of HW become seeper, ours becomes flaer. This is due o he forces of convergence, which are absen in HW. Finally, HW argue ha 90 years afer he reform, oupu per capia will be higher han is level wihou such a reform by abou 26%. Our simulaions do no suppor his viewpoin; hey imply a much more moderae impac: afer 90 years from he educaional reform oupu per capia is only 10.4% higher han is level wihou a reform. GDP Reform o No-Reform Raio HW and Our Simulaion of a GDP Impac of an Educaional Reform of 25 Poins Addiion o Tes Scrores HW Esimaions Our Esimaions Years from Reform Figure 2: The raio beween GDP per capia afer reform and wihou reform for our resuls and previous resuls. 6 Growh and Level Impac of Educaion HW sugges channels ha may generae he growh e ec of cogniive skills. Firs, i migh be ha invesmen in cogniive skills accelerae R&D. Second, wih higher cogniive skills, he economy may absorb beer new echnologies. 13 Boh hese channels imply ha he echnical change should depend on 13 A hird channel would be of cogniive skills exernaliies. Neverheless, he evidence for such exernaliies are mixed. Acemoglu and Angris (2001), for insance, find very weak evidence for such exernaliies. 13

14 he level of cogniive skills. This is he assumpion we assume in his secion. In his case: g A i = Ai +1 A i 1= q h i. (8) This assumpion, which suggess ha he higher he average level of cogniive skills per worker, he higher he echnical change, is consisen wih he endogenous growh lieraure (e.g., Ha and Howi (2007)), 14 and is similar o he assumpion in Benhabib and Spiegel (1994). The res of our model does no change. I urns ou, ha in he seady sae, oupu per worker equals: apple y i s i K = n i + p h i + 1 h i A i, (9) where, as in he previous model, h i = h 1 s i H is he seady sae level of cogniive skills. I is sraighforward ha since in he seady sae cogniive skills is consan, so is he growh rae of echnology. As a resul, he erm in he squared brackes is consan. This implies ha in he seady sae oupu per worker grows a a consan rae, p h i. The level of cogniive skills, on he oher hand, may di er from one counry o he oher, as boh he invesmen rae and iniial level of cogniive skills may di er beween counries. As a resul, he level of cogniive skills, which has a growh e ec in his model, may yield di eren growh raes in di eren counries, as HW sugges. To es his specificaion, we ake logs from boh sides of (9) and subrac from boh sides log y0 i. Finally, we subrac and add o he righ hand side of (9) log A 0. This yields he following equaion: ln(y i ) ln(y0)= i apple 1 ln s i K n i + p h i + +ln(h i )+ln(a i ) ln(a i 0) ln y i 0 +lna i 0. (10) Noe ha along he seady sae, he echnological level grows a a consan rae, which is a funcion of he seady sae level of cogniive skills. Close o he seady sae, he echnological level grows also from he accumulaion of cogniive skills. As a resul, in (10), ln A i ln A i 0 = p q h i + h i 0,where h i 0 hi h i 0. Hence, he growh e ec of he level of cogniive skills level is capured in wo elemens of his equaion. Firs, in he expression in he squared brackes, n i + p h i +, and second, in he expression of convergence oward he seady sae, p q h i + h i 0. In order o esimae his las equaion, we assume, ha ln A i 0 =lna + i,wherelna is he average 14 Noe ha he endogenous growh heory does no rule ou convergence. See, for insance, Howi (2000). 14

15 level of ln A i. Consequenly, (10) can be wrien as: g i y = apple 1 ln s i K n i + p h i + ph q +ln(h )+ i i + h i 0 ln y i 0 +lna + i. (11) Esimaing h i 0 The measure of cogniive skills developed by Hanushek and Woessmann (2012) is calculaed as an average of each counry in he inernaional ess i had paricipaed in. Unforunaely, only 13 counries paricipaed in hese ess long enough o allow us o invesigae is dynamics. In order o overcome his problem, we calculae he di erence in he level of cogniive skills under di eren assumpions regarding he average schooling years, as repored in Barro and Lee (2013). Firs, for each counry we esimae h i 0 by he di erence in average schooling years. Second, we exrapolae he resuls in he inernaional ess by using he growh rae of he average schooling years. 6.1 Resuls Table 3 summarizes he resuls from esimaing hese wo specificaions. Columns (1) and (2) presen he resuls of he esimaions wih our firs and second specificaions, respecively. As in he previous secion, he average invesmen rae in physical capial is posiive and close o 0.07; The coe cien of he iniial level of oupu per worker in 1960 is negaive, significan and close o is level in he previous secion. The coe cien of he level of cogniive skills is again close o 1, bu recall ha his impac is he level e ec we found in he previous secion, and no he growh e ec we are aemping o esimae here. The coe ciens a sake are he coe cien of n i + g(h i )+ and he coe cien of he change in cogniive skills. The firs coe cien is negaive and saisically significan, jus as in he previous secion. Ineresingly, is magniude is similar o he one obained in he previous secion. This raises he quesion wheher he level of cogniive skills indeed has an impac on he growh rae. In order o es his quesion we run wo more regressions, repored in columns (3) and (4), where we omi g(h i ) from he expression n i + g(h i )+. Comparing he coe ciens of n + in columns (3) and (4) o he ones of n i + g(h i )+ in columns (1) and (2) respecively, reveals ha hese coe ciens are idenical, suggesing ha hese regressions do no provide any evidence ha cogniive skills indeed has a growh e ec. Finally, in none of he esimaions repored, he e ec of cogniive skills on he growh rae of TFP (he coe cien of he change in cogniive skills) is saisically significan. We conclude from all hese 15

16 resuls ha we find no evidence in he daa for he assumpion ha he level of cogniive skills has a growh e ec. Table 3: Oupu per Worker Growh in a Model of Endogenous Growh Oupu per Worker Growh, AModelwihn + (h)+ AModelwihn + alone (1) (2) (3) (4) s i K 0.07*** 0.07*** 0.07*** 0.07*** n + (h i ) ** -0.40** (0.02) (0.02) (0.02) (0.02) (0.15) (0.15) Cogniive Skills level 1.21*** 1.16*** 1.12*** 1.07*** (0.27) (0.29) (0.29) (0.31) y i *** -0.70*** -0.72*** -0.70*** (0.12) (0.14) (0.12) (0.14) CS change, firs specificaion (0.41) (0.41) CS change, second specificaion (0.52) (0.52) n i ** -0.40** (0.15) (0.15) Adjused-R Observaions Noes: Sandard error esimaes are repored in parenheses; All regressions include a consan; *** denoes saisical significance a he 1% level, ** a he 5% level, and * a he 10% level, all for wo-sided hypohesis ess. 7 Panel Daa Analysis In secions 4-6 we argued, using cross counry daa, ha he daa suppor he hypohesis ha invesmen in cogniive skills has a level e ec raher han a growh e ec. In order o idenify he model we assumed ha all economies were a heir seady saes by Panel daa follow a sample of counries over ime and herefore hey provide a beer basis for esing he level vs. growh e ec of cogniive skills. Furhermore, panel daa allow o idenify counry specific fixed e ecs, and his way o disenangle he poenial bias caused by some omied variables ha are counry specific. 16

17 7.1 Panel Daa Specificaion Consider, once again, a producion funcion in counry i: ln Y i =lna i + ln K i + ln(h i L i ). (12) Assume also, as suggesed by HW, ha he growh rae depends on he level of human capial: g A i = g A (h i )= + h i, (13) where g A i is he growh rae of TFP in counry i a period, which depends on wo elemens: an exogenous elemen, denoed by, and he level of human capial in counry i. We assume ha he relaion beween he level of human capial and he growh rae of TFP is linear and capured by. This equaion is a reduced form of boh jusificaions of HW for inerpreing heir resuls as a growh e ec, namely: (i) endogenous growh heory; and (ii) a more skilled labor force can absorb echnologies more easily. Subracing ln(l i ) from boh sides of (12) and hen subracing wo consecuive periods from one anoher yields he following equaion: g y i = g A (h i )+ g K i (1 )g L i + g h i = + h i + g K i (1 )g L i + g h i, where g y i is he growh rae of GDP per worker in counry i beween wo consecuive periods; g K i is he growh rae of he capial sock in counry i in wo consecuive periods; g L i is he growh rae of he number of persons employed in counry i in wo consecuive periods; h i is he level of cogniive skills in counry i a period ; and g h i is he growh rae of cogniive skills in counry i in wo consecuive periods. Noe ha h i represens he growh rae e ec of cogniive skills, and g h i represens he level e ec. Hence, he panel provides us a simple specificaion o assess if cogniive skills have a level e ec or a growh e ec, wihou assuming any assumpions of he laws of moion of each facor of producion as well as on he sae of he economy. In his secion, hen, we esimae he following equaion: g y i = + h i + g K i (1 )g L i + g h i + i + i, (14) where i is counry ime-invarian fixed e ecs and i is an error erm. If cogniive skills have a growh 17

18 e ec, one would find a posiive and saisically significan esimaor of, whereas if cogniive skills have a level e ec, one would find a posiive and saisically significan esimaor of. Noe ha mos previous sudies, which used panel daa, aemped o esimae a neoclassical growh model and is convergence rae. As such, hey used he level of oupu per worker as he dependen variable (e.g., Islam (1995)). We, on he oher hand, ry o idenify he growh and level e ecs. Consequenly, we use he growh rae of oupu per worker as our dependen variable. 7.2 Daa In he panel daa analysis, we do no assume ha he counries are in heir seady sae, nor we assume any laws of moion on any sae variables. As a resul, he daa we use di ers from he ones we used in he cross secion analysis. In order o esimae (14), we use direc measures of he socks of physical capial and employmen raher han heir average annual change wihin he enire period examined in he cross secion. We use daa from PWT on he real capial and labor socks, and real oupu for he he counries in our sample for he period For each counry, we calculae he annual level of oupu per worker. We hen divide he enire period of o sub-periods of 5 years long each. We calculae for each sub-period he average annual growh rae of oupu per worker, capial sock and labor sock. This approach, as well as he lengh of he sub-periods is very common in he lieraure (e.g., Islam (1995)). 16 In order o consruc a measure of cogniive skills for his period, we resric our analysis only for counries ha paricipaed in he inernaional ess long enough. The inernaional ess were iniiaed in 1964, and since hen hey ook place several imes a decade. Table 4 presens he hireen counries ha paricipaed eiher in he firs ess in 1964, or in he second ones in 1970 and hence consruc our sample. The able shows ha hese counries paricipaed in a leas five di eren ess (he average among hese counries is 7.07). Noe ha all hese counries are advanced, suggesing ha we canno analyze in his secion di eren growh paerns of developed and developing counries. We use he mehodology developed by HW o consruc a measure of cogniive skills, ye unlike HW, we consruc for each counry a series of his measure. 17 For each of hese counries, we calculae he measure for each year he counry paricipaed in he inernaional ess. Since mos counries did no 15 We resric our analysis unil 2005 in order o avoid some biases ha may emerge due o he Grea Recession. 16 For a horough survey of he lieraure using panel daa in growh regressions, see Secion VI.ii Durlauf e al. (2005). 17 See Hanushek and Woessmann (2012) for a deailed explanaion of he mehodology. 18

19 Table 4: Counries wih Early Paricipaion in Inernaional Tess & Average Years of Schoolinh, 1970, 1990 Counry Year of Firs No. of Times Avg. Years Avg. Years Paricipaion Paricipaed of Schooling, 1970 of Schooling, 1990 Ausralia Belgium Unied Kingdom Finland France Germany Israel Ialy Japan Neherlands New Zealand Sweden Unied Saes paricipae in all he ess ha ook place, and since he ess did no ake place in all he years in our sample, we linearly inerpolae he resuls for hese missing years. Figure 3 presens he cogniive skills measure in hese counries over ime. For mos of he counries ha paricipaed in 1964, here is a sharp rise in he measure of cogniive skills beween 1964 and However, afer 1970 he dynamics are mixed: some counries experience a moderae increase (e.g. Ausralia); some experience a relaive decline (e.g., Israel) and oher counries do no have a specific rend (e.g., Sweden and Belgium). Noe also ha he measure of cogniive skills has no risen sharply for none of hese counries. This raises he quesion wheher an increase in cogniive skills much above he range presened in he figure is feasible. Furhermore, i is no clear wheher hose counries which experienced some increase in heir cogniive skills indeed experienced a higher growh han hose which did no. The inernaional ess are aken a he ages of 10, 14 and Mos of he exams are for he ages of 14 (45%) and 17 (31%). Since we aemp o capure how variaion in he es scores a eced long run growh, we use he cogniive skills measure wih a lag of 5 years, which means ha he individuals who ook he exams 5 years earlier are 15, 19 and 22 years old, respecively. Table 4 explains why we use a five year lag. For he counries in our sample, he able provides he average years of schooling of he year old cohor in 1970 and 1990, as well as he share of his cohor ha graduaed high school and college (in percenage poins). As can be seen in he able, he 18 Mos of he exams for 10 year old sudens ook place owards he end of he 1990 s and as such hey form a small par in our sample. 19

20 Cogniive Skills Measure, Ausralia Belgium Finland France Cogniive Skills Germany Israel Ialy Japan Neherlands New Zealand Sweden USA Unied Kingdom Year Figure 3: The measure of cogniive skills for counries which paricipaed in inernaional ess since 1964 or 1970 average schooling years in 1970 for he cohor of year olds was 9.5. This suggess ha on average, individuals enered he labor force around he age of 17. This means, ha sudens who paricipaed in he inernaional ess when hey were 14 enered he labor force on average 3 years laer. The same mehodology reveals ha in 1990 he average schooling years of he year old cohor was 11.43, suggesing ha on average sudens who ook he es when hey were 14, enered he labor force 5 years laer. Noe ha a five year lag for all exam ha had aken place a he age of 17, implies ha he vas majoriy of he populaion is already in he labor force Resuls Our esimaed model is a model wih counry fixed e ecs, as he Hausman es rejecs he random e ecs model. Table 5 presens our resuls for esimaing (14) using he daa described above. In he firs column we es wheher here is a growh rae e ec, wihou any conrols (ha is, assuming ha 2, 3 and 4 equal zero). The coe cien of he cogniive skills is negaive and no saisically significan. In column (2) we add he change of physical capial, and labor sock, ye he coe cien of he level of cogniive skills is sill negaive and no significan. In column (3) we es wheher cogniive skills have a level e ec, wihou any conrols (ha is, assuming ha 1, 3 and 4 equal zero). The coe cien is 19 As described above, exams for he 10 year old were no so prevalen during mos of he period we analyze. Consequenly, we emphasize more on individuals who ook he exams when hey were 14 and

21 posiive and saisically significan a he 1% level. In column (4) we add he conrols of he change in capial and labor socks. The coe cien of he change in cogniive skills declines in magniude (from 1.37 o 0.86), ye i is sill posiive and saisically significan a he 5%. Finally, in column (5) and (6) we include as independen variables boh he change in he cogniive skills and is level, and only he change in cogniive skills is saisically significan a he 5%. In column (6) we add o he analysis back he change in he capial and labor socks, and none of he coe ciens of he cogniive skills is significan. We conclude from his able ha he daa suppors he level e ec hypohesis raher han he growh rae e ec. Table 5: Growh Rae vs. Level E ec Analysis Annual GDP per Capia Growh Growh E ec Alone Level E ec Alone Boh E ecs (1) (2) (3) (4) (5) (6) (0.02) (0.02) (0.02) (0.02) 1.37*** 0.86** 1.22** 0.63 (0.44) (0.34) (0.45) (0.36) 0.29*** 0.25*** 0.26*** (0.07) (0.07) (0.07) (0.16) (0.15) (0.16) Adjused-R Observaions Noes: Sandard error esimaes clusered a he level of he counry fixed e ecs are repored in parenheses; *** denoes saisical significance a he 1% level, ** a he 5% level, and * a he 10% level, all for wo-sided hypohesis ess; All regressions include a consa. Robusness One concern wih our resuls are ha hese are driven by he lag ha we chose. Tables C.1, C.2 and C.3 in Appendix C provide evidence ha his is no he case. These ables provide he resuls of esimaing (14) wih lags of 3, 6 and 10 years for our measure of cogniive skills (and heir change), respecively. As can be seen, he level of cogniive skills ( 1 is never posiive and saisically significan. In fac in Table C.2 i is negaive and saisically significan a he 5%. The change in he cogniive skills measure is always posiive, and saisically significan eiher a he 1% or he 5% when he lag we use is eiher 3 or 6 years. I is no saisically significan when we use a 10 year lag. This, however, may be due o he decline in he sample of 13 observaions ha happens due o he large lag we impose in his able. 21

22 Anoher poenial concern wih a fixed e ecs model in panel daa may arise due o he relaively small number of observaions in each counry. In such a case, since he beween variaion is no used for esimaing he coe ciens, he sandard errors of he coe ciens may be large. 20 In order o overcome his problem, we esimae a random e ecs model. Is resuls are presened in Table C.4. As can be seen in he able, no only are our resul una eced by he random e ec model, bu also heir significance is higher. 8 Conclusions This sudy asks wheher invesmen in cogniive skills has a growh e ec or a level e ec. In order o answer his quesion, we consruc a simple neoclassical growh model, in which cogniive skills only has a level e ec by assumpion. We esimae our baseline model using daa from PWT and HW, and show ha he model suppors he level e ec hypohesis. Furhermore, we show ha he daa do no fi an exended model in which we assume ha he level of cogniive skills has a growh e ec. We also use panel daa based on 13 OECD counries o answer his quesion. The daa reveal ha he level of cogniive skills among hese counries had mixed dynamics, and in all of he counries he level of cogniive skills is close o a cerain level (of 5). This raises he quesion wheher he level of cogniive skills is bounded from above. Using he panel daa, we es a model ha incorporaes boh he level and he growh e ecs. We show ha he daa suppor only he level e ec, and no he growh e ec. Furhermore, we show ha he resuls are robus for di eren poenial concerns. We conclude from his analysis ha here is no evidence ha he level of cogniive skills a ecs he long run growh rae of oupu per worker. As a resul, we show quaniaively ha he impac of cogniive skills on oupu per worker is much smaller ha under he assumpion ha i has a growh e ec. This sudy raises several quesion for fuure research ha have some policy implicaions. Firs, i highlighs he possibiliy ha cogniive skills are bounded from above. If his is he case, policies ha aemp o raise he average level of cogniive skills by increasing he level of all he sudens migh overshoo heir arge. Insead, i may be beer o arge educaion policies o reduce he dispersion of sudens achievemens in he inernaional ess. This may increase he average cogniive skills and hence simulae economic prosperiy by helping more he less abled sudens. 20 For a deep discussion of his problem, see Secion VI.ii in Durlauf e al. (2005). 22

23 Second, his paper, as well as HW, emphasizes he role of cogniive skills in promoing economic prosperiy. However, empirical evidence also sgges ha high es scores resul also from non-cogniive skills such as ambiion, moivaion and adequae personaliy rais. 21 While exploring he impac of hese non-cogniive skills on economic developmen is beyond he scope of his sudy, we find i imporan for undersanding he role of educaion in he process of developmen. References Daron Acemoglu and Joshua Angris. How large are human-capial exernaliies? evidence from compulsory-schooling laws. In NBER Macroeconomics Annual 2000, Volume 15, pages MIT PRess, World Bank. Educaion qualiy and economic growh Rober J Barro and Jong Wha Lee. A new daa se of educaional aainmen in he world, Journal of developmen economics, 104: , Rober J Barro and Xavier Sala-i Marin. Convergence. Journal of Poliical Economy, pages , Jess Benhabib and Mark M Spiegel. The role of human capial in economic developmen evidence from aggregae cross-counry daa. Journal of Moneary economics, 34(2): , Giorgio Brunello and Marin Schloer. Non-cogniive skills and personaliy rais: Labour marke relevance and heir developmen in educaion & raining sysems Daniel Cohen and Marcelo Soo. Growh and human capial: good daa, good resuls. Journal of economic growh, 12(1):51 76, Seven N Durlauf, Paul A Johnson, and Jonahan RW Temple. Growh economerics. Handbook of economic growh, 1: , Rober C Feensra, Inklaar Rober, and Timmer Marcel P. The nex generaion of he penn world able. The American Economic Review, 105(10): , See, for insance, Brunello and Schloer (2011). 23

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