Does Government Spending on Education Promote Growth and Schooling Returns?

Transcription

1 Does Governmen Spending on Educaion Promoe Growh and Schooling Reurns? Paranap Basu Durham Universiy, UK Keshab Bhaarai Hull Universiy, UK November 23, 2009 Work in Progress, Commens Welcome Absrac Since human capial is a major driver of growh, he convenional wisdom suggess ha he governmen should direc more resources o educaion. However, surprisingly he cross counry daa show lile posiive correlaion beween growh and public spending on educaion. In fac, he paern is raher puzzling. The public spending on educaion ends o lower growh and schooling reurns. In his paper, we revisi his issue and ry o undersand hese puzzling facs in erms of an endogenous growh model. We model reurn o schooling by adoping an asse pricing approach and show he explici linkage beween governmen inervenion and growh via his schooling reurn.. 1

2 1 Inroducion The e ec of public expendiure on growh is an unresolved issue. Greaer governmen spending on educaion creaes an unproducive bureaucracy ha may no have any bearing on growh and produciviy (Priche, 2001). Sylweser (2000) demonsraes ha he conemporaneous educaion expendiure has a negaive e ec on growh. Temple (2001) revisis Priche s empirical evidence and shows wih alernaive saisical procedures ha he link beween educaion expendiure and growh is "clouded wih uncerainy." In his paper, we revisi his issue and focus speci cally on he relaionship beween public expendiure on educaion, reurns o schooling and growh. The cross counry developmen facs summarized in Table 1 show some curious paerns. Counries wih a higher share of public educaion spending in GDP have lower growh raes and lower reurns o schooling while growh and reurns o schooling are posiively correlaed. Table 1: Correlaion coe ciens among educaion spending, growh and reurns o schooling Educaion Spending Growh Reurns o Schooling Educaion Spending Growh 1.39 Reurns o Schooling 1 The daa encompass a sample of 44 counries for which he reurns o schooling daa are available. 1 The negaive correlaion beween public spending on educaion and growh survives for a bigger sample of counries alhough he correlaion is sensiive o he choice of he sample of counries as poined ou by Bosworh and Collins (2003). Figure 1 plos he relaionship for a larger sample of 180 counries. Despie he remendous cross counry growh dispersion, he correlaion coe cien is -.15 and signi can a he 6% level. The negaive correlaion is weak for counries in he upper echelon 1 The daa encompass a sample of 44 counries for which he reurns o schooling daa are available. Rae of reurn daa used in his analysis were consruced from he rae of reurn educaion daabase of he World Bank available a heir websie. The growh and public spending on educaion series were compiled from he World Developmen Indicaors. 1

3 of educaion spending. In fac, for counries in he op quarile range of educaion spending, he correlaion urns posiive a.04 and for he boom quarile range, he correlaion is We looked ino possible nonlineariy in he relaionship beween growh and educaion spending by adding a quadraic erm in he growh-educaion regression. The quadraic erm is posiive and signi can a he 20% level. This means a U shaped relaionship beween growh and educaion which suggess ha growh-educaion spending relaionship reverses sign from negaive o posiive for counries wih higher educaion spending. 20 Fig 1: Growh Rae and Public Spending in Educaion Grrowhrae Linear (Grrowhrae) The objecive of his paper is o undersand hese sylized facs. Our paper is novel because we model reurns o schooling by inegraing wo facors, (i) public policy in educaion and (ii) geneically deermined alens of pupils which one may call cogniive skills. We ake an asse pricing approach o formulae he reurns o schooling. Human capial is viewed as an asse which yields ow reurns which are earnings from he goods secor. We show ha (i) and (ii) have very di eren e ecs on reurns o educaion and growh. Increase in he size of he governmen in he educaion secor has a nonmonoonic U- shaped e ec on growh and schooling reurns. This happens because wo opposing e ecs are a work when he governmen spends more on educaion by divering resources from he goods secor. Since he 2

4 goods secor is more capial inensive, his ransfer of resource acs as an implici ax on capial. Since along a balanced growh pah, reurn o physical capial equals he reurn o human capial, agens have o reallocae more ime o goods producion and less o educaion o preserve his long run arbirage condiion. An increase in governmen spending on educaion hus crowds ou privae schooling e ors along a balanced growh pah. This crowding ou e ec has an adverse consequence for schooling reurns and growh. A early sage of governmen inervenion in educaion, his disorionary e ec dominaes. Once a hreshold level of governmen inervenion is reached, he posiive growh e ec picks up. If he economy is subjec o greaer adjusmen cos of physical invesmen, i akes more inervenion by he governmen o have his posiive growh e ec. A di eren picure emerges when one varies cogniive skills. Greaer alens of pupils means higher reurns o educaion, and growh. Counries wih a bigger cohor of alened pupils will hus pu more e ors a schooling o augmen human capial. This will creae a larger ax base for he governmen o spend on educaion. The seady sae share of governmen spending on educaion will hus be higher. When one looks a he cross counry daa for growh and share of governmen spending in educaion, hese wo opposing e ecs may be a work. Counries wih a greaer degree of governmen inervenion in he educaion secor will show a negaive correlaion beween public educaion spending and growh while counries wih more alened pupils will show he opposie paern. Our paper is relaed o a growing lieraure ha shows he connecion beween growh and educaion spending (Basu, 2009, Krueger and Lindhal, 2001, Glomm and Ravikumar, 1997, Zhang, 1997). The closes paper is Blankeau e al. (2007) who also esablish a nonmonoonic relaionship beween growh and public spending on educaion using an endogenous growh model. There are a several major di erences beween our approach and Blanekeau e al. Firs, Blankeau e al. do no explicily model reurns o schooling by inegraing ime allocaion beween work and educaion. Second, hey use an overlapping generaions model while we use an in nie horizon seup making he model amenable o calibraion. Third, unlike 3

5 Blankeau e al. in our model here is a physical adjusmen cos for changing he capial sock ha is crucial for undersanding how long i akes for he governmen spending o have a posiive e ec on growh and schooling reurns. In he following secion, we lay ou he heoreical model. Secion 3 performs some quaniaive analysis on he balanced growh equaions of he model. Secion 4 concludes. 2 The Model 2.1 Schooling Technology The model is an adapaion of he Lucas-Uzawa (Lucas, 1988) model. There are wo secors, goods and educaion. A xed ime (normalized a uniy) is allocaed beween schooling and goods producion. Time l H allocaed o schooling a dae creaes e ecive labour or human capial (h +1 ) in he following period. The produciviy of schooling e or which is he same as he qualiy of schooling depends on individual cogniive skills (A H ) ha is exogenous and he public spending on educaion (g ) : The human capial hus evolves following he echnology: h +1 = (1 h )h + A H g (l H h ) 1 (1) where0 < < 1: g is he governmen provided inpu for human capial acquisiion. This inpu ha resembles Barro (1990) akes he form of public school infrasrucure faciliies, expendiure on eachers, school lunch programme and oher aids o promoe learning. Wihou his governmen suppor here is diminishing reurns o human capial. There is a xed rae of depreciaion, h of human capial. The parameer represens he degree of governmen inervenion in he educaion secor. This governmen inervenion parameer is modelled as a schooling echnology. This inervenion depends on he insiuional feaures of a counry which we do no model in his paper. Absen he governmen 4

6 role in he educaion ( equals zero), he schooling echnology revers o he Lucas (1988) form. 2.2 Goods Producion Final goods (y ) are produced wih he help of human and physical capial via he Cobb-Douglas producion echnology: y = A G k (l G h ) 1 (2) where l G ( ha equals 1 l H ) is he remaining ime allocaed o he producion of goods and A G is he oal facor produciviy (TFP) in he goods secor Invesmen Technology The invesmen goods echnology as follows: k +1 = 1 k + i (3) k k where k is a xed rae of depreciaion of physical capial.. The parameer 2 (0; 1) represens he exen of adjusmen cos. For = 1; he invesmen echnology reduces o a sandard linear depreciaion rule. This adjusmen cos is a parameric version of he Lucas and Presco (1971) adjusmen cos funcion. Similar parameric form wih 100% depreciaion of capial has been used in he lieraure (Basu, 1987, Hercowiz and Sampson, 1991). 2.4 Governmen The home counry s governmen nances he educaion spending (g ) by levying lump-sum axes on he households. The educaion spending is hen se a an e cien level ha maximizes socieal uiliy. 2 We assume ha lesure ime is xed. 5

7 The home counry receives insananeous uiliy U(c ) from consumpion (c ) a dae and has an in nie horizon wih a subjecive uiliy discoun facor. I chooses he sequences {c g; fi g; fl H g; fg g ha maximizes Max subjec o he resource consrain: and (1) hrough (3). 1X U(c ) =0 c + i + g = y (4) 3 Balanced Growh Properies Hereafer we specialize o a logarihmic uiliy funcion, U(c ) = ln c ; o analyze he balanced growh properies of he model. The appendix deails he soluion of he balanced growh pah. There are hree key balanced growh equaions. Based on he rs order condiion for he physical capial sock we ge: (AG (y=k) + 1 k ) G = ; (5) 1 (1 ) From he rs order condiion for he human capial sock, one ges: G = (1 h ) + A H (1 ) 1 (1 ) :(1 l H ) (y=h) (6) where y=h and l H are consans along he balanced growh pah. Finally, using he human capial echnology (1), we ge a hird balanced growh equaion: (1 ) G = 1 h + A H (1 ) :l H l 1 H l A (1 ) Gl G (k=h) (7) G 6

8 These hree equaions solve for hree unknowns, namely k=h, l H and G: The appendix provides full expression for he seady sae levels of hese wo variables. The share of public spending in GDP is given by: g = 1 y 1 :l H (8) l G A higher inervenion of governmen in he educaion secor (meaning larger ) raises his raio. On he oher, greaer ime o school (l H ) also raises his share because he posiive growh e ec of educaion increases he ax base for he economy. 3.1 Reurn o Schooling In his model, he human capial is an asse which yields a ow reurn. Think of human capial as a Lucas ree whose valuaion is q h which is akin o Tobin s q of physical capial: This valuaion is driven by he reurn and opporuniy cos of going o school. I is easy o verify ha his value of human capial is he same as he raio of he shadow price of consumpion o ha of invesmen in schooling. In oher words, q h = (9) where and are he lagrange mulipliers associaed wih he schooling echnology (1) and he ow resource consrain (4). using he Euler equaion for human capial (see (A.7), one ges he following valuaion equaion for he human capial: q h = m +1 fq+1[1 h h +A H g+1(1 )(1 l G+1 ) 1 h +1 ]+fa G (1 )k+1h (10) where m +1 is he ineremporal marginal rae of subsiuion in consumpion given by +1 = : 7 +1l 1 G+1 g

9 Nex verify from (A.5) in he appendix ha q h = MP HG MP H E (11) where MP H G and MP H E are he marginal producs of e ecive labour in he goods and educaion secors respecively. Rewrie (10) as q h = m +1 q h +1 (1 h + l H+1 MP H E +1) + l G+1 MP H G +1 (12) The valuaion equaion for human capial looks similar o a Lucas (1978) ree valuaion equaion. The value of his ree a dae is he discouned nex period marginal produc of human capial in he goods secor, l G+1 MP H G +1 and he impued nex period value of unused porion of he ree (1 h )q h +1 plus he replenishmen of i, l H+1 MP H E +1 due o new educaion. The reurn o schooling (R h +1 ) is hus given by: R h +1 = q h +1 (1 h + l H+1 MP H E +1) + l G+1 MP H G +1 Along he balanced growh pah, q h is consan. Using (11) one obains he following expression for he seady sae reurn o human capial: q h R h = 1 h + MP H E (13) Using (13) one can rewrie he balanced growh equaion as follows: 1 + g = R h (14) 3.2 Cogniive Skills, Reurns o Schooling and Growh The model has sharp implicaions for he relaionship beween reurns o schooling, growh and cogniive skills. Long run growh is proporional o reurn o schooling as eviden from (14). The reurn o schooling is enirely driven by he marginal produc of e ecive labour in he educaion secor as seen from (13). This marginal produc is a funcion of he combinaion of 8

10 he cogniive skills of pupils A H, he degree of governmen inervenion () in he educaion secor as well as he privae schooling e ors, l H : 3.3 The Physical Capial Adjusmen Cos Wedge Generally, wih 2 (0; 1) ; he physical capial adjusmen cos drives a wedge beween he reurns o physical capial and reurn o schooling. This wedge depends on he human capial invesmen. To see his noe he following useful relaionship: R h = (1 + ) [1 + MP K k ] : (15) + where MP K is he marginal produc of capial in he goods secor. In he benchmark case of no adjusmen cos ( = 1), i follows from equaion (6) ha he radiional Euler equaion holds, meaning 1 + g = (1 k + MP K); (16) In he presen seing, he adjusmen cos wedge or he user cos of capial depends non-rivially on he long run growh rae. To see his, use (15) and (6) o obain he following expression for he user cos of capial: 1 h + MP H E 1 k + MP K = 1 (1 + ): : (17) + G (1 )= For any growing economy, he righ hand side of (17) is always a posiive fracion. This means ha 1 h +MP H E < 1 k +MP K: This inequaliy resul can be inerpreed as implying ha he physical capial adjusmen cos creaes a user cos wedge ha causes a lower physical capial o e ecive labor raio in equilibrium han when = 1: And his is consisen wih our noion ha accumulaing physical capial is more cosly in he presence of adjusmen cos, as in Lucas (1967). Wha is novel in he presen seing is he ineracion beween his user cos wedge and he invesmen in human capial via he long run growh rae, g. 9

11 4 Quaniaive Analysis In his secion, we carry ou some quaniaive analysis of he model s balanced growh properies o undersand he sylized facs repored in Table 1. The model has 10 parameers, namely ; h ; k ; ; ; A H ; ; A G : Using he US economy as he benchmark, is xed a.36, a.99, k =.1 and h = :05. The governmen inervenion parameer is chosen a.05 which is approximaely he cross counry average share of educaion spending in GDP for our sample of counries. For he baseline economy we assume ha here is no adjusmen cos which means = 1:The remaining produciviy parameers, A G and A H are varied in a range o arge abou a 4 o 6% 3 growh rae of world GDP and k:h raio around uniy. Doing so we x A G = 2:2; A H = :15: Figure 2 plos he e ec of governmen inervenion ( ) in educaion on growh and schooling reurns. Greaer inervenion lowers growh and reurns unil a hreshold level of inervenion is reached. Afer his he posiive growh e ec picks up. Decline in growh and schooling reurns in response o governmen inervenion is sharper if a 20% adjusmen cos is added ( = :8): In he presence of adjusmen cos, i akes more inervenion by he governmen before he posiive growh e ec picks up. Fig 4 plos he e ec of governmen inervenion on schooling e ors l H: Greaer degree of governmen inerference in he educaion secor unambiguously crowds ou privae schooling e ors. 4 A fundamenal arbirage condiion is a work o engender his crowding ou e ec. To see his, ignore adjusmen cos. Along he balanced growh pah, he reurn o human capial equals he reurns o physical capial. Based on (A.9) i is easy o see ha ceeris paribus, an increase in divers resources from he goods o he educaion secor. This is an implici ax on capial because he goods secor is capial inensive. If he social planner canno change ime alloca- 3 Since here is no availble esimae of physical o human capial raio, we ake uniy as a reasonable benchmark. 4 The e ec is quaniaively very similar in posiive adjusme cos scenario which we do no repor here. 10

12 Fig 2: Growh, Schooling Reurns and Governmen Inervenion: No Adj Cos Scenario growh Schooling Reurns Fig 3: Governmen Inervenion, Growh and Schooling Reurns: Posiive Adjusmen Cos Scenario Growh Schooling Reurns Ea 11

13 Fig 4: Governmen Inervenion and Schooling Effors Ea ion l H ; his resuls in a lower k=h: Once he planner has conrol over he ime allocaion, ime will be reallocaed from educaion o goods secor o preserve his long run arbirage condiion. Two opposing e ecs are a work when he governmen inervenes more in he educaion secor. I disors privae secor incenive o pu ime in schooling. This has adverse e ecs on growh and schooling reurns. On he oher hand, complemenariy beween human capial and governmen provided services booss growh and schooling reurns. The former negaive e ec dominaes when he size of he governmen in he educaion secor is small. Figure 5 plos he relaion beween growh and he share of public educaion spending in GDP. The relaionship beween educaion and GDP is non-monoonic and resembles Figure 2. Noe ha public spending on GDP is endogenous in he model and is deermined by direc inervenion of he governmen in educaion and he privae secor response o his inervenion (see equaion (8)). 12

14 Fig 5: Growh and Educaion Spending: No Adj Cos Pub Educaion Spending/GDP Fig 6: Growh and Public Spending on Educaion: Posiive Adjusmen Cos Economies Pub Spending on Educ/GDP A very di eren picure emerges if one performs comparaive saics by changing he pupil s alen parameer, A H (Table 3). Counries wih more alened pupils will show greaer schooling paricipaion. This happens because a higher A H raises reurn o educaion, R H : Agens reallocae more 13

15 ime o educaion. This lowers he raio of physical o human capial hus raising he reurns o he goods secor as well. The ne oucome is a higher reurns o schooling, higher growh, and greaer educaion share in GDP. : Fig 7: Cogniive Skills, Growh and Schooling Reurns Growh Schooling Reurns Cogniive Skills Fig 8: Cogniive Skill and Schooling Reurns Cogniive Skill 14

16 Fig 9: Cogniive Skill and Public Educ Expendiure Share in GDP Cogniive Skill 5 Conclusion In his paper we revisi he issue wheher public spending on educaion has favourable e ecs on growh and schooling reurns. The model demonsraes ha here is a clear nonmonoonic relaionship beween public spending on educaion and growh. Posiive e ecs of governmen spending appear for economies wih a large size of he governmen in he educaion secor. I is also well known ha richer counries spend more on educaion (Armellini and Basu, 2009). The immediae implicaion is ha public spending on educaion has favorable e ecs on growh and schooling reurns for rich counries wih large share of public spending. Blankeau e al. (2007) also provide con rmaion of his hypohesis. Our model demonsraes ha despie his posiive e ec on growh greaer governmen inervenion in educaion lowers privae schooling e ors. This disincenive e ecs of governmen educaion spending bears also on a di eren srand of lieraure which advocaes for privaizaion of educaion in erms of aucioning o educaion vouchers. Fuure research can explore his implicaion furher. 15

17 References [1] Armellini, M and P, Basu (2009), "Alrusim, Educaion and Growh," Mimeo. [2] Barro, R.J (1990), "Governmen Spending in a Simple Model of Endogenous Growh," Journal of Poliical Economy, 98, 5: Par II, S103-S125. [3] Basu, P (1987), "An Adjusmen Cos Model of Asse Pricing," Inernaional Economic Review, Vol. 28, No. 3, pp [4] Basu, P (2009) Too Hungry o Read: Is an Educaion Subsidy a Misguided Policy for Developmen? Chaper in Handbook of Research in Cos Bene Analysis, Edward Elgar Publishing Limied. [5] Blankeau Bill, Nicole Simpson and Marc Tomljanovich "Public Expendiure on Educaion, Taxaion and Growh: Linking Daa o Theory, American Economic Review, Papers and proceedings, [6] Glomm, Gerhard and B. Ravikumar Producive Governmen Expendiures and Long-Run Growh. Journal of Economic Dynamics and Conrol, 21:1, pp [7] Hercowiz, Zvi and Sampson, Michael "Oupu Growh, he Real Wage, and Employmen Flucuaions," American Economic Review, American Economic Associaion, vol. 81(5): , December. [8] Krueger, Alan B. and Mikael Lindahl Educaion for Growh: Why and for Whom? Journal of Economic Lieraure, 39:4, pp [9] Landau, Daniel Governmen and Economic Growh in he Less Developed Counries: An Empirical Sudy for Economic Developmen and Culural Change, 35:1, pp [10] Lucas R.E., Jr. (1988), "On he Mechanics of Economic Developmen", Journal of Moneary Economics, 22:1:

18 [11] Lucas, R.E., Jr., (1967), Adjusmen Coss and he Theory of Supply, The Journal of Poliical Economy, 75 (4, Par 1, Augus): [12] Lucas, R.E and E.C. Presco (1971), "Invesmen under Uncerainy," Economerica, 39, 5: [13] Priche, L. (2001). Where has all he educaion gone? The World Bank Economic Review, Vol 15, No 3, pp [14] Sylweser, K. (2000). Income inequaliy, educaion expendiures and growh. Journal of Developmen Economics, Vol 63, Issue 2, pp [15] Zhang, Jie Opimal Public Invesmens in Educaion and Endogenous [16] Growh. Scandinavian Journal of Economics, 98:3, pp [17] Temple, J. (2001). Generalizaions ha aren? Evidence on educaion and growh. European Economic Review 45, pp A Appendix Le ; ; ;! be he lagrange mulipliers associaed wih he ow budge consrain (4), human capial echnology, (1), he physical invesmen echnology (3). The lagrange is: P L = 1 P U(c ) + 1 [A G k (l G h ) 1 c i g ] =0 =0 P + 1 [(1 h )h + A H g (l H h ) 1 h +1 ] =0 P + 1 i k h1 k + i k k +1 =0 17

19 Firs order condiions are: c : U 0 (c ) = (A.1) i : + 1 k + i 1 = 0 (A.2) k " k +1 : k + i +1 i +1 : 1 k + i # y +1 = 0 k +1 k +1 k +1 k +1 (A.3) h +1 : = +1 [1 h + A H+1 g +1(1 )h +1 l fa G+1 (1 )k +1h +1l 1 G+1 H+1 ] (A.4) l G : (1 )A G l G k h 1 (1 )g A H h 1 l H = 0 (A.5) g : = A H g 1 (h l H ) 1 (A.6) A.1 Derivaion of he Balanced Growh Equaions Along he balanced growh pah, we also exploi he fac ha he raw labour allocaion variables l G and l H are consan Using (A.2), (A.3) and (3) one ges he balanced growh equaion (5). Rewrie (A.4) as: 18

20 = : +1 [1 h + A H g +1(1 )(1 l G+1 ) 1 h +1 ] (A.7) + +1 fa G (1 )k +1h Nex use (A.6) o subsiue ou condiion using (A.1) ha +1 yields: From (A.5), one can wrie +1l 1 G+1 and also use he balanced growh = =(1 + g) which upon subsiuion above = (g =h ) 1 A H l 1 H Use (A.6) and (A.5) o ge he following compac expression for g =h : g = 1 h 1 :l H : y l G h (A.8) which immediaely gives he following expression for he educaion share in GDP: g = 1 y 1 :l H l G (A.9) Noe ha along a seady sae (g=h)1 A H l 1 H is a consan which means = : Use his fac in (A.7) and also use he fac ha +1 = 1+g o ge: 1 = 1 h + A H (1 )l 1 H 1 + g (g=h) g : A Hl 1 H (g=h) : (1 )A 1 G (k=h) l 1 G (A.10) Plugging (A.8) ino (A.10) and simplifying one ges (6). Using (1) one ges he hird balanced growh equaion (7). 19