Aurangzeb * Abstract. 1. Introduction

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1 Auangzeb 1 Relaionship beween Healh Expendiue and GDP in an Augmened Solow Gowh Model fo Pakisan: An Applicaion of Co-inegaion and Eo-Coecion Modeling Auangzeb * Absac This pape examines he empoal inedependence beween goss domesic poduc and healh expendiue pe capia fo Pakisan in an augmened Solow gowh model suggesed by Mankiw, Rome and Weil (1992) fo he peiod of This pape is an exension of he MRW model by incopoaing healh capial poxied by healh expendiue o he augmened Solow model. Moeove, an openness vaiable is also included in he model in ode o capue he effec of echnological changes on gowh. The pape employs co-inegaion, ECM mehodology and seveal diagnosic and specificaion ess. The empiical findings show a significan and posiive elaionship beween GDP and Healh Expendiue, boh in he long- and sho-un. 1. Inoducion Since he classic pioneeing wok of Solow (1956), hee have been significan developmens in he heoeical and empiical lieaue on endogenous gowh models. This iniial wok analysed economic gowh by assuming a neoclassical poducion funcion wih deceasing euns o capial in which aes of saving and populaion gowh wee consideed exogenous. The model was augmened by Mankiw, Rome and Weil (1992) wih he inclusion of human capial known as he MRW model. Lae, Bao (1997); Gemmell (1996) found human capial as a significan faco in deemining gowh. Similaly, Mille and Upadhyay (2000) examined a significan impac of ineacion beween human capial and openness as a measue fo he couny s abiliy o absob echnological advances; his has a significan effec on oal faco poduciviy. An impoan issue in his pespecive has been highlighed by Siddiqui, Afidi, and Haq, (1995) ha impovemen in he healh saus of he populaion is an impoan * The auho is Reseach Office a he Social Policy & Developmen Cene, (SPDC) Kaachi

2 2 The Lahoe Jounal of Economics, Vol.8, No.2 componen of human capial fomaion. Impoved healh saus of a naion ceaes an ouwad shif in he labou supply cuve and inceases poduciviy of labou wih an incease in he poduciviy of invesmen in ohe foms of human capial, paiculaly educaion. Mos of he sudies in his aea have been based on he cosscouny panel daa (see fo example Blomqvis and Cae 1997; Gedham e al. 1992; Hansen and King 1996; Hiiis and Posne 1992; Knowles and Owen 1997; Nancy and Paul 2001; Temple 1999) wih no indicaion of any ime-seies couny specific sudy. Moeove, wih he excepion of Hansen and King (1996), Nancy and Paul (2001), he pevious sudies have no focused on he saionaiy and co-inegaion popeies of he daa. The objecive of his sudy is o examine he pesence of co-inegaion beween Goss Domesic Poduc (GDP) and healh capial poxied by healh expendiue pe capia in an augmened Solow gowh model fo Pakisan. Alhough he Solow model has been augmened in diffeen ways, hee ae a few sudies ha have examined he effecs of healh capial on gowh; fo insance, Knowles and Owen (1995; 1997) have examined he effecs of incopoaing healh capial in he MRW model. 1 This pape is an exension of he pevious lieaue fo numeous easons. Fisly, i augmens healh capial in he Solow gowh model fo Pakisan. Secondly, he modeling appoach is based on he mulivaiae maximum likelihood-based infeence of co-inegaed veco auoegession (VAR) models developed by Johansen (1988, 1991, and 1995). As is well known, he mulivaiae modeling saegy offes a majo advanage in ha muliple co-inegaing elaions can be modeled in a sysem wihou he need o impose abiay nomalisaions necessay in he single-equaion Engle-Gange wo-sep co-inegaion appoach. The pape compises five secions including he pesen one. Secion 2 descibes he gowh model which has been augmened by inclusion of invesmens in human capial, paiculaly healh. Secion 3 pesens issues peaining o daa. Secion 4 offes he empiical analysis. The las secion povides he conclusion. 2. The Healh Capial Augmened Gowh Model 1 In hei model, he labou vaiable in an aggegae poducion funcion of educaion and healh was augmened. Thei esul suggess ha, incopoaing human and healh capial as labou augmening o as sepaae facos of poducion does no change he conclusions empiically.

3 Auangzeb 3 We begin by specifying a Cobb-Douglas poducion funcion wih wo faco inpus, capial and labou, Y = K A L (1) α Whee Y is eal income, K epesens physical capial, L is labou, and A is level of echnology paamee eflecing how well a couny does a ansfoming inpus ino oupus. A is specified as: ln A = Π (2) X Whee Π is he paamee veco o be esimaed and X is a veco of vaiables deemining oal faco poduciviy (TFP). The veco X conains he log-level of he degee of openness of he economy O since a couny ha is moe open o he es of he wold has geae abiliy o absob echnological advances geneaed in leading naions (Rome, 1992; Bao and Sala-i-Main, 1995). Fo simplificaion, labou is assumed o gow exogenously a aes of a defined as. a L = L e 0 (3) Defining ( K L ) y = Y L as he sock of capial and he level of oupu pe uni of labou especively, he evoluion of capial is govened by k = and ( ) k k α k = ω y ( a + δ ) k = ω k ( a + δ ) k (4) k Whee a do indicaes change ove ime, ω is a facion of oupu invesed in physical capial in peiod, and δ is he ae of depeciaion. The sock of capial (K ) conveges o he seady sae value of capial ( k ) defined as. k k 1 [ ω ( n + + δ )] ( ) = g (5) k Subsiuing he value of fom (4) in (1) and aking naual logs on boh sides, he seady sae income pe capia is wien as:

4 4 The Lahoe Jounal of Economics, Vol.8, No.2 α k α ln y = β 0 + lnω ln( n + g + δ ) + ε (6) Whee β 0 is he inecep and ε is he andom disubance em. Equaion (6) is he simplified fom of he Solow model and has been used as he basic model in empiical specificaions (see fo example Summe and Heson 1988; Bao and Sala-i-Main 1992; Islam 1995). Lae on human capial was included as anohe inpu of poducion (see Bao and Lee (1993), Benhabib and Siegel (1994), Sodebom and Teal (2001)). Augmenaion of human capial in he gowh model poved o be useful concening he pedicion powe and he size of α, exclusion of human capial ceaes a specificaion biased. The poducion funcion in equaion (1) is now wien as: α β β Y = K H A L α + β < 1 (7) Whee H is he sock of human capial (a poxy by aveage level of educaion) in addiion o he gowh in physical capial in equaion (3). The sock of human capial gowh is deemined by: h h β h = ω y ( a + δ ) h = ω h ( a + δ ) h (8) h Whee ω is a facion of oupu invesed in human capial in he ime peiod and h = ( H L ) is he human capial pe uni of labou. Hence, he equaion (6) is now wien as: α k β h α + β lny = β 0 + lnω + lnω ln( n+ g+ δ) + ε (9) β β β Simila o he human capial augmenaion, he Solow model can be augmened o invesmens in healh. The evoluion of healh expendiue is deemined by. e e γ e = ω y ( a + δ ) e = ω h ( a + δ ) e (10) e ω Whee is a facion of oupu invesed in healh capial in he ime peiod and e = ( E L ) is human capial pe uni of labou. Now he equaion (9) is wien as:

5 Auangzeb 5 α k β h γ e ln y = β0 + lnω + lnω + lnω β γ β γ β γ α+ β + γ ln( n+ g+ δ) + ε β γ The model in equaion (10) can be esimaed wih OLS. In he new endogenous gowh heoy i has been agued ha he degee of absopion of echnological advances inceases wih inceases in he openness of a couny. Consideing his view he openness vaiable (poxied by ade inensiy) is also included in his model in ode o capue he effec of echnical pogess. This will also aenuae he specificaion bias and incease he obusness of he infeences dawn. Similaly, he addiion of human and healh capial along wih physical capial impoves he pefomance of he Solow model. Invesmens in human, healh and physical capial ae expeced o have a posiive effec on pe capia income. Similaly, he openness vaiable is also expeced o have a posiive influence on pe capia income. I helps in emoving he lack of echnological needs, so ha an incease in he make size o in he availabiliy of poducion echnology affecs he euns o innovaion and heefoe leads o highe pe capia income. 3. The Daa The daa has been acquied fom vaious issues of he Economic Suvey of Pakisan and Saisical Supplemens published by he Minisy of Finance. The daa is on an annual basis coveing he ime peiod of The ime seies includes populaion, eal GDP, eal goss fixed capial fomaion, eal physical capial 2 and goss enollmens in pimay, seconday and eiay levels of educaion aken as a poxy fo human capial, because enollmen aes measue he quaniaive addiions in he fom of yeas of schooling o he sock of human capial. Healh expendiue is aken as a poxy fo healh capial wheeas ade inensiy defined as ade o GDP aio is aken as a poxy fo openness. 4. Mehodology and Empiical Findings Following he convenion fo ime seies mehodology, he ode of inegaion of he individual seies has been esed pio o he coinegaion analysis and esimaion of he Eo-Coecion Model (ECM). (11) 2 The consucion of he capial seies is discussed in Annexue I

6 6 The Lahoe Jounal of Economics, Vol.8, No.2 The Augmened Dickey-Fulle (ADF) and Phillips-Paen (PP) ess ae used fo his pupose. The ADF es is based on he following equaion: ΔS = α + β + δs p 1 + γ jδs j + j= 1 e (12) The lag p is chosen o ende he esiduals fee of seial coelaion. We hen es he composie null hypohesis H 0 : β = 0, ρ = 1 using he Dickey- Fulle (1981) saisic φ 3. If H 0 is ejeced, hee is no uni oo and he pesence of dif and end can be asceained by convenional -es on α and β especively. If H 0 is no ejeced we e-esimae Equaion (11) seing β = 0 and hen use he Dickey-Fulle (DF) saisic τ μ, o es he hypohesis H 0 : ρ = 1. If H 0 is favoued, we ge addiional confimaion abou he pesence of a uni oo. We may hen eso o he saisic φ 2 o es he null hypohesis H 0 : α = 0, ρ = 1 Rejecion of H 0 agues fo he pesence of a uni oo wih dif, and is non-ejecion is defined as having a uni oo wihou dif. The same pocedue is epeaed fo he fis diffeenced (gowh) seies, and if necessay fo highe-ode diffeenced seies unil a saionay seies is obained. Howeve, he Dickey-Fulle es mehodology suffes fom a esicive assumpion ha he eo em is i.i.d. When economic ime seies exhibi heoscedasiciy and non-nomaliy in aw daa, hen Phillips-Peon (PP) es is pefeable o he DF and ADF ess. Phillips and Paen (1988) developed a genealisaion of he Dickey- Fulle pocedue ha allows fo he disibuion of he eos. The pocedue consides he following egession equaion. S = a~ + a~ S + a~ ( T / 2) + u (13) Whee T is he numbe of obsevaions and disubance em u is such ha E(u )= 0, bu hee is no equiemen ha he disubance em is seially un-coelaed o homogenous. The ADF es is vey sensiive o he assumpion of independence and homogeneiy. I is fo his eason ha he PP es is pefeed o he ADF es. The esuls of he ADF and PP ess, applied o level and fis diffeence daa, ae epoed in Annex II Table 1. I is obseved fom he esuls ha none of he seies ae non-saionay a level, bu all he seies ae saionay a fis diffeence (a 5% level of significance). Once he ode of inegaion of he seies is deemined he nex sep is he co-inegaion analysis.

7 Auangzeb Co-inegaion analysis The es fo co-inegaion is given in Annex III Table 1. The Johansen echnique (Johansen, 1988, 1991; and Johansen and Juselius, 1990) has been used o es he exisence of co-inegaion in he undelying seies. Boh, he maximum eigenvalue (λ max ) and ace (τ) es saisics have been used o deemine he numbe of co-inegaing vecos. The null hypohesis esed was ha hee can be no co-inegaing vecos among he vaiables of equaion (10). The esul shows ha he null hypohesis of no co-inegaion is ejeced in boh ess a he 1% significance level. Theefoe, hee is a song and sable long-em elaionship exisen among he vaiables in equaion (10). Given ha he Johansen co-inegaion echnique indicaed he exisence of moe han one co-inegaing veco, he quesion is whehe i is bee o have one o many co-inegaing vecos among he undelying seies. The exisence of many co-inegaing vecos may indicae ha he sysem unde examinaion is saionay in moe han one diecion and hence moe sable (Dickey e al., 1994) Long-un paamee esimaes The long-un paamees esimaed by using he Johansen echnique ae nomalised on he basis of he GDP vaiable by seing is esimaed coefficien a -1. The coefficiens and hei especive sandad eos ae given in Table1. Table 1: Esimaed long-un paamees Nomalised on he basis of GDP pe capia Equaion Coefficien Sd. Eo Y -1 - K 0.29* 0.04 H 0.37* 0.04 E 0.13* 0.03 O 0.11* 0.09 Consan -1.61* 0.17 Noe: * indicaes significance a he 1%-level.

8 8 The Lahoe Jounal of Economics, Vol.8, No.2 Sho-un ECM esimaion: Accoding o Engle and Gange (1987) co-inegaed vaiables mus have an ECM epesenaion. The majo advanage of he ECM epesenaion is ha i avoids he poblems of spuious coelaion beween dependen and explanaoy vaiables, and makes use of any sho- and longun infomaion in he daa. Table 2 pesens he sign of he cumulaive coefficiens and hei especive lag sucues. The especive lag lengh fo each vaiable and he sequence in which he vaiables ae eneed in he ECM have been seleced by using Akaike (1969) FPE cieion and he Caines, Keng and Sehi (1981) Specific Gaviy (SGC) cieion especively 3. Refe o Annex IV, Table 1 fo deails abou he sho un elasiciies and hei especive -saisics. Table 2: Eo-coecion Specificaion Gowh Equaion: Δ Y + 2 m = 1 = α 4 m 2 i = 1 Δ E α 1 i m Δ Y i 1 n = 1 + α 5 3 α 2 j Δ K j + j = 1 k = 1 5 n Δ O n α 6 EC α 1 3 k + ε Δ H k Whee he symbol Δ is he fis diffeence opeao, ε is a whie noise. The egesso EC 1 coesponds o he one yea lagged eocoecion em and i is expeced haα 6 < 0. Wih he dynamic specificaion of he model he sho-un dynamics ae influenced by he deviaion fom he long-un elaionship depiced by EC -1. Noice ha he ECM model in Table 2 does no conain an inecep em. The eason is ha he eo-coecion EC -1 aleady includes an esimae of i. The empiical esuls show ha healh expendiue is a saisically significan and eliable deeminan of gowh. Hence, in he sho-un gowh is an inceasing funcion of all hee ypes of capials. Howeve, he 3 Fo deails see Akaike, H. (1969) Saisical pedico idenificaion and Caines, P.E.C., Keng, W. and Sehi, S.P. (1981) Causaliy analysis and mulivaiae auoegessive modeling wih an applicaion o supemake sales analysis

9 Auangzeb 9 openness vaiable shows a significan bu negaive effec on gowh in he sho-un. Vaious diagnosic and specificaion ess have been applied in ode o check he validiy of he policy conclusions, which ae gaheed fom he esimaion of he ECM model (fo deail see Annex IV Table1). 5. Summay and Conclusion Based on he economic modeling of pevious sudies using annual daa of Pakisan s economy, he pape invesigaed he possible coinegaion beween healh expendiue and GDP in an augmened Solow gowh model in a Cobb-Douglas funcional fom. I used Johansen coinegaion analysis, ECM mehodology and diffeen diagnosic ess. Befoe poceeding o esing fo co-inegaion, uni-oo ess wee pefomed using ADF and PP ess. The epoed -values esuling fom he ADF and PP es indicaed ha he undelying seies appea o be saionay in fis diffeences. The Johansen co-inegaion es confims he exisence of a song and sable long-em elaionship among he vaiables in he gowh model. The ECM echnique is applied o avoid he spuious egession phenomenon. The ECM model esimaes confim he exisence of a shoand long-em posiive and significan elaionship beween healh expendiue and economic gowh. Fuhemoe, he sho-un paamees of he ohe wo capials (i.e. physical and human capial) also have a significan posiive effec on he gowh vaiable. In ems of adjusmens made o he long-un equilibium, he eo-coecion em EC -1 is found o be saisically significan. The specificaion and diagnosic es yields saisfacoy esuls. Hence an inclusion of healh expendiue as a poxy fo invesmen in healh capial also impoves he significance of he coefficiens of human and physical capial in he gowh model.

10 10 The Lahoe Jounal of Economics, Vol.8, No.2 Consucion of Capial Sock Seies ANNEXURE I Iniial capial sock: The pocedue fo esimaing he oveall iniial capial sock is shown in Table 1 below. A depeciaion ae of 5 % is assumed 4. Hence, he aveage life span of capial is 20 yeas (i.e. 1/0.05 = 20 yeas). If he 5 pecen depeciaion ae is indeed ue, hen he amoun invesed in 1953 would have zeo value in Thus, he value of invesmen in 1953 of Rs million in 1981 pices will be zeo in 1973 as shown in he Table. Similaly, he invesmen in 1954 of Rs million will have a emaining value of Rs. 442 million in 1973, while fo 1955 invesmen will have emaining value of Rs. 954 million. If one coninues his pocess unil 1973, hen one can obain he value of he oveall capial sock in 1973, which is Rs. 22,8266 million a pices. Table 1: Esimaion of iniial capial sock GCF Iniial capial sock in 1973 a pices = 22,8266 Capial Sock Seies: The seies fo capial sock was deived by using he pepeual capial invenoy mehod. Tha is: K (1 δ) + I = K 1 Whee K is he capial sock in yea, K-1 is he capial sock in he pevious yea, δ (=0.05) is he depeciaion ae, and I is he invesmen in yea. 4 Ohe sudies have also applied 5 % depeciaion ae (see Ausia and Main, 1992)

11 Auangzeb 11 ANNEXURE II Table 1: Tess fo Uni-Roos Level Fis Diffeence VARIABLES ADF PP ADF PP Y * -4.24* K * -3.49** -3.84* H * -5.66* E ** -4.60* O * -4.25* L ** -5.22* Noe: *(**){***}significan a 1%, 5% and 10% level.

12 12 The Lahoe Jounal of Economics, Vol.8, No.2 Null H 0 ANNEXURE III Table1: Johansen Co-inegaion Tes Resuls Maximal Eigen-value Tes Alenaive Eigen- Ciical H 1s value Value (95%) Null H 0 Ciical Tace Tes Alenaive LR-aios H 1 Value (95%) =0 = ** =0 > ** 76.1 =1 = ** > ** 53.1 =2 = ** > ** 34.9 =3 = ** > ** 20.0 =4 =5 9.54** >5 9.54** 9.2 Noe: ** significan a 5% level.

13 Auangzeb 13 ANNEXURE IV Table 1: ECM Esimaes Vaiables Coeff. Sho-un Elasiciies -sas Δ Y 1 Δ Y 2 Δ K Δ K Δ K 3 Δ K 4 Δ K H H H E E O EC Adj. R 2 = 0.88 DW = 1.82 F a5 = 0.19 F he = 0.67 JB = 0.53 EC is he eo coecion em obained fom he esimaed longun elaionship. The las hee ess ae he diagnosic ess of he esiduals fom he esimaion: F a3 is F-sas of up o 3 d ode esidual seial coelaion, F he ess auoegessive condiional heoscedasiciy and JB is he Jaque-Bea es fo nomaliy of he esiduals.

14 14 The Lahoe Jounal of Economics, Vol.8, No.2 Refeences Akaike, H Saisical Pedico Idenificaion, Annals of he Insiue of Saisical Mahemaics 21, Bao, R. J. and J-W. Lee Inenaional Compaisons of Educaional Aainmen, Jounal of Moneay Economics 32, Bao, R. J. and Sala-i-Main, X Economic Gowh. New Yok, McGaw Hill. Bao, R. J Deeminans of Economic Gowh: A coss-couny empiical sudy, Cambidge Massachuses, The MIT Pess. Benhabiib, J. and M. Speigel The Role of Human Capial in Economic Developmen: Evidence fom Aggegae Coss-couny Daa, Jounal of Moneay Economics 34, Blomqvis, A.G. and R.A.L Cae Is Healh Cae Really a Luxuy?, Jounal of Healh Economics 16, Caines, P.E.C., Keng, W. and Sehi, S.P Causaliy Analysis and Mulivaiae Auoegessive Modeling wih an Applicaion o Supemake Sales Analysis, Jounal of Economic Dynamic and conol 3, Dickey, D. A. and W.A. Fulle Disibuion of he Esimaos fo Auoegessive Time Seies wih a Uni Roo, Jounal of Ameican Saisical Associaion 74, Dickey, D. A., D. P. Hasza, and W. A. Fulle Tesing fo Uni Roos in Seasonal Time Seies, Advanced Tex in Economeics. Oxfod, New Yok, Toono and Melboune, Oxfod Univesiy Pess, Engle, R. F Esimaes of he Vaiance of U.S. Inflaion Based upon he ARCH Model, Jounal of Money, Cedi, and Banking 15, Engle, R. F. and Gange W.J Coinegaion and Eo-coecion: Repesenaion, Esimaion and Tesing, Economeica 35,

15 Auangzeb 15 Gemmell, N Evaluaing he impacs of human capial socks and accumulaion on economic gowh: some new evidence, Oxfod Bullein of Economics and Saisics 58: Gedham, U.G. e. al An Economeic Analysis of Healh Cae Expendiue: A Coss-Secion Sudy of he OECD Counies, Jounal of Healh Economics 11(1), Hansen, P. and A. King The Deeminans of Healh Cae Expendiue: a coinegaion appoach, Jounal of Healh Economics 15, Hiiis, T. and J. Posne The Deeminans and Effecs of Healh Expendiue in Developed Counies, Jounal of Healh Economics 11, Johansen, S Saisical Analysis of Coinegaion Vecos, Jounal of Economic Dynamic and Conol 12, Johansen, S. and Juselius, K Maximum Likelihood Esimaion and Infeence on Coinegaion wih Applicaions fo he Demand fo Money, Oxfod Bullein of Economics and Saisics 52, Knowles S. and P.D. Owen Educaion and Healh in an Effecive- Labou Empiical Gowh Model, The Economic Recod 73(223), Mankiw, N.G., D. Rome and D.N. Weil A Conibuion o he Empiics of Economic Gowh, Quaely Jounal of Economics 107, Mille, S.M. and M.P. Upadhyay The Effecs of Openness, Tade Oienaion and Human Capial on Toal Faco Poduciviy, Jounal of Developmen Economics 63, Nancy, D. and H. Paul Healh Cae Spending and Economic Oupu: Gange Causaliy, Applied Economic Lees 8(8), Osewald-Lenum, M A Noe wih Quaniles of he Asympoic Disibuions of he Maximum Likelihood Coinegaion Ranks Tes Saisics: Fou Cases, Oxfod Bullein of Economics and Saisics 54,

16 16 The Lahoe Jounal of Economics, Vol.8, No.2 Phillips, P.C.B and P. Peon Tesing fo a Uni Roo in Time Seies Regession, Biomeika 75, Rome, P Endogenous Technical Change, Jounal of Poliical Economy 98, Siddiqui, R., U. Afidi, and R. Haq Deeminans of Expendiue on Healh in Pakisan, The Pakisan Developmen Review 34(4), Södebom, M. and F. Teal Tade and Human Capial as Deeminans of Gowh, Cene fo he Sudy of Afican Economies Woking Pape, 01/10. Solow R.M A Conibuion o he Theoy of Economic Gowh, Quaely Jounal of Economics 70, Summes R.M. and A. Heson A New Se of Inenaional Compaisons of Real Poducs and Pice Level Esimaes fo 130 counies, , Review of Income and Wealh 34, Temple, J. 1999a. A Posiive Effec of Human Capial on Gowh, Economic Lees 65, Temple, J. 1999b. The New Gowh Evidence, Jounal of Economic Lieaue 37,

A Weighted Moving Average Process for Forecasting. Shou Hsing Shih Chris P. Tsokos

A Weighted Moving Average Process for Forecasting. Shou Hsing Shih Chris P. Tsokos A Weighed Moving Aveage Pocess fo Foecasing Shou Hsing Shih Chis P. Tsokos Depamen of Mahemaics and Saisics Univesiy of Souh Floida, USA Absac The objec of he pesen sudy is o popose a foecasing model fo