Transitional Dynamics of the Thai Economy in the Exogeneous Growth Models

Transcription

1 Transiional Dynamics of he Thai Economy in he Exogeneous Growh Models Nipi Wongpunya ABSTRACT Two alernaive coninuous-ime models of neoclassical exogenous growh, he consan saving rae model and he opimal growh model, are used o analyze he ransiional dynamics of Thailand. The models are calibraed o mach imporan feaures of he Thai economy from The esimaion for he speed of convergence is oo high according o Thailand s daa. I appears ha he opimal growh model predics faser convergence han he exogenous saving model. The ransiional dynamics are proraced wih high value of coefficien of relaive risk aversion. The paper also indicaes ha he absolue and condiional convergences are consisen wih he observaion of he Asian counries. In order for he neoclassical model s ransiional dynamics o explain a convergence in one economy owards anoher, he model requires an impossible high growh and rae of reurn in he early sage of he ransiion. Keywords: ransiional dynamics, exogenous growh, convergence :

2 BU ACADEMIC REVIEW. INTRODUCTION The saring poin for almos all sudies in economic growh is he neoclassical growh model, which was inroduced independenly by he work of Solow (956, p. 66) and Swan (956, p. 33), wih emphasis in he producion funcion and he law of moion of capial accumulaion. The main elemen of heir heory exhibis how economic policy can raise an economic growh rae by inducing people o save more. However, he model akes he fracion of income saved o be consan. In he long run, he economic growh rae of oupu per capia will be he rae of echnological progress which he model akes as being independen of decisions of economic agens. The Solow-Swan model is known as an exogenous growh model. I would seem necessary o incorporae an endogenous mechanism o permi economic facors o deermine saving behaviour. Cass (965, p. 33) and Koopmans (965, p. 8) developed he opimal growh model by providing an endogenous deerminaion of he saving rae. Noneheless, he growh rae of echonology progress is sill exogenous even in he case of he endogeneiy of saving. Transiional dynamics in growh models and convergence across counries have currenly received more aenion such as he work of Baumol (986, p. 75), De long (988, p. 38), Lucas (988, p. 6), Lucas (99, p. 9), Barro (99, p. 7), Barro & Sala-i-Marin (99, p. ), Barro & Sala-i-Marin (3, p. ), King & Regelo (993, p. 9), and Mankiw, Romer & Weil (99, p. ). However, he ransiional dynamics are largely unexplored for developing counries and in Thailand paricularly. The main purpose of his paper is o sudy he ransiional dynamics in growh models under consan saving and opimal saving. The paper conducs dynamic simulaions using a range of parameer values which are calibraed for he Thai economy. The res of he paper is organized as follows. The following secion inroduces he srucures of he models. Secion 3 briefly discusses he soluion mehod. The se of calibraed parameers for Thai economy are documened in secion. The ransiional dynamics are presened in secion 5. Secion 6 examines he ransiional dynamics wih respec o differen parameer values. Secion 7 discusses he absolue and condional convergence applicaion. A case sudy of Thailand, Vienam and Souh Korea growh in he framework of neoclassical model s ransiional dynamics is discussed in secion 8. Secion 9 saes he policy implicaion, and conclusion appears in Secion.. THE MODELS This secion iniially considers he basic neoclassical model of capial accumulaion ha will be used in our analysis. One is ha of Solow model and anoher is ha of he opimal growh model inroduced by Cass-Koopmans model. The models are presened in coninuous ime version for he analysis.. The Solow-Swan Model In his model economy, an agen produced a single homogenous good which is used eiher for consumpion or invesmen. Saving is a consan porion of oupu. The good used in he producion funcion is physical capial. The main assumpion of he Solow model assumes a decreasing reurn o scale in each inpu bu under a consan reurn producion funcion. Y AF( K, X N ) () where Y is oupu. A is oal facor produciviy and i denoes a producion scale facor affecing he produciviy of boh facors. Changes in A will shif he producion fronier. K is physical capial. X is he labor produciviy and is assumed o grow a a consan rae or X Xe. N is labor inpu. I is assumed o grow a a consan rae n or n N Ne if N is he iniial labor. X and N ener muliplicaively. X N is refered o as effecive labor and grows a rae n. The producion funcion is homogenous of degree, concave and wice coninuously differeniable. Mahemaically, FK (.), FK, K(.) and FNX (.), FNX, NX (.). Moreover he producion funcion obeys he Inada condions afer (Inada, 963, p3), lim F (.) lim F (.) and lim F (.) lim F (.). K K XN XN K K XN XN The assumpion is ha each worker has a uni of ime available in each period so ha i is supplied inelasically o a compeiive labor marke. We can idenify he number of workers and he supply of labor in each period. Anoher assumpion is ha here is full employmen in he economy and labor supply equals o employmen. Therefore, oal populaion can be used as inpu in he producion fucion.

3 Oupu is divided beween consumpion, C, and invesmen, I. The naional income ideniy becomes, Y C I () The model assumes ha saving is a consan porion of oupu, S sy, and equals o invesmen, S I. As saving is consan, so is he invesmen rae. The capial accumulaion akes he following form, K I K (3) where K dk d. is a depreciaion rae of physical capial and is consan. The equaion (3) says ha he change in capial equals gross invesmen less depreciaion of capial. The key variables can be represened in erm of effecive labor raio. Given k K XN denoes he sock of capial per uni of effecive labor and y as oupu per uni of effecive labor, y Y XN AFK ( XN,). For a Cobb- Douglas producion funcion as Y AK ( XN), we will have f ( k ) Ak where denoes he capial share. The law of moion of he economy in coninuous ime analysis can be wrien as, k sak ( n ) k () The equaion () implies ha he sock of capial per uni of effecive labor decreases if oal capial depreciaion exceeds saving per capia. The iniial capial sock k is given exogeneously. A he seady sae, k. Seady sae of capial, k SS, is characerized by, k ss sa n ( ) (5) Equaion (5) implies ha he seady sae level of capial-labor raio is posiively relaed o saving rae and is negaively relaed o eiher he rae of populaion growh, he depreciaion rae of capial, or he rae of growh of produciviy.. The Cass-Koopmans Model We now urn our aenion o he opimal growh model. In he Solow-Swan Model as described in secion, here are no economic decisions being made. However, i is believed ha in realiy, individuals can make uiliy maximising decisions. The Cass-Koopmans model assumes ha individuals have preferences over consumpion pah and are able o make opimal decision. Therefore, saving is no longer consan bu i is endogenously deermined by he opimal consumpion choices which in urn deermine he capial accumulaion process and producion possibiliy and growh. This secion mainains he srucural assumpions of he Solow- Swan model in he previous secion. The agens experience insananeous uiliy uc ( ) which depends on he flow of consumpion. 3 The agen s uiliy is defined as he discouned inegral of presen and fuure uiliy. 3 The uiliy funcion uc ( ) exhibis posiive bu diminishing marginal uiliy and herefore u ( c ) and u ( c ). Moreover i follows Inaday condiion CC lim u ( c ) and lim u ( c ). C C C C C 3

4 BU ACADEMIC REVIEW The economy seeks o maximize he lifeime uiliy wih he consrain as follows, Max e c u( c ) d subjec o, k f( k ) c ( n ) k (6) where is he rae of ime preference ha agens consider for fuure consumpion. The ime discoun facor is less han indicaing ha agens are impaien. They yield less uiliy from he same amoun of consumpion if ha consumpion occurs laer. The iniial capial sock k is again given exogeneously. The agens have he following insananeous uiliy funcion u (.) over consumpion sequence c as, c for < < or > uc ( ) log( c ) for = (7) where and is called a coefficien of relaive risk aversion. I measures he degree of risk aversion of he agen. The elasiciy of ineremporal subsiuion is defined as. I is he key parameer defining he agen s desire o smooh consumpion over ime. The high subsiuion economy is represened by he low value of. Agens are more willing o subsiue consumpion over ime. The special case of uiliy, U( c) c, is known as he consan relaive risk aversion (CRRA) uiliy funcion. The coefficien relaive risk a version, cucc ( c ) UC () c, is. The elasiciy of he marginal uiliy of consumpion is and he ineremporal elasiciy of subsiuion of consumpion is. As he ineremporal subsiuion of consumpion decreases, he uiliy funcion is more concave.

5 Wrie down he Hamilonian for he dynamic opimizaion problem, (8) H( c, k,, ) uc ( ) [ f( k) c( n )] k where is he coninuous-ime equivalen of a Lagrange muliplier. The firs-order necessary condiions characerizing he opimum can be wrien, uc( c) (9) k f( k) c ( n ) k () [ f ( k ) ( n )] () k The seady sae where k will be characerized by he per capial level of capial, k SS, and consumpion, c SS, ( ) A kss () n c Ak ( n ) k (3) SS SS SS 3. SOLVING THE MODELS The equilibrium equaions resuling from he opimizaion problem basically are non-linear. However, we canno easily analyze he model wih non-linear equaions. In his secion, we ransform he equilibrium linearly around he seady sae and hen solve he resuling linear sysem numerically. The log-linearized version of he Solow s capial accumulaion equaion evaluaed a he seady sae is, ˆ k sa( ) k kˆ SS () where k ˆ k k and k ˆ dln k where k ˆ describes he log-deviaion from is seady sae. A he seady sae, we use equaion (5) and equaion () o obain he following expression, ˆ k ( )( n ) kˆ (5) 5

6 BU ACADEMIC REVIEW The second case is he Cass-Koopmans model. By log-linearizing equaion (9) and () around he seady sae, leaving and ( )( n ) c ˆ ˆ k (6) ˆ ˆ ( n )( ) k ˆ k c (7) Therefore, we obain he fundamenal dynamic sysem of he Cass-Koopmans model. ( n )( ) kˆ ˆ k c ˆ ( )( n ) cˆ (8) The sandard numerical mehods for solving differenial equaions can be used o solve he enire ime pahs of c and k and oher concern variables. 5. MODEL CALIBRATION FOR THE THAI ECONOMY In his secion, we presen he calibraion for a se of parameers. The characerisics of he calibraion are ha he model parameers are deermined by he long-run properies of he economy. We choose model parameers in which he long-run behaviour of he model maches he long-run observaions from he Thai daa. In his paper, we use Thailand s daa series for he period 985-9, obained from Office of he Naional Economic and Social Developmen Board of Thailand (NESDB). The parameers of he model are seleced as follows. According o he model, he growh rae of echnological change is chosen o equae he growh rae of real oupu per capia in Thailand during he las which is.3% annually. Populaion growh rae n is he average growh rae of economy s populaion which is.9% per year. The saving rae s is he amoun invesed and i is he fracion of oupu ha is no consumed. Over he sample period, saving-oupu raio for he Thai economy is 3.86%. 6 The lending ineres rae adjused for inflaion is used for he real ineres rae. The 5 We can consider his sysem as z Mz. The sysem could be decoupled using he sandard eigenvalue-eigenvecor decomposiions: M PP where is he eigenvalues of M and P is he marix of eigenvecors wih columns corresponding o he eigenvalues. Since he sysem has one unsable eigenvalue and marix P depends on parameers of he model, he endogenous variable, c, has o wipe ou he unsable dymanics. We choose consumpion so ha we have bounded soluion. The deails of his procedure can be found in Novales, Perez and Ruiz (, p. 5). Mulligan and Salai-Marin (99, p.3) use a procedure called ime-eliminaiion mehod o solve he policy funcion numerically. 6 The model assumes ha oupu is eiher consumed or invesed. However, he naional income accoun provided by NESDB is Y C I G NX. I is necessary o reorganize he naional income accoun o mach he income and expendiure caegories in he model. We have o adjus and rearrange governmen spending G and ne expor NX in he naional income accoun. The governmen spending G caergories in he naional income accoun are classified as public consumpion. Therefore, he governmen spending G should be added ino consumpion. The invesmen caergories in he naional income accoun are already classified as public and privae invesmens. Expors or impors do no exis in he model because he model economy is closed. If a counry is in a rade surplus, i is lending o he res of he world. Sae differenly, he counry is accumulaing claims o fuure oupu from he res of he world. Noe ha invesmen is made for increasing fuure oupu. By his reason, invesmen is reduced by he amoun of rade defici and is added by he amoun of rade surplus. 6

7 average real ineres rae provided by he World Bank is 8.9% annually. 7 The capial s share of income a he seady sae is defined as rsskss yss. The average capial-oupu raio is chosen o be he capial-oupu raio a he seady sae which is 3.97 on he annual basis. I follows ha he capial s share of income is.83 and labor s share is simply We choose he depreciaion rae o be.% annually according o he capial accumulaion equaion in per capia erm. 9 We normalize he value of oal facor produciviy A o. The parameer is difficul o obain from long-run observaions and previous lieraures always choose i independenly. Then we se for Thai preference following many lieraures. The ime discoun facor in he conious ime version of he Cass-Koopmans model is derived from equaion () when i is evaluaed a he seady sae. Table summarizes he values of he calibraed parameers of he Thai economy. Table The lis of calibraed parameers during The echnology growh rae.3 The populaion growh rae n.9 The oal facor produciviy A The saving rae s.386 The relaive risk aversion The capial depreciaion. The capial share parameer.89 The real ineres rae r.89 The ime discoun facor.79 7 King and Rebelo (993, p.96) use he annual average real reurn on equiy as he seady sae real ineres rae for he poswar Unied Saes. The average real reurn on equiy for Thailand during is 6.89% per year. 8 /3 is a common parameer. King and Rebelo (993, p.96) use /3 according wih he esimaes documened in Maddison (987, p.659). However, if we use he annual average reurn of he Thai sock marke which is 6.89%, he share of capial would be.59. This high capial share will be invesigaed in secion 6. 9 Given n.9,.3, s.386 and yk.86, we obain. from he capial accumumaion equaion evaluaed a he seady sae [( n)( ) syk ( )]. There is a wide range for reasonable value of. The majoriy of he esimaes is beween and 3. We se for his analysis. A seady sae,. Therefore, r ( n ). 7

8 BU ACADEMIC REVIEW 5. THE TRANSITIONAL DYNAMICS Having parameerised he model o mach he Thai growh facs, his secion analyzes he ransiional dynamics, he ime pah of he neoclassical models given he iniial capiial sock ha is away from is seady sae value. This experimen chooses he capial sock in 985 as he iniial capial sock of he Thai economy which is 37.3% of he average capial sock observed over As shown in secion 3, he sudy of he convergence behaviour of he Cass-Koopsman model is slighly more complicaed han is he case for he Solow-Swan model. Afer linearizing he models, he Solow-Swan model has only one firs order differenial equaion while he Cass-Koopsman model has he sysem of firs order differenial equaion. Nonheless, he ransiional dynamics can be examined in a sraighforward manner. The ransiional dynamics of he models calibraed for he Thai economy are depiced in Figure. We are ineresed in he convergence pahs of he variables, so we ake a 8 year inerval and examine if he economy converges o is seady sae level. In each panel, he case of Solow-Swan model is he solid dark line while he dashed line is for he case of Cass-Koopsman model. There are several ineresing feaures from Figure. In he early, agens pospone consumpion in response o he high real rae of reurn. The iniial response of consumpion in he opimal growh model is negaive and is lower han ha in he exogenous saving model. Agens save more and consume less in he very early sage because he high rae of reurn. Comparing o he consan saving in he exogenous model, he saving in he early sage is high and falls monooneously in he opimal growh model. Similar o saving rae, invesmen in he opimal growh model monoinically falls. Oupu has an increasing level and diminishing growh rae. The enire ime pah of oupu and capial of he opimal growh model are above ha of he exogenouse saving model. Oupu growh rae prediced by he opimal growh model is higher han ha prediced by he consan saving rae model. However, hese facs are reversed afer approximaely. Time pah of ineres rae depends on how capial sock moves during he ransiion because ineres rae equals he marginal produc of capial less he depreciaion of he physical capial. In his paper, we are also equally concerned how rapid he economies converge. I is essenial o idenify he pace of convergence since i helps us o know he proporion of he economy s growh experiences wheher hey are ruled by ransiion or no. By looking a he ransiion pahs, we would see ha he pace of convergence is very rapid. The Solow-Swan model predics a convergenvce speed of 7. percen per year while he opimal growh model predics even a higher rae of.3 percen per year. 3 Obviously, he opimal growh model predics even faser convergence han he exogenous saving model. One-half he disance from he iniial level of oupu o is seady sae is removed wihin abou for he exogenous saving model and 6 for he opimal growh model. The reason could be seen in he ime pah of real ineres rae. The model envisages he high ineres rae of over % in year and. This becomes he driving force for agens o cu down consumpion in favour of invesmen oday. The esimaion for he speed of convergence is oo high according o he Thai daa. The relevan esimae based on he Thai daa is.3% per year which is he long erm growh rae of real GDP per capia corresponding in heory o he parameer,. King and Rebelo (993, p.96) documen ha in he opimal growh model, he ineres rae and oupu growh rae in he early sage ake he unrealisic high values. Barro and Sala-i-Marin (3, p.6) also repor he similar resuls corresponding o he iniial capial sock per effecive labor equal o % of is seady sae value or k.k SS. To reduce he unrealisic high values of he real ineres rae and growh of oupu, Barro and Sala-i- Marin increase he capial share coefficien from.3 o.75. For he calibraed parameers over he observaion peirod of he Thai economy k.37k SS he oupu growh rae and he rae of reurn are more reasonable. If we assume k.k SS for he Thai economy, we ge percen for he iniial growh rae of oupu and 33 percen for he iniial real ineres rae. Those iniial values are implausibly large. Therefore, he iniial level of capial sock or he posiion where we sar in he ransiional pah could also play an imporan role for he response of iniial ineres rae and growh of oupu. 3 The speed of convergence of he Solow-Swan model is where ( )( n ).7. To have a sable dynamic sysem for he Cass-Koopmans model, he eigenvalues of he ransiion marix for he sysem of he differenial equaion (8) mus be whereas. and and he eigenvalues associaed wih his dynamic sysem. For he Thai economy, we have. and.3. The sable eigenvalue is and indicaes how fas he economic oupu per effecive labor approaches is seady sae value. 8

9 Oupu 6 8 Oupu growh rae (percenage) Saving Consumpion Capial 6 8 Capial-Oupu Raio Invesmen. 6 8 Ineres rae (percenage) Figure The ransiional dynamics Solid line for he Solow-Swan model and dashed line for he Cass-Koopsman model. The eigh panels depic he dynamic pahs per uni of effecive labor of oupu, oupu growh rae, saving, consumpion, capial, capialoupu raio, invesmen and ineres rae. 9

10 BU ACADEMIC REVIEW 6. COMPARATIVE ANALYSIS Firs, we change he coefficien of relaive risk aversion by increasing i o as shown in Figure. The ineremporal subsiuabiliy of consumpion,., is reduced as rises. For, he pace of convergence is slower wih a half life of 5 raher han 6 when. Wih higher, agens are willing o smooh consumpion over ime. The finding shows ha he iniial consumpion is higher bu grows a slower pace han he case of. A higher consumpion implies a lower saving or invesmen. Therefore, he ransiional dynamics are proraced wih high. Noneheless, he rae of reurn is high for a long ime because savings are reduced. Low rae of saving quickly pushes up he marginal produc of capial..8 Oupu.5 Consumpion Thea= Thea= 6 8 Thea= Thea= Figure The ransiional dynamics of alernaive If we choose he seady-sae real ineres rae of 6.89% per year corresponding o he annual average real reurn on invesmen in he Thai sock marke during he observed period, his reurn implies he share of capial of.59. Therefore, we increase he share of capial o.59 for our sensiiviy analysis. Figure 3 displays how changing affecs oupu and he real ineres rae. Oupu rises as increases. If we use higher, he iniial ineres rae is considerably lower and he speed of converence of oupu is slower. Relaive o 6 for.89, he half-life of oupu is abou 6 where.59. As in King and Rebelo (993, p.98), he capial s share in a Cobb-Douglas producion funcion dicaes how fas he marginal produc of capial diminishes wih he capial sock. A greaer he value of, he marginal produc increases less sharply. Less amoun of capial is used o produce he same amoun of oupu. There is less incenive o accumulae capial. Therefore, he economy moves more slowly owards is seady sae. 5 Oupu Ineres rae Alpha=.89 Alpha= Alpha=.89 Alpha= Figure 3 The ransiional dynamics of alernaive

11 We change he value of he ime discoun facor o see he characer of ransiional dynamics. There are hree differen ways in which he Thai people can value more, less, or he same fuure consumpion relaive o he curren consumpion. If Thai people value he same fuure consumpion relaive o he curren consumpion, he fuure uiliy is no discouned or. The lower is he discoun facor, he more he agens value consumpion if hose consumpions occur laer. They are willing o comsume less in he early sage of he ransiion. As shown in figure, we examine hree differen values of for Thai people,,.8 and.. For higher value of he discoun facor, he pace of convergence goes more rapidly. The lengh of ime o cover half he gap o seady sae is four for. while i is seven for. The higher he ime discoun facor, he faser he resources are invesed and he capial sock is accumulaed. However, he early sage level of oupu is high when he discoun facor is low because agens pospone consumpion o he fuure and save more in he iniial period, resuling in a greaer invesmen and oupu. Figure 5 plos he ime pah of he economy under differen raes of he depreciaion of capial. The larger he depreciaion, he more he capial is required and accumulaed o replace worn-ou capial. Therefore, under higher depreciaion rae of capial, he economy moves faser o is seady sae. The lengh of ime o cover half he gap o seady sae is four for.. A high populaion growh resuls in a high depreciaion of physical capial. Therefore, he effec of populaion growh and he depreciaion rae resul in he similar characer of he ransiion pah of he economy.. Oupu.8 Oupu rho=.8 rho=. rho= Figure The ransiional dynamics of alernaive. dela=. dela=. 6 8 Figure 5 The ransiional dynamics of alernaive 7. ABSOLUTE AND CONDITIONAL CONVER- GENCE APPLICATION One inerpreaion of he resuls of he growh models is o show predicions of how he iniial of capial affecs he growh rae per capia. By using equaion, we yield he resuls linking growh rae of capial o he capial level in efficien uni of labor for he Solow-Swan model. The relaionship is negaive or k k. Lower capial level in effeicien uni of labor is associaed wih higher growh rae of capial. Therefore, he Solow-Swan model predics ha lower capial and oupu level have higher growh rae of capia and also growh rae of oupu. As shown in secion. equaion () and (3) in he case of he Cass-Koopsman model, i predics ha he economies will converge o he same seady sae for he same underlying parameers. The model also suggess he negaive correlaion beween he iniial and growh of oupu. Barro and Sala-i-Marin (3, p.7) sugges ha his conclusion is unambiguous for he Cobb-Douglas producion funcion.

12 BU ACADEMIC REVIEW CHI 9 8 Growhrae,9859 IND VIE THA KOR MAL HNK SIN PHI JAP AUS LogofpercapialGDPin985 Figure 6 Average annual growh rae of GDP per capia agains log of iniial level of GDP per capia for seleced Asia counries Noe: THA is Thailand, KOR is Korea, MAL is Malaysia, HNK is Hong Kong, SIN is Singapore, VIE is Vienam, CHI is China, IND is India, PHI is Philippines, JAP is Japan and AUS is Ausralia. For Vienam, he log of he iniial level of GDP per capia is in 99 due o he shorage of he daa. The convergence propery of oupu prediced by he growh models is ha, given he same underlying parameers, he wo economies converge o he same seady sae. However, he marginal produc of capial in efficien uni of labor is higher in he poor economies han in he rich ones. The poor will accumulae more capial and grow faser han he rich. The absolue convergence hen implies he negaive relaionship he iniial GDP per capial and he growh rae of GDP per capia. Therefore, we can es he absolue convergence applicaion of he model using he daa in Asian counries. The seleced Asia counries counries migh have similar parameers such as echnology possibiliy, saving rae and populaion growh rae. Figure 6 plos he average annual growh rae of GDP per capia from 985 o 9 agains he log of GDP per capia in 985 for seleced Asia counries of which daa were obained from IMF. The counry poins in he Figure are nicely locaed along a decreasing sraigh line. Therefore, his negaive relaionship suggess ha he absolue convergence applies for he seleced Asia counries. 5 5 B Barro and Sala-i-Marin of counries he absolue convergence does no (3, p.5) sugges ha for a sample apply for a broad cross secion of counries. The relaionship of growh rae and iniial level of real GDP per capia is slighly posiive. For he world as naions are no as similar as o one anoher, he absolue convergence is bound no o hold. However, absolue convergence applies for he 8 OECD counries. In addiion, he condiional convergence is bound o hold for cross-counry daa. Baumol (986, p.75) finds ha from among he 6 indusrial counries, per capial income in 87 is negaive correlaed o per capia income growh.

13 Noneheless, differen counries have differen srucural parameers and hey in urn have differen seady saes. The seady saes are condiional on differen underlying parameers. If he counries converge o differen seady saes, we canno make any conclusion abou heir relaive speed of convergence. This is called he condiional convergence. This concep saes ha he counries ha sar furher below heir seady saes should grow faser. Barro and Sala-i-Marin (3, p.) show, for he Solow-Swan model, he idea of he condiional convergence algebraically using he saving a he seady sae condiion from equaion, s[( n ) Ak ] SS. Growhrae, CHI VIE THA KOR IND HNK SIN MAL JAP AUS PHI TheraioofheGDPin985oheaverageGDPfrom9859 Figure 7 Average annual growh rae of GDP per capia agains he raio of iniial level of GDP per capia o he average GDP for seleced Asia counries. Noe: he same as Figure 6. They subsiue he saving rae back ino he same equaion, hen he growh rae of capial can be expressed as k kk ( n).[( kkss ) ] which saes ha he growh rae of capial depends on he disance beween curren and seady sae capial in effecive labor raio. The Cass-Koopsman model has similar argumen on he condiional convergence. Figure 7 illusraes he negaive relaionship beween growh rae of GDP per capia agains he raio of iniial level of GDP per capia o he average GDP. The lower raio of he iniial level of GDP per capia o he average GDP indicaes ha he economy is furher below is seady sae level and i grows faser. Thus, he condiional convergence also implies for he seleced Asian counries. The condiional convergence of neoclassical model has been found o exis for a broad sample of counries and also for he region wihin a counry. Such findings follow he work of Barro and Sala-i-Marin (99, p.7), Barro and Sala-i-Marin (99, p.33), Barro and Sala-i-Marin (3, p.6), and (Mankiw, Romer &Weil, 99, p. ) 6 6 Mankiw, Romer and Wiel (99, p.5) employ a simple cross-secional regression o esing for convergence. The more sophisicaed panel daa approach is used by Caselli, Esquivel and Lefore (996, p.) and Canova and Merce (995, p.7). 3

14 BU ACADEMIC REVIEW Real GDP per capia 8. A CA ASE STUDY: ECONOMIC C GROWTH H OF THAILA AND, VIETNA AM AND SOU UTH KOREA A This secion uses he daa from a sample of hree Asian coounries whichh are Thailannd, Vienam and Souh Korea K o illussrae he appplicaion of he neoclassical ransiionaal dynamics. The comparrison p capia GD DP for Thailaand, Vienam and of real per Souh Korea K is displlayed in Figuure 8. Afer he prolongedd 3 of o he Vienaam war endedd in 75, he war leef Vienam aan uerly imp poverished 97 cou unry. Howevver, afer he reform of h he counry from m a planned o a marke--oriened econ nomy, he Vieenamese econnomy has rapiidly grown an nd enered he significan period p of deevelopmen ass well as nsformaion. A comparaivve look a per capia c real ran GD DP of Vienam me agains he Thai level reeveals ha i moves m from 6% % in 99 o aabou % in Years r per capia GDP and gro owh for Thailand, Vienam m and Souh Ko orea Figgure 8 The comparison of real Triaangle do-line for he Souhh Korea, squarre do-line for Thailand andd diamond do--line for Vien nam. Souh Korean hass achieved hee hree decadees of exraordinnaly growh ha leads her h o an exppororiened counry. Souh Korea odaay is considerred a wealhy developed counry. Coomparively, he r per capiaa real GDP of o Vienamesse is growh rae lowes duuring and is average a of 5 year duraion is quie sabble. Souh Korean K and Thai T m down from f abou 7.8% during 9985growh moves 99 o abou a 3.7% duuring 5-8. To examine e how w he neoclasssical ransiiional dynamicss can explainn he paern of Figure 8,, we Vie enamese grow wh rae of per capia c real GDP 5 mulaed he moodel under oppimal consum mpion for sim wo o counry pairrs, one is Vienam and Thaailand and ano oher is Koreaa and Thailannd. We invessigae he ime pah of Vienamese economy using u he paraameers from m Table. Thherefore, we can make wo o key assumpions. These aare, firsly, haa he Thai and d Vienam economies havee he same underlying u paraameers and, secondly, s Thaailand was on is seady sae pah in The simuulaion period d sars in and he Vienamese V reeal GDP per capia in was 6 perceen of Thailannd s level. V Vienamese gro owh rae of pe er capia real GDP G Figure 9: Comparison C off simulaed Th hai and Vienaamese growh 6 8

15 The assumpion is ha Thai economy was in is seady sae in 985 for he lef panel. The assuumpion is ha Thai economy was in is seady sae in 8 for he righ panel. The ransiional dynamics of he Thai growh rae is. Figure 9 depics ha he Vienamese ransiional growh would have been nearly achieved in he firs 3. In oher words, he Vienamese economy akes abou 3 o converge o he same level of he Thai economy in 985. According o he model s predicion, he Vienamese economy in 5 will be in he same level as he Thai economy was in 985. If we assume ha Thai economy is in is seady sae pah in 8, i will ake he Vienameses economy abou o converge o he same level of he Thai economy in 8. The ime o converge o he seady sae is shorer for he laer experimen because he economy is furher below is seady sae level. Tha means he Vienameses economy in 5 would have been he same as Thai economy was in 8. These wo experimens leave ou wha seems essenial o counerfacual condiion. Firsly, as shown from Figure 9, he Vienamese growh rae is absurdly high during he firs 5 o. Secondly, from Figure 8, he Vienamese economy in 5 was only abou percen of he Thai economy in 8. The neoclassical model unrealisically predics ha he ime pah o seady sae is shorer if he economy is sared furher below is seady sae. The Vienamese economy in 5 will be more likely o be he same level as he Thai economy was in 985. By assuming ha he Souh Korean economy is in is seady sae in 985, we are able o evaluae he ransiional dynamics of he neoclassical model for he evoluion of Thai economy by comparing o Souh Korea economy. We resric addiional assumpion in which he Thai and Souh Korean economies have he same underlying parameers as appeared in Table. The per capia real GDP of Thailand is abou 6 percen of Souh Korean level in 985. Wih his iniial condiion, i will ake roughly for Thai economy o converge o he similar level of he Souh Korean economy in 985 as depiced in Figure. Sae differenly, he model esimaes ha in he year 5, he Thai economy will have he same real oupu per capia as he Souh Korean economy was in 985. However, he fac shows he opposie direcion in Figure 9. The Thai real oupu per capia in 8 was jus slighly higher han he Souh Korean level in 985. Raher han using he calibraed parameers lised in Table, if we simulaed he model economy by using paricular calibraed parameers for he Souh Korean economy iself, he predicions would become more accurae and realisic. 5 Growh rae of per capia real GDP Figure : Comparison of simulaed Thai and Souh Korean growh The ransiional dynamics of he Souh Korean growh rae is. 9. POLICY IMPLICATION The exogenous growh models discussed in his sudy can be used o guide an economic policy. Naion saves and invess play, according o he models, a key role of is people s sandard of living. The policy makers should wan o increase he rae of saving and invesmen. The approaches in which he governmen affecs naional saving are hrough public saving and privae saving. The governmen can influence privae saving using incenive hrough a variey of public policies. The policies such as low ax raes on capial including he corpoae income ax, he federal income ax and he exae ax encourage privae saving by increasing he rae of reurn ha invesers gain. In addiion, he models show ha susained growh in income per capia mus come from echnological progress. The public policies should be designed o simulae echnology progress. The governmen should encourage he privae secor o devoe resources o echnological innovaion. 5

16 BU ACADEMIC REVIEW. CONCLUSION Time pah of saving deermines he differenes of he ransiional dynamics of he wo models. Time pah of saving is consan under he Solow-Swan model while ime pah of saving is endogeously deermined by he opimal consumpion choices. For he Thai economy during 985-9, he paper finds ha he iniial response of consumpion in he opimal growh model is negaive and lower han ha in he exogenous saving model. The enire ime pah of oupu and capial of he opimal growh model are above ha of he exogenous saving model. In addiion, he pace of convergence is very rapid. The opimal growh model predics even faser convergence han he exogenous saving model. The esimaion for he speed of convergence is oo high according o he Thai daa. This paper examines he dynamic evoluaion wih respec o differen parameer values under he opimal growh model. The ransiional dynamics are proraced wih high value of coefficien of relaive risk aversion. A high capial share lowers he iniial ineres rae and he speed of converence of oupu. For higher value of he discoun facor, he pace of convergence goes more rapidly. The economy moves faser o is seady sae wih a higher depreciaion rae of capial. The paper also indicaes ha he absolue and condiional convergences are consisen in he conex of he Asian counries. In order for one economy convergence owards anoher, he model requires an unachievable high growh and rae of reurn in he early sage of he ransiion. The model unrealisically predics ha he ime pah o seady sae is shorer if he economy is sared furher below is seady sae. The model predics ha he Vienamese economy, saring from 985, akes abou 3 o converge o he same level of he Thai economy in 985 while i will ake only abou o converge o similar level of he Thai economy in 8. I is a challenging open quesion o find some plausible aleraions of he basic model o explain he discrepancy. The producion funcion is he main feaure of he neoclassical model. The neoclassical echnology exhibis he diminishing reurns o capial. King and Rebelo (993, p.97) poin ou ha his assumpion leads o counerfacural implicaions when he model s ransiional dynamics is used o explain susained cross-counry differences in growh rae. The ransiional dynamics are imporan in he very early sage because he diminishing reurns o capial induce ineremporal reallocaion. The diminishing reurns o capial induce a high marginal produc of capial which ranslaes ino a high real rae of reurn. Therefore, we expec he unrealisically high real rae of reurn and growh rae for he beginning of he ransiion. This paper reaches he same conclusion o ha documened by previous research of King and Rebelo (993, p.99). Furher reseaches for he growh of Thai economy should be direced o overcome he assumpion of he diminishing reurns o capia of he neoclassical echnology. The endogenous growh models including human capial such as hose of Uzawa (96, p.) and used by Lucas (988, p.7) or he AK model such as hose of Romer (986, p.8), Romer (987, p.56), Romer (99, p.s78) and Rebleo (99, p.57) elimiae he diminishing reurns o capial. Differen funcional forms of producion could be an alernaive o improvemens in explaining Thailand s long-erm growh. REFERENCES Barro, R. J. (99). Economic growh in a crosssecion of counries. Quarerly Journal of Economics, 6(), 7-3. Barro, R., & Sala-i-Marin, X. (99). Convergence across saes and regions. Brookings Papers on Economic Acivi,, 7-8. Barro, R. & Sala-i-Marin, X. (99). Convergence. Journal of Poliical Economy,, 3-5. Barro, R. & Sala-i-Marin, X. (997). Technological diffusion, convergence, and growh. Journal of Economic Growh, (), -6. Barro, R., & Sala-i-Marin, X. (3). Economic Growh ( nd ed.). MIT: Cambridge. Baumol, W. J. (986). Produciviy growh, convergence and welfare: Wha he long-run daa show. American Economic Review, 76, Canova, F., & Merce, A. (995). The poor say poor: Non-convergence across counries and regions. (Discussion paper ). Souhampon, UK. Universiy of Souhampon, Division of Economics, Cener for Economic Policy Research. Caselli, F., Esquivel, G., & Lefore, F. (996). Reopening he convergence debae: A new look a cross-counry growh empirics. Journal of Economic Growh,, Cass, D. (965). Opimal growh in an aggregaive model of capial accumulaion. Review of Economics Sudies, 3, 3-. De Long, J. B. (988). Produciviy growh, convergence and welfare: A commen. American Economic Review, 78, Inada, K. (963). On he wo secor-model of economic growh: Commens and a generalizaion. Review of Economics Sudies, 3, 9-7. King, R. G., & Rebelo, S. (993). Transiional dynamics and economic growh in he neo-classical model. American Economic Review, 83, King, R. G., Plosser, C. I., & Rebelo, S. (988a). Producion, growh, and business cycles, I. The basic neoclassical model. Journal of Moneary Economics,, Koopmans, T. (965). On he concep of opimal economic growh. The Economic Approach o Developmen Planning, Chicago: Rand McNally,

17 Lucas, R. E. (988). On he mechanics of economic developmen. Journal of Moneary Economics,, 3-. Lucas, R. E. (99). Why doesn capial flow from rich o poor counries? American Economic Review, 8, Madison, A. (987). Growh and slowdown in advanced capialisic economies. Journal of Economic Lieraure, 5, Mankiw, N. G., Romer, D., & Weil, D.N. (99). A conribuion o he empirics of economic growh. Quarerly Journal of Economics, 7(), Mulligan, C. S., & Sala-i-Marin, X. (99). A noe on he ime-eliminaion mehod for solving recursive dynamic economic models. (Working paper 99-6). Souhampon, UK. Universiy of Souhampon, Division of Economics, Cener for Economic Policy Research. Novales, A., Fernandez, E., & Ruiz, J. (). Economic growh: Theory and numerical soluion mehods ( s ed.). Springer-Verlag Berlin Heidelerg: Germany. Rebelo, S. (99). Long-run policy analysis and longrun growh. Journal of Poliical Economy, 99(3), 5-5. Romer, P. M. (986). Increasing reurns and long-run growh. Journal of Poliical Economy, 9(5), -37. Romer, P. M. (987). Growh based on increasing reurns due o specializaion. American Economic Review, 77(), Romer, P. M. (99). Endogenous echnological change. Journal of Poliical Economy, 98(5), Par II, S7-S. Solow, R. M. (956). A conribuion o he heory of economic growh. Quarerly Journal of Economics, 7(), Swan, T. M. (956). Economic growh and capial accumulaion. Economic Record, 3, Uzawa, H. (96). Opimal growh in a wo secor model of capial accumulaion. Review of Economics Sudies, 3(), -. Dr. Nipi Wongpunya received his Ph.D. in Economics from Universiy of Bah, England, UK.; Maser s degree in Economics from Boson Universiy, MA, USA., MBA in Finance from San Francisco Sae Universiy, CA, USA. and he held a bachelor s degree in Mechanical Engineering from Chaingmai Universiy, Chaingmai, Thailand. He worked as a full ime eaching fellow for he deparmen of economics, Universiy of Bah for a year before he came back o Thailand. He is a he momen eaching a Ph.D. level course in he advanced macroeconomics a he Deparmen of Economic, Chulalongkorn Universiy. He is currenly a full ime insrucor in Economics a Universiy of Phayao. He has published a book eniled The Inroducion o Saisics. 7