ECONOMIC GROWTH AND REGIONAL CONVERGENCE THE CASE OF PAKISTAN Mudassar Nazir and Hafiz M. Yasin 1 Absrac The quesions concerning he prevalence of povery and he deepening gulf beween rich and poor have always been he burning issues all over he world. These issues, irrespecive of heir causaion facors, bear far reaching economic and poliical consequences. The federaion of Pakisan displays complex regional diversiies; he componen unis differ no only in linguisic, culural, and demographic erms bu also in he level of socio-economic developmen. Alhough he consiuion of Pakisan guaranies equiable shares for all provinces in naional resources, he level of growh across regions has no been uniform. During he pas half a cenury, invesmen in physical and social secors concenraed in seleced pars of he counry, paricularly in big ciies. This pracice has led o creaion of economic dispariies and a number of socio-poliical problems like errorism, regional ensions, weakening of he federaion and difficuly in consensus on issues of naional ineres. Growh heory provides a powerful analyical framework o analyze he issue of regional convergence. Given he assumpion of perfec markes, he counries wihin a geographical region are supposed o converge overime o a common seady sae level of income, provided hey are similar in oher socio-economic condiions. Pu differenly, if counries differ significanly in hese condiions, hen each uni is likely o follow an independen growh pah. This is also rue for differen regions wihin he same counry/ poliical eniy. The objecive of his sudy is o invesigae empirically if here is any evidence of convergence across differen regions of Pakisan. The sudy uilizes he convenional analyical ools and ime series daa over he period 1979-2005 for he four provinces, disaggregaed ino rural and urban secors. As expeced, no evidence of absolue convergence could be observed obviously due o presence of vas differences across he provinces in erms of he growh deerminans. In conras, he income dispariies across he regions exhibied a widening endency during he period under reference. However, he daa did suppor condiional convergence, which implies ha differen regions followed independen growh pahs. The findings furher indicae ha cerain socio-economic condiions are crucial o explain he persisence of income dispariies. The quesion as o why he deerminans of growh differ so widely across he consiuen unis of Pakisan inhibiing absolue convergence is ofen discussed a differen economic and poliical forums. The sudy concludes wih some policy recommendaions ha may improve he siuaion. 1 The auhors are working as (i) Research Officer a he Planning Commission, Gov. of Pakisan, Islamabad::<muddasar.mphil49@iiu.edu.pk>, and (ii) Associae Professor a IIIE, Inernaional Islamic Universiy Islamabad: <yasin.iiie@gmail.com>
1.0 Inroducion Growh and developmen are he closely relaed erms ha convey more or less he same message o he general reader. However, where growh heory concenraes on he facors responsible for uplifing he gross and per capia incomes, he heory of developmen focuses on he overall socioeconomic srucure and insiuional se-up ha move ahead wih he passage of ime. The growh rae of income is cenral o he process of economic developmen. The relaionship beween growh and developmen resembles ha of an engine and he carriage. Following he impeus of growh in income/ oupu, he enire social and insiuional srucure of an economy begins o improve in all direcions. If he growh process susains overime, he social srucure moves gradually owards modernizaion, democraic aiudes, broadness in oulook along wih equiy in disribuion, reducion in povery and general improvemen in he sandard of living. The borders of growh and developmen ge coincide when a researcher considers he quesion of equiy in income disribuion across differen households and he quesion of convergence across differen regions. The erm convergence has been used in growh lieraure o imply a narrowing down of he differences in incomes across regions and hereby a endency owards a common equilibrium over ime. Alhough he concep is quie old 2, he issue came o he surface since he lae eighies when he new emerging economies exhibied rapid and susained growh bu he old indusrial counries experienced relaively a slowing down. As noed by Abramoviz (1986), i was believed (wih a sor of fear) ha Eas Asians Counries, which embarked on growh pah a a laer sage, will cach up wih heir Wesern counerpars in he near fuure. I was argued ha innovaion is ofen difficul whereas imiaion is easier. Naurally some may be he innovaors and leaders in growh, while majoriy of ohers may be he imiaors and followers. The conrasing argumens were also floaed in ha he leaders have, afer all, an edge over he followers. The evidence, boh in favour and agains, could now be raced hrough he vas lieraure on growh and convergence 3. 2 3 The origin of convergence goes back o mid-18 h cenury and imporan insighs can be found in he scholarly wriings of David Hume (1742) and Josiah Tucker (1776): See Bruce Elmslie (1995) for deails. William Baumol (1986) was among he pioneer economiss who provided saisical evidence of convergence among some counries and also for is absence among ohers. 2
The hypohesis implies equalizaion of per capia income and produciviy overime across he world economies. In his connecion, one has o disinguish beween absolue and condiional convergence. The former is inerpreed as convergence of differen economies o a common seady sae level, given idenical preferences and echnologies. This implies ha relaively poor regions (should) grow faser han heir richer counerpars despie differences in he sar-up poins. In conras, if hey exhibi significan differences in srucural characerisics, hen every region will converge o is specific seady sae level raher han o a common equilibrium. This laer behaviour is ermed as condiional convergence, since he growh rae of an economy is affeced by oher feaures like populaion growh, naure of echnology, poliical and social characerisics ec. Anoher imporan concep ofen used in he analysis of regional dispariies is he dispersion from he seady sae (denoed by sigma: ζ). If he dispersion or variabiliy of real per capia income across regions decreases wih he passage of ime (in oher words, if hey ge closer o one anoher), hey are said o exhibi sigma convergence. The convergence hypohesis has been esed by researchers using differen daa sources, mehodologies and saisical echniques. For large sample of counries (wih differen socio-economic srucures), mos of he empirical sudies fail o suppor absolue convergence. Pu differenly, his kind of behaviour is suppored only for smaller ' homogeneous groups' wihin specific geographic regions. For insance, Barro and Sala-i-Marin (1992), and Mankiw, Romer and Weil (1992) rejec absolue convergence for a diverse group of counries in he global conex bu do no rejec is occurrence for regions like OECD counries, where echnologies, preferences and oher social srucures are more or less similar. In general, mos of he sudies repor in favor of condiional convergence. 2.0 Raionale and Objecives of he Sudy The quesions concerning he prevalence of povery, he deepening gulf beween rich and poor and he rising rend in oher economic dispariies across regions, secors and classes, have always been he burning issues all over he world. These issues, irrespecive of heir causaion (srucural or policy discriminaion), bear far reaching 3
economic and poliical consequences. In order o devise appropriae policies for relaively even disribuion of he benefis of growh, i is essenial o invesigae ino regional dispariies and o undersand heir causes and impacs. In fac, regional growh is as imporan for a counry as naional growh on he grounds of boh equiy and poliical harmony. In his connecion, he convergence analysis provides an appropriae framework for idenificaion of he naure and causes of dispariies. Examples of such aemps are numerous, boh for he developed and developing counries 4. The Federaion of Pakisan displays complex regional diversiies, i.e. he geographic regions differ no only in linguisic, culural, and demographic erms bu also reflec eviden diversiies in he level of social and economic developmen. During he pas half a cenury, invesmen in physical and social secors has largely concenraed in seleced pars of he counry, paricularly big ciies like Karachi. This pracice has led o large scale migraion o ciies in search of employmen, creaed economic dispariies and aggravaed he problems of povery and inequaliies. These dispariies have in urn led o developmen of a sense of deprivaions among rural populaion, weakening of he federaion, regional ensions, poliical insabiliy, errorism and difficuly in building consensus on issues of naional ineres. I may be ineresing and useful o invesigae he exisence of convergence in Pakisan, o idenify is naure and o pinpoin he various impedimens in is way. A number of indicaors like lieracy rae, populaion densiy, life expecancy, degree of urbanizaion, he rule of law ec; speak of much dispariy across he socio-poliical regions. Furher, hese dispariies are increasing over ime. This provides sufficien raionale o focus aenion on he issue of growh and convergence using he formal models and sandard procedures. For his end, we discuss he mehodology and analyical framework in he nex secion. This is followed by a brief discussion of he available daa and hen an analysis of he main findings. The final secion is reserved for conclusions and policy recommendaions as usual. 4 For insance, Juan-Ramon and Rivera-Baiz (1996) analyzed he issue for he saes of Mexico, Cashin & Sahay (1996) and Bajpai & Sachs (1996) for Indian saes, Jian, Sachs & Warner (1996) and Gundlach (1997) for Chinese provinces, and Hossain (2000) for various regions of Bangladesh. 4
3.0 Analyical Framework I seems appropriae o presen a brief hisorical skech of he models used for he purpose before we concenrae on empirical analysis. 3.1 Hisorical Perspecive The neoclassical growh model, pioneered by Solow (1956), which was originally mean o resolve he razor-edge problem of he Harrod model (1939), could also successfully explain as o why cerain counries on he globe are so rich and ohers so poor. A equilibrium, he growh raes of per capia income and capial inensiy are closely inerrelaed. The producion funcion ofen employed in growh models is Cobb-Douglas, wih CRS specificaion and labour-augmening echnical progress plus he usual neoclassical assumpions. I may be expressed in he reduced form; wih all variables in per capia erms: Y () K () [A () L (1 ) () ] y () A The symbols carry heir usual meaning; Y sands for gross oupu, K for capial sock, L for he labour force, k=k/l for capial inensiy and A denoing he echnology growing exogenously a a rae g. Nex uilizing he aggregae saving funcion (S () =sy () ) and he incremenal capial-oupu raio (ν=dk/dy), he fundamenal equaion of moion is readily obained: dk / d A( ) sk( ) nk( ) A he seady sae equilibrium, he capial inensiy sops changing. The ime pah of his variable depends direcly on saving rae s and inversely on he growh rae of labour force/ populaion n. This in urn leads o he relaionship of per capia income wih he same variables/parameers: k * 1/(1- ) * /(1- ) /(1- ) () {A() s/n} y() B().{s/n} B().{1/ } (3) The symbols wih aserisks denoe he seady sae values of he variables concerned, and he erm B () = A α/(1-α) (). I is now sraigh forward o show he growh rae of per capia income by he relaion: ln y () () ln B { /(1 )}ln s { /(1 )} ln n (4) () k () (1) (2) 5
This relaionship conveys an imporan message: oher hings remaining he same, counries wih high invesmen and saving raes will grow faser while hose wih high populaion densiy will lag behind in he race. This is he crux of he model. However, he basic neoclassical model came under criicism from wo main angles. Firs, he model failed o explain he (large) residual componen in growh accouning. Solow aribued his facor o he measure of our ignorance. However, i was believed o arise primarily due o he way echnical progress was considered. The conroversy during 1960 s revolved around he quesion wheher echnical progress is exogenous or endogenous and wheher i could be considered as embodied or disembodied. Furher research led o he inroducion of endogenous growh models ala Romer (1989) and Barro (1990) ha emphasized on he role of human capial in developmen and growh. This also rejeced he hypohesis of secular sagnaion. Second, he original model prediced ha economies are likely o converge o he seady sae equilibrium overime. However, his very noion of convergence has been inerpreed in differen ways. Tradiionally, i was believed ha every economy may follow an independen growh pah and converge o some seady sae level peculiar o i. On he oher hand, i was argued by some researchers ha differen economies are likely o converge o some common seady-sae equilibrium in he long-run and ha he growh rae ends o be inversely relaed o he saring level of income per capia. Thus, relaively poor economies could grow quickly as compared o heir rich counerpars over ime. However, he cross-counry empirical evidence failed o suppor his predicion of caching-up. As emphasized by he endogenous growh models, rich economies have o grow faser and indefiniely due o higher rae of capial formaion and echnological advancemen. In oher words, he very exisence of seady sae equilibrium was refued, given ha invesmen in human capial leads o increasing reurns and ha human capial is a public good. 3.2 The Framework for Convergence Analysis The primary source of convergence is believed o arise from he very assumpion of diminishing reurns o reproducible capial. Oher sources of convergence include labour migraion from poor o richer economies and he diffusion of echnology. The caching- 6
up phenomenon is raionalized on he grounds ha imiaion and adopion of discoveries is comparaively cheaper han innovaion and discoveries iself. In oher words, echnical progress may be relaively slower in leaders and rapid in follower economies 5. 3.2.1 Absolue Convergence The conemporary sudies on convergence generally follow he mehodology suggesed by Barro and Sala-i-Marin (1991). Log linearizaion of he differenial equaion (Eq-2) around he seady sae gives he following relaionship 6. ln y e ln y0 (1 e ) ln yss (5) In he above equaion, y 0 is he iniial value of income per effecive worker, y is he income a ime () so ha i converges o equilibrium value (y ss ) in he limi as. The parameer β capures he speed of convergence, which is deermined by echnology and preferences. If he echnical progress is labour augmening, we may rewrie he variables in per capia unis, since he erms expressed in efficiency unis are no direcly observable. If he income per effecive worker is denoed by y = Y /A.L, where A = A 0 e g and L = L 0 e n, one ges he modified form by aking he logarihms and rearranging he erms as under: ln y g e ln y0 (1 e ) ln A0 (1 e ) ln yss (6) If he lengh of inerval beween he iniial and presen ime is years, hen by subracing (ln y 0 ) from boh sides of he above equaion, dividing hrough and rearranging he erms, an expression for he average growh rae is obained: y ^ g ( 1/ )(1 e )[ln y0 ln A0 ln y The above relaion indicaes ha growh comprises wo componens, he conribuion due o echnical progress (shifing of he P.F.) and he fracion due o he gap beween he iniial and seady sae levels of income per capia (expansion along P.F.), where he speed of convergence is given by he slope parameer [ - (1/)(1-e -β )]. In addiion o he single equaion models, he researchers have also employed he panel daa framework for convergence analysis. I allows pooling of he cross secion and ime ss ] (7) 5 6 See Barro and Sala-i-Marin (2004) For deails, see Gandolfo (1996) pp 175-89. 7
series daa for a number of economies or regions. To derive he economeric model, we may consider equaion (7) wih one period inerval ha applies o he i h economy in he sample. The annual growh rae is given by he following relaion (wih inercep given by: α = g + (1- е -β ) ln (y ss + A -1 ). The random error erm (ε, ) may be included wih usual properies. y ^ ln y ln y (1 e ) [ln y ln A ] 1 1 1 (8) Equaion (8) provides he framework generally used for esing absolue β-convergence. I may be possible o divided he enire ime span ino smaller sub-periods (of lengh d ) so ha he average growh rae of income per capia (beween ime and -d ) for he economy concerned may be regressed on he level of income in he pas period. Thus he above equaion may be wrien in he modified forma as under: y ^ ( 1/ d)ln [ y / y ] ln y d d (9) The slope parameer, given by: λ = (1/d)(1- е -β ) capures he speed of convergence, whereas he inercep erm, given by: γ= g + λ (ln y ss + A -d), capures he effecs of echnical progress and oher unobservable deerminans of seady sae. The above specificaion, however, suis he economies ha are closer o one anoher in srucural characerisics (e.g. OECD); and herefore may exhibi absolue convergence. The common inercep in such models consrains all he economies o have he same seady sae level, which is a highly resricive assumpion. Obviously, his kind of model may no be suiable for convergence analysis in oher economies exhibiing vas differences in socio-economic srucures. 3.2.2 Condiional Convergence The occurrence of absolue convergence is a rare phenomenon as compared o condiional convergence, which is mos likely o hold. In his case, he economies are expeced o converge owards heir peculiar seady saes raher han o a common equilibrium (Mankiw, Romer, and Weil 1992). As such, a single variable (iniial level of per capia income) migh no be sufficien o explain he differences in growh raes across heerogeneous economies. Many empirical sudies on condiional convergence have used specificaions similar o he general forma given below. The growh rae of income per capia in an economy 8
(g ) and for a given period is regressed on he income per capia wih one period lag (y -1 ) and he se of condiioning variables (x i. ) mean o conrol for he differences in he seady sae of economy 7. g xi, y 1 (10) However, his general (informal) specificaion provides no informaion regarding he values of srucural parameers since i is based on reduced form equaion. In order o avoid his limiaion, i is necessary o inroduce explicily a number of condiioning variables like invesmen raes, populaion growh raes, differences in he indusrial srucures, ne migraion rae of labour, some proxies for accumulaion of human capial and cerain dummies o conrol for oher differences across he economies. The researchers have herefore ried o esimae he srucural convergence equaions derived explicily from he formal models 8. Mankiw e al (1992) resor o he assumpions of diminishing reurns o reproducible capial and ha echnical progress is a public good (diffuses evenly hrough all economies); boh facors responsible for convergence as discussed above. We discuss he fundamenals of he augmened growh model 9 used for condiional convergence. The producion funcion may be rewrien in he modified form so as o capure he impac of human capial accumulaion. Again, he specificaion may be Cobb-Douglas and he model may also be wrien in reduced form: Y K H [A L ] (1 ) y k h * (11) The symbol H denoes he sock of human capial, assumed o be a public good, and he coefficiens α and measure he parial oupu elasiciies wih respec o facor inpus. The labour force (measured in efficiency unis) should grow a he composie exponenial rae (n+g). The augmened producion funcion now exhibis increasing reurns o scales in aggregae bu he propery of diminishing marginal reurns applies o individual facors. 7 8 9 The researchers have used up o 50 differen condiioning variables, following Barro (1991). Barro and Sala-i-Marin (1992) use he Cass-Koopman s opimal savings version of he neoclassical growh model while Mankiw, Romer, and Weil (1992) derive he specificaion from Solow-Swan model. For deails please refer o Barro and Sala-i-Marin (2004), and Mankiw (1995) 9
As before, he quaniies per uni of effecive worker may be expressed by: y = Y /A.L, k = K /A.L, and h = H /A.L. Likewise, he fracion of income invesed in physical and human capial may be denoed by he proporions s k and s h respecively such ha hese sum up o he aggregae saving rae: s k + s h = s = S/Y. Wih hese manipulaions, along wih incorporaion of he depreciaion rae (denoed by δ), he equaions of moion for physical and human capial may be expressed as under (he counerpars of Eq-2): dk d dh d sk k h ( n g ) k and sh k h ( n g ) h (12 a,b,) The seady sae equilibrium is said o occur in he long run where he levels of physical and human capial per effecive worker sop changing furher. Uilizing his informaion and solving for he resulan equaions, one ges he seady sae values for physical and human capial per effecive worker 10. Subsiuing hese values back ino producion funcion, and by aking logs, he deerminans of seady sae are readily obained. The seady sae income depends on he parameers: A, s k, s h, n, g, δ, α and ω. ln y * ln A g [ ]ln sk [ ]ln sh [ ]ln ( n g ) 1 1 1 (13) The condiional convergence explicily akes ino accoun he possible differences in he deerminans of seady sae and hence demands incorporaion of appropriae variables. The imporan consideraions as o, which variables ough o be included, which elemens should be allowed o vary and how, and which should be assumed o remain consan across economies; have been debaed in growh lieraure. Condiional convergence hen implies ha he growh rae of an economy is posiively relaed o he disance beween is seady sae level and curren level of income. To examine he dynamics of regional economies along ransiion o heir seady saes, he speed of convergence (β) can be expressed as 11 d d (ln y ) [ln yss ln y ] (14) In he above relaion, β = (1-α-ω) (n+g+δ), which implies ha for given seady sae, an economy wih higher level of per worker income a he sar exhibis a lower growh rae 10 11 For deails, please see Gandolfo (1996) pp 286-87. See Mankiw, Romer and Weil (1992). 10
and vice versa. On solving he above differenial equaion, we ge an expression for convergence as under: ln y In his relaion, e ln y (1 e ) ln yss (15) y is he iniial value of income per effecive worker and τ is he y saring poin. Subsiuing for ln from above in equaion (13), and hen ransforming he per worker erms ino per capia erms, we ge he following relaion: ln y ln y (1 e (1 e )[ln A )[( 0 1 ln y )ln s k ] [(1 e ( 1 )ln s ) g e h ( 1 g ] )ln ( n g )] (16) The above relaion provides he requisie specificaion for empirical analysis. If he speed of convergence λ is posiive, α >0, ω>0 and (α+ ω) < 1 as assumed by he model, he signs of he coefficiens can be easily prediced. Mankiew e al (1992) have also employed he basic neoclassical model o invesigae he hypohesis of condiional convergence. The deerminans of growh hen simply include he echnology level and he observable variables like saving raes, iniial level of income per worker and populaion growh raes. The model assumes he following shape and predics no only he sign of each coefficien bu also is magniude: ln y ln y (1 e (1 e ) ln A ) ln y 0 [(1 e (1 e ) g e ) ( 1 g ] )[ ln s ln ( n g )] 3.2.3 The Dynamic Panel Framework As discussed above, he panel daa approach can correc he omied variable bias by allowing for differences in echnologies across regions. Islam (1995) resrucures he neoclassical model and inerpres he erm: (1-е -λη ) ln A (0) as he ime-invarian regionspecific effec while using he panel framework. Using he noaion of panel daa approach, we may rewrie equaion (16) for a given region as: (17) 11
ln 3 j y ln y 1 j1 j x V i (18) where V 3 e (1 e [(1 e )(, (1 e 1 1 ) g e ), x 1, )( ln s 1 g ], (1 e i k, x ), 2, 2 (1 e ln s h )ln A 0,. x 3, )( 1 ), ln( n g ), The se of condiioning variables (denoed by x i ) capure he differences in he seady saes across regions. The V erm signifies he ime specific effecs, which include he rae of echnological change. The nex erm μ i is region-specific facor ha represens he combined effec of insiuions, resource endowmen, climae, cusoms and radiions ec. This componen varies across regions and picks up he effec of any omied variable ha does no vary over ime in a panel. Finally, is he ime inerval of four/five year period and ε i represens he usual error erm ha varies across regions and ime. 4.0 Daa and Mehodology In order o es he hypohesis of income convergence across differen regions of Pakisan over ime, he appropriae economic uni migh be he disric or even he union council. However, he requisie daa is available only a he provincial level, forunaely wih rural-urban disaggregaion. The ribal areas (FATA), he norhern areas (Gilgi- Balisan) and Azad Kashmir are excluded due o daa consrains. The available informaion covers he period from 1979 o 2005. The imporan daa ses used in he analysis comprise he household per capia income, savings raes, lieracy raes, combined enrollmen raios, dependency raios, populaion growh raes, crude birh raes and infan moraliy raes 12. Human capial is an imporan deerminan of economic growh and convergence besides physical capial and labour force. I is indicaed by educaion, raining and experience as well as good healh and physique; bu i is difficul o measure. Mankiw, Romer and Weil (1992) have used he secondary school enrollmen rae as proxy for human capial, whereas Sala-i-Marin (1997) has used life expecancy a birh as proxy 12 The daa is derived from official sources like he Economic Survey, he HIES (PSLM), Demographic Survey, he Labor Force Survey, he Educaion and Developmen Saisics of he provinces ec. 12
for non-educaional human capial and school enrollmen rae for educaional human capial. We have preferred o consruc a composie index of human capial following he consrucion of Human Developmen Index (HDI) by he UNDP (1997).The proposed index includes proxies for boh educaion and healh 13. Panel daa esimaion is made possible by dividing he available period-wise informaion for each region ino several shorer ime spans. We consider a span of four/five years o be appropriae, which is also he sandard pracice followed in empirical research work. Dividing he oal ime period (1979-2005) ino shorer spans, we obain a oal of six panels for each of he province. The consruced inervals are 1979-1984, 1984-1988, 1988-1993, 1993-1997, 1997-2001, 2001-2005. The dependen variable is he logarihm of per capia (per worker) income by he end poin of each ime span where he mos imporan explanaory variable is he lagged value of income per capia (in log form). Oher variables such as saving raes, labour force growh raes and human capial are averaged over four/five year period for each region 14. An imporan issue ha arises while using he panel daa is wheher he individual region-specific effecs should be considered fixed or random. The disurbance erm (OLS specificaion) does no ake ino accoun he unobserved differences among he regions, which may be imporan. The fixed effec specificaion may hen be appropriae choice. The dynamic panel growh model wih fixed effec allows us o conrol for he unobserved differences among he seady saes of regions in addiion o he observed differences, he laer capured by he se of condiioning variables. The empirical work based on single cross-secion regressions may suffer from wo inconsisencies, i.e. omied variables and endogeneiy bias. The firs bias arises when he region-specific effecs are assumed o be uncorrelaed wih oher explanaory variables and he second arises when cerain explanaory variables happen o be endogenous 15. The reliabiliy and consisency of he esimaes is hen a serious issue. Islam (1995) has used a fixed effec specificaion (leas square dummy variable echnique) o esimae he panel daa 13 14 15 Firs we esimae he educaion index by giving 2/3 weigh o lieracy and 1/3 o secondary school enrollmen, where he maximum is 100 and minimum is zero. Nex we esimae he healh index by giving 60% weigh o infan survival and 40% o crude birh rae, where he maximum expecancy is 85 years and minimum is 25 years. The compound human capial index is hen he simple average of he wo indices. The daa se used in he analysis can be provided on reques. For deails, see Casell Esquivel and Lefor (1996) and Durlauf and Quah (1999). 13
model so as o address hese limiaions. Casell e al (1996) suggesed ha he firs difference GMM approach deals successfully wih boh he issues. Durlauf and Temple e al (2004) poin ou ha omied unobserved region-specific effecs in dynamic panel model cause he leas square esimaors o be biased and inconsisen. The fixed effec or wihin groups esimaor, which akes ino accoun he unobserved region-specific effecs, also provides biased and inconsisen esimaes. This is due he fac ha he lagged dependen variable is correlaed wih he mean of individual errors. Bond, Hoeffler & Temple (2001) and Durlauf & Temple e al (2004), sugges ha he 'leas square esimae' may provide he (approximae) upper bound on he coefficien of lagged variable and he 'wihin group esimae' can be regarded as he (approximae) lower bound. Thus an esimae lying beween he wo may be consisen. 5.0 Empirical Analysis and Resuls We applied differen esimaion echniques, discussed above, o he panel daa so as o compare he resuls and find consisen esimaes. We confroned he daa se o es for absolue as well condiional convergence. The resuls are discussed below. 5.1 The Absolue Convergence To see he exisence of uncondiional (absolue) convergence, he model given by equaion (9) is used, in which he only regressor is he lagged value of he dependen variable - he growh rae of real per capia income. As noed above, he slope parameer (λ) capures he speed of convergence. The coefficien wih a negaive sign and saisically significan value would imply absolue convergence o he seady sae common for all regions and vice versa. By implicaion, a zero value of he parameer (or non-zero bu insignifican) indicaes no convergence or divergence, which shows ha each region follows an independen growh pah. Nex we focus on he analysis. 5.1.1 Aggregae Analysis Table-1 repors he cross-secional regression resuls, which cover a period of weny six years (1979-2005) and correspond o income per worker. We have divided his ime span ino hree sub-periods, (1979-1988), (1988-1998) and (1998-2005) in order o find he evidence of convergence, if any, separaely. Anoher reason for his division ino 14
sub-periods is o es wheher he poliical and macroeconomic sabiliy (insabiliy) bears any implicaions for absolue β-convergence 16. Table 1: Cross-Secional Tess for Absolue Convergence (Aggregae) Dependen variable ln (y /y -1 ) (Overall) (..Period-wise..) PERIODS (1979-2005) (1979-1988) (1988-1998) (1998-2005) CONSTANT 4.349 4.318** 0.123-2.288 sandard error 3.488 0.668 9.764 5.351 T- value 1.247 6.461 0.013-0.428 P- value 0.339 0.023 0.991 0.711 Ln (y-1) - 0.522-0.533** - 0.018 0.317 sandard error 0.454 0.087 1.235 0.684 T- value - 1.149-6.121-0.014 0.464 P- value 0.370 0.026 0.990 0.688 ß=Implied speed 0.028 0.074 0.002 N/A R 2 0.397 0.924 0.060 0.503 NOTE: All regressions are for he four provinces of Pakisan. ** Significan a 5% level Column (1) repors he resuls for he enire period. The coefficien for he explanaory variable is negaive bu saisically insignifican. Thus, he daa do no provide any evidence in favour of β-convergence in Pakisan. For he sub-period (1979-1988), here coefficien is negaive and saisically significan. This is a srong evidence of convergence during he period concerned where he R 2 is quie high and he implied speed of convergence is 7.4% per annum, which is respecable. In oher words, he hypohesis of convergence canno be rejeced for he sub-period under reference. However, his rend could no be susained during he nex decade (1988-1998), where he sign is correc (negaive) bu he coefficien is close o zero and saisically 16 The firs and hird sub-periods represen he miliary-guided, semi-democraic regimes of General Zia-ul-Haq and General Pervez Musharaf respecively. The second sub-period shows he so called fake-democraic regime. Alhough he counry was ruled by publicly eleced governmens during his period bu hese were poliically unsable. Four elecions were held during 10/11 years bu no eleced governmen could complee is enure. 15
insignifican. During he hird sub-period (1998-2005), he resuls are jus in he opposie direcion. The concerned coefficien bears a posiive sign, however i is saisically insignifican. This implies a weak signal of divergence. The resuls suppor he claims ha povery and inequaliies have increased across Pakisan during he recen pas. To sum up, here are no signs of convergence when he enire ime span is considered. However, he signs of regional income convergence could be seen during he subperiod (1979-1988) only, which can be raionalized on he basis of cerain ground realiies. For insance, he overall economic performance was beer relaive o oher developing counries around he globe; he growh rae was high and inflaion rae was mild, which may be seen from he World Bank repors 17. There was a sharp increase in worker s remiances during he era, which boosed up he living sandard of masses. Nadeem-ul-Haq (1999) believes his o be he mos imporan facor in reducion of povery during 1980s. 5.1.2 Urban-Rural Analysis Nex we confron he available daa in rural and urban breakdown for convergence analyses in rural and urban areas separaely. The rural and urban areas can be considered as separae eniies due o he obvious difference in heir socio-economic and poliical srucure. Alhough he concep of convergence in rural and urban areas is more difficul o imagine wihin he exising adminisraive se up, however he available informaion allows us o see he dynamics and have some useful insighs. Table 2 is concerned wih rural areas. We follow he same mehodology as for he aggregae analysis. I can be seen ha he coefficien for he explanaory variable concerning he enire period (1979-2005) is negaive, bu significan only a 10% level. However, when he ime span is divided ino hree sub-periods, (1979-1988), (1988-1998) and (1998-2005), he slope coefficien alernaes in sign bu no significanly differen from zero. The very base and he vial componen of our rural economy is he agriculural secor, which primarily depends on he forces of naure. Therefore, he resuls migh have been affeced by shocks o agriculural produce. Our rural economy, 17 The average real GDP growh rae per annum was 6.15% and inflaion rae of Pakisan was 6.74% during 1980s as compared o he average raes of developing counries: annual real GDP growh rae of 4.49% and inflaion rae of 34.72% during he decade. 16
Table 2: Cross-Secional Tess for Absolue Convergence (Rural Areas) Dependen variable ln(y /y -1 ) (Overall) (..Period-wise..) PERIODS (1979-2005) (1979-1988) (1988-1998) (1998-2005) CONSTANT 3.385* 2.497-0.530 2.013 sandard error 1.071 2.327 4.751 3.236 T- value 3.161 1.073-0.112 0.622 P- value 0.087 0.396 0.921 0.597 Ln (y-1) -0.399* -0.284 0.061-0.241 sandard error 0.135 0.316 0.612 0.424 T- value -2.947-0.900 0.100-0.567 P- value 0.098 0.463 0.930 0.628 ß=Implied speed 0.020 0.033 N/A 0.039 R 2 0.685 0.288 0.005 0.577 NOTE: All regressions are for he four provinces of Pakisan. *Significan a 10% level of significance especially in Punjab and Sindh provinces, performs beer in he years when agriculural produciviy is high. Table 3: Cross-Secional Tess for Absolue Convergence (Urban Areas) Dependen variable ln(y /y -1 ) (Overall) (..Period-wise..) PERIODS (1979-2005) (1979-1988) (1988-1998) (1998-2005) CONSTANT 4.351*** 8.427 9.673** 0.360 sandard error 0.107 5.986 2.456 2.253 T- value 40.555 1.408 3.938 0.160 P- value 0.001 0.294 0.059 0.888 Ln (y-1) -0.489*** -1.035-1.173* -0.022 sandard error 0.013 0.748 0.301 0.273 T- value -36.457-1.384-3.892-0.080 P- value 0.001 0.301 0.060 0.944 ß=Implied speed 0.026 N/A N/A 0.003 R 2 0.998 0.489 0.825 0.003 NOTE: All regressions are for he four provinces of Pakisan. Levels of saisical significance are indicaed by aserisks. 17
*** Significan a 1% level of significance ** Significan a 5% level of significance * Significan a 10% level of significance Similar resuls can be seen in Table 3 ha concerns wih he urban regions. The regression coefficien for he explanaory variable has he correc sign and i is saisically significan even a 1% level for he enire period from 1979 o 2005. The regression has a good fi. However, when he ime span is divided ino sub-periods, he coefficiens urn ou o be insignifican, alhough he signs are correc. In his case, he regression is good fi for he period (1988-98) only. The implied speed of convergence for he rural and urban economies works ou o be 2% and 2.6% per year respecively, when we consider he enire period. These resuls indicae ha rural and urban economies are no likely o converge o he common seady sae; raher hey are following heir independen growh pahs. However, more ess are needed o explain he naure and causes of growh in rural and urban economies separaely since he lonely variable (iniial per worker income) is no sufficien o explain he complex process of growh and convergence. 5.2 The Condiional Convergence In he absence of saisfacory evidence on absolue convergence, i is necessary o verify he hypohesis under specific regional condiions. The exisence of significan naural, social and hisorical differences among differen geographical regions of Pakisan renders hem less likely o converge owards he same equilibrium. This diversiy can be seen via a number of indicaors like he lieracy rae, rae of saving, populaion densiy, life expecancy, infrasrucure faciliies, degree of urbanizaion, he rule of law, social and family srucure ec. Furhermore, hese dispariies have been increasing over ime across differen regions. We have ried hree esimaion echniques, namely he OLS esimaors, he Fixed or wihin groups esimaors and he GMM esimaors mean for he panel daa framework. To explore he evidence of condiional convergence, we employ wo differen specificaions of he neoclassical growh model. Firs is he original neoclassical model due o Solow (1956) and second is he modified version due o Mankiw, Romer and Weil (1992) ha augmens he former wih human capial. Nex we focus on he resuls. 18
5.2.1 Esimaion via he Basic Neoclassical Model We begin our analysis wih he basic neoclassical model wihou any provision for human capial. The specificaion for he panel daa esimaion is provided by equaion (17), in which he inercep capures he region-specific effecs. The evidence of convergence ress on he sign and size of he coefficien for lagged real per capia income. A saisically significan value of he coefficien bearing a negaive sign implies condiional convergence. Oher variables on he righ hand side measure differences in he seady sae levels. The resuls are presened in Table-4. The firs column repors he OLS esimaion obained by simply pooling he ime series and cross secion daa. The second column repors esimaion hrough he fixed effecs model or Wihin Groups (WG) esimaors. The hird column repors he resuls of firs differenced Generalized Mehod of Momens (GMM) ala Arellano and Bond (1991). Table 4: Panel Daa Tess for Condiional Convergence Esimaion via he Basic Neoclassical Mode) Dependen Variable ln Y -- ln Y -1 Variables Leas squares Fixed Effec (WG) DIF-GMM ln (y -1 ) - 0.238 (0.148) -1.262** (0.177) - 0.331*** (0.074) ln (s ) 0.012 (0.019) 0.024* (0.013) 0.020* (0.012) ln (n +g+δ) - 0.733 (0.457) - 0.260 (0.294) - 0.319* (0.191) Implied λ 0.054 N/A 0.080 J-saisic 14.402 Insrumen rank 16.000 Sargan Tes(P-value) 0.346 Noes: Daa used over four/five years inervals beween 1979 and 2005. The symbol (λ) denoes he convergence speed. Sandard errors given in parenheses. * Significance a 10% level, ** Significance a 5% level, *** Significance a 1% level. The figures repored for he Sargan es are he p-values of he null hypohesis for valid specificaion. J-saisic is simply he Sargan es of over-idenifying resricions. A comparison of he resuls in he firs row reveals ha he OLS provides higher esimaes han WG mehod. The signs in boh cases are correc. The OLS esimaes a value of ( 0.238) and WG provides a value of ( 1.262) for he coefficien (he iniial level of per capia income). Forunaely, he value given by he GMM esimaor (- 0331) falling wihin he upper and lower bound and herefore i is more likely o be unbiased 19
and reliable. The validiy of he insrumenal variables used in he GMM esimaion can be checked by Sargan es. The p-value (0.346) srongly suggess ha he insrumenal variables used in he analysis are valid. In view of he above, he resuls obained from he firs differenced GMM echnique seem o be appropriae. All he coefficiens are saisically significan and bear he expeced signs. In paricular, he coefficien of lagged per capia income suppors condiional convergence across regions. The coefficien of saving indicaes ha one percen increase in saving rae will lead o a small increase of 0.02 percen in growh of real income. Likewise, an increase of one percen in he growh rae of populaion will be followed by 0.32 percen decline in growh rae of real income. The speed of convergence λ can be esimaed from he coefficien of lagged income. The implied speed of convergence is 8 % per year 18. The resuls show ha mos of he regions are nearer o heir respecive seady saes level. The differences across he regions in he prevailing income levels can be explained by he differences in he facors ha deermine he respecive seady sae levels. These facors or condiioning variables migh no only be differen across he regions bu also migh be changing wihin a region over ime. 5.2.2 Esimaion via he Augmened Model Human capial is anoher imporan variable ha is considered in empirical lieraure on growh besides savings and populaion growh raes. We esimae an augmened version in which he producion funcion also includes he sock of human capial, as shown in equaion (18) above. The panel daa resuls are repored in Table-5. For he firs differenced GMM esimaor, he coefficien of lagged income is highly significan. I falls beween he upper and lower bounds given by he OLS and WG esimaes and i is also consisen wih he resuls of Table-4. The p-value (0.366) given by he Sargan es does no rejec he validiy of he insrumens used in he analysis. Likewise, he coefficiens of saving and populaion growh have he expeced signs. The coefficien of human capial is posiive and saisically significan, which indicaes is 18 The half life of convergence process is given by he formula: T = ln (2)/λ, and if λ = 0.08, T= 8.67 years. The esimaed half life of convergence (he ime i akes o eliminae half of he gap beween seady sae and acual real per capia income). 20
imporance for growh. The speed of convergence λ is slighly higher han he esimae given by he basic neoclassical model and shown in Table-4. Table 5: Panel Daa Tess for Condiional Convergence (Esimaion via he Augmened Neoclassical Model) Dependen Variable ln Y -- ln Y -1 Variables Leas squares Fixed Effec(WG) DIF-GMM ln (y -1 ) - 0.238 (0.152) ln (s ) 0.011 (0.020) ln (n +g+δ) - 0.731 (0.472) ln (h ) - 0.009 (0.492) - 1.315*** (0.176) 0.031** (0.014) - 0.256 (0.287) 0.732 (0.539) - 0.359*** (0.028) 0.027* (0.014) - 0.302 (0.245) 0.665** (0.337) Implied λ 0.054 N/A 0.089 J-saisic 14.106 Insrumen rank 17.000 Sargan Tes(P-value) 0.366 Noes: Sandard errors are given in parenheses, (λ) denoe he annual convergence rae. * Significance a 10% level, ** Significance a 5% level, *** Significance a 1% level. 5.2.3 Esimaion via he Resriced Models In his secion, we address he quesion wheher he esimaes obained are consisen wih he predicions of growh models or oherwise. The daa is considered o suppor predicions if he esimaed coefficiens carry he prediced signs and have he expeced magniudes. The signs and magniudes of he coefficiens as prediced by he formal models and shown in Tables 4 and 5 make i convenien o es he models under resricions. The resriced leas squares echnique can help in his regard. Firs, wih reference o he basic neoclassical model, we apply he resricion ha he coefficiens of saving and populaion growh raes [ln(s) and ln(n+g+δ)] are equal in magniude bu opposie in sign. Alhough, he concerned esimaes repored in Table-4 are somewha differen, however we re-esimae he model by imposing his resricion. This also enables us o find he implied share of physical capial (α). Equaion (17) may be rewrien in modified form as under. ln( y / y ) ln y [ln s ln ( n g )] 1 0 1 1 2 (17 a) The coefficiens denoe: 0 = (1- е -λ )ln A 0, 1 = -(1- е -λ ), 2 = 3 = (1- е -λ ) (α/(1-α). 21
The regression resuls, afer incorporaing he resricion, are repored in Table-6. The p- value (0.0861) for GMM echnique given by he Wald es clearly rejecs he hypohesis ( 2 + 3 = 0), which implies ha our daa do no suppor he predicions of he neoclassical model. The implied value of he share of physical capial esimaed in GMM case is 0.064, which is very low. Table 6: Panel Daa Tess for Condiional Convergence (Resriced Basic Neoclassical model) Dependen Variable ln Y -- ln Y -1 Variables Leas squares Fixed Effec(WG) DIF-GMM ln (y -1 ) -0.0068 (0.0178) ln (s ) - ln (n +g+δ) 0.0154 (0.0192) -1.2306*** (0.1707) 0.0236* (0.0133) -0.2866*** (0.0693) 0.0197 (0.0155) Implied λ 0.001 N/A 0.07 Implied α 0.6931 0.019 0.064 Wald es: p-value 0.199 0.131 0.0861 Noes: Sandard errors in parenheses. Three aserisks, wo aserisks, and one aserisk denoe saisical significance a 0.01, 0.05, and 0.10 levels respecively. Table 7: Panel Daa Tess for Condiional Convergence (Resriced Augmened Neoclassical Model) Dependen variable ln( Y ) - ln( Y ) Variables Leas squares Fixed Effec(WG) DIF-GMM ln (y -1 ) - 0.100 (0.093) -1.302*** (0.174) - 0.353*** (0.045) ln (s ) ln (n +g+δ) 0.019 (0.020) 0.028* (0.013) 0.025** (0.013) ln (h ) ln (n +g+δ) 0.371 (0.363) 0.340 (0.248) 0.367* (0.242) Implied λ 0.021 N/A 0.087 Implied α 0.039 0.017 0.033 Implied β 0.758 0.204 0.493 Wald es: p-value 0.27 0.41 0.2545 Noes: Sandard errors in parenheses. Three aserisks, wo aserisks, and one aserisk denoe saisical significance a 0.01, 0.05, and 0.10 levels respecively. Second, wih reference o he augmened neoclassical model, we may examine he resricions ha he coefficiens of physical capial (saving rae) and populaion growh 22
rae as well as he coefficiens of human capial and populaion growh rae sum o zero. In his regards, equaion (16) may be rewrien as under: ln( y / y ) ln y [ln s ln ( n g )] [ln h ln ( n g )] 1 0 1 1 2 3 (16 a) The coefficiens are defined as: 2 = (1- е -λ ) [α/(1-α)], 3 = (1- е -λ ) [ω/(1-α)], where α is he share of physical capial and ω is he share of human capial in per capia income. The esimaed resuls from he resriced regression are repored in Table-7. The resricion implied by he augmened neoclassical model can no be rejeced a he convenional levels of significance (i.e. wih p-value 0.2545). The resuls from firs differenced GMM show he share of physical capial o be 0.033, which is very low and unrealisic, and he share of human capial is 0.49, which is quie reasonable. So i can be concluded ha he daa suppor he predicions of augmened model o some exen bu does no do so in case of basic neoclassical model. Moreover, we can observe ha esimaes of convergence coefficien are no affeced by resricing boh he models and remain almos same as hose obained from unresriced models and repored in Table (4 and 5). This behaviour indicaes ha he coefficiens are consisen wih he specificaions shown above, and he resuls for he speed of convergence are robus. 5.3 The Sigma Convergence Some ineresing resuls could also be derived by confroning he daa o analyze sigma-convergence. By comparing he findings beween per capia and per worker income, he regional dispariies in erms of per capia incomes appeared o be more severe han ha of per worker incomes. The finding implies ha he number of dependen or inacive members of he populaion is responsible for higher dispersion of per capia income. This is in line wih he convenional wisdom, since a higher dependency raio means higher consumpion or lower saving raes and hereby lower growh raes. An applicaion of he model o rural and urban areas separaely revealed ha he inra-regional differences in he socio-economic condiions are as serious as he iner-regional differences. To sum up, he findings indicae ha incomes per capia 23
across he provinces are moving farher away from one anoher overime and here is lile endency for reducing of dispariies 19. 6.0 Conclusions and Policy Implicaions The evidence on condiional convergence indicaes ha each regional economy converges o is specific seady sae, raher han o a common equilibrium. However, i does no ell abou prevalence of regional dispariies; as o how hey appeared or graviaed overime and how hey could be addressed. Hence, condiional convergence neiher implies necessarily a reducion in regional dispariies nor does i conradic wih rends of increasing dispariies. The presen sudy has examined he phenomenon of convergence of per capia income o seady saes across he four provinces of Pakisan wih rural-urban splis over he period from 1979 o 2005. We could find no evidence of absolue convergence for he enire ime span of 26 years from 1979 o 2005 excep for he period 1979-88, when he signs of regional convergence could be observed. However he rend could no coninue hereafer, raher he sympoms of divergence were observable for he period 1998-2005. Pu differenly, he absence of absolue convergence predics an increase in dispariies over ime across regions. On he oher hand, a srong evidence of condiional convergence could be observed boh in aggregae and rural-urban divisions. The findings imply ha differences in he socio-economic condiions prevailing across he poliical eniies are crucial and responsible for economic dispariies o persis. Pakisan has been undergoing subsanial srucural changes in recen years, so he seady sae deerminans also changing consanly 20. The differences in social, culural and poliical behaviors across he four provinces of he federaion are naural and can be easily undersood. However, he prevalence of abjec povery and gross inequaliies over he long run, boh across he regions and wihin he regions in rural-urban bifurcaion, is posing problems. This siuaion needs serious aenion and calls for immediae remedial measures, failing which he dangerous sense 19 20 We do no repor he deailed resuls for space consrains, which may be provided on reques. These changes migh be in response o he afermahs of 9/11 even ha have drasically upse he geo-poliical environmen in Afghanisan and Pakisan. The US inervenion has resuled ino massive desrucion via erroris aciviies in all pars of he counry and has aggravaed problems in FATA and Baluchisan. 24