Alternative hypotheses of cross-country convergence. A non-parametric analysis of manufacturing sectors

Transcription

1 Alernaive hypoheses of cross-counry convergence. A non-parameric analysis of manufacuring secors Silvia Dal Bianco Universiy of Pavia December 2, 21 Absrac I adop he disribuion dynamics framework o sudy labor produciviy convergence, in he period , among 28 developed and developing counries, in differen manufacuring sub-secors, idenified, as according heir echnological conen ino Resource Based, Low Technology, Medium Technology and High Technology. I find ha, excepion made for High Technology and Manufacuring as a whole, all subcomparmens are prediced o converge wihin small groups, validaing he so-called club-convergence hypohesis. Thus, as high ech secors are he ones opening he bes growh-equiy prospecs, developing counries should arge hese kind of producions. JEL Classificaion Code: C14, O33, O47. Keywords: Ialian Regions; Neoclassical and Technological Convergence; Disribuion Dynamics. 1

2 1 Inroducion In he pas fory-five years, world gross domesic produc has seadily increased a an annual average rae of 3.5%. 1 Conemporaneously, GDP per capia and GDP per worker disribuions have been characerized by wo ineresing feaures: firs, he emergence of wo disinc peaks, corresponding o poor and rich counries; and, second, he reducion of inra-disribuion inequaliies, ha is a reducion in he spread beween relaively poor and relaively rich economies, Durlauf and Quah (1999). This sylized evidence, summarized in Figure 1, promped a resurgence of ineres in crosscounry convergence. The poin o be seled being wheher or no developing counries are caching-up wih heir richer counerpars, in erms of income per capia or per worker. In his work I sudy labor produciviy convergence endencies, in he period , among 28 developed and developing counries, in differen manufacuring sub-secors, idenified, as according o Lall (2b) echnological axonomy, ino Resource Based, Low Technology, Medium Technology and High Technology. 2 Table 1 repors sample s deails. 3 More in deail, I employ an unified disribuion dynamics framework, as originally developed by Quah (1996a), o examine he hree exbook (and compeing) convergence hypoheses, namely: absolue, condiional and club convergence. 4 I is well known ha according o he absolue convergence predicion, poor economies end o grow faser han rich ones; hen, conemporaneous per capia income differences are only ransiory and will be null in he long run, Sala-i-Marin (1996). Condiional convergence assers, insead, ha he long run equalizaion of per capia income will arise only among counries ha have idenical srucural characerisics (i.e. saving raes, iner- 1 Own calculaion from World Bank, World Developmen Indicaors, for he period The classificaion of Lall (2b) disinguishes manufacuring comparmens according o heir research inensiy, measured as Research and Developmen (R&D) expendiure share over sales value. In paricular, Resource Based indusries are he ones in which he value of producion is essenially given by he possession of primary resources (e.g. processed food, manufacured obacco, refined peroleum producs); Low Technology includes producions whose R&D expendiure is below 1% of sales value (e.g. garmens, foowear, poery and culery); in Medium Technology, R&D expendiure is beween 1% and 4% (e.g. auomoive indusry, agriculural machinery, perfumery and pesicides) and in High Technology R&D expendiure is greaer han 4% of sales value (e.g. elecronics and scienific insrumens). 3 I mus be noed ha he choice of he counries and of he ime span was dicaed by daa availabiliy. Only very recenly (i.e. April 21) new disaggregaed daa for manufacuring have become available. The mos promising daa-se, wih he aim of enriching he analysis wih respec o boh cross-secional and ime-series dimensions, seems o be he Unied Naions Indusrial Developmen Organizaion (i.e. UNIDO), Indusrial Saisics Daabase 21 a he 2 digi level of he Inernaional Sandard Indusrial Classificaion (i.e. ISIC) Code (Revision 3). This is lef for (near) fuure research. 4 For an exhausive review on he differen convergence hypoheses and he so-called conroversy on convergence, in boh is heoreical foundaions and empirical assessmens, see he aricles of Durlauf (1996), Bernard and Jones (1996b), Galor (1996), Quah (1996b) and Sala-i-Marin (1996), all colleced in The Economic Journal Vol.16, No

3 emporal preferences, developmen sage,...), Barro(1991). Finally, when club convergence hypohesis is no rejeced, i means ha in he long run counries will converge only wihin small groups and no alogeher. In oher words, overall convergence comes up only if boh counries srucural characerisics and iniial condiions are evened ou, Galor (1996). Wih respec o club convergence, i is imporan o clarify ha in his paper I will consider physical capial sock and echnological level as he key drivers of clusering dynamics. Tha is, paraphrasing Galor and Zeira (1993), he iniial disribuion of capial sock (echnology) affecs aggregae oupu and invesmen boh in he shor and in he long run.moreover, he choice of physical capial is inspired by he lieraure on criical hresholds while he one of echnological level follows he radiion of echnological cachup and absorpive capabiliies. 5 My work represens a significaive conribuion o he convergence lieraure because his is he firs sudy ha assesses compeing hypoheses concerning labor produciviy convergence beween advanced and laggard economies, in manufacuring secors, employing disribuion dynamics. In fac, previous analysis on alernaive convergence predicions have been focused on he behavior of GDP per capia or aggregae labor produciviy, eiher using parameric or non-parameric echniques. 6 Moreover, when convergence endencies have been invesigaed in differen economic secors (i.e. agriculure, mining, services,...) or sub-secors (i.e. manufacuring indusries), only OECD counries have been considered. The secoral analysis I am referring o are he ones of Broadberry (1993) and Bernard and Jones (1996a) and he sub-secoral ones of Dollar and Wolff (1988)(1993), Boheim e al.(2) and Caree e al.(2). Ineresingly, he secoral sudies fail o find convergence in manufacuring secor as a whole, while he sub-secoral ones confirm such an hypohesis in all indusrial comparmens. A his poin, I wan o menion ha in Dal Bianco (21) I invesigaed, hrough sandard parameric ools, wheher cross-counries convergence in Lall s echnological secors is manly due o capial accumulaion (i.e. neoclassical convergence) or o echnological cach-up (i.e. echnological convergence), employing a panel of 5 developed and developing counries, observed a five-years inervals, for he period In paricular, 5 See Azariadiz and Drazen (199) and Durlauf and Johnson (1995) for formal illusraions of criical hreshold s frameworks; Baumol (1986) and Durlauf (1993) for, respecively, seminal conribuion and formal reamen of echnological cach-up and absorpive capaciies. 6 See Islam (23) and Durlauf e al.(25) for exhausive and auhoriaive reviews. 7 The careful reader migh noe ha, in my parameric sudy, boh he ime series and he cross-secional dimensions are larger han he presen ones. This is mainly due o he choice of collecing he relevan variables a 5-years inervals. See foonoe 3 for furher deails on daa-limiaions problems. 3

4 I found ha boh hypoheses hold in all secors and counries and, more precisely, ha capial accumulaion is he fundamenal convergence deerminan for (and in) indusrialized economies, while echnological cach-up is more imporan for (and in) emerging ones. Alhough, given he economeric echniques employed, such resuls are exclusively indicaive of he behavior of he average economy. Thus, as he issue of convergence is innerly relaed o he relaive economic performance of disinc counries, in he presen work I employ disribuion dynamics precisely because i allows o rack such a relaive performance along ime. Moreover, i has he grea advanage of no requiring any sample spli for he assessmen of he club convergence predicion, as for example in Desgois (1999), Bloom e al.(23) and Graham and Temple (26). Finally, a by-produc of he presen exercise is represened by new series on Toal Facor Produciviy (i.e. TFP), esimaed employing he superlaive index approach of Caves(1982a) and Caves e al.(1982b), and on ne physical capial sock, obained applying he Perpeual Invenory Mehod, wih delayed efficiency and random service life. 8 Having explained he novelies of my conribuion, I wish o furher moivae he presen research. The choice of invesigaing manufacuring secors is due o a wofold moivaion. Very synheically, he firs is ha if any cross-counry convergence should be shown, i should be shown exacly here. Before explaining his saemen, I pass o he second moivaion ha concerns, more specifically, he policy implicaions ha could be rerieved from he analysis of manufacuring comparmens. Tha is, as differen counries migh have sronges convergence endencies in differen indusries due, for example, o comparaive advanages ha can cause employmen shifs from less o more producive secors, as shown by Dollar and Wolff (1988)(1993), such secor-specific growh poenial migh call for selecive indusrial policies or for he suppor of paricular aciviies, as according he infan indusry argumen. 9 Turning now o he firs argumen, his is grounded on boh heoreical consideraions and sylized evidence. 8 Alhough of some poenial ineres, describing in deail he echniques employed will make he presen work (even) longer. So ha, I refer o Griffih e al.(24) for furher deails on TFP esimaion and o Maffezzoli (26) for wha concerns capial sock. Wih he laer respec, i migh be worh o briefly menion ha I se he curvaure parameer of he efficiency funcion (i.e. β) equal o.5; ha I used a runcaed normal as moraliy funcion; ha I have used OECD s counries average secor-specific service lives and, finally, o iniialize capial sock series I have followed Caselli (25), seing he depreciaion rae δ equal o.6. Needless o say, all he series are available upon reques. 9 See Lall (2a) for an effecive review. 4

5 In he firs insance, since he seminal conribuion of Lewis (1954), manufacuring has been idenified as he locus of economic growh. In fac, once subsisence level of food is ensured by agriculure, he developmen of he indusrial secor promoes inensive economic growh, ha is an increasing per capia income over ime. 1 In Figure (2.a), i could be appreciaed he decline of agriculural value added ogeher wih he increasing share of indusrial and service s producion. Second, manufacuring is echnologically he mos dynamic secor in he world economy, in he sense ha he greaes research effors are made o launch new manufacures or o improve exising ones, Cornwall (1977). I is ineresing o noe ha his evidence holds for boh high and low income economies. In fac, according o he World Inellecual Propery Organizaion, beween 1985 and 25, he number of paen applicaions, by boh residen and non-residen invenors, has doubled in developed counries and i has increased by four imes in developing ones. Third, as effecively described by he Unied Naions Conference on Trade and Developmen (i.e. UNCTAD) in is World Invesmen Repors, indusrial producion is nowadays world inegraed. This feaure is crucial in convergence analysis because developed and developing counries inerac wih each ohers and heir growh pahs are inerlinked. The las wo panels of Figure (2) give a flavor of he degree of world-inegraion, mapping Foreign Direc Invesmen and expors. 11 Noiceably, laggard economies ouward foreign invesmens are increasing and heir high echnology expors have reached he level of advanced economies. To reassess his evidence, i is worh saring from he argumen of Bernard and Jones (1996a). Tha is, radable goods are highly differeniaed, as well as heir producion echnologies, and ha producive inpus endowmens vary a lo across counries. Alhough, he fac ha capial is flowing owards (and from) low income economies and ha fronierechnologies are geing diffused, lead o hink ha manufacuring is he perfec sage for cross-counry convergence. Passing now o he choice owards Lall s axonomy, his is moivaed by wo consideraions. Firs: as any sub-secoral aggregaion, Lall s one makes iner-secoral comparisons possible and, as already menioned, his fac drives o poenially nice policy implicaions. Second: i offers he possibiliy o esablish a 1 o 1 correspondence beween he employed classificaion and he Inernaional Sandard Indusrial Classificaion (i.e. ISIC) (Revision 1 See, for example, Masuyama (1992). 11 For a very up-daed sysemaic review of he effecs of Foreign Direc Invesmen on economic growh in low income counries, see Bruno and Campos (21). 5

6 2), which is he one followed by he Unied Naions Indusrial Developmen Organizaion (i.e.unido) for he collecion of sub-secoral manufacuring daa. 12 Table 2 repors he correspondence beween ISIC and Lall s classificaions. No casually, UNIDO daa consiue he basis for my empirical analysis. This represens a major advanage wih respec o oher classificaions, like Pavi (1984), ha, alhough effecive in disinguishing indusrial comparmens, presen huge overlaps beween heir caegories and ISIC s ones. To conclude, I wan o skech he main resuls of my analysis. In paricular, I found supporive evidence for absolue convergence in High Tech secors and Manufacuring as a whole, while echnological iniial condiions deermine he club convergence behavior of Resource Based and Medium Tech, while he ones on capial sock shape he clusering dynamics of Low Tech indusries. The main policy lesson ha can be rerieved is in line wih he one of Lall (1997), ha is: as high ech secors open he beer growh-equiy prospecs, wih he minimum effor, developing counries should concenrae more on his kind of producions. This is because, in high ech secors, even labor inensive aciviies, such as assembly, are more sable, skill-creaing and posiive exernaliy generaing han in radiional ones. The paper is organized as follows. The second par presens he economeric mehodology employed. Deails on empirical implemenaion and daa sources are horough he ex. The hird illusraes and discusses he resuls obained. Final commens and possible lines for fuure research conclude. 2 Mehodology 2.1 An Overview on Disribuion Dynamics and Daa The kernel densiy esimaor and he sochasic kernel are he wo building blocks of disribuion dynamics esimaion. The former is employed o esimae he densiy of a random variable and i can be hough as a refinemen of he hisogram. In paricular, while in he hisogram he frequency disribuion is calculaed for disjoin saes, wih he kernel esimaor he frequency disribuion is esimaed for a large number of overlapping 12 In paricular, Lall (2b) echnological axonomy was originally developed employing he Sandard Inernaional Trade Classificaion (i.e. SITC) (Revision 2). Thanks o Eurosa ables, which pu in in correspondence ISIC Revision 2 wih ISIC Revision 3, SITC Revision 2 wih SITC Revision 3 and, finally, SITC Revision 3 wih ISIC Revision 3, is hen possible o obain a 1 o 1 relaion beween UNIDO daa and Lall s manufacuring secors. 6

7 class inervals, which gives a much smooher appearance, resembling a probabiliy densiy funcion. The sochasic kernel maps, insead, he densiy of a random variable a one poin in ime ino he densiy in a subsequen period, where he densiy funcions have been calculaed hrough kernel densiy esimaors. In oher words, he sochasic kernel, which can be hough as a se of condiional densiies, describes he law of moion of a sequence of disribuions and i serves o rerieve he evoluion of he probabiliy disribuion of a random variable along ime, Quah (1993). As already menioned, his ool is very convenien for convergence analysis. In fac, i allows o disinguish wheher economies are converging overall or hey are clusering wihin clubs. My empirical analysis focuses on he evoluion along ime of labor produciviy disribuion and i employs wo ypes of sochasic kernel: 1. uncondiioned sochasic kernels 2. condiioned sochasic kernels The uncondiioned sochasic kernels give informaion on he likelihood ha an economy, saring from a given relaive posiion in he iniial period, will end up improving or worsening is relaive posiion in he final period + s. More echnically, uncondiioned sochasic kernels measure he ransiion probabiliies from a labor produciviy saus o anoher in a given ime span. Uncondiioned sochasic kernels are used here o deec polarizaion endencies and o assess, as i will be clarified soon, he absolue convergence hypohesis. Condiioned sochasic kernels are an exension of uncondiioned ones and hey allow o idenify he facors ha evenually lead o inra-disribuional changes. In fac, he effecs of condiioning are idenified by changes in shape and locaion of he sochasic kernel wih respec o he uncondiioned case. I will use condiioned sochasic kernels for assessing boh he condiional and club convergence hypoheses. More in deail, when disribuion dynamics is employed, any convergence predicion is discharged if he corresponding long-run labor produciviy disribuion (i.e. ergodic disribuion) is muli-peaked and relaively highly dispersed. So ha, in my empirical exercise, I sar wih analyzing he behavior of labor produciviy disribuion, as esimaed via uncondiioned sochasic kernels, in order o assess he absolue convergence predicion; hen, if he uncondiioned ergodic is muli-peaked, I pass o evaluae condiional conver- 7

8 gence, looking o he ime evoluion of he labor produciviy disribuion condiioned o seady-sae proxies; and, finally, if also his ergodic urns ou o be muli-modal, providing supporive evidence for he club convergence hypohesis, I assess wheher such a clusering dynamics can be ascribed o insufficien capial accumulaion (echnical upgrading) adding capial sock per worker (echnological proxy) o he se of seady sae condiioning facors. Thus, as his laer ergodic disribuion is likely o be single-peaked, i can be concluded ha is (previous) mulimodal shape was due o capial sock (echnology) iniial condiions. So ha, smoohing cross-counry differences in erms of capial sock (echnology) ensures labor produciviy equalizaion in he long run. For wha concerns he daa employed and heir sources, he variable of ineres is he log of manufacuring value added per worker in each counry and secor. In paricular, I racked he ime-evoluion of he relaive labor produciviy disribuion, ha is I normalized individual counries daa wih he ones of he leading economy. In his case, Unied Saes are he leader because hey exhibi he highes labor produciviy in all secors, along he whole period considered. In he spiri of Quah (1996a) and Desme and Fafchamps (26), his normalizaion is useful for removing some of he rend from he cross-secion and, hus, for avoiding degenerae long-run disribuions. 13 Finally, i is imporan o clarify ha secoral labor produciviy is expressed in 1996 inernaional dollars o allow inernaional and iner-emporal comparisons. Concerning he seady sae proxies, following Quah (1996a), 14 I ook he invesmen raes in boh physical and human capial and a developmen dummy, where he reference group is made by high-income economies. In he empirical implemenaion, such variables, dummy apar, are aken in naural logarihms and hey are normalized wih respec o US values. In assessing club convergence deerminans, I employed originally esimaed secoral capial sock and TFP series. 15 In paricular, capial sock per worker is normalized o Unied Saes and i is expressed in naural logarihms. The echnological variable, insead, is 13 I is worh noing ha a cross-counry average, insead of he leader, could have been used. My choice is moivaed on he basis of he echnological ransfer lieraure, according o which he dynamics of innovaion in he leader counry and imiaion in he laggard economies is a he hearh of boh growh and convergence processes. See wih his respec, he seminal conribuions of Gerschnkron (1954), Nelson and Phelps (1966), Pack and Wesphal (1986) and Hansson and Henrekson (1994). Moreover, i is ineresing o noe ha Caselli and Wilson (24) ackle his issue looking o embodied echnological change, ha is capial sock. 14 See Durlauf e al.(25) and Sala-i-Marin e al.(24) for up-o-dae discussions on he problem of (significan) growh deerminans. 15 See Inroducion and foonoe 8, for furher deails on capial sock and TFP esimaes. 8

9 modeled as an ineraced TFP gap (i.e. TFPgap). 16 More clearly, following Griffih e al.(24), TFPgap, calculaed as he difference beween leader s TFP and he one of any follower, is aken o proxy he poenial for echnological imiaion while secondary schooling aainmen raes, in logs and normalized wih respec o Unied Saes, are used as absorpion capabiliy proxy. 17 Turning o daa sources, labor produciviy were obained combining UNIDO Indusrial Saisics Daabase 24, a 3-digis of ISIC Code (Revision 2), World Bank Developmen Indicaors and he Penn World Tables (PWT 6.1). 18 Secoral invesmen raes in physical capial refer o Gross Fixed Capial Formaion share o manufacuring value added, aken again from UNIDO. To proxy human capial accumulaion raes in each counry, I use he average years of schooling in he populaion over age 15. This series, ogeher wih secondary schooling aainmen daa, comes from Barro and Lee (2) daa-se. Wih respec o human capial variables, hree aspecs mus be clarified. Firs, he Barro and Lee (2) daa are regisered a five-years inervals. To overcome his difficuly, I inerpolae he available daa implicily assuming ha he beween-observed values lie on a sraigh line. Second, my preference owards populaion over age 15, insead of 25, which is also available, is due o he fac ha working age in developing counries can be quie low, as documened by Bennell (1996). Finally, he choice of secondary schooling as absorpive capabiliy proxy is moivaed on he basis of Gemmell (1996), which shows ha for middle income counries, which are well represened in my sample, secondary educaion maers more han primary and eriary ones. 2.2 Uncondiioned sochasic kernels In his secion I provide a echnical illusraion of he mehodology employed o esimae uncondiioned ransiion probabiliies, which are used o invesigae he absolue convergence hypohesis. 16 For furher clarificaions see Rogers(23). 17 For seminal conribuions on absorpive capaciies, see Baumol (1986) and Cohen and Levinhal (1989). 18 From UNIDO I colleced disaggregaed daa on workers and on manufacuring value added in Local Currency Uni (LCU); from World Bank Developmen Indicaors (WDI), GDP daa in LCU; finally, from Penn World Tables (PWT 6.1), GDP daa expressed in Purchasing Power Pariy. Afer having calculaed secoral value added in manufacuring as percenages of GDP, using World Bank and UNIDO daa in LCU, I combined such percenages figures wih WDI and PWT6.1. My preferred measure of real value added in manufacuring is based on Penn World Tables Real GDP Chain Index (RGDPCH). This is because RGDPCH does no suffer from he so-called Laspeyres fixed-based problem and, hen, i is he mos appropriae measure when iner-emporal comparisons are a issue, Summers and Heson (1991). 9

10 Secoral convergence endencies are inferred analysing he dynamic behaviour of crosscounry disribuion of log relaive labour produciviy. 19 Individual counry i labour produciviy, in secor j, a ime is called y i, where I omied he secor index for noaional convenience (i.e. y i = log(y ij /Y USj )). Cross counry, secor specific, labour produciviy disribuion, a ime, is denoed as f Y (y ), where Y indicaes he corresponding random variable. I assume ha year-o-year changes in he disribuion of labour produciviy can be represened by an homogeneous Markow process, in such a way ha, : 1. f Y+1 Y (y +1 y ) = f Y+1 Y (y +1 y, y, y,...) 2. f Y+1 Y (y +1 y ) = f Y Y (y y ) The firs propery guaranees ha only previous period income disribuion impacs on nex period one (i.e. hisory does no maer). The homogeneiy assumpion in 2 ensures ha he ransiion probabiliies do no vary wih he ime. Alhough quie resricive, boh hypoheses are necessary for esimaing long run ransiion probabiliies given he available daa. Condiional densiy funcions, f Y+1 Y (y +1 y ), represen he cornersone of disribuion dynamics convergence analysis. This kind of disribuion, in fac, encodes informaion abou individual economies passages over ime. Thus, i sheds ligh on boh inradisribuion dynamics and exernal shapes, making inference abou convergence endencies possible. For example, observing condiional densiy mappings, is i possible o know wheher poor counries are caching-up wih heir richer counerpars, wheher rich counries are sill enriching, wheher counries are converging overall or are clusering wihin clubs. The empirical esimaion of condiional densiies is handled by non-parameric echniques. As for is definiion, in he empirical implemenaion, he condiional disribuion is obained simply dividing he join disribuion by he marginal disribuion. Formally: f Y+1 Y (y +1 y ) = f Y +1,Y (y +1, y ) f Y (y ) (1) The join disribuion of (Y +1, Y ) can be esimaed non paramerically using a bivariae sochasic kernel, while he marginal disribuion of Y is obained by numerical inegraion 19 Please noe ha in wha follows relaive labour produciviy and labour produciviy are used inerchangeably. 1

11 of he join disribuion. Finally, he condiional disribuion is simply obained by dividing one o he oher, afer appropriae discreizaion of he join suppor. 2 Long run endencies owards convergence are encoded by he ergodic disribuion. This is he saionary disribuion of labor produciviy, which will be approached in he long run should cerain echnical condiions hold. 21 In paricular, if he ergodic disribuion is unimodal and has a low variance, hen long run cross-counry convergence can be claimed. Formally, he ergodic is he disribuion f which solves he following funcional equaion: f(y +1 ) = + f Y+1 Y (y +1 y )f(y )dy (2) In order o compue he ergodic disribuion, i is necessary o make he suppor of Y discree. I is imporan o noe ha, following Desme and Fafchamps (26), I employ such a discreizaion only for calculaing he ergodic. The sandard approach would have been, insead, o make he Y suppor discree also for compuing he join and marginal disribuions in Equaion (1), as in Quah (1996a). Bu, as shown by Desme and Fafchamps (26), his leads o ransiion marices which are usually quie coarse, due o he fac ha he smoohing properies of he kernel esimaors are no exploied. Geing now ino ergodic calculaion s deails, he suppor of Y is discreized in a se of N equally large inervals, where inerval h is denoed as Ω h. 22 Then, he probabiliies of ransiion from one inerval o anoher are calculaed. Formally, he probabiliy of ransiion from he inerval Ω h o anoher Ω k, in one ime period, is denoed as: α kh = P r(y +1 Ω k y Ω h ) A his poin, i is useful o adop a compac marix noaion. Hence, he ergodic disribuion is he vecor p ha solves he following sysem of equaions: p = Ap (I A)p = 2 Bivariae sochasic kernel esimaion is performed using he command kdens2 in STATA 8.2. Marginal, condiional and ergodic disribuions are calculaed in Malab. All programs are available from he auhor upon reques. 21 See Sockey, Lucas and Presco (1989); Luenberger (1979). 22 To avoid crude ergodic calculaions, i is necessary o work wih a sufficienly high N. My calculaions have been done for N=5. Using N=2 and N=5 do no aler any conclusions bu i has he disadvanage of slowing down compuer s rouines. Also he program for ergodic calculaion is available upon reques. 11

12 where each componen of he vecor p represens he probabiliy of Y assuming a value comprised in a given Ω and A is he marix of ransiion probabiliies α kh. Since each column of marix A is a condiional densiy and, hen, is elemens sum o 1; A does no have full rank and, by consequence, he sysem does no have a unique soluion. To find a unique soluion i is sandard o simply drop one row of A (o make is columns linearly independen) and hen add he resricion ha he enries of vecor p sum o Then, marix A is rewrien as B: 1 α α 1N... 1 α ii... B= α N,1... α N,N The modified sysem is hen: Bp = b where he vecor b, for he consrain added, has all enries equal o excep he las one, which is equal o 1. A his poin, he unique ergodic disribuion, p, can be easily found invering B: p = B b 2.3 Condiioned sochasic kernels and condiioning echniques This par oulines he condiioning echnique I used o assess condiional convergence and club convergence deerminans. Under he condiional convergence hypohesis, cross-counry produciviy equalizaion can no be found in he original relaive labor produciviy disribuion, f Y, bu in he condiioned one, f Y X, where X denoes seady sae proxies. Then, he objec of ineres are he ransiion probabiliies of he par of labor produciviy no explained by he seady sae proxies (i.e. he residuals, ɛ). Employing he former noaion, such ransiion 23 This consrain mus hold for he definiion of probabiliy. 12

13 probabiliies are formally wrien as: f Y+1 Y,X (y +1 y, x ) (3) Exploiing Chamberlain(1984) resuls, he par of labor produciviy orhogonal o auxiliary variables is compued as Ordinary Leas Squares (OLS) residuals of he projecion of labor produciviy growh on each of he seady sae proxies. 24 Such calculaion involves hree seps: 1. esimaing he par of counries relaive produciviy growh rae explained by condiioning seady sae variables; 2. finding he iniial level of relaive labor produciviy explained by condiioning seady sae variables ; 3. combining he previous resuls o find he level of relaive labor produciviy unexplained by he auxiliary variables (i.e. orhogonal o seady sae proxies). Call g i he growh rae of y i (i.e. log relaive produciviy in counry i, secor j a ime ), where again he secor index is omied for noaional convenience. Name ĝ i he par of g i explained seady sae proxies, which are: invesmen rae in boh physical and human capial, indicaed as r i and h i, and he dummy developmen, ddev. Finally, he par of labor produciviy orhogonal o seady sae proxies, which is he objec of ineres, is called ɛ i. Sep 1. is implemened regressing g i on a wo sided disribued lag of condiioning variables and saving he fied values. For each seady sae proxies one of such regressions is run. Then, cumulaing he fied values, by counry and secor, he par of counries relaive produciviy growh rae explained by condiioning seady sae variables, ĝ i, is obained. Noe ha in empirical work, muli-sided regressions are employed o handle endogeneiy issues, which are represened in his specific case by he likely bidirecional causaliy beween labor produciviy growh rae and seady sae proxies. This echnique, inroduced by Sims (1972), has been exensively used by Quah, who noed ha jus 2 leads and 2 24 Quoing Quah(1996a), Chamberlain(1984) finds ha: he projecion of growh on invesmen, no allowing for individual effecs, is precisely he bes linear predicor and, hus, correcly gives residuals ha are he componens unexplained by (or, more correcly, orhogonal o) invesmen. 13

14 lags are sufficien o clear he esimaed growh rae from feedback effecs, Quah (1996a). Sep 2. is aken running a pooled OLS regression of y i on ime averages of seady sae proxies (i.e. r i and h i ) and he esimaed growh rae (i.e.ĝ i ). For each secor, he coefficiens ha solves he following minimizaion problem are used o pin down he iniial level of labor produciviy explained by seady sae variables, ŷ i : 25 min β1,β 2,β 3 [y i (β 1 r i + β 2 h i + β 3 ddev + ĝ i )] 2 i In fac, hanks o he esimaed coefficiens, βs, he iniial level of log relaive labor produciviy explained by condiioning variables can be expressed as: ŷ i = β 1 r i + β 2 h i + β 3 ddev Then, adding he growh raes of sep 1, he level of relaive labor produciviy explained by seady sae variable is calculaed as: ŷ i = ŷ i + ĝ i Finally, ɛ i, which represens he produciviy level no accouned for (or condiional o) seady sae proxies is simply found subracing from acual he esimaed relaive labor produciviy: ɛ i = y i ŷ i Once counry and secor specific ɛ i series have been calculaed, he empirical implemenaion for assessing condiional convergence is he same as absolue (or uncondiional) convergence. In paricular, bivariae sochasic kernel densiies fi cross-counry, secor specific, disribuion of relaive produciviy orhogonal o seady sae variables, which I denoe as fê+1,ê( ɛ +1, ɛ ). By numerical inegraion of he join disribuion, he marginal densiy fê ( ɛ ) is obained. Finally, he ransiion probabiliies of Equaion(3) are found dividing he join disribuion, fê+1,ê ( ɛ +1, ɛ ), by he marginal disribuion, fê ( ɛ ). Long-run disribuion of relaive labor produciviy condiioned o seady sae variables is rerieved from he ergodic disribuion of random variable ɛ. Such a disribuion is 25 As Quah(1996a) explains, his echnique explois he cross secion variaion of condiioning variables o compue he iniial value of produciviy explained seady sae proxies. 14

15 calculaed as for he uncondiional case (previous secion). Turning now o club convergence analysis, i should be inuiive ha he condiioning scheme described so far can be easily exended o deermine he relaive srengh of club convergence inner drivers. In paricular, when club convergence hypohesis holds, he objec of ineres becomes he dynamics of labor produciviy disribuion condiioned o boh seady sae proxies and club convergence driving forces, namely capial and echnological iniial condiions. Formally, he following ransiion probabiliies have o be compued: f Y+1 Y,X,Z (y +1 y, x, z ) (4) where he variable Z represens eiher iniial capial sock or iniial echnological level, which has been proxied by TFPgap and school aainmen rae. To rerieve he relaive srengh of capial sock (or echnology) as club convergence deerminan, relaive labor produciviy orhogonal o boh seady sae proxies and capial sock (or echnology) iniial level mus be calculaed. This is done implemening he hree seps previously described, aking ino consideraion capial sock (or echnology) as exra condiioning variable. By he same okens as before, he densiy in Equaion (4) and he ergodic disribuions are compued. 3 Resuls 3.1 Inerpreing resuls I now provide he fundamenal ools for inferring convergence endencies from Figures 3 o 16, which consiue he firs se of resuls of my analysis. Such diagrams, mapping uncondiioned and condiioned sochasic kernels allow o invesigae all he convergence hypoheses under scruiny. Panels (a) and (b) of he aforemenioned figures describe eigh-years horizon evoluion of labor produciviy disribuions and hey are used o esablish medium run endencies o convergence. 26 More precisely, he firs ype of graphs shows a ridimenional plo of 26 I also calculaed ransiions over one year horizon. Alhough he resuls do no change significanly over such a shorer period, mobiliy is slighly lower and emerging paerns seem more difficul o race. 15

16 ransiion probabiliies; he second, mapping he level curves, represens he sochasic kernels in jus wo dimensions. In boh diagrams, he floor axis, marked as Period and Period + 8, measure he log of relaive produciviy in differen imes. To make graph inerpreaion easier, Table 3 repors Period and Period + 8 relaive labor produciviy values in percenage erms wih respec o he Unied Saes (i.e. he leader). From such graphs, convergence endencies in he medium run can be claimed if he kernel roaes clockwise and accumulaes on a single ridge parallel o Period axis. Tha is, relaive produciviy levels become equal across counries, regardless of economies iniial posiion. Persisence is found when he mass concenraes along he 45 degrees line. So, counries iniial and he final posiions coincide. Improvemens, wih respec o he iniial posiion, are deeced if he mass piles above he 45 degrees line; by he same oken, worsening occur when he mass lies below he diagonal. Club convergence is signalled by disinc peaks along he diagonal. As explained in he mehodological secion, long run endencies, should he curren dynamics persis, are assessed hrough ergodic disribuions, as in Panels (c). 27 I is worh recalling ha, in general erms, supporive evidence for any alernaive convergence hypohesis is found when he corresponden ergodic disribuion is unimodal and has a low variance. 3.2 Discussing resuls The general resuls of my analysis can be inferred from he evidence provided by Figures 3 o 16 and by Table 4, which repor he suppors and some basic descripive saisics for he ergodic disribuions, esimaed under he relevan alernaive convergence hypoheses. In paricular, my findings are consisen wih he hypohesis of club convergence in Resource Based (i.e. RB), Low Technology (i.e. LT) and Medium Technology (i.e. MT) secors and wih he one of absolue convergence in High Techonology (i.e. HT) and Manufacuring as a whole (i.e. TOT). More precisely, echnological and capial iniial condiions seem o be he inner drivers of clusering behavior in, respecively, RB and LT while he dynamics of MT indusries is less clear-cu. Then, excepion made for MT, observing he couner plos 27 I migh be of some ineres o noe ha he shape of he ergodic disribuion is likely o be anicipaed by sandard mobiliy analysis. 16

17 of he relevan graphs, 28 i could be appreciaed ha cross-counry produciviy differences end o shrink over ime. Tha is, poor counries are likely o improve heir relaive posiion (i.e. mass piled above he 45 degrees line), while rich are more likely o ge worse (i.e. mass below he same diagonal). Moreover, looking o he ergodics of he same figures and o Table 4, i could be seen ha he relevan long run disribuions are single-peaked and exhibi he lowes dispersion (i.e. coefficien of variaion). 29 Geing ino more deails now, i is ineresing o discuss firs wo facs ha seem quie well esablished in he lieraure: ha manufacuring as a whole converges in absolue erms, while is sub-secors do no, and he absence of supporive evidence for he condiional convergence hypohesis. Wih he firs respec, his resul is consisen wih he findings of Dollar and Wolff (1988)(1993) and Dal Bianco (21), for wha concerns manufacuring secors, and wih he ones of Bernard and Jones (1996a), wih respec o disaggregaed GDP (i.e. agriculure, mining, indusry and services). In paricular, hese works show ha converging endencies in he aggregae secor are differen from he ones prevailing in is sub-secors. More specifically, he aggregae converges faser han is pars, because he cross-secion dispersion is lower for he aggregae han for he pars. Looking o Table 4, i could be seen ha his kind of explanaion holds also in he presen case. Moreover, i is worh noing ha he similar paerns of HT and TOT can no be auomaically inerpreed as if he echnology inense comparmens were leading he whole indusrial performance. In fac, if on he one hand i is rue ha, in he period considered, HT has grown faser han all oher secors (i.e. 8% vs 4% on average); on he oher, HT accouns for only he 12% of oal manufacuring producion. Passing now o condiional convergence, from Figure 19 and Table 4, i could be seen ha when seady saes differences are aken ino accoun, he locaion of he ergodic disribuions of RB, LT and MT shif owards higher values, because some counries overake he leader (i.e. log relaive produciviy greaer han zero), bu such disribuions are no characerized by unimodaliy and low dispersion. This finding, consisenly wih he ones of Quah(1996a) and Bandyopadhyay (26), shows ha srucural facors, alhough relevan for enhancing he level of labor produciviy in each counry and, hus, cross-counry 28 The relevan graphs are Panel(b) of Figures: 6, RB, Club convergence echnology; 9, LT, Club convergence capial; 15 and 16, HT and TOT absolue convergence. 29 I prefer he coefficien of variaion (i.e. sandard deviaion divided by he mean) o he sandard deviaion because he former indicaor overcomes he problems relaed o a changing mean. 17

18 average, as prediced by he sandard neoclassical growh model, are unable o affec he dynamics of he enire disribuion, as according o he heory of povery raps, Azariadis and Sachurski (24). A his poin I wan o show ha my resuls on labor produciviy club convergence are consisen wih he prediced dynamics of capial accumulaion and echnological upgrading. In he spiri of Johnson (25), Figure 17 and Figure 18 show he ergodic disribuions of relaive physical capial sock per worker and he ineraced TFPgap, while Table 5 synheically repors he main lines for inerpreing his evidence. In paricular, looking o HT and overall manufacuring, i could be easily seen ha boh capial and echnology are prediced o converge in he long run, so ha he club convergence hypohesis can be discharged. On he conrary, considering LT, as he ergodic disribuion of capial sock is bimodal and he one of TFPgap is no, one migh expec ha capial sock would be a he roo of club convergence in his secor. Or, pu in oher erms, ha cross-counry convergence will be reached only if capial sock differences will be evened ou. Similar reasoning applies o echnological clubs in RB and MT, alhough i is worh anicipaing ha MT secors deserve some furher clarificaions. For a deailed discussion of my resuls, I mainly refer o Figures 19 and 2 and, again, o Table 4. These graphs repor cross-counry inra-secoral and iner-secoral long-run scenarios. From he economic policy poin of view, his exercise appears paricularly valuable. In fac, comparing he ergodics resuling from alernaive convergence predicions, wihin he same secor, i is possible o rerieve some indicaions on he secor-specific long-run growh and inequaliy perspecives. The iner-secoral comparisons, insead, allows o evaluae which secor is relaively mos promising, again in erms of he levels and he dispersion of living sandards. I sar wih commening he behavior of each echnological secor, as in Figure 19. Regarding RB, my finding is ha dissimilar echnological iniial condiions are prevening from overall convergence. In paricular, for how I consruced he echnological proxy, backwardness migh be due eiher o a limied-in-scope imiaive poenial or o insufficien absorpive capabiliies. Concerning he firs explanaion, alhough i is very difficul o say which echnology is poenially relevan for a specific secor, in he sense pu forward by Baumol (1986), Lall (21) suggess o consider he focal aciviies of Mulinaional Corporaions (i.e. MNCs). As shown by UNCTAD (22),(23),(25), in he pas 3 years, op 5 world MNCs has been invesing in High Technology secors while op 5 de- 18

19 veloping counries s MNCs, 33 of whom from Souh Eas Asia, operae in LT and service secors. Thus, he limied invesmen in radiional secors, which accoun for an average 77% of laggards economies manufacuring value added, migh have lowered he poenial for echnological upgrading. However, i mus also be noed ha, according o UNCTAD (25), he degree of mechanizaion in RB secors has sensibly increased in he las 5 years. So ha, echnological backwardness migh be due o insufficien capaciies of undersanding, employing and exploiing new echnologies. Finally, looking o Table 4, i could be seen ha he prediced mean income associaed wih smooh echnological iniial condiions lies beween he one linked o condiional convergence and he one of club capial convergence. 3 The firs fac migh be explained recalling he imporance of a relaively wide echnological gap, which is prediced o shrink once echnology is diffused; he second one, insead, seems o sugges ha he accumulaion of (rough) capial will no ensure sensible economic growh nor cross-counry equiy. Turning now o LT, i is eviden ha labor produciviy gap will be closed in he long-run hrough capial accumulaion and no hrough echnological cach-up. This resul, in line wih he esablished lieraure, is hardly surprising. In fac, i mus be recognized ha such indusries employ maure echnologies, already spread around he world, and hey are characerized by low knowledge barriers, in he sense ha he absorpive capaciies necessary for echnological progress are limied and, hen, imiaive aciviies are easier, Lall (2b), (21), Caree e al.(2) and Dal Bianco (21). Furher confirmaive evidence on his poin is found when looking o he very low prediced mean income associaed o club echnological convergence. Wih some cauion, i migh be said he growh poenial associaed o innovaive and imiaive effors in hese indusries is quie limied when compared o he opporuniies opened by increasing he scale of producion. As already menioned, he resuls concerning MT indusries are quie ricky. On he one hand, he long run behavior of club convergence deerminans repored in Figures 17 and 18 lead o he conclusion ha he lack of cross-counry convergence is due o echnological iniial condiions bu, on he oher, Figure 19, Panel (c), clearly shows ha also capial sock plays a role. Moreover, one could be emped o asser ha my resuls are consisen wih he condiional convergence predicion. I hink his is no he case. In fac, looking o Table 4, i could be seen ha he cross-secion dispersion increases wih respec 3 Noe, wih some indulgence, ha wih he expression club capial convergence ( club echnological convergence ) I refer o he labor produciviy disribuions (i.e. condiioned sochasic kernels) condiioned by seady sae variables and capial sock (echnological) iniial condiions. 19

20 o he absolue convergence case. So ha, he boom line of he analysis is ha neiher srucural facors, nor capial or echnological differences alone can accoun for club convergence dynamics. This migh be due, and his is he explanaion I propose, o MT indusries peculiar feaures. Narraive evidence suggess ha hey have complex echnical requiremens and hey demand for large-scale producion. Thus, o fill he produciviy gap developing counries have o properly develop dynamic advanages (i.e. echnology and skill) as well as srenghen credi markes, in order o reach he criical hreshold level of capial sock per worker. Concerning HT, as menioned, my analysis suppors he absolue convergence hypohesis. Tha is, in he long run counries will converge o he same produciviy level, regardless heir srucural and iniial condiions. 31 This resul sounds quie surprising. In fac, due o he high echnological conen of such producions, echnical and capial deficiencies in developing counries migh have been expeced. However, a leas wo inerpreaions can be proposed. The firs one sars from echnological cach-up lieraure predicions and i is suppored by he esablished lieraure. In words: foreign capial inflows, ogeher wih argeed educaional and indusrial policies, have provided good iniial condiions in HT indusries and have effecively rescued laggard economies, making labor produciviy convergence possible. In fac, if, on he one hand convergence sudies on manufacuring secors in developed economies find ha labor produciviy and TFP convergence has been weaker in High Tech indusries han in radiional secors, Caree e al.(2) and Scarpea and Tressel(24), on he oher, when developing counries are included in he cross-secion, sandard parameric analysis shows ha high-ech comparmens exhibi he fases converge speed, Dal Bianco (21). However, his poin should be invesigaed furher. Narraive evidence, in fac, suggess ha, in he period considered, he majoriy of HT producion in low income counries was due o he delocalizaion sraegies of Wesern firms, UNCTAD (25). Thus, developing counries migh have aced jus as oudoor plans, assembling foreign inermediaes, and, ypically, re-exporing hem, Singh (26). As solving his problemaic issue goes beyond he scope of he presen work, his is lef for fuure research. The second one relaes, insead, o sample selecion problems. The presen analysis is 31 To confirm he robusness of uncondiional convergence predicion, I have used as counerfacuals HT labor produciviy disribuions condiioned o seady sae proxies alone and ogeher wih capial or echnological iniial condiions. As hese ergodics are muli-peaked, he uncondiional convergence predicion is validaed. To save space I did no repor hese resuls, which are available upon reques. 2

21 based on a cross-secion of jus 28 counries, among which old and new Asian Tigers are well represened. As clearly demonsraed by Lall (1997), hese economies are very producive in HT indusries, so ha his resul may lack of represenaiveness and i migh be biased owards convergence. Alhough, i mus be said ha his evidence could be consisen wih fuure scenarios. According o Sala-i-Marin (26), in fac, world s income per capia differences have shrunk in he las 5 years because of he specacular growh raes of iniially poor counries. 32 Wha prevens from hinking ha new igers will roar? Turning now o iner-secoral comparisons, observing Figure 2, Panel (a), i could be said for sure ha HT is he comparmen ha pays more wih he he minimum effor, in erms of boh growh and equiy. Panel (e), insead, shows ha when cross-counry equiy is a issue or, pu in oher erms, under he relevan convergence hypohesis, RB secors are he ones ha open he beer prospecs: highes mean income and lowes dispersion. Bu he precondiion o be me, in his case, is o smooh ou seady sae and echnological differences. Finally, when comparing he scenarios which ensure he highes inra-secoral mean, as in Panel (f), i could be seen ha, again, HT indusries ensure he beer combinaion in erms of long-run labor produciviy and cross-secional dispersion. Alhough poenial biased by sample selecion, my analysis suppors he hypohesis of Lall (1997), ha is HT secors ensure he relaively higher produciviy gains. So ha, from he policy perspecive, i seems advisable ha insead of relying on saic comparaive advanages associaed o LT secors, low income economies concenrae heir indusrial policy in he search of dynamic comparaive advanages, as he ones of opened by HT producion. This is because, in high ech secors, even labor inensive aciviies, such as assembly, are more sable, skill-creaing and posiive exernaliy generaing han in radiional ones. 4 Conclusions In his paper I have assessed hrough an unified disribuion dynamics framework he hypoheses of absolue, condiional and club convergence, among 28 indusrialized and emerging economies, in differen manufacuring sub-secors, during he period My analysis has shown ha, excepion made for High Technology and Manufacuring as a 32 Sala-i-Marin employs disribuion analysis o show ha China s and India s growh experiences caused he increase of world s living sandards and he decrease of world income inequaliy. 21