CONVERGENCE IN OECD COUNTRIES: TECHNICAL CHANGE, EFFICIENCY AND PRODUCTIVITY *

Transcription

1 CONVERGENCE IN OECD COUNTRIES: TECHNICAL CHANGE, EFFICIENCY AND PRODUCTIVITY * Jaquín Mauds, Jsé Manuel Pasr and Lrenz Serran * WP-EC 98-2 Crrespndence J. Mauds: Universia de València. Faculad de Ciencias Ecnómicas. Dep. de Análisis Ecnómic. Campus de ls Naranjs, s/n VALENCIA. Tel: / Fax: / jaquin.mauds@uv.es Edir: Insiu Valencian de Invesigacines Ecnómicas, S.A. Firs Ediin Ocber 998. ISBN: Depósi Legal: V IVIE wrking-papers ffer in advance he resuls f ecnmic research under wa in rder encurage a discussin prcess befre sending hem scienific jurnals fr heir final publicain. * The auhrs acknwledge he cmmens f an annmus referee and he financial suppr f he CICYT PB * J. Mauds: Universia de València e Insiu Valencian de Invesigacines Ecnómicas; J.M. Pasr L. Serran: Universia de València..

2 CONVERGENCE IN OECD COUNTRIES: TECHNICAL CHANGE, EFFICIENCY AND PRODUCTIVITY Jaquín Mauds, Jsé Manuel Pasr and Lrenz Serran R E S U M E N El rabaj iene cm bjeiv básic analizar la cnribución de las disinas fuenes del crecimien a la cnvergencia en prducividad del rabaj en ls países de la OCDE en el perid Más cncreamene, uilizand ds aprximacines frnera disinas (índices de prducividad de Malmquis un enfque de frnera escásica), se disingue la cnribución del cambi écnic de ls cambis de eficiencia a la cnvergencia en prducividad del rabaj. Ls resulads benids cnradicen ls benids en rs rabajs que uilizan aprximacines n frnera a la medición de la prducividad, rechazándse la exisencia de cnvergencia ecnlógica, dad que el prgres écnic ha sid mar en ls países cn mar prducividad del rabaj. Palabras Clave: Cnvergencia, cambi écnic, eficiencia, índice Malmquis de prducividad. A B S T R A C T The aim f his sud is analze labr prducivi cnvergence in he cunries f he OECD ver he perid A nn-parameric frnier apprach is used calculae he Malmquis prducivi index. B breaking i dwn, he cnribuin he grwh f labr prducivi f echnical prgress, f changes in efficienc, and f he accumulain f inpus per wrker are quanified. Unlike her sudies, he resuls bained shw ha echnical change has wrked agains labr prducivi cnvergence, since i has alwas been greaer in he cunries wih higher labr prducivi. Kewrds: Cnvergence, echnical change, efficienc, Malmquis prducivi index. 2

3 . INTRODUCTION The sud f cnvergence beween cunries in erms f per capia incme and labr prducivi has given rise he develpmen f a ver wide-ranging lieraure (see Barr and Sala-i-Marin (995) fr a surve f he empirical evidence). In paricular, he exisence f cnvergence, hugh a a mderae rae, has been prfusel dcumened in he case f he cunries f he OECD, his quesin being a he cener f he debae n ecnmic grwh. Wih he aim f undersanding beer he frces underling his prcess f cnvergence, a par f he lieraure has been deved analzing he hphesis f cachingup in he levels f al facr prducivi (TFP) amng he cunries f he OECD. This cach-up hphesis claims ha pr cunries end grw faser han rich cunries hrugh he inernainal diffusin f knwledge and echnlg. In he sudies in which his hphesis is esed, TFP grwh is due bh diffusin f echnlg and innvain. Hwever, hese sudies ha relae cnvergence TFP usuall bain he laer b means f Törnqvis indices r her prxies such as grwh accuning which, in he wrds f Grsskpf (993), ignre efficienc. The underling prblem is ha hese mehds, valid nl in he case f echnical efficienc, and allcaive efficienc, lead biassed esimaes f echnical prgress in he presence f inefficienc. Furhermre, i is n pssible break dwn he grwh f TFP, hus miing he fac ha par f his grwh is due gains in efficienc and n nl echnical prgress. There are varius sudies ha, in rder alleviae hese prblems, have incrpraed explicil he exisence f inefficienc in he analsis f he grwh f prducivi and f Dwrick and Nguen (989), using aggregaed daa, ffer evidence ha cnvergence in TFP (residuall defined) has ssemaicall been he main surce f cnvergence in labr prducivi during he perid Dllar and Wlff (994) dcumened he exisence f TFP cnvergence in indusrial secrs during he perid , and aribued i he greaes par f cnvergence in labr prducivi levels. Hwever, in his case he phenmenn is n ssemaic, as n he cnrar, he prcess was especiall inense during he perid , becming mre mderae frm 973 nwards. Fr heir par, Bernard and Jnes (996a and b) highligh he exisence f cnvergence in TFP during he perid , alhugh wih excepins such as he manufacuring secr. 3

4 echnical prgress in he inernainal sphere b he use f frnier echniques 2. The resuls bained in all hese sudies demnsrae he exisence f subsanial levels f inefficienc ha var widel amng cunries and ver ime, indicaing ha he missin f inefficienc frm he analsis ma subsaniall affec he validi f he resuls 3. In general, his secnd pe f lieraure has cncenraed n he grwh f TFP and is breakdwn in echnical prgress and changes in efficienc wihu enering in he analsis f cnvergence. Fecher and Perelman (992) cnsider he unequal level f efficienc be ne f he pssible deermining variables f he grwh f TFP and bain a ssemaic negaive crrelain wihin each secr fr he perid as a whle, alhugh he evidence is less rbus bh a cunr level and acrss differen perids. Perelman (995) aemped explain he causes f he grwh f TFP and f is cmpnens (echnical prgress and efficienc) b means f regressins in which unequal efficienc was included geher wih her explanar variables, likewise finding evidence favrable he hphesis f echnlgical caching-up. Even in hese w cases he cnribuin f TFP cnvergence in levels f labr prducivi was sill n analzed. Likewise, alhugh Färe e al. (994) analze prducivi gains and heir breakdwn in efficienc and echnical prgress, he d n shw heir effec n cnvergence in labr prducivi. T dae, here are nl w published papers ha analze he imprance f efficienc change and echnical change n he cnvergence f labr prducivi. Taskin and Zaim (997) analze he caching-up hphesis fr a grup f cunries f he OECD shwing ha echnical change is higher in rich cunries while pr cunries gave a higher efficienc change. Mauds e al. (998) uilize als he Malmquis prducivi index in he Spanish regins baining ha echnical prgress has plaed agains cnvergence in labr prducivi since richer regins have experienced larger raes f echnical prgress. In his cnex, he aim f his sud is analze labr prducivi cnvergence in he cunries f he OECD ver he perid disinguishing he cnribuin f he differen surces -echnical prgress, changes in efficienc and accumulain f inpus per wrker- b 2 Thus, Färe e al. (994) sudied he grwh f prducivi a aggregae level in 7 cunries f he OECD during he perid b means f Malmquis prducivi indices; Fecher and Perelman (992) used he schasic frnier apprach evaluae he grwh f TFP and analse is causes wih secr daa relaing a sample f 3 cunries f he OECD during he perid Finall, Perelman (995) esimaed he grwh f TFP during he perid in a cnex f 8 indusrial secrs and cunries f he OECD using bh he schasic frnier apprach and he nn-parameric DEA apprach. 3 Färe e al. (994) and Fecher and Perelman (992) cmpare heir resuls he TFP grwh bained hrugh he sandard prx f grwh accuning frmulaed b means f Törnqvis's index number. In bh cases here are significan differences, hus cnfirming he limiain placed n he esimain f TFP b ignring he exisence f inefficienc. 4

5 means f frnier appraches. Fr his purpse we use bh he schasic apprach and he Malmquis prducivi index, bained b means f nn-parameric mehds f linear prgramming. Wih he laer apprach, i will be pssible aribue he accumulain f inpus per wrker and he grwh f TFP he par ha crrespnds hem, disinguishing wihin TFP he pars crrespnding echnical change (due innvain) and efficienc change (due diffusin f echnlg). The srucure f he paper is as fllws. Secin 2 ses u he imprance f disinguishing he cnceps f echnical prgress and efficienc as well as he implicains f adping a paricular apprach he measuremen f prducivi. Secin 3 is deved describing he sample used and he resuls bained in erms f efficienc, echnical change and prducivi. Secin 4 analses he imprance ha gains in efficienc, echnical prgress and al facr prducivi have had in he prcess f labr prducivi cnvergence. Finall, Secin 5 cnains he cnclusins f he sud. 2. EFFICIENCY, TECHNICAL CHANGE AND PRODUCTIVITY: TECHNIQUES OF MEASUREMENT The radiinal apprach he analsis f prducivi b means f nn-frnier mdels, which includes bh grwh accuning apprach (Slw, 957; Denisn, 972; ec.), and he index number apprach 4 (indices f Divisia, Törnqvis, ec.), incrprae he implied assumpin ha all individuals are efficien, s ha he grwh f prducivi is inerpreed as mvemen f he frnier funcin (echnical change). Hwever, in he presence f inefficienc he esimain f echnical prgress wuld be biased. Furhermre, even in he absence f echnical inefficienc, he accuning esimain f he grwh f TFP wuld be a biased esimain if he paricipains used in is calculain are n hse ha minimize cs, i.e. here is allcaive inefficienc 5. On he her hand, frnier appraches he analsis f prducivi ake explicil in accun he pssible inefficien behavir f he unis analzed, measuring as inefficienc he penial increase in he bserved value f prducin, his being measured agains he maximum echnicall achievable value defined b frnier f prducin r echnlg. In his 4 See amng hers Bauml (986), Bauml and Wlff (988), Abramviz (986, 990, & 994), Bernard and Jnes (996a & b), Dllar and Wlff (994), Wlff (99). 5 See a mre deailed expsiin in Grsskpf (993). 5

6 sud we use his frnier apprach and cmpare he resuls f parameric mehds (schasic frnier apprach, SFA) wih nn-parameric mehds (Malmquis index based n DEA). Ne ha he frnier is esimaed frm bserved daa and because f his i cann be cnsidered as he rue frnier bu as he bes pracice. In his sense, he efficienc measures shuld be inerpreed as relaive efficienc regard he bes pracice 6. a) Parameric mehds: Schasic frnier apprach, (SFA) The schasic frnier apprach was inrduced simulaneusl b Aigner e al. (977) and Meeusen e al. (977). This apprach mdifies he sandard prducin funcin b assuming ha inefficienc frms par f he errr erm. This cmpund errr erm herefre includes an inefficienc cmpnen and a purel randm cmpnen ha capures he effec f variables ha are bend he cnrl f he prducin uni being analsed (weaher, bad luck, ec.). Thus, he schasic frnier apprach has as is principal advanage he fac ha i allws us islae he influence f facrs her han efficienc. Hwever, is disadvanages are ha i is a parameric apprach (i is necessar impse a priri a paricular funcinal frm) and ha i is necessar specif disribuinal assumpins in rder separae he w cmpnens f he errr erm. Being aware f he limiains ha i presens, we will aemp alleviae hem in w was: a) b adping he ms flexible funcinal frm pssible; and b) b esing he sensiivi f he resuls agains differen disribuinal assumpins fr he inefficienc erm. The basic schasic prducin frnier mdel psis ha he bserved prducin f an ecnm deviaes frm he frnier as a cnsequence f randm flucuains (v i ) and f inefficienc (u i ). Tha is sa, [ ] LnY i =LnF(X i, β) exp.(v i -u i ) i=,,n; =,,T where Y i is he bserved prducin and X i is he inpu vecr f cunr i a ime, β is he vecr f parameers be esimaed, and LnF(X i, β) is he lgarihm f pimum upu. The randm errr erm v i is assumed be independen and idenicall disribued, and he erm u i 6 There is n cnsensus n which is he bes frnier apprach because all echniques have heir wn advanages and disadvanages. The sraeg used in his paper is explain briefl he w ms cmmnl used alhugh fr he aim f he paper ( es he caching-up hphesis differenciaing he effec f efficienc change frm he echnical prgress) he schasic frnier apprach has as a main disadvanage ha des n allw us esimae echnical change b cunries. 6

7 is assumed be disribued independenl f v i. The indicar f efficienc, bained as he rai f pimum upu bserved upu, is bained as exp(u i ) 7. Since inefficiencies can nl decrease prducin belw he frnier, i is necessar specif asmmerical disribuins fr he inefficienc erm. Usuall, i is assumed ha v i is disribued as a nrmal wih zer average and variance σ 2 v, and u i as a half-nrmal, runcaed nrmal, expnenial, ec. On he assumpin ha bh cmpnens f he errr erm are disribued independenl, he frnier funcin can be esimaed b maximum likelihd, inefficienc being esimaed n he basis f he residuals f he regressin. Mre specificall, individual esimains f inefficienc can be bained b using he disribuin f he inefficienc erm cndiined he esimain f he cmpund errr erm (Greene, 993). Empiricall, he differen disribuinal assumpins fr he inefficienc erm ma lead differen resuls, a leas in erms f he inefficiencies esimaed. Fr his reasn i is impran analze he sensiivi f he resuls under differen alernaive assumpins wih he aim f chsing he assumpin ha bes fis he daa. Alhugh in his apprach he esimain f echnical prgress can be dne easil b inrducing ime dummies r a rend, i has he disadvanage ha echnical prgress, calculaed n he basis f he parameers esimaed, is he same fr all cunries. b) Nn-parameric mehds: Malmquis prducivi index and DEA The Malmquis prducivi index allws changes in prducivi be brken dwn in changes in efficienc and echnical change. Furhermre, unlike he SFA, i ffers a differen rae f echnical change fr each individual, which is mre adequae fr ne f he purpses f his sud, he analsis f echnical change b cunries. Als, if i is esimaed using a nn-parameric frnier mdel (daa envelpmen analsis, DEA), which is he ms cmmnl used apprach, i will n be necessar impse an funcinal frm n he daa nr make disribuinal assumpins fr he inefficienc erm, unlike he SFA. 7 Values higher han uni impl ha he cunr is echnicall inefficien; he higher he efficienc index he greaer he inefficienc. 7

8 The main disadvanage f his apprach is ha he esimain f inefficienc ma shw an upward bias, capuring as inefficienc he influence f her facrs, such as errrs in daa measuremen, bad luck, weaher, ec. The Malmquis index uses he nin f disance funcin, s is calculain requires prir esimain f he crrespnding frnier. In his sud we use he deerminis nnparameric frnier mehdlg (DEA). T illusrae he calculain f he Malmquis index 8, le us assume ha he ransfrmain funcin ha describes he echnlg in each perid is: [ 2 ] F ={(x, ): x can prduce } =,,T where =(,, N ) R N is he vecr f upus and x =(x,,x M ) R M denes he vecr f inpus bh crrespnding perid. Fllwing Shephard (970) r Caves e al. (982) echnlg can be represened alernaivel b means f he disance funcin: [ 3 ] D (x, ) =inf{ϑ, : (x, /ϑ, ) F }=[sup{ϑ, : (x, ϑ, ) F }] - This funcin is defined as he reciprcal f he maximum expansin which i is necessar subjec he vecr f upus f perid ( ), given he level f inpus (x ), s ha he bservain sands a he frnier f perid. This funcin characerizes cmpleel he echnlg in such a wa ha D (x, ) if and nl if (x, ) F. Furhermre, D (x, ) = if and nl if he bservain sands a he limis f he frnier, which ccurs when he bservain is efficien in he sense used b Farrell (957). Figure illusraes he abve cnceps fr a siuain wih a single upu and a single inpu. The bservain (x, ) sands belw he echnlgical frnier f perid, which means ha i is n echnlgicall efficien. The disance funcin wuld be calculaed as he inverse f he greaer increase in 8 See Malmquis (953). 8

9 upu, given he inpu, in such a wa ha he expanded upu reaches he echnlgical frnier. In he graph, he maximum upu wuld be represened b, = /ϑ,. The value f he disance funcin f he bservain in, wih respec he echnlg in, ϑ,, wuld be represened b OA/OB= /, =ϑ,. Farrell's upu-riened measuremen f echnical efficienc measures hw much upu culd increase, given he inpus. In figure i can be bserved ha Farrell's measuremen f echnical efficienc fr he bservain (x, ) is OB/OA=, / =/ϑ,. Ne ha s far he disance funcin has been defined fr a single perid. Specificall, we have cmpared bservains f ne perid wih he echnlg f he same perid. T define he Malmquis index i is necessar define disance funcins wih respec echnlgies f differen perids. [ 4 ] D (x, ) =inf{ϑ, : (x, /ϑ, ) F } In he abve expressin, he disance funcin D (x, ) measures he maximum prprinal increase in upus, given he inpus, make he bservain f perid, (x, ), feasible in perid. In he siuain represened in figure, he bservain (x, ) is uside he feasible se represened b he echnlg in, s he value f he disance funcin will be OE/OC= /, =ϑ,. In a similar wa, i is pssible define he disance funcin f an bservain in, (x, ), make i feasible in relain a echnlg curren in, D (x, ). Ne ha when cmparing bservains f ne perid wih echnlgies f differen perids, he disance funcin ma be higher han uni. In paricular D (x, ) and D (x, ) ma be higher han uni if here has been echnical prgress and echnical regressin respecivel 9. On he basis f he abve cnceps, he Malmquis prducivi index based n upus analze prducive change beween perids and, aking he echnlg f perid as reference, is defined as 0 : [ 5 ] M (,,x, ) x D = D ( x, ) ( x, ) 9 Ne ha in he siuain represened in he graph, D (x, )>, indicaing ha here has been echnical prgress. 0 See Caves e al. (982). 9

10 )LJXUH 0DOPTXLVW RXWSXWEDVHG SURGXFWLYLW\ LQGH[ F, F E (x, ) F, D, C, B A (x, ) x x x M > indicaes ha he prducivi f perid is higher han ha f perid, since he expansin necessar in he upus f perid fr he bservain be feasible in is lwer han ha applicable he upus f perid. On he her hand, M < indicaes ha prducivi has descended beween perids and. Alernaivel i is pssible define he Malmquis index b aking he echnlg f perid : M x, = D [ 6 ] (,,x ) D ( x, ) ( x, ) In all he abve definiins nl w perids ( and ) have been cnsidered, and he definiins have been made aking as reference he echnlg f perid r. Hwever, when we wish analze he prducive change f a lnger ime series, he use f a fixed echnlg ma cause prblems he furher we ge frm he base ear. Als (Mrsen, 96), he chice f base ear is n neural in he resuls. T aemp slve hese prblems w In his case he inerpreain is similar. M > indicaes ha he prducivi f perid is higher han ha f perid, since he expansin necessar in he upus f he perid fr he bservain be feasible in is lwer han ha applicable he upus f perid. 0

11 mehdlgies are ffered. The firs cnsiss f calculaing w indices based n pairs f cnsecuive ears which ake as base he echnlg f he w perids and and calculaing he gemeric mean f he w, hus allwing he echnlg f reference change, minimizing he prblems caused b he change (Grifell and Lvell, 997). Anher prcedure, used b Berg e al. (992) slve he abve-menined prblems is cnsider w frniers f reference crrespnding he iniial and final ears, and ake he gemeric mean f he w Malmquis indices. In his sud, because he ime series used is ver lng (25 ears) we will fr he reasns given abve use he firs f he alernaives: [ 7 ] ( ) ( ) ( ) ( ) ( ) 2,, x D, x D, x D, x D =,x, x M Re-wriing he abve expressin i is pssible break dwn he Malmquis index in he caching-up effec and echnical change r mvemen f he frnier 2 : [ 8 ] ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2,, x D, x D, x D, x D, x D, x D =,x, x M The caching-up effec r change in relaive efficienc beween perids and is represened b he firs rai, which will be higher han uni if here has been an increase in efficienc. Similarl, he gemeric mean f he w rais beween brackes measures he change r mvemen f echnlg beween perids and. The abve breakdwn can again be illusraed using figure. [ 9] ( ) 2 2,,, = = OB OD OC OF OB OA OF OE OD OA OA OB OF OE OC OE OA OB OF OE x x M If he bservain has n varied is efficienc beween and, he firs erm will be equal and he prducive change experienced beween he w perids (M ) will be explained nl b he mvemen f he frnier. On he her hand, if he secnd erm is (he frnier has n mved), he changes in prducivi esimaed b M will be explained nl b 2 See Berg e al. (992) and Grifell e al. (997).

12 he changes in efficienc f firms in he w perids (caching-up). In her cases, he prducive changes refleced in M will be a mixure f changes in efficienc and mvemens f he frnier. The Malmquis index can be calculaed in several was (Caves e al. 982). In his sud, as we have said befre, we calculae he Malmquis index using a nn-parameric echnique f linear prgramming. Le us suppse ha in each perid here exis k=,...,k cunries which use n=,...,n inpus (x nk ) prduce m=,...,m upus ( mk ). The calculain f he Malmquis index fr a cunr j requires calculain f fur pes f disance funcin; D (x, ), D (x, ), D (x, ) and D (x, ). Making use f he prper whereb he disance f upu is equal he reciprcal f he Farrell upu-riened echnical efficienc measuremen (Färe and Lvell, 978) we have ha fr D (x, ): [ 0 ] [ D ( x, )] s.. K = Maxϑ, λ ϑ m =,..., M k = K λ x x n =,..., N k = k k k j mk nk j nj mj j, j λ 0 k =,..., K The calculain f D (x, ) is bained in a similar wa bu subsiuing fr. Finall, he calculain f he firs f he disances referred w differen mmens in ime D (x, ) is dne in he fllwing wa 3 : [ ] [ D ( x, )] s.. K = Maxϑ, λ ϑ m =,..., M k = K λ x x n =,..., N k = k k k j mk nk j nj mj j, j λ 0 k =,..., K 3 In which cnsan reurns scale have been impsed. This impsiin is sufficien guaranee ha he sluin f he prblem f pimisain exiss when using bservains f differen perids f ime. Wih variable reurns scale he sluin is n guaraneed. 2

13 Ne ha he bservain (x, ) is cmpared wih he echnlg in, frmed b he se f bservains exising in, s i ma ccur ha he bservain is n feasible, given he echnlg curren in (F ) and he sluin is greaer han uni. The secnd, D (x, ), is dne in he same wa bu subsiuing fr and fr. 3. DATA AND RESULTS The sample used fr he esimain f he frnier prducin funcin cnsiss f he cunries f he OECD 4 in he perid using he Summers and Hesn daabase (Penn Wrld Table, Mark 5.6) 5. The variables fr each cunr are: ) aggregaed upu measured b real Grss Dmesic Prduc (GDP) (Y), expressed in inernainal prices; 2) aggregaed labr inpu (L) measured b al emplmen, cmpued frm real GDP per wrker; and 3) al capial sck (K) calculaed frm he nn-residenial capial per wrker. Table cnains he annual grwh raes f GDP, capial and emplmen in he differen cunries f he OECD. Several sub-perids can be disinguished: he cmplee perid and he sub-perids f grwh (965-73), crisis (973-85) and recver (985-90). The ms usanding feaure is he fac ha Japan is he cunr ha experienced he highes grwh rae in GDP as a resul f he inense rae f capial accumulain. On he her hand, emplmen grew a a rae similar he average fr cunries f he OECD, which mus cnsequenl be ranslaed in a subsanial grwh in he capial-labr rai. Table 2 shws he average levels f efficienc esimaed fr he perid and fr he hree sub-perids f he sample using he nn-parameric apprach described earlier. One usanding feaure is he fac ha he USA sands a he frnier hrughu he perid, while cunries like Japan, Finland and Greece presen high levels f inefficienc 6. 4 The sample used cnsiss f Canada, USA, Japan, Ausria, Belgium, Denmark, Finland, France, German, Greece, Iceland, Ireland, Ial, Luxemburg, Nrwa, Prugal, Spain, Sweden, Swizerland, Turke, UK, Ausralia and New Zealand. 5 This is an updaed versin f Summers and Hesn (99). 6 Technical efficienc is defined as he rai f he real upu he maximum upu ha culd be prduced wih he inpus used. In his sense, measure efficienc accurael i is necessar crrec inpus b he degree f uilizain f capial, his infrmain is n available. 3

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15 Table 2: Average echnical efficienc (DEA) Canada USA Japan Ausria Belgium Denmark Finland France German Greece Iceland Ireland Ial Luxemburg Nrwa Prugal Spain Sweden Swizerland Turke UK Ausralia New Zealand Mean Ne: Values higher han uni impl ha he cunr is echnicall inefficien; he higher he index he greaer he inefficienc.. The grwh raes f TFP as well as hse f is w cmpnens (echnical change and changes in efficienc) are refleced in able 3. The cmparisn b sub-perids shws he exisence f impran differences ver ime. Thus, alhugh in he sub-perids f grwh (965-73) and crisis (973-85) lsses in prducivi ccurred, in he sub-perid prducivi grew a an annual rae f.29%. Furhermre, he cnribuin f efficienc (caching-up) and f echnical prgress (mvemen f he frnier) was n unifrm ver ime. Whereas in he sub-perid f crisis he lsses in prducivi were due he fall in efficienc, in he sub-perid i is he lack f echnical prgress ha is respnsible fr he fall in prducivi in spie f he gains in efficienc experienced. In he las sub-perid, bh gains in efficienc and a lesser exen echnical prgress were respnsible fr he gains in prducivi. 5

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17 B cunries, impran differences can again be bserved. Thus, in he paricular case f Japan, he lsses in prducivi unil 985 were due bh lsses f efficienc and he absence f echnical prgress, alhugh prducivi grew in he las sub-perid as a cnsequence, abve all, f he impran gains in efficienc. On he her hand, he USA's gains in TFP in he sub-perid were due exclusivel echnical prgress. We wuld als highligh he behavir f Canada, Finland, Ial, Nrwa, Swizerland and Ausralia since in all he sub-perids he experienced gains in prducivi. On he her hand, Denmark and Iceland suffered lsses f prducivi in all he sub-perids. The resuls bained are similar hse f Färe e al. (994) wh bserved imprvemens in efficienc (caching-up) in he case f he Japanese ecnm in he perid Hwever, unlike his las sud, her cunries f he sample experienced imprvemens in efficienc greaer han hse f he Japanese ecnm. The reasns fr his discrepanc ma be diverse: firsl, he differen perid f ime analsed; and secndl, he differen sample f cunries cnsidered. Neverheless, in spie f he discrepancies, he resuls are in agreemen as regards he high levels f inefficienc f he Japanese ecnm. Since he grwh rae f labr prducivi can be brken dwn as he sum f he grwh rae f efficienc, he rae f echnical prgress and he cnribuin f he increase in he inpus used per wrker 7, i is f ineres analze he surces f grwh f labr prducivi. Table 4 shws he grwh rae f labr prducivi and f is hree cmpnens fr he cunries f he OECD and fr he differen sub-perids f ime cnsidered. 7 In principle we can evaluae he cnribuin f inpus grwh frm fr he echnlg curren in each f hese perids, and bain an apprpriae esimae b means f a gemeric mean f he w. Fllwing he represenain f figure : \ W \ W W W W \ W W \ W 2& 2) = 2% 2' Thus, grwh ( / ) can be brken dwn muliplicaivel in he grwh f TFP (Malmquis index) and he cnribuin f he accumulain f inpus: \ \ 0 ([ \ [ \ ) W W W W W \ 2( W W W W = W R W W W = W \ \ \ 2$ In he same wa he grwh f labr prducivi is brken dwn muliplicaivel in he Malmquis index and he cnribuin f he accumulain f inpus per wrker.

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19 The analsis b sub-perids shws ha fr he average f he OECD, he fases rae f grwh f labr prducivi ccurred in he perid f grwh (965-73), due he inense rae f capial accumulain (4.24%), he cnribuins f efficienc (0.43%) and echnical prgress (-0.78%) being negligible. On he her hand, in he perid he average gains in efficienc (0.73%) explain arund 30% f he grwh in labr prducivi (2.40%). Cncenraing nce again n he USA and Japan, he resuls enable us bserve he greaes grwh f labr prducivi in Japan (4.5%), his subsanial grwh being a cnsequence f he high prcess f capializain f he Japanese ecnm (is cnribuin being 5.34%), he negaive influence f efficienc and echnical prgress being negligible. Neverheless, in he sub-perid alms a hird f Japan's labr prducivi grwh (3.68%) was due gains in efficienc (.6%). On he her hand, he grwh f labr prducivi in he USA (.70%) was much lwer as a resul f he reduced grwh f he capial-labr rai (0.96%). The resuls f able 4 als enable us bserve he imprance f explicil cnsidering efficienc as a surce f prducivi grwh. Thus, in cunries like Greece, Ireland, Prugal, Spain, Turke and he UK, he gains in efficienc explain a high percenage f gains in labr prducivi in he perid , which is illusraive f he bias remarked upn in nnfrnier appraches he analsis f prducivi. In rder es he rbusness f he resuls bained b means f he nn-parameric apprach, we esimaed a ranslgarihmic prducin funcin f a schasic naure under hree alernaive disribuinal assumpins (half-nrmal, nrmal-runcaed and expnenial). Mre specificall, he ranslg prducin funcin be esimaed adps he fllwing specificain: [ 2 ] Ln Y i = β β 0 L Ln L β LK i β Ln L i K Ln K Ln K i i (/2) β 90 =65 LL λ TE Ln L v i 2 i (/2) β u i KK Ln K 2 i where TE are emprar effecs ha capure he effec f echnical prgress 8, and u i and v i are inefficienc and he errr erm, respecivel. 8 The measuremen f echnical prgress hrugh emprar effecs is mre flexible han he inrducin f a rend, as i allws us bain a differen rae f echnical prgress a each mmen in ime. 9

20 Table 5 cnains he esimain f he prducin funcin under he hree alernaive disribuinal assumpins fr he inefficienc erm: Half-nrmal (HN), runcaed-nrmal (TN), and expnenial (EXP). Ne ha he parameers esimaed are similar irrespecive f he disribuinal assumpin adped and ha bh he squares f he variables capial and labr and heir crssed prduc are highl significan, which indicaes he rejecin f he Cbb-Duglas specificain adped in her sudies (Fecher and Perelman, 992). Table 5: Translg schasic prducin funcin: parameer esimaes Half-nrmal (HN) Truncaed (TN) Expnenial (EXP) Cnsan ( ) (807.00) ( ) LnK (8.00) (2.862) (24.42) LnL (23.076) (3.07) (34.99) 0.5LnK² (-7.380) (-3.856) (-5.657) 0.5LnL² (-8.036) (-.825) (-2.28) LnKLnL (8.223) (4.525) (5.730) Lg-lik σ 2 V σ 2 u σ u /σ V (0.23) (3.582) µ/σ u.7 (0.904) Thea (6.22) Ne: a) -suden in parenheses. b)time dummies have been inrduced in he esimain. 20

21 Table 6 cnains he average levels f he efficienc indicar crrespnding he runcaed-nrmal mdel 9. The cmparisn f he resuls wih hse ha appear in able 2 shws ha he average inefficienc f he sample is lwer in he schasic apprach, a resul ha ma be due he fac ha he nn-parameric esimain is upwardl biased because i capures randm facrs as inefficienc 20. Neverheless, he evluin f efficienc ver ime (figure 2) is similar in all he appraches. Table 6: Average efficienc (SFA-TN) Canada USA Japan Ausria Belgium Denmark Finland France German Greece Iceland Ireland Ial Luxemburg Nrwa Prugal Spain Sweden Swizerland Turke UK Ausralia New Zealand Mean Ne: Values higher han uni impl ha he cunr is echnicall inefficien; he higher he index he greaer he inefficienc. 9 The resuls are ver similar in he her mdels. Thus, fr he average f he perid , he crrelain beween he efficienc indices f mdels HN and TN is 0.97, beween HN and EXP i is 0.96, beween HN and DEA i is 0.73, beween TN and EXP i is 0.99, beween TN and DEA i is 0.64, and beween EXP and DEA i is I is difficul assess a priri he effec f his biass n he surces f cnvergence f he nex secin. The bes wuld be use a nn-parameric schasic apprach, if such echnique is n reliable a he mmen. 2

22 The evluin f efficienc ver ime shws ha alhugh he USA was ne f he ms efficien cunries f he sample in he perid , i has graduall ls he leadership unil i sands a levels f inefficienc similar he Eurpean average, and belw Canada. Japan cninues be ne f he leas efficien cunries, alhugh i has reduced differences wih he her cunries afer he il crisis shck f The resuls in erms f he cumulaive effec f echnical prgress are ver similar in all he mehds as can be appreciaed in figure 3. Thus, whereas unil he mid-970s here was echnical regress, frm hen nwards he exisence f echnical prgress can be clearl appreciaed SOURCES OF CONVERGENCE The use f echniques ha incrprae in he analsis f grwh he exisence f inefficienc in he uilizain f he facrs f prducin has enabled us break dwn in an apprpriae wa he ecnmic grwh f he cunries f he OECD. Thus, we have verified ha, while in sme cases he predminan surce f grwh was he accumulain f facrs f prducin, in hers i was TFP. Als, we have been able disinguish which par f he grwh f TFP was due mvemen f he echnlgical frnier (echnical change) and which par was due evluin in relain he echnlgical frnier (change in efficienc). This breakdwn makes i pssible analze in deail he prcess f cnvergence in labr prducivi experienced b he cunries f he OECD during he perid Earlier sudies have highlighed he ssemaic cnribuin f TFP he cnvergence f hese cunries, aribuing i he effec f echnical prgress. (Dwrick and Nguen, 989; Dllar and Wlff, 994; Abramviz, 994; Bernard and Jnes, 996 a & b; amng hers). Hwever, hese sudies d n cnsider he exisence f inefficienc as ne f he cmpnens f TFP. 2 The differen behaviur f efficienc wih regard DEA ma be due he fac ha in SFA i is necessar impse a cmmn rae f echnical prgress. 22 Observe ha he resuls are similar hse bained fr he perid b Färe e al. (994), wh shw he exisence f echnical prgress. 22

23 Figure 2: Efficienc in OECD cunries: ,45,40,35,30,25,20,5,0,05,00 SFA-HN SFA-TN SFA-EXP DEA Figure 3: Technical change in OECD cunries: ,04,00 0,96 0,92 0,88 0,84 0,80 0,76 SFA-HN SFA-TN SFA-EXP DEA 23

24 The analsis f he influence ha each f he surces f grwh (echnical change, caching-up in efficienc and increase in inpus per wrker) ma have had n cnvergence in he OECD is he subjec f his secin. In he case f abslue cnvergence i ineress us knw wheher he grwh f labr prducivi due each f hese facrs has been greaer in he cunries wih lwer iniial labr prducivi, in which case his facr will have cnribued cnvergence; lwer in he cunries wih lwer iniial labr prducivi, in which case i will have generaed divergence; r has n cnnecin wih he iniial siuain, in which case i will n have an effec n cnvergence. In each perid we can esimae b means f rdinar leas squares (OLS) he regressin f he average grwh f labr prducivi during he perid, and f each f is cmpnens, n he lgarihm f he iniial labr prducivi. The effec n cnvergence will depend n he sign f he parameer ha accmpanies he lg f iniial prducivi. A negaive sign indicaes cnvergence and a psiive ne indicaes divergence. Als, i is eas see ha he al cnvergence parameer is equal he sum f he parameers crrespnding he surces f grwh, s we can break dwn labr prducivi cnvergence in he cnribuins due echnical prgress, changes in efficienc, and he uilizain f mre inpus per wrker. In paricular, we can esimae he relaive cnribuin f each facr cnvergence beween ears 0 and T b aking lgarihmic differences beween he w and b means f he fllwing regressins: di [ 3 ] = c b lg i ui T [ 4 ] dei = ce be lg i uei T [ 5 ] dtci = ctc btc lg i utci T [ 6 ] dtfpi = ctfp btfp lg i utfpi T 24

25 dii [7] = ci bi lg i uii T where lg i0, he lgarihm f he iniial labr prducivi level, is alwas he nl repressr. The dependen variable is he annual rae f grwh f labr prducivi in equain [3], he cnribuin ha grwh f gains in efficienc (E) in equain [4], he average cnribuin f echnical prgress (TC) in equain [5], he average cnribuin f TFP grwh in equain [6], and he average cnribuin f he accumulain f inpus per wrker in equain [7]. Furhermre, he fllwing relainship is esablished amng hese parameers: [ 8 ] E = E E E = E E ( 7&, 7)3, Table 7 ffers he resuls fr he perid and fr he sub-perids , and In clumn we can bserve cnvergence in he levels f labr prducivi ver he whle perid. Is cumulaive magniude (-.77%) and is ime paern, agree wih he resuls habiuall ffered b he lieraure (see Barr and Sala-i-Marin, 995). Thus, cnvergence was mre inense in he perid (-2.85%) han during he crisis f (-.04%) and recvered again in he final sub-perid (-3.03%). Of greaer ineres is he analsis f he breakdwn f his prcess f cnvergence in erms f he differen surces f grwh. Clumn 2 ffers he effec n cnvergence induced b he change in efficienc. As can be bserved, he cumulaive effec ver he perid as a whle (-0.09%) is negligible and is n saisicall significan. Smehing similar ccurs in he sub-perid , als wih a negligible effec (-0.22%). Hwever, in he perid he change in efficienc was indeed significan and was an impran surce f divergence (0.97%). During he perid f inernainal ecnmic crisis he cunries wih higher levels f labr prducivi experienced gains in efficienc in relaive erms, demnsraing a greaer capaci fr adjusmen he varius shcks suffered b he indusrialized cunries. On he her hand, during he perid efficienc was a significan surce f cnvergence (-2.87%), due he fac ha i is nw he cunries wih lwes labr prducivi ha imprve heir efficienc in relaive erms. In shr, he cnribuin f efficienc labr prducivi cnvergence is characerized b is variabili, since in sme perids i generaes divergence and in hers cnvergence, and b is ever greaer magniude. 25

26 Table 7: Cnvergence in labr prducivi and is surces. Surces f cnvergence Perid () (2) (3) (4)=(2)(3) (5) Tal Efficienc Technical TFP Inpus per prgress wrker (K/L) (-7.74) (-0.34) (4.65) (2.29) (-6.7) [0.72] [0.0] [0.5] [0.20] [0.68] (-5.58) (-0.67) (4.0) (2.49) (-5.44) [0.60] [0.02] [0.44] [0.23] [0.59] (-2.63) (.97) (4.2) (2.94) (-6.4) [0.25] [0.6] [0.46] [0.29] [0.66] (-3.70) (-3.89) (3.09) (-.37) (-2.43) [0.39] [0.42] [0.3] [0.08] [0.22] Ne: -suden in parenheses. R 2 in squared brackes. Clumn : Average annual rae f abslue cnvergence f labr prducivi accrding equain (). Clumns 2-5: Cnribuin cnvergence f each f he cmpnens f grwh accrding equains (3)-(7). The effec f echnical change is shwn in clumn 3. The resuls indicae ha echnical change was a ssemaic and significan surce f divergence. Bh in he perid as a whle and in each f he sub-perids cnsidered, he cunries wih highes iniial prducivi experienced greaer relaive echnical prgress. Thus, he effec ver he perid as a whle was.0%, being smewha higher in he sub-perids f expansin (.78%) and (.64%), and less during he crisis (0.65%). This resul seems reasnable if i is cnsidered ha i is he ms develped cunries ha make he innvains. This means ha he are he firs adp hem, and als ha echnical change is adaped he characerisics f his pe f ecnm. Fr all hese reasns echnical change benefis in he shr erm especiall he mre develped cunries 23. Clumn 4 shws he resuls crrespnding TFP. Given ha he grwh f TFP is 23 Taskin and Zaim (997) bain he same resul. 26

27 he aggregain f he change in efficienc and f echnical change, is cnribuin cnvergence is equivalen he ne effec f bh. Cnsequenl is cumulaive effec in he perid was divergen (0.92%) due echnical prgress, cnradicing he evidence ffered b earlier sudies (Dwrick and Nguen, 989; Dllar and Wlff, 994; Bernard and Jnes, 996b; Wlff, 99; ec.). The same hing happens in he sub-perid (.55%) fr idenical reasns. During he sub-perid i cninued generae divergence (.62%) since he effecs f he change in efficienc and f echnical prgress reinfrced each her in his sense. Hwever, during he las sub-perid TFP appeared generae a sligh cnvergence, alhugh his resul is n significan. This is because he cnvergence induced b he behavir f efficienc is parl ffse b he divergence due echnical prgress. Finall, he effec f he accumulain f inpus per wrker, which culd be assciaed wih he pical ne-classical mechanism f cnvergence, can be appreciaed in clumn 5. This is a ssemaic and significan surce f cnvergence bh in he perid as a whle (-2.69%) and in each f he sub-perids: (-4.40%); (-2.66%) and (-.80%). Thus, he accumulain f facrs f prducin was greaer in he cunries wih lwer iniial levels f labr prducivi and as a resul he laer has ended cnverge in he OECD. Hwever, he resuls shw ha is cnribuin is becming less and less. I is nw pssible lk mre clsel a he evluin f labr prducivi in he OECD. Thus, he magniude f cnvergence in he sub-perid is similar ha f he sub-perid Hwever, he siuains are ver differen. In he firs case i is due he inense cnvergence effec f he accumulain f facrs, in he secnd i is mre he effec f change in efficienc, wih a greaer relaive apprach he echnlgical frnier b he less develped cunries f he OECD, han f he ever-weaker influence f facr accumulain. Als f ne is he divergen effec caused b echnical change. This phenmenn, geher wih he prer cunries apparen lesser flexibili agains shcks refleced b he daa n efficienc during he sub-perid , ma explain in large measure he slwness f cnvergence. Since grwh is cnsubsanial wih he prgressive mvemen f he echnlgical frnier i can be cnsidered ha divergence is linked grwh due he ver naure f he laer. Thus, lng erm grwh cann be achieved b means f imprvemens in efficienc, bu nl b means f echnical change. The resuls bained have enabled us break dwn he cnribuin labr prducivi cnvergence f he differen surces f grwh, amng hem change in efficienc, alhugh he evluin f he inequaliies f efficienc beween cunries remains be analsed. Wih his aim, figure 4 shws he evluin f he sandard deviain f efficienc ver he whle perid. Hwever, his prcess f cnvergence was n unifrm, as perids f 27

28 cnvergence (inense unil he earl 970s and in he lae 980s) c-exised wih perids f divergence r lack f cnvergence. 5. CONCLUSIONS The sudies ha have analzed he prcess f cnvergence in he cunries f he OECD have shwn he imprance f he assimilain and diffusin f echnlg as a mechanism f labr prducivi cnvergence. Thus, sudies such as ha f Dwrick and Nguen (989) shw ha he prcess f echnlgical caching-up has cnribued labr prducivi cnvergence in he cunries f he OECD, is cnribuin being even higher han capial inensi in he perid The sudies ha have analsed he imprance f echnlgical cnvergence are generall based n he sud f TFP, his being esimaed b means f nn-frnier appraches (grwh accuning r index numbers). Hwever, he prblem presened b his apprach he measuremen f TFP is ha i bains biased esimaes f echnical prgress in he presence f inefficienc. Cnsequenl, echnical prgress cann be idenified wih gains in TFP in he presence f inefficienc. In his cnex he aim f his sud has been analze he imprance f efficienc change (diffusin) and echnical change (innvain) in he prcess f labr prducivi cnvergence bserved in he cunries f he OECD, using fr his purpse w frnier appraches he measuremen f prducivi. The resuls bained shw he exisence f subsanial levels f inefficienc in he cunries f he OECD, alhugh here was a reducin f hese levels in he perid analsed. The cmparisn f levels f efficienc beween cunries shws he exisence f subsanial inequaliies, Japan being he ms inefficien cunr in he sample, well abve he Eurpean average, he USA and Canada. 28

29 0,20 Figure 4: Sigma cnvergence in efficienc in OECD cunries: (Sardard deviain f lg) 0,8 0,6 0,4 0,2 0,0 0,08 SFA-HN SFA-TN SFA-EXP DEA The resuls are cnrar hse bained in earlier sudies ha d n cnsider he exisence f inefficienc in heir analsis. Thus, far frm here being a prcess f echnlgical caching-up, echnical change wrked agains labr prducivi cnvergence in all he subperids cnsidered, since echnical prgress has alwas been greaer in he richer cunries. Thus, he resuls sugges ha cunries wih lw iniial labr prducivi levels cach up a a faser rae and cunries wih relaivel high labr prducivi levels benefi frm echnlgical prgress. Neverheless, he breakdwn f gains in prducivi in gains in efficienc and echnical prgress shws ha, in he sub-perid , efficienc was an impran mechanism f labr prducivi cnvergence, is cnribuin being even mre impran han he accumulain f capial (capial inensi). Thus, he resuls bained cnradic hse f her sudies ha shw he greaer gains in TFP b he prer cunries as favring labr prducivi cnvergence. On he cnrar, he resuls bained in his sud shw ha i is he rich cunries ha have experienced greaes grwh in TFP (paricularl hrugh greaer echnical prgress), cnsequenl acing as a mechanism f divergence. In cnclusin, far frm here having been a mechanism f 29

30 cnagin b means f echnlg ransfer, he main mechanism f cnvergence has been he greaer rae f capial accumulain f he prer cunries. As a final cnclusin, i is impran remark ha in he lng erm ecnmic grwh is pssible nl if here exis innvars ha shif he frnier f echnlg alhugh efficienc gains (caching up) can be an impran surce f grwh in he shr erm. 30

31 REFERENCES Abramviz, Mses. (986). Caching Up, Frging Ahead, and Falling Behind, Jurnal f Ecnmic Hisr, 46, pp Abramviz, Mses (990). The Cach-up Facr in Pswar Ecnmic Grwh, Ecnmic Enquir 28(), -8. Abramviz, Mses (994). Cach-up and Cnvergence in he Pswar Grwh Bm and Afer, in Cnvergence f Prducivi, Crss-Nainal Sudies and Hisrical Evidence, 86-25, Edied b Bauml, William J., Nelsn, Richard, R. and Wlff, Edward N, Oxfrd Universi Press. Aigner, A., Lvell, C.A.K. and P. Schmid (977). Frmulain and Esimain f Schasic Frnier Prducin Funcin Mdels, Jurnal f Ecnmerics 86, Barr, R.J., N. and X. Sala-i-Marin (995). Ecnmic Grwh, McGraw-Hill. New Yrk. Bauml, William (986). Prducivi Grwh, Cnvergence, and Welfare: Wha he Lng Run Daa Shw, American Ecnmic Review 76(5), December, Bauml, William and Wlff, Edward (988). Prducivi Grwh, Cnvergence and Welfare: Repl, American Ecnmic Review 78(5), December, Bauml, William J., Nelsn, Richard, R. and Wlff, Edward N. (994). The Cnvergence f Prducivi, Is Significance, and Is Varied Cnnains, in Cnvergence f Prducivi, Crss-Nainal Sudies and Hisrical Evidence, 4-9, Edied b Bauml, William J., Nelsn, Richard, R. and Wlff, Edward N, Oxfrd Universi Press. Berg, A.N., F.R. Førsund and E.S. Jansen (992). Malmquis indices f prducivi grwh during he deregulain f Nrwegian Banking , Scandinavian Jurnal f Ecnmics 94, Bernard, Andrew B. and Jnes, Charles I. (996a). Technlg and Cnvergence, The Ecnmic Jurnal 06, Bernard, Andrew B. and Jnes, Charles I. (996b). Prducivi Acrss Indusries and Cunries: Time Series Ther and Evidence, The Review f Ecnmics and Saisics, Caves, D.W., L.R. Chrisensen and W.E. Diewer (982). The Ecnmic Ther f Index Numbers and he Measuremen f Inpu, Oupu and Prducivi. Ecnmerica 50, Denisn, E.F.(972). Classificain f Surces f Grwh, Review f Incme and Wealh 8, -25. Dllar, David and Wlff, Edward N. (994). Capial Inensi and TFP Cnvergence b Indusr in Manufacuring, ", in Cnvergence f Prducivi, Crss-Nainal Sudies and Hisrical Evidence, pp , Edied b Bauml, William J., Nelsn, Richard, R. and Wlff, Edward N, Oxfrd Universi Press. Dwrick, S. and Nguen, D. (989). OECD Cmparaive Ecnmic Grwh : Cach-up and Cnvergence, American Ecnmic Review, December, 79(5), pp Färe, Rlf; Grsskpf, Shawa; Mrris, Mar and Zhang, Zhngang (994). Prducivi Grwh, Technical Prgress, and Efficienc in Indusrialized Cunries, American Ecnmic Review 84(),

32 Färe, R. and C.A.K. Lvell (978). Measuring he Technical Efficienc f Prducin, Jurnal f Ecnmic Ther 9, Farrell, M. (957). The Measuremen f Prducive Efficienc, Jurnal f he Ral Saisics Scie, Series A, General, 20(3), Fecher, Fabienne and Sergi Perelman (992). Prducivi Grwh and Technical Efficienc in OECD Indusrial Aciviies, in Indusrial Efficienc in Six Nains,, Richard Caves (Ed.), MIT Press, Cambridge Massachuses. Greene, W. (993). The Ecnmeric Apprach Efficienc Analsis, in The Measuremen f Prducive Efficienc: Techniques and Applicains, Harld O. Fried, C.A.K. Lvell and Sheln S. Schmid (Eds.), Oxfrd: Oxfrd Universi Press, Grifell, E. and C.A.K. Lvell (997). The Surces f Prducivi Change in Spanish Banking. Eurpean Jurnal f Operainal Research, 98(2), Grsskpf, Shawa (993). Efficienc and Prducivi, in The Measuremen f Prducive Efficienc: Techniques and Applicains, edied b Harld O. Fried, C.A.K. Lvell and Sheln S. Schmid, Oxfrd: Oxfrd Universi Press, Malmquis, S. (953). Index Numbers and Indiference Surfaces. Trabajs de Esadísica Mauds, J.; Pasr, J.M. and Serran, L. (998): Cnvergencia en las regines españlas: cambi écnic, eficiencia prducividad, Revisa Españla de Ecnmía, frhcming. Meeusen, W. and J. Van den Breck (977). Efficienc Esimain frm Cbb-Duglas Prducin Funcin wih Cmpsed Errr, Inernainal Ecnmic Review 8, Mrseen, R.H. (96). On he Measuring Prducive Pencial and Relaive Efficienc. Quarerl Jurnal f Ecnmics 75, Perelman, S. (995). R&D, Technlgical Prgress and Efficienc Change in Indusrial Aciviies The Review f Incme and Wealh 4(3), Shephard, R.W. (970). Ther f Cs and Prducin Funcin, Princenn Universi Press. Princenn, NJ. Slw, Rber W. (957). Technical Change and he Aggregae Prducin Funcin, Review f Ecnmics and Saisics, Augus 39(3) Summers, Rber and Hesn, Alan (99). The Penn Wrld Table (Mark 5). An Expanded Se f Inernainal Cmparisns, ", Quarerl Jurnal f Ecnmics, Ma, 06(2), -4. Wlff, Edward (99). Capial Frmain and Prducivi Grwh ver he lng-erm. American Ecnmic Review 8, Taskin, F. and Zaim, O. (997): Caching-up and innvain in high- and lw-incme cunries, Ecnmics Leers, 54,