The effects of biased technological changes on total factor productivity: a rejoinder and new empirical evidence

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1 The effecs of biased echnological changes on oal facor produciviy: a rejoinder and new empirical evidence Crisiano Anonelli, Francesco Quararo To cie his version: Crisiano Anonelli, Francesco Quararo. The effecs of biased echnological changes on oal facor produciviy: a rejoinder and new empirical evidence. Journal of Technology Transfer, Springer Verlag, 2014, 39 (2), pp <hal > HAL Id: hal hps://hal.archives-ouveres.fr/hal Submied on 1 Oc 2014 HAL is a muli-disciplinary open access archive for he deposi and disseminaion of scienific research documens, wheher hey are published or no. The documens may come from eaching and research insiuions in France or abroad, or from public or privae research ceners. L archive ouvere pluridisciplinaire HAL, es desinée au dépô e à la diffusion de documens scienifiques de niveau recherche, publiés ou non, émanan des éablissemens d enseignemen e de recherche français ou érangers, des laboraoires publics ou privés.

2 The effecs of biased echnological changes on oal facor produciviy: A rejoinder and new empirical evidence 1 Crisiano Anonelli a,c and Francesco Quararo b,c a) Universiy of Torino, Deparmen of Economics and Saisics, Lungo Dora Siena 100A, Torino (Ialy) b) GREDEG, CNRS and Universiy of Nice Sophia Anipolis, 250 rue Alber Einsein, Valbonne (France) c) BRICK, Collegio Carlo Albero, Via Real Collegio 30, Moncalieri (Ialy) ABSTRACT. The paper by Ji and Wang (2013) calls new aenion on he analysis of he effecs of he direcion of echnological change. The aim of his paper is o beer ariculae and es he heoreical argumens ha he direcion of echnological changes has specific effecs on he efficiency of he producion process and o sudy he incenives and he processes ha lead o is inroducion. The decomposiion of oal facor produciviy growh ino he bias and he shif effecs enables o ariculae he hypohesis ha he ypes of echnological change wheher more neural or more biased reflec he variey of he innovaion processes a work. The evidence of a large sample of European regions ess he hypohesis ha regional innovaions sysems wih a srong science base are beer able o inroduce neural echnological changes while regional innovaion sysems ha rely more upon learning processes and aci knowledge favor he inroducion of direced echnologies a form of mea-subsiuion ha aims a exploiing he opporuniies provided by he mos inensive use of locally abundan facors. JEL Classificaion Codes: O33 Keywords: Biased Technological Change, Mobiliy, European Regions, GMM Sysem, Transiion Probabiliy 1 This paper conribues he research projec Policy Incenives for he Creaion of Knowledge: Mehods and Evidence (PICK-ME), funded by he European Union D.G. We wish o hank Crisophe Feder for insighful discussions on he opic, and he edior Al Link for his deailed commens. 1

3 1 Inroducion Increasing evidence gahered in he inernaional lieraure shows wih clariy a he counry level ha echnological change is no neural and i is characerized by a srong direcionaliy ha has deep economic effecs (Hall and Jones, 1999; Caselli and Coleman, 2006; Jerzmanowski, 2007). Much aenion has been paid on he effecs of biased echnological change on he facor markes (Acemoglu, 1998, 2002, 2003, 2010). Lesser aenion has been paid o he effecs of biased echnological change on he efficiency of he producion process in erms of oal facor produciviy a he microeconomic level. Consequenly lile analysis has been implemened o undersand he deerminans of he direcion of echnological change a he firm level (Ruan, 1997, 2001). The paper by Ji and Wang (2013) calls new aenion on he analysis of he effecs of he direcion of echnological change. The direcion of echnological change, i.e. he mix of oupu elasiciy and hence he choice of inpus ha, for given levels of coss, are used more inensively, has major economic effecs. The aim of his paper is o provide a reply o he criicisms raised by Ji and Wang (2013) and, in so doing, o beer ariculae and es he heoreical argumens ha: i) he inroducion of biased echnological changes, able o favor he more inensive use of cheaper inpus, has a clear posiive effec on he efficiency of he producion process, and ii) he grasping of he effecs of biased echnological change on he efficiency of he producion process enables o beer focus he incenives and he processes ha lead o is inroducion. Biased echnological change can be considered as a mea-subsiuion process by means of which more expensive inpus are subsiued by less expensive ones wih posiive effecs on he efficiency of he producion process. The idenificaion of he effecs of biased echnological change in erms of oal facor produciviy enables o beer grasp he ypology of innovaion processes ha are a he origin of is inroducion in erms of (Anonelli, 2002, 2003, 2006, 2012; Anonelli and Quararo, 2010). The res of he paper is organized as i follows. Secion 2 presens he noion of echnological congruence and is direc relaionship wih he decomposiion mehodology of TFP growh. Secion 3 applies he resuls o sudy he dynamics of biased echnological 2

4 change and is effecs in erms of TFP growh in a sample of European regions. The conclusions summarize he main findings of he paper. 3

5 2 Theoreical framework 2.1 The direcion of echnological change and growh accouning The undersanding of he effecs of he inroducion of biased or direced echnological changes on he efficiency of he producion process and he ariculaion of he correc mehodology o idenify hem requires a deailed reurn o very origins of he noion of efficiency. I seems appropriae o sar wih a quoe from Rober s Solow founding conribuion: The reader will noe ha I have already drifed ino he habi of calling he curve of Char 2 ΔA/A insead of he more general ΔF/F. In fac a scaer of ΔF/F agains K/L (no shown) indicaes no race of a relaionship. So I may sae as a formal conclusion ha over he period , shifs in he aggregae producion funcion need ou o be approximaely neural. Perhaps I should recall ha I have defined neuraliy o mean ha he shifs were pure scale changes, leaving marginal raes of subsiuion unchanged a given capial/labor raios (Solow, 1957: 316). The aenive reading of Solow (1957) makes clear ha Solow was well aware ha biased echnological change does affec oupu levels. His reading of he empirical evidence for he aggregae producion funcion of he US in he years jusifies a growh accouning mehodology ha does no ake ino accoun he effecs of biased echnological change. According o Solow echnological change in he years has been neural and his jusifies his mehodology. I is consequenly clear ha Solow s mehodology applies does no apply when echnological change is biased. According o Solow (1957:313) Euler s heorem enables o check wheher echnological change is neural or biased. The applicaion of Euler s heorem, assuming consan reurns o scale wihin he frame of a Cobb Douglas producion funcion, enables o consider he share of revenue disribuion as a reliable measure of he oupu elasiciy of each inpu. All changes in he share of revenue paid o each inpu denoe he inroducion of biased echnological changes. The nex sep is o assess wheher he inroducion of biased- as opposed o neural- echnological change affecs oupu levels. The noion of echnological congruence is relevan o undersand wheher he inroducion of biased echnological changes has a direc bearing upon oupu levels. The maching beween he relaive prices of producion facors and heir oupu elasiciy, i.e. he 4

6 maching beween he slope of he isocos and he slope of he isoquan, has clear effecs on oupu levels. The larger is he oupu elasiciy of he producion facor ha is locally more abundan ad hence cheaper and he larger is he oupu and hence he efficiency of he producion process. The clear undersanding of he effecs of echnological congruence enables o grasp he incenives o he inroducion of biased echnological changes. Firms based in a labor abundan region have a clear incenive o inroduce labor inensive echnologies. Firms based in a capial or knowledge abundan region have insead, a clear incenive o inroduce respecively capial or knowledge inensive echnologies. Direced echnological change exers a clear mea-subsiuion process. The increase in efficiency ha sems from he inroducion of biased echnological change in fac is he direc consequence of he subsiuion of cheaper inpus o more expensive ones. The inroducion of biased echnological change, in oher words, amplifies and magnifies echnical subsiuion wih a echnological subsiuion. Ji and Wang (2013) seem o ignore no only Solow s ex (p. 316) bu also he famous noe o column 7 in Table 1 of Solow (1957: 315) ha denoes wihou ambiguiy he use of a Cobb-Douglas producion funcion o measure he residual 2. Moreover, hey fail o appreciae ha he inegral of Solow s equaion (2b) leads o equaion (1a) only when and if echnological change is neural. From his viewpoin i can be claimed ha A/A coincides wih F/F if and only if his laer is independen of K and L (Feder, 2014). In Solow s aricle, he residual is calculaed as he difference beween he increase of he acual oupu hisorically measured and he expeced one. The expeced oupu is calculaed as he produc of he share of propery in income and he increase of he employed capial per man-hour. Consisenly wih he explici use of he Euler s heorem Solow uses he share of propery in income as a reliable indicaor of he oupu elasiciy of capial. Because of he assered neuraliy of echnological change in ha period of ime Solow allows he oupu elasiciies o change The inspecion of able 1 shows indeed ha he share of propery in income flucuaes from in 1909 o a peak of in 1932 o decline evenually o in The flucuaion does no allow he idenificaion of a clear rend. This jusifies Solow s assumpion 2 Acually he boom line of Ji and Wang is ha he mehodology proposed in Anonelli and Quararo (2010) is wrong because he original was wrong. However, Solow s paper is focused on neural echnological change, as his seemed o be appropriae for analyzing he US evidence. I is a maer of fac ha he mehodology developed by Solow allows o capure only he shif in he producion facor. 5

7 ha echnological change had been neural in he period Only because of his specific evidence Solow allows he share of propery in income o change year from year in he calculaion of he residual. This procedure for he calculaion of he residual enables Solow o measure he shif effecs engendered by he inroducion of echnological change as if i were neural, bu does no grasp he effecs of biased echnological changes semming from changing levels of he oupu elasiciy of inpus. Keeping he share of propery in income consan a he 1909 level would have enabled Solow o measure he effecs of boh he shif of he producion funcion and he bias. I is clear, however, ha he hisorical evidence on which Solow works is such ha he difference beween he wo mehodologies is absoluely negligible. When and if he share of propery and labor in income exhibis wider changes, he difference beween he calculaion of he residual respecively wih consan and changing levels of oupu elasiciy is larger. The larger is he change in he oupu elasiciy and he larger is he difference beween he wo procedures. Acually he difference beween he wo procedures can be regarded as a reliable measure of he exen o which he inroducion of biased echnological changes affecs he efficiency of he producion process. The growh accouning procedure wih consan oupu elasiciy measures he oal effec of echnological change, i.e. he sum of shif and bias effecs. The growh accouning procedure wih changing oupu elasiciy grasps jus he shif effecs. Their difference measures he biased effecs. The use of he Euler s heorem is crucial for he foundaion of his mehodology. The use of alernaive procedures such as he economeric esimae of ranslog producion funcions, as suggesed by Ji and Wang (2013) 3 misses compleely he poin because he idenificaion of he acual oupu elasiciy a each poin in ime is crucial o appreciae he effecs of heir own changes (Link, 1987; Bailey, Irz, Balcombe, 2004). This mehodology allows o idenifying a variey of effecs ranging from pure neural echnological change ha engenders only shif effecs o pure direced echnological change ha engenders only bias effecs. The range includes a coninuum of inermediary effecs ha 3 Acually Ji and Wang propose an index o capure boh he shif and he bias effec which is exacly he Toal Technology Produciviy (TTP) index proposed by Barnard and Jones (1996). The idea is modify he Solow s index by freezing he levels of capial and labour, so as o have he very same values for all regions/counries which remain consan over ime. However his index allows o disenangling he exac conribuion of facor changes, and no he conribuion of changes of facors shares. Moreover, besides he drawbacks already emphasized by Bernard and Jones, i has also undesirable feaure o be very sensiive o changes in he condiions of labor markes. 6

8 accouns for echnological changes ha consis in boh a shif of he map of isoquans and a change in heir slope. The idenificaion of he specific effecs of he inroducion of biased echnological changes, as disinc from he shif effecs enables o ry and ariculae he analysis of he deerminans and incenives o he inroducion of eiher form of echnological change. The exploraion of he empirical evidence o confirm wheher echnological change is subsanially neural as no only Solow on a solid background, bu also he following lieraure has assumed, or insead he inroducion of biased echnologies has lef clear marks on he changes of he shares in income of producion facors, is mos relevan. In his conex i seems necessary o explore as much as possible a disaggregae evidence, such as he regional one, in order o check wheher he apparen neuraliy a he aggregae level is he resul of compensaing dynamics a he disaggregae one. The idenificaion of subsanial heerogeneiy and variance in he changes in he shares in income of inpus would provide he appropriae conex o ry and explore he deerminans of such a variey of ypes of echnological changes a work. 2.2 Microeconomic deerminans and effecs of he direcion of echnological change The economics of innovaion and he economics of echnical change have grown apar wih reciprocal damage. The former specializes in invesigaions a he macroeconomic and aggregae level. The laer is mainly confined a he firm and indusrial level. The crossing of boh he ools and he fields of empirical invesigaion is likely o yield major advanages. Specifically he inegraion of he debae upon he direcion of echnological change, and is implicaion for he growh accouning mehodologies, wo of he mos imporan legacies of he economics of echnical change, wih he recen advances of he microeconomics of innovaion and knowledge provides imporan opporuniies o idenify he variey of ypes of innovaions and knowledge generaion processes a work, he relaed variey of ypes of echnological changes, and heir deerminans. More specifically he inegraion of he economics of knowledge and innovaion wih he economics of echnological change enables o idenify he maching beween he ypes of echnological change being inroduced and he ypes of firms. This in urn enables o appreciae he microeconomic deerminans of he direcion of echnological change appreciaing he effecs of he sharp differences across 7

9 regional innovaion sysems wih respec o: i) heir srucure in erms of size of firms and secoral composiion; ii) he differen sources of echnological knowledge and he srucure of he knowledge base; iii) he variey of ypes of knowledge generaion processes; iv) he differen ypes of knowledge exploiaion sraegies; v) he differen ypes of producion processes; vi) he differen ypes of innovaions inroduced; and vii) he differen ypes of marke forms wihin produc markes. Wihin local innovaion sysems characerized by he small size of firms and he srong role of radiional indusries, echnological change is mainly biased owards he inensive use of locally abundan inpus. Direced echnological change, able o engender only bias effecs, can be considered as he resul of knowledge generaion processes based upon he accumulaion of aci knowledge by means of processes of learning by doing and learning by using and knowledge exploraion sraegies based upon localized sources of exernal knowledge (Anonelli, 2008). Firms ry and exploi he new echnological knowledge wih he inroducion of process innovaions ha rely upon echnologies ha are beer able o ake advanage of he local facor markes. Innovaion sysems ha rely more sysemaically upon he command of localized echnological knowledge, based upon inernal compeence and exernal aci knowledge, made available by knowledge ineracions wih firms co-localized in he same local knowledge pools, can inves lower amoun of resources in he knowledge generaion processes and can rely on inellecual propery righs o a minor exen o exploi i (Soneman, 2010). Technological change consiss mainly of process innovaions aimed a reducing producion coss in produc markes characerized by high levels of price compeiion. Producion processes are characerized by lower levels of capial inensiy and hence lower levels of swiching coss. As a consequence hey are beer able o inroduce incremenal echnological innovaions ha consis of a minor shif and hence a small change in he posiion of he isoquan, bu, being less consrained by swiching coss, will find i more convenien o inroduce new and superior echniques wih a sronger bias owards a direcion ha enables hem o make a more inensive and sysemaic use of locally abundan producion facors (Vaona and Piana, 2008; Piva, Sanarelli, Vivarelli, 2006). Wihin regional innovaion sysems characerized by he role of large firms acive in high ech indusries echnological change is mainly neural. Neural echnological change, i.e. he one able o engender only shif effecs, can be considered as he resul of science based 8

10 innovaions. The generaion of echnological knowledge mainly based upon new scienific breakhroughs is ypically inroduced by large firms able o search and exploi he science based generaion of new echnological knowledge (March, 1991). Large firms wih a global scope of aciviy are less rooed in he condiions of heir local facor markes. Innovaion sysems characerized by large firms are beer able o impinge upon scienific advances as a major source for echnological knowledge and can inves larger resources in formalized R&D procedures and generae new echnological knowledge ha suppors he inroducion of radical innovaions, can rely upon inellecual propery righs o exploi heir echnological knowledge, face larger swiching coss in he inroducion of new echnologies, he incenives exered by facor coss accoun for a small fracion of he overall posiive effecs of he new echnologies. Technological change consiss mainly of produc innovaions ha are used in oligopolisic markes o suppor a srong monopolisic compeiion based upon produc rivalry (Scherer, 1984). The inroducion of a superior neural echnology ha enables o remain in he close proximiy of he previous equilibrium echnique is a superior opion. These sysems will be beer able o concenrae heir innovaion aciviies owards he localized inroducion of major echnological changes along he original isocline. Such echnological change can be beer characerized as a change in he posiion of he map of isoquans. The new echnology will be characerized by much a sronger movemen owards he origin accompanied by a negligible change in he oupu elasiciy of inpus consising in he inroducion of laborinensive or more specifically skill-inensive echnologies, raher han capial inensive ones. The variey of echnological aciviies in regional innovaion sysems also maers in shaping firms echnological aciviies. Acually, echnological knowledge is he oucome of a collecive process, in which he ineracions and he access o exernal knowledge play a key role (Savioi, 2007; Foray, 2004; Anonelli, 1999). In his direcion, he noion of recombinan knowledge is especially relevan This approach views new ideas as being generaed hrough he recombinaion of exising ideas, under he consrain of diminishing reurns o scale in he performance of he research and developmen (R&D) aciviies necessary o apply new ideas o economic aciviies (Weizman, 1998; Fleming and Sorenson, 2001; Caminai, 2006). Firms in regional innovaion sysems herefore produce new knowledge by combining ogeher differen knowledge inpus available in he geographic and echnological space. The regional knowledge base can be regarded as a heerogeneous consruc, which gahers ogeher echnologies ha esablish complemenariy and/or similariy relaionships amongs 9

11 hemselves. The effeciveness of innovaion aciviies as well as produciviy growh (à la Solow) have been found o be posiively relaed o he average degree of inegraion and complemenariy of he knowledge base (Nesa and Savioi, 2005; Quararo, 2010). Neural echnological change is more likely o sem from resource inensive innovaion aciviies, which exhibi high effeciveness degree due o exploiaion of highly complemenary locally available knowledge inpus. 3 Daa, Mehodology and Empirical Sraegy 3.1 The daa In order o invesigae he dynamics and he deerminans of biased echnological change in European regions, we have drawn daa from he Eurosa regional saisics, which gahers ogeher saisical informaion regarding European regions since Due o daa consrains, we focus our economeric exercise on a balanced sample of NUTS II regions across differen European Counries, i.e. Ausria, Belgium, Germany, Spain, Finland, France, Ialy, Hungary, Poland and UK over he period For wha concerns he calculaion of he produciviy indexes, we needed oupu, labor and capial services, and he labor and capial shares. As a measure of oupu (Y i ) we used he real GDP (2000 consan prices). Eurosa also provides wih esimaion of capial sock (K i ) and employmen, alhough i does no provide daa abou hours worked a he regional level. For his reason we used average hours worked a he counry level provided by he Groningen Growh and Developmen Cenre ( and hen calculae oal hours worked (L i ). Alhough his does no allow us o appreciae cross-regional difference in average hours worked, noneheless i allows us o accoun a leas for cross-counry differences. The labor share (β i ) is calculaed using daa on he compensaion of employees and he GDP according 4 We acknowledge ha he use of adminisraive regions o invesigae represens only an approximaion of he local dynamics underpinning economic aciviies. Indeed adminisraive borders are arbirary, and herefore migh no be represenaive of he sponaneous emergence of local ineracions. I would be much beer o invesigae hese dynamics by focusing on local sysems of innovaion. However, i is impossible o find ou daa a such a level of aggregaion. Moreover, he idenificaion of local sysems involve he choice of indicaors and hreshold values according o which one can decide wheher o unbundle or no local insiuions. This choice is in urn arbirary, and herefore i would no solve he problem, bu i would only reproduce he issue a a differen level. Thus we hink ha despie he unavoidable approximaion, our analysis may provide useful informaion on he dynamics under scruiny. 10

12 o equaion (5a), while capial oupu elasiciy has hen been calculaed following equaion (5b). The daa abou he unemploymen raes across European regions, as well as hose concerning populaion densiy, he oal regional value added and he regional value added in manufacuring indusries have been drawn by he Eurosa regional saisics. For wha concerns he role of formalized innovaion effors in he localized inroducion of echnological change, we decided o use paen applicaions o European Paen Office (EPO) as proxies of regional innovaive aciviies. The ime series provided by he EPO sar in 1978, and assign paens o regions according o invenors addresses. The limis of paen saisics as indicaors of innovaion aciviies are well known. The main drawbacks can be summarized in heir secor-specificiy, he exisence of non paenable innovaions and he fac ha hey are no he only proecing ool. Moreover he propensiy o paen ends o vary over ime as a funcion of he cos of paening, and i is more likely o feaure large firms (Pavi, 1985; Griliches, 1990). Neverheless, previous sudies highlighed he usefulness of paens as measures of producion of new knowledge, above all in he conex of analyses of innovaion performances a he aggregae regional level (Acs e al., 2002). Besides he debae abou paens as an oupu raher han an inpu of innovaion aciviies, empirical analyses showed ha paens and R&D are dominaed by a conemporaneous relaionship, providing furher suppor o he use of paens as a good proxy of innovaion (Hall e al., 1986). 3.2 Mehodology In order o single ou an index for he effecs of BTC on TFP, we elaborae upon he so-called growh accouning mehodology, which draws upon he seminal conribuion by Solow (1957) furher implemened by Jorgenson (1995) and OECD (2001). In order o confron direcly our approach wih he seminal conribuion by Solow (1957), we shall rely on a Cobb-Douglas producion funcion as in Anonelli and Quararo (2010 and 2013). 11

13 Le us recall he main passages in wha follows. The oupu Y of each region i a ime, is produced from aggregae facor inpus, consising of capial services (K) and labour services (L), proxied in his analysis by oal worked hours. TFP (A) is defined as he Hicksneural augmenaion of he aggregae inpus. Such a producion funcion has he following specificaion: Y i, i, ( i, i, A f K, L ) (1) The sandard Cobb-Douglas akes he following forma: i, i, Y i, Ai, Ki, Li, (2) We can hen wrie TFP as he raio beween he acual observed oupu and he oupu ha would have been produced hrough he sheer uilizaion of producion facors: A Y (3) i, i, i, i, Ki, Li, Or in logarihmic form: ln A i, lnyi, i, ln Ki, i, ln Li, (4) Where α i, and β i, represen respecively he oupu elasiciy of capial and labour for each counry a each year. I is worh recalling ha, according o Solow s formulaion, oupu elasiciies of capial and labour are allowed o vary over ime. In so doing he effecs of heir change on produciviy are compleely neuralized. Nex, following Euler s heorem as in Solow (1957), we assume ha oupu elasiciies equal he facors shares in oal income, as we assume perfec compeiion in boh facor and produc markes. In view of his, he oupu elasiciy of labour can be expressed as follows: w L i. i, i, (5a) Yi, If we also assume consan reurns o scale, he oupu elasiciy of capial can be obained as follows: i, 1 i, (5b) The measure of A obained in his way, accouns for any kind of shif in he producion funcion (Solow, 1957: 312). By means of i Solow inended o propose a way o segregaing shifs of he producion funcion from movemens along i. Solow is righ if and 12

14 when echnological change is neural, and/or facors are equally abundan. Insead, he effecs of biased echnological innovaions inroduced in counries where facors are no equally abundan, are made up of wo elemens. Once we obain he TFP accouning for he shif in he producion funcion, we can invesigae he impac of he bias effec wih a few passages. Firs of all we obain a measure of he TFP ha accouns for he sum of boh he bias and he shif effecs (for his reason we call i oal-tfp or ATOT), by assuming oupu elasiciies unchanged wih respec o he firs year observed. This measure can be herefore wrien as follows: ATOT Y i, i, i, 0 i, 0 Ki, Li, (6) The oupu elasiciies for boh labour and capial are frozen a ime =0, so ha a each momen in ime he ATOT is equal o he raion beween he acual oupu and he oupu ha would have been obained by he sheer uilizaion of producion facors, had heir elasiciies been fixed over ime 5. This index may be also expressed in logarihmic form as follows: ln ATOT i, lnyi, i, 0 ln Ki, i, 0 ln Li, (7) Nex we ge he bias effec (BIAS) as he difference beween ATOT and A: BIAS i, ATOTi, Ai, (8) The index obained from Equaion (8) is sraighforward and easy o inerpre. Indeed is criical value is zero. When BIAS in one counry is above (below) zero, hen is echnological aciviy is characerized by he righ (wrong) direcionaliy, and he slope of isocoss differs from uniy. 5 The differences wih he mehodology by Ji and Wang (2013) are clear. Acually heir index is sensiive o changes in facor prices even if hese did no engender any creaive reacion aimed a inroducing a biased echnology. In order Jin and Wang s mehodology o hold, facor s coss and firms budge mus be consan. In his sense, while our mehodology allows o assessing he exen o which he direcionaliy of biased echnological change mached local facor endowmens, Ji and Wang s index allows o evaluaing he exen o which he change in facors endowmens mached he locally available echnology. See Feder (2014) for an illusraion of such drawbacks. 13

15 3.3 Empirical sraegy Condiional average disribuion of capial s oupu elasiciy In order o invesigae he dynamics of biased echnological change a he regional level we firs invesigae he evoluionary paerns of he oupu elasiciy of capial (α). Acually, Solow proposed o leave aside any consideraion of change in facors oupu elasiciies due o he specific evidence concerning he US economy in he early 1900s. We inend o show insead ha oupu elasicies do change boh across economic unis (in our case he regions) and over ime. A firs sep in his direcion consiss in he analysis of he condiional average disribuion of α. This mehodology is usually used o invesigae he changing paerns of echnological or rade specializaion (Canwell, 1989; Pavi, 1989; Zaghini, 2005; Uchida and Cook, 2005; Alessandrini and Bauo, 2010; Chiappini, 2013). In line wih his lieraure, we esimae he following equaion using he Ordinary Leas Square (OLS) esimaor: (9) Where is he average of he disribuion of α beween 2003 and 2004 for he region i, is he average of he disribuion of α beween 1995 and 1996 of region i, a and b are he coefficiens o be esimaed and e is he error erm 6. Inerpreaions of he esimaion resuls are as follows. If b = 1, he disribuion of α remains sable. If b > 1, α increases in regions already showing high levels of i. If 0 < b < 1, here is a endency o convergence in he levels of α. This means ha on average he value of α has increased in regions where he iniial value of he index was low and has decreased in regions for which he iniial value of he index was high. If b = 0, here is no relaionship beween iniial and final disribuion of α. Moreover, Canwell (1989) shows ha: (10) 6 The choice of he ime span is shaped by daa consrains, which do no allow us o calculae elasiciies a he regional level before he year 1995, when Eurosa inroduced he sandard accouning procedure (ESA).. Ten years can be regarded is a sufficien ime spam o allow o appreciaing he emergence of srucural shifs. 14

16 Whereρ is he correlaion coefficien obained from he regression, while and are he variance of he dependen and explanaory variable respecively. The correlaion coefficien in his empirical seing can be inerpreed as a measure of he mobiliy of regions along he disribuion of capial s oupu elasiciies in he wo periods. On he basis of he comparison beween b and ρ one could observe hree differen oucomes: i) b = ρ, i.e. he dispersion of he variable in he wo periods has no changed; 2) b>ρ, i.e. he dispersion in he end period is higher han he saring period; 3) b<ρ, i.e. he dispersion in he end period is lower han he saring period Inra-disribuion dynamics of capial s oupu elasiciy A beer way o esimae inra-disribuion dynamics and he srucural sabiliy of he oupu elasiciy of capial over ime is o rely on he General Markov Chain model. Following previous empirical lieraure (Chiappini, 2013; Mancusi 2001, 2012; Redding 2002; Zaghini 2005; Alessandrini e al. 2007; Alessandrini and Bauo 2010), we implemen a Markovian model, which is usually used in he cross-counry growh and income lieraures bu can provide useful insighs also in he analysis, a a less aggregae level, of he evoluion of crossregional disribuion of oher economic variables (Quah 1993, 1996, 1997). The idea underlying he Markov model is ha, in absence of disurbances, he space of possible values of α can be pariioned ino a number of discree inervals. If one le hese inervals be he quariles of he disribuion of α, he ransiion probabiliy marix P allows o evaluaing he probabiliy ha he region i, which is locaed in a given quarile a ime, moves o anoher quarile a ime +1. These probabiliies can be esimaed by couning he number of ransiions ou of and ino each cell. We can inerpre he mobiliy or persisence hroughou he enire disribuion of α using he ransiion probabiliy marix. Indeed, high values of a ransiion probabiliy along he diagonal denoe high persisence, while higher values of he off-diagonal erms indicae high mobiliy. More deailed informaion on paerns of specialisaion can be derived using indices of mobiliy. Two indices are proposed in he empirical lieraure (see Shorrocks, 1978) and are easily measurable using he ransiion probabiliy marix. The firs (M1) evaluaes he race of 15

17 he ransiion probabiliy marix; he second (M2) evaluaes he deerminan (de) of he ransiion probabiliy marix. ( ) (11) ( ) (12) For boh indices, a higher value indicaes greaer mobiliy of he regions hroughou he disribuion, while a zero value implies complee immobiliy Economeric esimaion of he deerminans of biased echnological change The previous seps allows o assessing he exen o which he oupu elasiciy of capial (and by symmery ha of labour) are sable or, insead, do change over ime and across regions. The evidence abou long run changes in hese measures suggess ha acually echnological change, a leas in his ime period, across European regions did no enail a neural shif of he producion funcion: On he opposie i exhibied a clear bias ha led o a change in he slope of he isoquans.. If biased echnological change maers, i seems necessary o enquire ino is effecs and is deerminans. The idenificaion of he effecs seems he firs necessary sep in order o grasp he deerminans. To his purpose we calculaed he index R i,, which is he raio beween he radiional TFP index and he BIAS index: (13) According o he heoreical framework ariculaed in secion 2, he weigh of biased echnological change in a region s innovaion aciviies is relaed firs of o he changing condiions in facors markes. For his reason we include he local wage rae (w i, ) as an explanaory variable in our empirical model. Moreover, he commimen of resources o R&D aciviies is also likely o shape he balance beween he bias and he shif effec. The inensiy of R&D, measured as a share of local GDP, is herefore included in he model (R&D i, ). Besides his, innovaion oucomes like paen applicaions are also likely o be associaed o he variable R i,. Paen applicaions are indeed a proxy of innovaion effors 16

18 leading o relevan oucomes. However, a beer suiable indicaor in his conex would be he cos of a paen, measured as he raio beween local R&D expendiures and oal paen applicaions (PATCOST i, ). On average, one would expec more expensive paens o yield significan effecs on produciviy which ranslae ino eviden shifs in he producion funcion. Cheaper paens, on he conrary, are more likely o be associaed o incremenal changes which allow for a beer maching beween changing condiions in facors marke and firms producion plans. Finally, he average complemenariy degree amongs locally available echnologies can be proxied by he knowledge coherence index (COH i, ). This can be defined as he average relaedness or complemenariy of a echnology chosen randomly wihin he secor wih respec o any oher echnology (Nesa and Savioi, 2005; Nesa, 2008; see Quararo (2010) for he deails of he calculaion of he coherence index a he regional level). Noe ha his index implemened by analysing he co-occurrence of echnological classes wihin paen applicaions, measures he degree o which he services rendered by he co-occurring echnologies are complemenary, and is based on how frequenly echnological classes are combined in use. The relaedness measure τ lj indicaes ha uilizaion of echnology l implies use also of echnology j in order o perform specific funcions ha are no reducible o heir independen use. If he coherence index is high, his means ha he differen pieces of knowledge have been well combined or inegraed during he search process. Due o a learning dynamics, he acors in he region have increased capabiliy o idenify he bis of knowledge ha are required joinly o obain a given oucome. In a dynamic perspecive, herefore, increasing values for knowledge coherence are likely o be associaed wih profiable echnological opporuniies. Higher degrees of coherence of he regional knowledge base are expeced o lead o he inroducion of significan improvemens which are conducive o shifs in he producion funcion. We can now specify he empirical model o be esimaed as follows: ( ) ( ) ( ) ( ) ( ) (14) 17

19 Equaion (14) can be esimaed hrough dynamic models for panel daa. We carried ou he empirical es by means of a dynamic panel daa regression, using he generalized mehod of momens (GMM) esimaor (Arellano and Bond, 1991). This esimaor indeed provides a convenien framework for obaining asympoically efficien esimaors in presence of arbirary heeroskedasiciy, aking ino accoun he srucure of residuals o generae consisen esimaes. In paricular, we use he GMM-Sysem (GMM-SYS) esimaor in order o increase efficiency (Arellano and Bover, 1995; Blundell and Bond, 1998). This approach insrumens he variables in levels wih lagged firs-differenced erms, obaining a dramaic improvemen in he relaive performance of he sysem esimaor as compared o he usual firs-difference GMM esimaor. The error erm is herefore decomposed in ρ i and Σψ, which are respecively region and ime effecs, and he error componen ε i. Moreover, in order o rule ou as much as possible he risk of spurious relaionships, all of he explanaory variables have been lagged one year. 4 Empirical Resuls 4.1 Dynamics of oupu elasiciies The variance in he observed values of oupu elasiiciies is a clear sign of he inroducion of biased echnological change in he producion process. Figure 1 provides a snapsho of he average disribuion of oupu capial elasiciy across European regions. >>>INSERT FIGURE 1ABOUT HERE<<< The map clearly shows a highly dispersion of he index across he sampled regions, he more peripheral being characerized by higher levels of capial s oupu elasiciy. However, as already saed, he idenificaion of acual oupu elasiciies a each poin in ime is crucial o appreciae he magniude of he bias effec of he inroducion of new echnologies in he producion process. For his reason, we have analyzed he change in he condiional average disribuion of oupu capial elasiciies over he period analyzed. We implemen he mehod proposed by Canwell (1989) and Pavi (1989), by regressing he values observed a he end of he period agains hose observed a he beginning. 18

20 The resuls of his esimaion are repored in able 1. The linear esimaion of he coefficien is posiive and significan. The magniude of he coefficien, lower han 1, suggess ha he average disribuion of capial s oupu elasiciy has changed over ime, suggesing a general decrease in he values of α across sampled regions. Moreover, by comparing he esimaed OLS coefficien and he correlaion coefficien ρ we can also conclude ha a convergence process is a sake as far as capial s elasiciy is concerned. Acually b is lower han ρ, and his implies ha he dispersion a he end of he period is lower han ha a he beginning. Thus, his former inspecion suggess ha he disribuion of capial s oupu elasiciy did change over ime, and in paricular a downwards shif of he disribuion can be deeced, being α a he end of he period on average lower and less dispersed han he beginning. >>> INSERT TABLE 1 ABOUT HERE <<< A graphical represenaion of his phenomenon can be implemened by resoring o he so-called Saler s curves developed by Saler (1960). Regions are ranked in a descending order according o he beginning of he period capial s oupu elasiciy. The larger is he slope of he curve, he higher is he dispersion of he index across he sampled regions. Saler curves of subsequen periods are ploed wih he regions sored in he same order as ha of he firs period. Areas of decreasing or increasing heerogeneiy can be idenified by looking where he Saler curve of a laer period lies above or below he Saler curve of he firs period. >>> INSERT FIGURE 2 ABOUT HERE <<< Figure 2 repors Saler s curves for he period (solid line) and (dashed line). The picure clearly suggess he exisence of high degree of heerogeneiy in he values of capial s oupu elasiciy in he firs period. If we look a he posiion of he curve for he (he ranking is sill based on values), we can observe ha he areas in which he dashed line i is below he solid line is predominan. This is a signal of increasing heerogeneiy in he disribuion and suggess he exisence of high mobiliy of sampled regions across he disribuion. These mehods allow only for a preliminary undersanding of he dynamics of capial s oupu elasiciy. In order o capure he evoluion of regions across he enire disribuion, we rely upon he mehodology proposed by Quah (1993, 1996, 1997) in his sudy of he per capia income convergence. 19

21 The resuls of his mehodology, explained in Secion 3.3.2, can be found in Table 2. This able repors a four by four ransiion probabiliy marix referring o he quariles of he disribuion. The firs line of he marix repors he likelihood o be in one of he four quariles a he end of he period, given ha he region was in he firs quarile a he beginning. In he second line, regions a he beginning were in he second quarile, and so on. This means ha along he diagonal we have a measure of he persisence of capial s oupu elasiciy in sampled regions. >>> INSERT TABLE 2 ABOUT HERE <<< The evidence suggess ha here is a fairly high rae of persisence mosly for hose regions locaed in he firs quarile a he beginning of he period. I is almos impossible ha hese regions jump o he hird or he fourh quarile. Regions moving from he second quarile show almos he same probabiliy o say here or o move o he firs one a he end of he period. Regions moving from he hird and he fourh quarile show almos similar probabiliy o move o he closes lower quarile. The likelihood of larger jumps is very low. I is almos impossible o observe regions moving from he fourh quarile ha ends up in he firs quarile. This evidence is consisen wih he resuls concerning he average condiional disribuion, which suggesed ha here is a downward convergence in he levels of capial s oupu elasiciies. Table 2 also repors he resuls of he calculaions for he wo mobiliy indexes described in Secion For boh of he wo indexes, values close o zero indicae complee immobiliy. The resuls of he calculaion sugges insead ha here has been some mobiliy of regions across he disribuion of capial s oupu elasiciy. This evidence is more sriking as far as he index M 2 is concerned. The European evidence discussed so far shows a siuaion nealy differen from he aggregae US evidence analysed by Solow in he early decades of he 20 h cenury. Acually, he oupu elasiciy of capial (and, by symmery, ha of labour) does change over ime in each of he observed regions, so ha regions move across he average disribuion. The diachronic and synchronic varieies are marked and sricly inerwined. The analysis of he deerminans of biased echnological change becomes herefore necessary. 4.2 The deerminans of biased echnological change 20

22 Oupu elasiciies in European regions in he period are no sable over ime. This suggess ha echnological change engendered shifs of he maps of isoquans ighly associaed wih clear changes in heir slope. The mehodology described in Secion 3.2 allows o grasping he effecs of echnological change on produciviy when neural shifs are no longer he only viable oucome. The analysis of he deerminans of biased echnological change as opposed o he neural one can be carried ou hrough he esimaion of equaion (13). >>> INSERT TABLE 3 ABOUT HERE <<< Table 3 provides he resuls of he analyses carried ou by implemening he GMM sysem esimaor. The firs column repors he baseline esimaion, in which he R i, (he raio beween neural and biased echnological change) is regressed agains he wage rae and R&D inensiy. As expeced, boh of he coefficiens are posiive and saisically significan (1%). Regional innovaion sysems characerized by he commimen of a large amoun of resources o formalized research aciviies are more likely o be feaured by he inroducion of echnological change engendering a shif of he producion funcion. The wage rae is also posiive. This evidence is consisen wih Anonelli and Quararo (2013), which found ha efficiency wages are likely o exer srong posiive effecs on produciviy growh, especially in conexs characerized by he rigidiy of labour markes. The figures in column (2) concern he model exended so as o include knowledge coherence as an explanaory variable. The sign and significance levels of wages and R&D inensiy are unchanged as compared o he previous esimaion. Knowledge coherence, as expeced, is characerized by a posiive coefficien, which is significan a he 10% level. Alhough weakly significan, he evidence on coherence suppors he idea ha he higher he average complemenariy amongs he echnological compeences residing in he region, he higher he produciviy gains ranslaing ino a neural shif of he producion funcion. In column (3) we include he uni cos of paens (PATCOST) in he regressor marix. The coefficiens on he wage rae and R&D inensiy are prey sable in erms of sign and significance. Knowledge coherence is now no significan, while PATCOST shows a negaive and significan coefficien (1%). The fac ha knowledge coherence is no longer significan is no surprising. Acually, he mechanisms behind he effecs of knowledge coherence concern he increased effeciveness of he innovaion process. This in urn ends up in an increase of produciviy growh engendering a shif effec. When paen coss are included in he model, we direcly accoun for he effecs of he effeciveness of he innovaion process on he 21

23 inroducion of neural echnological change. Acually, he higher he effeciveness of he innovaion process, he lower of he uni cos of paens. This explains he negaive sign on he PATCOST variable, which is likely o be highly correlaed wih knowledge coherence. Finally, in column (4) we drop knowledge coherence from he regressor marix, in order o check for he sabiliy of he coefficien on PATCOST. I can be observed ha all of he coefficiens are sable in erms of sign and significance levels, supporing he idea ha neural echnological change is beer associaed o highly effecive innovaive processes, he commimen of large amouns of resources o formalized R&D aciviies and high (efficiency) wages. I is also fair o noe ha he auoregressive erm is always posiive and significan, alhough always lower han one. Since all variables are expressed in log, his suggess he exisence of a kind of convergence in growh raes of raio beween neural and biased echnological change. 5 Conclusions The economics of innovaion and knowledge has basically ignored he legacies of he economics of echnological change, as much as he economics of echnological change has ignored he ools and he heurisics of he economics of innovaion and knowledge. Lile effor has been made o explore he relaions beween he debaes upon he correc growh accouning mehodology and he direcion of echnological change on he one hand and he characerisics of innovaion processes a work wihin innovaion sysems on he oher. As a maer of fac he inegraion of he microeconomics of innovaion and knowledge wih he analysis of he direcion of echnological change and is effecs on oal facor produciviy is a ferile field of invesigaion ha deserves o be beer explored. The decomposiion of oal facor produciviy growh ino is wo key componens, he shif and he bias effec, enables o disinguish beween ypes of echnological change and o invesigae he effecs and he deerminans of is inroducion. The decomposiion of oal facor produciviy enables, in fac o idenify he wide range of ypes of echnological changes comprised beween he wo exremes of pure neural and fully direced echnological changes. The laer engenders only shif effecs based upon he proporionae reducion of inpus necessary for he producion of a given oupu, he former only bias effecs based upon he mea-subsiuion of more expensive inpus wih cheaper ones. The exploraion of he coninuum beween he wo exremes enables o idenify 22

24 a variey of ypes of echnological changes and relae i o he underlying variey of innovaion processes and he ypology of knowledge generaion processes a work. The evidence of a large sample of European regions confirms ha he direcion of echnological change as measured by he changes in he oupu elasiciy of inpus is far from negligible. The empirical evidence suggess ha a variey of ypes of echnological changes is a work. The empirical evidence a he disaggregae level confirms ha echnological change is far more direced han sandard growh accouning assumes. Underneah he aggregae evidence of small changes in inpus shares in income, he disaggregae evidence exhibis quie a relevan variance. This is urn has made i possible o invesigae he relaionship beween he ypes of echnological change wheher more or less direced and he variey of innovaion processes. The economeric analysis has made i possible o confirm ha innovaions sysems ha base heir generaion of echnological knowledge upon learning processes are more likely o inroduce direced echnologies in order o ake advanage of he mea-subsiuion dynamics. Innovaion sysems where he generaion of echnological knowledge can rely upon a srong science base are more likely o inroduce neural echnologies. 23

25 References Acemoglu, D. (1998), Why do new echnologies complemen skills? Direced echnical change and wage inequaliy, Quarerly Journal of Economics 113, Acemoglu, D. K. (2002), Direced echnical change, Review of Economic Sudies 69, Acemoglu, D. (2003), Labor- and capial-augmening echnical change, Journal of European Economic Associaion 1, Acemoglu, D.K. (2010), When does labor scarciy encourage innovaion?, Journal of Poliical Economy 118, Alessandrini, M., Bauo, M.E. (2010), The rade specialisaion of SANE: Evidence from manufacuring indusries, European Journal of Comparaive Economics 7, Anonelli, C., (2002), Innovaion and srucural change, Economie Appliquèe 55, Anonelli, C., (2003), The economics of innovaion new echnologies and srucural change, Rouledge, London. Anonelli, C., (2006), Localized echnological change and facor markes: Consrains and inducemens o innovaion, Srucural Change and Economic Dynamics 17, Anonelli, C. (2008), Localized echnological change. Towards he economics of complexiy, London, Rouledge. Anonelli, C. (2012), Technological congruence and produciviy growh, in Andersson, M., Johansson, B., Karlsson, C., Lööf, H., (eds.), Innovaion and Growh - From R&D sraegies of innovaing firms o economy-wide echnological change, Oxford Universiy Press, Oxford, pp Anonelli, C., Quararo, F., (2010), The effecs of biased echnological change on oal facor produciviy. Empirical evidence from a sample of OECD counries, Journal of Technology Transfer 35, Anonelli, C., Quararo, F. (2013), Localized echnological change and efficiency wages: The evidence across European regions, Regional Sudies 47, Bailey, A., Irz, X., Balcombe, K. (2004), Measuring produciviy growh when echnological change is biased. A new index and an applicaion o UK agricolure, Agriculural Economics 31, Caminai, M., (2006), Knowledge growh, complexiy and he reurns o R&D, Journal of Evoluionary Economics 16, Canwell, J. (1989), Technological innovaion and mulinaional corporaions, Blackwell Publisher, Oxford. 24