MERIT-Infonomics Research Memorandum series. Education and Training in a Model of Endogenous Growth with Creative Destruction

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1 MERIT-Infonomic Reearch Memorandum erie Education and Training in a Model of Endogenou Growth with Creative Detruction driaan van Zon & Roberto ntonietti MERIT Maatricht Economic Reearch Intitute on Innovation and Technology PO Box MD Maatricht The Netherland T: F: ecr-merit@merit.unimaa.nl International Intitute of Infonomic c/o Maatricht Univerity PO Box MD Maatricht The Netherland T: F: ecr@infonomic.nl

2 Education and Training in a Model of Endogenou Growth with Creative Detruction by driaan van Zon and Roberto ntonietti Second draft, March 2005

3 Education and Training in a Model of Endogenou Growth with Creative Detruction driaan van Zon* and Roberto ntonietti** Firt draft September 2004; econd draft November 2004 Keyword: education, on-the-job training, technology adoption, wear and tear effect, endogenou growth JEL Claification: J24, O31, O41 btract By formulating an endogenou growth model that combine element from Romer 1990, ghion and Howitt 1992, and van Zon and Yetkiner 2003, the preent paper tudie the contribution of education and training on economic growth through their impact on the rate of innovation. The article addree two main iue. The firt i the optimum proviion of on-thejob training neceary to be able to adopt, and adapt to new technologie. The econd i the impact of both formal education and on-the-job training on the innovative capacity of an economic ytem that i the ultimate caue of output growth. In our et-up, education enhance R&D activitie and lower adjutment cot to new technologie, thu facilitating their adoption, while on the other hand on-the-job training enure the poibility to implement the new coming technologie and reap all the related future profit. We aume that the adoption of a new technology conit of two period, i.e. the training phae during which newly hired worker acquire the right amount of know how in order to become familiar with the pecific new technology, and the implementation or production phae in which profit flow arie for firm and in which the cot aving that can be realized arie from productivity increae in the previou phae. By extending the training phae, entrepreneur run a greater rik of hortening the production phae for a given arrival rate of new technologie that progreively erode the profit flow obtained from exiting technologie. The paper how firt that it i poible to find a profit-maximizing, endogenouly determined, amount of training that depend on the worker educational attainment. Thu, a ituation in which better educated worker may be diproportionately elected for training iue i poible, epecially in time of rapid technological change. However, the paper alo how that a non-linear relationhip between education and technological change and growth exit, o that an increae in the formal level of education can even reult in a reduction in the rate of growth. The reaon for thi i the increae in creative detruction that raie technology adoption cot in term of output foregone during re-training pell that arrive at a fater rate. The reult offer ome inight that are intereting from an education policy perpective. cknowledgement We would like to thank Theo Dunnewijk, Thoma Zieemer and Lex Borghan for their ueful comment on the preliminary verion of thi paper. Roberto ntonietti i particularly grateful to Gilberto ntonelli, leandro Romagnoli, Giueppe Vittucci Marzetti and Sandro Montreor for their valuable advice during the PRIN workhop on Dynamic Capabilitie Between Firm Organization and Local Production Sytem, Lecce Italy, June The uual diclaimer applie. * Department of Economic and MERIT, Maatricht Univerity. P.O. Box MD Maatricht The Netherland. driaan.vanzon@merit.unimaa.nl. ** lma Mater Studiorum Univerity of Bologna Department of Economic. Strada Maggiore, Bologna Italy. antonietti@pbo.unibo.it. 1

4 1. Introduction The purpoe of the paper i to tudy the contribution of education and training to economic growth through their impact on the rate of innovation, by formulating an endogenou growth model that combine element from Romer 1990, ghion and Howitt 1998 and van Zon and Yetkiner The model take the endogeneity of firm training deciion into account and addree two main iue. The firt concern the profit-maximizing proviion of workplace training neceary to be able to adopt, and adapt to, new technologie. The econd concern the impact of formal education and on-thejob training on the innovative capacity of an economic ytem that i the ultimate caue of output growth. In our et-up, education and employerprovided training fulfil two different function: general education programme, whoe cot are mainly borne by individual, houehold and public adminitration, increae the opportunitie for future reearch and lower adjutment cot to new technologie, thu facilitating their adoption, while firm-pecific training programme enure the profitable adoption of the new technologie. Our etting link the labour economic literature on education and training and the endogenou growth literature on human capital formation a the primary caue of productivity growth. So far, training, and epecially it interaction with formal chooling, ha hardly been invetigated in the growth literature. The reaon why we have choen to purue thi combination of different trand of literature i that, ince the 1980, maive hift have occurred in kill requirement in the workforce a a reult of rapid technological progre and kill-biaed technical change David, 1990; cemoglu, 1996, 2002; Lopez-Baol, 2002; Bartel et al., Thi emphaize at leat the practical importance of the availability of kill through education and training for economic growth. Brehnahan et al. tate: The hift toward more killed worker appear to have accelerated in the lat 25 year relative to , epecially over the period 1980 until the mid Over thi period, demand ha trongly hifted from low-and middle-wage occupation and kill toward highly rewarded job and tak, thoe requiring exceptional talent, training, autonomy, or management ability 2002, p With the breakthrough of ICT in the 1990 a a general purpoe technology GPT, many occupation and profeion now require kill that are a mix of tudie that are privately undertaken and which are neceary to enter certain egment of the labour market, and kill which have been acquired on the job. Therefore, formal education i not ufficient anymore for explaining international difference in growth performance: whenever pecialization matter, on-the-job training, at leat, play a crucial role beide chooling New technology and training: an overview of the literature The way in which an economy repond to the arrival of a new major technology ha been analyzed both at microeconomic and at macroeconomic level. t microeconomic level, the firt attempt emphaizing the importance of education and training invetment in relation with technological change are the one by Nelon and Phelp 1966 and Mincer 1962, Beide thee 2

5 eminal contribution, we have alo to conider the recent literature borne around the iue of new technology adoption, the tandard theory of the firm and the relative choice in term of human capital invetment and organizational change Pencavel, 1972; Paron, 1990; Kalaitzidaki, 1997, Gander Outide the tandard theory of the firm an important contribution which analyze the interaction between the creation of pecific human capital and the detruction of thi ame human capital engendered by the technological and organizational change i the one by ntonelli and Maggioni In their model, thi relationhip i non-linear and how ome feature aociated with the catatrophe theory. In particular, a the rate of technological change increae, the long-term equilibrium of a worker pecific human capital diminihe. fter a certain threhold i reached, thi ame worker will no longer be able to accumulate human capital through work and will therefore be eliminated from the productive proce. t macroeconomic level, the way in which an economic ytem repond to the arrival of a new major technology ha been decribed in the growth literature focuing on general purpoe technologie GPT. In that literature reearcher have been mainly intereted in invetigating the role played by mechanim like econdary innovation, diffuion, and learning by firm Greenwood and Yorokoglu, 1997; Helpman and Trajtenberg, 1998a, 1998b; ghion and Howitt, 1992, In particular, in their model ghion and Howitt put the attention on the role played of R&D activity on economic growth, and on the proce of Schumpeterian creative detruction activated by fat technological change on output growth. In their etup, growth i generated by a tochatic equence of quality improving innovation that reult from uncertain reearch activitie. The main characteritic of vertical innovation i that new invention make old technologie or product obolete. Thi obolecence, alo called creative detruction, implie a negative relationhip between current and future reearch, which reult in the exitence of a unique teady-tate equilibrium and alo in the poibility of cyclical growth pattern. The model lead to the concluion that if the rate of technological progre in plant i very fat, then plant will have a hort lifetime and hence the proportion of worker releaed every period will be high. The rapid flow of worker into unemployment will generate a high teady-tate unemployment rate. In addition, the fater rate of plant obolecence reduce the payout period to a firm invetment in plant. By dicouraging the creation of the new plant that are the ource of new job opening, it thu tend to reduce the jobfinding rate in the economy, leading to a higher teady-tate unemployment rate. We can call thi effect indirect creative detruction ghion and Howitt, 1998, p Recently, Heplman and Rangel 1999 and Krueger and Kumar 2002, focu the attention on a new mechanim, the interplay between technological change and two type of human capital: technology-pecific experience or vocational education and training. The firt of the two model how that technological change requiring more education and training o that a technology-education complementarity arie, like computerization and ICT diffuion, necearily produce an initial lowdown, wherea technological change requiring le education and training technology and education are ubtitute, like the move from artian hop to the factory, can produce either a boom or a but. The econd, intead, how that economic ytem whoe 3

6 policie favour vocational education, like European Union, will grow lower than ytem favouring general education, like the US, thi gap increaing with growth rate of available technology. 4

7 1.2 The interaction between general education and pecific training in adopting new technologie: theory and evidence from the literature The literature on labour economic ince the ha often treed the importance of activitie like training, learning by doing and experience in the proce of human capital accumulation, both at the individual and at the firm level. For, a early a 1962, Mincer tate that formal chool intruction i neither an excluive nor a ufficient method of training the labour force. Graduation from ome level of chooling doe not ignify the completion of a training proce. It i uually the end of a more general and preparatory tage, and the beginning of a more pecialized and often prolonged proce of acquiition of occupational kill, after entry in the labour force. Thi econd tage, training on the job, range from formally organized activitie uch a apprenticehip and other training program to informal procee of learning from experience. ccording to cemoglu: Training i important when new technologie are adopted, or in the proce of a radical change in the environment, for example the hift from low to high kill job taking place in mot OECD countrie today 1996, p The importance of the ditinction between formal education and workplace training ha been alo empirically treed in many reearch tudie. The firt we mention wa carried out in 1979 and concerned worker in Germany Pichke, 2001, while the econd and the third 2 concerned Canadian worker in 1989 and 1993 repectively. Moreover, we can alo mention a fourth ource of evidence: the Eurotat Continuing Vocational Training Survey CVTS OECD, 2003.The main concluion from that tudie are that: i the mot common channel through which manufacturing worker obtain the mot important kill for the labour market i continuou formal on-the-job training; ii the mot important place where they received the mot ueful kill for the labour market i the firm, the workplace, the econd being chool and higher education intitution. Other indicative data in thi field are the one provided by the BLS Survey of Employer-Provided Training Frazi et al., 1995, the US Educational Quality of the Workforce National Employer Survey EQW-NES and Lynch ccording to thee analye, companie provide training becaue firm-pecific kill are needed, becaue of change in technology, and to retain employee; not only, but baic kill are often eaier to learn when taught in the context of a job. While there i ample empirical evidence that the ditinction between education and on-the-job training i important in haping and improving individual kill endowment, the logical next quetion i whether thee type of training are really ubtitute or complement. The poitive link dicued above between training and technical change on the one hand and education and technical change on the other, ugget uch a poitive correlation alo for education and training. direct, albeit partial, anwer to thi quetion alo come from Mincer 1962, who recognize that the degree of ubtitutability 1 We are referring to the human capital revolution driven by the Chicago School Lewi, Mincer, Becker even if we hould alway keep in mind that the very eminal contribution on thi field ha been provided by dam Smith in the 18 th century. 2 In particular we are referring to the Survey of Manufacturing Technology 1989 and the Survey of Innovation and dvanced Technology

8 between the two varie among job and over time with change of technology. However, he alo admit that a poitive aociation between education and training i not definitional but i an empirical inference from the oberved income data. More chooling, in fact, eem to involve more training, both formal and informal, though not necearily in a fixed proportion. School education, indeed, i a prerequiite, a bai on which to build additional, more pecialized, training. Due to the difficulty collecting data at the firm and the individual level, the empirical evidence i ambiguou. What we do know from the data i that a poitive aociation between education and job training can and ha been inferred from differential lope of experience profile of wage Mincer 1984, 1988a, 1988b. The more recent emphai on worker training tem from the evidence that a more highly-killed workforce i needed, and that effective training i cloely linked to the workplace and to employer need. The earning and employment opportunitie of le-educated worker have declined ubtantially over the lat decade. The earning gap between more and le educated worker widened, a did the level of earning diperion among worker with the ame level of education. Thee trend have led many reearcher to conclude that there ha been a teady increae in the demand for killed worker Bartel, 1995; Brehanan et al., 2002; U.S. DOL, International evidence on the complementary nature of education and training come alo from Brown 1989, Lynch and Black 1995, Brunello 2001 and OECD dult with high level of educational attainment are alo more likely to receive more training. On average, three time a many jobrelated training hour are inveted in adult with a tertiary qualification compared to thoe with le than an upper-econdary qualification. Moreover, training tend to reinforce kill difference reulting from an unequal participation in initial education. Participation rate in both job-related continuing education and training and in all continuing education and training rie with level of educational attainment. Bartel and Lichtenberg 1987 and Lillard and Tan 1986 how that the poitive aociation between initial education and participation in continuing education and training remain trong even after controlling for other characteritic affecting participation in training. Worker tend to receive more training in countrie with higher overall average level of educational attainment, a well a in countrie that devote a larger hare of GDP to reearch and development, or that achieve a trong trade performance in high-tech indutrie. Thee pattern ugget that initial education and continuing education and training are mutually reinforcing, and that education combine with other factor to make adult training leat common among thoe who need it mot. Still other empirical upport for the complementary nature of education and training come from Heijke et al. 2003, who find a poitive correlation between the level of generic competencie acquired through tertiary education and training participation of young worker. In addition, the amount of on-the-job training needed i poitively related to the actual vocational competencie mimatche, a training i needed to adjut the acquired competencie to the required one. Human capital theory offer a general anwer to why higher-educated worker engage in more training on the job: peron that have greater learning ability and better opportunitie to finance the cot of human capital invetment, do indeed invet more in all form of human capital, including 6

9 chooling and job training Mincer, Moreover, ome analyt claim that chool education i a complementary factor to job training in producing human capital: thi i in line with the idea that generic competencie acquired in higher education reduce the cot of further learning by providing higher learning abilitie for graduate. In other word, education enhance the productivity of job training at work. It i clear, however, that chooling can alo be a ubtitute for job training: thu, the decline in apprenticehip ha been attributed to growth in educational level over the long-run. Finally, both chool education and job training are more profitable where productivity growth i more rapid. 1.3 Stylized fact regarding the link between technology adoption, education and training Empirical fact about the link between technical change and education and training can be ummarized a follow: 1. a more rapid pace of technology in a ector generate an increaed demand for education and training of the ectorial workforce Bartel and Lichtenberg, utor et al alo how that indutrie with greater growth in employee computer uage or with more computer per worker have upgraded the kill of their workforce at a fater rate. Increaing ue of computer technology, retructuring of buine, and a growing global economy are ome of the factor economit cite a contributing to change in the employment tructure of the U.S. economy ince the early Furthermore, there i coniderable growth projected to occur in occupation with higher educational requirement; the job claification that currently ue low-killed worker are experiencing "upkilling," which tranlate into a need for more reponibility, more knowledge, and ultimately more kill; and, there ha been tagnation and even a decreae in the number of job that are unkilled or very low killed Barnow et al. 1990; 2. more-educated worker are utilized the younger the age of equipment, and thi effect i magnified in R&D-intenive indutrie Bartel and Lichtenberg, In addition countrie inveting a higher hare of GDP in R&D or having a higher hare of reearcher in the workforce alo tend to have higher training rate and better educated worker OECD, 1999; 3. there i a greater prevalence of on the job training in ector in which meaure of productivity growth are higher Lillard and Tan, Brenahan et al alo find that ICT meaure, in particular ICT and workplace organization, are correlated with policie for greater invetment in human capital, i.e. training and creening of new employee on the bai of their education; 4. over the long run, technologically more progreive indutrie tend to utilize more-educated worker among the younger worker Gill, 1988; Brenahan et al., 2002; Lopez-Baol, 2002; 5. the bia of technological change toward human capital mean that in the hort run, wage of more-educated worker increae more or are reduced le in ector with more-rapid productivity growth. Thu, wage profile are teeper in progreive ector a profitability of training and experience increae Bartel, 1995; Muyken and Ruholl, 2001; 7

10 6. finally, Lazear 2002 and European Commiion 2001 how that tudent who have a more general curriculum have a higher chance of becoming entrepreneur, a trend that proxie the ucceful adoption of new technologie. nd that eem to be more frequent in the US where the emphai i put on the development of general kill - rather than in Europe where more vocational-oriented training programme eem to prevail. Summariing the point above, education and training are in higher demand where productivity growth i more rapid becaue the technological change in production procee that underlie productivity growth, require the training and retraining of worker. Fater technical change require a fater replacement of kill that become obolete. Thi require more training on the one hand and/or a greater ability to train, i.e. a higher level of education. In fact, if technological change and the relative proce of adoption/aborption are in ome degree firm-pecific, the firm will tend offer training after initially hiring more educated and more-adaptable individual who, in turn, erve a the teacher making ue of the partial non excludability of knowledge. 1.4 Roundup and baic model feature Rounding up, there are five important relation between education, training and technological change that we can extract from the theoretical and empirical tudie referred to above: 1. The poitive link between productivity on the one hand, and training and education on the other; 2. The poitive link between high level of education and R&D; 3. The poitive link between high level of R&D and growth; 4. The nature of the interplay between education and training; 5. The nature of the link between high level of growth through technical change and training, i.e. the relative increae in importance of education a a ource of growth relative to training in time of fat technical change Lindbeck and Snower, We conider the firt two relation to be tylied fact comparable in nature to logical premie. The third point derive from the baic aumption of R&Dbaed endogenou growth model and i upported by numerou econometric tudie. Point 4 and 5 we conider to be relation that hould logically follow from the premie 1 to 3. We ue thee relation a the bai for the contruction of an endogenou growth model that upport our belief that human capital, in the form of not only education but alo time-conuming onthe-job training, ha a poitive impact on innovation - and thu economic - growth. t the ame time we think that chooling a a proxy for human capital endowment i not ufficient to decribe the proce through which worker and firm cope with innovation and rapid technological change. General education i important for making people more flexible in learning pecific kill, while on-the-job training i eential in order to reduce the vocational mimatche Heijke et al., 2003 that new product, new procee and new organizational practice create. In our etting it i technical progre that open the poibility to have a mimatch between the competencie embodied in individual through 8

11 chooling and the competencie that firm require in their production procee. Technological change generate new job or tak that, in turn, require new and/or more complex kill: thee competencie are not completely acquired through formal chooling, but they can only be learnt and experienced on the job, thu reducing time per worker that can effectively be allocated to the actual production proce. Thu, the firm face a trade-off: by pending reource and time in educating it workforce on the job, the firm, by one ide, build it knowledge-bae, but, on the other ide, it ha to pend time out to learn about the new production proce aociated with new technologie/product. By doing that, it alo run the rik that a new technology will come on-line making the pecific competencie jut acquired by the workforce rapidly obolete. We implement thi general trade-off by adopting the link 1-3 lited above, and by conidering both formal chooling and on-the-job training a the main channel through which individual acquire generic and technologypecific competence. In doing o we will aume that human capital endowment of individual are a combination of vocational competencie of a particular field of tudie and generic competencie. The former include fieldpecific theoretical knowledge and field-pecific knowledge of method, while the latter include learning abilitie, reflective thinking, problem-olving abilitie, analytical competencie, documenting idea and information. One of the main aumption of the model i that the effectivene by which more-educated worker are able to improve their competencie and their labour productivity i determined by the level of kill acquired during the initial phae of education. higher level of education i therefore ueful in three way: firt, it i the bai for future R&D activitie; econd, it poitively affect individual labour productivity; third, it allow taking part in training with a higher productivity ince higher-educated individual learn more quickly and are therefore le cotly to re- train. By modelling the productivity of a worker a a geometric average of hi level of education and training, we will effectively be treating thee two channel a direct ubtitute at the microeconomic level. We will then look at the aociation between education and training at the macroeconomic level to find out whether we can reproduce tylied fact number 4, that i omewhat ambiguou in that mot material eem to point to a poitive, and thu complementary, link between education and training, while ome material point to a negative link between education and training, and hence education and training would have to be ubtitute, not only at the micro-level, but alo at the macro-level. Premie 2 and 3 are covered by uing the Romer 1990 model a a template for our own exercie. The remainder of the article i organied a follow. Section 2 contain a decription of the model, including enitivity analye that we have performed to how how training and education depend on each other in the framework of intertemporal profit maximiation. We alo how how the integration of thi training behaviour in a general equilibrium growth etting influence the growth reult. Becaue the model i trongly non-linear, we ue numerical imulation to how how it work, and what kind of concluion can be reached regarding the growth, education and training nexu. Section 3 provide the reult of ome numerical experiment we have performed with the model, while ection 4 include a ummary and ome concluding remark. 9

12 2. The model 2.1. Baic model et-up The model combine element from variou endogenou growth model, epecially the one by Romer 1990 and ghion and Howitt It alo ue inight from imilar modelling exercie in van Zon and Yetkiner In order to keep the model a imple a poible, we only have two type of labour a factor of production. The one type of labour i low-killed 3 that only ha a ue in producing output and high-killed labour that ha an alternative ue in the form of deigning blueprint for new production technologie. There i no capital, o no aving deciion need to be made. The model tart from the aumption that the introduction of a new technology require the uer to learn how to adopt them effectively and efficiently. In order to do that, the workforce aociated with a new technology need to be trained firt. 4 During their training period, the worker are uppoed to earn a competitive wage, ince they are aumed to be indifferent between working and o earning their keep and training thu learning to earn their keep later on. During the training period, worker that are trained are not working; hence they do not produce anything. Therefore, the cot of training include both the direct cot of wage that have to be offered to the trainee and the opportunity cot of not producing anything while training. No direct, fixed or unk outlay are conidered here. The benefit from training are an increaed productivity later on during the production phae of a technology. Thi increae in productivity enable the owner of the firm that ue new technologie to economie on wage-cot during the production phae. Training therefore generate cotreduction in the future in return for current cot-increae. Becaue we aume that there i no production while training, it follow immediately that a model with complete creative detruction of old technologie through the arrival of new technologie i le uited for our purpoe, ince it would generate odd growth pattern that can not be oberved in reality. For, in uch a creative detruction etting, the arrival of a new uperior technology would lead to a zero level of output, while the workforce i re-trained to be ued with the new technology. Intead, a Romer 1990 like approach eem to be more uited, ince in that cae new technologie do not fully replace old one, but gradually drive them out of the market. Thi i the creative wear and tear effect referred to in van Zon and Yetkiner In uch a love of variety etup, old technologie never die, but imply become le important and therefore le ued with the progre of time. Thi creative wear and tear continuouly and gradually releae labour reource that can be re-employed by the new firm created with the aim of uing the new technologie that arrive on the market. 3 The eye-hand coordination of Romer Thi implie that the know-how of worker with repect to uing other technologie i not readily applicable to new technologie. Hence all worker that are aigned to a job need to learn how to perform effectively in that job, through qualifying training, workplace practice training, formal job kill training and o on. 10

13 While labour productivity can be increaed directly by training, the productivity of the training proce i poitively influenced by the level of formal education attained by the workforce during the firt part of their live. In addition, we aume that the productivity of reearcher i poitively influenced by the level of kill they have accumulated through formal chooling. The et-up outlined above ugget that we may expect an intereting reult to arie in which creative wear and tear that i induced by fater arrival of new technologie on the market will lead to horter payback period for the training cot involved in aborbing thoe new technologie. Thi ugget that fater technological change due to a higher educated population alo induce a hift in emphai from pecific training toward more general education cf. Lindbeck and Snower, The reaon i that a better educated workforce would be more able to adapt to fater changing production circumtance a they would arie from a fater arrival of new technologie. In hort, we would expect there to be a premium on formal education rather than pecific training in time of rapid technological change. However, we would expect alo that an increae in the formal level/duration of education could even reult in a reduction of growth becaue of the increae in technology aborption cot in term of output foregone during re-training pell that arrive at a fater rate, but may take a horter time. Thi ugget that, from growth perpective at leat, there may be an optimum level of formal education which would eem to be a reult that i very ueful from an education policy perpective. The remainder of thi ection i organied a follow. In ection 2.2 we firt pay ome attention to the different kind of labour and their upply. Then in ection 2.3 we decribe the demand for labour from a micro-perpective a part of our training and production model. In ection 2.4 we how how the outcome regarding optimum training duration and quai-rent depend on the tructural parameter of the model. Section 2.5 decribe the aggregate demand for production labour, while ection 2.6 decribe the demand for R&D labour. In ection 2.7 all the part of the model are integrated, and ince it ha become a highly non-linear model, we ue numerical imulation to how the main relationhip between education, training and economic growth at the aggregate level. 2.2 Labour upply There are two type of labour, low-killed labour further called L, and high-killed labour further called H. L i ued in final output production only, while H i ued a R&D labour further called H R or high-killed production labour further called H P. For reaon of implicity we will not formulate a fully-fledged overlapping generation model. However, we aume the population to remain fixed, but contantly needing education, a we would expect it to occur in real life too due to the fact that older educated generation die, and the younget are born with a clean educational late. We will model thi by auming that at any time jut a fraction 0 1 ϕ 1 of the high-killed population i available for final output production and R&D activitie, wherea the complement of that fraction, i.e. ϕ, i being educated. To implify thing even further, we aume that L 11

14 doe not need any education. 5 Given the above, we mut have that the entire population P i given by: P = L + H 1 where H i the part of the population that i uitable to fill high-killed job in final output production and in reearch activitie. From the expoition above, it follow immediately that: 1 ϕ. H = H R + H P 2 Equation 2 tate that the part of the high-killed population that i not in the educational ytem i either engaged in R&D activitie H R or in final output production activitie H P, while H P itelf i in part engaged in training T and in production J: H P = T + J 3 Equation 2 and 3 reflect the aumption that market are alway clearing, and o there i no unemployment pool that aborb exce upply. Equation 2 alo indicate that educated high-killed R&D labour i a perfect ubtitute for high-killed production labour, and the other way around. 2.3 Labour demand The demand for intermediate The demand for labour i derived from the aumption that output i produced under perfectly competitive circumtance, by aembling the intermediate output of a et of imperfectly ubtitutable production technologie uing low-killed labour only. We ue an Ethier function to decribe thi final output production proce: B 1 α i Y = L α x 0 di 4 In equation 4, Y i final output, B i the index of the latet technology that ha entered the production phae, and x i i the volume of intermediate output aociated with production technology i. 1 α i the partial output elaticity of low-killed labour. For reaon of implicity, we aume that one unit of each intermediate good require the ue of one efficiency unit of high-killed labour. Efficiency unit of labour ued in the production of x i are called h i. We therefore have: h i = x 0 i B 5 i 5 Thi i a trong aumption, but it reflect the notion that high-killed worker generally have been educated for far longer period than low-killed worker OECD,

15 We ubequently aume that one phyical unit of high-killed labour aociated with technology i further called j i can generate π, ϕ efficiency unit of labour. The term π, ϕ i therefore the productivity of labour, and meaure the length of time pent training by thi worker, while ϕ i a direct indicator of the time pent in formal education/chooling. Conitently with human capital theory, we aume π / > 0, π / ϕ > 0. We therefore have: j i hi xi = = 0 i B π, ϕ π, ϕ 6 The demand for each intermediate, given it price p i, can be obtained from the firt order condition for profit maximiation by the perfectly competitive final output ector: p i Y = x i = L 1α α x α 1 i x i pi = L α σ 7 1 where σ = > 1 i the elaticity of ubtitution between intermediate. 1α The correponding demand for labour in phyical unit can immediately be obtained by ubtituting 5 and 6 into 7: j i σ pi L α = 8 π, ϕ Equation 8 repreent the derived demand for labour for each intermediate good producing firm, given the price it et for it intermediate Maximiing the net preent value of expected quai-rent The price etting behaviour referred to above, together with the behaviour that determine how long the training period hould be, can be formulated a the olution to the problem of maximiing the net preent value of the flow of quai-rent that can be obtained by hiring a population of worker, training them for time-unit, and then uing thee trained worker to generate output that i old conditional on the invere demand curve 7 and it expected evolution over time. For, a we will how later on, in a ituation of teady tate growth, wage may be expected to grow equally teadily, and o price being et uing a mark-up over marginal cot can be expected to grow teadily too. Becaue of the ymmetry between firm - all firm have the ame production technologie and contribute in the ame way to final output -, the training period will be the ame for all relatively new firm too. Hence, wage are the ame for each firm too. We aume furthermore that wage offered to trainee are the ame a thoe for high-killed worker aociated with firm 13

16 that are in their production phae already. The tructure outlined above ha been depicted in Figure 1. In Figure 1, the demand for labour to produce an intermediate invented at time t = 0 i depicted for all moment in time after t = 0, for a given and contant growth rate of wage. n intermediate come onto the market after a training phae of duration. During that phae, the wage rate i aumed to rie at a given proportional rate, and conequently ee equation 8 and 10 further below the demand for labour at time t> that i aociated with the intermediate invented at time t = 0, i.e. j t, will fall. However, it would be a wate of reource to train more worker than would actually be needed from the tart of the production phae at time, hence a rational entrepreneur would hire j worker during the training phae of the intermediate and then lide down the labour demand curve from the tart of the production phae at time. j t j 0 t Figure 1 Figure 1 i formalied a follow. One hould recall that due to the ymmetry between firm, the training period will be the ame for all firm, including new one. Hence, wage are the ame for each firm too. uming furthermore that wage offered to trainee are the ame a thoe for high-killed worker aociated with firm that are in their production phae already, the net preent value of the expected flow of quai-rent further called Q for a firm that ha bought the latet blueprint at the current time taken to be time zero, i given by: Q = e ρτ p T x T xt ρτ w. T dτ j e wt dτ π, ϕ

17 where ρ i the rate of dicount, and w T i the expected wage rate per phyical unit of labour at time T T 6. In equation 9, where we have ued 6 to replace high-killed labour demand by the demand for intermediate, the firt integral decribe the flow of quai-rent, ince labour i the only factor of production. That flow tart only after the training-phae ha ended and the production-phae ha begun. The training-phae take unit of time. During the training-phae, j phyical unit of labour need to be trained, ince that i the amount of labour needed when the production-phae tart. There are training cot involved, and the preent value of thee cot i given by the econd integral in 9. The intermediate good producer now ha two independent control to be determined. The firt one i the Q - maximiing price of intermediate, and the econd one i the Q - maximiing length of the training period. It hould be noted that equation 9 can be maximied with repect to the price of intermediate only for the future in a far a it refer to the production phae. 7 By differentiating 9 with repect to p T for T, we immediately obtain: Q p T = x T 1+ ε 1 p T wt = 0 π, ϕ p T wt = [ α π, ϕ] 10 which i the familiar moroo-robinon price-etting rule, where 1 ε = σ = i the price-elaticity of the demand for intermediate ee alo 1α equation 7 and where marginal cot are wage cot per efficiency unit of labour. 8 In order to find the Q - maximiing value of, we have to ue Leibniz rule for differentiating integral, ince the bound of both integral in 9 depend on. We therefore get the firt-order condition: Q = 0 = p x e x w.. e π, ϕ ρτ ρ xτ wτ. π ϕ, dτ j e ρ j w 0 w e τ ρτ dτ 11 The firt term of 11 within curly bracket i the preent value of the lo in quai-rent that occur by extending the training-phae by 1 unit of time marginal opportunity cot of training. The econd term i the preent value of 6 Note that we have dropped the technology ubcript, becaue the ymmetry of 4 and 5 implie that the net preent value problem i eentially the ame for all intermediate good producer. 7 The price of a good that i not produced and therefore not old can hardly be regarded a an effective control. 8 Cf. ghion and Howitt

18 the additional training cot for a given number of trainee aociated with a marginal increae in total marginal training cot. The third term i the preent value of the increae in total training cot for a change in the number of required trainee that could be expected to occur if the production phae tart 1 unit of time later, i.e. if the training-phae i extended by 1 unit of time marginal direct cot of training 9. The final term repreent the preent value of the benefit from extra training marginal training benefit, ince thee would increae labour productivity and hence decreae production cot for the entire duration of the production phae. Equation 11, indeed, repreent the equality condition between marginal benefit and marginal cot of additional training. In order to find the optimum length of the training phae, it i neceary to pecify the productivity function π, ϕ. In order to keep the analyi a imple a poible and to accommodate the tylied fact that the higher an individual level of education the fater he learn, o reducing training cot born by firm Roen, 1976 we have choen the following Cobb-Dougla labour productivity-augmenting pecification: π ϕ = γ ϕ γ 1 1γ 1, 0 12 where γ 0 and γ 1 are poitive and contant parameter and where 0 γ 1 1. From equation 12 it i clear that ome training and education are alway neceary, ince otherwie productivity would be zero. One oberve that the productivity level of a worker i a geometric weighted average of the worker educational level, a proxied byϕ, and the level of training a proxied by, where γ 1 i the relative weight or intenity of training in productivity, and γ 0 i a contant cale parameter 10. Equation 12 how that a contant level of productivity of a worker can be attained for different combination of and ϕ, where a decreaing value of mut be compenated by an ever increaing value of ϕ in order to keep productivity contant, and vice-vera. Hence, at the microlevel, education and training are aumed to be imperfect ubtitute. 2.4 Senitivity analyi By ubtituting 10 and 12 into 11, we obtain the equation that can be ued to find the optimum value of. Unfortunately, that equation i trongly non-linear which preclude finding a cloed form olution for. However, we can get an impreion of the enitivity of the net preent value of the quairent, i.e. Q, for change in by drawing Q a a function of, for given value of the parameter. Thee bae-run parameter value are given in Table 1 further below. It hould be noted that the equation derived above contain endogenou variable that are given from the point of view of the individual 9 Indeed, a we will how later on, technical change lead to a continuou upward preure on wage, and hence to a continuou downward adjutment of the demand for labour. So, by extending the training period, one would normally need le people to train becaue of the anticipated fall in the demand for labour per technology over time in the teady tate. 10 For intance, we can interpret γ 0 a a proxy of worker effort while working. 16

19 entrepreneur, but that will change endogenouly over time in the full model that we will pecify later on. Preently, we are only concerned with howing that the pecification we have choen for the production tructure and the productivity function enure that there i indeed an optimum amount of on the job training that depend in an intuitive way on the parameter lited in the Table below. It hould be noted that thee parameter value are jut ome fake number not reflecting any empirical regularitie, except for their ign. Parameter Value Parameter Value α ŵ ρ γ γ ϕ x w L δ Table 1. Bae-run parameter value In thi Table ŵ i the expected intantaneou growth rate of wage, wherea ρ i the rate of dicount. 11 x i a cale factor for the demand for intermediate that will be modelled explicitly later on. For our preent illutrative purpoe the only thing that i relevant i that it i a contant. δ i the intrinic productivity of R&D worker, which will be made more clear later on. In Figure 2, the downward loping curve i the one aociated with Q /. One oberve that for the pecific parameter et choen here, Q itelf ha a maximum, but Q i relatively irreponive to change in in the neighbourhood of that maximum. The maximum of Q i reached for a value of about equal to Q,dQd Figure 2 11 Obviouly, in the full imultaneou model, the expected growth rate of w will be an endogenou variable. 17

20 By changing the parameter underlying Q, we can find out more about the qualitative and quantitative behaviour of Q and the conequence for the optimum value of. In order to do thi, we have increaed each of the parameter individually by 10% a compared to it bae-run value 12, and then obtained the correponding graph of Q. The hift in the graph of Q are a direct indication then of the partial derivative of Q with repect to the parameter under conideration for the entire range of value of. But rather than howing all the graph aociated with thee partial derivative, we provide information in tabular form below in Table 2. The firt column of that Table hold the name of the parameter we have changed, while holding the other parameter contant. The column labelled Q and hold information regarding the ign of the partial derivative of Q and the optimum value of hence the hift in the Q -curve with repect to the parameter under conideration. Parameter Q Parameter Q α - - γ ŵ - - ϕ + + ρ - - x + + γ w Table 2. Parameter enitivity From Table 2 we can conclude that the ign of the change in Q and are alway the ame. Thi indicate that a variation in ome parameter change the hape of the Q-curve roughly proportional in all direction meaured from the origin. Looking at the effect of individual parameter change, we ee that an increae in α implie an increae of the price-elaticity of demand. Thi in turn lower the profit margin, hence profit themelve, hence the preent value of the quai-rent Q too. Thi will lower the optimum amount of training, a one would expect, ceteri paribu. n increae in the rate of dicount ρ ha qualitatively the ame effect. The preent value of the quai-rent i negatively affected, and o i the optimum amount of training. rie in the productivity parameter γ 0 raie both the preent value of the quai-rent and the value of the optimum amount of training, again a expected. Thi fact can open the poibility to tet a poitive relationhip between the effort of worker on the job ee footnote 11 and the amount of training the firm offer them. rie in γ 1 raie the contribution of training to productivity. It alo reduce the contribution of education to productivity. The net effect on the preent value of the quai-rent i poitive but very mall, while the effect on the optimum 12 The enitivity analyi ha been carried out for ±1% and ±10% variation in the parameter value. In the paper we report only the +10% cae. 18

21 amount of training i ditinctly poitive. change in the amount of formal education ϕ ha a poitive effect on productivity, hence on Q. It alo raie the optimum amount of training, indicating that the optimizing behavior underlying the choice of the amount of training turn education and training into complement from an obervational point of view 13 rather than the ubtitute that they formally are, given the pecification of the productivity function we have choen cf. 12. change in the growth rate of wage reduce Q. It alo reduce the optimum amount of training, ince not only training cot rie during the training phae, but in addition to thi, quai-rent during the production phae will fall. Similar reult can be oberved for a rie in the initial wage rate. Both Q and the optimum amount of training fall, becaue profit flow are negatively affected, a with the rie in the expected growth rate of wage. Moreover, the payback period i reduced, thu putting a bonu on tarting the production phae earlier than with lower initial wage. Finally, a rie in the autonomou demand for the intermediate under conideration would raie both Q and the optimum amount of training, a one would expect. We conclude that the enitivity reult are all plauible, but more importantly, the profit maximiing behaviour underlying the deciion how long to train the workforce turn education and training into obervational complement, even though they enter the productivity function given by 12 a direct ubtitute. 2.5 Technological change and the demand for labour at the aggregate level in the Romer 1990 model, a new intermediate input i produced in accordance with the newet blueprint coming from the R&D ector. The index of the newet blueprint produced at time t i t, and R&D worker produce thee blueprint at a proportional rate that i itelf proportional to the number of R&D worker, a in Romer We therefore have: d ˆ = = δ. H R. 13 dt uming teady tate growth in at a rate Â, we hould have that the latet intermediate that i actually in the production phae mut be the intermediate that ha jut ended the training phae of length. Let Bt be the blueprint index of the marginal intermediate jut entering the production phae at time t. In that cae we mut have that: ˆ B t = t = t e 14 Becaue of the ymmetry of 4 with repect to each intermediate, we mut furthermore have that the demand for labour active in the production phae i the ame for each intermediate. Hence, the demand for all labour in the production phae mut be given by: 13 Thi hold under the ceteri paribu aumption. Thing will change omewhat in the context of the full model, a we will ee later on. 19