NN40, May 2008
Education for Sustainable Development? Or The Sustainability of Education Investment? A Special Issue
Education and Training in a Model of Endogenous Growth with Creative Wear-and-Tear
By Adriaan Van Zon [a] and Roberto Antonietti [b], a ? Maastricht University; b - University of Padua
Emails: adriaan.vanzon@merit.unimaas.nl and roberto.antonietti@unipd.itKeywords
Education, Endogenous Growth, On-The-Job Training, R&D, Creative Wear-and-Tear.
Summary
What is the relationship between human capital and technology-driven sustainable growth? In particular, how does the rate at which firms adopt new technologies affect the level of education and training of a country?s workforce? The effect of faster technological change is to increase the importance of general skill accumulation through education and to (re-) train more people for shorter periods of time.
There is a strong consensus in both the academic and anecdotal literature that human capital is an important determinant of productivity at the individual and at the aggregate level. At the macroeconomic level, in particular, there is evidence that human capital investments on the aggregate productivity growth does not only have a positive impact in the short run, but also in the long run, through their contribution to technological progress, particularly through the creation and adoption of new technologies and the improvement of existing production processes. In this sense, human capital becomes the crucial element for a technology-driven sustainable growth, in which new, superior, technologies continuously replace existing ones, but also require people to continuously learn how to efficiently operate them.
The role of human capital for a sustainable economic growth has been particularly emphasised in the Lisbon strategy of the European Union aiming to take advantage of the growth and employment opportunities offered by new technologies through increased and more efficient investment in knowledge and human skills.
However, human capital as such encompasses different types of investments in people. The main economic literature studying the determinants of aggregate productivity growth generally focuses on a single dimension of human capital, i.e. education. However, since the seminal contribution of Becker (1964), labour economists have acknowledged the existence of other types of human capital, in particular the accumulation of technology-specific skills through learning-by-doing (Arrow, 1962), experience and, more generally, on-the-job training (Mincer, 1962). There are two central questions in studying the relationship between technology and human capital: how does the rate at which firms adopt new technologies affect the level of education and training of a country?s workforce? And, if technological change turns existing knowledge obsolete and then tends to foster general, rather than firm-specific skills, what would be the optimum level of education spending be in the face of a faster arrival of new technologies?
We try to answer these questions by developing an endogenous growth model that borrows elements from Romer (1990), Aghion and Howitt (1992) and Ramsey (1928), and that combines private households investment in education with private firms investment in workplace training in a context of costly technology adoption and Schumpeterian creative destruction. In our model set-up, each production activity is time-consuming. The total amount of time available can be spent for three purposes: the accumulation of human capital, the production of goods and the production of new technologies. The labour time available can be subdivided in turn into training activities necessary for adopting the newest technology, and current intermediate goods manufacturing activities.
The accumulation of general knowledge occurs within the educational system, where people spend their time either as pupils or as teachers. We assume that teachers earn a competitive wage covered by fees paid by private households who, by accumulating human capital, expect to earn higher future wages in the labour market through higher labour efficiency and trainability. Technological knowledge is produced through R&D and is embodied in new intermediate goods that are patented and sold to final good producers. In line with Schumpeterian R&D-based endogenous growth models, we assume that the rate at which new designs arrive onto the market is the result of the time spent in research activities and the amount of education acquired by R&D workers. However, new technologies do not fully replace old ones, but instead drive the latter technologies gradually out of the market, as in a ?wear-and-tear? process of knowledge obsolescence and profit erosion.
Finally, knowledge is used at the plant level for the production of intermediate goods. However, the arrival of a new intermediate requires workers first to learn how to use it effectively, through a time-consuming on-the-job training activity that is entirely financed by the firm.
In our model, education pervades the entire economy and plays three different roles. First, from a consumers? point of view, more education means higher future labour earnings due to the higher trainability and efficiency of individuals. Second, from an R&D point of view, more education means higher arrival rates of new technologies and thus faster technological change. Third, from the point of view of the firm, more education means lower training costs, and thus the possibility to adopt new technologies sooner in time, thus bringing revenues forward in time.
As part of a general equilibrium setting, we introduce both the households? educational choices ? that are driven by the possibility to reap higher future wage rates ? and the level of education as a factor that determines the productivity of R&D workers as well as that of high-skilled production workers. As a result, we obtain a hump-shaped relationship between the rate of technical change and the level of education, since time spent in the education system cannot be utilized either for final good production or for new technology production. This means that, on the one hand, it is possible to derive an optimum amount of education that maximizes the rate of technological change, while on the other hand, too much time spent in acquiring ? or teaching - skills at school reduces the time available for production activities, thereby reducing the time and financial resources available for the production of future innovations. Moreover, a faster rate of technological change has two effects. On the one hand, it increases aggregate productivity growth while leaving the optimum level of education unchanged. On the other hand, it decreases the duration of training, whereas the number of people in the training phase increases. So the effect of a rise in R&D labour productivity is to (re-) train more people for shorter periods of time.
Interestingly, when we include households education decisions in the analysis, we see that the optimum private level of the duration of education, which is driven by their wish to earn higher future wages, is strictly below the growth maximising duration of education: from a growth perspective, therefore, households tend to under-invest in education. Similar results emerge when we look at the general equilibrium relationship between education and training. In this case we find that the observational complementarity between the duration of education and training turns into a U-shaped relationship, indicating observational substitutability for low levels of education-time and complementarity for higher levels of education-time. This observational substitutability arises from a general equilibrium effect that pushes up wages as the rise in the time devoted to education raises the growth rate of the economy and hence the demand for production labour. This also reduces the optimum duration of training.
We also observe that when technological change speeds up, the human capital composition of the workforce changes in favour of general education. Because a higher rate of innovation increases the number of people being (re-) trained, the number of workers available for direct production decreases, since the number of R&D workers increases. Nonetheless, output grows faster than before.
With respect to households? education decisions, we find that the privately optimal level of training is higher than its growth maximising level, suggesting that households do not invest enough to minimize firms? training costs, thus forcing producers to provide more training than would be necessary for maximizing growth. A change in education fees may alter the level of education such that training costs are reduced by more than training fees are lowered for households.
In summary, we reproduce the stylised fact that general skills become a more important a source of growth relative to technology-specific skills in times of faster technological change. Our model also corroborates the mixed nature of the relationship between general and specific training by showing conditions under which they act as substitutes and the conditions under which they behave like complements.
Our model shows that in times of increasing technical change, the optimum ?portfolio-mix? between education and training changes in favour of the former, since that provides a relatively solid basis for the development of technology-specific skills that are prone to creative destruction. However, when we ?endogenise? education costs, we see that private households? decisions regarding education seem to leave growth opportunities and training cost reductions unexploited, suggesting that there is room for public policy intervention.
Our model also suggests that the sustainability of growth, as exemplified by the relative permanence of the trend in growth as opposed to technology induced movements/fluctuations around that trend, would be directly affected by the portfolio-mix of education and training, even though we have focussed on the steady state (i.e. the ?trend?), rather than the corresponding transitional dynamics (?fluctuations around the trend?) to keep the model as simple as possible. However, the idea of ?growth-risk-diversification? by means of a careful composition of human capital portfolios seems to be an interesting and useful future extension of the general education and training framework that the present model provides.
References
Aghion P. and Howitt P. (1992), A model of growth through creative destruction, Econometrica, vol. 60, pp. 323-351.
Arrow K.J. (1962), The economic implications of learning by doing, Review of Economic Studies, vol. 29, pp. 155-173.
Becker G.S. (1964), Human capital, New York, National Bureau of Economic Research.
Mincer J. (1962), On-the-job training: costs, returns and some implications, Journal of Political Economy, vol. 70, n. 5 (supplement), pp. 50-79.
Ramsey F. (1928), A mathematical theory of saving, Economic Journal, vol. 38, pp. 543-559.
Romer P.M. (1990), Endogenous technological change, Journal of Political Economy, vol. 98, pp. 71-103.
Further resources
Adriaan Van Zon is Associate Professor in macroeconomics and international trade at the Maastricht University, Faculty of Economics and Business Administration and senior research fellow at UNU-MERIT. His research interests concern skill-asymmetries and employment, endogenous growth and technical change, health and growth and sustainable growth.
>>Web page.
Roberto Antonietti is Assistant Professor in Economics at the University of Padua, Faculty of Law. His interests range over the economics of labour and human capital, the economics of innovation and skill-biased technological change, the determinants and the effects of international fragmentation of production on employment and productivity.
>>Web page.
Previous versions of the paper have been presented at the IX Conference Dynamics, Economic Growth and International Trade (DEGIT), Reykjavìk, 11-12 June 2004, at the II EALE-SOLE World Conference, San Francisco, 2-5 June 2005 and at the UKFIET Conference Going for growth? School, community, economy, nation, Oxford, 11-13 September 2007.
A former working paper version is available as MERIT-Infonomics research memorandum n. 2005/11 (http://www.merit.unu.edu/publications/wp.php).
The current version of the paper is available as ?Marco Fanno? working paper n. 57/2007, Department of Economics and Management ?Marco Fanno?, University of Padua (http://www.decon.unipd.it/pubblicazioni/wp/index.php).
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