YILMAZKUDAY
EC HAKAN 601 ECONOMIC GROWTH
LECTURE NOTES
WEEK 3
LEARNING BY DOING
It is accepted that the growth rate of per capita income cannot be explained
by only changes in labor-capital ratios since this does not capture the fact that
knowledge increases by producing more output. Thus the Solow model is incapable
of explaining the productivity increasing by the accumulation of knowledge. This fact
comes into picture when we analyze the convergence between countries that have
the same level of capital accumulation.
Arrow (1962) refers to this fact by stating that different countries have
different production functions even apart from differences in natural resource
endowment. He introduces an endogenous theory of the changes in knowledge in
order to explain these differences. In his model, the acquisition of knowledge is
termed learning or in more recent terms learning by doing. Learning is a product
of experience that takes place during activity since it usually occurs through the
attempt to solve a problem.
Verdoorn (1956) relates current output to cumulative output in order to
explain learning by doing. This is an important contribution because it points out an
indicator of the acquisition of knowledge. Arrow (1962) refers to the study of
Lundberg that supports this idea by analyzing the Horndal iron works in Sweden.
Although no new investment is made the production of the firm increases on the
average 2% per annum. This can be explained by only the increase in the cumulative
output, thus, learning by doing.
Although there such examples of learning by doing given above, the formal
analysis of it has been made by Arrow (1962), the focus of this paper. In his model,
the possibility of capital-labor substitution is ignored; the theorems about the
economic world have probably differed from those in most standard economic
theories; profits are the result of technical change; net investment and the stock of
capital become subordinate concepts, with gross investment taking a leading role.
Opposed to Verdoorn (1956), Arrow takes cumulative gross investment as an
index of experience, because he claims that only gross investment can capture the
productivity of capital. Each new machine produced and put into use is capable of
changing the environment in which production takes place, so learning is taking place
with continually new incentives. The learning enters in the production function as in
the model of Solow in which technical change is completely embodied in new capital
goods.
Barro and Sala-i-Martin (1995) summarize Arrows two crucial assumptions
as follows. First, learning-by-doing works through each firms investment.
Specifically, an increase in a firms capital stock leads to a parallel increase in its stock
of knowledge. Second, knowledge is a public good that any other firm can access at
zero cost. In other words, once discovered, a piece of knowledge spills over instantly
across the whole economy1. The second assumption allows us to retain perfect
competition equilibrium, although the outcomes are not Pareto optimal.
Under these assumptions, Arrow (1962) finds out that the production
function yields increasing returns to scale in gross investment and labor used. This
result relies on the fact that each new input is used more effectively than the old
ones. This can be explained by only one thing: learning by doing.
1
Romer (1986) mentions about this fact as a form of externality.
2
However, the existence of increasing returns to scale does not alter the
distribution of the output among the factors of production and they continue to be
paid their marginal products. This fact is because of the absence of knowledge
distribution in the market. That is to say, in a competitive market, there is not such a
mechanism that leads to socially optimal equilibrium by achieving the distribution of
knowledge. In other words, the social rate of return on investment is higher than the
private rate of return on investment. This can be remedied in two ways. First, we can
accept the presence of a social planner who can realize the accumulation of
knowledge and include (distribute) it in the market. Second, as Barro and Sala-iMartin (1995) claims, purchases of capital good can be subsidized, or, alternatively,
the government can generate the optimum by subsidizing production.
Romer (1986) refers to another problem of the model of Arrow (1962). This
problem, together with the problem of existence of social optimum, concerns the
finiteness of objective functions. In a standard optimizing growth model that
maximizes a discounted sum or integral over an infinite horizon, the presence of
increasing returns raises the possibility that feasible consumption paths may grow so
fast that the objective function is not finite. An optimum can fail to exist even in the
sense of an overtaking criterion. In Arrows model, this difficulty is avoided by
assuming that output as a function of capital and labor exhibits increasing returns to
scale but that the marginal product of capital is diminishing given a fixed of
labor. supply As a result, the rate of growth of output is limited by the rate of growth of the
labor force. Interpreted as an aggregate model of growth, this model leads to the
empirically questionable implication that the rate of growth of per capita output is a
monotonically increasing function of the rate of growth of the population. Like
conventional models with diminishing returns, the model of Arrow (1962) predicts
that the rate of growth in per capita consumption must go to zero in an economy
with zero population growth.
3
As a result, since the model of Arrow (1962) considers the positive effect of
capital accumulation on productivity, it, in fact, refers to the reduction of the wages
of labor by the effect of experience. That is to say, learning by doing is a process that
can be achieved by only labors. Even if there is no external technological progress in
the production function, the labors product more effectively by the help of
experience. The level of new capital is only an indicator of this experience of the
labors. When the amount of capital reaches a profound level, this means that the
labors have experienced a profound level of production. In Arrows terms, the labors
have experienced lots of newly problems, and through the solving process, they have
learned by doing.
EXTENSIONS TO THE MODEL
Although the model of Arrow (1962) sets up a newly model which includes
technological changes via learning by doing of labors, the accuracy of the model is
doubtful. In order to remedy this problem, Sheshinski (1967) tests the Learning by
Doing hypothesis against the experience of several manufacturing industries in the
United States and other countries. He begins with defining Arrows model and
focuses on important implications of the model such as the following.
As we mentioned in the above analysis, if the extra knowledge that
investment leads to cannot be sold or appropriated in a competitive market,
then the private benefit from investment is less than the social benefit. The
result of this situation is that investment under competitive conditions tends
to fall below the socially optimal level.
4
Part of pattern of international specialization can be explained in terms of an
early start. Certain industries are unable to compete on equal terms in
world markets because foreign enterprises have been established longer and
are therefore more experienced in their line of production.
In developing planning, socially optimal methods to support the learning
process have to be taken into account.
Opposite to Arrow, Sheshinski (1967) assumes that variations in the labor-
capital ratio are possible at all times. This version greatly simplifies the analysis and
retains the leading feature of Arrows model: the relation between technical progress
and investment.
Sheshinski is also suspicious about the index of experience that should be
used. He examines two alternative assumptions. First, that cumulative experience
depends on cumulated gross investment, and, second, that cumulated experience
depends on cumulated output. The first assumption views investment as being
capable of changing the environment, in which production takes place, provides the
continually new stimuli required for learning to take place. The second assumption
means that even in the absence of investment, the production process itself
stimulates and generates additional learning. If learning is a true phenomenon, the
decision as to which description is more appropriate has to depend upon the
empirical evidence. Sheshinski, judging by the goodness of fit in his empirical studies,
finds out that the first assumption seems to fare better than the second assumption
although both give close results. Thus we can say that Arrow (1962) has an appropriate
assumption for indexing the level of experience.
The main result of Sheshinski (1967) is that there is evidence to confirm the
learning by doing hypothesis that productivity growth in manufacturing is correlated
with the amount of investment. However, he reminds that he had disregarded
5
embodiment effects, quality changes (of labor and capital), statistical errors of
measurement, and probably other factors that could be consistent with the same
correlations reported in this paper. Thus, he recommends a more careful statistical
analysis, utilizing additional independent information (on quality changes, average age
of equipment, etc.) to establish the precise role of learning by doing.
6
References:
Arrow, K. J., 1962, The Economic Implications of Learning by Doing, The
Review of Economic Studies, V.29, N.3, pp.155-173.
Barro, R. J. and Sala-i-Martin, X, 1995, Economic Growth, McGraw-Hill, New
York.
Romer, P. M., 1986, Increasing Returns and Long-Run Growth, Journal of
Political Economy, V.94, N.5, pp.1002-1037.
Sheshinski, E., 1967, Tests of the Learning by Doing Hypothesis, The Review
of Economics and Statistics, V.49, N.4, pp.568-578.
Verdoorn, P. J., 1956, Complementarity and Long-Range Projections,
Econometrica, 24, pp. 429-450.
7