The New Palgrave Dictionary of Economics

Living Edition
| Editors: Palgrave Macmillan

Growth and Learning-By-Doing

  • Paul Beaudry
Living reference work entry
DOI: https://doi.org/10.1057/978-1-349-95121-5_2027-1

Abstract

Learning by doing refers to improvements in productive efficiency arising from the generation of experience obtained by producing a good or service. The formal modelling of learning by doing was initiated in Arrow (1962) and was motivated by two main factors. The first motivating factor was empirical: several studies of wartime production found that input requirements decreased as a result of production experience. For example, Searle (1945) studied productivity changes in the Second World War shipbuilding programmes. During the Second World War, US production of ships increased dramatically, from 26 vessels in 1939 to 1,900 ships in 1943, an almost fiftyfold increase. Searle (1945) noticed that unit labour requirements decreased at a constant rate for a given percentage increase in output. On average, a doubling of output was associated with declines of 16 to 22 per cent in the number of man-hours required to build Liberty ships, Victory ships, tankers and standard cargo vessels. Alchian (1963) studied the relationship between the amount of direct labour required to produce an airframe and the number of airframes produced in the United States during the Second World War. He found that a doubling of production experience decreased labour input by approximately one-third. Other empirical studies of learning by doing include Rapping (1965), Irwin and Klenow (1994) and Thornton and Thompson (2001).

Keywords

Arrow, K. Economic growth theory Learning by doing Lucas, R. Productive efficiency 

JEL Classifications

O4 

Learning by doing refers to improvements in productive efficiency arising from the generation of experience obtained by producing a good or service. The formal modelling of learning by doing was initiated in Arrow (1962) and was motivated by two main factors. The first motivating factor was empirical: several studies of wartime production found that input requirements decreased as a result of production experience. For example, Searle (1945) studied productivity changes in the Second World War shipbuilding programmes. During the Second World War, US production of ships increased dramatically, from 26 vessels in 1939 to 1,900 ships in 1943, an almost fiftyfold increase. Searle (1945) noticed that unit labour requirements decreased at a constant rate for a given percentage increase in output. On average, a doubling of output was associated with declines of 16 to 22 per cent in the number of man-hours required to build Liberty ships, Victory ships, tankers and standard cargo vessels. Alchian (1963) studied the relationship between the amount of direct labour required to produce an airframe and the number of airframes produced in the United States during the Second World War. He found that a doubling of production experience decreased labour input by approximately one-third. Other empirical studies of learning by doing include Rapping (1965), Irwin and Klenow (1994) and Thornton and Thompson (2001).

The second motivating factor behind the work of Arrow (1962) was a search for a theory of economic growth which did not rely on exogenous change in productivity as a driving force. In particular, Arrow’s contribution and its extensions in Levhari (1966a, b) were to show how economic growth could be sustained in a market with perfect competition. Arrow’s original model is quite sophisticated, but the main insight can be derived in a simpler setting, as shown in Sheshinski (1967) and presented here. Consider a one good economy, where the production of the good requires capital and labour input according to the constant returns to scale production function:
$$ Y=F\left(K,AL\right),F\left(\lambda K,A\lambda L\right)=\lambda F\left(K,AL\right). $$
In this specification of the production technology, A represents the efficiency of labour in producing the good. The main idea in the learning by doing literature is that A is a function of past experience. Arrow assumed that experience can be measured by cumulative investment or, in other words, the capital stock. The form of the relationship between A and the capital stock is posited to be:
$$ {A}_t={\left({K}_t\right)}^{\alpha },0<\alpha <1 $$
where the assumption that 0 < α < 1 is motivated by the empirical studies. In order to close the system, assume that the labour force grows exponentially at the rate η and let capital accumulation be driven by a constant saving rate out of incomes, s where, in the absence of depreciation, this implies
$$ \dot{K}=sY $$
In this environment, on the assumption that the change in A is an unintended consequence of production, it can be shown that a balanced growth path exists where per-capita income and per-capita capital grow at the rate
$$ \alpha \frac{\eta }{1-\alpha } $$
The two important aspects to note about the resulting growth rate is that it is positive if η > 0 and it is independent of the savings rate s. The additional property – that the rate of growth of income is tied to a positive rate of population growth – is generally seen as a weakness of this type of model. This property can be partially remedied, as shown in Romer (1986), if one assumes that α = 1. In this case, even in the absence of labour force growth there exists a balanced growth path where the rate of growth is given by
$$ sF\left(1,L\right) $$
The drawback of this specification (α = 1) is that the growth rate now depends on the size of the labour force, which is referred to as a ‘scale effect’. The attractive feature of this specification is that the growth rate can be modified by an economic decision variable such as the savings rate. An alternative way of modifying Arrow’s original model is to posit, as in Lucas (1988), that A depends on the per-capita value of the capital stock instead of on the level of the capital stock. This assumption is justified in Lucas (1988) on the grounds that A reflects the knowledge of the average worker with respect to how best to operate the technology. In the case where the relationship is given by \( A=\frac{K}{L} \), the steady growth rate of per-capita output is given by sF(1, 1) η. This formulation has the attractive property that it is positive even if η = 0, and it does not exhibit a scale effect. Accordingly it offers a succinct theory of economic growth. Lucas conjectured that the assumption of constant returns to learning (that is, α = 1) could be justified in a model where there is bounded learning in any one good but where there is continual entry of new goods over time. This idea is formally studied in Stokey (1988) and Young (1993). There is also a large literature that discusses how learning by doing can interact with international trade and potentially give rise to income divergence across countries; see for example Lucas (1993) and Young (1991).

Bibliography

  1. Alchian, A. 1963. Reliability of progress curves in airframe production. Econometrica 31: 679–693.CrossRefGoogle Scholar
  2. Arrow, K. 1962. The economic implications of learning by doing. Review of Economic Studies 29: 155–173.CrossRefGoogle Scholar
  3. Irwin, D., and P. Klenow. 1994. Learning by doing spillovers in the semiconductor industry. Journal of Political Economy 102: 1200–1227.CrossRefGoogle Scholar
  4. Levhari, D. 1966a. Further implications of learning by doing. Review of Economic Studies 33: 31–38.CrossRefGoogle Scholar
  5. Levhari, D. 1966b. Extensions of arrow’s ‘Learning by Doing’. Review of Economic Studies 33: 117–131.CrossRefGoogle Scholar
  6. Lucas, R. Jr. 1988. On the mechanics of economic development. Journal of Monetary Economics 22: 3–42.CrossRefGoogle Scholar
  7. Lucas, R. Jr. 1993. Making a miracle. Econometrica 61: 251–272.CrossRefGoogle Scholar
  8. Rapping, L. 1965. Learning and World War II production functions. Review of Economics and Statistics 47: 81–86.CrossRefGoogle Scholar
  9. Romer, P. 1986. Increasing returns and long run growth. Journal of Political Economy 94: 1002–1037.CrossRefGoogle Scholar
  10. Searle, A. 1945. Productivity of labour and industry. Monthly Labor Review 61: 1132–1147.Google Scholar
  11. Sheshinski, E. 1967. Optimal accumulation with learning by doing. In Essays on the theory of economic growth, ed. K. Shell. Cambridge, MA: MIT Press.Google Scholar
  12. Stokey, N. 1988. Learning by doing and the introduction of new goods. Journal of Political Economy 96: 701–717.CrossRefGoogle Scholar
  13. Thornton, R., and P. Thompson. 2001. Learning from experience and learning from others: An exploration of learning and spillovers in wartime shipbuilding. American Economic Review 91: 1350–1368.CrossRefGoogle Scholar
  14. Young, A. 1991. Learning by doing and the dynamic effects of international trade. Quarterly Journal of Economics 106: 369–405.CrossRefGoogle Scholar
  15. Young, A. 1993. Invention and bounded learning by doing. Journal of Political Economy 101: 443–472.CrossRefGoogle Scholar

Copyright information

© The Author(s) 2008

Authors and Affiliations

  • Paul Beaudry
    • 1
  1. 1.