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been resuscitated as the “new growth theory,” pioneered by Paul Romer and others.16 The thrust of this research is to allow for investment in knowledge-improving activities. Such investments improve society’s technologies, and a higher level of investment in knowledge will change society’s production possibilities and may improve the long-run growth rate of the economy. Virtually all studies of induced innovation have been theoretical.17 With few exceptions, they do not lay out a set of testable hypotheses or ones that can be used to model the innovation process at an industrial level.18

The alternative approach to modeling induced innovation is the learning model. This approach has become particularly popular in recent years as models increase the granularity of the technological description down to individual technologies. It has also been attractive in policy studies because it can rationalize early investments in technologies that are presently uneconomical but have the promise, if they can “move down the learning curve,” of being competitive in the future.

The present study examines the analytical and statistical basis of learning models. This is a technical study because the issue that is raised is primarily a statistical issue of identification of learning functions. The basic message, however, is simple. First, the paper shows that there is a fundamental statistical identification problem in trying to separate learning from exogenous technological change. As a result of the identification problem, estimated learning coefficients will generally be biased upwards. Second, we present two empirical tests that illustrate the potential bias in practice and show that learning parameters are not robust to alternative specifications. Finally, we show that an overestimate of the learning coefficient will generally lead to an underestimate of the total marginal cost of output; because of this underestimate, optimization models tend to tilt toward technologies that are incorrectly specified as having high learning coefficients. This implies that policy proposals that rely upon learning models are likely to overestimate the returns to research investments to the extent that they use estimated learning coefficients.

The present note provides the basic results of the study. The full study with tables and figures is available as the background paper cited in the first footnote.

The Fundamental Identification Problem

Models of learning and experience have a long history in studies of manufacturing productivity.19 Because of their perceived successes in technological forecasting, they have recently been introduced in policy models of energy and global warming economics to make the process of technological change endogenous.

This approach has serious dangers. We proceed to examine this issue in three steps. In the present section, we show that there is a fundamental statistical identification problem in trying to separate learning from exogenous

16

See Paul Romer, “Endogenous Technological Change,” Journal of Political Economy, vol. 98, October 1990, part 2, pp. S71-S102. Also see the extensive survey in Dale W. Jorgenson, “Technology in Growth Theory,” in Jeffrey C. Fuhrer and Jane Sneddon Little, eds, Technology and Growth, Conference Proceedings, Federal Reserve Bank of Boston, 1996. pp. 45-77.

17

For a recent overview, see Vernon Ruttan, Technology, Growth, and Development, Oxford University Press, New York, 2001.

18

One example of incorporating technological change in policy analysis is the work of Dale Jorgenson and his colleague; see for example Dale W. Jorgenson and Peter J. Wilcoxen, “Reducing U. S. Carbon Dioxide Emissions: The Cost of Different Goals,” in John R. Moroney, ed., Energy, Growth, and the Environment, 1991, JAI Press Greenwich, Conn., pp. 125-128.Also see Lawrence H. Goulder and Stephen H. Schneider, “Induced technological change and the attractiveness of CO2 emissions abatement policies,” Resource and Energy Economics, 1999, 21: 211-253. An explicit calibrated model is contained in William Nordhaus, “Modeling induced innovation in climate-change policy,” in Technological Change and the Environment, edited by A. Grübler, N. Nakicenovic and W. D. Nordhaus. Washington, DC: Resources for the Future, 2002, pp. 182-209 and in David Popp, “ENTICE: endogenous technological change in the DICE model of global warming,” Journal of Environmental Economics and Management, 2004, 48: 742-768.

19

The literature on learning curves is vast, going back more than a century, and no single reference can adequately capture the major issues. The original concept of an experience curve was documented with telegraph operators in W.L. Bryan and N. Harter, “Studies on the Telegraphic Language: The Acquisition of a Hierarchy of Habits,” Psychology Review, 6:345-75, 1899. Two particularly influential articles were T.P. Wright, “Factors Affecting the Cost of Airplanes,” Journal of Aeronautical Sciences, Vol. 3, No. 4, 122-128, 1936; and K. J. Arrow, “The Economic Implications of Learning-By-Doing,” Review of Economic Studies, Vol. 29, 155-173, 1961. A recent comparison of alternative approaches is in Boyan Jovanovic and Yaw Nyarko, “A Bayesian Learning Model Fitted to a Variety of Empirical Learning Curves,” Brookings Papers on Economic Activity. Microeconomics, (1995), pp. 247-305. A comprehensive survey of learning curves is contained in Louis E. Yelle, “The Learning Curve: Historical Review and Comprehensive Survey,” Decision Sciences, 10, 302-328, 1979).



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