The Perils of the Learning Model for Modeling Endogenous Technological Change.

• Author: Nordhaus, William D.

1. THE PROBLEM OF ENDOGENOUS TECHNOLOGICAL CHANGE

   Most studies and models of environmental and climate-change policy--indeed of virtually all aspects of economic policy--have sidestepped the thorny issue of endogenous technological change or induced innovation. These terms refer to the impact of economic activity and policy upon research, development, invention, innovation, productivity change, and the diffusion of new technologies. Most models assume that technological change is exogenous, that is, it proceeds with a rate and direction that is determined by fundamental scientific and technological forces but is unaffected by prices or tax and regulatory incentives. (1,2)

   This shortcoming has been recognized for many years. (3) It arises both because of the lack of a firm empirical understanding of the determinants of technological change as well as because of the inherent difficulties in the modeling of economic processes with externalities and increasing returns to scale. While we suspect that we know the direction of the omission of induced innovation--to overestimate the cost of emissions reductions and the trend increase in climate change--we have little sense of the magnitude of the effect or the importance of this omission. Would including induced innovation have a large or small impact on climate change and on climate-change policies? This is a major open question.

   There have been two major approaches to including induced innovation--the research model and the learning model. The research model of induced innovation arose in the 1960s in an attempt to understand why technological change appears to have been largely labor saving. (4) More recently, theories of induced technological change have been resuscitated as the "new growth theory," which was developed by Paul Romer and others. (5) 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. 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. (6)

   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. (7)

   The present study examines the analytical and statistical basis of learning models. The basic messages are 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. Using both aggregate and industry data, I show that empirical estimates of learning parameters in simple models are not robust to alternative specifications.

   The last section shows 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 are likely to overestimate the returns to research investments to the extent that they use estimated learning coefficients.

2. THE FUNDAMENTAL IDENTIFICATION PROBLEM IN LEARNING CURVES

   Models of learning and experience have a long history in studies of manufacturing productivity.8 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 technological change and that the estimated learning coefficient will generally be biased upwards. In the next section, we present two empirical tests to examine the potential bias in practice. In the final section, we show that an overestimate of the learning coefficient will generally lead to an underestimate the total marginal cost of output and tile policies toward technologies that are incorrectly specified as having high learning coefficients.

   The basic idea behind the learning model is that productivity improves or costs decline as workers or firms gain experience with a production process. While there can be little doubt that productivity benefits from experience, the exact mechanism is poorly understood. In particularly, it is unclear whether the learning is embodied in individual workers and firms, whether there are interindustry or international spillovers, whether the improvements lead to durable technological changes, and even whether the learning effects can be distinguished from other technological changes. An important study by Irwin and Klenow provides detailed estimates of where the learning spillovers occur for a particular industry, semiconductors. (9)

   In this section, we focus on the problem of identifying differences in productivity due to learning from other sources of technological change. We begin by showing why it is impossible without further identifying assumptions to distinguish learning from exogenous technological change as represented by time, and why the learning coefficient is generally biased upwards.

   To simplify for this exposition, we assume that all processes are exponential. Output ([Q.sub.t]) is assumed to grow at constant growth rate g, which will be determined by the growth of demand, discussed shortly. So [Q.sub.t], = [Q.sub.0][e.sup.gt]. Cumulative output at time t ([Y.sub.t]) is therefore:

   [mathematical expression not reproducible] (1)

   Taking the logarithmic derivative of (1) shows that the growth rate of [Y.sub.t] is also g.

   The experience curve is assumed to have a true experience coefficient, b. In addition, there is an assumed constant rate of exogenous technological change at rate h. Assume that the current average and marginal cost are independent of current production. The cost function is given by:

   [mathematical expression not reproducible] (2)

   "Exogenous technological change" in this context denotes all sources of cost declines other than the learning-curve-determined technological change. It would include inter alia spillovers from outside the industry, the returns to research and development, economies of scale and scope, as well as exogenous fundamental inventions.

   Assume that prices are proportional to current instantaneous marginal cost, so the rate of decline in cost ([c.sub.t]) equals the rate of decline of price ([p.sub.t]), which is given by the following. (I denote declines of price and cost as positive for expositional convenience.)

   [P.sub.t] = [c.sub.t], = h + b[g.sub.t], (3)

   Because marginal cost is constant, price is under these assumptions exogenous to current demand. Demand is determined by a demand function with an assumed constant price elasticity (taken as positive for convenience, [epsilon] > 0). In additional, there is an exogenous growth in demand given by population growth and the growth of income given by [z.sub.t]. These yield the growth in output (demand) as:

   [g.sub.t] = [epsilon][p.sub.t]+[Z.sub.t] (4)

   Solving (3) and (4), we get the following reduced-form equations for the rate of cost (price) decline and the rate of output growth. Since the growth rates are constant, we...