Simulating Long-Run Technical Change by Duncan K. Foley Graduate Faculty, New School University
[email protected] 1. Introduction There is considerable, if not conclusive, scientific evidence that the atmospheric accumulation of carbon dioxide, methane, and other "greenhouse" gases emitted through the combustion of fossil fuels will lead to major changes in the earth's climate, with important economic effects. The nations of the world have agreed at the Kyoto Conference in 1997 to put in place some system of economic incentives to control the emission of greenhouse gases. The economic evaluation of alternative policies for emission control, such as carbon taxes or a system of tradeable emissions permits on a world scale, poses novel challenges to economic methodology. Economic policy evaluation requires the creation of a model in which the economic behavior at issue (in this case the emission of greenhouse gases in production) and the policy parameters (in this case the level of a carbon tax or the number of emissions permits issued) are linked, so that analysis or simulation can trace the impact of particular policies on the path of the behavior. The problems of global climate change, however, pose some new challenges to this general approach. The global warming scenario, for example, unfolds on a time scale of 200 to 400 years, due to the geophysical time constants (such as the half-life of atmospheric carbon dioxide) involved. This greatly exceeds the longest time scales considered in most economic models, which range from business cycle model horizons of 2--5 years, through investment planning model horizons of 5--25 years, long-run growth model horizons of 10-50 years, to demographic models with horizons of 25--100 years. The particularly critical issue in evaluating policies for controlling global warming is the prediction of the impact of higher economic costs to the emission of greenhouse gases on the technologies of production discovered and adopted. Conventional economic growth theory approaches this problem in the framework of a production function, in which the issue appears to be the substitutability of other factors of production, such as labor and capital, for emissions. But on the time scale involved in global warming, it seems likely that the impacts of economic incentives on patterns of technical change will be much more important than substitution among known technologies. In this paper I will investigate some of the issues raised by this perspective. The time scale of the global warming problem raises another serious problem for any attempt to model the impact of economic incentives, the need to calibrate the model against historical data. The difficulty here is that we have little experience with patterns of economic behavior over such long time periods. One parallel to the problem of understanding the impacts of economic incentives on induced technical change in greenhouse gas emissions is the Classical/Marxian theory of technical change under capitalist production relations. Marx, in criticizing Ricardo's theory of the stationary state, argued that capitalist social relations set in motion a powerful social engine of induced technical change because each capitalist producer has a strong incentive to discover and adopt cost-reducing techniques of production. This line of thinking offers an alternative
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to the static production function as a framework within which to approach the problem of induced technical change.
2. A framework for analyzing technical change The aim here is to investigate patterns of long-run technical change. The setting is a production system with one output, taken as the numéraire, and two inputs, capital (regarded as a stock of output used in production), and labor, which is paid a wage in output. A technique of production is a list 8r, x< where r denotes the ratio of output (net of depreciation of the capital stock) to the stock of capital, x denotes the ratio of net output to the labor input. and d is the depreciation rate. k = x ê r is the capital intensity of the technique. I will risk abusing language by referring to r as the "productivity of capital". When the real wage is w the profit rate of a technique is: ÄÄÄÄÄÄkÄÄ ÄÄÄÄÄÄ = rH1 - ÄÄwxÄÄÄÄ L = r p - d . r = ÄÄHx-wL Here 1 - p = w ê x is the wage share, and p is the profit share. It is convenient to define the rates of change of capital and labor productivity as ct = rt+1 ê rt and gt = xt+1 ê xt . The rate of growth of the capital intensity, k = x ê r, is thus equal to g - c. The basic idea of the Classical/Marxist approach to technical change in capitalist economies is that capitalist entrepreneurs will select technologies on the basis of the expected profit rate, that is, will adopt innovative technologies that promise to raise the profit rate at the existing wage. Such techniques are called viable. Thus a technique 8r', x'< will be adopted over 8r, x< at the wage w if r' H1 - ÄÄwx'ÄÄÄÄ L' ≥ rH1 - ÄÄÄwxÄÄÄÄ L . Notice that if a labor-saving alternative technique is viable at a wage w it is also viable at any higher wage. It is straightforward to show that the viability condition is equivalent to p c + H1 - pL g > 0, where c and g are the percentage changes in capital and labor productivity between the two techniques. The long-run dynamics of this process depend critically on the assumption of what happens to the wage as techniques of production change (as emphasized by Okishio, 1961 and the extenders of his argument such as Roemer, 1977). We represent this factor in the analysis in general by making the wage in any period a function of the technology in use in that period, w@8r, x c. It is important to emphasize that the increases in k and x are monotonic with respect to time (see Michl, 1996). There is very little data that directly addresses the question of the reversibility of the relation between x and k. The neoclassical interpretation of this data as an intensive production function with diminishing returns to capital, which underlies the huge literature on the Solow growth model, implies that this relationship, at least in part, is reversible. (The Solow growth literature also introduces the idea of an irreversible "Harrod-neutral", that is, labor-augmenting, technical progress in the productivity of labor to complement the assumed effect of capital accumulation on the productivity of labor.) The Classical/Marxist vision capitalist development sees this plot as the fossilized historical record of an irreversible evolutionary process. Third, there is some suggestion in the data of a constant or falling productivity of capital, r, which appears in the graph as the slope of the chord connecting the origin to each point. In the notation of this paper, c, the rate of growth of capital productivity is not only less than g, the rate of growth of labor productivity, but is often negative and rarely positive. Since the notion that capital productivity falls and labor productivity rises in the course of capitalist economic development is also a key aspect of Marx's theory of the tendency for the rate of profit to fall, where it is expressed as a rise in the "organic composition of capital", I call the pattern of positive g and negative c "Marx-biased technical change". (The pattern of positive g and zero c is conventionally referred to as "Harrod-neutral technical change".) The assumption of a concave intensive production function also implies that r falls with rising k. We will look at the question of falling capital productivity more closely later in the discussion. Fourth, this presentation powerfully underlines the presence of two separate historical phases in U.S. economic development. The first group of points, up to about 1929, lies in a pattern that appears to be quite distinct from the that of the second group of points, starting in the 1930s. Duménil and Lévy call this shift a "Great Leap Forward", and call attention to the qualitative similarity in the evolution in the two homogeneous subperiods and the sharp break in pattern between them.
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Other historical episodes illustrate similar patterns. For example, if we look at the Penn World Tables data with Adalmir Marquetti's (1997) estimates of the value of the capital stock and potential real Gross Domestic Product for the U.S. from 1963--90, we see a similar pattern of rising x and k, with a steady or slightly falling r.
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U.S. Potential 1963−−1990
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Figure 2 Penn World Tables data with Adalmir Marquetti's estimates of capital stock and potential Gross Domestic Product for the U.S. economy from 1963 to 1990.
Similar plots for Japan and France reveal quite similar qualitative patterns.
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Figure 3 Penn World Tables data with Adalmir Marquetti's estimates of capital stock and potential Gross Domestic Product for the Japanese economy from 1963 to 1990.
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France Potential 1963−−1990
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Figure 4 Penn World Tables data with Adalmir Marquetti's estimates of capital stock and potential Gross Domestic Product for the French economy from 1963 to 1990.
While these figures do not show strong support for the existence of concave production function relationship, Marquetti (1997) has found some evidence of such a relationship in aggregated data across countries. In terms of modeling, then, we seek a model of technical change that can reproduce the broad patterns of rising labor productivity, rising capital intensity, and stable or falling capital productivity we see in typical economic growth data.
4. An evolutionary model of technical change Duménil and Lévy (1995) propose an evolutionary representation of the Classical/Marxist theory of technical change. In their model, new technologies are generated by a random process, and the wage adjusts to changes in labor productivity. Their aim is to reproduce the specific time profile of capital and labor productivity they observe in time series generated by the U.S. economy. Here we explore this process in more generality, with the aim of identifying its structural characteristics. Following Duménil and Lévy's method, we make successive draws from a random technical change distribution, described by a probability density function f @8 c, g
