Reformulating Technical Change and Growth Theory Gary Jefferson Economics Department, Brandeis University Working Paper Series 2017| 111 ` Reformulating Technical Change and Growth Theory* Gary H. Jefferson [email protected] Brandeis University February 28, 2017 For review and comment only Suggestions will be most welcome Abstract This paper clarifies certain errors and inconsistencies that have become embedded in the conventional neoclassical growth model. The paper demonstrates that characterizing technical change in the Solow model as “purely Harrod-neutral labor augmenting” seriously compromises the role of capital and neoclassical principles in framing the process of economic growth. The basic argument of this paper is that by ignoring the actual elements of the so-called “degeneration” of Hicks-neutral or other capital-labor augmenting technical change, conventional presentations of the Solow model have foreclosed avenues for a deeper understanding of key features of economic growth. The paper develops the paradigm of Hick-Harrod technical change that is consistent with steady state growth under a wide range of values of the substitution elasticity, while also enabling a simplification of conditions required for the steady state. By endogenizing significant aspects of the growth process, the model opens the door to possibilities for a more unified theory of neoclassical growth, endogenous growth, and growth accounting. *The author deeply appreciates the opportunity to have presented portions of this paper in seminars in the Economics Department at Brandeis and at the Department of Economics at the University of Macau. In particular, the author appreciates the helpful suggestions and support of George Hall, as well as suggestions from Michael Coiner, Adam Jaffe, Fung Kwan, James Mirrlees, Dwight Perkins, Tom Rawski, Jian Su, and Tony Yezer. The author alone is responsible for the content of this paper. 1 “There are always aspects of economic life that are left out of any simplified model. There will therefore be problems on which it throws no light at all; worse yet, there may be problems on which it appears to throw light, but on which it actually propagates error.” Robert M. Solow (2000, pp. 1,2) “If I have seen further it is by standing on the shoulders of giants.” Sir Issac Newton (1676) 2 1. Introduction The economics literature is amply sprinkled with congratulatory assessments of the achievements of growth theory. According to Aghion and Howitt (2007, p. 79): Fifty years after its publication, the Solow model remains the unavoidable benchmark in growth economics, the equivalent of what the Modigliani–Miller theorem is to corporate finance, or the Arrow–Debreu model is to microeconomics…. In Chapter 8 of his tome, Introduction to Modern Economic Growth Theory, Acemoglu (2009) variously refers to the Solow model as “the workhorse model of macroeconomics” (p. 26) and “the most important model in macroeconomics” (p. 317). Finally, in their paper, Jones and Romer (2010, p. 225) assert a conclusive consensus framing the canonical growth model: “There is no longer any interesting debate about the features that a model must contain to explain [the Kaldor facts]. These features are embedded in one of the great successes of growth theory in the 1950s and 1960s, the neoclassical growth model.” Specifically, the model seeks to capture within a single economic framework the following six stylized facts of growth summarized by Kaldor (1961): output per capita grows over time; the capital-labor ratio grows over time; capital’s marginal product is roughly constant over time; the capital output ratio is roughly constant over time; capital and labor’s factor income shares are roughly constant over time; and the growth of output per capita differs substantially across countries. While Solow’s model (1956) explains or is consistent with five of these six stylized facts, it does an inadequate job of modeling and explaining the last of the facts; that is the difference in the growth of living standards across countries. As such, it is also largely unable to explain differences in cross-country levels of output per capita (Romer, 1994b). The inability of the neoclassical growth model to embed a parameter or equation to explain these differences has given rise to an abundance of endogenous growth literature, which while rich and diverse has not yet resulted in a single, widely-accepted account of the creation and diffusion of technical change comparable to the consensus enjoyed by Solow’s seminal innovation. In addition, Kaldor’s list of stylized growth facts omits one critical fact of long-run growth: that is, the phenomenon in which the quality of capital progresses over time. That this 3 measure of technical advance should not be included in an economist’s list of stylized facts is not altogether surprising, since the sine qua non of the economist’s measure of quality improvement is the factor’s marginal product. Kaldor correctly notes that over the long-run, capital’s marginal product and its economic return have remained roughly constant. Yet, through the lens of casual observation, capital’s constant economic return does not negate the fact that the machinery and processes driving manufacturing activity, as well as its production outcomes, such as communi- cation and transportation equipment, including air and space travel, are far more accessible, efficient, and inexpensive than they had been in the Stone Age. It is precisely this progressive improvement in the quality of capital, the essence of the Industrial Revolution that has been most responsible for capital deepening and rising living standards. This critical stylized fact of economic growth – quality improvements in capital – is entirely absent from Solow’s model. The ability of the basic neoclassical model to incorporate quality-augmenting technical change for capital has been seriously impaired by a central principle of steady state growth; that is the requirement that in the steady state technical change must take the form of “purely labor – augmenting” Harrod-neutral technical change. This characterization of technical change has its origins in Uzawa’s Growth Theorem (1961) in which he shows that if in the steady state the capital-output ratio is fixed and if output and capital together grow faster than the natural growth of labor, then the “effective” supply of labor must be balanced by labor-augmenting technical change. Hence, technical change in the steady state must be “represented” as being of the purely labor-augmenting variety. As elaborated by Jones and Scrimgeour (2005, p. 4), “As is well- known, in the case of Cobb-Douglas production, capital- and labor-augmenting technical change are equivalent. One sometimes sees the theorem interpreted as saying that technical change must be labor augmenting or the production function must be Cobb-Douglas. This is equivalent to the statement of the (Uzawa) theorem as given.” i.e., that in the steady state technical change must be represented as labor augmenting (italics added). Thus, given that with the Cobb-Douglas function, all the alternative forms of technical change degenerate in the steady state to the labor-augmenting mode and that the Cobb-Douglas function is limited to the restrictive case of a unitary substitution elasticity (i.e., σ = 1), the literature has rendered “purely labor-augmenting” Harrod-neutral technical change as a canonical feature of the neoclassical growth model. Hence, within the environment of a Cobb-Douglas production function with σ = 1, the growth literature seems to have adopted the presumption of 4 technical change equivalency. Many attempt clarifying explanations for this restrictive interpretation of technical change. Grossman et al. (2016) explain: “The ‘problem,’ it would seem, stems from the model’s assumption of an inelastic supply of effective labor that does not adjust to capital deepening over time.” Jones and Scrimgeour (2005) are more explicit about the passive role of the capital stock whose function it is to “inherit” or endogenously submit to the conditions presented to it by exogenous change, which is purely labor-centric. Hence the “workhorse” of neoclassical growth theory and the “workhorse” of production technology, the Cobb-Douglas production function, share an uneasy relationship that has resulted in a deeply unsettling outcome: the basic model of neoclassical growth cannot account for or accommodate to a fundamental and inescapable stylized fact of long-run economic growth – that is, quality improvements in the ever-expanding realm of capital goods. Given this dependence of our basic textbooks account of economic growth as “purely labor augmenting,” it is understandable why both Solow and Acemoglu have raised serious reservations regarding the assumption of the nature of technical change in long-run growth. According to Solow (2000, p. 31,32), “…it is possible to give theoretical reasons why technological progress might be forced to assume the particular form (“called labor-augmenting”) required for the existence of a steady state. They are excessively fancy reasons, not altogether believable.” Acemogulu (2009, pp. 62) simply characterizes the assumption as “At some level…distressing.” Arguably the Solow model co-exists with both a weak-form of the Uzawa Theorem and a strong form. According to the weak form, within the “neighborhood of the equilibrium path,” technical change must be represented as labor-augmenting Harrod-neutral technical change.1 Presumably, provided that it “degenerates” to Harrod-neutral technical change within the steady state, beyond the neighborhood of the steady state, other than a purely labor-augmenting bias is permissible. The strong form of the Uzawa Theorem, that which generally appears in the standard textbook presentation, is that in all phases of neoclassical growth, technical change is to be characterized as of the “purely labor-augmenting” Harrod-neutral variety. A large literature, of course, has developed that focuses on the role of capital in endogenous growth; that is, the role of both physical and human capital as inputs to the process of knowledge production and as outputs of knowledge production.