پویایی های انتقالی خروجی، دستمزد و سود در رشد منجر به نوآوری؛ تجزیه و تحلیل تعادل عمومی

This paper focuses on the transition between steady states of innovation-led growth, in the context of a general-equilibrium model in which the exogenous appearance of a new technological paradigm triggers a wave of endogenous, stochastic, incremental innovations through which it is implemented. The analysis demonstrates existence of a unique Markov-perfect equilibrium, and shows that its transition dynamics conform in expected values to commonly observed empirical patterns. These include an initial productivity decline followed by a greater increase in productivity; and ‘creative destruction’ that reduces the market value of traditional, incumbent firms while creating new value in innovative entrants.

Transitional dynamics play a key role in innovation-led growth. When technological change is ubiquitous, long-run steady states may be few and far between though short-run equilibria prevail in individual markets (Nelson and Winter, 1982). Detailed studies of major innovations describe the singular impact of specific ‘paradigm shifts’ setting off Schumpeterian waves of technological diffusion that last for decades before approaching a steady state (Freeman et al., 1982 and Dosi, 1982).1 Such waves have been associated with the introduction of electric power (Freeman, 1982 and David, 1991), crop hybridization (Griliches, 1957; ‘the invention of a method of inventing’), synthetic fibers (Hollander, 1965) and semiconductors (Braun and MacDonald, 1982), each of which set off an extended diffusion process. More recently, Greenwood and Yorukoglu (1997) have argued from a macroeconomic perspective that the productivity slowdown in the 1970s was a transitional phenomenon that marked the beginning of a new industrial revolution based on radical innovation in information technologies.2 Models of innovation-led growth that focus on steady-state outcomes are poorly suited to describing such trajectories of technological progress, which are driven by the singular introduction of new technological paradigms. The present paper focuses instead on the transitional dynamics of innovation-led growth to describe such trajectories, while placing their development in a general-equilibrium context. It models growth as triggered by the appearance of a radical innovation that challenges the ruling technological paradigm, followed by subsequent incremental innovations through which the economic impact of the new paradigm is realized and diffused.3 While the appearance of a paradigm shift is treated as an exogenous, random occurrence that is not explained by the model, the incremental innovations that follow it are viewed as the stochastic result of endogenous investment in research and development by profit-maximizing firms.4 Analysis of the model shows that under reasonable assumptions such trajectories can be described as random realizations of a unique, Markov-perfect Nash equilibrium in contingent consumption, production and innovation strategies; and that the trajectory of expected values of this unique stochastic equilibrium has certain properties commonly observed in actual paradigm shifts. The first of these is the shape of the wave, which typically follows a characteristic sigmoid pattern. Diffusion begins slowly because initially the new radical technology is not well understood, and then gains momentum as ‘… the appearance of one or a few entrepreneurs facilitates the appearance of others, and these the appearance of more, in ever-increasing numbers’ (Schumpeter, 1934, p. 228). Eventually, success breeds a surplus of economic capacity, which “… when in full swing … would eliminate entrepreneurial profit” (p. 235). This decline in incentives for innovative effort results in a fall in the rate of incremental innovation that persists until the next paradigm shift sets off a new wave of innovative activity. A second property of such paradigm shifts, which the analysis demonstrates, is an initial fall in measured productivity—mirroring observed slowdowns in measured productivity at the beginning of the current IT revolution and, historically, in the first Industrial Revolution in Britain and in the early years of the American Industrial Revolution.5 This decline in measured productivity occurs because resources are expended on research and development—to assimilate the new paradigm—before actual gains are realized. Inasmuch as the assets created by this effort are intangible they do not directly contribute to conventionally measured output,6 though subsequent productivity gains more than offset this loss. A third property of paradigm shifts demonstrated by the model is the ‘creative destruction’ of established firms that lack the agility to incorporate the new technological paradigm, and lose market value, while new value is formed in the start-ups that spearhead the technological revolution.7 Dramatic increases in the market value of young information-technology (IT) companies overtaking the manufacturing giants of the past vividly illustrate this trend, which is also mirrored in the relative movement of the NYSE and NASDAQ indices at the beginning of the current IT revolution.8 Finally, the analysis shows that two of Kaldor (1963) stylized facts of growth hold along the technological trajectories described by the model. Real wages rise steadily throughout the dynamic transition that characterizes innovation-led growth. Initially, the increase is the result of the appearance of the new paradigm stimulating demand for labor in innovation-related activities. Then, as the new paradigm is assimilated in the production sector, productivity gains fuel further increases in real wages. Consequently, the share of profits in national income moves pro-cyclically, initially falling due to increased spending on research and development, and then rising as a result of productivity gains until it returns to its level before the appearance of the new paradigm. This trendless fluctuation in the functional distribution of income is the second of Kaldor's stylized facts shown to hold in the model. The analysis developed in this paper brings together two important strands of the formal economic literature on innovation: stochastic partial-equilibrium models of strategic innovation, and macroeconomic models of innovation-led growth. Formal investigation of the interaction between technological innovation and diffusion was initially pursued in the context of partial equilibrium models of strategic competition between first-movers and imitators within an industry (Reinganum, 1985, Jovanovic and Rob, 1990 and Jovanovic and MacDonald, 1994). This was then extended to the strategic adoption of new technological paradigms in multiple sectors, characterized as Markov-perfect equilibria, though still within a partial equilibrium framework (Bresnahan and Trajtenberg, 1995 and Justman, 1996). At the same time, growing recognition of the macroeconomic significance of technological progress as a force for economic development, which can be traced back to Solow (1957) seminal empirical analysis, and the advent of endogenous growth theory, spurred efforts to articulate the role of innovation and diffusion in the context of general equilibrium macro-models of growth. Grossman and Helpman (1991) influential formulation of innovation-led growth was followed by Aghion and Howitt (1992) characterization of technological development as comprising alternating phases of innovation and diffusion. This approach was further elaborated in Chou and Shy (1993) formal model of technological revolutions; Cheng and Dinopoulos (1996) dynamic, multi-sectoral, general-equilibrium model of Schumpeterian growth through a succession of ‘breakthroughs and improvements;’ and Bental and Peled (1996) characterization of technological development as resulting from an interaction between technological discovery and wealth accumulation. Where these latter efforts sought to understand the sources of radical technological innovations, and therefore, treated their appearance as endogenous, other general equilibrium analyses focused instead—as we do here—on the dynamics of the technological trajectories set off by paradigmatic innovations, and therefore, took the initial impulse of radical innovation as exogenous. Work in this vein includes Andolfatto and MacDonald (1998) real-business-cycle model in which technological shocks require costly effort before they are absorbed in the economy; Helpman and Trajtenberg (1996) analysis of the diffusion of ‘General Purpose Technologies’ (GPTs) in the different sectors of the economy; and, closest to the present paper, Helpman and Trajtenberg (1994) analysis of the macroeconomic impact of GPTs.9 The present paper shares Helpman and Trajtenberg (1994) dynamic, multi-sectoral, general-equilibrium perspective on Schumpeterian growth, and reaches similar conclusions with regard to an initial drop in output and productivity, a secular increase in real wages and pro-cyclical variation in the share of profits in national income. However, the two papers differ on several key points. Thus Helpman and Trajtenberg describe the appearance of new GPTs as deterministic events that recur at fixed, known intervals, where the present paper views paradigm shifts as essentially uncertain events of indeterminate timing and duration; and where they characterize the firms that develop the intermediate inputs that embody these GPTs as infinitesimal monopolistic competitors requiring a critical mass, the present paper retains the strategic, stochastic structure of partial equilibrium models that describe the interaction between early and late incremental innovators—an interaction that has both complementary and competitive aspects. Consequently, where Helpman and Trajtenberg (1996) cycles comprise two phases, the distinction between which ‘is very pointed and involves sharp discontinuities’ (p. 18), the technological wave described here moves smoothly between three stages—an initial decline followed by accelerated growth and then a final period of slow growth—that capture the characteristic S-shaped pattern of technological diffusion.10 Another important difference between the two approaches lies in the variation of real wages, which move sharply up and down in Helpman and Trajtenberg (1994, Fig. 5), and here describe a gradual upward trend. Yet another salient difference can be found in the behavior of the stock market: where Helpman and Trajtenberg's model implies that the introduction of a new GPT precipitates an immediate decline in the real value of the stock market, even sharper than the decline in real output, the present paper distinguishes between established firms that lose market value when a new technological paradigm appears and the creation of possibly greater new value in startups.11 Finally, where Helpman and Trajtenberg's model allows multiple equilibria, and predicates complementary innovation on ‘optimistic’ expectations that others will similarly innovate (universally ‘pessimistic’ expectations that none will do so are self-fulfilling), the present paper demonstrates existence of a unique stochastic Markov-perfect equilibrium in contingent innovation, production and consumption strategies that describes a single trajectory of expected values. This unique trajectory allows a continuum of possible realizations while providing a focal point for analyzing the dynamic macroeconomic properties of radical technological change. The structure of the paper is as follows: Section 2 defines the model. Section 3 demonstrates existence of a unique equilibrium. Section 4 analyzes its properties and illustrates them with a numerical example. Section 5 concludes with a brief summary.

The paradigm shifts and non-monotonicities that empirically characterize technological progress suggest that growth models that focus exclusively on steady-state outcomes cannot fully describe the macroeconomic dynamics of innovation-led growth. The present paper, by focusing, within a general-equilibrium framework, on the economy's path in transition between steady states provides an alternative perspective on technological progress. The model it puts forward describes a Schumpeterian cycle of growth that begins with the exogenous appearance of a new technological paradigm that is of no direct economic value itself, but which triggers a wave of incremental innovations through which the new paradigm is applied to the production of final goods. These incremental innovations are modeled as endogenous stochastic events that respond to the calculated efforts of rational entrepreneurs acting on profit opportunities. The paper demonstrates existence of a unique Markov-perfect general equilibrium in contingent development, production and consumption strategies, which conforms in expected values to several observed empirical patterns. It implies an initial slowdown in measured productivity at the beginning of the technological revolution because of accelerated investment in intangible knowledge-based assets, mirroring similar productivity slowdowns observed historically and at the outset of the current revolution in information technology. It also indicates that established manufacturing firms—not as well-positioned as young innovative firms to assimilate the new technological paradigm—can be expected to lose value initially, while new value is created in successful startups. This is consistent with actual trends in the market value of firms. The model also replicates several of Kaldor (1963) stylized facts of growth: a secular increase in productivity growth that more than compensates for the early deceleration, a steady rise in real wages, an upward trend in profits, and trendless pro-cyclical movement in the share of profits in national income. These dynamic patterns are analytically shown to hold in the model, and illustrated by a numerical example that also exhibits a monotonically increasing sigmoid pattern of diffusion in the application of the new technological paradigm to the production of final goods. The present analysis suggests a feasible approach to integrating the transitional dynamics of technological revolutions within a general equilibrium framework that retains the explicit rationality and consistency in which neoclassical analysis is anchored. Furthermore, by demonstrating existence of a unique fully specified stochastic equilibrium that describes a unique trajectory of expected values, it provides a focal point for analyzing technological change and technology policy in a macroeconomic context. Applications of this approach could be used to address the impact of technology policy on employment, investment and trade, and to analyze the implications of labor, credit and trade policies for technological progress.