نقش جایگزینی فاکتور در تئوری های رشد اقتصادی و توزیع درآمد: دو مثال
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|11196||2008||26 صفحه PDF||سفارش دهید||11756 کلمه|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Journal of Macroeconomics, Volume 30, Issue 2, June 2008, Pages 604–629
While much empirical evidence suggests that the Cobb–Douglas production function may be a reasonable benchmark for aggregate analysis, we argue that the practice, particularly prevalent in contemporary growth theory, of adopting the Cobb–Douglas technology, may lead to misleading implications. Using two examples, we show that key implications of the models are highly sensitive to small deviations of the elasticity of substitution from unity. The first employs the standard neoclassical model and emphasizes the sensitivity of the speed of convergence to small changes in the elasticity of substitution. This in turn has profound consequences for wealth and income distribution. The second deals with foreign aid and highlights how the relative merits of “tied” versus “untied” aid are also very sensitive to the elasticity of substitution.
The practice of factor substitution in response to relative price changes is fundamental for productive efficiency. The notion of the elasticity of substitution is central to describing this process and the constant elasticity of substitution (CES) production function, pioneered by Pitchford, 1960 and Arrow et al., 1961 provides an elegant formulation for parameterizing different (constant) degrees of production flexibility. For nearly 50 years now, the CES production function has played a key role in production theory, growth theory, and income distribution.1 But despite the importance of the CES formulation, the bulk of the recent literature on growth theory employs the Cobb–Douglas production function; see e.g. Lucas, 1988, Barro, 1990 and Jones, 1995, among the most influential. Part of the reason for this is that for many countries, the Cobb–Douglas production function in fact characterizes the aggregate economy rather well. Many of the empirical estimates of the elasticity of substitution are insignificantly different from unity, suggesting that the Cobb–Douglas serves as a reasonable working hypothesis.2 In this paper, we suggest that, even if one accepts the empirical estimates supporting a unitary elasticity of substitution, one should nevertheless be careful in restricting oneself to the Cobb–Douglas function, as contemporary growth theory frequently does. Even small deviations from this specification, well within typical statistical sampling errors, can lead to very different implications for economic growth, income distribution, and welfare.3 We illustrate this using two examples from the growth literature of the last 50 years. The first example is a neoclassical growth model in which agents have heterogeneous initial endowments of physical capital. Assuming agents’ utility functions are homogeneous with respect to consumption and leisure, the macroeconomic equilibrium has a simple recursive structure. First, the dynamics of the aggregate stock of capital and leisure are jointly determined, independently of distribution across agents. The individual allocations are then obtained as individuals respond to factor returns, determined by the aggregate behavior of the economy, in light of their own specific endowments. Thus we are able to characterize the transitional dynamics of the distribution of wealth, and ultimately, income. Within this framework, we investigate the effect of the elasticity of substitution on the speed of convergence, which in turn is shown to have important consequences for wealth and income distribution. With the heterogeneity of the initial endowments being the source of income inequality, the faster the speed of convergence, the more rapidly the return to capital converges to its long-run equilibrium following a shock, and the less the degree of income inequality thereby generated. One of our main conclusions is that the speed of convergence and consequently the degree of income inequality are highly sensitive to small deviations in the elasticity of substitution from unity. The speed of convergence has a long tradition in growth theory and has been studied from various perspectives. Following the initial formal development of the neoclassical growth model in the 1950s and early 1960s, several authors addressed the issue of the speed of adjustment toward the steady state. Thus, even early on, this was recognized as being important, for the reason that the convergence speed is the crucial determinant of the relevance of the steady state relative to the transitional path. The range of estimates of convergence speeds obtained in this early literature was extensive, being sensitive to the specific characteristics of the model, such as the returns to scale, the structure of the technology, the rate of technological progress, and number of sectors.4 Recently, the speed of convergence has been debated in the context of the new developments in growth theory. But whereas the early analysis was concerned with providing a general characterization of convergence speeds in terms of structural aspects of the economy, the current literature is motivated more by trying to replicate the empirical evidence. In this respect, influential empirical work by Barro and Sala-i-Martin, 1992b, Sala-i-Martin, 1994 and Mankiw et al., 1992 and others established 2–3% as a benchmark estimate of the convergence rate.5 However, recent studies have questioned the accuracy of these original benchmark estimates, suggesting that they ignore a number of econometric issues, as a result of which they are downwardly biased. Once one controls for these factors, the estimates of the convergence rates both increase and become more sensitive to the time period, the set of countries and their stages of development; see e.g. Islam, 1995, Caselli et al., 1996, Evans, 1997 and Temple, 1998. The sensitivity of the rate of convergence to the elasticity of substitution suggests that theoretical analysis of convergence in the new growth literature, being based on a Cobb–Douglas production function, is overly restrictive. The implied rate of convergence then reflects the rate of capital accumulation, conditional on this specification of the technology. But this suffers from the limitation that the accumulation of capital – the crucial determinant of the rate of convergence – is only one margin along which short-run adjustments may occur, and the extent to which this occurs depends upon the scope for intratemporal substitution. This point was recognized in an early contribution by Ramanathan (1975). The second example is based on the endogenous growth model. The specific problem we discuss pertains to the structure of foreign aid. This has given rise to a long-standing debate as to whether international transfers should be “tied”, in the sense of being linked to investments in public infrastructure projects, or “untied”, in the sense of not being subject to restrictions by donors. Thus the question of what form foreign aid should take has led to a large, but inconclusive, empirical literature on the link between foreign aid, economic growth, and development; see Hansen and Tarp, 2000, Burnside and Dollar, 2000 and Easterly, 2003. Recently, Chatterjee et al., 2003, Chatterjee and Turnovsky, 2004 and Chatterjee and Turnovsky, 2007 have developed a general equilibrium growth framework within which these issues can be conveniently analyzed. Their results indicate that the consequences of tied and untied aid programs for economic growth and welfare depend crucially upon a number of key structural characteristics of the recipient economy. These include: (i) the costs associated with installing capital, (ii) the substitutability between public and private capital in production, (iii) the degree of access to the world financial market, and (iv) the opportunities for co-financing infrastructure projects using domestic resources, and (v) the government’s fiscal position. We focus our discussion on the role of the elasticity of substitution as a crucial determinant of the relative merits of tied versus untied aid. The role of the elasticity of substitution turns out to be complex, depending upon the elasticity of labor supply and possible production externalities of public capital in the production process; see Chatterjee and Turnovsky (2007). On the one hand, both the short-run and the long-run welfare gains from untied aid are remarkably uniform over time, and relatively insensitive to the elasticity of substitution in production. This is because untied aid impacts directly on debt reduction and hence is reflected quickly in enhanced consumption, with relatively little impact on the productive side of the economy and thus on additional future consumption. By contrast, because tied aid impacts directly on the productive capacity of the economy, its short-run and the long-run welfare effects are both highly sensitive to the elasticity of substitution. Moreover, because the benefits of increased productive capacity take time to reach fruition, the effects of tied transfers on the economy’s consumption time profile, and therefore on welfare, occur only gradually. These differences in the nature of the welfare gains associated with these two forms of aid are thus reflected in their relative merits from a welfare standpoint. For example, for the benchmark case of a Cobb–Douglas production function, and for what we view as a plausible elasticity of leisure in utility, tied aid is marginally superior to untied aid from an intertemporal welfare perspective. But marginal changes in the elasticity of leisure in utility and/or the elasticity of substitution in production can lead to either a strengthening of this superiority or to a reversal in the ranking.
نتیجه گیری انگلیسی
For nearly a half century now the CES production function has played an important role in the analysis of economic growth, income distribution, and economic welfare. While much empirical evidence suggests that the Cobb–Douglas production function may serve as a reasonable benchmark for aggregate analysis, we argue that the practice, particularly prevalent in contemporary growth theory, of adopting the Cobb–Douglas technology, may lead to misleading implications. Using two examples we show that key implications of the models may be highly sensitive to small deviations of the elasticity of substitution from unity, well within typical statistical sampling fluctuations. The first example employs the standard neoclassical model and emphasizes the sensitivity of the speed of convergence to small changes in the elasticity of substitution. For example, using a plausible parameterization we find that an estimate of the speed of convergence of 5.6%, obtained from a Cobb–Douglas production function, could statistically be as low as 3.4% or as high as 8.6%. This in turn has profound consequences for wealth and income distribution. The second example dealing with foreign aid and highlights how the relative merits of “tied” versus “untied” aid are also very sensitive to the elasticity of substitution (among other structural characteristics). This finding carries with it some important policy advice. It suggests that when donors decide on whether or not foreign aid should be tied, careful attention should be paid to the recipient’s opportunities for substitution in production, as well as other aspects of its economy. It is perfectly possible for a tied transfer to have a presumably unintended adverse effect on the recipient economy, if that economy is structurally different from what the donor perceived. These two examples confirm the important role of the CES production function in both helping interpret empirical evidence as well as in determining the effects of economic policy. They suggest that it will continue to play an important role in the future. Given the sensitivity of key aspects of economic behavior to the elasticity of substitution it is important that we continue to improve our empirical estimates of this crucial parameter, as well as embedding it in more general production structures.