قیمت تجهیزات، سرمایه انسانی و رشد اقتصادی

This paper presents a multisectoral model of economic growth in which endogenous technological progress is embodied in new equipment capital. The difference in the intensity of use of human capital across sectors creates aggregate dynamic non-convexities, and hence the model may generate multiple balanced growth paths. Under standard parameter values, our model can explain the observed correlations, found for a pool of countries, between investment rates in equipment capital and income growth, on the one hand, and between the rate of decline in equipment prices and income growth, on the other. The model is then used to study the effectiveness of two public policies that have been widely implemented to promote economic growth: An equipment investment tax credit, and a tax incentive to human capital accumulation. Our results indicate that both policies have positive effects on equipment investment and on long-run growth.

It has long been recognized that the ability to produce better and cheaper machines provoked the economic takeoff in the West. The idea that technology embodied in machines is one of the most important factors in the process of economic growth dates back to the Industrial Revolution. Support for this view has been recently provided in a series of papers. De Long and Summers (1991), using data from 1960 to 1985 for a sample of 25 nations, find a strong, positive statistical relationship between national rates of equipment investment (electrical and non electrical machinery), and productivity growth. Moreover, they also conclude that this association is causal, that is, higher equipment investment drives a faster economic growth. Structures investment has, however, an insignificant effect on growth. These authors show that the pattern for equipment prices across countries also seems to maintain an unambiguous relation with economic growth. Countries with lower equipment prices invest more in equipment capital, and then enjoy a more rapid growth. Furthermore, countries with faster economic growth are those that underwent sharper declines in equipment prices. Jones (1994), using data for 65 countries for the same period, 1960–1985, reaches similar conclusions. He includes the relative price of equipment in a growth regression, and finds a strong, negative relationship between growth and equipment prices. In postwar U.S. economy, the most striking observations on equipment investment, as pointed out by Greenwood et al. (1997), are the decline of the relative price of equipment at an average annual rate of more than 3 percent, and the increase of the equipment-to-GNP ratio. The decline in the relative price of equipment has been interpreted as an improvement in the supply conditions of equipment goods, relative to final output. In other words, the production of equipment goods has experienced a faster technological change than the production of final output. Following this line, Greenwood et al. (1997) propose a model featuring exogenous technological change in the production of new equipment. More specifically, the amount of equipment that can be purchased for one unit of output increases at an exogenous rate. The model is then calibrated for the U.S. economy, and used to study the role of investment-specific technological change as an engine of growth. In their model, however, the relative price of equipment and its rate of change are exogenously set. Thus, since this price is not determined by equilibrium conditions, the long-run equipment investment rate, and the growth rate are trivially pinned down. The main aim in this paper is to show that the endogenization of investment-specific technological change may have important consequences on the equilibrium dynamics. Indeed, when the relative price of equipment is endogenized, it depends on a ratio of marginal productivities, which in turn depends on the stock of wealth in the economy, and on the allocation of inputs across production sectors. The decision on how much to invest in equipment goods depends crucially on its relative price. When this latter price is high, it is optimal to produce final output with relatively more labor and less equipment. The low demand for equipment restrains technological change in the equipment-goods sector, thus preventing equipment prices from falling. The equilibrium dynamics then leads the economy to a long-run equilibrium with high equipment prices and no growth. On the contrary, when the price of equipment is low, the high demand for equipment goods fosters technical change. The equilibrium dynamics then leads to a long-run equilibrium with falling equipment prices and sustained growth in per capita income. As follows from these arguments, the composition of the initial stock of wealth, through its effects on the initial price of equipment goods, is an important determinant of the process of growth. Thus, having access to a technology that enables the production of cheaper equipment goods does not guarantee that it will be used in equilibrium, and hence it is not a sufficient condition for sustained growth. This idea is presented in a standard endogenous growth model based on the Uzawa (1965)–Lucas (1988) framework. The new ingredient in this paper is that physical capital is disaggregated into structures and equipment capital. Our key assumption is that these two types of physical capital are produced with different technologies, the production of equipment capital being more intensive in human capital than the production of structures and consumption. That is, labor employed in the production of equipment goods is more intensive in human capital. Human capital, or workers’ skills, is produced in the educational sector. We abstract from production externalities, and assume standard, constant returns to scale production functions in all sectors. Our assumption that labor in the equipment-goods sector is relatively more intensive in human capital is supported by the combination of the two following observations. First, Kremer and Maskin (1996) find evidence, for the U.S., Britain and France, of an increasing segregation of high- and low-skill workers into separate firms. For instance, in the U.S. economy, the correlation between the wages of manufacturing production workers in the same plant rose from 0.76 in 1975 to 0.80 in 1986. Second, Berman et al. (1998), using data on U.S. and British industries from the 1970's and 1980's, find that the sectors with higher skill upgrading are those producing electrical and non-electrical machinery. The asymmetry in the use of human capital across sectors introduces some complementarities between the allocation of current labor supply and the value of human capital. Depending on the magnitude of these complementarities, the model may generate aggregate dynamic non-convexities. As is well known, non-convex models may display multiple balanced growth paths and, therefore, long-run convergence depends on initial conditions. For a calibrated version of our model that matches key U.S. observations, we obtain two stable balanced growth equilibria. There is an interior balanced growth equilibrium (this is the equilibrium that matches U.S. observations) with a high rate of equipment investment, declining equipment prices, and sustained growth in per capita income. There is also a non-interior balanced growth equilibrium with a low rate of equipment investment, constant prices for equipment goods, and no growth in per capita income. Countries with a higher proportion of human capital in the initial stock of wealth supply less time to work in the final output sector, and thus enjoy lower equipment prices. Consequently, these countries have greater incentives to invest in human capital, and to supply more time to the production of equipment goods. Hence, equilibrium dynamics drives the economy to the interior balanced growth path with sustained growth. Countries with a lower proportion of human capital in the stock of initial wealth will be driven to the long-run equilibrium with low equipment investment and no growth in income per capita. The consideration of public policies aimed at promoting equipment investment is imperative in this framework. The use of fiscal policies to weaken the relationship between initial conditions and equipment prices seems to be a natural way to put economies on their track to a balanced growth equilibrium with sustained growth. We study two such policies: A tax credit to equipment investment, and a fiscal incentive to human capital accumulation. Even though tax credits may cause inflation in the short run (see Goolsbee (1998) for an empirical investigation of the short-run effects of an investment tax credit in the U.S. economy), they turn out to be highly effective in the long run. Using our calibrated economy, we show how these policies can be used to enhance equipment investment and long-run growth. An alternative explanation for the decline in equipment prices can be found in Krusell (1998). Like us, this author interprets the decline in prices for equipment goods as growth in investment-specific technology. However, he endogenizes technological change as the result of R&D decisions taken by monopolistic firms. Our framework has some advantages. First, we are able to give a neater characterization of equilibrium paths. Second, our approach is more appropriate to conduct public policy experiments in calibrated economies. The paper is organized as follows. In Section 2, we present a simplified version of our model in order to highlight the role played by our assumptions in generating multiple balanced growth configurations with different rates of equipment investment and economic growth. Section 3 introduces our general model with structures, equipment and human capital accumulation. The model is then calibrated, and the multiple long-run equilibria are computed. In Section 4, we study the consequences of two public policies aimed at promoting economic growth. Section 5 concludes, and Section 6 contains the appendix.

In the model studied in this paper, which is essentially taken from Greenwood et al. (1997), production takes place in three different sectors: There is a consumption-goods sector, an equipment-goods sector, and an education sector. The main feature of this model is that technology is embodied in new equipment goods. Even though this is an old idea which had been already used by different authors, it was not until the work of Greenwood et al. (1997) that it was introduced in a computable general equilibrium model with the purpose of explaining the evolution of total factor productivity in the U.S. economy. Our main contribution in this paper is to show that in a model with technology embodied in equipment goods, initial conditions, through their effects on the relative price of equipment, play a crucial role in the process of growth. Thus, countries which are appropriately endowed with human capital will start producing new equipment goods that can lead the economy to a long-run equilibrium with sustained growth in income per capita. On the contrary, countries with relatively low human capital may end up in an equilibrium with no long-run growth. When the model is calibrated to match some key U.S. observations, we find that there is also a balanced growth path with no growth and constant equipment prices. This model might then be used to explain the observed persistence in income inequality across countries in terms of differences in history. The results in this paper can also be seen as a contribution to the theoretical literature on dynamic non-convexities. In this regard, our model provides microeconomic foundations for the existence of such non-convexities. Contrary to previous models in this literature, we do not need to assume non-convexities at the disaggregate level. Indeed, we show that with constant returns to scale in all sectors, and with asymmetric labor quality across sectors, the dynamic production possibility function is non-convex. This important effect of the lack of symmetry in the quality of labor across sectors seems to be unnoticed in the growth literature. This point should then be emphasized as an important factor in the growth process.