Trade and factor returns: Empirical evidence from U.S. economy

In this paper we examine the relationship between labor supply and industry-level output in the context of the specific factors model. Jones (Trade, balance of payment and growth: essays in honor of Charles P. Kindleberger, Amsterdam, pp 3–21, 1971) shows that a rise in the amount of labor in the economy will increase the output in all industries. We empirically show which industry output is predicted to expand more when the size of labor force grows. Unlike the commonly used Rybczynski Theorem (Economica 22:336–341, 1955) of the Heckscher-Ohlin model, the specific factors model shows that a comparison both of labor intensities and labor demand elasticities plays an important role in determining which output expands relatively more when the size of labor force grows. For this purpose, we illustrate the importance of the parameters of the model in determining how changes in the labor supply affect the output change, with special reference to elasticities of substitution in production. We estimate the elasticity of substitution by using CES production function and show how these estimates describe the general equilibrium of production with one mobile factor (labor) and 25 industries of the US economy using data for 1979–2001. We show that the increase in the supply of labor raise output in all industries, but the magnitudes of the increases in some industries are more than others depending on the value of the elasticity of substitution along with factor intensities between industries. The largest output effect occurs for educational, health care and social service, where a 1 % supply of labor increase would raise output 10.5 %. However, the growth in the labor supply has a small impact on output growth in the range of 0.1–0.6 % in agriculture, petroleum, coal product and finance and insurance industries.

In a recent article, Amano (1977) used a two-commodity, three-factor model, developed by Jones (1971) and extended by Mayer (1974) and Mussa (1974), to analyse the role of specific factors in international trade and investment. His analysis concentrated on two aspects: first, on examining the importance of specific and mobile factors in determining comparative advantage in this structure; second, on commenting on certain features of Caves' (1971) consideration of the determinants and consequences of international investment in this framework, in which foreign investment is viewed as inter-country flows of industry-specific capital. The purpose of this paper is to extend Amano's analysis into a new structure, which combines elements of the standard Heckscher-Ohlin-Samuelson (H-O-S) and specific factor (SF) models, and is better equipped to handle international mobility of specific factors. The difficulty with the SF, as with H-O-S, model, when all capital is internationally mobile, is that the location of world production is then indeterminate. Within a certain range, therefore, the movement of capital from one country to the other merely alters the location of production, without altering its total. As Amano notes, this property implies that any tariff is prohibitive, short of specialization, since capital flows, responding to the return differential created by the tariff, simply relocate production until trade, at least in the sense of a two-way commodity flow, is eliminated. A one-way commodity flow may continue if foreign earnings are repatriated. But unless factor movements are restricted or taxed, the tariff alone loses all flexibility as a method of adjusting domestic production. Since this is both a strong and largely undesirable property, the development of a new structure, which retains most of the traditional features of trade models yet permits capital mobility without such extreme consequences, seems worthwhile. Section I gives a brief diagrammatic exposition of Amano's results for the SF model, and the consequences of full capital mobility. Section II then introduces our hybrid structure, and relates the determinants of comparative advantage and the consequences of capital mobility to those discussed by Amano. The fact that all the main ingredients are familiar from the H-O-S and SF models considerably facilitates our discussion.

This paper analyzes the effects of changes in relative commodity prices on the distribution of income among factors of production in the context of two models of a simple, two-good economy. In the first model capital is treated as a specific factor in each industry, with labor mobile between industries. The assumption of specificity determines the direction of factor income changes, with magnitudes depending on substitutability between factors and on intensities of factor use within the two industries. In the second model, capital is viewed as a quasi-fixed factor. For the short run, this model is identical to the model first considered. For the long run, this model is identical to the Stolper-Samuelson model in which the direction and magnitude of factor income changes depend solely on relative factor intensities. The difference between the short-run and long-run determinants of changes in factor incomes gives rise to a conflict between factor owners' short-run and long-run interests.

Multi-sector specific factors model with two mobile factors

JN recent years, economists have presented empirical evidence that improvements in efficiency have accounted for most of the growth in aggregate output in the United States and many other countries during the past half century. Robert M. Solow has presented a Cobb-Douglas production function model in which he explicitly assumes that this increased efficiency (technical progress) is due to improvements which are embodied in new physical equipment.' The model is easily extended to the case in which improvements may be embodied in new physical equipment, or may be due to other causes (i.e., disembodied improvements).2 Furthermore, Solow has demonstrated that the explicit assumption that technical progress must be embodied in new physical equipment can be incorporated in a constant elasticity of substitution (CES) production function model.3 Such a model is more general than the embodied Cobb-Douglas model in that the latter implies that the elasticity of substitution is not only a constant, but also equal to one. Solow did not consider the case in which technical progress may also be disembodied, but again it is easy to incorporate this into the CES model. This will be done below. The purpose of this paper is to point out one striking difference between Solow's Cobb-Douglas, and his CES model, when it is assumed that technical progress may be either embodied or disembodied. Embodied technical progress in the Cobb-Douglas model has no influence on the elasticities of output with respect to labor and with respect to the net capital stock. In that model, it is not possible to isolate the influence of embodied technical progress from that of disembodied progress. In the case of the CES model, however, the elasticity of output with respect to capital relative to the elasticity with respect to labor is influenced by the rate of embodied progress. Another feature of the CES model is that it is possible to state output per labor unit as a function of the marginal product of labor, and of a time shift factor which is accounted for only by disembodied technical progress. Given these facts, given data on output, labor, and the net capital stock, and finally, given the assumption that labor and capital tend to be paid their marginal products, it is possible to obtain upper and lower bound estimates of the influence of embodied and disembodied progress on output. The procedure in this paper will be: first, to outline the derivation of the Cobb-Douglas model in which progress is assumed to be either embodied or disembodied; second, to describe the extension to the CES model; and third, to demonstrate how the CES model allows us to distinguish between the effects of embodied and disembodied progress on output, and to discuss some of the implications of the CES model.

We contribute to an emerging literature that brings the constant elasticity of substitution (CES) specification of the production function into the analysis of business cycle fluctuations. Using US data, we estimate by Bayesian-Maximum-Likelihood methods a standard medium-sized DSGE model with a CES rather than Cobb–Douglas (CD) technology. We estimate a elasticity of substitution between capital and labour well below unity at 0.15–0.18. In a marginal likelihood race CES decisively beats the CD production and this is matched by its ability to fit the data better in terms of second moments. We show that this result is mainly driven by the implied fluctuations of factor shares under the CES specification. The CES model performance is further improved when the estimation is carried out under an imperfect information assumption. Hence the main message for DSGE models is that we should dismiss once and for all the use of CD for business cycle analysis.

The role of labor endowments on industry output in the short run: Evidence from U.S industries

This study analyzes the impact of trade on wages in the context of the specific factors model by focusing on the link between trade and the average real wage. A recent paper by Jones and Ruffin (Rev Int Econ, 16:234-249, 2008) shows how one can use the specific factors model to predict how labor should fare from an improvement in the terms of trade. For this purpose, I use annual firm-level data on the manufacturing sector in Ghana during the period 1991-1997. I find that a ceteris paribus increase in the price of exportables in the wood industry would help labor but labor would be hurt by price increases in the food-baker, furniture, textile-garment, and metal-machinery industries.

Purpose: To specify a Variable Elasticity of Substitution function (VES), in which the estimated Elasticity of Substitution (ES) can give some implications for the tendency of economic growth in the Vietnames manufacturing sector. Design/Methodology/Approach: The contribution and the relevant methodology is based on the Bayesian approach having some advantages over the frequentist method: (i) the simulation and prediction results are more reliable in Bayesian analysis due to combining prior knowledge about parameters with obverved data to compose a posterior model, whereas the frequentist approach is based only on available data; (ii) in probability sense, Bayesian credible intervals have a straightforward interpretation compared to frequentist confidence intervals. The Bayesian nonlinear regresion performed is suitable for fitting production functions and depicting economic growth. Findings: The specified VES function has the ES greater than one and this finding contradicts many previous empirical studies in the growth theory. This result points to the possibility of unbounded endogenous growth in the Vietnamese manufacturing sector. Practical implications: Based on the empirical results, in order to realize the possibility of endogenous growth for the studied Vietnamese manufacturing sector, policies of enforcing investment are needed. To raise the level of science and technique, as well as human capital of the Vietnamese enterprises, at the same time, there is great necessity to encourage R&D activities in both the private and public sectors. Originality/Value: Although this study organically builds upon recent studies about the link between the VES, the elasticity of factor subsitution and economic growth, its results proved that the VES is more appropriate than the Cobb-Douglas and the Constant Elasticity of Substitution (CES) to explain economic growth in the view of capital-labor relationship.

Interpreting the Hours-Technology Time-Varying Relationship

In this article we shall give a generalization of Cobb–Douglas, Constant Elasticity of Substitution (CES), Lu–Fletcher, Liu–Hildebrand, Variable Elasticity of Substitution (VES) and Kadiyala production functions. We compute the principal indicators such as the marginal products, the marginal rate of substitution, the elasticities of factors and the elasticity of substitution. Finally, we formulate three theorems of characterization for the functions with a proportional marginal rate of substitution, with constant elasticity of labour and for those with constant elasticity of substitution (for n = 1).

A note on scale effects

The Translog cost function extimation approach has been used in this paper, to estimate important industrial policy parameters. The translog approach differs from the more frequently used techniques viz, the generalized Cobb-Dauglas production function (C0D) approach and the Constant Elasticity of Substitution (CES or ACMS) approach, in that restrictive assumptions about the elasticity of substitution between factors do not have to be made. The translog approach also has the additional advantage of providing cost shares for each factor, pair-wise elasticity of substitution, and own and cross price elasticities for the inputs. Thus, a whole range of policy parameters can be simultaneously estimated. While estimates of elasticity of substitution between capital and labour, and capital and materials are not significantly different from one, the parameter estimate is significantly below unity for substitution between labour and materials. The cross price elasticities show that the three inputs capital, labour and materials are complements in production. The own price elasticities have the appropriate signs and are all significantly below one. As expected the cost share of raw materials is the largest (78.9%) followed by labour’s share (14.6%) and capital’s share (6.5%). Alternative hypotheses regarding scale economies have also been tested. Data from the manufacturing sector of Bangladesh for the period 1969/70 to 1978/79 have been used.

Can variable elasticity of substitution explain changes in labor shares?

In the past, growth models have been constructed and analyzed with the help of a production function subject to certain restrictive features. For quite some time, the Cobb-Douglas production function (CD) with its input exponents adding upto unity and a unitary elasticity of substitution were mostly used by the economists for analysis. In recent times, the constant elasticity of substitution production function (CES) which includes CD, as well as Leontif production function as its special case has been widely used in various studies. One major limitation of this production function is that the elasticity of substitution parameter is not variable along an isoquant, though it can take different values for different values for different industries. We have made an attempt to test whether the estimated values of elasticity of substitution between labour and capital for a sector tend to change from one year to another and also whether it is CD or CES production function that characterizes a particular sector.