Can variable elasticity of substitution explain changes in labor shares?

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).

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.

Productive government investment and the labor share

This paper studies the coevolution of the fall in the US corporate sector labor share and the rise of business activity in tax-preferred, pass-through form. Reallocating activity to the form it would have taken prior to the Tax Reform Act of 1986 accounts for one third of the decline in the corporate sector labor share between 1978 and 2017. Our adjustments are concentrated among mid-market firms in services, leaving a larger role for the manufacturing sector and superstar firms in driving the remaining decline in the labor share. Our findings highlight the importance of tax policy when measuring factor shares.

SummaryChina's labor share has declined since late 1990s. Using the methodology developed by Oberfield and Raval, this paper estimates China's aggregate capital‐labor elasticity of substitution, leveraging the estimated micro‐level elasticities. The findings indicate that China's aggregate capital‐labor elasticity falls within the range of 0.9 to 1. Utilizing this estimated aggregate elasticity for labor share decomposition, we find that the bias of technical change emerges as the predominant factor driving the decline in labor share.

In a recent article of this REVIEW, Sato and Hoffman (1968) derive an explicit form of production function with variable elasticity of factor substitution (hereafter VES production function) and give some estimates of VES functions for United States and Japan. The authors contend that the overall impression (of regression results.) is that VES functions are more realistic than CES (C-D) (Sato and Hoffman: p. 457). The purpose of this note is to show that their results both for United States and Japan, which they report to be most useful ones among other estimates under alternative forms of VES functions, are not valid, primarily because their estimates are not logically consistent with their a priori estimates used for estimating VES functions.

Energy and other factors of production are the primary inputs in the context of sustainable economic growth. This makes energy relatively strategic in the development stage and in the energy importers economies. In this study, the effect of elasticity of substitution on economic growth is investigated for 31 OECD countries over the period from 1990-2014. Although the effect of elasticity of substitution between capital and aggregate energy consumption on economic growth has been examined in many studies, the issue of how this effect changes between the different sources of energy has not been adequately addressed. The research is aimed at contributing to the related literature in this regard. The effect of elasticity of substitution between capital and different energy sources on economic growth is examined within the neoclassical Solow-Swan Growth model. In this model, technology is defined by a variable elasticity of substitution (VES) production function. The empirical model is estimated by the non-linear least squares (NLLS) method. The results show that oil and primary energy consumption are substitutes; natural gas, coal, and hydroelectricity consumption are the complement in the final production of output.

Interpreting the Hours-Technology Time-Varying Relationship

This article analyzes the constant elasticity of substitution (CES) production function when there are increasing returns to scale and the elasticity of substitution exceeds 1, which I refer to as the explosive case of the CES. For this explosive case of the CES, the article demonstrates a new and surprising result: marginal and average products of labor and capital approach infinity as either labor or capital approach infinity. Obviously, in this explosive case of the CES, the law of diminishing marginal returns is eventually violated in a dramatic way. Some implications of this result for growth theory are discussed. The article concludes by deriving, for this explosive case of the CES, lower and upper bounds for the capital labor ratio which are consistent with the law of diminishing marginal returns.

While the US labor share has declined, especially in manufacturing and retail, the labor share of a typical firm in these sectors has risen. This paper introduces a model where firms incur fixed costs to automate tasks. In response to lower capital prices, the model reproduces the labor share patterns observed in the data: large firms automate more tasks, reducing the aggregate labor share; while the median firm continues to operate a labor-intensive technology with a rising labor share. Using our model, we decompose the labor share decline and the rise in sales concentration in each sector into a part driven by lower capital prices and a part driven by reallocation to higher-markup firms. Reallocation played a minor role in explaining the labor share decline in manufacturing and some role in retail and other sectors during 1982-2012.

Capital Composition and the Declining Labor Share

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.

Worktime has been falling slowly though real wages have risen dramatically. We show that in a general equilibrium model with CES utility and production functions, worktime falls with real wages if and only if the elasticity of substitution between consumption and leisure is less than that between capital and labour, but always rises with labour's income share and concerns with relative income. While a falling labour share may not reduce worktime due to market inflexibility, stronger income comparison increases inefficient overwork. Hence, more flexibility, higher income taxes and a basic income are needed to reduce working hours and raise social welfare.

PurposeThe purpose of this paper is to explore the properties of the variable elasticity of substitution (VES) production function, and examine the dynamics of growth associated with it.Design/methodology/approachThe VES production function is incorporated into an otherwise standard Diamond overlapping generations model.FindingsDepending on parameter combinations, the economy can achieve a unique and stable steady state akin to that observed in the Solow-Swan model, reach a poverty trap or transition towards an upper bound of per capita capital stock. A special case of the VES production function is also consistent with unbounded growth.Research limitations/implicationsThe paper is theoretical in nature. Further empirical analysis could shed deeper insights into the results presented in this study.Practical implicationsThe VES production function, when applied to the context of the Diamond model, can capture a variety of growth experiences observed in the empirical literature.Social implicationsIn the context of the Diamond model, a higher value of a particular parameter in the production function leads to greater intergenerational income and consumption inequality. Hence, the study provides a potential explanation for intergenerational inequalities observed in practice.Originality/valueThe study demonstrates the empirical value of the VES production function in explaining observed differences in factor shares, rewards and elasticities within and between countries over time.

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.