CES technology and business cycle fluctuations

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.

Interpreting the Hours-Technology Time-Varying Relationship

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.

This paper assesses the validity of the constant elasticity of substitution (CES) and the Cobb‐Douglas (CD) production functions in modelling the aggregate production function and computing the total factor productivity (TFP) in South Africa for the period 1970‐2006. The CES function is estimated with Nerlove's two‐step procedure using the autoregressive distributed lag (ARDL) cointegration and the Kalman filter estimation techniques, while the CD production function is estimated using the Kalman filter technique. The results of the forecast performance of the two model specifications show that the CD specification outperforms the CES for the period 1970‐2006, although the CD specification may be too restrictive.

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).

According to Jevon's paradox, energy efficiency leads to more energy consumption instead of low. So, calculating the size of energy rebound effect is need of the time to devise sustainable environmental and energy policies. This paper aims to analyze the impact of energy efficiency on energy consumption of transport sector in Pakistan by using time series data from 1980 to 2018. This incremental energy consumption channelizes through intensity and output effects. The study uses both Cobb-Douglas (C-D) and constant elasticity of substitution (CES) aggregate production functions to find the magnitudes of energy rebound effect. As the analysis of energy rebound effect is sensitive to the selection of data, model, and methodology. C-D production function deals with energy rebound effect, while CES provides extra information in the form of energy intensity and output effects along with energy rebound effect. The C-D function is estimated with linear estimation technique, while the CES function is estimated through nonlinear optimization method. The results indicate relatively low magnitudes of energy rebound effect in case of C-D function, e.g., 2% in the short run and about 36% in the long run while about 70% energy rebound, 63% energy intensity, and 7% output effect in the transport sector of Pakistan in the long run by using CES function. As anticipated, energy efficiency is less effective in terms of energy savings in transport sector due to energy rebound effect. Therefore, policy makers should incorporate energy rebound effect to achieve sustainable environmental goals along with economic growth path.

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.

We revisit three major US recessions through the lens of a standard medium-scale DSGE model (Smets, F., and R. Wouters. 2007. “Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach.” The American Economic Review 97: 586–606) augmented with financial frictions. We first estimate the DSGE model using a Bayesian approach for three alternative periods, each containing a major US recession: the Great Depression, the Stagflation and the Great Recession. Then, we assess the stability of structural parameters, and analyze what frictions were particularly important and what shocks were the main drivers of aggregate fluctuations in each historical period. This exercise can be understood as a test of the standard New-Keynesian DSGE model with financial accelerator in closed economies. We find that the estimated DSGE model is able to provide a sound explanation of all three recessions by closely relating both estimated structural shocks and frictions with well known economic events.

This paper clarifies the concepts of factor-augmenting, factor-biased and factor-saving technical change by tracing back to the original definitions and using CES production function. Make a comparison between Hicks factor-biased technical change and Harrod factor-biased technical change. Use time-series data of China from 1978 to 2008 to estimate elasticity of substitution between capital and labor, then compute the value of factor-augmenting and factor-biased technical change. The results show that in the sample period elasticity of substitution between capital and labor is less than 1, and in most years the direction of technical change is factor-biased.

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.

This investigation extends the constant elasticity of substitution (CES) batch process production model of Lin et al. (J. Management syst. 2002; 9: 173) for an uncertain exchange rate by considering an export‐oriented manufacturer who can decide to switch freely between domestic and foreign locations. The export‐oriented manufacturer is risk averse and has rational expectations. As the entry cost declines, the export‐oriented manufacturer's entry trigger for the CES production function increases for transferring from a domestic and to a foreign location. Additionally, the manufacturer's exit trigger for CES production function increases for transferring from a foreign and to a domestic location. Moreover, the exit cost resembles the entry cost. Copyright © 2002 John Wiley & Sons, Ltd.

Estimated substitution elasticities of a nested CES production function approach for Germany

An Information Theory Based Framework for the Measurement of Population Health

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.

Gravity Redux: Estimation of gravity-equation coefficients, elasticities of substitution, and general equilibrium comparative statics under asymmetric bilateral trade costs