Constant Elasticity Of Substitution Model Research Articles

Endogenous Bargaining Power and Declining Labor Compensation Share

Workhorse search and matching models assume constant bargaining weights, while recent evidence indicates that weights vary across time and in cross section. We endogenize bargaining weights in a life-cycle search and matching model by replacing a standard Cobb-Douglas (CD) matching function with a general constant elasticity of substitution (CES) matching function and study the implications for the long-term labor share and bargaining power in the U.S. The CES model explains 64 percent of the reported decline in the labor share since 1980, while the CD model explains only 28 percent of the decline. We then use the model to recover changes in bargaining power and find that workers' bargaining power has declined 11 percent between 1980 and 2007 because of a decline in tightness.

Revisiting taste change in cost-of-living measurement

This paper compares conditional and unconditional cost-of-living indexes (COLI) when tastes change, focusing on the Constant Elasticity of Substitution model. A consumer price index typically targets a conditional COLI, which evaluates price change given set of preferences. An unconditional COLI aims to also capture the welfare effects of changing tastes, but it requires stronger assumptions. Using retail scanner data for food and beverage products, I find COLIs conditioning on current period tastes exceed those conditioning on prior period tastes. Consistent with previous studies, I find an unconditional COLI tends to reflect negative direct contributions from taste change.

A Skeptical Note on the Role of Constant Elasticity of Substitution in Labor Income Share Dynamics

The constancy of the elasticity of factor substitution (σ) makes its role as a driver of the labor income share exogenous. The constant elasticity of substitution (CES) production function has predominantly been used to support this causal relationship. We argue that (i) capital-labor ratio determines the value of σ, and (ii) both capital-labor ratio and σ vary over time. We use a variable elasticity of substitution (VES) production framework that allows both labor income share and σ to change over time. Statistically significant empirical support is provided using the Japanese industrial productivity data. This suggests that the CES model may not be an ideal choice to examine the factor income share dynamics.

Impact measurement of tariff changes when experimentation is not an option—A case study of Ontario, Canada

This paper presents the first year results of a three-year study that was designed to measure the impact of time-of-use rates in the Canadian province of Ontario. Unlike prior studies, which have analyzed such impacts in an experimental setting featuring the randomized allocation of customers to treatment and control groups, this study deals with a situation where the deployment of time-of-use rates was not experimental in nature. It was part of a full-scale program. By carefully drawing samples across four local distribution companies, we were able to interpret the study as a natural experiment and construct control groups and treatment groups. We used the Addilog model of consumer demand to estimate elasticities of substitution between peak, mid-peak and off-peak periods. The Addilog model includes as a special case the constant elasticity of substitution model that has been widely used in the literature on customer response to time-of-use rates. The estimated elasticities are well behaved and consistent with those found in the literature.

CES technology and business cycle fluctuations

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 Impact of Dynamic Pricing on Residential and Small Commercial and Industrial Usage: New Experimental Evidence from Connecticut

Among U.S. households, a quarter have smart meters but only one percent are on any form of dynamic pricing. Commissions and utilities continue to study the potential benefits of dynamic pricing through experimentation but most of it involves the residential sector. We add to that body of knowledge by presenting the results of a pilot in Connecticut which included small commercial and industrial (C&I) customers in addition to residential customers. The pilot featured a time-of-use rate, two dynamic pricing rates and four enabling technologies. Customers were randomly selected and allocated to these rates, to ensure representativeness of the final results. The experiment included a total of around 2,200 customers and ran during the summer of 2009. Using a constant elasticity of substitution model, we find that customers do respond to dynamic pricing, a finding that matches that from most other experiments. We also find that response to critical-peak pricing rates is higher than response to peak-time rebates, unlike some other experiments where similar results were found. Like many other pilots, we find that there is virtually no response to TOU rates with an eight hour peak period. And like the few pilots that have compared small C&I customer response to residential response, we find that small C&I customers are less price responsive than residential customers. We also find that some enabling technologies boost price responsiveness but that the Energy Orb does not.

A Stochastic Non-Homogeneous Constant Elasticity of Substitution Production Function as an Inverse Problem: A Non-Extensive Entropy Estimation Approach

The document proposes a new entropy-based approach for estimating the parameters of nonlinear and complex models, i.e. those whose no transformation renders linear in parameters. Presently, for estimating such class of functions, various iterative technics like the Gauss Newton algorithm are applied and completed by the least square methods approaches. Due to conceptual nature of such methods, de nitely estimated functions are di erent from the original nonlinear one and the estimated values of parameters are in most of cases far from the true values. The proposed approach, being related to the statistical theory of information, is very di erent from those so far applied for that class of functions. To apply the approach, we select a stochastic non-homogeneous constant elasticity of substitution aggregated production function of the 27 EU countries which we estimate maximizing a non-extensive entropy model under consistency restrictions related to the constant elasticity of substitution model plus regular normality conditions. The procedure might be seen as an attempt to generalize the recent works (e.g. Golan et al. 1996) on entropy econometrics in the case of ergodic systems, related to the Gibbs Shannon maximum entropy principle. Since this nonlinear constant elasticity of substitution estimated model contains four parameters in one equation and statistical observations are limited to twelve years, we have to deal with an inverse problem and the statistical distribution law of the data generating system is unknown. Because of the above reasons, our approach moves away from the normal Gaussian hypothesis to the more general Levy instable time (or space) processes characterized by long memory, complex correlation and by a convergence, in relative long range, to the attraction basin of the central theorem limit. In such a case, fractal properties may eventually exist and the q non extensive parameter could give us useful information. Thus, as already suggested, we will propose to solve for a stochastic inverse problem through the generalized minimum entropy divergence under the constant elasticity of substitution model and other normalization factor restrictions. At the end, an inferential con dence interval for parameters is proposed. The output parameters from entropy formalism represent the long-run state of the system in equilibrium, and so, their interpretation is slightly di erent from the ceteris paribus interpretation related to the classical econometrical modeling. The approach seems to produce very e cient parameters in comparison to those obtained from the classical iterative nonlinear method which will be presented, too.

Dynamic Pricing in a Moderate Climate: The Evidence from Connecticut

While many dynamic pricing experiments have been carried out in warm climates, few have been carried out in moderate climates. We analyze data from a pilot in New England which featured a time-of-use rate, two dynamic pricing rates and four enabling technologies. Unlike most other pilots, it included small commercial and industrial (C&I) customers in addition to including residential customers, for a total of around 2,200 customers. Using a constant elasticity of substitution model of consumer behavior, we find that customers do respond to dynamic pricing even in a moderate climate, that response to critical-peak pricing rates is higher than response to peak-time rebates, that there is virtually no response to TOU rates with an eight hour peak period and that small C&I customers are less price responsive than residential customers. We also find that some enabling technologies boost price responsiveness.

Non-linearity, Complexity and Limited Measurement in the Relationship Between Satisfaction with Specific Life Domains and Satisfaction with Life as a Whole

In this article we defend that the adoption of a non-linear approach, theoretically framed on complexity theories can make some contribution to the bottom-up approach, which explains the levels of satisfaction with life as a whole through the combination of the levels of satisfaction in different life domains. Two approaches have been tested: (Rojas in J Happiness Stud 7:467–497, 2006) constant elasticity of substitution model and the model with quadratic terms and interaction effects (Gonzalez et al. in Soc Indic Res 80:267–295, 2006; Gonzalez et al. in Qual Quant 42:1–21, 2008). In order to prevent obtaining false non-linear relationships they have been analysed twice taking into account or not limited measurement of satisfaction with life as a whole. Results show that: (a) any of the two non-linear models fits better than the linear one; (b) any of the models failing to take into account limited measurement fits worse; (c) the non-linear model with quadratic terms and interaction effects fits better than Rojas’. The implications for the study of psychological well-being are discussed.

Symmetry Constraints and Variable Returns to Scale in Logit Models

This article addresses two problems with earlier applications of the linear logit model of cost shares. The first problem is that symmetry holds only for one set of cost shares. In this article, an iterative, nonlinear estimation procedure is used to impose symmetry for all predicted shares. The second problem is that analytical expressions for the integrals of log-linear cost shares cannot be derived analytically, although they exist, given the continuity of the logit share equations. This article proposes a procedure for approximating the underlying cost function by using the share predictions as stochastic, numerical approximations of these integrals. The model has constant but unequal elasticities of substitution. This feature does not contradict the Uzawa impossibility theorem, which holds for integrable functions, because the logit model is essentially a numerical approximation of the constant elasticity of substitution model. Another interesting property is that the concavity conditions are relativ...

Embodied and Disembodied Technical Progress in the Constant Elasticity of Substitution Production Function

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.