Constant Elasticity Of Substitution Research Articles

Skill Premiums and the Supply of Young Workers in Germany

In this paper, we study the development and underlying drivers of skill premiums in Germany between 1980 and 2008. We show that the significant increase in the medium to low skill wage premiums since the late 1980s was almost exclusively concentrated among the group of workers aged 30 or below. Using a nested CES production function framework which allows for imperfect substitutability between young and old workers, we investigate whether changes in relative labor supplies could explain these patterns. Our model predicts the observed differential evolution of skill premiums very well. The estimates imply an elasticity of substitution between young and old workers of about 8, between medium- and low-skilled workers of 4 and between high-skilled and medium/low-skilled workers of 1.6. Using a cohort level analysis based on Microcensus data, we find that long-term demographic changes in the educational attainment of the native (West-)German population – in particular of the post baby boomer cohorts born after 1965 – are responsible for the surprising decline in the relative supply of medium-skilled workers which caused wage inequality at the lower part of the distribution to increase in recent decades. We further show that the role of (low-skilled) migration is limited in explaining the long-term changes in relative labor supplies.

Logit, CES, and Rational Inattention

We study fundamental links between two popular approaches to consumer choice: the multinomial logit model of individual discrete choice and the CES utility function, which describes a multiple choice of a representative consumer. We base our analysis on the rational inattention (RI) model and show that the demand system of RI agents, each of which chooses a single option, coincides with the demand system of a fictitious representative agent with CES utility function. Thus, the multiple choice of the representative agent may be explained by the heterogeneity in signals received by the RI agents. We obtain a new interpretation for the elasticity of substitution and the weighting coeficients of the CES utility function. Specifically, we provide a correspondence between parameters of the CES utility function, prior knowledge and marginal cost of information.

Economic Growth and the CES Production Function with Human Capital

Employing a neoclassical growth model with a constant elasticity of substitution production function, we develop a comparative static and dynamic analysis of the effects of the elasticity of substitution between inputs on the steady state growth path, growth threshold, speed of convergence and savings rates. Unlike earlier studies along these lines, we incorporate human capital, along with physical capital and raw labor, as a third input in the production function. We prove that a higher elasticity of substitution between inputs can lead to a higher steady state level for income per effective unit of labor. To illustrate the quantitative significance of the elasticity of substitution, we consider two ways in which human capital enters the production function. Employing cross country data, we find estimates for the normalized CES production functions with human capital to be significantly below unity.

Whence the Beef?: The Effect of Repealing Mandatory Country of Origin Labeling (COOL) Using a Vertically Integrated Armington Model with Monte Carlo Simulation

Increasingly, international trade policy analysis explores the economic effects of changes in ad-valorem tariffs, or ad-valorem equivalent non-tariff measures, on vertically integrated markets for which high quality data are not available. Standard Constant Elasticity of Substitution (CES) Armington models fail to account for either vertical linkages or parameter uncertainty. Here we introduce a modified Armington CES vertically integrated two-sector model, with nested Armington Elasticities, that incorporates uncertainty in the estimates of Armington Elasticities and market shares through a Monte Carlo simulation. As an illustrative case, we model the effects of changes in country of origin labeling (COOL) rules on the market shares of domestic and foreign cattle in the U.S. beef market. By accounting for parameter uncertainty in this way, we are able to illustrate the distribution of potential effects of repealing mandatory COOL. Moreover, we are able to decompose the effect of repealing COOL via its effect on relative prices, information available to consumers, and the quasi-general equilibrium effect. Finally, we uncover the conditions under which Canada and Mexico would benefit from the repeal of mandatory COOL by at least as much as they claim in their WTO filings against the regulation.

A Simple Universal Dynamic Framework for Endogenous Preference Change

Although the demand for a framework with endogenous preference change was formulated back in the 1970s, it has remained unfulfilled. In this paper we propose a universal discrete dynamic framework for endogenously changing preferences based on changes in elasticity of substitution σ: almost unlimited selection of intertemporal dependency forms and functional choices make this framework universally applicable. We develop two cases: a baseline with CES utility and a monopolistic market and a relaxed model with incomplete information and oligopolistic competition and investigate numerically the dynamics of market parameters. Both investigated setups are consistent with reality. Finally, we discuss the possibilities of empirical applications with the SEDS model due to Coloma (2006).

A Comment on Recent Contributions on the Value of Life

Two articles (Hugonnier et al., 2013; Cordoba and Ripoll, 2017) have proposed a recursive formulation of utility functions combining a positive value of life, preference homotheticity, and a constant elasticity of substitution. However, when the elasticity of substitution is below one and mortality rates take plausible values, this recursive formulation admits only a unique solution where utility is constant and equals zero everywhere. Non-constant solutions may only exist if mortality rates are assumed to remain low at all ages, namely in a world of perpetually young agents. Such solutions are therefore unsuitable for studying the value of life in demographically relevant settings and yield counterfactual predictions for saving behavior. We conclude this clarifying paper by reviewing various recursive specifications that can be used to study the value of life with no such problems.

Who provides the capital for Chinese growth: the public or the private sector?

ABSTRACTWe focus on the role of the government in the provision of investment in China, through the medium of a Dynamic Stochastic General Equilibrium model of the economy in which the form of the production function reflects this governmental role. Using indirect inference, we estimate and test for the elasticity of substitution between government and nongovernment capital in both Constant Elasticity of Substitution (CES) and Cobb–Douglas technologies. The results underscore the strong substitution relationship between government and nongovernment capital from 1949, supporting CES rather than the Cobb–Douglas technology. They also show that the orientation of public investment changed after the start of the ‘Socialist Market Economy’ in 1992: government capital became more complementary to nongovernment capital as it focused more on infrastructure and withdrew from industrial production, intervening only in times of crisis, for stabilization purposes, indirectly via the state banks.

RETHINKING THE PURPOSE OF MICRO ENTERPRISES IN DEVELOPING COUNTRIES: EVIDENCE FOR MEXICO

A large body of economic literature has established that the primary purpose of any firm assuming unitary and constant elasticity of substitution of production inputs, among other necessary conditions, is profit maximization. However, the prevailing operating conditions of the micro enterprises raise concerns about the applicability of this formalization. Through an empirical study for Mexico using a four-input translog function (capital, labor, energy and supplies), and based on cross-sectional data, we find that the elasticities of substitution between production inputs are not unitary; in fact, some of them are complementary. This forces us to consider that instead of seeking to maximize profits, some types of micro enterprises are looking to optimize their installed capacity or achieve financial survival of the owner and their family, thus relaxing the foundations of economic analysis for the very small-scale and nascent micro enterprises.

Advantageous redistribution with three smooth CES utility functions

We present a parametric example of three-country advantageous redistribution with two Cobb–Douglas utility functions and one CES utility function for which the elasticity of substitution is 1/2. This paper indicates that the possibility of advantageous redistribution strongly depends on the three countries’ taste patterns, endowment distributions, and the elasticity of substitution. In particular, we will show with specific examples that greater difference between the donor and recipient’s taste patterns and a lower elasticity of substitution can increase the chance of advantageous redistribution.

Including System Integration of Variable Renewable Energies in a Constant Elasticity of Substitution Framework: The Case of the WITCH Model

Abstract The penetration of variable renewable energies (VREs) in the electricity mix poses serious challenges in terms of management of the electrical grids, as the associated variability is in contrast with the requirement that the load be instantaneously equalized by the generation. One of the goals of Integrated Assessment Models (IAMs) is to simulate the evolution of electricity demand and generation mix over time, therefore a proper modeling of VRE system integration is crucial. In this paper we discuss how different modeling mechanisms can profoundly impact the evolution of the electricity mix, and specifically renewable penetration. In particular, we focus on the effects of introducing a set of explicit system integration constraints in a model, WITCH, characterized by a Constant Elasticity of Substitution (CES) framework. The role of the implementation of storage is discussed as well.

Including system integration of variable renewable energies in a constant elasticity of substitution framework: The case of the WITCH model

The penetration of variable renewable energies (VREs) in the electricity mix poses serious challenges in terms of management of the electrical grids, as the associated variability is in contrast with the requirement that the load be instantaneously equalized by the generation. One of the goals of Integrated Assessment Models (IAMs) is to simulate the evolution of electricity demand and generation mix over time, therefore a proper modeling of VRE system integration is crucial.In this paper we discuss how different modeling mechanisms can profoundly impact the evolution of the electricity mix, and specifically renewable penetration. In particular, we focus on the effects of introducing a set of explicit system integration constraints in a model, WITCH, characterized by a Constant Elasticity of Substitution (CES) framework. The role of the implementation of storage is discussed as well.

The Labor Share Fluctuation

Recent empirical studies show that labor shares are rarely stable but are volatile and have heterogeneous cyclicality among countries, that are not successfully explained by existing standard models. To fill in the gap, this paper gives a comprehensive view to understand the cyclical patterns of labor share fluctuation. The model is a dynamic stochastic general equilibrium small open economy, composed of tradable and nontradable sectors with CES production functions. In the environment, there are two margins of the labor share fluctuation over the business cycle: i) fluctuation of capital-labor ratio in each sector, ii) fluctuation of the relative value of sectoral productions. Estimated models using Bayesian technique show procyclical and excessively volatile labor share in Argentina, and countercyclical and near-output volatile labor share in Canada, that are all observed in the data. In addition, estimated models predict that main sources of fluctuation of the labor share are financial shocks, and indicate that capital and labor are gross substitutes in Argentina, whereas they are gross complements in Canada.

MONETARY POLICY, FACTOR SUBSTITUTION, AND CONVERGENCE

In this paper, we examine the influence of monetary policy on the speed of convergence in a standard monetary growth model à la Sidrauski allowing for differences in the elasticity of substitution between factors of production. The respective changes in the rate of convergence and its sensitivities to the central model parameters are derived both analytically and numerically. By normalizing the constant elasticity of substitution (CES) production functions both outside the steady state and within the steady state, it is possible to distinguish between an efficiency and a distribution effect of a change in the elasticity of substitution. We show that monetary policy is the more effective, the lower is the elasticity of substitution, and that the impact of monetary policy on the speed of convergence is mainly channeled via the efficiency effect.

Estimation of Resource-Specific Technological Change in a Production Function

Technological change plays a critical role in economic growth. Prevailing approaches to estimation of total technological change are associated with total factor productivity (TFP) based on a Cobb-Douglas (CD) production function. To estimate resource-specific technological change, previous studies typically assume an alternative specific functional form other than a CD function such as a transcendental logarithmic (translog) or a Constant Elasticity of Substitution (CES) function. In this article, we argue that under certain conditions, a resource-specific technological change can be estimated from observed resource intensity/productivity data over time, irrespective of which functional form is adopted. We also illustrate that if the estimated technological change is applied to a CD production function, the estimated resource elasticities can differ considerably from that estimated by the prevailing TFP approach. In our case of a panel data for 40 regions 1995-2009, our approach shows that a CD function is plausible across regions compared to the TFP approach.

Solving the consumer’s utility-maximization problem with CES and Cobb-Douglas utility function via mathematical inequalities

This paper presents a new, non-calculus approach to solving the consumer’s utility–maximization problem with constant elasticity of substitution (CES) utility function, as well as with Cobb-Douglas utility function in case of \(n\ge 2\) commodities. Instead of using the Lagrange multiplier method or some other method based on differential calculus of several variables which might give complicated terms and equations difficult to handle, the utility–maximization problems are solved by using Jensen’s inequality and weighted arithmetic-geometric mean (weighted AM–GM) inequality. In comparison with calculus methods, such approach does not require checking first and second order conditions.

Horizontal differentiation and economic growth under non-CES aggregate production function

We present a model of economic growth driven by horizontal innovation in which, unlike the existing literature, the final output sector employs a non-specified, non-CES, additive production function. Our motivation in conducting such analysis is based on the recognition that the use of a CES aggregate production function in the final output sector leads to the unrealistic conclusion that the gross markup of price over marginal costs set in the monopolistically-competitive intermediate sector is constant. We derive necessary and sufficient conditions for an equilibrium with perfect competition in the final output market to exist even in the presence of a non-CES technology. These conditions generalize the usual properties of the CES case. We also analyze the long-run relation between economic growth and variable markups.

Technological Advance and the Labour Share of National Income in the European Union

This article tests the hypothesis that member states of the EU have been experiencing a declining share of labour income due to technological advance. It discusses factors that lead to the fall in the labour share, including technological advance, which is a tendency found in the capitalist system. We also identify the undesirable effects of a fall in the labour shares. The results of an econometric test conducted in our study, based on a labour demand equation that was derived from the CES production function, confirm the hypothesis that technological progress negatively affected the labour share of income, everything else remaining constant. This finding has important implications for EU Member States, namely that some form of policy intervention would seem to be necessary, as technological progress could lead to a continuing fall in the share of labour income if left to its own devices.

A New Class of Production Function Model and Its Application

AbstractUnder some circumstances, the studies on economic growth theory can be translated into the researches on production function which will beneficial for the government to analyze the pattern of economic growth and then make reasonable policies. The commonly used production functions include C-D production function, CES production function, VES production function with different elasticity of substitution. This paper will put forward to a new class of production function which elasticity of substitutionσis a non-linear function ofK/L. With this new model, a calculation formula for accurately measure the influence rates of various factors to economic growth will be derived, which is significant for in-depth studies on functions and scientific measurement. The empirical analysis on the influence rates of China’s economic growth factors and its good results will be presented in the end of this paper.

Hàm sản xuất một mức với nhịp độ tăng năng suất tới hạn phụ thuộc mọi nhân tố sản xuất

By using of rates of limit productivity’s growth dij in this work, the following fundamental theorems for one-level production functions with constant elasticity of substitution are proved. With these sentences the building of all such function is possible. However, for the construction of almost all such functions we have a simple theorem. The smooth function of one –level production function with constant elasticity of substitution is the function with the same constant of elasticity of substitution.

Tính lồi-lõm của hàm sản xuất một mức với độ co giãn thay thế không đổi

On the base of the theorem [4]: Necessary and sufficient conditions for the constancy of elasticity of substitution (sij=s) of one – level production functions y=f(x1, x2,…, xn) is djj +1/(sijxj) = dji, where dji the following theorem is followed: In the region W ={xj ³ 0, j=1..n} the one-level production functions with constant elasticity of substitution s is: a. Convex in W1 ÌW if and only if b. Concave in W1 if and only if in this region to say the least of it and • , where {1,2,..,k} if {1,2,..,n} and k=1..n.