Constant Elasticity Of Substitution Research Articles

Decreasing Hours, the Labor Share, and the Elasticity of Substitution

The decline in the labor share has attracted the attention of economists in recent years. Empirical literature has documented that this decline can be explained by the increasing capital intensity of the U.S. economy. This paper proposes a mechanism that accounts for the increasing capital intensity - the slowdown of labor-augmenting technology. Under substitutability of capital and labor, such slowdown induces an increase in the rental rate to wage ratio, thus decreasing the labor share. To asses the empirical validity of this mechanism, I construct a general equilibrium model with a CES production function, a utility function compatible with decreasing hours of work, and use a supply-side system to estimate the model’s parameters. I simulate the solution of the model using the actual series for the exogenous variables and I find that the model can account for between half and almost the full decline, depending on the particular specification considered.

Energy-biased technical change in the Chinese industrial sector with CES production functions

We develop a theoretical framework to study energy-biased technical change considering capital, labor and energy as inputs. The framework involves a first order condition estimation of elasticity and technical change parameters for a three factor-nested Constant Elasticity of Substitution (CES) function. Technical change parameters, elasticities and time derivatives of marginal products are combined to compute technical change bias. Conceptually, we introduce total bias in order to estimate the direction without requiring a direct comparison with another factor. For Chinese industries from 1990 to 2012, the optimal structure is capital and energy to be combined at the composite level and then with labor to form total output. Technical change is found to be unambiguously energy biased, it increases in every year, and the bias is predominately away from labor. The results show that Chinese industrialization was fuelled by fossil fuels and energy-intensive technologies. Nonetheless, the growth rate of energy-biased technical change decreased during the 2000s that may result from more energy efficient development.

Another Look at Panel Estimates of the Elasticity of Substitution between Capital and Labor

We construct a broad panel with aggregate data for 94 countries over the period 1970-2014 from the latest version of the Penn World Tables (PWT) dataset, version 9.0. We estimate the elasticity of substitution between capital and labor based on the linearization of a Constant Elasticity of Substitution (CES) production function. In our preferred econometric specification, we find estimates of the elasticity of substitution that are below one. We obtain the same result when we correct the variables for cross-country differences in human capital. Additionally, estimation of a linearized CES for alternative panels constructed with data from older versions of the PWT corroborate our initial estimates. The finding that the elasticity of substitution is below one casts doubts on the Cobb-Douglas assumption commonly adopted in development accounting exercises, as well as on the recent literature on declining labor shares which assumes that the elasticity of substitution is above one.

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 equivalent nontariff measures on vertically integrated markets for which high quality data are unavailable. Standard Constant Elasticity of Substitution (CES) Armington models fail to account for either vertical linkages or parameter uncertainty. Here, we introduce a vertically integrated, nested two‐sector Armington model that incorporates uncertainty in the estimates of Armington elasticities through 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 cattle in the U.S. beef market. By accounting for parameter uncertainty in this way, we are able to estimate the distribution of potential effects of repealing mandatory COOL. Ultimately, we predict that, in all but the most extreme cases, Mexico and Canada would not gain as much market share from the repeal of mandatory COOL as they claim in their World Trade Organization (WTO) filings against the regulation.

The Turning Tide: How Energy Has Driven the Transformation of the British Economy Since the Industrial Revolution

Since the Industrial Revolution, the economy of the UK has transformed from that of an industrial manufacturing giant to a service economy and a central hub for the financial sector. Energy and energy services derived from fossil fuels have played a key role as drivers behind this structural change. Using data from 1855 — 2015 on capital, labor, and energy in a CES production function, we show that during this period input factors were mostly gross complements. However, between 1960 and 1980, the elasticity of substitution of energy increased substantially, from around 0.7 to more than 2.4. These high elasticity estimates were not permanent, and this wave of change that characterized the transition has since dissipated. Elasticities have since returned to even lower values around 0.3, indicating that energy services which depend primarily on fossil fuel inputs, such as transportation, pose a serious limit to the efficacy of efforts aimed at reducing fossil fuel consumption.

Factor Substitution and Productivity in New Zealand

This paper produces aggregate and industry estimates of total factor productivity (TFP) for New Zealand. TFP is estimated based on constant elasticity of substitution (CES) production functions that permit varying assumptions about factor augmentation and that allow for industry‐specific values of the elasticity of substitution between inputs. The CES approach simultaneously explains changes in labour share and output over time, and provides estimates of the contribution of capital and labour to productivity in New Zealand. The results suggest that negative capital‐augmenting technical change in several industries has weighed on productivity in New Zealand.

Estimation of parameters of constant elasticity of substitution production functional model

Nonlinear model building has become an increasing important powerful tool in mathematical economics. In recent years the popularity of applications of nonlinear models has dramatically been rising up. Several researchers in econometrics are very often interested in the inferential aspects of nonlinear regression models [6]. The present research study gives a distinct method of estimation of more complicated and highly nonlinear model viz Constant Elasticity of Substitution (CES) production functional model. Henningen et.al [5] proposed three solutions to avoid serious problems when estimating CES functions in 2012 and they are i) removing discontinuities by using the limits of the CES function and its derivative. ii) Circumventing large rounding errors by local linear approximations iii) Handling ill-behaved objective functions by a multi-dimensional grid search. Joel Chongeh et.al [7] discussed the estimation of the impact of capital and labour inputs to the gris output agri-food products using constant elasticity of substitution production function in Tanzanian context. Pol Antras [8] presented new estimates of the elasticity of substitution between capital and labour using data from the private sector of the U.S. economy for the period 1948-1998.

Application of a New Superposition CES Production Function Model

Abstract In the analysis on economic growth factors, calculating the contribution rate of influencing factor to economic growth using the CES production function model is a common and important research field. The CES production function model has a variety of forms, and the superposition CES production function model proposed in the paper is a new model. With regard to the model’s parameter estimation, the paper proposes a modified particle swarm optimization which has a fast convergence rate and a high precision. With regard to the calculation of factor contribution rate, the paper offers a new scientific calculation method with the superposition CES production function model. At last, the paper makes an empirical analysis on the contribution rate of Chinese economic growth factors and the result obtained consists with the reality.

Optimal Control in the Resource Allocation Problem for a Two-Sector Economy with a CES Production Function

We consider the resource allocation problem in a two-sector economy with a Constant Elasticity of Substitution (CES) production function on a given sufficiently long finite planning horizon. The performance criterion being optimized is one of the phase coordinates at the terminal time. The scalar control u satisfies the geometrical constraint u ∈ [0, 1]. The optimal control contains a singular section. Analyzing the Pontryagin maximum principle boundary-value problem we find the extremal triple and prove its optimality using a special representation of the functional increment (the theorem of sufficient conditions of optimality in terms of maximum-principle constructs). The solution is constructed with the aid of a Lambert special function y = W(x), that solves the equation ye y = x. The optimal control consists of three sections: the initial section that involves motion toward the singular ray L sng = {x 1 = x 2 > 0} , the singular section that involves motion along the singular ray, and terminal section that involves motion under zero control. When the initial state is on the singular ray, the optimal control consists of two sections — singular and terminal. The article is related to a number of the authors’ publications using other production function.

CGE MODEL OF CHINA�S WIND POWER INDUSTRY AND SITUATIONAL SIMULATION RESEARCH

ABSTRACT In this paper, we analyzed the development of the wind energy industry in China, and we constructed the CGE model for the country’s wind power industry. We used the CES production function and trade function to describe the demand and distribution of the country’s production and product. We used the GAMS software to analyze the impact of wind power policies on the wind power industry and social economy. We also constructed a static CGE-LHR model for the purpose of this research. We obtained the results of our simulation using the CGE model on the effect of energy taxes and subsidies on the development of the wind power industry. We gave our recommendations for the future development of the country’s wind power industry at the end of our paper. Keywords wind power industry; CGE model; wind power subsidies; situational simulation

Constant elasticity of substitution functions for energy modeling in general equilibrium integrated assessment models: a critical review and recommendations

Applying constant elasticity of substitution (CES) functions in general equilibrium integrated assessment models (GE-IAMs) for the substitution of technical factor inputs (e.g., replacing fossil fuels) fails to match historically observed patterns in energy transition dynamics. This method of substitution is also very sensitive to the structure of CES implementation (nesting) and parameter choice. The resulting methodology-related artifacts are (i) the extension of the status quo technology shares for future energy supply relying on fossil fuels with carbon capture, biomass, and nuclear; (ii) monotonically increasing marginal abatement costs of carbon; and (iii) substitution of energy with non-physical inputs (e.g., knowledge and capital) without conclusive evidence that this is possible to the extent modeled. We demonstrate these issues using simple examples and analyze how they are relevant in the case of four major CES-based GE-IAMs. To address this, we propose alternative formulations either by opting for carefully applied perfect substitution for alternative energy options or by introducing dynamically variable elasticity of substitution as a potential intermediate solution. Nevertheless, complementing the economic analysis with physical modeling accounting for storage and resource availability at a high resolution spatially and temporally would be preferable.

The Resilience of the Firm: A Production Theory Approach

As a result of catastrophic events, firms and other organizations are faced with input shortages and price shocks. Firms can respond to these events using a variety of “resilience” actions, or tactics. Here we provide a microeconomic foundation for analyzing a comprehensive range of these tactics, incorporating both inherent and adaptive concepts of resilience. We classify these tactics and derive optimality conditions for production with the use of each class of resilience in the context of a nested Constant Elasticity of Substitution (CES) function consisting of aggregated Capital (K), Labor (L), Infrastructure (I), and Materials (M). The framework has broad applicability, including measurement and scoring of resilience, cost-effectiveness assessment of resilience tactics individually and as a group, calculation of resilience indices, and supply-chain management.

Changing age structure and input substitutability in the Thai agricultural sector

The rapidly aging society and agricultural abandonment by young people in Thailand have changed the age structure of Thai agricultural labor, and influenced the potential for agricultural production. Thus, it is important to study the feasibility of other inputs as a substitute for labor. This paper estimated the degree of elasticity substitution of inputs, particularly young labor, older labor, and physical capital. The elasticity of input substitution was estimated using a nested constant elasticity of substitution (CES) production function and nonlinear regression analysis. Research data were obtained from the annual secondary data of government sources from 1990 to 2013. The findings indicated that the input substitutability of young and older labor was low. However, capital and labor could substitute for each other. Moreover, capital better substituted for young labor than older labor. The results suggested that both the public and private sectors should encourage young people to engage in the agricultural sector, and support investment in farm machinery as a labor substitute.

A Strategy to Increase Employment in a Dual Economy: The South African Case

From Arthur Lewis’ seminal paper to Michael Todaro’s model, there has been an attempt to explain migration from rural to urban areas. However, no attempt has been made to determine the trajectory of employment in a dual economy in order to increase employment. In this paper, we set up a planning model to determine the optimal trajectory of employment in a dual economy. A CES production function is used to determine the trajectory of the short-run employment and minimize the distance between the two trajectories. From this result, we suggest a strategy to increase employment in South Africa.

REGULARITY AND STABILITY OF EQUILIBRIA IN AN OVERLAPPING GENERATIONS GROWTH MODEL

In an exogenous-growth economy with overlapping generations, the Cobb–Douglas production, any positive life-cycle productivity, and time-separable constant elasticity of substitution (CES) utility, we analyze local stability of a balanced growth equilibrium (BGE) with respect to changes in consumption endowments, which could be interpreted as a transfer policy. We show that generically, in the space of parameters, equilibria around a BGE are locally unique and are locally differentiable functions of endowments, with derivatives given by kernels. Furthermore, those equilibria are stable in the sense that the effects of temporary changes decay exponentially toward ±∞.

Comparative advantage and strategic specialization

AbstractThis paper shows that a strong comparative advantage is necessary for free trade and specialization in a 2 × 2 symmetric Ricardian model to be achieved in a Nash equilibrium. Governments strategically control labor distribution across industries, and representative agents maximize Cobb–Douglas utilities. A Nash equilibrium with complete specialization is achieved if and only if relative productivity exceeds a key value of 3, which is considered a very large number based on previous empirical studies. This paper also introduces a two‐stage game where each government chooses labor distribution first and then tariffs. In this two‐stage game, complete specialization is never achieved for any relative productivity level. Finally, by generalizing the Cobb–Douglas model into constant elasticity of substitution (CES) preferences, I show that if immiserizing growth effects exist, complete specialization could not be achieved for any level of relative productivity.

Speed and Contribution of Educational Scientific and Technological Progress in Development of Primary Forestry Industry in China

Our purpose is to analyse the speed and contribution of the educational scientific and technological progress in the development of the primary forestry industry. In order to research the role of the educational scientific and technological progress in the development of the primary forestry industry more scientifically, the article employs the modified multi-factor two-level CES production function model, and the data from 31 provinces over 19 years (1994-2012), to measure and calculate the speed and contribution of the educational scientific and technological progress in the development of the primary forestry industry from the two dimensions, time and space. The speed of educational scientific and technological progress in the primary forestry industry was 2.8% from 1994 to 2012, and the contribution rate of educational scientific and technological progress to the development of the primary forestry industry was 49.6%. Through the measuring and calculating of different periods, it is found that there were big differences between different periods regarding to the contribution of the educational scientific and technological progress to the development of the primary forestry industry, and the contribution grew quickly in the last few years. Through the measuring and calculating of different areas, it is found that there were huge differences between different areas regarding to the contribution of the educational scientific and technological progress to the development of the primary forestry industry, due to the difference in nature, society and economic environment. Along with the development of the economy, the structure of the forestry industry needs important changes. The dominating status of the primary forestry industry in the forestry industry should be strengthened. The educational science and technology investment of the primary forestry industry should be boosted, to lead the development of the primary forestry industry onto a path relying on the progress of educational science and technology. In the process of making the development policy and investment policy on the primary forestry industry, it shall not impose uniformity in all cases. On the contrary, the policy shall vary according to the different situations; and it is noticed that the comparative advantages of different areas with different social economic and natural resources shall be exerted.

Weighting Health Outcomes by Socioeconomic Position Using Stated Preferences.

BackgroundThe trade-off that society is willing to make to promote a more equitable distribution of health can be represented as a social welfare function (SWF). SWFs are an economic construct that can be used to illustrate concerns for total health with aversion to inequalities between socioeconomic groups.ObjectiveThis study used people’s preferences to estimate the shapes of health-related SWFs (HRSWFs). We tested the suitability of this method to derive equity weights.MethodsA questionnaire was used to elicit preferences concerning trade-offs between the total level of health and its distribution among two socioeconomic groups. The participant group was a sample of convenience that included a mix of health researchers, academics, clinicians, managers, public servants and research students. The data collected were used to develop HRSWFs with a constant elasticity of substitution. The weight was calculated using the marginal rate of substitution.ResultsA marginal health gain to the lowest socioeconomic position (SEP) group was valued 14.1–81.4 times more than a marginal health gain to the high SEP group.ConclusionsOur results provide evidence to support the idea that the public may be willing to make trade-offs between efficiency and equity, and that they value health gains differently depending on which socioeconomic group receives the health gain. Further evidence is required before such indicative weights have practical value.Electronic supplementary materialThe online version of this article (doi:10.1007/s41669-017-0036-1) contains supplementary material, which is available to authorized users.

The Complexity of Non-Monotone Markets

We introduce the notion of non-monotone utilities, which covers a wide variety of utility functions in economic theory. We then prove that it is PPAD-hard to compute an approximate Arrow-Debreu market equilibrium in markets with linear and non-monotone utilities. Building on this result, we settle the long-standing open problem regarding the computation of an approximate Arrow-Debreu market equilibrium in markets with CES utility functions, by proving that it is PPAD-complete when the Constant Elasticity of Substitution parameter ρ is any constant less than − 1.

Double limit analysis of optimal personal income taxation

A double limit analysis is developed to determine the optimal personal income tax based on the principle that moving a marginal dollar of tax revenue from one income interval to another should not raise social welfare. The first order condition can be differentiated with respect to an interval boundary to yield a second order differential equation for the optimal income tax that can be solved to yield specific solutions. Application of an optimal income tax to a broader income range in general reduces tax revenues and requires greater subsidies at low-income levels. Optimal solutions are provided assuming Cobb-Douglas or Constant Elasticity of Substitution (CES) utility and lognormal or Pareto productivity distributions.