Constant Elasticity Of Substitution Function Research Articles

Energy efficiency and energy rebound, intensity, and output effects in transport sector of Pakistan.

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.

NLRIS: Modeling and Analysis of Non-local Influence of Research Output of Institutions

In this paper, we posit a novel metric for ranking academic institutions based on the extent of influence their publications have on the global research community. We quantify the university’s global research impact using a calculated internationality score we call ’Non-local Research Influence Score’ (NLRIS). We propose the evaluation metric which is fair to the institutions which are smaller in size and do not qualify to be considered for the reputed ranking schemes but are performing well in terms of research quality and attracting citations and collaborators around the world. Our work calculates the scores of 75 universities using the Constant Elasticity of Substitution (CES) function. This score is calculated as a function of the global influence in terms of citations (Nonlocal Influence Quotient - NLIQ) and the extent of international research collaboration International Collaboration Ratio - ICR). The CES function accepts 2 variables, K and L as input and produces the variable Q as an output. In our model, we substitute K and L with the calculated values of ICR and NLIQ. The output of the CES function provides us with the desired internationality score of each institution. PSO is used to model the constrained optimization problem. In this paper, we also define a metric for representing NLIQ and ICR of individual universities. We have also performed a comparison between QS ranking and our calculated internationality scores.

Implementation of Constant Elasticity of Substitution Function and Data Envelopment Analysis: Productivity and Technical Efficiency of Large Industry Creative Economy in Craft Subsector Indonesia

Indonesia has undergone a transformation from agriculture to the manufacturing industry in 1971-1997. In the 2001-2015 period there was de-industrialization in developed countries. Likewise, Indonesia which shows a decrease in the contribution of GDP and manufacturing sector workforce to the economy. However, deindustrialization in Indonesia is premature / too fast. One of the policies to overcome this problem is with attention to the creative industry. With the existence of the creative industry, it can achieve several SDGs goals, namely the 8th goal, namely decent work and economic growth, the creative economy can increase economic growth, create jobs and increase exports (UNCTAD, 2010). However, the creative industry GDP growth that is below the RPJMN target is thought to indicate low productivity of the creative industry. According to IBS data, the craft sub-sector creative industry has a low production value. To see productivity can use technical efficiency. This study aims to evaluate the technical efficiency of creative industry in the craft sub-sector as well as to analyze the trend of variables that affect technical judgments. The method used is the CES production function and Data Envelopment Analysis. The results show that industries that have high total production factor values have a tendency to have high technical efficiency values as well. Furthermore, those arranged according to technical categories and binary logistic regression are used to determine trend variables that affect technical judgments. The technical efficiency of the craft, significantly by wages, investment status and company scale.

Định dạng hàm sản xuất CES bằng phương pháp hồi qui phi tuyến tính Bayes (Specifying a CES Production Function Using a Bayesian Non-linear Regression)

Vietnamese Abstract: Đa phần cac nghien cứu tại Việt Nam sử dụng ham sản xuất Cobb-Douglas va cac biến thể của no như một cong cụ trong phân tich va dự bao kinh tế. Dạng ham nay co nhược điểm la cac tiền đề của no qua cứng nhắc ma khong phu hợp với hiện thực trong nhiều trường hợp, đặc biệt trong phân tich động thai tang trưởng kinh tế. Ham CES (constant elasticity of substitution) với tiền đề linh hoạt hơn, cụ thể la hệ số co gian giữa vốn va lao động khac một, được sử dụng ngay cang phổ biến. Do vậy, nghien cứu nay được thực hiện nhằm định dạng ham CES dựa tren dữ liệu của cac doanh nghiệp phi tai chinh niem yết tren thị trường chứng khoan Việt Nam. Bằng việc sử dụng phương phap hồi quy phi tuyến tinh Bayes thong qua thuật toan lấy mẫu Random-walk Metropolis Hastings (MH), tac giả kham pha rằng, ham sản xuất được ước lượng cho cac doanh nghiệp phi tai chinh Việt Nam la dạng ham CES với hệ số co gian thay thế giữa vốn va lao động nhỏ hơn một, tức la lao động va vốn bổ sung nhau. Phat hiện nay cho thấy nền kinh tế Việt Nam co thế đối diện với đa trạng thai dừng (multiple steady-states) va cac bẫy ngheo đoi (poverty traps) nen chưa đạt được cac khả nang cho tang trưởng nội sinh (endogenous growth). English Abstract: Most studies in Vietnam use the Cobb-Douglas production function and its variants as a tool in economic analysis and forecasting. A great disadvantage of this functional form is that its propositions are extremely rigid, which is not in agreement with reality in many cases, especially in analyzing economic dynamics. The CES (constant elasticity of substitution)function with more flexible propositions, namely the elasticity of substitution between capital and labor different from unity, is used more and more popularly. Therefore, this study was conducted to specify a CES function based on data of non-financial businesses listed on Vietnam's stock market. By using a Bayesian non-linear regression through the Random-walk Metropolis Hastings (MH) sampling algorithm, the author finds that the estimated production function for Vietnamese non-financial enterprises is a CES one with the elasticity of substitution between capital and labor smaller than one. This finding shows that Vietnam's economy might face multiple steady-states and poverty traps, so it has not yet reached the possibilities of endogenous growth

Inverse problems in analysis of input-output model in the class of CES functions

Abstract The article proposes a modification of the approach to the analysis of inter-industry balance. Instead of linear models of inter-industry balance, based on the hypothesis of W. Leontief about the constancy of the cost standards of production factors, the article studies nonlinear models. For the case of production functions with constant elasticity of substitution (CES) an algorithm for solving the inverse problem is proposed, which allows to identify the model of nonlinear inter-industry balance based on the data of the symmetric input-output table. Based on the Young transform and Fennel duality, with the help of this model, we develop a technology for analyzing inter-industry relationships. The technology has been tested on the data of economic statistics of Russia.

Constant elasticity of substitution function based RANSAC for image stitching

Feature matching is very important in image stitching. RANSAC algorithm is a representative algorithm for feature matching. However, RANSAC still has many shortcomings such as a large number of iterations, a large computational complexity and cannot completely eliminate mismatches. To address above problem, in this paper, we propose a novel method termed constant elasticity of substitution function based RANSAC (CES-RANSAC) for image stitching. Specifically, CES-RANSAC improves the RANSAC algorithm by constructing a utility function, optimizing the boundary of the utility function, calculating Cobb-Douglas coefficients. It also introduces Lindahl equilibrium to derive the return value t to help eliminate mismatches. Experiments show that compared with the traditional RANSAC algorithm, CES-RANSAC has improved matching accuracy and increased computational efficiency, which further improves the efficiency of the image matching algorithm.

Endogenous Economic Growth: The Arrow-Romer Theory and a Test on Vietnamese Economy

The Arrow-Romer growth model helped to overcome the main drawback of the Solow-Swan model, where technical change is created exogenously, not by the firms making decisions, and formulated the conditions for endogenous growth in an economy. Nonetheless, the presentation of the Arrow-Romer model and corresponding empirical studies by the Cobb-Douglas functions hides the role of the capital-labor relationship for economic growth. A constant elasticity of substitution (CES) function, constructed by Arrow et al. (1961), allows solving this problem. So, the purpose of the current research is to test the endogenous growth of the Vietnamese economy, which has experienced a more than 30-year market-oriented reform through specifying an aggregate CES function. By applying Bayesian nonlinear regression, the research results revealed the elasticity of factor substitution (ES) lower than one. This work theoretically and empirically contributes to the endogenous growth theory in problems concerned with emerging economies. Investments in physical and human capital and technological progress are the determinants of endogenous growth. From the findings obtained, the author concludes that even though having achieved a rather impressive growth rate over more than three decades, the Vietnamese economy has not yet generated the possibility of endogenous growth, and suggests that endogenous growth can be hardly generated in emerging economies like Vietnam if important growth policies related to accumulation of physical and human capital as well as enhancement of R&D activities are not simultaneously implemented. It is indispensable to focus on substantially improving institutional quality.

How to Explain When the ES Is Lower Than One? A Bayesian Nonlinear Mixed-Effects Approach

Most studies in Vietnam use the Cobb-Douglas production function and its modifications for economic analysis. Extremely rigid presumptions are a main weak point of this functional form, particularly if the elasticity of factor substitution (ES) is equal to one, which hides the role of the ES for economic growth. The CES (constant elasticity of substitution) production function with more flexible presumptions, concretely its ES, is not unitary, and has been used more and more widely in economic investigations. So, this study is conducted to estimate the average ES through the specification of an aggregate CES function for the Vietnamese nonfinancial enterprises. By performing Bayesian nonlinear mixed-effects regression via Random-walk Metropolis Hastings (MH) algorithm, based on the data set of the listed nonfinancial enterprises of Vietnam, the author found that the CES function estimated for the researched enterprises has an ES lower than one, i.e., capital and labor are complimentary. This finding shows that Vietnamese nonfinancial enterprises can confront a downward trend of output growth.

Avoiding Mis-estimation of the CES Function: Unit Matters

ABSTRACTWe demonstrate that unit errors of measurement will lead to significant biases in estimating the constant elasticity of substitution (CES) function. Monte-Carlo simulations show that estimation results tend to reach Cobb–Douglas (CD) functions or extreme values if units of input variables are incorrectly used. To avoid this problem, we suggest adding an overall efficiency parameter and a unit correction parameter which is similar to biased technological change parameter when estimating CES functions. Any unit error of measurement can be captured by these two parameters while allowing researchers to get unbiased estimation results of other parameters.

An Analysis of Input Substitution Elasticity in Natural Resource-Based Industry in Indonesia. The Application of CES Function

The proportion of resource-based industry groups in the industrial structure in Indonesia is 42.01%, yet its productivity is low because of its labor-intensive nature and limited capital, despite the direct contribution of the use of capital and labor to the creation of output. To optimize production, an input can be substituted by another input. However, it depends on the elasticity of substitution of the two inputs. The main objective of this research is to analyze the level of substitutability of inputs used in the natural resource-based industry group in Indonesia. Using the function of Constant Elasticity of Substitution (CES), the results of the study show that the substitutability level of capital and labor is inelastic, meaning that input substitution is relatively difficult. The results of this study imply that to increase its productivity, this industry group needs to strengthen the support from (government) policies to improve its workforce quality.

A Grey CES Production Function Model and Its Application in Calculating the Contribution Rate of Economic Growth Factors

In analyses of economic growth factors, people generally use the CES (Constant Elasticity of Substitution) production function model to calculate the contribution rates of the factors that influence economic growth. However, the traditional CES function model that is built directly from economic data often shows apparent errors in parameter estimation due to data fluctuations. Such a model also may cause a negative calculation of the contribution rates of economic growth factors, or it may create abnormal fluctuations for some periods, and thus it fails to meet economic growth laws. In this paper, we propose a grey CES production function that can eliminate the random fluctuations of data and make the estimated parameters more reasonable, and this model can reflect the relationship between inputs and outputs more accurately. With regard to model application, the paper puts forward a scientific calculation method to avoid the calculation deviations caused by the substitution of difference equation for a differential equation with Solow’s formula. With the grey two-level nested CES production function model and the calculation method proposed, the paper makes an empirical analysis of the contribution rates of factors that influence China’s economic growth.

Skewed information transmission: The effect of complementarities in a multi-dimensional cheap talk game

We analyze a cheap talk game in a two-dimensional framework, with complementarities between the dimensions. A receiver chooses a two-dimensional costly effort in a productive activity. The Receiver’s effort profile is determined by his individual ability profile, of which he is unaware. He is advised by an informed Sender, who makes one of two recommendations to maximize the Receiver’s output. Output is a Constant Elasticity of Substitution function of the Receiver’s two one-dimensional contributions. The credibility constraint on the Sender’s recommendations requires her to truthfully contrast the Receiver’s abilities. As a result, the Receiver associates greater (resp. less) effort with greater (resp. less) perceived ability in one (resp. the other) dimension. However, when there are strong complementarities, the Sender becomes more interested in the mismatch between effort and ability. Thus, strong complementarities preclude the Sender from making credible recommendations. By contrast, weaker complementarities allow the Sender to make credible recommendations, using either: (i) a symmetric comparison of abilities; or (ii) an asymmetric comparison, in which one ability could be perceived as greater, even if it is not. Sufficient complementarities make the asymmetric information revelation more stable and more productive.

Capital-labour-energy substitution in a nested CES framework: A replication and update of Kemfert (1998)

The ease with which firms can substitute away from energy to other inputs is an important determining factor in the costs of climate change mitigation policies. Climate policy simulation models usually represent this substitutability by using the Constant Elasticity of Substitution (CES) function with parameter values often taken from econometric studies. Hence, the accuracy of the estimated substitution parameters has a strong influence on the validity of the climate policy simulation. In this article, we attempt to replicate the results presented in a widely cited article in this field: Kemfert (1998) (‘Estimated substitution elasticities of a nested CES production function approach for Germany’, Energy Economics, 20, 249–264). We first use the data and software reported in that article and compare our results with those reported in the original study. We then test the same data and a new, more recent, data set on German industrial data with an improved econometric approach. Despite applying various approaches and modifications, we are not able to replicate the results in Kemfert (1998). We furthermore conclude that the data sets that are typically used to estimate nested CES functions often have too few observations and too little independent variation of the explanatory variables to obtain reliable estimates when using a direct non-linear approach.

On Estimation of Deep Nested CES Production Functions

The constant elasticity of substitution (CES) function is an important function that is widely used in both theoretical analysis and applied economics. We propose a systematic framework to estimate the deep nested CES function using the nonlinear least squares (NLS) method. This method fills the gap between current empirical studies and large-scale applied economic models such as computable general equilibrium (CGE) models. We estimate the elasticities of substitution at both the regional and sectoral levels using this framework. The results indicate that some elasticities of substitution are larger than those in the existing literature. In addition, our results emphasize the heterogeneity of the elasticities of substitution across regions and sectors during application.

Factor substitution in rice production function: the case of Vietnam

Vietnamese rice production has achieved remarkable success over the last couple of decades. This is due to land and market reforms, known as ‘Doi Moi’. There were noticeable changes in policies, such as land and production systems, which were transformed from a collective to an individual contract system in the 1980s. Vietnam made progress in rice production through the legalisation of the privatisation of farm properties and a huge investment in irrigation systems. The country not only ensured its domestic demand, but also started exporting rice and gradually became the second largest exporter in the world. An estimate of the Constant Elasticity of Substitution function (CES) for Vietnam’s rice production is essential for the government to design effective policy on agricultural production. This study makes the first attempt to estimate the nested CES model for Vietnamese rice production in 2012. The paper finds that the elasticity of substitution of Vietnam's nested CES model lies between 0.44 and 0.46. The results indicate the weak substitutability between land and the capital-labour composite in the nested CES model. This also suggests that it is impossible to take labour as the substitutable factor for land and capital.

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.

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.

Energy-Extended CES Aggregate Production: Current Aspects of Their Specification and Econometric Estimation

Capital–labour–energy Constant Elasticity of Substitution (CES) production functions and their estimated parameters now form a key part of energy–economy models which inform energy and emissions policy. However, the collation and guidance as to the specification and estimation choices involved with such energy-extended CES functions is disparate. This risks poorly specified and estimated CES functions, with knock-on implications for downstream energy–economic models and climate policy. In response, as a first step, this paper assembles in one place the major considerations involved in the empirical estimation of these CES functions. Discussions of the choices and their implications lead to recommendations for CES empiricists. The extensive bibliography allows those interested to dig deeper into any aspect of the CES parameter estimation process.

Energy biased technology change: Focused on Chinese energy-intensive industries

Technical change bias has predominately been measured through two-factor models. Resulting from the rising importance of energy we devised a framework to estimate technical change bias for three input factors. The framework involves an estimation of elasticity and technical change parameters for a constant elasticity of substitution function with capital, labour and energy, which is derived from the elasticities and marginal output. We apply the framework to investigate eleven Chinese energy-intensive industries. The optimal nested structure for eight of the industries is for capital and energy to be combined first at the composite level and then with labour to form total output. Between 1990 and 2012, six of the industries were energy biased, three were towards capital, one towards labour and one mixed. The results show that recent Chinese energy intensity reduction programs are not sufficient to induce energy efficient development. The policy recommendations target specifically the energy biased industries to achieve desired energy savings in the future.

Piketty’s Elasticity of Substitution: A Critique

ABSTRACTThis article examines Thomas Piketty’s explanation of a falling wage share. Piketty explains rising income inequality between labor and capital as a result of one parameter of a production function: an elasticity of substitution, σ, between labor and capital greater than one. This article reviews Piketty’s elasticity argument, which relies on a non-standard definition of capital. In light of the theory of land rent, it discusses why the non-standard capital definition is a measure of wealth, not capital and is problematic for estimating elasticities. It then presents simple long-run estimates of σ in constant elasticity of substitution functions for Piketty’s data as well as for a subset of his capital measure that comes closer to the standard definition of productive capital. The estimation results cast doubt on Piketty’s hypothesis that σ is greater than one.