Constant Elasticity Of Substitution Research Articles

An elementary approach to solving the optimal taxation of a perfectly competitive firm with CES production function as a bilevel programming problem

An elementary approach to solving the optimal taxation of a perfectly competitive firm with CES production function as a bilevel programming problem

Estimating the elasticity of substitution when compiling the CES cost of living index on scanner data

AbstractScanner data are electronic transaction data that specify turnover and the number of items sold by barcodes, e.g., the Global Trade Article Number. These data are of particular value and interest to theorists and practitioners who wish to measure the Cost of Living Index or the Consumer Price Index, since their complete content makes it possible to compute any price index formula, including superlative indices or CES (Constant Elasticity Substitution) indices. Since the CES index requires the estimation of the elasticity of substitution, this paper focuses on verifying various methods of estimating this parameter based on scanner data. The paper considers both algebraic methods and methods based on the panel regression approach. The main achievement of the paper is the separation of the main factors that affect the estimated value of the elasticity of substitution, i.e., the type of data filter used and the level of data aggregation. The paper also verifies how the elasticity of substitution estimates affect the differences between the values of the CES indices based on these estimates.

Measuring the propagation effect of production networks: is China more susceptible to shocks?

ABSTRACT The production network, formed by inter-industrial input-output linkages, propagates and amplifies shocks. Accurately measuring the propagation effect is crucial for risk management. However, most empirical research measuring the effect rely on specific assumptions on parameters and production function forms, such as Cobb-Douglas, constant elasticity of substitution (CES) functions, leading to varying results depending on the setting of assumptions. This paper derives a flexible modified measuring method that does not make assumptions on specific production function forms, reducing subjectivity in the measuring results. The new method indicates that the propagation effect mainly depends on the heterogeneity of Domar weights across sectors in the production network, consistent with our empirical findings from the United States, China, Japan, Germany, and the United Kingdom. Due to stronger heterogeneity in its production networks, China has a significantly higher propagation effect compared to the other four countries. Additionally, we found that the weighted degree of production networks follows exponential distributions instead of the commonly assumed power-law distributions. This study contributes to a quantitative understanding of systemic risk within production networks.

Less work and higher tax can raise wellbeing

AbstractWorktime has been falling slowly though real wages have risen dramatically. We show that in a general equilibrium model with CES utility and production functions, worktime falls with real wages if and only if the elasticity of substitution between consumption and leisure is less than that between capital and labour, but always rises with labour's income share and concerns with relative income. While a falling labour share may not reduce worktime due to market inflexibility, stronger income comparison increases inefficient overwork. Hence, more flexibility, higher income taxes and a basic income are needed to reduce working hours and raise social welfare.

Economic Implications of the Nationally Determined Contribution (NDC) of Vietnam: A CGE Analysis with Capital-Energy Substitution Elasticities Estimated Using Firm-level Data

Purpose - The purpose of this paper is to assess the economic implications of Vietnamese Nationally Determined Contribution (NDC) targets towards emission reduction. Design/Methodology/Approach - We devised four scenarios corresponding to economy-wide emission reduction targets and sector targets specified in the most up to date NDC of Vietnam and the NDC technical report. The scenarios were then simulated in a CGE framework to reveal how important economic indicators and welfare change relative to baseline scenarios in 2030. The capital-energy substitution elasticities of 24 Vietnamese sectors were also estimated using a nested CES production function and used for model calibration. Findings - The results indicate that the coal mining sector undergoes a significant decline in output in response to the imposition of emission reduction schemes. Outputs of sectors with high capital-energy substitution elasticities such as non-metallic mineral, metal, and agriculture are more resilient to mild restriction policies compared with sectors with low elasticities. Imposing a moderate economy-wide restriction might lead to slight improvements in GDP and welfare. Under aggressive emission policies, the CGE model predicts major trade shifts in key export sectors, including electronics, electrical equipment, and machinery, and losses in allocative efficiency due to reduced input tax revenue. Research Implications - We recommend excluding the coal mining sector from NDC, providing short-term tax cuts or cost subsidies for exporting industries under aggressive sector-specific emission policies, and imposing a carbon tax on sectors insensitive to emission restrictions to offset the loss in tax revenue.

How constant is constant elasticity of substitution? Endogenous substitution between clean and dirty energy

The degree of substitutability between clean and dirty energy plays a central role in leading economic analyses of optimal environmental policy. Despite the importance, assuming a constant and exogenous elasticity of substitution has been a dominant theoretical approach. We challenge this assumption by developing a dynamic general equilibrium model with an endogenous elasticity of substitution that interacts with the relative share of clean inputs in the economy. We find strong dynamic feedback effects arising from endogenous substitution capacity that amplifies the impact of directed technical change and accelerates the transition to a green economy.

Differences in Total Factor Productivity and the Pattern of International Trade

In this work, we develop a trade model that explains the pattern of trade between countries based on differences in total factor productivity (TFP) while also accounting for differences in relative factor endowments. The novelty stems from the introduction of production functions derived by combining the Ricardian and Heckscher–Ohlin–Samuelson (H-O-S) theories, with TFP differences serving as the basis of comparative advantage. To this end, a testable hypothesis is derived. For the empirical measurement of the TFP in each industry and country, a constant elasticity of substitution (CES)-type production function was employed, and the TFP was calculated as the Solow residual from the production function’s fixed term. To offer a better understanding, the model was tested for the bilateral trade between Germany and Russia, and Germany and the Czech Republic. It was found that TFP differences can be used as a basis for explaining comparative advantages and, consequently, the bilateral pattern of trade between two countries.

Exchange rate dynamics and consumption of traded goods

A Constant Elasticity of Substitution (CES) aggregator of domestic and foreign goods is assumed in virtually any model of international macroeconomics with multiple traded goods. If baskets of traded goods are allocated optimally across countries, the CES aggregator links trade flows to exchange rate dynamics implying a condition for optimal allocation of individual traded goods across countries. The condition holds irrespectively of assumptions about preferences or endowment processes. This paper analyzes optimal allocation of traded goods empirically for 9 OECD countries and finds that it is mostly rejected by data. The finding casts doubts on the ability of international macroeconomic models to jointly explain dynamics of consumption and exchange rates.

Controlling Chaotic Fluctuations through Monetary Policy

Abstract This paper applies the chaos control method (the OGY method) proposed by Ott, E., C. Grebogi, and J. A. Yorke. (1990. “Controlling Chaos.” Physical Review Letters 64: 1196–9) to policy-making in macroeconomics. This paper demonstrates that the monetary equilibrium paths in a discrete-time, two-dimensional overlapping generations model exhibit chaotic fluctuations depending on the money supply rate and the elasticity of substitution between capital and labor under the assumption of the constant elasticity of substitution (CES) production function. We also show that the chaotic fluctuations can be stabilized by controlling the money supply rate by using the OGY method and that even when the OGY method does not work due to periodic attractors, adding moderate stochastic shocks to the model can successfully stabilize the economy.

Correlation Analysis of International Student Exchange and the Enhancement of China’s International Cultural Communication Power Based on the Subsumption Sorting Algorithm

Abstract International students are a bridge between Chinese and foreign cultures, but they still face multiple dilemmas in Chinese cultural communication due to different cultural backgrounds and values. In this paper, we utilize the subsumption sorting algorithm to sort the amount of cultural communication of international students’ exchanges, which is dynamically switched by a combination of two methods: back-block forward interpolation and header exchange. The D-S monopolistic competition model is used to construct the theoretical model of international student exchange that affects China’s international cultural communication power. The CES utility function is used to construct China’s international cultural communication network, which calculates the total amount of communication culture of cross-cultural exchanges between international students. In the end, an analysis of 85 international student samples revealed a correlation between international student exchanges and China’s international cultural communication. The results show that the correlation coefficient between international student exchanges and China’s international cultural communication is 0.305 p > 0.05, indicating that international student exchanges have a positive promotion effect on China’s international cultural communication. This study examines the general law of international cultural communication, which is crucial in promoting Chinese culture worldwide.

Neoclassical production, scarcity of skills and Pareto distributions

The distribution of top earnings follows a “power-law”: the top tail of the distribution is thick relative to other distributions and is approximately Pareto-distributed. There are different mechanisms proposed in the literature that yield Pareto distributions and power-laws. This paper shows that a simple general equilibrium model where aggregate production is assumed of the constant-elasticity-of-substitution (CES) type over multiple labor inputs generates distributions in earnings and wages that follow power-laws. The finding is very general as the distribution of the skill-types is irrelevant for the shape parameter (the Pareto exponent) of the power-law. The model displays a tight relationship between the Pareto exponent and the elasticity of substitution between the labor inputs. Available empirical estimates of the elasticities of labor substitution and of the labor supply predict a Pareto exponent consistent with its empirical counterpart for the distribution of earnings in the US.

Analysis of a Growth Model with a CES Production Function

Analysis of a Growth Model with a CES Production Function

Study of the Spatio-Temporal Variation of Agricultural Sustainability at National and Provincial Levels in China

As an important pillar of human civilization, the development of agriculture has gradually become the focus of the international community to solve the development dilemma and promote the implementation of the global Sustainable Development Goals (SDGs). Agricultural sustainability issues are widely addressed in scientific literature and various reports by international organizations. However, there are some problems in the existing studies, such as the design of agricultural sustainable development evaluation indicators does not consider the differences in development stages and data statistical capacity of various countries, and the research depth of spatial and temporal change of agricultural sustainable development is insufficient. Agriculture has become a bottleneck for the world and China to achieve the SDGs. Based on the global indicator framework of the Sustainable Development Goals and comprehensive consideration of agricultural development common problems and regional characteristics, this work has established a basic index library consisting of 86 indicators to evaluate the agricultural sustainable development in China and provide the basis for the assessment in different regions. In the indicator optimization process, having considered the development stage of China, the basic characteristics of agriculture, data availability, and reliability, we determined an evaluation index system of China’s agricultural sustainable development that includes 25 specific indicators. The constant elasticity of substitution (CES) model was used to assess the temporal and spatial changes in agricultural sustainability in China at the national, regional, and provincial levels. The results showed that China’s Agricultural Sustainable Development Index (ASDI) score increased from 44.76 in 2011 to 59.22 in 2021, and the ASDI scores of all agricultural regions and provinces also increased to varying degrees. In terms of goal scores, SDG2, SDG6, SDG7, SDG8, SDG9, and SDG12 all exhibited an overall upward trend, in which SDG6 performed the best, and SDG2 performed the worst, scoring 84.76 and 43.05 in 2021, respectively. This paper will provide a basis for systematically evaluating the progress of agricultural sustainable development goals and accurately identifying unsustainable problems in agricultural development to help China implement the 2030 Agenda for Sustainable Development.

Path mechanism and spatial spillover effect of green technology innovation on agricultural CO2 emission intensity: A case study in Jiangsu Province, China

Green technology innovation (GTI) is one of the most important factors influencing agricultural carbon emission intensity (ACEI). Various studies have explored the impact of GTI on ACEI, but the path mechanism has not been fully explained. This study incorporates GTI and ACEI into the constant elasticity of substitution (CES) production function and constructs a theoretical model to analyse their direct impact mechanisms. Drawing on the substitution effect theory and the Marshall–Arrow–Romer (MAR) externalities theory, this study introduces two regulatory mechanisms: optimization of energy structure and agricultural industry agglomeration (AIG). Additionally, it explores the pathway mechanisms under the influence of spatial spillover effects based on Tobler’s first law of geography. Then, taking Jiangsu Province in China as a case study, empirical tests are conducted using LSDVC and dynamic spatial SAR models. The results are as follows. (1) GTI effectively inhibits ACEI directly, and has significantly positive spatial spillover effects on ACEI reduction in the short and long terms. (2) Energy structure optimization positively regulates the effect of GTI on ACEI reduction, and energy structure optimization in nearby cities may help GTI restrain ACEI in the local city in the short term. (3) AIG has a positive regulating effect on GTI reducing ACEI, and the moderating effect of AIG has positive spillover effects in the short term. (4) When both regulatory pathways are employed simultaneously, the moderating effect of AIG in local or neighbouring areas is expected to become ineffective. These findings are useful for solving the problem of ACEI reduction by managing the transfer and distribution of GTI between different regions, considering spatial spillover and moderating effects.

Intermediate Goods–Skill Complementarity

Abstract Recent research has begun to imply intermediate goods–skill complementarity; however, this possible complementarity has been hypothesized but not statistically tested, despite the increasing importance of intermediate goods in production. This study provides statistical evidence regarding whether intermediate goods are more complementary with skilled labor than with unskilled labor. Using panel data from 40 countries over the period 1995–2009, we estimate a two-level constant elasticity of substitution (CES) production function. Our major findings are fivefold. First, at the aggregated one-sector level, the elasticity of substitution between intermediate goods and unskilled labor is 1.22, which is significantly greater than that between intermediate goods and skilled labor of 1.05, indicating intermediate goods–skill complementarity. Second, at the disaggregated level, such complementarity is primarily observed in heavy manufacturing industries and the service sector, whereas complementarity is observed between intermediate goods and unskilled labor in the primary sector and light manufacturing industries. Third, the normalization of the data and the cumulant estimators exhibit stronger results. Fourth, our baseline results are confirmed applying several robustness checks, such as switching skilled and unskilled labor or considering capital–skill complementarity. Finally, intermediate goods–skill complementarity tends to be higher for industries that use more imported intermediate goods.

Local government debt and labor income share: Evidence from China.

This study employs a CES production function to construct a theoretical model of labor income share and uses a two-way fixed effects model to test the causal effects of local government debt (LGD) on the labor income share of enterprises. Local government debt governance policies are utilized as exogenous shocks, and a DID (Difference-in-Differences) model is applied for endogeneity testing. The results have passed a series of robustness checks. The findings suggest that LGD decreases the share of firms' labor income. The mechanism analysis suggests that LGD lowers the labor remuneration of residents, the employment of labor in enterprises, and the size of bank loans mainly; while raising the cost of using funds in enterprises. Moreover, this negative effect is more apparent in non-state-owned enterprises, small and medium-sized enterprises, and enterprises with high financing constraints. This study presents new evidence on how the labor income share of enterprises is affected from the perspective by local governments in China. It has important implications for further deepening local government debt governance and achieving common prosperity.

Technology of Input–Output Analysis with CES Production: Application for Studying the Kazakhstan Supply Chain during the COVID-19 Pandemic

Input–output analysis finds widespread application in estimating the shock effects on production networks within both local and global economies. We are developing a new technology for intersectoral analysis that takes into account the substitution of production factors within a complex supply network triggered by external or internal shocks. This technology is based on the explicit solution of a pair of convex programming problems: the resource allocation problem under the assumption of Constant Elasticity of Substitution (CES) technologies and the special dual Young problem. Solving these problems, we can ascertain the equilibrium inputs and price indexes of goods within the production network. In this paper, we apply this technology to analyze the economy of Kazakhstan in the context of the COVID-19 pandemic. Our calculations provide us with the means to discuss the macroeconomic responses of the multi-sectoral production network in Kazakhstan to both external and internal shocks stemming from the pandemic.

Non-CES Aggregators: A Guided Tour

The constant-elasticity-of-substitution (CES) aggregator and its demand system are ubiquitous in business cycles theory, macroeconomic growth and development, international trade and other general equilibrium fields; this is because the CES aggregator has many knife-edge properties that help to keep the analysis tractable in the presence of many goods and factors. However, this also makes it hard to tell which properties of CES are responsible for certain results. Furthermore, it is necessary to relax some of those properties for certain applications. In this article, I review several classes of non-CES aggregators, each of which removes some properties of CES and keeps the rest to introduce some flexibility while retaining the tractability of CES as much as possible. These classes are named after the properties of CES they keep. I explain how these classes are related to each other and discuss their relative strengths and weaknesses to indicate which classes are suited for which applications.

A generalization of the Symmetric Translog functional form

Feenstra and Weinstein introduced a special case of the translog cost function, the Symmetric Translog (ST) Cost Function, which replaced all of the second order parameters which are present in the Translog functional form by a single positive parameter. The ST functional form is useful in the context of estimating consumer preferences over related products and provides an alternative to the use of Constant Elasticity of Substitution (CES) preferences in this context. The ST functional form has a potential advantage over the CES functional form that it produces finite estimates for reservation prices for missing products whereas the CES reservation prices are always infinite. The present paper proposes a Generalized Symmetric Translog Cost Function which also generates finite reservation prices but is more flexible than the ST functional form.

Consensus manipulation in social network group decision making with value-based opinion evolution

Opinion evolution is a common phenomenon in social network group decision-making (SNGDM), where the key issue is modelling trust weights among individuals. In social and economic networks, the links among individuals represent trust relationships that can offer value. However, extant studies on trust weight distribution have failed to consider individual network values. Moreover, in some scenarios, the external stakeholder may want to manipulate the opinion evolution process to achieve the desired consensus outcome. Therefore, this study proposes value-based opinion evolution and discusses consensus manipulation in SNGDM. First, we measured the total value of an individual in a network, which consisted of two parts: intrinsic value and network value. Notably, we used the constant elasticity of substitution from economics as an operator to aggregate intrinsic and network values. Based on this, we described value-based opinion evolution and established an optimisation-based consensus manipulation model for SNGDM with value-based opinion evolution (CM-VBOE). Furthermore, we conducted some sensitive analyses, which indicate that an individual’s value in the network increases with the decay factor and decreases with the elasticity of substitution, and provide a comparative analysis, which expands on the importance of accounting for the decay factor and elasticity of substitution when modelling value-based opinion evolution. Finally, a hypothetical application for crowdfunding project selection is presented to illustrate the applicability of the proposed CM-VBOE.