Constant Elasticity Of Substitution Research Articles

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.

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.

Delay Solow Model with a Normalized CES Production Function

This study analyzes the relationship between the elasticity of substitution and the economic stability/instability. To this end, we adopt a CES production function that consistently involves all its variants and introduce two delays, called a gestation delay and a depreciation delay, into the Solow model. In the case of one delay, we find that the gestation delay is harmless, the depreciation delay has a destabilizing effect, and the two delays having the equal length possesses a stronger stabilizing effect than the destabilizing effect of the depreciation delay. In the case of two different delays, we analytically construct the stability switching curve that divides the parametric region into the stability and instability regions. We also demonstrate that the location of the stability switching curve depends not only on the elasticity of substitution but the baseline values of the CES function and the parametric values of the dynamic equation.

The impact of climate change on economic growth: Evidence from a panel of Asian countries

Asia is recognized as one of the most vulnerable regions. This research aims to identify climate change effects on economic growth. It proposes a new and comprehensive perspective to examine the climate-economy nexus in this region and provides an underpinning for assessing the pathway of the growing Asian economy under the SSP climate scenario (CMIP6). We apply a macroeconomic-climate modeling approach with a climate damage function. The damage function, which is based on the temperature anomaly, was examined under three classes of damage severity. The climate change effect has been examined by including the direct effect on the output as the level effect and two more channels, including capital depreciation and productivity growth reduction. The augmented Solow growth model framework that considers different types of capital, including physical, human, social, and environmental capital, was applied. The labor productivity or technology is assumed to depend on trade-related variables, including trade openness, financial development, and foreign aid inflows. Also, in order to test the constant returns to scale assumption, the CES production function, which is the flexible production technology, was used. The study relied on the country-year panel of GDP per capita and other macroeconomic variables such as labor force, capital formation, financial development index, trade openness, and foreign aid gleaned for 1994–2017 to estimate production functions using the GMM estimation method. The climate data on the annual mean temperature and projections of future temperature are based on ICMP6 by 2100 for Asian countries. Based on the CES estimation results, constant returns to scale or Cobb-Douglas production function was adopted. The estimation results show that physical and environmental capital account for the highest contribution to the output per worker. However, the contribution of trade-related variables was found to be insignificant. The projected pathway by 2100 establishes that climate change would significantly reduce Asian output per worker, especially if severe damage function is examined, and climate change stays on the SSP scenario-anticipated trajectory. The output elasticity with respect to temperature under the most severe scenario was obtained −22.80, corresponding to the output per worker reduction of 46.7 percent in 2100. Among the three channels of the climate effect, productivity growth reduction showed the most adverse effect on output. The lower flexibility of the production function that restricts the environmental replacement with other inputs, may lead to a more binding role under growing scarcity conditions. It was also found that labor and technology could contribute dampening the capital damage induced by higher temperatures. From the research results, the findings suggest measures aiming at providing flexible production technology, development of capital-embodied technologies, and lower dependence on environmental capital.

Do biased technological advances affect carbon productivity of service sector: Evidence from China

Increasing carbon productivity is regarded as one of the significant ways to strike a balance between national economic growth and environmental protection. As the proportion of China’s service sector in the national economy rises and the severity of environmental pollution increases, the matter of carbon productivity in service sector required to be explored in depth. This paper focuses on the biased technological advances index of China’s service sector and its impact on carbon productivity by constructing a two-layer nested CES production function, proposing policy countermeasures to raise service sector’s carbon productivity in China, which is of great practical significance in reducing carbon emissions of China’s service sector, improve carbon productivity of China’s service sector and promote the green transformation and sustainable development of China’s service sector. The results are as follows. (1) The average value of the biased technological advances index of services in China is negative, indicating that technological advances of services in China are biased towards non-energy elements. The biased technological advances indexes of China’s service sector in the western, middle and eastern regions are also negative, and the index of the eastern region is the smallest, indicating that the technological advances of the service sector in the eastern region are biased towards non-energy elements to the highest extent. (2) There is a negative correlation between the biased technological advances index and carbon productivity of services in China. In the western, middle and eastern regions of China, the bias of technological advances in eastern China has the greatest effect on China’s productivity of carbon in service sector. The policy implication is that in order to increase China’s services’ productivity of carbon, it is essential to reduce the biased technological advances index of China’s service sector.

A Theory of Intrinsic Inflation Persistence

AbstractWe propose a novel theory of intrinsic inflation persistence by introducing trend inflation and Kimball (1995)‐type aggregators of individual differentiated goods and labor in a model with staggered price‐ and wage‐setting. Under nonzero trend inflation, the non‐CES (constant elasticity of substitution) aggregator of goods and staggered price‐setting give rise to a variable real marginal cost of goods aggregation, which becomes a driver of inflation. This marginal cost consists of an aggregate of the goods' relative prices, which depends on past inflation, thereby generating intrinsic inertia in inflation. Likewise, the non‐CES aggregator of labor and staggered wage‐setting lead to intrinsic inertia in wage inflation, which enhances the persistence of price inflation. With the theory we show that inflation exhibits a persistent, hump‐shaped response to monetary policy shocks. We also demonstrate that lower trend inflation reduces inflation persistence and that a credible disinflation leads to a gradual decline in inflation and a fall in output.