Constant Elasticity Of Substitution Research Articles

Technologies for endogenous growth

I microfound endogenous growth through neoclassical technologies with substitutable inputs created by monopolistically competitive innovators. Investment delivers innovations of declining profitability, but increasing labor force generates growth depending on structural technological parameters that determine the elasticities of profits and output with respect to the mass of inputs. For instance, with a Cobb–Douglas technology in labor and a CES aggregator of inputs, the growth rate declines with the substitutability between inputs and increases in the share of inputs in production. I also explore other classes of technologies and novel specifications that can deliver long run growth.

Optimal contracting with asymmetric belief and complementarity

PurposeIn this study, a dynamic contracting model is developed between a venture capitalist (VC) and an entrepreneur (EN) to explore the influence of asymmetric beliefs regarding output-relevant parameters, agency conflicts and complementarity on the VC's posterior beliefs through the EN's unobservable effort choices to influence the optimal dynamic contract.Design/methodology/approachThe authors construct the contracting model by incorporating the VC's effort, which is ignored in most studies. Using backward induction and a discrete-time approximation approach, the authors solve the continuous-time contract design problem, which evolves into a nonlinear ordinary differential equation (ODE).FindingsThe optimal equity share that the VC provides to the EN decreases over time. In accordance with the empirical evidence, the EN's optimistic beliefs regarding the project's profitability positively affect its equity share. However, the interactions between the optimal equity share, project risk and both partners' degrees of risk aversion are not monotonic. Moreover, the authors find that the optimal equity share increases with the degree of complementarity, which indicates that the EN is willing to cooperate with the VC. This study’s results also show that the optimal equity shares at each time are interdependent if the VC is risk-averse and independent if the VC is risk-neutral.Research limitations/implicationsIn conclusion, the authors highlight two potential directions for future research. First, the authors only considered a single VC, whereas in practice, a risk project may be carried out by multiple VCs, and it is interesting to discuss how the degree of complementarity affects the number of VCs that ENs contract. Second, the authors may introduce jumps and consider more general multivariate stochastic volatility models for output dynamics and analyze the characteristics of the optimal contracts. Third, further research can deal with other forms of discretionary output functions concerning complementarity, such as Cobb–Douglas and constant elasticity of substitution (See Varian, 1992).Social implicationsThe results of this study have several implications. First, it offers a novel approach to designing dynamic contracts that are specific and easy to operate. To improve the complicated venture investment situation and abate conflict between contractual parties, this study plays a good reference role. Second, the synergy effect proposed in this study provides a theoretical explanation for the executive compensation puzzle in economics, in which managers are often “rewarded for luck” (Bertrand and Mullainathan, 2001; Wu et al., 2018). This result indicates a realistic perspective on financing and establishing cooperative relationships, which enhances the efficiency of venture investment. Third, from an empirical standpoint, one can apply this framework to study research and development (R&D) problems.Originality/valueFirst, the authors introduce asymmetric beliefs and Bayesian learning to study the dynamic contract design problem and discuss their effects on equity share. Second, the authors incorporate the VC's effort into the contracting problem, and analyze the synergistic effect of effort complementarity on the optimal dynamic contract.

A novel method for calculating the contribution rates of economic growth factors

<abstract><p>The common production functions include the Leontief production function, the Cobb-Douglas (C-D) production function, the constant elasticity of substitution (CES) production function, the variable elasticity of substitution (VES) production function and so on. With different elasticity of substitution of factor, the production functions have different ranges of applications. In the production functions, the C-D production function is used the most widely because of its simple form, while the CES production function and the VES production function have limitations in applications due to their complicated forms. However, the C-D production function has the elasticity of substitution of factors of 1, and the CES production function has the elasticity of substitution of factors which is not 1 but a constant, so the two production functions both have limitations in applications. The VES production function with the variable elasticity of substitution is more practical in some application cases. This paper studies the applications of the VES production function model and gives a method of calculating the contribution rates of economic growth factors scientifically. As for the parameter estimation of the model, this paper gives an improved Sine Cosine Algorithm (SCA) to enhance the convergence rate and precision. Finally, the paper makes an empirical analysis on the contribution rates of economic growth factors of Shanghai City, China, using the method proposed.</p></abstract>

Nonlinear Input-Output Model with Nested CES Technologies for the Analysis of Macroeconomic Effects of a Foreign Trade Shock

Nonlinear Input-Output Model with Nested CES Technologies for the Analysis of Macroeconomic Effects of a Foreign Trade Shock

A Contribution to the Empirics of Total Factor Productivity’s Theory Based on a CES Production Function-Case of Moroccan Economy

Some propositions related to about growth theory are not valid for all production functions. This is the case for the estimation of total factor productivity based on the growth accounting’s approach which is easily verified with a Cobb-Douglas production function, but difficult to obtain with a CES production function. In this paper, we will try to do that estimation using Moroccan data.

Do more get more: Monopoly appropriation of labor income in manufacturing companies

In recent years, the overtime culture has generally emerged in Chinese enterprises (CEs), the length of workers’ working hours has been lengthened, and their intensity has increased. Still, the labor income share has declined, which deserves in-depth analysis. This paper introduces a relative labor intensity indicator to estimate the trend of the labor income share based on the general factor-enhanced CES production function in China. The econometric model is then introduced to analyze in-depth the influencing factors leading to this trend using relevant data from 2001 to 2020. If the elasticity of substitution is less than 1 and capital and labor are complementary, then the labor income share tends to decrease. This is because the relative labor intensity tends to increase while the growth rate of the capital-labor ratio tends to decrease. The empirical results also show that the decrease in labor income share and labor compensation is related to monopoly and the amount of capital input. If the amount of capital input is higher and the degree of monopoly is higher, then the labor income is lower, and the share of labor income is lower. Monopolies and capital intercept most of the value created because of the increased labor intensity, and laborers receive only a small profit.

The Nonlinear Model of Intersectoral Linkages of Kazakhstan for Macroeconomic Decision-Making Processes in Sustainable Supply Chain Management

We provide a nonlinear model of intersectoral balance with constant elasticity of substitution (CES) production functions of industries and CES utility function of final consumer for the study of intersectoral linkages in the Kazakhstan economy. The model is formalized in terms of the primal problem of resource allocation and the corresponding Fenchel dual problem which solution gives costs of inputs of industries in a supply network. We identify the model with the actual data of the Input-Output tables of Kazakhstan and estimate the elasticity of substitution of production factors for the aggregated industry complexes. With the help of developed framework, we evaluate the inter-industry financial flows in the aggregated supply network for the period 2013–2020 and compare the results with the actual data of Kazakhstan. The developed framework can be used to support decision-making processes in sustainable supply chain management in a situation of the government economic policy change and external shocks. Using the developed framework, we evaluate the risks for Kazakhstan’s supply chains in scenario of sharp weakening of the national currency.

ESTIMATION OF EFFECT ON GROSS DOMESTIC PRODUCT OF PRODUCTION FACTORS USING CES AND TRANSLOG PRODUCTION FUNCTIONS: AN APPLICATION TO CHINA ECONOMY

In this study, the effects on the economic growth (GDP) of capital, labor and energy input factors for the Chinese economy are investigated with the help of the CES and Translog production functions. According to the empirical findings of the study, it can be said that the GDP data obtained using the CES production function are less efficient than the estimates obtained using the Translog production function. The Ridge regression technique was used for parameter estimation of Translog production model since there is multicollinearity between the variables in the model. The output elasticities and the substitution elasticities between each input factor are then dynamically estimated, based on the appropriate Translog production model that includes the capital, labor and energy input factors. In addition, the inputs of the Translog production model were estimated using the Holt-Winter's method to predict the future economic growth of the Chinese economy. Consequently, output elasticities of all input factors are positive, and we can rank the input factors as labor, capital and energy according to their degree of impact on GDP, respectively. This shows that the Chinese economy is labor and capital intensive.

Generalizing the General: generalizing the CES production function to allow for the viability of input thresholds

ABSTRACT The original specification of the Constant-Elasticity-of-Substitution (CES) production function introduced by Arrow, Chenery, Minhas, and Solow is considered to be a general production specification that nests multiple types of production functions, i.e. Leontief, Cobb-Douglas, and linear. However, even this general specification of production functions is restrictive in several ways. This paper proposes a generalized variant of the CES production function that allows for the inclusion of the minimum required levels of inputs. Not allowing for this potential attribute is, in fact, one shortcoming of the original CES production-function specification, which in turn could result in misleading conclusions about essential levels of inputs. Accordingly, a solution is proposed to overcome the mentioned shortcoming. Input thresholds are incorporated in the CES production specification, and empirical applications are provided for irrigation and nitrogen. To illustrate the proposed approach in this paper, two empirical applications in irrigation and fertilizer response using the famous Hexem-Heady experimental dataset as well as several datasets produced using Monte-Carlo experiments with different data-generating processes are provided. Finally, implications for modelling input thresholds are considered and discussed.

The Optimal Urban Scale from Different Perspectives and under Different Development Goals Based on the CES Utility Function

To analyze the differences in the optimal urban scale of a country, a government, and residents under different urban development goals and to provide a reference for urban development, an urban development model is constructed based on the constant elasticity of substitution (CES) utility function. The objective function includes four indicators: the economic level, the traffic level, environmental quality, and living conditions. The urban development model is constructed by integrating an urban road planning model, bus route planning model, land use model, and four-stage traffic sharing and traffic allocation model. Based on the setting of different development goals, this model is used to calculate the urban utility value perceived by each stakeholder at different urban scales. Through comparative analysis, we determine the following: (1) When the urban development goals are different, the optimal urban scale of residents and the government differs greatly, and the optimal scale of the country differs very little. (2) When facing the same development goal, the optimal urban scales of the three stakeholders are not the same. However, the three stakeholders are closely related to urban development. Therefore, the selection of the optimal urban scale should comprehensively consider the interests of the three stakeholders.

On a Geometric Programming Approach to Profit Maximization: The Case of CES Technology

The profit maximization problem takes a central place in the theory of the firm, especially when conditions for perfect competition hold. In this paper, we solve the profit maximization problem of a perfectly competitive firm when the constant elasticity of substitution (CES) production function with n≥2 inputs describes its technology. Commonly, this problem is solved by using multivariable differential calculus. However, to avoid tedious algebraic manipulations and bypass checking nontrivial necessary and sufficient conditions, we employ geometric programming (GP), and the power mean inequality (PMI) as an elegant complementary tool to multivariable calculus. Since the GP and the PMI are simple optimization techniques without derivatives, they can provide new insights into the given problem to managers, students, and other audiences who may be unfamiliar with multivariable differential calculus. Additionally, by using the properties of limits, we show that the solution to the profit maximization problem with Cobb-Douglas technology is a limiting case of our result.

Link investment substitutability: A factor influencing network formation

Studies on network formation employ rather different assumptions on link formation and make different predictions. We propose a constant elasticity of substitution (CES) link formation specification that generalizes commonly used link formation assumptions and parametrizes a factor that could affect network formation, namely, link investment substitutability (LIS). We apply this approach to the model by Galeotti and Goyal (2010) that studies public good provision on an endogenously formed network and find that results on equilibria differ significantly depending on whether link investments are substitutes or complements. Additionally, when link investments are complements, we find that LIS governs the unequalness of equilibrium structures. We also explore how LIS influences the relationship between the public good provision of a player and her utility.

Sermaye Birikiminin Fonksiyonel İfadesi ve Solow Uzun-Dönem Büyüme Modelinde Kararlı-Denge Koşulları

This paper proposes a general solution to Solow’s original differential equation explaining the rate of change of capital-labor ratio. Determining the time path of capital-labor ratio, we obtain novel general conditions under which the capital-labor ratio can reach a stable steady-state value. Finally, we apply our findings to the Solow’s CES production function example and we demonstrate that in addition to identification of steady-state conditions, we can obtain exact time period when the economy can reach its stable steady-state capital per labor magnitude. Our results state some policy implications that can be outlined as follows. First, in economies where elasticity of substitution between capital and labor is lower than unity, the economic policies should be different than those implemented in economies where elasticity is greater than unity. Second, the main source of uncertainty in perspective of policy makers is not to determining exactly when the economy activity would reach a stable steady-state path and our findings aim to shed light on this uncertainty.

An Evolutionary Game to Model Offshoring and Reshoring of Production Between Developed and Developing Countries

A dynamic model is proposed to describe the time evolution of production location choices of a multinational enterprise that can decide between two possible manufacturing locations: a stylized developed economy and a developing economy. The model is based on an evolutionary approach according to a replicator dynamics driven by expected profits. The production in each country is determined by the availability of labor inputs and their relative productivity, on wages of skilled and unskilled workers, as well as on cost externalities due to knowledge spillovers and public goods availability. The model includes the effects of relative demand and supply on earnings distribution with two different types of workers (high and low skilled) and the substitution between the two categories is captured by a CES aggregate production function. Behavioral parameters are also considered, such as the cognitive bias that overestimates the convenience of offshoring in term of labor cost and the “made in” effect that brings consumers to pay higher prices for products manufactured in a developed country.

Identification of dynamic latent factor models of skill formation with translog production

SummaryIn this paper, we highlight an important property of the translog production function for the identification of treatment effects in a model of latent skill formation. We show that when using a translog specification of the skill technology, properly anchored treatment effect estimates are invariant to any location and scale normalizations of the underlying measures. By contrast, when researchers assume a CES production function and impose standard location and scale normalizations, the resulting treatment effect estimates vary with the chosen normalizations. Access to age‐invariant measures does not solve this problem since arbitrary scale and location restrictions are still imposed in the initial period. We theoretically prove the normalization invariance of the translog production function and then complete several empirical exercises illustrating the effects of location and scale normalizations for different technologies and types of skills measures.

Is your netflix a substitute for your telefunken? Evidence on the dynamics of traditional pay TV and OTT in Latin America

Are audiovisual over the top (OTT) services in Latin America substitutes for the traditional Pay TV services (cable or satellite), complementary or independent? To respond to this question, we develop a simple theoretical model based on a CES utility function and estimate simultaneously, using non-linear least squares, demand functions for both audiovisual services. Our results, based on original database covering 17 Latin American countries from 2011 to 2020, suggest no substitution of Pay TV for OTT. However, during the more recent period (2015–2020), we find evidence of gross substitution (i.e., similar enough, although not completely equivalent for consumers) between these audiovisual services. This confirms, although only partially, the existence of the so-called cord-cutting and cord-saving phenomena, due to the expansion of fast internet and the richer OTT offers, and their relatively lower prices. These results suggest regulators should include OTT services in their scope and produce in-depth analysis on the country level to update and optimize regulations, as well as implement regulatory sandboxes to advance towards smart regulation, as shown in the financial industry.

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.

The Relationship Between Production Inputs, Factor Substitution, and Economic Growth

Factors of production and elasticity of substitution play an essential role in economic growth accounting. Although production functions with constant elasticity of substitution between factors are more commonly utilized in growth accounting, studies based on production functions with variable elasticity of substitution are also conducted. Since production functions with variable elasticity of substitution provide more flexibility in parameters, they are more advantageous than other production functions. Besides, most studies focus on the elasticity of substitution between capital and labor. Studies on the sub-components of production factors are relatively few. In this study, capital stock is analyzed by dividing it into two subcomponents as public capital stock and private capital stock. The empirical results, in general, show that the elasticity of substitution between the public capital stock and the private capital stock is less than unity. In this context, public and private capital stock can be expressed as complementary inputs in the final production of goods and services. As a result, public expenditures on infrastructure can boost economic growth by raising the efficiency of private investments.

Technical change and the Common Agricultural Policy

This paper adopts an alternative method for the analysis of the CAP’s impact on farms’ productivity based on a system of equations derived from a non-nested three-factors CES production function. With this method, we estimate the elasticity of substitution between labour, capital, and land in the EU agricultural sector, the magnitude and direction of technical change, and the impact of the CAP subsidies. The system of equations is estimated using the GMM estimator on a farm-level panel dataset covering 117,179 farms from all EU MS for the period from 2004 to 2015. Our results suggest that land, labour, and capital in EU farms are complementary production factors characterised by a slow decline or stagnation in the land-, labour-, and capital-augmented technical change. Higher levels of Pillar I and Pillar II CAP payments as percentage of total agricultural income have negative or no impact on farms’ technical change, but higher nominal amounts of Pillar I decoupled subsidies, Pillar II investment and LFA subsidies have a positive impact. Moreover, the larger the share of subsidies in total agricultural income the stronger is the negative impact of the CAP on agricultural technical change.