Elasticity Of Substitution Production Function Research Articles

Young Duality for Variational Inequalities and Nonparametric Method of Demand Analysis in Input–Output Models with Inputs Substitution: Application for Kazakhstan Economy

The global macroeconomic shocks of the last decade entail the restructuring of national production networks and induce processes of input substitution. We suggest mathematical tools of Young duality for variational inequalities for studying these processes. Based on the tools we provide, a new mathematical model of a production network with several final consumers is created. The model is formulated as a pair of conjugated problems: a complementarity problem for optimal resource allocation with neoclassical production functions and the Young dual problem for equilibrium price indices on network products. The solution of these problems gives an equilibrium point in the space of network inter-industry flows and price indices on goods. Based on our previous results, we suggest an algorithm for model identification with an official economic statistic in the case of constant elasticity of substitution production functions. We give an explicit solution to the complementarity problems in this case and develop the algorithm of the inter-industry flows scenario projection. Since the algorithm needs the scenario projection of final sales structure as its input, we suggest a modified methodology that allows the calculation of scenario shifts in final consumer spending. To do this, we employ the generalized nonparametric method of demand analysis. As a result, we develop new technology for scenario calculation of a national input–output table, including shifts in final consumer spending. The technology takes into account a substitution of inputs in the network and is based on officially published national statistics data. The application of the methodology to study tax collection scenarios for Kazakhstan’s production network is demonstrated.

Reaching Paris Agreement goal through carbon dioxide removal development: A compact OR model

A compact operations research (OR) model is proposed to analyse the prospects of meeting the Paris Agreement targets when direct air capture technologies can be used or not. The main features of the OR model are (i) the representation of the economy and energy use with a nested constant elasticity of substitution production function; (ii) the representation of climate policy through the use of a safety emissions budget concept; and (iii) the representation of an international emissions trading scheme for the implementation of climate policy. Using dynamic optimisation, several contrasting scenarios are analysed and the potential use of the model in future developments of climate/economy modelling is discussed.

External finance and agricultural productivity growth

AbstractWe propose a new method to estimate the impact of external finance on productivity. Using a nested constant elasticity of substitution production function, finance has an indirect influence on productivity through its effect on capital augmenting‐technological change and depends on the elasticity of substitution between equity and debt, as well as on the quantity and price of external finance and net value added. We develop and test a theoretical model using Farm Accountancy Data Network regional data covering all EU Member States and different subsamples by EU regions, size of farms, and farm types. In the 2004–2018 period, land, labor, and capital complemented each other but had a decreasing or stagnating productivity, reaffirming the importance of external finance to improve productivity. Results suggest that external finance and productivity follow an inverted U‐shaped curve, with a positive impact on less capitalized farms with lower debt‐to‐equity ratios, while capital‐intensive farms are not benefiting from excess finance. Rethinking the general assumption that agricultural growth has a positive and linear effect with access to credit lead to different strategies in the use of external finance. [EconLit Citations: G30, O16, O33, Q14].

Extraordinary economy policies amid Covid-19 pandemic crisis: economic growth, labour productivity and elasticity of substitution

Purpose- This study investigates current financial, fiscal and monetary policies implemented to enhance growth rate in developed economies. First main theoretical findings of neoclassical growth theory are reconsidered. Second, current economy policies from the perspectives of Central banks and Treasury departments are analyzed. Finally, the relationship between these two is investigated and whether the policies are adequate to theoretical findings is examined. Methodology- From the perspective of descriptive statistics, first; time evlotion of labor's share of output from 1947Q1 through 2016Q3 is analyzed. Second, time evolution of percentage change in labor productivity with respect to real hourly compensation are considered from 1948Q1 through 2022Q1. In addition, to identify the accelerating gap between labor productivity and compensation over recent decades, annual index levels from 1973 to 2022 for labor productivity with respect to real hourly compensation are taken into account. Third, the phase-space representation of rate of real growth for output per capita is developed. In methodological perspective, both time-space and phase-space analyses on output per capita, labor productivity and labor compensation clear the way to establish a theoretical model, which explains the interaction between these variables based on constant elasticity of substitution production function. Findings- For case of elasticity of substitution lower-than-unity, the relationship between rate of real growth for marginal productivity and average productivity of labor is obtained and is used to enlighten current U.S. monetary and fiscal policy implementations. Conclusion- The results demonstrate that amid Covid-19 pandemics, U.S. fiscal policy and monetary policy do not optimally match and hence the fiscal policy should be calibrated. U.S. fiscal policy increased minimum wages and U.S. monetary policy addressed tighter and perfectly competitive labor market. These two policies do not coincide in terms of efficiency. In other words, simultaneous application of these two policies will not give desired compound result. Keywords: Economic growth, labor productivity, fiscal policy, labor compensation, monetary policy JEL Codes: E62, O40, O41

Delayed retirement policy and unemployment rates

This paper examines the impact of retirement policy on the unemployment rates for both young and old workers. It employs a labor search framework with a constant elasticity of substitution production function and cross-market matching to investigate the channels through which the delayed retirement policy has impacts. The findings show that through the cross-market matching channel, retirement policy increases the unemployment of young workers (it is ambiguous for old workers) and has a negative effect on the wages of cross-market matched workers. The latter effect is negative for young workers (positive for old workers) through the capital-skill complementarity. The paper calibrates the model to the U.S. data and quantifies the effects of retirement policy during the first decade of this century. Counterfactual experiments highlight the contribution of each channel.

Complementarity and macroeconomic uncertainty

Macroeconomic uncertainty regularly fluctuates in the data. Theory suggests complementarity between capital and labor inputs in production can generate time-varying endogenous uncertainty because the concavity in the production function influences how output responds to productivity shocks in different states of the economy. This paper examines whether complementarity is a quantitatively significant source of time-varying endogenous uncertainty by estimating a nonlinear real business cycle model with a constant elasticity of substitution production function and exogenous volatility shocks. When matching labor share and uncertainty moments, we find at most 16% of the volatility of uncertainty is endogenous. An estimated model without exogenous volatility shocks can endogenously generate all of the empirical variation in uncertainty, but only at the expense of significantly overstating the volatility of the labor share.

Income and factor substitution: an investigation on the Solow growth model under the constant elasticity of substitution

PurposeThe purpose of this study is to examine whether the elasticity of substitution (ES) varies between developed and developing countries.Design/methodology/approachThe author derives the growth regressions from the Solow model under the constant elasticity of substitution production function by using the first-order Taylor series expansion and estimate them for each country group classified based on time-varying behavior of income per worker using the data-driven algorithm.FindingsThe ES is not unitary and varies among country groups. Developed countries generally have a higher ES than developing countries.Originality/valueFor the first time, the author uses the first-order Taylor series expansion to linearize the steady-state value of income per worker, as the author considers this approach to be relatively more straight-forward and tractable. Furthermore, the author estimates the equations using both cross-section and panel data techniques and employs the data-driven algorithm proposed by Phillips and Sul (2007) to classify countries.

ESTIMATING CONSTANT ELASTICITY OF SUBSTITUTION PRODUCTION FUNCTION FOR AGRICULTURAL COMPANIES IN IRAQ

This research aims to estimate production functions through which production relations, possibilities for production elements substitution, measurement of its substitution elasticity, and efficiency and distribution coefficients can be analyzed. This would be done through estimation of constant elasticity of substitution production function for agricultural companies in Iraq depending on data from Iraqi Stock Exchange reports of 2005-2016. The researcher had used panel data model and estimated its three models: the Pooled Regression Model (PRM), the Fixed Effect Model (FEM) and the Random Effect Model (REM). A comparison was made for theses three models using F, LM, Husman tests. Tests show that Fixed Effect Model (FEM) is the best estimated one and depended as the explanation of the constant elasticity of substitution production function. The results of this function referred that a 1% increase in capital stock and labor would increase the agriculture production of the agricultural companies with 0.73 and 0.48 % respectively. The capital stock helps in using the production technology. Also, there were no indications that the production technology effects on production value (i.e there is no increasing in efficiency value with the increasing of capital stock; note that the timeline of the study was 12 years in which supposed to show the applied production technology used by the agricultural companies and if it happened, it would be of no important. The elasticity substitution was 10, which is high and indicates that there are other substitutions available to the companies. The researcher recommends to put the scientific resources management, the changing of production and competence, the information technology, and the market changes into consideration so as to have a great competent.

The Decline in Capital Efficiency and Labour Share

We calibrate and simulate a neoclassical growth model with a variable elasticity of substitution production function and three types of technological change: labour‐augmenting, capital‐augmenting and investment‐specific. In this framework, we find that the decline in US labour share was caused by a large decline in capital efficiency, which led to a decrease in the ratio of effective capital to effective labour in a context in which capital and labour are gross complements. Moreover, the decline in the relative price of investment contributed to reducing the fall in US labour share, while the increase in the economic depreciation rate of US fixed assets accounted for a small reduction in US labour share.

Substitutability between production factors and growth. An analysis using VES production functions

This work investigates the economic growth problem of establishing a relation between the elasticity of substitution between production factors, capital and output per-capita levels when dealing with a non constant elasticity of substitution production function. Starting from a discrete-time setup, some definitions of elasticity of substitution associated to an attractor are proposed and a general method to measure it is suggested. Thanks to this methodology a government may select a proper economic policy in order to reduce production costs without decreasing the capitalisation trend of the economy. The method proposed is applied to the Solow’s type growth model with differential savings using a Variable Elasticity of Substitution (VES) production function with constant returns to scale. It is found that when shareholders save more than workers or the elasticity of substitution is higher than one, a country characterised by production functions with higher elasticity of substitution experiences higher capital and output per-capita equilibrium levels. On the other hand, when the elasticity of substitution is lower than one and workers save more than shareholders, an ambiguous relation between elasticity of substitution and asymptotic dynamics is shown.

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.

Public and private education expenditures, variable elasticity of substitution and economic growth

We develop an overlapping generations model to examine how public and private education expenditures impacts on an economy's long run outcomes. Young agents' education is “produced” according to a variable elasticity of substitution production function where the inputs are public education and private expenditures undertaken by parents. Results reveal that higher substitutability between these inputs enables agents to reduce private education expenditures and spend more on consumption and investment, leading to better economic outcomes. Higher aggregate substitutability therefore also implies that a higher tax rate is optimal, since this reduces the need for private educational expenditures to supplement public education expenditures. Analytical results reveal that, depending on initial conditions, the economy could either achieve smooth convergence towards the long run outcome or experience fluctuations during transition. However, numerical analysis suggests that a smooth transition is more likely. Fluctuations during transition may occur when the share of parental human capital in determining an agent's human capital is high. Hence, institutional reforms that reduce the importance of inherited human capital by providing everyone better access to high quality education could facilitate smooth convergence to the long run outcome.

Regional total factor productivity and local employment growth: evidence from Korea

Abstract This paper examines the effect of regional total factor productivity (TFP) on local employment growth using regional panel data from 2000 to 2014 in Korea. The employment equation derived from the constant elasticity of substitution production function is a function of wage rate, capital stock, and regional TFP. The demand for labor accounts for dynamics since there is a cost to adjusting demand for labor in the long-run. This paper introduces a dynamic panel regression model that considers the effect of lagged employment. TFP is a more appropriate measure of technology than Research and Development (R&D) expenditure or the number of patent applications. This paper measures regional TFP using a growth accounting method as a proxy variable of technology. This paper shows that an increase in regional TFP has a positive effect on local employment growth that is greater in the long-run than in the short-run. This suggests that employment policy such as vocational training adapting to the technological progress for product and process innovations increases labor force productivity in the long-run.

Theoretical Explanations for the Inverted-U Change of Historical Energy Intensity

Historical experience shows that the economy-wide energy intensity develops nonmonotonically like an inverted U, which still lacks direct theoretical explanations. Based on a model of structural change driven by technological differences, this paper provides an attempt to explore the underlying mechanisms of energy intensity change and thus to explain the above empirical regularity accompanied by structural transformation, through introducing a nested constant elasticity of substitution production function with heterogeneous elasticities of substitution. According to some reasonable assumptions, this extended model not only describes the typical path of structural change but also depicts the inverted-U development of economy-wide energy intensity. With the availability of Swedish historical data, we take calibration and simulation exercises which confirm the theoretical predictions. Furthermore, we find that: (1) elasticities of substitution may affect the shapes and peak periods of the inverted-U curves, which can explain to a certain extent the heterogeneous transitions of economy-wide energy intensity developments in different economies; and (2) over long periods of time, the economy-wide energy intensity determined by the initial industrial structure and sectoral energy intensity tends to grow upward, while structure change among sectors provides a driving force on reshaping this trend and turning it downward.

Development accounting, the elasticity of substitution, and non-neutral technological change

We construct a broad panel with 84 countries over the period 1970-2014 with data from the Penn World Tables (PWT) 9.0. We apply the tools of development accounting to our panel. However, we depart from the traditional Cobb-Douglas hypothesis and Hicks-neutral technological change, and assume a Constant Elasticity of Substitution production function, which allows for a constant but non-unitary elasticity of substitution, and for non-neutral technological change. For different values of the elasticity of substitution, and different representation of technological change, we find that the cross-country variation in GDP per worker that can be accounted for by factor inputs is decreasing over time until the mid-2000s, when it reverses its decreasing trend. In addition, our estimates suggests that in the more recent period the proportion of the cross-country variation in GDP per worker explained by factor inputs is around 20%. Finally, we obtain similar results with broad panels from PWT versions 8.1 and 7.0, corroborating our initial findings.

Analysis of Nonlinear Duopoly Games with Product Differentiation: Stability, Global Dynamics, and Control

Many researchers have used quadratic utility function to study its influences on economic games with product differentiation. Such games include Cournot, Bertrand, and a mixed-type game called Cournot-Bertrand. Within this paper, a cubic utility function that is derived from a constant elasticity of substitution production function (CES) is introduced. This cubic function is more desirable than the quadratic one besides its amenability to efficiency analysis. Based on that utility a two-dimensional Cournot duopoly game with horizontal product differentiation is modeled using a discrete time scale. Two different types of games are studied in this paper. In the first game, firms are updating their output production using the traditional bounded rationality approach. In the second game, firms adopt Puu’s mechanism to update their productions. Puu’s mechanism does not require any information about the profit function; instead it needs both firms to know their production and their profits in the past time periods. In both scenarios, an explicit form for the Nash equilibrium point is obtained under certain conditions. The stability analysis of Nash point is considered. Furthermore, some numerical simulations are carried out to confirm the chaotic behavior of Nash equilibrium point. This analysis includes bifurcation, attractor, maximum Lyapunov exponent, and sensitivity to initial conditions.

Economic Growth and the CES Production Function with Human Capital

Employing a neoclassical growth model with a constant elasticity of substitution production function, we develop a comparative static and dynamic analysis of the effects of the elasticity of substitution between inputs on the steady state growth path, growth threshold, speed of convergence and savings rates. Unlike earlier studies along these lines, we incorporate human capital, along with physical capital and raw labor, as a third input in the production function. We prove that a higher elasticity of substitution between inputs can lead to a higher steady state level for income per effective unit of labor. To illustrate the quantitative significance of the elasticity of substitution, we consider two ways in which human capital enters the production function. Employing cross country data, we find estimates for the normalized CES production functions with human capital to be significantly below unity.

Goods-Time Elasticity of Substitution in Health Production.

We examine how inputs for health production, in particular, medical care and health-enhancing time, are combined to improve health. The estimated elasticity of substitution from a constant elasticity of substitution production function is significantly less than one for the working-age population, rejecting the unit elasticity of substitution used in previous studies. Copyright © 2016 John Wiley & Sons, Ltd.

A Generalized Constant Elasticity of Substitution Production Function Model and Its Application

AbstractThe constant elasticity of substitution production function describes the relationship between production results and production factors in the technological production process. The common production factors include capital and labor. In order to comprehensively reflect the input-output relationship, this paper generalizes the model and adds factors including energy, consumption, and import and export. With respect to estimating the parameters of the model, the paper proposes a high-precision and high-speed nonlinear regression method. The constant elasticity of substitution production function model is mainly used to calculate the contribution rates of economic growth factors, and this paper proposes a scientific and reliable calculating method. The final section of the paper proposes an empirical analysis of the contribution rates of Chinese economic growth factors.

Monopsony in the Labor Market, Minimum Wages and the Time Horizon: Some Unresolved Issues

This article discusses development of optimal solutions for monopsony in the labour market for the long run (when labour and capital are both flexible). It is shown that binding minimum wages up to a certain degree pushes the monopsonists to choose a high capital intensity of production, just as high as or even higher than that chosen when there is no regulation for minimum wages. Thereby, we demonstrate the existence of re-switching effects in the tradition of Piero Sraffa. The second part of the paper recalculates and analyzes earlier results by making use of the rather general constant elasticity of substitution production function. Based on a numerical solution for optimal monopsony under different regimes (no minimum wage, minimum wages of different values, etc.), we formulate a two-period game between the government and the monopsonistic firm (‘minimum wage game’). Finally, we analyze the relationship between the elasticity of substitution on the one hand and likely levels of employment on the other hand, after introduction of minimum wages.