Substitution Production Function Research Articles

Automated machines and the labor wage gap

This paper analyzes how the increase in the proportion of automated machines to general capital inputs affects the wage gap of the labor force complementary to the two types of capital, the general equilibrium model and constant elasticity of substitution production function are introduced and the impact mechanism is explored using a task-based model. Data for listed Chinese manufacturing companies from 2012 to 2020 is used and a double fixed effects model is invoked for empirical testing. The findings show that (1) a rise in the proportion of automated machines to general capital inputs increases the wage gap of labor complementary to automated machine capital and general capital, and a rise in the proportion of demand for both types of labor complementary to automated machines and general capital is an influential mechanism; (2) the productivity-enhancing effect suppresses the widening of the wage gap between the two types of labor; and (3) the results of heterogeneity analysis show that an increase in automated machine inputs among non-state-owned manufacturing firms and technology-intensive firms widens the labor wage gap. This paper makes a contribution to both theoretical and empirical analysis and provides references for the alleviation of the labor wage gap.

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.

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.

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.

Could the Lacking Absorption Capacity of the Inflowing Capital Be the Real Cause of the Resource Curse?—A Case Study of Transition Economies

The present study proposes an alternative explanation for the negative natural-resource-growth nexus. Based on the theoretical analysis, the study shows that a balanced capital–labor ratio plays an essential role in the absorption of complex capital goods. It estimates the parameters of the constant elasticity of the substitution production function in Mathcad using nonlinear least squares, i.e., an approximate Marquardt method of optimization. The empirical analysis is based on the time-series data of these countries for the time interval between 2000 and 2020. We conducted analyses by calculating the elasticity of substitution between capital and labor. Specifically, for these countries, the elasticity of substitution of capital and labor appeared to be less than one, which indicates a lack of labor, or, more precisely, a qualified labor force. Each of these countries receives windfall profits from the exploitation of natural resources, which greatly influences the import of capital-intensive products of complex technologies—in other words, the import of capital. However, the lack of an adequate labor force that could utilize the increased capital led to a decrease in the elasticity of capital and labor substitution. A comparison of the optimal and the observed capital–labor ratio coefficient shows that this coefficient is significantly higher than optimal in all three countries. Therefore, while keeping the wage fund in balance with fixed capital costs, investments in the knowledge economy and human capital appear to be the preferred areas for the efficient allocation of oil revenues.

TÜRKİYE’DE İMALAT VE HİZMET SEKTÖRLERİNDE İSTİHDAM ESNEKLİĞİ

The main purpose of this study is to investigate the relationship between employment intensity and growth in Turkey’s manufacturing and service sectors via taking into consideration the Eurostat technology classification for the period between 2003 and 2015. Relying on a - Constant Elasticity of Substitution (CES) production function, employment demand functions are estimated for different manufacturing sub sectors with different technology levels and service sectors with different information content. The results reveal that real wages are the main determinant of employment demand with a negative coefficient, in line with the related literature. Employment elasticities of output have been positive and statistically significant, except for the medium-low (ML) technology sub sectors. Manufacturing sub sectors has relatively low and insignificant coefficients which could be considered as a weak sign of jobless growth. The interest rate seems to be negative and statistically significant. On the other hand, we did not find any significant relationship between inflation (inf) and employment demand except for less knowledge-based service (LKIS) sectors.

Can variable elasticity of substitution explain changes in labor shares?

In CES production functions, the magnitude of the elasticity of substitution between capital and labor (σ) is crucial to explain the evolution of the labor share. The decline in labor share observed worldwide can be explained by capital accumulation if σ>1. However, empirical evidence on the value of σ is mixed. To shed light on this issue, we employ a Variable Elasticity of Substitution (VES) production function where σ is an endogenous driver of the labor share. Using macro data for six advanced OECD economies from 1980 to 2020 we provide estimates of σ under imperfect competition. We test the prediction of the model by means of simulations. Mainly, we find that capital deepening, markup and technological change explain a significant part of the observed decline in labor shares. The results suggest complementarity between labor and capital in all the countries except the United States.

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>

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.

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.

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].

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.

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

An estimation of macroeconomic energy rebound, intensity, and output effect: An evidence from Pakistan

The outcomes of energy efficiency are conditional on the size of energy rebound effect, which further promotes energy consumption instead of reducing it. Therefore, evaluating the energy rebound effect is a crucial constituent for environmental sustainability. In that perspective, the present paper examines macroeconomic rebound, intensity, and output effects of exogenous energy efficiency improvements for Pakistan using time series data from 1980 to 2018. For this, constant elasticity of substitution (CES) production function is estimated with two non-linear estimation techniques Nelder and Mead (NM) and Broyden Fletcher Goldfarb Shanno (BFGS). Moreover, three effects of energy efficiency are calculated for long run and short run with both constant returns to scale and variable returns to scale. The study finds about 65% partial energy rebound effect in both cases of NM method while BFGS method provides partial rebound effect (27%) in case of constant returns to scale and backfire (136%) in case of variable returns to scale. Moreover, the magnitudes of three effects in the long run are relatively high as compared to the short run effects. As anticipated, energy efficiency is relatively less effective; therefore, energy and environment policies should incorporate the energy rebound effect to achieve a sustainable economic growth path.

Does an Empirical Economic Relation Have a Life?

Does an Empirical Economic Relation Have a Life?

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.

Economy-wide Impacts of Tariff Cuts and Productivity Improvements in Agriculture: A Computable General Equilibrium (CGE) Analysis for Sri Lanka

This study provides a quantitative assessment of the likely economy-wide impacts of tariff cuts and productivity improvements in agriculture for Sri Lanka. A static, multisector, Computable General Equilibrium (CGE) model, using the Supply and Use Table (SUT) of 2010, was employed highlighting specified agricultural sub-sectors and their interactions with other production sectors in the economy. Constructing a CGE model entailed the development of a Social Accounting Matrix (SAM) to represent the Sri Lankan economy. The SUT, household income and expenditure survey, economic stat of the Department of Census and Statistics, and economic data library of the Central Bank of Sri Lanka were used to develop the SAM. The SAM was used to calibrate the CGE model. Coding and operationalization of the CGE model were executed using the PATH solver of the General Algebraic Modeling System software using a modified version of the standard CGE model. Production was specified as a Constant Elasticity of Substitution (CES) production function whereas consumption was specified as a Linear Expenditure System (LES). Using the HIES data, the LES was estimated using a seemingly unrelated regression model. The CGE model included a representative household, two factors of production <em>i.e.</em>, labor and capital, commodities, activities, the government, savings, and investment and trade. Productivity improvements in the selected agricultural subsectors lead to a significant positive response in the paddy, vegetables, coconut growing, and livestock sectors. However, productivity improvements in the specified agricultural sectors lead to a decline in demand for labor because of improved primary factor productivity and the decline of market prices. A cut in prevailing tariffs in agricultural industries shows negative impacts on households as a whole.

The energy use of capital inputs: Towards cleaner production in Nigeria

To reduce fossil energy consumption and mitigate carbon emission in an economy, it is important to examine the energy use of the physical capital factor input, taking the Nigerian production process as an example, given that Nigeria is the largest economy in Africa by Gross Domestic Product (GDP), Purchasing Power Parity (PPP), Population, etc. On the other hand, while existing literature assumes energy-use as an independent factor input, this article argues that energy-use is a dependent factor input in a production function relationship. Therefore, this paper seeks to model the production processes differently, by considering energy-use as a dependent factor input of production. Hence, the Energy Efficient Constant Elasticity of Substitution (EE-CES) production function is proposed to model the aggregate production process in Nigeria while taking energy-use as a capital-dependent input factor. The Indirect Least Square (ILS) results show a 19% actual capital energy-efficient level in Nigeria. The marginal productivity of energy-efficient capital exceeds that of labour and energy-inefficient capital. The Nigerian factor inputs exhibit increasing returns to scale with a homogenous of degree three-second. On average, the Nigerian production process is more labour intensive than capital intensive. Therefore, conscious efforts are required to simultaneously make the Nigerian production process more capital-intensive and improve the energy-efficiency of the capital input. The implication of this study is not peculiar to Nigeria but includes other developing economies, mostly African economies, with a more labour-intensive production system.

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.