Output Elasticity Research Articles

Synergistic development path of conventional and unconventional water in China: From the perspectives of output and substitution elasticities

Exploring the synergistic relationship between conventional water (CW) and unconventional water (UW) is a better way to alleviate water scarcity. However, research remains lacking on the complex relationship between CW and UW from a water resources subdivision perspective. By constructing a heterogeneous trans-log stochastic frontier model, this study estimated the technical efficiency, output elasticity, and substitution elasticity; further, the study innovatively explored five development pathways for CW and UW. The results are as follows. First, China's overall technical efficiency demonstrated a fluctuating upward trend over the study period, which was significantly boosted by higher levels of research and development investment and an increased number of granted patents. Second, compared with UW, CW made a more substantial contribution to output. The output elasticity of CW demonstrated a “low in the center, high on the periphery” pattern, with the lowest elasticity areas clustered in the middle and lower reaches of the Yellow River. Conversely, the output elasticity of UW followed a “high in the east and low in the west” pattern, which was similar to that of capital. Third, with 2012 as the turning point, CW and UW shifted from a substitution to a complementary relationship. Fourth, this study proposes alternative structural optimization paths under various scenarios, namely balanced development of CW and UW, CW-driven, UW-driven, coordinated development of CW and UW, and aided development of CW and UW.

Regional Economic Development, Climate Change, and Work Force in a Gender Perspective in Chile: Insights from the Input–Output Matrix

Most nations fulfilled the commitment to reduce their emissions after the Paris Climate Agreement, and as a result, each nation has produced suitable plans to reach those goals. In this sense, Chile is hardly an exception. The emission multiplier product matrix (eMPM) and labor multiplier product matrix (lMPM), which are associated with the gender differences in the labor market, a state-of-the-art technique that integrates CO2 emissions with multi-region input–output table (MRIO) databases and elasticity to estimate the pollution caused by inter-industrial activity in the nation’s various north, center, and south regions, are used in this article to analyze the emissions of Chilean industries. This approach, by studying the economic territorial consistency (ETC) issue, is expected to establish a connection between each region’s production structure and interregional relationships between gender and the main industries that produce emissions. Indeed, the study aims to determine which regions foster economic development from an equitable perspective through the ETC study. The ETC in Chile depends on some variables, such as labor force, gender and CO2 emissions. The improvement in terms ofion will depend on the use of technology and the proper state regulation in line with the promises gained by Chile following the convening of COP25.

The Elasticity of Aggregate Output with Respect to Capital and Labor

It is often assumed that the elasticity of GDP with respect to capital is one-third, but this assumes zero markups and an aggregate production function. I estimate the elasticity allowing markups to vary by industry and with a rich input-output structure. Assumptions about capital costs provide bounds on elasticity. In the United States from 1948–1995, the capital elasticity ranged from 0.19–0.32 and shifted to 0. 24–0.37 by 1996–2018. Excluding housing or decapitalizing intellectual property lowers bounds to as low as 0. 11–0.26. Based on these elasticities, common estimates of total factor productivity growth represent a lower bound. (JEL E13, E22, E23, E25, N12)

AI-driven capital-skill complementarity: Implications for skill premiums and labor mobility

To explain the newly discovered coevolution of capital and labor structures, this study presents a modified capital-skill complementarity hypothesis within the framework of structural transformation. We propose that artificial intelligence (AI) and skilled labor exhibit relative complementarity. Specifically, advancements in AI services or AI-enhanced technologies incentivize the mobilization of skilled labor across different industry sectors. The direction of this labor movement is contingent upon variations across industry sectors, including AI output elasticity and the substitutability between AI and conventional production methods. This structural transformation process also induces fluctuations in skill premiums.

R&D investment: A dynamic efficiency approach in the EU countries

This paper aims to analyze the role of research and development (R&D) in the production efficiency of European Union Member States. Utilizing Bayesian methods within a dynamic framework, the study jointly estimates production functions and efficiency for a sample of 27 countries over the 2000–2021 period. The findings reveal that human capital investment exhibits a higher output elasticity compared to physical capital investment. Additionally, the results indicate that inefficiencies persist due to escalating costs—both monetary and temporal—as inputs expand. Across the studied countries, an upward trend in R&D expenditure is associated with increasing technical efficiency levels, establishing a positive relationship between R&D spending and technical efficiency scores. Geographically, eastern and southern European regions exhibit lower average efficiency levels. These insights are crucial for policymakers seeking to foster innovation-driven policies, highlighting the importance of maintaining or increasing R&D spending to achieve the economic and social objectives of the European Union. Through appropriate R&D policies, policymakers can enhance technical efficiency, ensure the EU's global competitiveness, and promote more equitable development across the Union.

Evaluating the Effects of Public Debt on Sri Lanka’s Economic Growth: A Short-term and Long-term Perspective

Aims: The objective of this paper is to examine whether public debt enhances economic growth in Sri Lanka by separating debt into domestic and external debt. Study Design: The paper adopts the Keynesian demand-side model to estimate GDP on demand-side and supply-side factors such as domestic debt, external debt, gross fixed capital formation (investment in short), labour force, general price level, money supply, government spending and trade openness. In a model where debt causes investment, public debt effects are netted out from investment by removing the estimated investment effects of domestic and external debt. Duration of Study: quarterly data from Q1 2010 to Q1 2023 are utilized to trace the long-term and the short-term effects of domestic and external debt on GDP. Methodology: The ARDL method of estimation is used and the model is estimated in double log form so that estimated parameters reflect output elasticities. A general to specific modelling approach is adopted to find the best suited model. Results: Variables such as government spending, money supply, general price level and labour force are not relevant while domestic debt, external debt, investment (debt effects netted out) and trade openness are significant in describing GDP. The long-term domestic debt elasticity of GDP is 0.588 while short-term domestic debt elasticity (sum of contemporaneous and lag effects) is about 0.63. The cumulative effects of domestic debt on GDP tappers off to 0.60 in the long-run. The result suggests negative impacts (-0.272 and -0.254) of external debt on the economic growth in short-term and long-term respectively. The negative effect of external debt can be justified if recent external borrowings have been used to repay loans taken to finance war and unproductive projects. Conclusion: The paper finds that the domestic public debt creates relatively strong positive effects on GDP in the short-term and the long-term. Contrary to the expectations, the effects of external debt on GDP have become negative both in the short-term and the long-term. The paper also finds that debt effects on GDP have been significantly reduced when debt effect-ridden investment variable is included in the regression in place of debt-effect netted out investment. Thus, this study recommends researchers to carry out further research on why the effects of external debt on GDP become negative. Further, it recommends policy makers to use both domestic and external debt to finance public investment and productivity enhancement projects rather than borrowing merely for the purpose of consumption and repaying of existing debt.

Inflation targeting, output stabilization, and real indeterminacy in monetary models with an interest rate rule

AbstractCentral banks set the nominal interest rate to target inflation and stabilize output. In monetary models, monetary policy affects output directly via the wealth effect. I show that in these models, the response of the central bank to fluctuations in output may induce real indeterminacy even if the Taylor principle is satisfied. I find that the determinacy conditions depend on the interest elasticity of output and generally, the Taylor principle is neither necessary nor sufficient for determinacy. This is in stark contrast with the New Keynesian model where a sufficiently strong policy response to inflation or output usually ensures determinacy.

From Fossil to Future: The Transformative Role of Renewable Energy in Shaping Economic Landscapes

In recent years, numerous countries have embarked on a transformative journey to reshape their energy portfolios by transitioning from fossil-based resources to renewable sources, significantly impacting economic growth. This study aims to scrutinize the influence of renewable energy consumption (REC) on GDP growth responsiveness in the top 20 renewable energy-consuming countries over the period from 1990 to 2021. To ensure robust panel analysis, the study addresses cross-sectional dependence using the diagnostic test proposed by Pesaran (2004). The long-run perspective reveals that both conventional factors of production, encompassing both renewable and non-renewable energy (Fossil Fuel Energy - FEF) consumption, make positive contributions to GDP growth in the sampled countries. Single-country time series analyses further underscore the positive long-run output elasticities concerning renewable energy in the majority of these nations. These findings highlight the pivotal role of renewable energy as a key determinant of sustained GDP growth, indicating that these countries are on a trajectory of sustainable development. The study's implications extend to policy considerations, urging collaborative efforts among governments, international organizations, and energy planners. There is a pressing need for the implementation of strategic renewable energy initiatives across nations. Governments are encouraged to adopt incentive-based policies to optimize the harnessing of renewable energy resources, fostering not only economic growth but also contributing to the global pursuit of sustainable and environmentally conscious practices.

Fuel substitution possibilities, factor productivity, and technological progress in the industrial sector of India

India is often referred to as the next development superpower, and generally, becoming a large-scale industrialization center is seen as an achievable goal for the country. This article investigates the output elasticity, substitution elasticity, and technological advancement between the various factors (i.e., labor, capital, and energy use) in the industrial sector of India. To investigate the factor's productivity, a trans-log production function was applied; however, ridge regression was used to analyze the various parameters to check the multicollinearity issue. The results show that (1) the analyzed inputs are optimistic and return-to-scale averages of 1.18, 1.41, and 1.24 between labor, capital, and energy, respectively, are increasing; (2) the pairs substitution between labor–industrial energy utilization and capital–industrial energy consumption is found to be 0.96 and 0.98, respectively, on average, indicating that capital, labor, and energy are good substitutes that need more attention in the production process; and (3) the technological progress between factors ranges from −0.4 to 0.02, in which labor–energy and capital–energy utilizations provide quicker outcomes than a capital–labor utilization. Finally, the industrial sector can attain maximum productivity if capital and skilled labor are improved under the sustainable development goals, as energy and capital are optimized for maximum efficiency. Finally, energy substitution and low-carbon technological efforts can be better suited for attaining dual-carbon goals in the industrial sector.

Quantum simulation of coopetition

We propose the rule engine of expert system consists of quantum algorithm in two folds: quantum mechanics and quantum computation. The simulation of quantum computation-based coopetition leads to explain the external economics scale (EES) and disruptive innovations of coopetition by the use of Brynjolfsson–Hitt computing productivity function as a real context of the proposed expert system. We show the quantum coopetition computation of Brynjolfsson–Hitt system on a global polyadic coopetition of globotics upheaval. The Schrödinger and Heisenberg pictures are discussed: the Schrödinger picture results the energy of coopetition environment, while the Heisenberg picture provides production function transformation due to quantum effect of production variables. The Composite Production Function is constructed through quantum algorithm, and the energy of member coopetition depends on quadratic of elasticity and production variables. It is shown that the composite production function of a coopetition depth is ≈O((n+δ)∑iβi), where it depends on the number of production function variables (n), the number of perturbation variables (δ), and the output elasticities of production function variables (∑iβi>1). Our findings suggest that the model has potential implementation for the expert system of coopetition on globotics upheaval era.

Research on collaborative innovation behavior of enterprise innovation ecosystem under evolutionary game

Establishing an innovation ecosystem revitalizes enterprises by fostering collaboration with other entities within the system. This collaboration results in increased resources for innovation and development, further strengthening participants' innovation and survival capacities. As the existing literature on collaborative innovation behavior within innovation ecosystems is relatively limited, the primary objective of this study is to investigate the evolutionary process and impact factors of players' collaborative innovation behavior in the enterprise innovation ecosystem (EIE). This study establishes an evolutionary game (EG) model that includes three players in an EIE to analyze their collaborative innovation behaviors in scenarios where their initial strategic probabilities are low, medium, and high. The simulation results indicate the existence of six potential evolutionary stable strategies (ESSs) within the system. The ideal ESS identified in this three-party evolutionary game model is characterized by “active collaboration, active collaboration, participation”. Furthermore, the player's behaviors in different states are affected by initial probability, synergy sensitivity, transformation efficiency, output elasticity, subsidy, punishment, and public impact. The results of this study reveal the mechanism of collaborative innovation behavior among different players in the EIE, providing beneficial references for its sustainable development.

Unleashing Economic Potential: Enhancing Cassava Production Efficiency in Nigeria

Purpose: This study is aimed at determining the economic efficiency of Manihot esculenta Crantz (Cassava) production in Nigeria’s Delta State. The study offers a detailed analysis of how socio-economic characteristics influence production output across both early and late farming seasons. Design/ Methodology/ Approach: This study employed a multi-stage random sampling approach in selecting a diverse cohort of 500 cassava farmers engaged in both early and late-season cultivation. Through rigorous personal interviews, primary data was gathered that was both comprehensive and insightful. Advanced parametric statistics and the Cobb-Douglas stochastic frontier function were used for the analysis. Findings: The mean economic efficiency scores were determined to be 0.63 for early-season farms, 0.78 for late-season farms, and 0.76 when considering all farms collectively. The output elasticities of material inputs, labour, and land were found to be 0.42, 0.61, and 0.05, respectively for all farms. For early-season farms, these values were 0.36, 0.68, and 0.04, whereas, for late-season farms, they were 0.31, 0.7, and 0.03. Research Limitation/Implications: This work concentrated on Cassava production efficiency within and around Nigeria’s Delta area. Practical Implication: Understanding the socio-economic factors that influence production during different seasons can help in designing strategies that maximize output in both early and late farming seasons. Social Implication: This study would help agricultural development economists and policy-makers in addressing the economic problems of Cassava farmers both present and future generations. Originality/Value: By examining both early and late farming seasons, the study provides a comprehensive understanding of how socio-economic factors vary across different agricultural cycles. This dual-season approach is relatively rare and offers more detailed insights into the dynamics of cassava production throughout the year.

Nexus Between Water Consumption and Economic Output for the Metallic and Non‐Metallic Mineral Products Sector: An Empirical Analysis at the Enterprise Level

AbstractWith rapid urbanization and industrialization in China, the demand for mineral products and subsequent water consumption have significantly increased, posing challenges to sustainable economic growth due to escalating water scarcity. Few studies have explored the nexus between water use and economic output from the enterprise perspective. This study focuses on the metallic and non‐metallic mineral products sector, quantifying the nexus between water consumption and economic output at the enterprise level, analyzing the heterogeneity of water consumption elasticity of economic output across different regions and sub‐sectors, and identifying key sub‐sectors within each region that are highly dependent on water consumption. The results indicate that for the metallic and non‐metallic mineral products sector, a 1% increase or decrease in water consumption leads to a corresponding increase or decrease in economic output by 0.096%. Water consumption elasticity of economic output varies from 0.056 to 0.131 according to the regions. And it ranges from 0.048 to 0.104 for different sub‐sectors. This study identifies regions and sub‐sectors where economic output is highly dependent on water resources. The findings may help tailor policies to measure the value of water, especially in the context of potential water shortages.

The Impact of Energy Efficiency on Economic Growth: Application of the MARCO Model to the Portuguese Economy 1960–2014

The benefits of energy efficiency are recognized in multiple socio-economic spheres. Still, the quantitative impact on macroeconomic performance is not fully understood, as modeling tools are not thermodynamically consistent—failing to explicitly include the useful stage of energy flows and/or thermodynamic efficiencies in primary–final–useful energy transformations. Misspecification in the link between energy use and the economy underplays the role of energy use and efficiency in economic growth. In this work, we develop and implement the Macroeconometric Resource Consumption model for Portugal (MARCO-PT), 1960–2014. Based on the post-Keynesian framework developed for the United Kingdom (MARCO-UK), our model explicitly includes thermodynamic energy efficiency, extending the analysis to the useful stage of energy flows. The model’s stochastic equations are econometrically estimated. The historical influence of key variables—namely thermodynamic energy efficiency—on economic output is assessed through counterfactual simulations and computation of year-by-year output elasticities. The MARCO-PT model adequately describes the historical behavior of endogenous variables. Although its influence has decreased over time, thermodynamic efficiency has consistently been the major contributor to economic growth between 1960–2014, with an average output elasticity of 0.46. Total useful exergy is also a major contributing factor, with an average output elasticity of 0.29. Both have a higher influence than capital, labor, or other energy variables (final energy, prices). An adequate integration of thermodynamic efficiency is thus crucial for macroeconomic models.

Information Technology and Returns to Scale

What are the implications of the dramatic fall in IT prices for aggregate technology? When firm-level technologies are continuously differentiable, a factor price shock leads to (i) a substitution between factors and/or (ii) an endogenous response of returns to scale. The second channel is governed by the output elasticity of relative factor demand. Using detailed firm-level data from France, we estimate this elasticity to be positive for IT factor demand. A quantitative exercise accounting for both technological channels shows that falling IT prices can explain much of the changes in concentration and the composition of aggregate labor share in France. (JEL D22, D24, D33, E25, L63, L86)

The heterogeneous effects of non-hydro renewable energy and water resources on industrial development of the Yellow river and Yangtze river basins

Exploring the relationship between non-hydro renewable energy (NHRE) and water resources can help achieve high-quality development in China’s industrial sector under the constraints of water conservation. This study investigated the interrelationships and regional heterogeneity of capital, labor, water and NHRE in the industrial sectors of 158 cities in the Yellow River Basin (YRB) and Yangtze River Basin (YZRB) in China using a heterogeneous stochastic frontier model. Based on reconstructed NHRE consumption data, it is found that the NHRE output elasticity (OE) in the NHRE-rich YRB (median value: 0.1) was lower than that in the NHRE-scarce YZRB (0.24), while the water OE in the water-rich YZRB (0.07) was lower than that in the water-scarce YRB (0.09). Classification analysis of infrastructure construction revealed that the energy OE in NHRE outflow regions (0.11) was lower than in NHRE inflow regions (0.28). This study also optimized the allocation of projected NHRE additions in China by 2030 and found that the optimized strategy can generate an additional industrial output of 8.8 × 1011 Yuan and save 8.6 × 107 tons of water compared to existing strategies. The results indicated that a win-win situation of industrial growth and water conservation could be achieved by reallocation of NHRE.

Optimal incentive power for inter-team competition

This article investigates optimal incentive power for team competition. We show that the optimal incentive power, represented by the elasticity of a sharing rule, is proportional to the firm’s output elasticity with respect to teams’ output and team size.

Assessment of natural resource endowment and urban-rural integration for sustainable development in Xinjiang, China

Water and land (W-L) resources become even more important in the context of urban-rural integration in China's arid northwest region in order to achieve sustainable development goals (SDGs). Our study used Gini coefficients to examine the relationship between natural resources and economic development in China's Xinjiang Uygur Autonomous Region. Cobb-Douglas (C-D) production functions were used to determine the economic impacts of W-L resources on rural-urban economic development. We also examined the spatiotemporal interaction characteristics of the growth drag effect of W-L resources. As a result of the decline in Gini coefficients between 2000 and 2020, Xinjiang experienced a decrease in water resources, land resources, and urban-rural GDP (gross domestic product). The output elasticities of urban-rural land and water resources were 0.3544 and 0.4790, respectively, whereas the output elasticities of urban-rural land resources were 0.1501 and 0.2185, respectively. As a result, water resources contribute to the growth of urban-rural GDP more than land resources, and W-L resources contribute to the economic development of rural areas more than it does to that of urban areas. Land resources were found to have a drag effect on urban and rural economies, respectively, in 7 and 56 counties, respectively, and water resources were found to have a drag effect on urban and rural economies, respectively, in 67 and 58 counties. In Xinjiang, water resources contributed more to economic growth than land resources. Even though W-L resources still have a drag effect on urban-rural economic growth, we can gain greater driving force by optimizing and improving resource use. However, this requires an optimal allocation and efficient use of water resources.

Reflections on Labour Productivity of the Sri Lanka Transport Board: An Analysis of Patterns and Evolution

The predominant reliance on buses, particularly by low-income commuters, has made the bus transportation industry one of the most pivotal contributors to the domestic economy. Therefore, as the single largest public bus transportation service provider in Sri Lanka, SLTB’s ability to generate higher volumes of output by employing fewer inputs is increasingly crucial. However, SLTB is a state-owned enterprise that has been criticised for its inefficient factor productivity for a long time. Such allegations against the leading transport service provider of the country would raise serious economic concerns. Thus, this study attempted to examine SLTB’s labour productivity in its physical dimensions as reflected through the elasticity of output on labour inputs to determine the underlying causes for any inefficiency in the utilisation of labour in the organisation. The scale and evolution of elasticities of output of SLTB’s operations on labour inputs between 2011 and 2019 were subject to econometric scrutiny in this study. The results of the study revealed that the SLTB’s elasticity of output on labour inputs has been negative at the overall national level. However, a favourable evolution of the elasticity of output on labour could be observed over the years. The results also revealed the presence of significant differences in region-specific effects on the elasticity of output on labour inputs compared to the national level, indicating that different regions have different labour productivity levels.

Classification of quasi‐product production models with minimal isoquants

The study of the minimality of (hyper)surfaces is a fundamental problem in mathematics with major applications in both fundamental and applied sciences. Recently, the minimality of production models in microeconomics has been investigated by several authors who obtained important classification results for quasi‐sum and quasi‐product production functions with two and three inputs. In the present work, we deal with the minimality of isoquants of production functions with arbitrary number of inputs, this being a key concept used in making the best decision for optimizing the production costs. In the main result of the article, we give the complete classification of quasi‐product production functions whose isoquants are minimal, showing that there are exactly nine production models with such a property. Among them, we can identify a particular classic model already widely used in economic analysis (viz., a Cobb–Douglas model with unit output elasticities with respect to some production factors) and various production models completely unknown until now and which will open new opportunities for applied research in the field of mathematical economics.