Directional Output Distance Function Research Articles

Evaluation of marginal abatement cost and potential reduction in China's industrial carbon emissions: A quadratic directional output distance function approach

As a relevant indicator for quantifying the value of carbon emissions, the marginal abatement cost (MAC) of carbon emissions has received increasing attention from academics and policymakers. This study uses a quadratic directional output distance function to analyse the technical efficiency, potential emission reduction and shadow prices of China's industrial carbon emissions. The results show that the technical efficiency of China's industry gradually decreased during the sample period. From the perspective of regions with different carbon intensity and industrial output, regions with lower carbon intensity and higher industrial output gradually closed to the optimal frontier for the technology use level and had relatively high technical efficiency. Rising technical inefficiency and carbon emissions led to a potential emission reduction that also exhibits an upwards trend. In addition, the MAC of industrial carbon emissions exhibits a U-shaped trajectory, with 2011 as the turning point. Generally, in recent years, regions with lower carbon intensity and those with higher industrial output have a relatively high MAC for industrial carbon emissions. The empirical findings reveal that a carbon emission reduction policy should be formulated and targeted to each province, and the principle of ‘easy before difficult’ can be followed to promote emission reduction.

CO2 emissions abatement costs and drivers for Indian thermal power industry

Indian power industry contributes nearly half of its overall CO2 emissions. In this study, we answer three related questions. First, what is the abatement cost of CO2 emissions for the Indian thermal power industry under three different policy scenarios - business as usual, emissions reduction only, and simultaneous emissions reduction and energy efficiency enhancement. Second, what are the determinants of these abatement costs of CO2 emissions. Third, which abatement policy scenario is more beneficial. For this, we employ a plant level dataset covering 93% of installed capacity and use a parametric quadratic directional output distance function to estimate marginal abatement costs by applying deterministic linear programming methods. Our findings are: First, the abatement costs range between US$ 46.43–71.11 per ton CO2, depending on the policy scenario chosen. Second, plant age, location, size, ownership, and CO2 intensity are all significant drivers of abatement costs. Third, while greater emissions reductions are possible under the emissions reduction only scenario vis-à-vis simultaneous emissions reduction and energy efficiency enhancement scenario, both scenarios are compatible with meeting the Paris agreement goals. This paper helps decision makers to allocate CO2 abatement targets to plants in line with their abatement costs and potential.

Assessing performance of directional output distance function: Simulation-based Analysis

Assessing performance of directional output distance function: Simulation-based Analysis

Carbon abatement in the European chemical industry: assessing the feasibility of abatement technologies by estimating firm-level marginal abatement costs

As many other industries, the chemical industry has to strongly reduce its' carbon emissions, for which various abatement technologies exist. We study the economic feasibility of these abatement technologies by estimating the Marginal Abatement Cost (MAC) of CO2 emissions for 24 firms in the European chemical sector over the period 2015–2020. We estimate the firm-level MAC by using a quadratic directional output distance function (DDF) model. We find a median MAC of 429 €/t CO2, which is significantly above current carbon prices, indicating that most firms in this industry prefer to use carbon allowances instead of reducing their own emissions. We conclude that carbon abatement in the chemical industry is only likely when the carbon price is significantly higher or when financial support is provided for certain abatement technologies, such as renewable hydrogen and bio-based ammonia.

Estimating the CO2 marginal abatement cost and implications for climate policies in China’s industrial sector: A firm-level analysis

ABSTRACT This paper presents an in-depth analysis of the Marginal Abatement Cost Curve (MACC) for CO2 of China’s industrial sector. Leveraging comprehensive firm-level panel data spanning the period 2011–2015, we employ a parameterized directional output distance function to estimate the shadow price of CO2. By doing so, we derive the marginal abatement cost for individual firms across different years, which provides crucial insights into two fundamental aspects: first, the variation in shadow prices as indicators of the economic efficiency of existing climate policies; and second, the carbon price levels necessary to achieve CO2 mitigation targets in the future. Furthermore, we conduct scenario simulations to assess the potential industrial output loss resulting from forthcoming carbon policies, such as the European Union’s Carbon Border Adjustment Mechanism (CBAM). Our findings underscore the necessity for a considerably higher tax rate to stimulate pollution reduction in order to meet the desired emission targets.

Assessing the costs of GHG emissions of multi-product agricultural systems in Vietnam

Besides a vital sector of the economy, agriculture is a primary source of greenhouse gas (GHG) emissions. The present paper investigates the impact of carbon tax policy on Vietnamese agriculture by focusing on multi-product systems such as rice, livestock, and aquaculture, traditionally called the Vuon (Garden)–Ao (Pond)–Chuong (livestock pen) system (VAC). In it, farmers use garden, pond, and pen by-products as fertilizer and feed. We use shadow prices and Morishima substitution elasticities as greenhouse gas emissions indicators, estimated with directional output distance function. Farmers in the Mekong Delta region are found to be technologically less efficient than in other regions of Vietnam, though the shadow prices of GHG emissions are lower there too. This indicates that farmers in the Mekong Delta, generally concentrating either on livestock or aquaculture, have greater potential for reducing GHG emissions by way of improvements in technical efficiency than do those in other regions. However, Morishima elasticity estimates show that policy impacts diminish more quickly in the Mekong than elswhere. We suggest the Vietnamese government encourage Mekong Delta farmers to employ technologically more efficient methods or shift to more balanced farming to reduce the shadow price of GHG emissions, encouraging more efficient emissions reduction.

Distance function approaches for efficiency analysis of organic production units: a critical review

Objectives: This review aims to make a comprehensive synthesis of distance function methods for the efficiency analysis of organic production units. Methodology and Results: The study reviewed and summarized the different approaches of distance functions applied in organic farming systems to assess performance. Original articles covering ten years, from 2010 to 2020 were identified through keyword searching using web search engines. After careful reading of the abstracts, 20 papers were finally retained. The selected papers were categorized based on study purpose and findings. Results showed a gap between the development of distance function methods and their usage in organic farming efficiency analysis. Four distance function methods were identified, and the most used in organic farming efficiency analysis were output distance function (40%) and directional output distance function (25%). Conclusion and application of findings: Results indicate that distance functions are powerful tools in modelling multi-input and multi-output production technology for assessing organic farming efficiency. Future research should focus on these methods to deepen their understanding and applications. Keywords: Distance function, efficiency analysis, literature review, organic farming

Environmental efficiency of wine grape production in Mendoza, Argentina

The natural characteristics are a valuable asset for the production of wine grapes, but the availability of quality water and the composition of the soil are decisive in semi-arid areas. The province of Mendoza is a prestigious region for the production of wine that is going through a period of water scarcity, which implies a greater use of groundwater that could compromise the availability of resources and trigger salinity levels. This paper evaluates the environmental performance of winegrowers in the face of a productive threat such as the saline content in irrigation water. We estimate environmental efficiency based on a directional output distance function using the salinity hazard of irrigation as an undesirable output. The average environmental performance is 0.88 and it can be reduced by participating in producer groups, receiving technical assistance, increasing the density of the vineyard, and receiving an energy subsidy for irrigation. In addition, the shadow price of the salinity hazard reveals that higher salinity content in irrigation water and soil characteristics cause excessive irrigation at the expense of environmental and economic performance. Furthermore, the pre-existing market price relationship, water balance and district characteristics can deflate shadow prices, but only vineyards with joint water sources can benefit from this.

Improving electricity supply reliability in China: Cost and incentive regulation

Electricity regulators pay attention to electricity supply reliability in many countries, considering that power interruption can cause damage and destruction as modern societies increasingly rely on electricity. Since 2020, China's regulators have designed incentive schemes to encourage power grid firms to improve electricity supply reliability in some regions. An effective incentive scheme requires that regulators identify the cost of reliability improvement and match it to the incentive scheme. Using provincial panel data for 2012–2018, this paper employs the directional output distance function approach to estimate the shadow price of power interruptions in China's grid system—that is, the marginal cost of electricity supply reliability improvements. Results indicate that the shadow price of 1 min of interruption per customer ranged from 59.66 to 74.65 RMB in 2012–2018. This estimation also shows that the shadow price of 1 min of interruption varies substantially among provincial grid utilities. The marginal cost of improving electricity supply reliability in China's grid system is lower than in developed countries. Since the incentives far from cover the cost of improvement, the schemes implemented in some Chinese regions cannot provide incentives for quality improvements.

Developing effective CO2 and SO2 mitigation strategy based on marginal abatement costs of coal-fired power plants in China

This study proposes a novel analysis framework to investigate the CO2 and SO2 emission efficiency, emission reduction potential, and marginal abatement cost (MAC) of 316 coal-fired power plants in China. The comprehensive analysis framework is based on the combined approach of utilizing the directional output distance function (DODF) and parametric linear programming (PLP). The average emission efficiencies of CO2 and SO2 were 0.48 and 0.61, respectively, which indicates that China’s coal-fired power plants have a large potential to reduce CO2 and SO2 emissions, on average by 52% and 39%, respectively. In 2010, the average CO2 and SO2 emissions reduction potential for the 316 investigated power plants were 1,517 kt and 3,773 t, respectively. The average MAC prices for CO2 and SO2 were estimated to be 598 yuan/tonne and 22,401 yuan/tonne, respectively, indicating that the reduction of such emissions is very expensive. Furthermore, I formulated an optimization problem for maximizing CO2 and SO2 emission reductions under the governmental budget constraint. Solving this optimization problem yielded the total cost for the maximum reductions of CO2 and SO2 emissions, the maximum possible reductions for CO2 and SO2 emissions for each allocated budget scale, and the optimal budget allocation for each power plant at a given budget scale. I finally suggest effective mitigation strategies for CO2 and SO2 emissions generated from China’s coal-fired power plants.

A new optimisation approach to assess optimal asset allocation in European non-life insurance companies

This study addresses the allocation of optimal assets in non-life insurance companies' environment with a new vision. Most previous studies are based on the maximisation of the utility function. However, in this paper, we focused on the maximisation of technical efficiency (TE). In order to validate our objective, we select a set of European non-life insurance companies (ENIC) over the period 2008-2014. In the first step, we estimate the production function characterised by the directional output distance function (DODF). In the second one, we use two metaheuristics (PSO and GA) to assess the optimal asset allocation (OAA). The empirical results show that the proportion allocated to the 'alternative investment with high-risk high-return' (AIhh) is on average lower than those found in previous studies. However, the percentage allocated to the 'risk-free assets' (RFA) is on average different from zero. This can be explained by the attention given to the competitiveness, survival and long-term profitability respecting the maximisation of TE. So, any insurance company must give more attention to the presence of different stakeholders and resolve the conflicts of interest between them.

A New Optimization Approach to Assess Optimal Asset Allocation in European Non-Life Insurance companies

This study addresses the allocation of optimal assets in non-life insurance companies' environment with a new vision. Most previous studies are based on the maximisation of the utility function. However, in this paper, we focused on the maximisation of technical efficiency (TE). In order to validate our objective, we select a set of European non-life insurance companies (ENIC) over the period 2008-2014. In the first step, we estimate the production function characterised by the directional output distance function (DODF). In the second one, we use two metaheuristics (PSO and GA) to assess the optimal asset allocation (OAA). The empirical results show that the proportion allocated to the 'alternative investment with high-risk high-return' (AIhh) is on average lower than those found in previous studies. However, the percentage allocated to the 'risk-free assets' (RFA) is on average different from zero. This can be explained by the attention given to the competitiveness, survival and long-term profitability respecting the maximisation of TE. So, any insurance company must give more attention to the presence of different stakeholders and resolve the conflicts of interest between them.

Shadow Prices of Non-performing Loans for Chinese Banks in the Post-Crisis Era

This paper examines how non-performing loans (NPLs) affect Chinese commercial banks before, during, and after the 2008 global financial crisis as well as the subsequent 2008--2010 stimulus. By accounting for NPLs as undesirable outputs, banks' technical efficiency is estimated using directional output distance function. The envelop theorem is applied to calculate the shadow price of NPLs. The shadow price of NPLs is the opportunity cost of reducing NPLs by one Chinese yuan. Empirical results show that the four major state-owned banks are the least technically efficient while foreign banks are the most efficient over the sample period 2007-2014. I also find that the crisis has a negative effect on banks' technical efficiency while the stimulus initially has a positive effect on four major stateowned commercial banks and joint-stock commercial banks, but later shows a negative effect with a higher default ratio and lower efficiency. Finally, the data show that the stimulus has greatly increased the shadow price of NPLs for four major state-owned commercial banks. Starting in 2011, the shadow prices of NPLs for four major state-owned commercial banks are much higher than all other bank types.

Technical inefficiency, abatement cost and substitutability of industrial water pollutants in Jiangsu Province, China

Environmental pollution, caused by industrial wastewater discharge, restricts the transformation of China’s industrial economy. In terms of its gross industrial product, Jiangsu Province has always been among the top-ranking areas of China. To ensure the green and sustainable development of Jiangsu’s industry, it is imperative to formulate specific strategies toward the reduction of industrial water pollutant emissions. First, by the parameter quadratic directional output distance function and the shadow price model, this paper estimates the technical inefficiency and marginal abatement costs of industrial chemical oxygen demand (COD) and ammonia nitrogen (NH3–N) in Jiangsu Province between 2006 and 2017. Second, spatial and temporal distributions as well as the dynamic evolution tendencies of technical inefficiency, and abatement costs of industrial COD and NH3–N are analyzed. Third, the Morishima elasticity model is utilized to measure the output substitution elasticity of industrial COD and NH3–N for Jiangsu. The results show that the technical inefficiency of industrial water pollutants in Jiangsu Province followed a decreasing trend from 2006 to 2017; moreover, significant differences were found in technical inefficiency among different regions. Over time, the regional disparity followed a polarization trend. For Jiangsu Province, the marginal abatement cost of industrial COD increased rapidly and continuously, while the marginal abatement cost of industrial NH3–N showed fluctuating and marginal growth from 2006 to 2017. The marginal abatement cost of industrial COD in southern Jiangsu exceeded that of other regions; however, the marginal abatement cost of industrial NH3–N in northern Jiangsu was highest. Additionally, the negative sign of the Morishima output elasticity for Jiangsu indicates a “trade-off” relationship between gross industrial output and industrial water pollutants. Finally, according to the empirical results, corresponding policy recommendations are proposed.

Shadow Prices of Non-performing Loans for Chinese Banks in the Post-Crisis Era

This paper examines how non-performing loans (NPLs) affect Chinese commercial banks before, during, and after the 2008 global financial crisis as well as the subsequent 2008—2010 stimulus. By accounting for NPLs as undesirable outputs, banks' technical efficiency is estimated using directional output distance function. The envelop theorem is applied to calculate the shadow price of NPLs. The shadow price of NPLs is the opportunity cost of reducing NPLs by one Chinese yuan. Empirical results show that the four major state-owned banks are the least technically efficient while foreign banks are the most efficient over the sample period 2007—2014. I also find that the crisis has a negative effect on banks' technical efficiency while the stimulus initially has a positive effect on four major state-owned commercial banks and joint-stock commercial banks, but later shows a negative effect with a higher default ratio and lower efficiency. Finally, the data show that the stimulus has greatly increased the shadow price of NPLs for four major state-owned commercial banks. Starting in 2011, the shadow prices of NPLs for four major state-owned commercial banks are much higher than all other bank types.

Imposing Regularity Conditions to Measure Banks’ Productivity Changes in Taiwan Using a Stochastic Approach

This paper develops a stochastic approach to impose regularity properties on a directional output distance function (DODF) and an output distance function, which can be estimated by maximum likelihood. We use the resulting parameter estimates to evaluate efficiency and total factor productivity (TFP) growth for Taiwan’s commercial banks over the period 2002–2015 and claim that the failure of considering the regularity restrictions and the exclusion of undesirables lead to miscalculated efficiency measures and productivity gains. The outcomes from the regularity-constrained DODF reveal that almost all data-points satisfy the regularity properties, that the managerial abilities of the banks improve after the subprime crisis of 2007, and that the sample banks’ TFP grow at an average rate of 1.93% per annum, whereby technical change is the driving force. However, our estimates show downward trends in the growth rate of TFP and technical change.

Measuring the capacity utilization of the 48 largest iron and steel enterprises in China

This paper aims to investigate the capacity utilization (CU) of selected large Chinese iron and steel enterprises by using the data envelopment analysis (DEA) approach. In this paper, we first propose a DEA model with an unrestricted capacity directional output distance function by incorporating two joint cost disposability relations and differentiating between non-emission-causing inputs and emission-causing inputs. Second, we define the status of decision-making units (DMUs) with excess capacity and design a method to identify insufficient variable inputs. We use a group of 48 largest Chinese iron and steel enterprises as our sample to investigate their performance in terms of CU indicator. The main findings are summarised and can be used to support the corresponding policymaking for the managers of both government and enterprises.

Adjusting productivity measures for CO2 emissions control: Evidence from the provincial thermal power sector in China

Abstract We examine productivity changes by the types of environmental regulations used to control CO2 emissions in the provincial, thermal power sector of China from 2009 to 2016. We derive a Tornqvist-type productivity index in which CO2 emissions are undesirable outputs. The shadow price of CO2, required for calculating the index, is estimated based on the duality between a revenue and a directional output distance function. Productivity changes are measured using both estimated shadow prices and the actual trading prices of CO2 in six pilot emissions trading systems. We find that productivity measurement is highly dependent on the choice of CO2 prices. We also investigate the impact of emission intensity and emissions per se on productivity measurement. We show that productivity measurement depends on the choice of environmental standard.

Tradeoffs between agricultural production and ecosystem services: A case study in Zhangye, Northwest China

Humans have increasingly intervened in the nature to advance socioeconomic development at the expense of ecosystem services. Tradeoffs between ecosystem services and socioeconomic development are inevitable and should be considered in sustainable ecosystem management. This is no exception in Zhangye where intensive agricultural activities have significantly affected its ecological conditions. Thus, this study evaluated the tradeoffs between agricultural production and key ecosystem services along with their spatial distributions at the watershed level in Zhangye based on multisource observation data. The key ecosystem services, including net primary productivity (NPP), water yield, and soil conservation, were evaluated for the years 2000, 2010, and 2015 using remote sensing data and the InVEST model. The Morishima elasticity of substitution (MES) between these ecosystem services and agricultural production were then estimated by applying a quadratic directional output distance function, and mapped to determine the tradeoffs. The results showed that the average NPP and annual water yield respectively increased by 22% and 24%, while annual soil conservation decreased by 22% during 2000–2015. The average MES values for agricultural production with NPP, water yield, and soil conservation were 0.14, −0.69, and −0.56, respectively. This indicated the existence of a synergetic relationship between agricultural production and NPP as well as tradeoff relationships between agricultural production and water yield/soil conservation. Differences in the spatial patterns of the relationships between agricultural production and these ecosystem services were observed. Significant tradeoff relationships were observed for agricultural production with water yield and soil conservation in the upper reach of Zhangye. It indicated that increasing agricultural production would be at the cost of decreased water yield and soil conservation, especially in the upper reach area. The quantification and spatial pattern determinations of tradeoffs between ecosystem services and agricultural production is useful for the development of regional ecological conservation policy and sustainable ecosystem management.

Shadow prices of non-performing loans and the global financial crisis

PurposeThis paper aims to determine the opportunity cost borne by US commercial banks to reduce non-performing loans (NPLs) by one unit within the global financial crisis framework.Design/methodology/approachTo achieve this aim, the authors use the directional output distance function to estimate the technical efficiency while considering NPLs as undesirable output. Then, they estimate the shadow prices of NPLs by using the envelope theorem and solving the revenue function.FindingsThe results indicate that medium-sized banks are the most efficient, while small banks are the most inefficient ones. Moreover, the shadow prices of NPLs of large banks are higher than those of small and medium-sized banks. This implies a more elevated cost when lessening bad loans in large banks. This is more prominent during the crisis given that the shadow prices of NPLs of large banks have risen sharply over that period.Practical implicationsShadow prices have important managerial implications given that they display the amounts of required reduced revenues to lessen NPLs. Accordingly, banks’ managers are called to reduce these loans by paying more attention when choosing their customers.Originality/valueWith the absence of an observable market price for bad loans in financial literature, the shadow price notion offers an adequate measure to evaluate them. To the best of authors’ knowledge, this is the first study that provides an estimation of the shadow price of NPLs in the US banking sector.