Shadow Price Approach Research Articles

Thermodynamic analysis and operation investigation of a cross-border integrated energy system based on steam Carnot battery

With the booming development of industrial parks in southern Belt and Road (B&R) countries, the demand for energy carriers such as electricity and steam grows rapidly. One key aspect of B&R initiative is to promote cross-border energy cooperation in these countries. However, this region has abundant renewable energy resources, while the electricity and steam supply required in industrial processes is insufficient. This paper proposes a cross-border integrated energy system (IES) based on Carnot battery technology. A steam Carnot battery (SCB) is designed based on phase change material with water/steam as the working fluid. This paper establishes thermodynamic model of the proposed IES and evaluates its performance. Based on a field investigation in a real cross-border China-Myanmar industrial park, this paper designs the corresponding IES and studies SCB’s impact on IES daily operation. A baseline IES having an electric battery is also proposed to facilitate the comparison. The result shows that IES based on SCB reduces 28.57% operating cost, 43.49% carbon emission, and 16.49% city grid electricity consumption compared with the baseline. This means electro-thermal complementarity is an essential feature of SCB in IES. Furthermore, shadow price approach is adopted to analyze the impact of SCB in IES with the development of the industrial park. Renewable electricity output and peak-valley ratio have high shadow prices. The operating cost of IES based on SCB is highly affected by the percentage of renewable energy introduction and pricing market, making it a promising choice in this region known for redundant hydropower. Although electricity storage capacity and SCB’s roundtrip efficiency have less impact on cost reduction, they can reduce carbon emission for IES. This study provides a new perspective for constructing the energy system in B&R initiative areas.

Monetary valuation of unsorted waste: A shadow price approach

Improving the management of municipal solid waste (MSW) is fundamental to promote circular economy and sustainability. Unsorted waste involves negative environmental impacts which often are ignored in economic feasibility studies due to its difficult valuation. In this study the shadow price of unsorted waste using the directional distance function was estimated. This methodological approach also allowed us to compute eco-efficiency scores of a set of municipalities in the provision of MSW services. The empirical application focused on a sample of 119 Chilean municipalities. The results showed that the average shadow price of unsorted waste was 297.66 €/ton which means that the environmental cost of left waste as unsorted was 297.66 € per ton. A regression tree model illustrated that population density, tourism intensity and the generation of waste per capita significantly influenced the shadow price of unsorted waste. Moreover, it was illustrated that Chilean municipalities were very inefficient in the management of MSW since the average eco-efficiency score was 0.272. The findings from this study reveal that additional and alternative policies should be adopted to improve the management of MSW and increase its recycling rate.

JUE Insight: Measuring the Stringency of Land Use Regulation Using a Shadow Price Approach

I propose a shadow price approach to measuring the stringency of land use regulation. A regulation is considered more restrictive if the land developer is willing to pay a larger amount for a marginal relaxation of the regulation. I show that existing theory-based measures of land use stringency are either equivalents or variations of this shadow price measure. Using data from China, I demonstrate that it is possible to compare the stringency of two kinds of land use regulation, a key advantage of this shadow price approach.

A shadow price approach examining service quality in a heavily captive U.S. freight transportation market: The case of grain transport

The aim of this study is to examine modal usage for shippers with limited transportation options to assess rail and truck quality of service. While service quality is an important consideration in shippers' mode choice decisions, freight studies often assume that shippers minimize total transportation costs subject to shipping rates. We test the cost minimization hypothesis using data on wheat shipments for individual grain elevators in the U.S. Great Plains where shippers are limited to rail and truck services with no direct access to navigable waterways, and find that shippers use a higher share of rail than they would if shipping rates alone determined their use of rail. This observation, in tandem with recent shipper surveys showing higher than expected ratings of service quality, suggests that shippers’ modal choice of rail likely stems from a perception of higher quality of service provision. Moreover, this suggests that railroads have provided high service quality despite perpetual captivity concerns. Our results support the idea that even in markets with limited intermodal competition, other types of competition, including geographic, product, and intramodal competition are sufficient to compel railroads to provide a level of service that meets or exceeds expectations.

Do marginal abatement costs matter for improving air quality? Evidence from China's major cities

This paper performs a two-stage analysis to investigate the trade-off between economic growth and pollution abatement. We first estimate the marginal abatement costs (MACs) of CO2, SO2, NOx, and particulate matter (PM) for 30 major Chinese cities from 2006 to 2015 via the shadow price approach under the directional distance function framework. The results show that the optimal directional vector is (11, −1, −1, −1, −1), which may indicate that increasing economic output is much more important than reducing the above undesirable outputs in these cities. Then, having examined the relationship between MACs and air quality by panel regression and dose-response analyses, we found ranges of positive and statistically significant treatment effects for the MACs of SO2 and PM on their respective concentrations. The overall results suggest that government officials in these cities may give precedence to economic growth over environmental protection.

The cost of reducing unplanned water supply interruptions: A parametric shadow price approach

Water companies are responsible for supplying water to customers 24 h per day. However, due to extreme natural events and/or anthropogenic actions, water companies suffer from unplanned water supply interruptions, which directly impact customers and incur expenses by the companies. In this study, for the first time, we estimated the shadow price (or implicit cost) of unplanned water supply interruptions using stochastic frontier techniques for a sample of 21 Chilean water companies over the period of 2007–2017. The results indicate that, on average, the Chilean water company needed to spend an extra 2.547€ in operating expenditures to avoid 1 h of interruption. Average shadow price of unplanned water supply interruptions was higher for concessionary and full private companies than public ones. These findings demonstrate that the regulatory agency may need to promote effective policies and incentives to ensure and improve the continuity of the water supply. This is very relevant to the Chilean water industry, where there is an ongoing policy debate regarding the use of penalties and compensations as an incentive to avoid unplanned water supply interruptions.

Efficiency and marginal abatement cost of PM2.5 in China: A parametric approach

This study aims to measure China's environmental efficiency and marginal abatement cost under PM2.5 restrictions. Because China's air pollution, especially PM2.5 pollution, is so serious that it forms an urgent policy issue affecting China's sustainable economic growth, this topic is important. However, few efforts have been made to explore the cost, potential and optimal plan of reducing emissions to control PM2.5 in China. To apply a parametric non-radial directional distance shadow price approach, panel data from 73 key monitoring cities in China from 2004 to 2016 are used to measure the PM2.5 environmental efficiency and marginal abatement cost. The results show that PM2.5 pollution in China presents regional and spatial correlations. The Beijing-Tianjin-Hebei region has more severe haze pollution than the Yangtze River Delta and the Pearl River Delta, resulting in the largest potential for emission reduction and the lowest marginal reduction cost. Overall, the average PM2.5 reduction potential for all cities is 42.6% without considering external sources and 40.4% when considering external sources. The average abatement cost of PM2.5 reaches 0.6308 billion yuan/μg·m3 when excluding external sources; when considering external sources, the average reduction cost in PM2.5 is 0.6378 billion yuan/μg·m3. Policymakers must be notified that PM2.5 pollution and other air emissions, such as CO2 and SO2 emissions, are very different from each other. PM2.5 pollution is spatially diffusive and exhibits regional heterogeneity. Therefore, policymakers must implement different policies in different cities.

Merton’s portfolio problem including market frictions: A closed-form formula supporting the shadow price approach

This paper formulates a portfolio optimization in a friction market as a suitable stochastic control problem with hyperbolic absolute risk aversion utility functions under a specific functional form of the amount of wealth invested in the risky asset inspired by the Merton optimal dynamics. The state variable is the amount of wealth invested in the risky asset, while the control variable is the share rate. This formulation has two advantages. First, it provides a portfolio where the optimality is obtained by minimizing the probability of large changes in the portfolio composition with consequently low frictions, while allowing for an explicit solution to the optimal control problem. Second, with this formulation, it can be proven that this optimal solution is the optimal solution of the frictionless Merton problem for corrected price dynamics. The corrected dynamics shows that the market friction increases the risk premium by an additional term that is an elementary function of the risk associated with the market frictions, as well the price of the risk, which also depends on the risk aversion of the investor. In addition, the corrected dynamics supports the existence of a shadow price in friction markets as already shown in Kallsen and Muhle-Karbe (2010). Finally, an empirical analysis to assess the model performance is illustrated on five-minute data of four major traded stocks, three market indexes, and four exchange rates including the Bitcoin/USD rate.

Marginal abatement cost of agricultural carbon emissions in China: 1993-2015

PurposeThe purpose of this paper is to estimate shadow prices of agricultural carbon emissions produced by agricultural inputs, rice paddy and burning crop residue, and to explore the impact of cropping pattern on marginal abatement cost (MAC).Design/methodology/approachThe shadow price of agricultural carbon emissions is estimated by applying directional distance function and non-parametric methods.FindingsThe estimated shadow price of agricultural carbon emissions ranges from 6.78 to 557.83 yuan/ton, and the average value is 62.50 yuan/ton (or $10.18/ton). The MAC value varies in different provinces and years. The regional difference of MAC shows a decreasing trend during the investigation period. Cropping pattern shows a significant negative impact on agricultural MAC. A 1 percent decrease of rice proportion leads to a 0.31 percent increase in MAC value. This implies that the higher the proportion of rice is, the lower the economic cost to reduce agricultural carbon emissions would be.Practical implicationsIt is feasible to draw up appropriate mechanisms for the allocation of emission reduction responsibilities according to conditions in various regions, with emphasis on the local cropping patterns. There is a trade-off between reducing carbon emission and increasing crop yields.Originality/valueThis study calculates agricultural MAC by using the shadow price approach, taking agricultural carbon emissions as undesired environmental output. The study also provides a reference emission right price and provides guidance to make use of cropping structure adjustment and optimization for exploring the emission reduction strategy.

Pollution havens: international empirical evidence using a shadow price measure of climate policy stringency

Given the ambiguous empirical results of previous research, this paper tests whether support for a climate policy-induced pollution haven effect and the pollution haven hypothesis can be found. Unlike the majority of previous studies, the analysis is based on international panel data and includes several methodological novelties: By arguing that trade flows of dirty goods to less dirty sectors may also be influenced by changes in policy stringency, trade information on primary, secondary, and tertiary sectors are included. In order to clearly differentiate between dirty sectors and sectors with high pollution abatement costs, separate measures for pollution intensity and policy stringency are implemented. For the former, two intensities, namely the sectors’ carbon dioxide emission intensity and the emission relevant energy intensity, are used to identify dirty sectors. For the latter, an internationally comparable, sector-specific measure of climate policy stringency is derived by applying a shadow price approach. Potential endogeneity between climate policy stringency, trade openness and the trade balance is controlled for by employing a dynamic panel generalized method of moments estimator. The results provide evidence for a pollution haven effect that is also present for non-dirty sectors, i.e., a sector’s net imports rise in general if the sector faces an increase in climate policy stringency. Moreover, a stronger pollution haven effect regarding carbon dioxide intensive and emission relevant energy-intensive sectors is revealed. However, no support for the stronger pollution haven hypothesis can be found.

Efficiency evaluation in the presence of undesirable outputs: the most favorable shadow price approach

Undesirable outputs are generally by-products of producing desirable ones, and they can thus be reduced only with an accompanying reduction in the latter. To capture this notion, the shadow price of the undesirable output must be negative, as opposed to positive for the desirable output. Based on this condition, this paper proposes a data envelopment analysis model that allows the production units being evaluated to determine the shadow prices for both the desirable and undesirable outputs by themselves so that the measured efficiency score will achieve the highest possible level. The proposed model satisfies the assumption of weak disposability of outputs. It is also shown that it falls into one category of the directional distance function model that has been widely applied in modeling undesirable outputs. However, different from the conventional directional distance measures, the proposed model is able to provide efficiency measures in the range of zero and one for easy comparison among inefficient production units.

Reducing CO2 emissions from drinking water treatment plants: A shadow price approach

The water industry is currently facing the challenge to reduce its carbon footprint. Although the majority of previous studies have focused on wastewater treatment energy issues, a non-negligible quantity of energy is consumed in drinking water treatment plants (DWTPs). To develop environmental policies aimed to reduce CO2 emissions, it is essential to estimate the shadow price of CO2 because this can provide information about the marginal abatement cost of CO2. This paper computes the shadow price of CO2 for a sample of Chilean DWTPs using directional distance function estimation. The potential reduction of CO2 emissions for each DWTP is also calculated. Finally, applying a non-parametric hypothesis test, factors that affect CO2 shadow prices are investigated. The results indicated that the Chilean DWTPs evaluated have notable room to reduce CO2 emissions. Moreover, the average shadow price of CO2 for DWTPs is 5.7% of the drinking water price. The methodology and results of this study are of great interest for water companies and policy makers to introduce incentives for promoting the transition towards an urban water cycle with a low carbon footprint.

Estimating the environmental and resource costs of leakage in water distribution systems: A shadow price approach

Water scarcity is one of the main problems faced by many regions in the XXIst century. In this context, the need to reduce leakages from water distribution systems has gained almost universal acceptance. The concept of sustainable economic level of leakage (SELL) has been proposed to internalize the environmental and resource costs within economic level of leakage calculations. However, because these costs are not set by the market, they have not often been calculated. In this paper, the directional-distance function was used to estimate the shadow price of leakages as a proxy of their environmental and resource costs. This is a pioneering approach to the economic valuation of leakage externalities. An empirical application was carried out for the main Chilean water companies. The estimated results indicated that for 2014, the average shadow price of leakages was approximately 32% of the price of the water delivered. Moreover, as a sensitivity analysis, the shadow prices of the leakages were calculated from the perspective of the water companies' managers and the regulator. The methodology and findings of this study are essential for supporting the decision process of reducing leakage, contributing to the improvement of economic, social and environmental efficiency and sustainability of urban water supplies.

Measuring climate policy stringency: a shadow price approach

To assess the effect of environmental policy on production structures, trade structures, or foreign direct investment, a measure for the stringency of policy is necessary. Measures typically used in empirical studies share several disadvantages: they are not available on a sectoral basis to reflect concerns of industry competitiveness; they are not available for a wide range of countries to allow for international comparisons; or they are not broad enough to reflect the multidimensionality of environmental policy. This paper develops a thorough, internationally comparable, sector-specific measure of multidimensional climate policy stringency where a shadow price approach serves as a basis. The approach is applied to climate policy by determining sector-specific emission-relevant energy costs on the basis of the sectors’ usage of emission-relevant energy carriers and the carriers’ respective prices. The resulting shadow price estimates are heterogeneous and can be applied in future research to test for carbon leakage and pollution havens.

Estimating the cost of improving service quality in water supply: A shadow price approach for England and wales

Service quality to customers is an aspect that cannot be ignored in the performance assessment of water companies. Nowadays water regulators introduce awards or penalties to incentivize companies to improve service quality to customers when setting prices. In this study, the directional distance function is employed to estimate the shadow prices of variables indicating the lack of service quality to customers in the water industry i.e., written complaints, unplanned interruptions and properties below the reference level. To calculate the shadow price of each undesirable output for each water company, it is needed to ascribe a reference price for the desirable output which is the volume of water delivered. An empirical application is carried out for water companies in England and Wales. Hence, the shadow price of each undesirable output is expressed both as a percentage of the price of the desirable output and in pence per cubic meter of water delivered The estimated results indicate that on average, each additional written complaint that needs to be dealt with by the water company includes a service quality cost of 0.399p/m3. As expected, when looking at the other service quality variables which involve network repair or replacement, these values are considerably higher. On average, the water company must spend an extra 0.622p/m3 to prevent one unplanned interruption and 0.702p/m3 to avoid one water pressure below the reference level. The findings of this study are of great importance for regulated companies and regulators as it has been illustrated that improvements in the service quality in terms of customer service could be challenging and therefore ongoing investments will be required to address these issues.

Capturing the least costly way of reducing pollution: A shadow price approach

The production analysis literature is increasingly concerned with estimating marginal abatement costs. Yet, most studies do not emphasize the ways in which pollutants may be reduced and their costs, which makes them unable to identify the least costly compliance strategy. This paper utilizes the materials balance principle to relate pollution to the employment of material inputs. A production model which allows input and output substitution, downscaling of operations, pollution control, and emission permits purchases as compliance strategies is proposed, and the implications of joint and non-joint pollution controls for the trade-off between pollutants and desirable outputs are considered. Marginal abatement costs, reflecting the least costly way of compliance, are derived by exploiting the duality between the directional distance function and the profit function.

Carbon emission values in cost benefit analyses

New infrastructure projects may affect CO 2 emissions and, thus, cost benefit analyses for these projects require a value to apply for CO 2. This may be based on the marginal social cost of emissions or on the shadow price resulting from present and future policies. This paper argues that both approaches are necessary, but for cost benefit analysis of infrastructure projects the latter should be the primary tool. A series of complications arise when applying this principle in practice. These are discussed in the paper. Even if the complications make the implementation of a shadow price approach difficult, we argue that the approach still is preferable to a social cost approach.

Optimal portfolios of a small investor in a limit order market: a shadow price approach

We study Merton’s portfolio optimization problem in a limit order market. An investor trading in a limit order market has the choice between market orders that allow immediate transactions and limit orders that trade at more favorable prices but are executed only when another market participant places a corresponding market order. Assuming Poisson arrivals of market orders from other traders we use a shadow price approach, similar to Kallsen and Muhle-Karbe (Ann Appl Probab, forthcoming) for models with proportional transaction costs, to show that the optimal strategy consists of using market orders to keep the proportion of wealth invested in the risky asset within certain boundaries, similar to the result for proportional transaction costs, while within these boundaries limit orders are used to profit from the bid–ask spread. Although the given best-bid and best-ask price processes are geometric Brownian motions the resulting shadow price process possesses jumps.

Objective over-education and worker well-being: A shadow price approach

This paper examines, for a sample of Flemish school leavers, the relation between objective over-education and job satisfaction by applying a shadow price approach. We differentiate between direct effects of over-education and indirect effects via other job characteristics that are associated with over-education. Additional fixed-effects estimates are executed to account for individual heterogeneity. The utility consequences of over-education are found to be large and cannot be compensated by a reasonable wage increase at the start of the first employment. These outcomes suggest that, at labour-market entry, over-education is largely involuntary, and is likely to induce negative productivity costs. The negative consequences of over-education are also found to diminish with years of work experience.

Shadow Price Approach to Total Factor Productivity Measurement: With an Application to Finnish Grass-Silage Production

This paper explores an intermediate route between the Fisher and the Malmquist productivity indexes so as to minimize data requirements and assumptions about economic behavior of production units and their production technology. Assuming quantity data of inputs and outputs and the behavioral hypothesis of allocative efficiency, we calculate the exact value of the Fisher ideal productivity index using implicit shadow prices revealed by the choice of input–output mix. The approach is operationalized by means of a nonparametric data envelopment analysis (DEA) model. Empirical application to Finnish grass silage farms suggests that the Malmquist and the Fisher productivity indices yield similar results when averaged over firms, but there can be major differences in the results of the two approaches at the level of individual firms.