Shadow Prices and Marginal Abatement Costs: Convex Quantile Regression Approach

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Marginal abatement cost (MAC) is a critically important concept for efficient environmental policy and management. In this paper we argue that most empirical studies using frontier estimation methods such as data envelopment analysis (DEA) over-estimate MACs. The first methodological contribution of this paper is to clarify the conceptual distinction between the shadow price and MAC in order to analyze three sources of upward bias due to the limited set of abatement options, inefficiency, and noisy data. Our second methodological contribution is to develop a novel MAC estimation approach based on convex quantile regression. Compared to the traditional methods, convex quantile regression is more robust to the choice of the direction vector, random noise, and heteroscedasticity. Empirical application to the U.S. electric power plants demonstrates that the upward bias of DEA may be a serious problem in real-world applications.
Original languageEnglish
Pages (from-to)666-675
Number of pages10
JournalEuropean Journal of Operational Research
Issue number2
Early online date24 Jul 2020
Publication statusPublished - 1 Mar 2021
MoE publication typeA1 Journal article-refereed


  • Data envelopment analysis
  • Environmental performance
  • Nonparametric regression
  • Production theory
  • Undesirable outputs


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