On estimating shadow prices of undesirable outputs with efficiency models: A literature review

Undesirable outputs (or bads) refer to the byproducts accompanied with desirable outputs (or goods) in a production process, e.g. sulfur dioxide and carbon dioxide in coal-fired power generation. The shadow price of undesirable output, which may be interpreted as the opportunity cost of abating one additional unit of undesirable output in terms of the loss of desirable output, could provide valuable reference information for policy analysis and making. A prevalent practice is to use the Shephard or directional distance function to derive the shadow price, which can be further calculated by parametric or nonparametric efficiency models. In application, earlier studies have estimated shadow prices at plant, sector and even economy levels. This study aims to conduct a systematic review of the studies on estimating shadow prices of undesirable outputs with efficiency models. We first introduce the methodological framework for deriving shadow prices as well as the nonparametric/parametric efficiency models for calculating their values. A systematic summary of over forty earlier studies in this field is then conducted, through which the key features of the existing studies are summarized and possible future research directions are identified.