This study contributes to three branches of literature: index number theory, the modeling of environmental production technologies, and index decomposition analysis. The first part of the study begins by analyzing a previous adjustment made to a popular graph space index, which is used to compute input-output efficiency scores, and shows that this adjustment fails to correct two serious flaws it was intended to rectify - satisfaction of an indication and weak monotonicity condition. The failure arises at the boundary of output space when zeros arise frequently in the data. We propose an alternative formulation to correct for these deficiencies and implement the proposed modification in two different empirical applications.
Next, we identify a conceptual flaw regarding tradeoffs between inputs, outputs, and pollutants when one production relation is used to model the joint production of pollution-generating technologies. We propose a superior modeling tactic to correct for the tradeoff implications when using only one implicit production relation. Using multiple production relations to capture intended and unintended production, and defining the reduced form technology as the intersection between these two production sets, we introduce the "by-production" technology. This novel formulation has direct implications on DEA estimation, which we derive and utilize in an application of efficiency measurement. Moreover, we show that constructing efficiency scores for "by-production" technologies isn't straight forward. We distinguish between efficiency in intended and unintended production, show that some traditional indexes are not appropriate for applications involving "by-production" technologies, and propose a modification of a previous index that has superior properties and decomposes into productive and environmental efficiency.
Lastly, this study applies the by-production modeling tactic developed earlier to reconsider index decomposition results previously derived under different assumptions regarding the nature of pollution-generating technologies. The application examines factors related to variations in electric power plant emissions through an index decomposition analysis and shows, in general, that previous results derived using the more primitive technological assumption of weak disposability and null-jointness are incongruent with the results derived under by-production. We conclude the final portion of the study by analyzing energy firm responses to the 1990 Amendment to the Clean Air Act Amendment.
