Nonparametric Measures of Efficiency in the Presence of Undesirable Outputs: A By-production Approach with Weak Disposability

In empirical research on productivity measurement adjusted for undesirable outputs on the side, the good and the bad outcomes are treated as joint-products of the underlying production process. In the present paper, following Murty, Russell, and Levkoff, we conceptualize the good output as technologically separable from the bad output. Moreover, we set up an integrated DEA optimization problem over the intersection of these two sub-technologies to measure the efficiency of a firm that produces a bad output alongside the good output. In an empirical illustration of our methodology, we use country level data for an unbalanced panel of 64 countries over the years 1986 through 2011 where per capita GDP is the good and per capita CO2 emission is the bad output. Weak disposability and null jointness is assumed between the bad output and fuel, the polluting input, rather than the good and bad outputs. We then utilize our DEA results to compute opportunity costs of a targeted reduction in CO2 emission in terms of required dollar amounts of reduction in per capita GDP for the individual countries in selected years.