Nonparametric measures of efficiency in the presence of undesirable outputs: a by-production approach

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. Joint disposability is assumed between the bad output and the polluting input, rather than weak disposability and null jointness between the good and bad outputs. Moreover, we set up an integrated DEA optimization problem over the intersection of these two subtechnologies 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 \(\hbox {CO}_{2}\) emission is the bad output. We then utilize our DEA results to compute opportunity costs of a targeted reduction in \(\hbox {CO}_{2}\) emission in terms of required dollar amounts of reduction in per capita GDP for the individual countries in selected years.