R. Fare et al., DERIVATION OF SHADOW PRICES FOR UNDESIRABLE OUTPUTS - A DISTANCE FUNCTION-APPROACH, Review of economics and statistics, 75(2), 1993, pp. 374-380
Many production activities generate undesirable byproducts in conjunct
ion with the desirable outputs they produce. Pittman (1983) showed how
to adjust productivity calculations, and Fare et al. (1989) showed ho
w to adjust efficiency measures, in the presence of undesirable output
s. Here we show how to estimate output distance functions as frontiers
in order to generate shadow values of the undesirable outputs that ar
e required to make both types of adjustment. An empirical application
is provided.