Estimating the shadow prices of SO2 and NOx for U.S. coal power plants: A convex nonparametric least squares approach

Weak disposability between outputs and pollutants, defined as a simultaneous proportional reduction of both outputs and pollutants, assumes that pollutants are byproducts of the output generation process and that a firm can “freely dispose” of both by scaling down production levels, leaving some inputs idle. Based on the production axioms of monotonicity, convexity and weak disposability, we formulate a convex nonparametric least squares (CNLS) quadratic optimization problem to estimate a frontier production function assuming either a deterministic disturbance term consisting only of inefficiency, or a composite disturbance term composed of both inefficiency and noise. The suggested methodology extends the stochastic semi-nonparametric envelopment of data (StoNED) described in Kuosmanen and Kortelainen (2011). Applying the method to estimate the shadow prices of SO2 and NOx generated by U.S. coal power plants, we conclude that the weak disposability StoNED method provides more consistent estimates of market prices.

► Develops methodology to estimate shadow prices for SO2 and NOx in the U.S. coal power plants. ► Extends CNLS and StoNED methods to include the weak disposability assumption. ► Estimates the range of SO2 and NOx shadow prices as 201-343 $/ton and 409-1352 $/ton. ► StoNED method provides more accurate estimates of shadow prices than deterministic frontier.