Substitutability among undesirable outputs

Abstract

In recent years, economists have started to move beyond calculating regulatory effects on a pollutant-by-pollutant basis since their interaction is important. In this study, we take up this issue. To allow for joint production of multiple pollutants and marketable output, we specify our technology using a directional distance function. This allows us to treat pollutants as joint outputs, yet accounts for their ‘undesirability’. We estimate the distance function for a sample of coal-fired electric power plants from 1985 to 1998, which includes the first 4 years of Phase I of the Clean Air Act Amendments of 1990. We focus on the interaction between SO₂ and NO _x , as they became more highly regulated and estimate shadow prices of the pollutants and the Morishima elasticity of transformation between two pollutants, NO _x and SO₂, as well as with respect to the desirable output, kilowatt-hours of electricity. As expected, we find that power plants increase NO _x emissions as they decrease SO₂, i.e. they are substitutes.

Acknowledgements

The authors thank the participants at the North American Productivity Workshop (New York University on 28 June 2006) for their comments on an earlier draft of this article. The author also thank Curtis Carlson for providing his CS and employment data. All views expressed in this study are those of the authors and do not reflect the opinion of the US EPA.

Notes

¹ Montero (2001) and Schmieman et al. (2002) developed theoretical models of joint abatement.

² While it is possible to use these elasticities to calculate welfare gains associated with allowing electric power plants to substitute between SO₂ and NO _x emissions, we focus our analysis on modelling the joint production technology.

³ All appendices and data are available from the corresponding author upon request.

⁴ For a more in-depth discussion of this topic, see Färe et al. (2005).

⁵ This function is a variation of Luenberger's (1992, 1995) shortage function.

⁶ Chambers (1998) proposed using a quadratic form to parameterize the directional distance function, while Tran and Smith (1983) used a translog function to analyse the joint production of four undesirable outputs. While the parameters of the translog function can be restricted to satisfy a homogeneity property, the directional distance function has the translation property. A quadratic form can be restricted to satisfy the translation property, while the translog function cannot be restricted to satisfy the translation property.

⁷ The estimates for the two cases were not significantly different. Results for both are available in Appendix B.

⁸ Because depreciation is not modelled when calculating the capital stock, vintage effects are not captured by the capital stock data used to estimate the production frontiers employed to derive the elasticities of transformation. Another potential source of error in the results is associated with treating all coal consumed as having the same quality (i.e. sulphur content). Hence, as currently specified, our model does not account for fuel switching as a strategy to reduce SO₂ emissions.

⁹ In 1995 the US Environmental Protection Agency (EPA) initiated a programme to measure SO₂ emissions. In order to maintain consistency with pre-1995 emission data, we continue to employ the US DOE engineering estimates of SO₂ emissions for 1995–1998.

¹⁰ It is possible to expand our sample to include power plants whose primary fuel is oil or natural gas. This can be accomplished in one of two ways. First, the plants can be added to the sample with their heat input listed as Btu's in the same manner in which we treat the coal-fired power plants in our sample. The drawback in this strategy is that it treats all power plants, regardless of fuel, as having identical production technologies. A second approach consists of modelling separate technologies for coal, natural gas and oil power plants, and calculating separate elasticities of transformation for each of the three production technologies. This approach would permit some insights into the emission consequences of switching from coal-fired power plants to either natural gas or oil power plants.

¹¹ Appendix A contains additional information about the data.

¹² The index value of SO₂ for an observation is its SO₂ production normalized by the mean SO₂ production of all observations.

¹³ We experienced convergence problems for the half-normal distributions when attempting to estimate the directional distance function on a year-by-year basis. All estimates were calculated using Stata.

¹⁴ The exception is when the directional distance function is estimated for 1995–1996 with an inefficiency term that follows an exponential distribution.