Estimating Shadow Prices of Bad Outputs under Heterogeneous Input Quality
Abstract: In recent decades, there has been an increasing concern for estimation of shadow prices of bad outputs which are produced jointly with good outputs. This measure allow for quantifying pollution abatement costs that can be used to guide regulation instruments such as emission trading schemes or fines. Precise estimates are therefore important to achieve socially optimal allocations. A majority of previous studies, e.g. Färe et al. (1993), Coggins and Swinton (1996) and Reig-Martinez et al. (2001), calculate shadow prices on the boundary of the production possibility set. However, Lee et al (2002) pointed out that, even if the same technology is applied by all firms, marginal abatement costs are likely to depend on firm efficiency. Our study does also recognize that shadow prices calculated for firms located below the best practice frontier are likely to differ from those calculated on the frontier. But, compared to previous studies of bad outputs, we emphasize that the best-practice frontier may not be achievable for all producers due to heterogeneous input quality i.e., differences in input quality are likely to contribute to the existence of multiple production frontiers in a given period. A wide range of shadow prices is then made possible as quality-induced frontier-shifts are likely to be biased. One may particularly expect that improved input quality will lower the costs of reducing bad outputs. We apply a framework for modeling polluting technologies developed by Färe et al (2005). A distinct characteristic of this framework is the assumptions of null-jointness and weak disposability of good and bad outputs. Hyperbolic distance functions with and without input quality indicators are used to derive estimates of production inefficiency and shadow prices. Comparing efficiency and shadow prices where quality is taken into account to estimates where quality is neglected allows us to show that input characteristics are important determinants of marginal abatement costs. The problem is illustrated with a panel data from the Norwegian aquaculture industry, where fish escapes from the farms is considered as a bad output. The effect of escapees on the stock of wild fish has been thoroughly debated in the biological literature and several studies indicate negative consequences from farmed and wild fish interactions, e.g. through genetic contamination and resource competition. The panel data covers the years 1994-2007 and includes reports on the level of escapes and proxies for input quality, among others. Preliminary results indicate that technical efficiency of the mean firm is underestimated when heterogeneity in input quality is not considered, implying existence of quality-dependent production frontiers. Accordingly, shadow prices for the bad output varies by quality levels and, as expected, farms with high quality inputs are found to have lower shadow prices. This indicates that input quality matters for the distribution of abatement costs and should be taken into account when imposing industry regulations.
Publisert i North American Productivity Workshop 2010, 2010
Les artikkelen her