Weak Disposability in Nonparametric Production Analysis with Undesirable Outputs

1. Weak Disposability in Nonparametric Production Analysis with Undesirable Outputs Timo Kuosmanen Wageningen University, The Netherlands 14th EAERE Annual Conference, 23-26 June 2005, Bremen, Germany

2. Background • Production activities typically generate some environmentally detrimental undesirable outputs as side-products • emissions, waste, noise, etc. • The treatment of undesirable outputs in nonparametric production analysis has recently attracted debate: • Hailu and Veeman, AJAE 2001 • Färe and Grosskopf, AJAE 2003 • Hailu, AJAE 2003

3. This paper • Shows that conventional formulations of weak disposability implicitly and unintentionally assume that all firms apply uniform abatement factors. • It is usually cost efficient to abate emissions in those firms where the marginal abatement costs are lowest. • Presents an alternative formulation of weak disposability that allows for non-uniform abatement factors

4. Notation • Firms transform inputs to (good) outputs, which causes undesirable side-products (bads). • Input quantities • Output quantities • Environmental bads • Production technology characterized by output set

5. Weak Disposability Definition (Shephard, 1970): Outputs are weakly disposable if and =>

6. Nonparametric production analysis (also known as Activity Analysis or Data Envelopment Analysis (DEA)) • Assume a sample of K observations • Estimate output set P(x) by a set of output vectors that consists of • all observed output vectors • output vectors that are feasible by the maintained production assumptions • and no other vectors

7. Nonparametric production analysis • Maintained assumptions • inputs x and (good) outputs v are freely disposable • bad outputs w are weakly disposable • outputs sets P(x) are convex for all x

8. v w Illustration • 3 observations, the same amounts of inputs

9. v w Illustration • Feasible set spanned by convexity

10. v w Illustration • Feasible set spanned by convexity and free disposability of v

11. v w Illustration • Feasible set spanned by convexity, free disposability of v, and weak disposability

12. Shephard’s formulation – uniform abatement outputs bads inputs VRS intensity weights abatement factor

13. Generalized formulation outputs bads inputs VRS intensity weights K abatement factors

14. Linearization Partition the intensity weights as where • represents the part of firm k’s output that is abated through scaling down of activity level, i.e., • represents the part of firm k’s output that remains active, i.e.,

15. Linearized formulation outputs bads inputs VRS intensity weights

16. Numerical example Firm AFirm BFirm C v 83 5 w 6 41 x514

17. Output sets: w not disposable

18. Output sets: weak disposability - Shephard

19. Output sets: weak disposability – this paper

20. Empirical significance • Static environmental efficiency analysis • Measurement of total productivity over time • Estimation of abatement cost functions • Etc...

21. Methodological significance • Production assumptions interact • The fundamental ”minimum extrapolation principle” by Banker et al. (Management Science 1984) can fail • The minimum set that satisfies the maintained assumptions and contains all observations may exclude production vectors that are feasible by the same set of assumptions => Need to reconsider the main principle of data envelopment analysis

22. Further details... • Paper accepted for publication in American Journal of Agricultural Economics • Questions / comments are welcome to • E-mail:Timo.Kuosmanen@wur.nl • Thank you for your attention!