Input aggregation bias in technical efficiency with multiple criteria analysis

Abstract

We extend the Tauer (2001) and Färe et al. (2004) analyses of aggregation bias in technical efficiency measurement to multiple criteria decision analysis. We show input aggregation conditions consistent with multiple criteria evaluation of overall efficiency in conjunction with the variation in aggregation bias.

Keywords:

• data envelopment analysis
• input aggregation
• multiple objectives

JEL Classification:

• C61
• D20

Notes

¹ Similar analysis is possible for aggregate outputs.

² The analysis can be extended to constant returns to scale.

³ We use the environmental condition to give meaning to the second set of input coefficients. This can be generalized to other problems.

⁴ For more on materials balance-based models of environmental efficiency, see Coelli et al. (2007). See also Hampf (2014) for a justification of the strong disposability condition in material balance-based models.

⁵ Similar analysis is possible for aggregate outputs.

⁶ The proof, omitted for reasons of space and because the procedure is identical to that of Primont (1993) and Färe et al. (2004), is available upon request from the authors. Program (Equation 3) has arguably more constraints than program (Equation 4) because the input constraint has to be satisfied for all prices.

⁷ For a determinate y^k or scale of production because we assume VRS (Tone, 1996; Krivonozhko and Førsund, 2010).

⁸ Tone and Tsutsui (2010) propose an equivalent category in a constant returns to scale model.

⁹ This condition can be proved by comparing the solutions of the dual of programs (Equation 4) and (Equation 5). The proof is omitted here but is available upon request from the authors.

¹⁰ Actually, all efficient units that are positive combinations of a and c are overall efficient for both criteria cost and environment together. And inefficient units enveloped by this part of the frontier are allocation-efficient.

¹¹ It is sufficient to write (C_cN, A_cN) and (C_aN, A_aN) as a function of the inputs of units a and c in (Equation 11). Further proof is available upon request from the authors.