Risk and Uncertainty Working Paper : R 07 # 8

Most, if not all, production technologies are stochastic. This article demonstrates how data envelopment analysis (DEA) methods can be adapted to accommodate stochastic elements in a state-contingent setting. Specifically, we show how observations on a random input, not under the control of the producer and not known at the time that variable input decisions are made, can be used to partition the state space in a fashion that permits DEA models to approximate an event-specific production technology. The approach proposed in this article uses observed data on random inputs and is easy to implement. After developing the event-specific DEA representation, we apply it to a data set for Western Australian wheat farmers. Our results highlight the need for acknowledging stochastic elements in efficiency analysis. Agricultural production technologies are inherently uncertain. Unpredictable climatic variables such as rainfall are essential to production and farmers must plan for a range of contingencies when making production decisions. However, with few exceptions, data envelopment models and methods used in making efficiency comparisons rely on the assumption that the underlying technology is deterministic, with any stochastic component being confined to an error term. O’Donnell, Chambers and Quiggin (2006) have shown that efficiency analysis, whether based on stochastic frontier or data envelopment models, can be seriously biased if methods developed for nonstochastic technologies are applied to data sets generated by firms facing truly stochastic technologies and decision environments. The purpose of this article is to demonstrate how data envelopment analysis (DEA) methods can be adapted to accommodate stochastic elements in a state-contingent setting. Specifically, we show how observations on a random input, not under the control of the producer and not known at the time that variable input decisions are made, can be used to partition the state space in a fashion that permits DEA models to approximate an event-specific production technology. After developing the event-specific DEA representation, we apply it to a data set from Western Australia to illustrate the differences in efficiency calculations that can emerge when the stochastic nature of the technology is taken into account. For our data set, allowing for the event-specific nature of the data set has dramatic consequences in calculated efficiency scores. In what follows, we first define a stochastic production technology. Then we show how information on a random input can be used to define a partition of the state-space that permits specification of an event-specific version of the technology, and we show how that specification can be implemented in a DEA framework. We discuss our data set next, and then we apply our method to that data set, discuss our findings, and then the article concludes. The Stochastic Technology The stochastic setting is represented by a measurable space (S, Ω) where S is the state space and Ω are its measurable subsets (events). In this setting random variables are treated as