Abstract
In a stochastic decision environment, differences in information can lead rational decision makers facing the same stochastic technology and the same markets to make different production choices. Efficiency and productivity measurement in such a setting can be seriously and systematically biased by the manner in which the stochastic technology is represented. For example, conventional production frontiers implicitly impose the restriction that information differences have no effect on the way risk-neutral decision makers utilize the same input bundle. The result is that rational and efficient ex ante production choices can be mistakenly characterized as inefficient—informational differences are mistaken for differences in technical efficiency. This paper uses simulation methods to illustrate the type and magnitude of empirical errors that can emerge in efficiency analysis as a result of overly restrictive representations of production technologies.
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Notes
More precisely, they are intended to represent nonstochastic frontiers. Banker (1993) has shown how the imposition of proper distributional assumptions on inefficiency yields a statistical interpretation of DEA models.
In particular, Ω can be either finite or infinite. In practice, the only change in what follows is in terms of the derivative concepts used.
As Chambers and Quiggin (2004) point out, this condition holds for any individual who strictly prefers more 0 period income to less, more period 1 income to less, and faces a financial market in which there exists a riskless asset. Therefore, as a practical matter it is more general than the net-returns formulation might suggest.
This presumes, of course, that individuals formulate unique probability measures. It is well recognized that otherwise rational individuals can behave as though they are not probabilistically sophisticated.
This condition may also be described by saying that the cost function is generalized Schur-concave with respect to the probability vector (0.75, 0.25).
We take 10 to be the highest plausible level of relative risk aversion. However, some researchers view levels of relative risk aversion as plausible if they lie in the range 1–4. These researchers would characterize 5 as extremely risk averse.
Strictly speaking, the term ‘predictor’ should be used if inferences are being drawn using a random effects stochastic frontier model. In that case, the object of inference (firm efficiency) is a random variable, not a parameter. However, for simplicity, we use the term ‘estimator’ in both contexts.
All results were generated using the SHAZAM software. The monotonicity constraint was not binding for these 25 data points. However, in a simulation experiment reported later in this section, the monotonicity constraint was binding in approximately 15% of replications.
That firm will also have an input-oriented DEA efficiency score of \( 0.5x^{-1}<1.\)
We thank an anonymous reviewer for suggesting this discussion to us.
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Acknowledgments
Earlier versions of this paper have been presented at several conferences and seminars. We would like to thank all participants, as well as the editors and reviewers of this Journal, for their contributions to our work.
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O’Donnell, C.J., Chambers, R.G. & Quiggin, J. Efficiency analysis in the presence of uncertainty. J Prod Anal 33, 1–17 (2010). https://doi.org/10.1007/s11123-009-0143-9
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DOI: https://doi.org/10.1007/s11123-009-0143-9