place all firms in the set S that yield probabilities of greater than some prespecified level
(1-α) for being within a distance δ of the best TE score. Because of the small differences
between Bayesian MCC and MCB analogs, we will simply refer to the BMC procedure
without using an additional C or B designation for control or best.
Within a numerical Bayesian estimation framework, whether dealing with simple
Monte Carlo integration, MCMC approaches such as Gibbs sampling, or even importance
sampling, one can always estimate the probability of a ranking being accurate (or correct)
by simple evaluation of the frequency of the ranking occurring within the large set of ran-
dom parameter draws employed in the numerical integration. For more discussion of the
foundations of numerical Bayesian methods, see Geweke (1999).
Horrace and Schmidt (2000) do not perform comparisons between groups or of a
single firm versus another single firm or subgroup. While the sampling theory MCC and
MCB approaches can be extended to accomplish the same tasks just introduced with
the Bayesian approach, to accomplish these different types of comparisons the statistical
foundation of their procedure must be resolved to yield the correct critical values for each
such comparison. Because the adjustment for the multiple comparisons is conditional on
the nature and number of such comparisons made, the MCC and MCB algorithms must
be adjusted whenever the format of the multiple comparisons changes. Thus, while there
is no theoretical barrier to stop MCC and MCB approaches from performing the same
sorts of comparisons as our BMC approach, the task is daunting until more work is done
to develop user-friendly software.
4. Empirical Application
We apply our methodology to a panel of U.S. electric utilities observed at five-year
intervals from 1980-1995. There are two outputs: the quantity of electric power generated