MULTIPLE COMPARISONS WITH THE BEST: BAYESIAN PRECISION MEASURES OF EFFICIENCY RANKINGS

according to their technical efficiency estimates (and the appropriate confidence in those
rankings). While the MCB and MCC methods do allow for such flexibility, it is a much
more complex matter to generalize the approach to compute such comparisons. Also, the
sampling theoretic-based MCC and MCB approaches do not yield finite sample probability
values to measure the differentiation between the TE scores of the firms. Instead, the
method provides the normal (for sampling theory statistics) all or nothing test results
where firms are either differentiated from the best (or index firm) or are not.

The greater information content and flexibility of the Bayesian approach are significant
advantages in providing statistical information about the precision of efficiency rankings.
Further, the method is more straightforward from a statistical viewpoint, requiring nothing
more complicated than a basic ability to generate random numbers from known statistical
distributions, a function available in nearly all of statistical and econometrics software
packages on the market today.

The application presented here used a distance function framework with some atten-
dant complications due to the presence of a bad output and endogeneity necessitating the
use of an instrumental variables approach. However, applications of the Bayesian approach
presented can be easily implemented for technical efficiency estimates from a stochastic
frontier model which could be estimated in a simpler manner. Regardless of the approach,
once the posterior distributions of the technical efficiency estimates have been derived (or
numerically approximated), the Bayesian Multiple Comparison (BMC) approach presented
here can be easily performed at little additional cost in terms of programming time and
effort. In contrast to the simplicity of the approach, the information generated by BMC
approach is quite rich. It yields considerable useful information for policy and decision
makers who wish to know the accuracy and differentiability of estimated rankings.

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