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



reported here; because these multiple parallel runs and subsamples produced very similar
empirical results, we can conclude that our Gibbs sampler has converged. Posterior means
are computed as the simple average of the Gibbs draws (or a function of the parameters
from each draw), while posterior medians are defined as the median value of a particular
parameter or function of parameters from all the draws.

4.4 Results

Estimated TEs for all 43 firms in the sample are displayed in Table 2. While a detailed
analysis for all 43 firms would be excessive, we more closely examine the results for the
most and least efficient firms in our sample. The least efficient firm is Alabama Power
with a posterior mean TE of 0.2795 (posterior standard deviation of the mean, 0.0015)
and posterior median of 0.2705. A symmetric (not shortest) 90% highest posterior density
region for Alabama Power’s TE ranges from 0.1625 to 0.4306. The most efficient firm is
Rochester (NY) Electric with a posterior mean TE of 0.9115 (posterior standard deviation,
0.0020)and posterior median of 0.9563. Rochester Electric’s 90% highest posterior density
region spans from 0.6888 to 1.0000.

An analysis of the 43 firms’ estimated technical efficiencies suggests grouping the firms
into four groups. Group 1 (G1) contains the seven firms with the highest posterior mean
TEs, all of which have at least a 90% posterior probability of being more efficient than at
least 25 other firms. Group 2 (G2) contains the next 14 firms, representing the remainder of
the top half of the firms when sorted by posterior mean TE. Group 3 (G3) contains the next
18 firms in this ranking by posterior mean. Finally Group 4 (G4) contains the bottom four
firms, the least efficient according to the posterior mean TEs. These firms were placed
in Group 4 due to their all having less than a 50% posterior probability of being more

22



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