as detailed above in section 2.2. When performed on the 43 firms in our sample using a
95% significance level, this set contains 29 firms; thus, only 14 firms are statistically less
efficient than the best.
Comparing these results to the values in Table 3 finds reasonable concurrence with
some interesting differences. All seven firms in G1 are in the set of possible best firms
computed by the MCB approach along with 12 out of 14 firms from G2. The two firms
from G2 excluded are F5 and F30, neither of which is near the bottom of the group in
terms of posterior mean TE. In fact, F5 is the median firm within G2. Rounding out the
set are 10 firms from G3, including F13 and F16 which have the 2 smallest posterior mean
TEs within G3. A The set of possibly efficient firms is denoted in Table 2 by a * in the
MCB efficient set column.
The inclusion of firms in the sampling theoretic MCB approach’s efficient set that
are fairly soundly rejected by the Bayesian approach (such as F13 and F16) is somewhat
difficult to explain. One possible explanation is that the sampling theory MCB approach
produces a conservative joint confidence interval. However, this cannot explain the fact
that the MCB approach rejects equality for firms with smaller gaps in point estimates
while fails to reject equality for firms with larger estimated efficiency gaps. Examining
these four firms further from the Bayesian side is interesting. The two firms from G2 that
are excluded from the MCB efficient set, F5 and F30, have Bayesian posterior probabilities
of being more efficient than F31 of only 2.2% and 2.8%, respectively, so their exclusion
appears to make sense. Yet the two bottom firms from G3 which are included in the
MCB efficient set, F13 and F16, both have a Bayesian posterior probability of being more
efficient than F31 of only 0.6%. This makes their inclusion while F5 and F30 are excluded
even more puzzling.
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