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

t = 1, . . . , T has the form

0 = γ0 +    γmlnymft +    γz ln bzft

+ Σ Yn ln Xnft + Ytlt + (1∕2)γt2t²
n

+ (1/2) 23 ∑Ymm∙' ln ym∙f* ɪn Vm'ft + (1/2)    ΣYzz' ɪn^fɪ ln ^f,z'f<

+ (1/2)

^γnn' ln Xnft ln Xn' ft +ΣΣY_mnlnymft lnXnft

+ ΣΣYzn lnbzft ln Xnft +ΣΣYzm lnbz ft lnymft

+    Ymt lnymftt +£Yzt ln bzftt

+ ∑^Ynt ln Xnftt + ln h(^eft),                                                 (4.9)

n

where

h(ft) = exp(vft - uft),                             (4.10)

so that ln h(ef_t) is an additive error with a one-sided component, uf_t, and a standard noise
component, vft, with zero mean.¹

In principle, the uf_t can be treated as fixed or random, but the choice between the two
entails a tradeoff. With the fixed effects approach, identification is potentially difficult,
since the number of parameters increases with the number of firms, F . To identify the
uft for each f and t, we require that additional restrictions be imposed on the pattern of
technical efficiency over time. Using the model for time-varying inefficiency proposed by
Cornwell, Schmidt, and Sickles (1990), we choose a specification of the form,

Q

Uft = ∑ βfq df t^q,     f = 1,...,F,                    (4.11)

q=0

¹ Since the inclusion of Vf_t makes the frontier distance function stochastic, it is possible for h(eʃt) to
be greater than 1.

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