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 +ΣΣYmnlnymft 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(eft) is an additive error with a one-sided component, uft, and a standard noise
component, vft, with zero mean.1
In principle, the uft 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 tq, f = 1,...,F, (4.11)
q=0
1 Since the inclusion of Vft makes the frontier distance function stochastic, it is possible for h(eʃt) to
be greater than 1.
12