Ceris-Cnr, W.P. N° 2/2002

inefficiency effects, uft, we also see that the γ estimate is significantly less than one71, to
indicate that our stochastic frontier model [3]-[5] may be significantly different from a
deterministic frontier specification, in which there are no random errors, vft, in the cost
function.
The predicted x-inefficiencies for each one of the 45 transit companies over the
different years involved are presented in Table 4. These estimates refer to the expression
defined by equation [7] and have been obtained using the predictor presented in
equation [A.20] of the Appendix. The mean overall cost inefficiency, corresponding to
square “all firms-all years”, is found to be 1.13772. This means that, on average, the cost
of production exceeds the minimum level frontier by 13.7 percent because of xinefficiency. The positive coefficient for τft in Table 1b (δτ = 0.0303) suggests that the
inefficiencies of the Italian LPT firms tended to increase throughout the seven-year
period. First row of Table 4, which reports the estimates for mean cost inefficiency over
time, confirms this tendency to worsen the performance: on average, the level of xinefficiency has increased slightly, from 12.2 percent in 1993 to 14.2 in 1999, with an
upward swing during 1993-1995 and 1998-1999 and a brief downward swing over the
period 1996 to 199773. As mentioned in Section 3.2, one can possibly trace the
deterioration of cost efficiency during the first half of the nineties in the laxity induced
by the several actions taken by the Government with the purpose of covering the old
deficits of LPT companies through extraordinary funds. On the contrary, the temporary
efficiency recovery during 1996-1997 could be linked to expectations of more tight
financial constraints triggered by the promulgation of the reform Law n. 549 in 1995,
whereas the new rise in x-inefficiency observed in the years 1998 and 1999 probably
reflects a let-up in the managerial effort induced by the delay in implementing the
reform.
Although there is a general increase in the x-inefficiency of the transit companies
over time, Table 4 shows that the individual predicted values vary considerably among
firms in each year and they also change up and down over time for a given company.
This leads to investigate the role played by the other z-factors included in model [5]
that, jointly with time, determine such a variability in the inefficiency levels.

71

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The test statistic is -2.532, that is larger (in absolute value) than the one-sided critical value of -2.326
for the standard normal distribution at the 1 percent level of significance.
This value is calculated as the arithmetic average of the predictors for the individual cost inefficiency
of the sample firms over all the observations involved.
We also computed the average annual rate of variation in the level of cost inefficiency. This is equal
to about +3%, which is consistent with the estimate for the parameter associated to the year of
observation in the inefficiency model [5], δτ .

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