estimated stochastic production functions are presented in Table C of the Appendix. If
the estimated parameters violate the assumptions of monotonicity and quasi-concavity,
elasticities and technical efficiency estimates can be misleading as discussed by Sauer et
al. (2006). This is particularly the case in the present application where the primary
purpose of the model is to produce accurate measures of firm level productivity.
It is reassuring here that the partial derivatives of the production functions are of the
appropriate sign at the sample mean in all cases with only few violations of the
monotonicity assumption throughout the sample as a whole. Curvature assumptions are
satisfied at the mean for most sub-samples (i.e., quasi-concavity in inputs) with the
exception of ISIC 31 and 34. In these cases, a more restrictive Cobb-Douglas
specification was chosen.23 The parameters of the final specification of each sub-sector
production function are presented in Table 6.24
[TABLE 6 ABOUT HERE]
A key assumption of the stochastic frontier approach is that all firms within a sub-sector
use the same technology, so this approach does not allow us to compare production
technologies across sub-sectors. Technical change is captured by the inclusion of fixed
time effects in the production function which controls for exogenous changes to the
environment in which the sector operates, and we assume that technical progress/regress
affects all firms in each sector in the same way.25 Controlling for these aspects, our
model produces one efficiency score for each firm in each sector, regardless of how
many time periods they are present in that sector. We calculate a relative efficiency
measure for each firm by comparing their estimated efficiency score relative to the top
performing firm in each sector in each year, thus adjusting for firms that exit, enter or
change activity. Scale effects capture the extent to which changes in the input mix
improve the performance of the firm.
23 While violations also occur for observations in ISIC 19 and 27, the results of the Cobb-Douglas and
translog models are very similar so we proceed with the more flexible translog specification. Efficiency
results are considered both including and excluding the observations which violate the curvature
assumptions with almost identical results found in all cases.
24 It should be noted that in estimating stochastic frontier production functions of this kind it is assumed
that technology is homogenous across each 2-digit sub-sector analysed.
25 Non-neutral technical change is not allowed for in our model given the short panel and problems with
parameter identificaiton.
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