3 Production frontier and efficiency measurement
3.1 Distribution-free approach to measuring productive efficiency
A point of reference is needed in measuring the productive efficiency of a firm. The stochastic
frontier model as proposed simultaneously by Aigner et al. (1977) and Meeusen and van den
Broeck (1977) is the most commonly used approach for measuring productive efficiency.2 The
stochastic frontier model of Battese and Coelli (1995) can be employed if panel data are avail-
able. Though the stochastic frontier models have some advantages in distinguishing efficiency
from other random influences on a firm’s output, they are based on rather restrictive assump-
tions. First, a distributional assumption on the inefficiency term is imposed, which may not be
supported by the data. For instance, Schmidt and Lin (1984) showed that if the skewness of
residuals resulting from an ordinary least squares (OLS) regression is positive, the stochastic
frontier approach should not be used.3 Second, it is assumed that productive efficiency and
production inputs are not correlated. In empirical applications, however, such a correlation is
actually likely to exist, resulting in inconsistent parameter estimates. Third, the conditional
mean model of Battese and Coelli (1995) can be estimated only for a moderate number of
explanatory variables because it is based on a single-step maximum likelihood (ML) proce-
dure. However, since the second step of our analysis includes more than 700 variables (e.g.,
dummies for industry and location), we cannot use available ML-based procedures. Fourth,
firm-specific efficiencies in the stochastic frontier approach are computed as expected values
(Jondrow, Lovell, Materov and Schmidt, 1982) and must be obtained indirectly from the resid-
ual term, whereas the fixed-effects approach provides direct estimates of the relative efficiency
of a firm.
Therefore, we take advantage of the panel character of our data and measure productive
inefficiency as a firm-specific effect.4 The basic specification is a deterministic transcendental
logarithmic (translog) production function, which can be written as (see Greene, 1997):
lnyit = lnαi + λt + ∑βklnXkit + ∑, β2k (ln×ku)2 + 1 ∑Yqw (lnXqit)(lnxwit)+ εit (1)
q=w
where k=1,. . . ,p, i=1,. . . ,N, t=1,. . . ,Ti and q=1,. . . ,p, w=1,. . . ,p, q=w. The term yit represents
output of firm i in period t; xkit denotes production input k, and λt represents a time-specific
effect. We have N firms and Ti observations for each firm. The assessment of productive
efficiency is based on the firm-specific fixed effects αi. The largest estimate of a firm-specific
2See Mayes, Lansbury and Harris (1995) and Kumbhakar and Lovell (2003) for an overview of different para-
metric approaches for assessing the efficiency of firms.
3An exception is Carree (2002) who proposes a stochastic frontier model with positive skewness of productive
efficiency. However, we are not aware of any empirical application using this approach to date.
4See Schmidt and Sickles (1984) and Sickles (2005) for a more detailed discussion on such an approach.
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