The production technology in this paper is therefore defined separately for each sub-
sector using a stochastic production frontier which expresses output as a function of
inputs, technical inefficiencies capturing the degree to which firms produce below the
optimal level of production and a random error component (Pitt and Lee, 1981).
yt = f ( xt ; β ) ev- ui
i =1,2, ,nj; t=1,2,...T
(1)
where yit represents the output of the i th firm in a particular sub-sector in time period
t , xit the vector of inputs into the production process, β the vector of parameters of the
production function, and vit statistical noise and other random external events
influencing the production process.12 The technical efficiency of the ith firm relative to
the stochastic frontier for its group is given by the ratio of observed output to the
corresponding stochastic frontier output:
TE =---y---
' f ( xt ; β ) evt
=e
ui
(2)
As such, ui are the firm specific inefficiency effects for a particular sector, and we
assume viv and ui are independent. If ui = 0 , the firm is efficient and operates on the
group specific production frontier. If ui > 0 , there are inefficiencies and the firm
operates beneath the best-practice frontier for the sub-sector.
The stochastic production function for each sub-sector can be estimated by specifying
an appropriate functional form for each model. We use a translog production function
which incorporates controls for exogenous fixed time effects ωv , for example, due to
technological change or policy changes which affect all firms equally.
K1KL
lnyt = α + ∑βk lnxtk +-∑∑βkl lnxtk lnxtι + ω + vt -U (3)
k=12 k=1 l=1
12 t 2
12 vij is assumed to be iid N (0,σvj