The short panel available to us prevents time varying components in the production
function and the inefficiency component from being separately identified (Greene,
2005). Inefficiency effects are therefore assumed not to vary over the course of the four
years. Average efficiency levels in an industry can only change from year to year if
firms exit or enter the sector. The inefficiency effects are assumed to be distributed as a
truncated normal distribution with mean μ . Where μ is found to be insignificant a half
normal distribution is assumed.
The estimated parameters of the production function and the efficiency estimates are
used to construct a generalised Malmquist index of total factor productivity growth for
each sector which allows us to determine which sectors are driving productivity growth
in the manufacturing sector as a whole (see Coelli et al. (2005) for an overview of this
approach). The purpose of constructing a productivity index is to measure output
growth that is net of input growth, that is, output growth due to efficiency change,
technical change or the contribution of scale economies. Relative technical efficiency
( RTEit , calculated as the ratio of a firms technical efficiency score relative to the
maximum in time t) can be interpreted in the same way as a distance function and as
such the change from one period to the next can be used to calculate an efficiency
change index comparable to that associated with the Malmquist index:
(4)
TEI, = RTEtIRTEt-1
The Malmquist index measures technical change as the geometric mean of the shift in
technology between two adjacent time periods evaluated at the input values associated
with each time period, respectively. Since non-neutral technical change is not
considered in our model, and so technological change is unaffected by year on year
changes in input values, a corresponding technical change index can be constructed
using the estimated parameters on the fixed time effects of the sector specific
production functions (equation (5)).
TCIt = exp[δt -δt-1]
(5)
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