In order to measure the technical efficiency of any observed
input-output bundle one needs to know the maximum quantity of output
that can be produced from the relevant input bundle. One possibility is
to explicitly specify a production function.
The value of this function
at the input level under consideration denotes the maximum producible
output quantity. It is common to estimate the parameters of the
specified function empirically from a sample of input-output data.
Because the least squares procedure permits observed points to lie above
the fitted line, in a stochastic frontier model one includes a
composite error.
The composite error is a sum of a one-sided disturbance
term representing shortfalls of the actually produced output from the
frontier due to inefficiency and two sided disturbance term representing
upward or downward shifts in the frontier itself due to the random
factors. The econometric procedure requires relation of a particular
functional form.The distance function representation of a production
technology, proposed by Shephard (1953, 1970), provides a multi output
primal alternative, which requires no aggregation, no prices and no
behavioural assumption.
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