the production function and separates the technical efficiency (one-sided) component of the residual from
other unobserved stochastic (two-sided) effects.
The production frontier, where Q is the output, and Z is a vector of observed inputs, such as land,
labor, fertilizer, seeds, machinery and draft animals is defined as follows:
Qi = f ( Zt ; β)exp( εi - ui )
where ui = ∣Ui∣ and Ui ~ N(0, σu2) [46]
and εi ~ N(0,σe2)
We assume that the two error terms are distributed normal and half-normal respectively. If ui =0,
production is at the stochastic frontier. Then, from [46], the technical efficiency (TEi) of farmer i is,
TE = [f(ZβQ)exp(ε)] = ex' (-ui) [47]
The conce't of technical efficiency can be illustrated using a sim'le isoquant diagram with land
and labor as the two in'uts [figure 4]. The isoquant q defines the frontier, or the set of efficient choices of
in'uts for a given out'ut level. Points such as A and B re'resent actual observed in'ut choices for the
out'ut level q. Assuming that the observed land-labor ratio is efficient, i.e. there is no allocative
inefficiency, technical efficiency of the farm is given by the distance between the observed 'oint and the
frontier along the ray that re'resents the actual in'ut ratio. Point B re'resents a technically efficient farm
because the distance to the frontier is zero.
This estimate of technical efficiency (TE) is inde'endent of stochastic errors and measures the
degree to which a farmer comes close to achieving the best 'ossible outcome conditional on his or her
in'ut choices and the 'roduction technology.21 Technical efficiency in farms may be determined by the
21 Although it is straightforward to estimate the stochastic frontier model using maximum likelihood methods, the derivation
of a technical efficiency measure (TEi) for each farmer is difficult because the two com'onents of the error term cannot be
easily decom'osed. We use the functional form 'ro'osed by Jondrow et. al [1982] and generally acce'ted in the literature
for the conditional distribution of the one-sided error term to ex'ress the conditional mean of the one-sided error term:
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