The name is absent

Review of Islamic Economics, Vol. 8, No. 2, 2004

u_l from the values of ɛɪ for each PU. For this we need distributional
assumptions on the two error components additional to those
underpinning the OLS, and also a different estimation technique to
obtain a consistent estimator of (the intercept and) the TE for each
PU. The required distributional assumptions are: υ_j^,s are normally
distributed, κ_j^,s follow non-negative half-normal. Both v_i and u_i are
distributed independently of each other and of the regression (Kebede,
2001: τ5-17). To recapitulate, the production oriented approach to
the measurement of efficiency aims at the maximization of output (y)
from the given inputs. But in the input oriented approach the
objective is minimization of cost, given the output. The two
approaches, if applied to the same case, would yield different results.
This is equally true of inefficiency measures. In any case, the cost
efficiency of a PU_i is defined as [exp (-u_j)↑. But as u_jcannot really be
observed, it is estimated by using the conditional E-[exp (- ι<₁∣ε_i)∣ as
the best predictor of u_lt at time t. Curtiss (2000: ɪɪ) provides the
derivation procedure as under:

E[exp(-w,∣ε )] =   ^ɑ;¹⁺^'^/tT|) exp (γε + w,_l /2)     ^(з)

I ∖-φγε_i∕σ₄)

where

r=σ_μ^2z(^σ_u²+<) ’ ^σ._l = √y(l-∕)σ²; ε(y.-x.β)

φ(.) is the density function of a standard normal random variable.
In an input oriented cost model, efficiency is measured at time t in the
usual manner as the ratio of minimum cost to observed cost:

It follows that in an output-oriented approach, i.e. where the
objective is to maximize production, exp(-u_j) is maximized for the
given inputs, but for measuring cost efficiency it has to be minimized.
Jemric and Vujcic (2002: 5-7) make this point at once explicit.

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