Erkie Asmare 1 and Andualem Begashaw

Stochastic frontier model specifications:
Theory usually 
presents the producers as successful optimizers by maximizing 
production, minimizing cost, and maximizing profits. Econometric 
techniques build on the basis to estimate production/cost/profit 
function parameters using regression techniques where deviations 
of observed choices from optimal ones are modelled as statistical 
noise [20]. Therefore, econometric estimation techniques should 
allow for the fact that deviations of observed choices from optimal 
ones are due to two factors: by either failure to optimize i.e., 
inefficiency or due to random shocks. According to Anonymous 
[21] and Mastromarco [22], the econometric approach to estimate 
frontier models uses a parametric representation of technology 
along with a two-part composed error term. According to Sharma 
et al. [23] and Wongnaa & Awunyo Vitor [24] the firm’s technology 
is represented by a stochastic production frontier as follows:
;
(
) 
=
+
i
i
i
Y
f X
b
e
(1)
Where Y
i
denotes output of the i
th
firm; X
i
is a vector of func-
tions of actual input quantities used by the ith firm; β is a vector 
of parameters to be estimated; and ε
i
is the composite error term 
defined as:
–
=
i
i
i
e
v
u
(2)
where v
i
is assumed to be independently and identically dis-
tributed random errors, independent of the u
i
; and the u
i
is non-
negative random variables, associated with technical inefficiency in 
production, which are assumed to be independently and identically 
distributed with mean, µ, and variance, 
δ
2
u (|N
µ, 
δ
2
u|).
Based on the nature of data (cross sectional, panel and time 
invariant), the stochastic frontier model has a certain difference 
as shown below. In case of cross-section stochastic frontier model 
(equation 3) the time dimension of the inefficiency term, u, will be 
kept constant over time. Whereas, for panel data stochastic frontier 
model (equation 4) time dimension of the inefficiency term, u, will 
be allowed to change over time. On the other hand, for time-invari-
ant inefficiency data type (equation 5), inefficiency component of 
the error term, u, is time-invariant.
–
i
i
i
i
y
bx
v
u
α
=
+
+
(3)
–
it
i
it
it
it
y
x
v
u
α
β
=
+
+
1, . . ., ;
1, . . .,
i
N t
T
=
=
(4)
–
it
it
it
i
y
x
v
u
α
β
=
+
+
1, . . ., ;
1, . . .,
i
N t
T
=
=
(5)
Where, y is the observed outcome (goal attainment), β′x + v is 
the optimal, frontier goal (e.g., Maximal production output or min
-
imum cost) pursued by the individual, β′x is the deterministic part 
of the frontier and v~N [0, σv2] is randomness or statistical noise 
and it is assumed to be normally distributed with zero mean [4]. On 
the other hand, the amount by which the observed individual fails 
to reach the optimum (the frontier) is u, in this context, u is the “in
-
efficiency.” Moreover, u represents the proportion by which y falls 
short of the goal, and has a natural interpretation as proportional 
or percentage inefficiency.
So, u=|U| and U~N [0, σu
2
]. Therefore, the economic logic be-
hind this specification is that the production process is subject to 
two economically distinguishable random disturbances: statistical 
noise represented by viand technical inefficiency represented by u
i
. 
The component u
i
is assumed to be distributed independently of vi-
and to satisfy u
i
≥0. The non-negativity of the technical inefficiency 
term reflects the fact that if u
i
>0 the country will not produce at the 
maximum attainable level.