4 - Central Institute of Brackishwater Aquaculture

Natlonal Workshop-cum-Tra~n~ng on BioinfonnatJa and Information Management In Aquaculture
output that can be produced by a farm with a given level of input and
technology. Farrell (1957) first developed frontier production models in
aquaculture. Since then several approaches to efficiency assessment have been
developed that can be classified into two broad categories: parametric and
nonparametric. Frontier techniques have been widely used in determining the
productive performance of farms which may be estimated either by a stochastic
frontier production function (Aigner et a/. 1977; Meeusen and van der Broeck
1977) or non-parametric linear programming approach, known as data
envelopment analysis (DEA). The stochastic frontier approach is preferred for
assessing efficiency in agriculture because of the inherent stochasticity involved
(Kirkley et al. 1995; Coelli et a/. 1998). There are several reviews of the
applications of the stochastic frontier approach in agriculture (Battese and Coelli
1992; Bravo-Ureta and Pinheiro 1993; Coelli 1995). Most applications of frontier
analysis in Asian aquaculture have used the stochastic approach (Sharma and
Leung, 1998; Sharma, 1999; Bimbao, et. at. 2000; Dey et al., 2000; Gunaratne
and Leung, 2001; Sharma and Leung, 2000 a; b; and Irz and McKenzie 2003).
Inefficiency models may be estimated with either a one step or a two-step
process. For the two-step procedure the production frontier is first estimated and
the technical efficiency of each farm is derived. These are subsequently
regressed against a set of variables, which are hypothesised to influence the
farm's efficiency. A problem with the two-stage procedure is the inconsistency in
the assumptions about the distribution of the inefficiencies. In the first stage, the
inefficiencies are assumed to be independently and identically distributed is order
to estimate their values. However, in the second stage, the estimated
inefficiencies distributions are assumed to be a function of number farm specific
factors, and hence are not identically distributed unless all the coefficients of the
factors are simultaneously equal to zero (Coelli, Rao and Battese, 1998).
FRONTIER uses the ideas of Kumbhakar, Ghosh and McKenzie (1991) and
Reifschneider and Stevenson (1991) and estimates all of the parameters in one
step to overcome this inconsistency. The inefficiency effects are defined as
functions of farm specific factors (as in the two stage approach) but they are
then incorporated directly into the maximum likelihood estimation.
The stochastic production frontier for sample carp producers of Kollery Lake area
is specified as follows taking into account the model developed and proposed by
Aigner etal. (1977) and Meeusen and van der Broeck (1977).
H
T,nr =fi,+Eflk~nxk, +V,-Lr ,..............................
(1)
k=1
where subscript i refer to the i-th farm in the sample; Ln represents the natural
logarithm; Y is output variable and Xs are input variables (Table 1 & 2). The
details of input and farm specific variables are defined in Table 1. ps are
unknown parameters to be estimated; V, is an independently and identically
distributed N (0, 0:) random error; and the U, is a non-negative random variable
associated with technical inefficiency in production, which is assumed to be
independently and identically distributed the inefficiency is assumed to here a
truncated normal distribution with mean, p, and variance, aU2 (IN (p,, nu2)().
According to Battese and Coelli (1995), the technical inefficiency distribution
parameter, pi is defined as: