Agriculture Reference
In-Depth Information
In fact, each input demand equation explains and forecasts the expected
value of a particular variable in terms of several explanatory variables. As
an example, the translog form is usually estimated in share form, and is
suitable for decomposition and explanation of changes of energy shares in
cost. Thus, the decomposition in Kako (1978), that uses a translog cost
function, is possible without using the estimates of the elasticities. Fousekis
and Pantzios (1999) have decomposed the rates of growth for the different
inputs in Greek agriculture, after estimating the demand system derived
from the differential approach. Some functional forms, such as the
generalised McFadden, are usually estimated in input to output ratios, thus
allowing for theoretically sound decompositions of input intensity effects.
Again, an elasticity-based decomposition, like that in the recent work of
Peeters and Surry (2000), is not needed. Additional reasons for preferring a
particular functional form are in the global theoretical properties of flexible
cost functions. This point is of particular interest for robustness of
extrapolation. It seems very important for forecasting and policy analysis
that projections hold correct theoretical properties. These are the reasons
why the generalised McFadden of Diewert and Wales (1987) is an
interesting prior choice of functional form for energy intensity analysis. It
is estimated with dependent variables in intensity form and curvature is
imposed without restricting elasticities of substitution.
2.3 The model
To capture all the above aspects in estimating changes in input demands, it
is assumed that the agricultural industry in each EU country has a twice
differentiable aggregate production function with constant returns to scale
relating the flow of gross output (
Q
) to the services of four variable inputs
(
E
), energy-based (
N
), biological inputs (
B
), and all other
intermediate inputs (
M
)] with prices
(i=E,N,B,M)
and three fixed inputs
(
L
)
,
capital (
K
), land (
R
)]. The characterisation of intermediate
consumption follows Lopez and Tung (1982).
There is a dual variable cost function which corresponds to such a
production function, and which reflects the production technology. The
general form for the restricted cost function with constant returns to scale
is:
G
=
G
(
p
,
F
/Q, t
), where
G
is variable cost,
p
is the vector of variable
input prices,
F
is the vector of fixed inputs,
Q
is the level of output, and
t
stands for time reflecting the state of production technology.
For reasons explained above, there is a preferred specification for
the variable cost function. The symmetric generalised McFadden with the
structure for fixed inputs introduced in Rask (1995) and constant returns to
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