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RESEARCH
βQ = 0. (12)
Finally, a Cobb-Douglas specification implies, in addition
to (5), (6) and (7), the following restriction:
βij = βiQ = 0. (13)
Pindyck (1976) states that we can test restrictions using
a simple chi-square test The appropriate test statistic
is :
-2 log C = n (log Ω* r - log Ω* u) (14)
where, IΩ*rI and IΩ*uI are the determinants of the
estimated error covariance
matrices for the restricted and unrestricted models respectively.
This statistic is distributed as chi-square with
degrees of freedom equal to the number of parameter
restrictions being tested.
To characterize the nature of the production process
further as represented by the cost functions, the study
also estimates the Allen elasticities of substitution and
elasticities of conditional input demands. From the cost
and share equations, the measures of the Allen elasticities
of substitutions are defined as:
σij = βij/Si*Sj - 1/Si + 1 , for i = j, (15a)
Where Si = cost share of input i
σij = βij/Si*Sj + 1 for i ≠ j (15 b)
The related own- and cross-partial elasticities of conditional
input demand are given by:
εij = βij/Si + Si - 1 , for i = j, and (16 a)
εij = βij/Si + Sj , for i ≠ j. (16 b)
Estimation of Economies of Scale:
Economies of scale are said to exist if an increase in
output, holding input prices constant, leads to a less than
proportional increase in total costs, causing a decline
in average costs. When two firms merge the size of the
firm rises proportionally. If internal management of the
combined firms improves and\or the synergies unlock,
these will manifest in scale of economies in the same
way as defined here. From the translog cost function
stated in equation (3) above, returns to scale measuring
cost responses resulting from changes in output, post
merger holding input prices constant, can be derived
as follows:
firm result in a more than proportional increase in output.
Evidence of scale economies, other things constant,
could be a rationale for M & A activity.
Investigation of synergy and technological Change
It is well known fact in economics that a change in
output holding the quantity and cost of inputs constant
can occur if there is a change in technology. This concept
has been employed in the present study in the context of
evaluation of M&A. unlocking of synergies and improvement
in internal management practices will be manifest
in the significant technology coefficient of the cost function
specified in the equation (3) above. Specifically, from
the cost side, holding input prices constant, technological
change permits the firm to produce the same level of
output at lower expenditure. Given the cost function in
(3), the rate of technological change can be measured
by:
Where
= rate of technological change
(18)
Technological change can be biased with respect to inputs
as well as with respect to the scale characteristics of
the production technology. With regard to input biases,
a technological change is Hicks-neutral, if the slope of
the production isoquants is independent of technological
change. A cost-neutral technological change, an analogous
(but not equivalent) concept, refers to a technical
change that does not affect relative cost shares of inputs.
From the share equation in (4), a measure of input bias
in technological change is:
(19)
A η = 0 imply a neutral technical change. η> 0 and
η < 0 imply ith factor-using and ith factor-saving technological
advancements respectively.
Technological change could also be biased with respect
to the scale property of the production technology.
Technological change may be scale-biased or non-neutral
in the sense that it might alter the range of outputs over
which a given scale economies can be attained, thus resulting
in a change in the cost-minimizing efficient firm
size. Define the cost elasticity to be C=1/S, S=elasticity
of scale. Technological scale bias is given by:
(17)
An estimate of S > 1 implies scale economies, indicating
that an equiproportional increase in all inputs of a
(20)
A TSB > 0, implies that technological change increases
scale economies and, conversely,
58 Need the Dough July-October - 2007