SPECIFICATION OF FACTOR DEMAND MODELS AND SHIFTWORKING‐ AN EXTENSION TO THE CES CASE
| Author | R. I. D. Harris |
| DOI | http://doi.org/10.1111/j.1467-9485.1983.tb01010.x |
| Date | 01 June 1983 |
| Published date | 01 June 1983 |
Scormh
/ournolo/
Poliricd
Economy,
Vol.
30,
No.
2,
June
1983
0
1983 Scottish
Econonuc
Society
Notes
and
Communications
SPECIFICATION OF FACTOR DEMAND
AN EXTENSION TO THE CES CASE
MODELS AND SHIFTWORKING-
R. I.
D.
HARRIS
The Queen's University
of
Beljhst
I
INTRODUCTION
In a recent article, Bosworth (1981) amended the Nadiri and Rosen (1969)
factor demand model to include shiftworking. The approach used was to
minimise the costs of production subject to a
Cobb-Douglas
production
function, and subject to the constraints imposed by the firm needing to
compensate workers both for longer hours worked (i.e. overtime) and the time
of day worked (i.e. shift system). The purpose of this note is to extend the model
to the case where the underlying production function is of the Constant-
Elasticity-of-Substitution type, and
so
allow for the possibility that the
elasticity of substitution
(a)
between factor services is not necessarily equal to
1. The need to allow for non-unitary elasticity
of
substitution
is
supported by
recent empirical evidence.
A
study by the author (1982) suggests that
a
is
generally less than
1
and is closer
to
0.5
for most
U.K.
manufacturing
industries.' Others have found similar evidence
;
for example, Briscoe and Peel
(1975) in estimating a labour-demand model for
U.K.
manufacturing found
a
to be equal to 0-68.* More recently, Bruno and Sachs (1981) found
a
to be
between 0.068 and 0.266 using various forms of a linearised CES model for
U.K.
manufacturing, 1956-1978 (see their Table
1).
While the latter estimates
appear rather
low,
Bruno and Sachs argue that they are probably obtained
from the short-run production model. An estimate using a non-linear model
resulted in an elasticity
of
substitution
of0.767,
which
". .
.
makes more sense in
a long-term context" (Bruno and Sachs, op. cit., p. 28).
These empirical findings mean that to base factor demand equations on a
Cobb-Douglas production function is
a
misspecification. Therefore, the
CES
*
Several industries were examined using the
CES
production function
to
be
given in equation
2,
and estimating
it
via non-linear least squares.
Sce
their Table
1.
p. 131,quation
1.
Since they have estimated a lagged-adjustment form
of
the
labour-demand
CES
marginal productivity side-relation
(see
Brown,
1966,
for
a proof), from the
coefficient they report
on
the
real
price
of
labour and
the
speed
of
adjustment coefficient
it
is
possible
to
infer that they found
u
=
068.
Date
of
receipt of final manuscript: 3 December 1982
170
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