THE SPECIFICATION OF THE SHORT‐RUN EMPLOYMENT FUNCTION: AN EMPIRICAL INVESTIGATION OF THE DEMAND FOR LABOUR IN THE UK MANUFACTURING SECTOR, 1955–1972
| DOI | http://doi.org/10.1111/j.1468-0084.1975.mp37002004.x |
| Published date | 01 May 1975 |
| Author | D. A. PEEL,G. BRISCOE |
| Date | 01 May 1975 |
THE SPECIFICATION OF THE SHORT-RUN
EMPLOYMENT FUNCTION:
AN EMPIRICAL INVESTIGATION OF THE DEMAND FOR LABOUR IN
TIlE UK MANUFACTURING SECTOR, 1955-1972
By G. BRISCOE AND D. A. PEEL*
1. INTRODUCTION
The behaviour of employment, and in particular its relationship to the level of
output, has long been at the centre of much macro-economic theorising and more
recently it has been the subject of several empirical investigations. Much of the
interest in this relationship stems from the observation that while employment
levels in several economies have varied cyclically through time, they have not
varied to the same degree as output. Such behaviour gives rise to pronounced
cyclical fluctuations in productivity and has thereby prompted investigators to
examine the relationship between output and employment more closely at various
levels of aggregation.
The most commonly chosen level of aggregation has been that of the sector,
and if we examine the annual movements of employment (total number of em-
ployees in employment) and output (the constant price index of industrial pro-
duction) experienced in the post-war UK manufacturing sector, we can begin to
get some appreciation of the problem. The coefficients of total variation for the
period 1948-72 were found to be 4.72% and 22.80% for employment and output
respectively. Since output grew during the period at a much higher rate than did
employmentin cumulative annual percentage terms the difference was 0.42%
for employment and 3.20% for outputthen a more meaningful comparison is the
coefficient of residual variation after the respective time trends have been removed.
These coefficients are 3.85% for employment and 5.28% for output, figures which
provide statistical confirmation of the greater cyclical variability of output com-
pared with employment. Similar results are suggested by a quarterly analysis but
the need to separate the cyclical component from the seasonal factors tends to
render such estimates less reliable. The overall conclusion to be drawn is that no
simple stable relationship is likely to exist between employment and output in
the short term and that attempts to explain the level of employment (and by
implication, the level of productivity) must look beyond current output levels for
an adequate explanation.
The concern of this paper, then, is with the short-term demand for employment
and how this is determined by output and various other key causal variables.
* G. Brjscoe is Senior Research Fellow in the Centre for Industrial Economic and Business
Research, University of Warwick and D. A. Peel is Lecturer in Economics, University of
Liverpool.
We are indebted to colleagues at both Warwick and Liverpool for providing useful com-
ments in preparing this paper. In particular we acknowledge the valuable discussions with
C. Roberts, T. Hazledine and R. Latham which helped to crystallize our thoughts on various
parts of the study.
115
116 BULLETIN
The employment function looks at the employment/output relationship from the
opposite side of the coin to the more familiar production function but it typically
takes account of the basic input/output restrictions in evolving its specification.
In the post-war period, various alternative neo-classical theories of the demand for
labour have given rise to different forms of the employment function which could be
tested empirically using both UK and USA data. However, in a recent review of
some of these theories Killingsworth [21] concluded 'that the world still awaits a
fully specified theory of the labour input which can stand up against a really
thorough confrontation with the data.' Since 1970, further specifications of the
demand for employment have appeared in the literature' but despite greater
sophistication in the theorizing and wider use of information (new variables)
there appears little reason to modify Killingsworth's conclusion.
The starting point for the present study is the collation of a consistent body of
data relating to a well-defined time period for which reasonably accurate observa-
tions on the variables are available. A significant problem with earlier empirical
attempts to compare and evaluate the suitability of different functional forms of
the employment model lay in the use of different data and the choice of varying
time periods. Moreover, in several studies there have been instances where the
data have not strictly measured the concepts which the theory requires them to
measure2 and while this study is not altogether free of such limitations, we have
searched widely to use the most appropriate series. Given a consistent set of data
for the UK manufacturing sector, the study seeks to apply a wide range of assess-
ment criteria (of both statistical and economic a priori nature) to determine how
well alternative specifications can describe the observed behaviour of the labour
input. The purpose of the exercise is to explore fully the specification of alter-
native employment models and to work out the implications for the underlying
structure which gave rise to the data. Although alternative functional forms may
appear to yield roughly similar results, frequently consideration of the theory
from which they are derived will suggest some very different conclusions.3
This study distinguishes three main groups of applied models which have been
developed to explain the demand for the number of employees and in some cases,
also to explain the associated demand for the number of hours worked. The
rationale for grouping the models is largely on the grounds of their empirical form
rather than on the basis of their theoretical derivation. In the following section
we first identify single equation employment functions, we then turn to these
systems of independent equations that jointly explain the demand for labour
input where output is exogenously determined, and finally we examine simiji-
taneous equation systems where the employment function is a central structural
relationship. A brief introduction to their derivation is provided and the models
are critically examined for their theoretical adequacy. In section 3, the data are
introduced and some comments are advanced on problems which arise from im-
'For a summary discussion of some of these more recent theories see Roberts [27].
2 For example, see the discussion in Fair [11] on the use of seasonally-adjusted data and the
use of proxy variables employed by Nadiri and Rosen [24].
See Griliches's commandments to the econometrician for virtuous living [13, p. 46].
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