A NOTE ON MEASURING THE RELATIONSHIP BETWEEN CHANGES IN EARNINGS AND CHANGES IN WAGE RATES

Published date01 March 1976
Date01 March 1976
DOIhttp://doi.org/10.1111/j.1467-8543.1976.tb00038.x
Brltlsh
Journal
of
Industrial Relations
Vol.
XIV
No.
1
A NOTE ON MEASURING THE RELATIONSHIP BETWEEN CHANGES
IN EARNINGS AND CHANGES IN WAGE RATES
ORLEY ASHENPELTER*
AND
JOHN H. PENCAVEL?
DURING the period
1950
to
1970
earnings per week have increased for manual
workers in Britain at about
6.2
per cent per year while the basic weekly wage has
increased at about
4.7
per cent per year.’ Thus the ratio of weekly earnings to the
basic weekly wage crept up by about
1.5
per cent per year.
In
this
paper we study
the causes of this increase in order to shed some light on two issues. First, weekly
earnings include all money payments for work and thus come closer to a measure
of
labour costs in production than does the weekly wage. Since most systematic
studies of the wage inflation process
in
Britain have used changes in weekly wages
as a dependent variable, it is important to know whether this is a legitimate
econometric procedure. Secondly, we want to initiate direct quantitative study of
the determinants of-the composition of the weekly pay packet, for this is an im-
portant issue in its own right.
In structuring the relationship between,
on
the one hand, changes in the actual
weekly earnings of manual workers and,
on
the other hand, changes in the weekly
wage rates
of
these workers as set down in collective bargaining agreements or as
determined by Wages Councils, we build upon the evidence from previous in-
dustry studies which have argued persuasively that it is appropriate to distinguish
those workers paid on time rates from those
on
some system of payment-by-
resultsS2 Since separate data
on
these two groups of workers are not available for
the period under investigation: we first examine the determinants of time-rate
workers’ earnings, then the relationship between time-rate earnings and the earn-
ings of workers on payment-by-results, and finally their combined effect
on
aggregate earnings.
Consider first the weekly earnings of a time-rate worker averaged over a given
period of time t, ET. If W, is his basic weekly wage,
Ct
his actual hours worked,
and H, the number of hours worked before overtime rates apply (in other words,
‘normal’ weekly hours), then the relation
(1)
ET
=
Wt
+
a(Wt/H&Ct
-
Hi)
=
Wt[l
+
U(Ct
-
HJ/HJ
holds as
an
approximate identity where
u
is the overtime premium Hence,
a(WI/Ht) is the hourly rate for overtime hours and
C,
-
H, measures the number
of
overtime hours worked. Since u(Ct
-
HJ/Ht is typically less than
0.20,5
In
[I
+
u(C,
-
H,)/H,I
z
o(C,
-
Ht)/Ht and the first difference in the (natural)
logarithm of
(1)
is
(2)
Aln
ET=
AlnW,
+
uA(Ct
-
HJH,
where we have assumed that the overtime premium ratio
(a)
has not changed.6
According to equation
(2),
the proportionate change in the weekly earnings of
time workers (A
In
E:) is the sum of two components; the ftrst is the proportionate
change in the basic weekly wage
(A
In
Wt
)
and the second is the overtime premium
ratio multiplied by the change in the ratio of overtime to normal hours. Alter-
natively, equation
(2)
says that the proportionate change in the ratio of weekly
earnings to wages
is
uA[(C,
-
Ht)/H,l. In fact, the ratio of overtime to normal
*
Director, Princeton University,
Industrial
Relations Section.
t
Associate Professor
of
Economics, Stanford University, Stanford, California.
70

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