The Suntory and Toyota International Centres for Economics and Related Disciplines
The Relation between Unemployment and the Rate of Change of Money Wage Rates in the
United Kingdom, 1861-1957
Author(s): A. W. Phillips
Source: Economica, New Series, Vol. 25, No. 100 (Nov., 1958), pp. 283-299
Published by: Blackwell Publishing on behalf of The London School of Economics and Political Science
and The Suntory and Toyota International Centres for Economics and Related Disciplines
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1958]
The Relation Between Unemployment and the Rate
of Change of Money Wage Rates in the
United Kingdom, 1861-19571
By A. W. PHILLIPS
I. HYPOTHESIS
When the demand for a commodity or service is high relatively to
the supply of it we expect the price to rise, the rate of rise being greater
the greater the excess demand. Conversely when the demand is low
relatively to the supply we expect the price to fall, the rate of fall being
greater the greater the deficiency of demand. It seems plausible that
this principle should operate as one of the factors determining the rate
of change of money wage rates, which are the price of labour services.
When the demand for labour is high and there are very few unemployed
we should expect employers to bid wage rates up quite rapidly, each
firm and each industry being continually tempted to offer a little above
the prevailing rates to attract the most suitable labour from other
firms and industries. On the other hand it appears that workers are
reluctant to offer their services at less than the prevailing rates when
the demand for labour is low and unemployment is high so that wage
rates fall only very slowly. The relation between unemployment and the
rate of change of wage rates is therefore likely to be highly non-linear.
It seems possible that a second factor influencing the rate of change
of money wage rates might be the rate of change of the demand for
labour, and so of unemployment. Thus in a year of rising business
activity, with the demand for labour increasing and the percentage
unemployment decreasing, employers will be bidding more vigorously
for the services of labour than they would be in a year during which
the average percentage unemployment was the same but the demand
for labour was not increasing. Conversely in a year of falling business
activity, with the demand for labour decreasing and the percentage
unemployment increasing, employers will be less inclined to grant wage
increases, and workers will be in a weaker position to press for them,
than they would be in a year during which the average percentage
unemployment was the same but the demand for labour was not
decreasing.
A third factor which may affect the rate of change of money wage
rates is the rate of change of retail prices, operating through cost of
living adjustments in wage rates. It will be argued here, however, that
cost of living adjustments will have little or no effect on the rate of
change of money wage rates except at times when retail prices are
1 This study is part of a wider research project financed by a grant from the Ford
Foundation. The writer was assisted by Mrs. Marjory Klonarides. Thanks are
due to Professor E. H. Phelps Brown, Professor J. B. Meade and Dr. R. G. Lipsey
for comments on an earlier draft.
283
A
284 ECONOMICA [NOVEMBER
forced up by a very rapid rise in import prices (or, on rare occasions in
the United Kingdom, in the prices of home-produced agricultural
products). For suppose that productivity is increasing steadily at
the Iate of, say, 2 per cent. per annum and that aggregate demand is
increasing similarly so that unemployment is remaining constant at,
say, 2 per cent. Assume that with this level of unemployment and
without any cost of living adjustments wage rates rise by, say, 3 per
cent. per annum as the result of employers' competitive bidding for
labour and that import prices and the prices of other factor services
are also rising by 3 per cent. per annum. Then retail prices will be
rising on average at the rate of about 1 per cent. per annum (the rate of
change of factor costs minus the rate of change of productivity).
Under these conditions the introduction of cost of living adjustments in
wage rates will have no effect, for employers will merely be giving
under the name of cost of living adjustments part of the wage increases
which they would in any case have given as a result of their competitive
bidding for labour.
Assuming that the value of imports is one fifth of national income,
it is only at times when the annual rate of change of import prices
exceeds the rate at which wage rates would rise as a result of com-
petitive bidding by employers by more than five times the rate of
increase of productivity that cost of living adjustments become an
operative factor in increasing the rate of change of money wage rates.
Thus in the example given above a rate of increase of import prices of
more than 13 per cent. per annum would more than offset the effects
of rising productivity so that retail prices would rise by more than
3 per cent. per annum. Cost of living adjustments would then lead to
a greater increase in wage rates than would have occurred as a result
of employers' demand for labour and this would cause a further increase
in retail prices, the rapid rise in import prices thus initiating a wage-
price spiral which would continue until the rate of increase of import
prices dropped significantly below the critical value of about 13 per
cent. per annum.
The purpose of the present study is to see whether statistical evidence
supports the hypothesis that the rate of change of money wage rates
in the United Kingdom can be explained by the level of unemployment
and the rate of change of unemployment, except in or immediately
after those years in which there was a very rapid rise in import prices,
and if so to form some quantitative estimate of the relation between
unemployment and the rate of change of money wage rates. The
periods 1861-1913, 1913-1948 and 1948-1957 will be considered
separately.
II. 1861-1913
Schlote's index of the average price of imports' shows an increase of
12 5 per cent. in import prices in 1862 as compared with the previous
I W. Schlote, British Overseas Trade from 1700 to the 1930's, Table 26.
1958] UNEMPLOYMENT AND MONEY WAGE RATES 285
year, an increase of 7 * 6 per cent. in 1900 and in 1910, and an increase of
7 0 per cent. in 1872. In no other year between 1861 and 1913 was
there an increase in import prices of as much as 5 per cent. If the
hypothesis stated above is correct the rise in import prices in 1862 may
just have been sufficient to start up a mild wage-price spiral, but in the
remainder of the period changes in import prices will have had little
or no effect on the rate of change of wage rates.
U 0
cf.
E? 2 -
0 0~~~~
cl)
? -2 0
. ~~~~~~~~~~*
.-40 1 2 3 4 6 $ 7 8 9 10 11
Unemptoyment, %.
Fig,t. 1861 - 1913
A scatter diagram of the rate of change of wage rates and the per-
centage unemployment for the years 1861-1913 is shown in Figure 1.
During this time there were 61 fairly regular trade cycles with an
average period of about 8 years. Scatter diagrams for the years of
each trade cycle are shown in Figures 2 to 8. Each dot in the diagrams
represents a year, the average rate of change of money wage rates
during the year being given by the scale on the vertical axis and the
average unemployment during the year by the scale on the horizontal
axis. The rate of change of money wage rates was calculated from
the index of hourly wage rates constructed by Phelps Brown and Sheila
Hopkins,' by expressing the first central difference of the index for
each year as a percentage of the index for the same year. Thus the rate
of change for 1861 is taken to be half the difference between the index
for 1862 and the index for 1860 expressed as a percentage of the index
IE. HI. Phelps Brown and Sheila Hopkins, "'The Course of Wage Rates in Five
Countries, 1860-1939," Oxford Economic Papers, June, 1950.
286 ECONOMICA [NOVEMBER
10
@i 10
X.
*-,Curve fitted to 1861-1913 data
6-
IV
4 64 63
c 2 E: 2- t-t 2 >
~~~~~62
-2
z ~~~~~~~~~67
I I I * a I I I I I B
0 0 1 2 3 4 5 6 7 8. 9 10 11
Unemployment, %.
Fig.2. 1861 - 1868
2 Curve fitted to 1861-1913 data
72
6-6
73
c)
0
3: 4l
Z'% 70
C
0 Unmpoyen,74.
Fig.3. 1868 -1879 ~ ~ ~ 7
1958] UNEMPLOYMENT AND MONEY WAGE RATES 287
- Curve fitted to 1861-1913 data
6-
4-
C 2-
0
E 62 86
64 657~~~9
o -4-
0 1 2 3 4 5 6 7 8 9 tO 11
Unemployment, %.
Fig.4. 1879 -1 886
Sz 8
*- Curve fitted to 1861-1913 data
,,
6- \
01
E 4
-3 0
018
t -2-
o -4
I I
, , , , , ,
I
0 1 2 3 4 5 6 7 8 9 10 11
Unemptoyment, %.
Fig.4a. 1879-1886, using Bowley's wage
index for the years 1881 to 1886
288 ECONOMICA [NOVEMBER
C
t1:
10-
-f1C Curve fitted to 1861 -1913 data
+' 6 \
06
0) 3 4 \9
o 90
E 87 86
-0
0 92 93
0) C -2
0 1 2 3 4 5 6 7 8 9 10 I
cr. Unemptoyment, %.
Fig.5. 1886- 1893
># 10
* \ Curve fitted to 1861-1913 data
6-
(U4
0 0
no4- \
E
0
@ ~~~~~01 02 os 04 94 93
X-2-
"o -4J
0 1 2 3 4 5 6 7 8 9 10 11
Unemployment, 1.
Fig.6. 1893 -1904
1958] UNEMPLOYMENT AND MONEY WAGE RATES 289
*- Curve titted to 1861-1913 data
1 4- <, 2 06 0
2-\
0~ ~ ~~~~0
E 0809
o4 07 - _ 0 07 04
C -2 -
u
o - I l
,, 0 1 2 3 4 5 6 7 8 9 10 11
x JUnemployment, '.
Fig. 7. 1904 - 1909
L
> 10-
*- Curve fitted to 1861-1913 data
6-
0)
U 4
12
2- 11
o 13
E 10
0
'E
09
c))
C
-2-
0 1 2 3 4 5 6 7 B 9 10 t1
r JUnempLoyment, %.
Fig.8. 1909 -1913
290 ECONOMICA [NOVEMBER
for 1861, and similarly for other years.' The percentage unemploy-
ment figures are those calculated by the Board of Trade and the Ministry
of Labour2 from trade union returns. The corresponding percentage
employment figures are quoted in Beveridge, Full Employmenit in a Free
Societp, Table 22.
It will be seen from Figures 2 to 8 that there is a clear tendency for
the rate of change of money wage rates to be high when unemployment
is low and to be low or negative when unemployment is high. There
is also a clear tendency for the rate of change of money wage rates at
any given level of unemployment to be above the average for that level
of unemployment when unemploymenit is decreasing during the upswing
of a trade cycle and to be below the average for that level of unemploy-
ment when unemployment is increasing during the downswing of a
trade cycle.
The crosses shown in Figure 1 give the average values of the rate of
change of money wage r-ates and of the percentage unemployment in
those years in which uInemployment lay between 0 and 2, 2 and 3, 3 and
4. 4 and 5, 5 and 7, and 7 and 11 per cent. respectively (the upper bound
being included in each interval). Since each interval includes years in
which unemployment was increasing and years in which it was
decreasing the effect of changing unemployment on the rate of change
of wage rates tends to be cancelled out by this averaging, so that each
cross gives an approximation to the rate of change of wages which
would be associated with the indicated level of unemployment if
unemployment were held constant at that level.
The curve shown in Figure 1 (and repeated for comparison in later
diagrams) was fitted to the crosses. The form of equation chosen was
y + a = bxc
or log (y + a) = log b + c log x
where y is the rate of change of wage rates and x is the percentage
unemployment. The constants b and c were estimated by least squares
using the values of y and x corresponding to the crosses in the four
intervals between 0 and 5 per cent. unemployment, the constant a being
chosen by trial and error to make the curve pass as close as possible to
the remaining two crosses in the intervals between 5 and 11 per cent.
unemployment.3 The equation of the fitted curve is
y + 0900 = 9*638x-1394
or log (y + 0 900) = 0.984 - 1* 394 log x.
1 The index is apparently intended to measure the average of wage rates during
each year. The first central difference is therefore the best simple approximation
to the average absolute rate of change of wage rates during a year. and the central
difference expressed as a percentage of the index number is an appropriate measure
of the average percentage rate of change of wage rates during the year.
2 Memoranda upon British and Foreignt Trade and Indutstrial Conditions (Second
Series) (Cd. 2337), B.P.P. 1905, Vol. 84; 21st Abstract oJ Labour Statistics, 1919-
1933 (Cd. 4625), B.P.P. 1933-34, Vol. 26.
3At first sight it might appear preferable to carry out a multiple regression of
y on the variables x and drx However, owing to the particular form of the relation
1958] UNEMPLOYMENT AND MONEY WAGE RATES 291
Considering the wage changes in individual years in relation to the
fitted curve, the wage increase in 1862 (see Figure 2) is definitely larger
than can be accounted for by the level of unemployment and the rate
of change of unemployment, and the wage increase in 1863 is also
larger than would be expected. It seems that the 12 * 5 per cent. increase
in import prices between 1861 and 1862 referred to above (and no
doubt connected with the outbreak of the American civil war) was in
fact sufficient to have a real effect on wage rates by causing cost of
living increases in wages which were greater than the increases which
would have resulted from employers' demand for labour and that the
consequent wage-price spiral continued into 1863. On the other hand
the increases in import prices of 7 6 per cent. between 1899 and 1900
and again between 1909 and 1910 and the increase of 7 0 per cent.
between 1871 and 1872 do not seem to have had any noticeable effect
on wage rates. This is consistent with the hypothesis stated above
about the effect of rising import prices on wage rates.
Figure 3 and Figures 5 to 8 show a very clear relation between the
rate of change of wage rates and the level and rate of change of unem-
ployment,' but the relation hardly appears at all in the cycle shown in
Figure 4. The wage index of Phelps Brown and Sheila Hopkins from
which the changes in wage rates were calculated was based on Wood's
earlier index,2 which shows the same stability during these years.
From 1880 we have also Bowley's index of wage rates.3 If the rate of
change of money wage rates for 1881 to 1886 is calculated from
Bowley's index by the same method as was used before, the results
shown in Figure 4a are obtained, giving the typical relation between
the rate of change of wage rates and the level and rate of change of
unemployment. It seems possible that some peculiarity may have
occurred in the construction of Wood's index for these years. Bowley's
index for the remainder of the period up to 1913 gives results which are
broadly similar to those shown in Figures 5 to 8, but the pattern is
between y and x in the present case it is not easy to find a suitable linear multiple
regression equation. An equation of the form y+ a = bxc + k (1 dx would
probably be suitable. If so the procedure which has been adopted for estimating
the relation that would hold between y and x if were zero is satisfactory, since it dt
1 dx
can easily be shown that . is uncorrelated with x or with any power of x pro-
vided that x is, as in this case, a trend-free variable.
1 Since the unemployment figures used are the averages of monthly percentages,
the first central difference is again the best simple approximation to the average rate
of change of unemployment during a year. It is obvious from an inspection of
Fig. 3 and Figs. 5 to 8 that in each cycle there is a close relation between the deviations
of the points from the fitted curve and the first central differences of the employment
figures, though the magnitude of the relation does not seem to have remained constant
over the whole period.
2 See Phelps Brown and Sheila Hopkins, loc. cit., pp. 264-5.
3 A. L. Bowley, Wages and Income in the United Kingdom since 1860, Table VII,
p. 30,
292 ECONOMICA [NOVEMBER
rather less regular than that obtained with the index of Phelps Brown
and Sheila Hopkins.
From Figure 6 it can be seen that wage rates rose more slowly than
usual in the upswing of business activity from 1893 to 1896 and then
returned to their normal pattern of change ; but with a temporary
increase in unemployment during 1897. This suggests that there may
have been exceptional resistance by employers to wage increases from
1894 to 1896, culminating in industrial strife in 1897. A glance at
industrial history' confirms this suspicion. During the 1890's there
was a rapid growth of employers' federations and from 1895 to 1897
there was resistance by the employers' federations to trade union
demands for the introduction of an eight-hour working day, which
would have involved a rise in hourly wage rates. This resulted in a
strike by the Amalgamated Society of Engineers, countered by the
Employers' Federation with a lock-out which lasted until January
1898.
From Figure 8 it can be seen that the relation between wage changes
and unemployment was again disturbed in 1912. From the monthly
figures of percentage unemployment in trade unions2 we find that
unemployment rose from 2 8 per cent. in February 1912 to 11.3 per
cent. in March, falling back to 3 - 6 per cent. in April and 2 - 7 per cent. in
May, as the result of a general stoppage of work in coal mining. If
an adjustment is made to eliminate the effect of the strike on unemploy-
ment the figure for the average percentage unemployment during 1912
would be reduced by about 0 8 per cent., restoring the typical pattern
of the relation between the rate of change of wage rates and the level
and rate of change of unemployment.
From a comparison of Figures 2 to 8 it appears that the width of
loops obtained in each trade cycle has tended to narrow, suggesting a
reduction in the dependence of the rate of change of wage rates on the
rate of change of unemployment. There seem to be two possible
explanations of this. First, in the coal and steel industries before the
first world war sliding scale adjustments were common, by which wage
rates were linked to the prices of the products.3 Given the tendency
of product prices to rise with an increase in business activity and fall
with a decrease in business activity, these agreements may have
strengthened the relation between changes in wage rates and changes
in unemployment in these industries. During the earlier years of the
period these industries would have fairly large weights in the wage
index, but with the greater coverage of the statistical material available
in later years the weights of these industries in the index would be
reduced. Second, it is possible that the decrease in the width of the
loops resulted not so much from a reduction in t