菲利普斯曲线

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 Stable URL: http://www.jstor.org/stable/2550759 Accessed: 04/06/2009 21:12 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. 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Blackwell Publishing, The London School of Economics and Political Science, The Suntory and Toyota International Centres for Economics and Related Disciplines are collaborating with JSTOR to digitize, preserve and extend access to Economica. http://www.jstor.org 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