The Relation Between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861–1957¹

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 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 rate 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 competitive 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. Schlote's index of the average price of imports11 W. Schlote, British Overseas Trade from 1700 to the 1930's, Table 26. shows an increase of 12·5 per cent. in import prices in 1862 as compared with the previous 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. A scatter diagram of the rate of change of wage rates and the percentage unemployment for the years 1861–1913 is shown in Figure 1. During this time there were 61/2 fairly regular trade cycles with an average period of about 8 years. Scatter diagrams for the years of each trade cycle are shown in 2-8. 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,11 E. H. Phelps Brown and Sheila Hopkins, “The Course of Wage Rates in Five Countries, 1860–1939,”Oxford Economic Papers, June, 1950. 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 for 1861, and similarly for other years.11 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. The percentage unemployment figures are those calculated by the Board of Trade and the Ministry of Labour22 Memoranda upon British and Foreign Trade and Industrial Conditions (Second Series) (Cd. 2337), B.P.P. 1905, Vol. 84; 21st Abstract of Labour Statistics, 1919–1933 (Cd. 4625), B.P.P. 1933–34, Vol. 26. from trade union returns. The corresponding percentage employment figures are quoted in Beveridge, Full Employment in a Free Society, Table 22. 1861–1913 1861–1868 1868–1879 1879–1886 1879–1886, using Bowley's wage index for the years 1881 to 1886 1886–1893 1893–1904 1904–1909 1909–1913 It will be seen from 2-8 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 unemployment is decreasing during the upswing of a trade cycle and to be below the average for that level of unemployment 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 rates and of the percentage unemployment in those years in which unemployment 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 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.33 At first sight it might appear preferable to carry out a multiple regression of y on the variables x and . However, owing to the particular form of the relation 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 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 can easily be shown that is uncorrelated with x or with any power of x provided that x is, as in this case, a trend-free variable. The equation of the fitted curve is 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 5-8 show a very clear relation between the rate of change of wage rates and the level and rate of change of unemployment,11 Since the unemployment figures are the of the first central difference is again the best simple approximation to the average rate of change of unemployment during a year. It is from an of 3 and 5-8 that in each cycle there is a close relation between the of the from the fitted curve and the first central of the employment the of the relation not seem to have constant the but the relation appears at in the cycle shown in Figure The wage index of Phelps Brown and Sheila from which the changes in wage rates were calculated was on Phelps Brown and Sheila Hopkins, which shows the same during these years. we have also Bowley's index of wage and in the United Kingdom since Table If the rate of change of money wage rates for 1881 to 1886 is calculated from Bowley's index by the same as was the shown in Figure are giving the relation between the rate of change of wage rates and the level and rate of change of unemployment. It seems possible that some may have occurred in the of index for these years. Bowley's index for the remainder of the period up to 1913 gives which are to those shown in but the is less regular than that with the index of Phelps Brown and Sheila Figure it can be seen that wage rates more than in the upswing of business from to and then to their of but with a increase in unemployment during This that there may have been by employers to wage increases from to in in A at The this During the there was a rapid of employers' and from to there was by the employers' to trade union for the introduction of an which would have a rise in hourly wage rates. This resulted in a by the of by the with a which until Figure 8 it can be seen that the relation between wage changes and unemployment was again in the figures of percentage unemployment in trade 21st Abstract of Labour Statistics, we find that unemployment from per cent. in to per cent. in falling to per cent. in and per cent. in as the result of a of in If an is to the effect of the on unemployment the for the average percentage unemployment during would be by about per the of the relation between the rate of change of wage rates and the level and rate of change of unemployment. a comparison of 2-8 it appears that the of in each trade cycle has to a in the of the rate of change of wage rates on the rate of change of unemployment. There seem to be two possible of in the and the first scale adjustments were by which wage rates were to the prices of the to Phelps Brown for this out to the tendency of prices to rise with an increase in business and fall with a in business activity, these may have the relation between changes in wage rates and changes in unemployment in these industries. During the years of the period these would have fairly in the wage but with the greater of the statistical in later years the of these in the index would be it is possible that the in the of the resulted not so much from a in the of wage changes on changes in unemployment as from the introduction of a time in the of wage changes to changes in the level of unemployment, by the of and by the of and If a time in the later years of the period the wage change in any year should be not to average unemployment during that year, but to the average unemployment by, This would have the effect of each in the diagrams part of the the of the year and it can easily be seen that this would the in the This fact it to at between the effect of time and the effect of of wage changes on the rate of change of unemployment. A scatter diagram of the rate of change of wage rates and percentage unemployment for the years 1913–1948 is shown in Figure 1913 to the are a of those for the period to the Ministry of index of hourly wage rates at the of of each Ministry of Labour has been the percentage change in the index each year being taken as a measure of the average rate of change of wage rates during that year. The Ministry of figures for the percentage unemployment in the United and have been for the years For the years the unemployment figures were taken from the of the Labour 1913–1948 It will be seen from Figure that there was an increase in unemployment in to a rise in the the of the to unemployment was low and wage rates The cost of living was also rising and for cost of living adjustments in wage rates but it is not clear whether the cost of living adjustments were a real factor in increasing wage rates or whether they merely increases which would in any case have occurred as a result of the high demand for labour. unemployment in but wage rates continued to rise until probably as a result of the rising import prices, which their in and consequent cost of living adjustments in wage rates. There was then a increase in unemployment from per in to per in by a fall of per in wage rates in of the fall can be explained by the rapid increase in unemployment, but a fall of per in the cost of a result of falling import prices, was no doubt also a In unemployment was per and wage rates by per cent. unemployment was high in this year it was decreasing, and the part of the fall in wage rates be explained by the fall of per in the cost of living index between and this trade less about for cost of living adjustments and the number of these to there were only changes in import prices and in the cost of In and unemployment was high but decreasing. Wage rates in and by per in It seems likely that if business had continued to after the changes in wage rates would have shown the of the of trade However, the to demand in an to the price level in to the at the of the of business and unemployment fairly between per and 12·5 per from to The average level of unemployment during these five years was per and the average rate of change of wage rates was per per year. The rate of change of wage rates calculated from the curve fitted to the 1861–1913 for a level of unemployment of per is per per year, in close with the average Thus the evidence not the which is that the of the price level of to of wage rates. The given the of unemployment which were have been fairly from a study of the if had inclined to carry out the The relation between wage changes and unemployment during the trade cycle the of the cycles in the 1861–1913 period except for the level of unemployment the cycle. The increases in wage rates in and are larger than would be to result from the rate of change of employment and part of the increases probably be to cost of living The cost of living index per in per in and per in the part of the increase in each of these years being to the rise in the of the in can the rise in prices be accounted for by rising import in and it seems likely that the to prices of home-produced agricultural a part in increasing prices and so the cost of living index and wage rates. The of unemployment may also have been a factor to increase the of wage changes during the upswing of business between and in import prices probably to the wage increases in and The in Figure for the remaining years show the of the an increase in unemployment in to and in to the we in to the fitted relation between unemployment and wage A scatter diagram for the years 1948–1957 is shown in Figure The unemployment shown are of the unemployment in during the years taken from the Ministry of Labour The Ministry of Labour not figures of the percentage unemployment in the United but from in the of the Labour it appears that unemployment in the United Kingdom was fairly about per than that in this The wage index was the index of wage rates, in the Ministry of Labour the percentage change during each year being taken as a measure of the average rate of change of money wage rates during the year. The Ministry not an index of hourly wage An index of hourly wage rates the years considered in this is, however, given in the Ministry of Labour of but an index of in the Ministry of Labour of shows a of per in and in and an average annual of per from to The percentage changes in hourly rates would therefore be greater than the percentage changes in rates by these 1948–1957 It will be argued later that a rapid rise in import prices during to a increase in retail prices in which to wage increases during but that this tendency was offset by the of wage by in the of that wage increases during were low as a result of the of wage that a rapid rise in import prices during and to a rapid rise in retail prices during and which cost of living increases in wage rates in excess of the increases that would have occurred as a result of the demand for labour, but that there were no factors of wage or rising import prices to affect the wage increases in or in the five years from to It can be seen from Figure that the for very close to the curve fitted to the 1861–1913 and that the for to on a this curve, the of the being the of the of the shown in 2-8. A in this result from a time in the of wage rates. If the rate of change of wage rates during each year is to unemployment to the average of the of unemployment from of the year to of that year, the scatter diagram shown in Figure 11 is The has and the for the years and to a curve which with the curve fitted to the 1861–1913 with unemployment 7 In Table 1 below the percentage changes in money wage rates during the years 1948–1957 are shown in The figures in are the percentage changes in wage rates calculated from the curve fitted to the 1861–1913 corresponding to the unemployment shown in Figure the average of unemployment On the hypothesis that has been in this these figures the by which wage rates would be to rise, given the level of employment for each year, as a result of employers' competitive bidding for labour, they the in wage The on the cost in wage is the percentage increase shown by the retail price index in the in which the are the index of the corresponding of the previous year. The average of these for each year is an appropriate measure of the in wage and these from the retail price index in the of The for is the average of the of the year. are given in The percentage change in the index of import Board of Trade during each year is given in Table 1 we see that in the cost was greater than the demand as a result of the effect on retail prices of the rapid rise in import prices during the previous year, and the change in wage rates was a little greater than be accounted for by the demand It would probably have been greater but for the of the trade in of wage In the cost was less than the demand and the change in wage rates was also much no doubt as a result of the of wage which is to have been in In the cost was than the demand and the wage change was to the demand prices very during and as a result of the of in and the outbreak of the in 1950. In the retail price index during and so that the cost in wage the demand The wage increase in each year also the demand so that these two years a clear case of cost In the cost was to the demand and in the years to it was below the demand In each of these years the wage increase was to the demand Thus in these five and also in there seems to have been demand The statistical evidence in to above seems in to the hypothesis stated in that the rate of change of money wage rates 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 is a rapid rise in import prices to offset the tendency for increasing productivity to the cost of years in which import prices rise to a wage-price spiral, which seem to very except as a result of and an increase in productivity of 2 per per year, it seems from the relation fitted to the that if aggregate demand were at a value which would a level of prices the associated level of unemployment would be a little under 2 per cent. as is demand were at a value which would wage rates the associated level of unemployment would be about 5 per cent. of the of the fitted relation in the of low percentage unemployment, there will be a average rate of increase of wage rates if unemployment is held constant at a given level than there will be if unemployment is to about that level. are of There is for much more into the between unemployment, wage rates, prices and