The Relation Between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861-1957

Phillips hypothesizes 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 years with a sufficiently rapid rise in import prices (Section I, “Hypothesis,” p. 283). The reasoning parallels ordinary price theory: “When the demand for a commodity or service is high relatively to the supply of it we expect the price to rise… Converse when the demand is low… we expect the price to fall.” Applied to labour, “when the demand for labour is high and there are very few unemployed we should expect employers to bid wage rates up quite rapidly,” while “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” – an asymmetry that makes “the relation between unemployment and the rate of change of wage rates… likely to be highly non-linear” (p. 283).

Phillips argues that in a year of rising business activity, with the demand for labour increasing and unemployment falling, employers will bid more vigorously for labour than in a year with the same average unemployment but no such improvement – and conversely when business activity and demand for labour are falling (Section I, p. 283). This produces a systematic pattern within each trade cycle: at a given level of unemployment, wage changes tend to run above the average for that level when unemployment is falling (the cyclical upswing) and below it when unemployment is rising (the downswing), tracing out the “loops” visible in the scatter diagrams for individual cycles (Section II, pp. 286-289).

Phillips argues cost-of-living wage adjustments have “little or no effect… except at times when retail prices are forced up by a very rapid rise in import prices” (pp. 283-284). Working through an illustrative case – 2 per cent annual productivity growth, imports equal to one-fifth of national income, and wage rates otherwise rising 3 per cent per annum from competitive bidding – he shows that cost-of-living adjustments only become “an operative factor” once import prices are rising by more than roughly 13 per cent per annum, a threshold high enough that in his account it “would more than offset the effects of rising productivity” and could initiate a self-sustaining “wage-price spiral” that continues until import-price inflation drops back below the critical rate (p. 284).

Phillips uses the Phelps Brown and Sheila Hopkins index of hourly wage rates and official (Board of Trade / Ministry of Labour) unemployment percentages from trade union returns, computing the annual rate of wage change as the first central difference of the wage index expressed as a percentage of that year’s index value (Section II, pp. 285-286). He averages years into unemployment bands (0-2, 2-3, 3-4, 4-5, 5-7, 7-11 per cent) to cancel out the cyclical rate-of-change effect, then fits a curve of the form y + a = bx^c (equivalently log(y+a) = log b + c log x) to these band averages by least squares (with the constant a chosen by trial and error), obtaining y + 0.900 = 9.638x^(-1.394) (p. 290).

Phillips reports that the relation holds “very clearly” in most of the seven trade cycles he examines (roughly 8 years each, Figures 2, 3, and 5 through 8), with 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” (Section II, pp. 290-291). He also flags specific deviations he attributes to the paper’s own import-price hypothesis: the unusually large wage increases in 1862 and 1863 coincide with a 12.5 per cent jump in import prices (linked to the American Civil War), while comparable-sized import price rises in 1872, 1900, and 1910 show no corresponding wage effect – which Phillips reads as consistent with the 13-per-cent threshold logic of Q3 rather than contradicting it (p. 291).

The 1879-1886 cycle (Figure 4) shows the relation “hardly appear[ing] at all,” which Phillips traces to the underlying wage index rather than to the economic hypothesis: the Phelps Brown-Hopkins index for this period rests on Wood’s earlier index, which shows unusual stability during these years (Section II, p. 291). Substituting Bowley’s independently constructed wage index for 1881-1886 (Figure 4a) restores “the typical relation between the rate of change of wage rates and the level and rate of change of unemployment,” and Bowley’s index for the remainder of the period to 1913 gives results “broadly similar” to the other cycles, though somewhat less regular (p. 291).

Phillips offers two candidate explanations, without fully adjudicating between them (Section II, pp. 292-293). First, pre-war sliding-scale wage agreements common in coal and steel – which linked wages directly to product prices and so would have reinforced the wage-unemployment relation – carried larger weight in the wage index early in the period than later, as statistical coverage broadened. Second, the growth of collective bargaining and, especially, arbitration and conciliation procedures may have introduced a response lag between unemployment changes and wage changes, which – if present – would itself tend to widen rather than narrow the loops, making it “difficult to discriminate at all closely between the effect of time lags and the effect of dependence of wage changes on the rate of change of unemployment” (p. 293).

Phillips finds the basic pattern reasserts itself once specific shocks (war, demobilisation, rapid import-price swings) are accounted for, and singles out 1925-1929 as a particularly clean test (Section III, pp. 293-295). During the deliberate policy of restricting demand to force the price level down and restore the pre-war gold parity of sterling, unemployment stayed between 9.7 and 12.5 per cent, averaging 10.94 per cent, while wage rates fell by an average of 0.60 per cent per year – almost exactly the -0.56 per cent per year the pre-war (1861-1913) fitted curve predicts at that unemployment level. Phillips concludes explicitly that “the evidence does not support the view, which is sometimes expressed, that the policy of forcing the price level down failed because of increased resistance to downward movements of wage rates” (p. 295): the outcome could have been predicted from the pre-war relation alone.

A raw scatter of 1948-1957 wage changes against contemporaneous unemployment (Figure 10) shows a loop running in the opposite direction from the pre-war cyclical loops (Section IV, pp. 295-296). Phillips shows that relating each year’s wage change instead to unemployment lagged seven months (averaged from June of the preceding year to May of that year) removes this reversed loop entirely (Figure 11): the points for 1950 and 1953-1957 then lie closely along a curve “almost exactly” coinciding with the one fitted to 1861-1913 data (p. 297-298). He interprets the reversed loop and the need for a lag as consistent with delays introduced by the post-war growth of formal collective bargaining and arbitration machinery.

For each year, Phillips compares the actual wage change (column 1 of Table 1) with a “demand pull” figure implied by the fitted curve given that year’s lagged unemployment (column 2), and with the contemporaneous rate of retail-price inflation as a “cost push” measure (column 3) (Section IV, pp. 296-298). The comparison identifies 1948 and especially 1951-1952 – following the September 1949 sterling devaluation and the Korean War import-price shock – as periods where cost push “considerably exceeded” demand pull and the actual wage increase tracked the cost-push figure, a “clear case of cost inflation”; by contrast, in 1950 and again from 1953 to 1957, cost push was at or below demand pull and “the actual wage increase was almost exactly equal to the demand element,” which Phillips calls “pure demand inflation” in those years.

Ignoring the rare years of an import-price-driven wage-price spiral, and assuming 2 per cent annual productivity growth, Phillips concludes from the fitted relation that unemployment “a little under 2.5 per cent” would be consistent with stable product prices, while unemployment of “about 5.5 per cent” would be consistent with stable money wage rates (Section V, “Conclusions,” p. 299). He adds a further implication of the curve’s strong convexity at low unemployment: “there will be a lower average rate of increase of wage rates if unemployment is held constant at a given level than there will be if unemployment is allowed to fluctuate about that level” – i.e., cyclical variability in unemployment around a given average raises average wage inflation relative to holding unemployment steady at that average, precisely because the fitted curve is non-linear.

Phillips explicitly labels his conclusions “tentative” and states there is “need for much more detailed research into the relations between unemployment, wage rates, prices and productivity” (Section V, p. 299). Within the paper itself he flags several sources of imprecision: the reliance on a hand-fitted curve (constants chosen partly “by trial and error”); the sensitivity of the 1879-1886 result to which wage index is used; the difficulty of separating a genuine dependence on the rate of change of unemployment from an unmodelled response lag in the pre-1913 loops; and the need for an ad hoc seven-month lag to fit the 1948-1957 data at all – each acknowledged directly in the relevant section rather than smoothed over in the conclusions.