The Trade-Off Between Inflation and Unemployment: A Survey of the Econometric Evidence for Selected Countries

Morris Goldstein

doi:10.5089/9781451969290.024.A006

Author:

Mr. Morris Goldstein

Mr. Morris Goldstein https://isni.org/isni/0000000404811396 International Monetary Fund

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Publication Date:: 01 Jan 1972

eISBN:: 9781451969290

Language:: English

Keywords:: SP; exchange rate; money wage rate; price guidepost; price change; rate of inflation; price equation; Wages; Unemployment; Wage setting

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THERE ARE FEW, if any, developed countries that have not expressed a commitment to full employment, price stability, balance of payments equilibrium, and rapid economic growth. However, at the same time it has become apparent that it may not be possible to achieve or even closely approximate all these policy targets simultaneously. More particularly, the reconciliation of full employment with price stability has emerged as an extremely troublesome task for macroeconomic policy in many countries. Judging from past experience, policymakers are faced with a trade-off dilemma: attempts to reduce the unemployment rate (by increasing the level of aggregate demand) usually lead to higher rates of inflation, while attempts to reduce the rate of increase of prices and wages usually lead to higher rates of unemployment.

Abstract

The primary purpose of this paper is to provide a review of the recent (post-1958) empirical literature on the trade-off between unemployment and inflation for a number of countries. Ideally, such a review should indicate if, when, and where such a trade-off exists and, if it exists, what its important properties are. While this review has been directed at these questions, it is only fair to warn the reader that only partial answers have been obtained.

To keep the survey in manageable proportion, a number of restrictions have been placed on its scope.¹ First, emphasis is placed on the empirical price and wage studies for only a few countries, namely, the United States, the United Kingdom, and Canada. Several multicountry studies that have estimated trade-offs between inflation and unemployment for Japan, France, Italy, Germany, Sweden, Belgium, Australia, Denmark, and the Netherlands are also discussed, but the coverage of the literature for these countries is admittedly spotty. Second, primary attention is given to those wage and price studies that report some association, be it significant or insignificant, with the unemployment rate. This decision reflects the view that the relationship between wage or price changes and the unemployment rate is particularly important because the unemployment rate is a direct policy target, whereas other measures of excess demand or disequilibrium in labor and product markets (the capacity utilization rate, the ratio of unfilled orders to shipments, the ratio of inventories to shipments, the quit rate, etc.) are not.² Third, very little discussion is given to definitions of and data sources for the wage, price, and unemployment variables used in the different studies, except where the method of construction of the variable has important implications for the trade-off between inflation and unemployment.³

The survey contains five sections. Section I presents the original Phillips hypothesis regarding the relationship between changes in money wage rates and the unemployment rate and reviews those studies that tested this hypothesis on U. K., U. S., and Canadian data. Section II discusses the major extensions and modifications of and challenges to Phillips’s hypothesis. These studies cover (a) the expansion of the wage function to include such variables as profits, changes in labor productivity, key wage bargains, trade union aggressiveness, threshold cost of living changes, and price and wage expectations; (b) the joint estimation of wage and price changes to take account of the feedback from wage changes to price changes in single equation wage studies, that is, the recognition and elimination of simultaneous equation bias in the aggregate wage equation (and in the aggregate price equation); and (c) alternative measures of both the excess demand for labor and the price of labor services to account for such factors as labor reserves (hidden unemployment), hoarded labor, job vacancies, and changes in the industrial or demographic composition of both employment and unemployment. Section III compares wage equations from a number of different studies to arrive at a consensus estimate of the past trade-off between wage inflation and unemployment in the United Kingdom, the United States, and Canada. Section IV briefly reviews those studies that have directly estimated the trade-off between the rate of price inflation and the unemployment rate by regressing price changes on the unemployment rate. Section V presents the study’s conclusions. A bibliography of recent (post-1958) empirical studies on the relationships among prices, wages, and unemployment appears at the end of the paper.

The following symbols are sometimes used in the text for expositional and notational convenience: $\overset{*}{W}$ for the percentage change in money wage rates

(\overset{*}{W_{t}} = \frac{W_{t} - W_{t - i}}{W_{t - i}}),^{4}

U for the unemployment rate, U⁻¹ for its reciprocal, $\dot{U}$ for the change in the unemployment rate $({\dot{U}}_{t} = U_{t} - U_{t - i}),$ $\overset{*}{P}$ for the percentage change in prices, $\overset{*}{Q}$ for the percentage change in labor productivity, π for the profit rate, $\dot{π}$ for the change in the profit rate $({\dot{π}}_{t} = π_{t} - π_{t - i}),$ and ΔT for the change in the percentage of the labor force that is unionized.⁵

I. Early Tests of the Phillips Hypothesis

In 1958, A.W. Phillips [62] published a controversial article that indicated that there was a significant trade-off between the rate of wage inflation and the rate of unemployment in the United Kingdom. More specifically, Phillips plotted and estimated a nonlinear relationship for the United Kingdom (for the periods 1861–1913, 1913–48, and 1948–57) between the percentage change in money wage rates $(\overset{*}{W})$ and the unemployment rate (U). He found this relationship to be statistically significant, inverse, and surprisingly stable over this 96-year period. In addition, Phillips argued that the change in the unemployment rate $(\dot{U})$ and the percentage change in retail prices $(\overset{*}{P})$ would also influence the percentage change in money wages. The change in the unemployment rate was assumed to be inversely related to the dependent variable, while the change in retail prices was assumed to be positively related. Phillips’s (implicit) wage function can be written as $\overset{*}{W} = F (U, \dot{U}, \overset{*}{P})$ where the expected signs of the partial derivatives are $\partial \overset{*}{W} / \partial U < 0, \partial \overset{*}{W} / \partial \dot{U} < 0, \partial \overset{*}{W} / \partial \overset{*}{P} > {0.}^{6}$

The policy implications that Phillips drew from his statistical analysis were (a) stable money wage rates in the United Kingdom implied an unemployment rate of about 5V2 per cent and (b) stable prices (assuming that $\overset{*}{Q}$ = 2 per cent a year and assuming that $\overset{*}{P} = \overset{*}{W} - \overset{*}{Q}$ ) were consistent with an unemployment rate of about 2½ per cent.

Given the importance of Phillips’s work as a starting point for later empirical wage studies, it will be useful to summarize the arguments behind his main hypotheses. His explanation for the inverse relation- ship between $\overset{*}{W}$ and U derives directly from traditional price theory. This theory argues that when the demand for a commodity or service is greater than the supply, the price of the commodity or service will rise, and the rise will be greater, the greater is excess demand. When there is excess supply, the converse will be true. Phillips merely applied this argument to the labor market by assuming that money wage rates are the price of labor services and that the unemployment rate is a good proxy for excess demand (or excess supply) in the labor market. His argument for the nonlinear shape of the relationship between wage changes and the unemployment rate is also quite straightforward. He argues that when the demand for labor is high (U is low), employers will continually bid up money wages above prevailing rates as each employer attempts to attract the most suitable labor from other firms or industries. On the other hand, when the demand for labor is low (U is high), workers will be reluctant to offer their services at less than prevailing money wage rates. Thus, so Phillips argues, the relationship between $\overset{*}{W}$ and U is likely to be highly nonlinear.

Phillips’s argument for including the change in the unemployment rate $(\dot{U})$ in the wage equation is less carefully explained but runs as follows. When the demand for labor is increasing ( $\dot{U}$ < 0), employers will bid more vigorously for the services of labor than when this demand is constant ( $\dot{U}$ = 0). Conversely, when the demand for labor is decreasing ( $\dot{U}$ > 0), employers will be less willing to grant wage increases and workers will be in a weaker position to press for wage increases than when this demand is constant. Thus, the relationship between $\overset{*}{W}$ and $\dot{U}$ will be inverse. Phillips appears to interpret the change in the unemployment rate as a proxy for employers’ and workers’ expectations of future tightness in the labor market; for example, when the unemployment rate is falling, employers may offer higher wages to fill existing job vacancies because they expect the labor market to become tighter and, hence, employee recruitment to be more difficult and more expensive in the future. If Phillips is correct, then a rapid decrease in unemployment from 4 per cent to 2 per cent should produce a larger percentage increase in wages than would a more gradual decline in unemployment to the same rate.

Phillips’s analysis of the effect of price changes $(\overset{*}{P})$ on wage changes is basically a threshold hypothesis. He claims that unless the price change is greater than the wage change that would result from the competitive bidding for labor, there will be no cost of living adjustment in the wage bargain; that is, price changes matter only if they threaten to reduce real wages. For example, according to Phillips, if the prevailing unemployment rate would produce a wage change of 3 per cent, only price changes in excess of 3 per cent would affect wage changes.

A rather thorough examination of Phillips’s results was undertaken by Lipsey [47] in I960.⁷ Lipsey confirmed Phillips’s main finding of a significant, inverse, nonlinear relationship between percentage changes in money wage rates and the unemployment rate, but he challenged some of Phillips’s other hypotheses.⁸ More specifically, he rejected Phillips’s threshold hypothesis about the effect of price changes on wage changes in favor of the simpler hypothesis that price changes would be partially reflected in money wage bargains. In a regression in which $\overset{*}{W}$ was regressed on U⁻¹, U⁻², $\dot{U}$ , and $\overset{*}{P}$ , Lipsey found that the coefficient on the percentage change in retail prices $(\overset{*}{P})$ was significant and equal to about 0.2 (for the period 1861-1913),⁹ If wage changes fully reflected changes in the cost of living (if wage earners were not subject to any money illusion), the coefficient on $\overset{*}{P}$ should be 1. Lipsey’s results therefore suggested that wage earners were subject to substantial money illusion.¹⁰ Lipsey also discovered that the relationship between $\overset{*}{W}$ and U was not as stable over time as Phillips had suggested. In particular, this relationship (known hereafter as the Phillips curve) was found to be weaker for the period 1919–57 than for the period 1861–1913. In view of this apparent instability of the Phillips curve, Lipsey concluded that Phillips’s trade-off estimates ( $\overset{*}{W}$ = 0 at U = 5.5, and $\overset{*}{P}$ = 0 at U = 2.5) had to be interpreted with a good deal of caution.

Given the intuitive appeal of the Phillips hypothesis, it was not long before the Phillips-Lipsey wage equation was fitted to data for other countries with the following rather mixed results.

Samuelson and Solow [69] plotted annual percentage changes in average hourly earnings in U. S. manufacturing against the civilian unemployment rate for the period 1900-58. Although the relationship between $\overset{*}{W}$ and U was not very stable over the whole time period, there did seem to be a clear tendency for wage rates to increase when the labor market was tight (when U was low), and the tighter the faster. The data also suggested that the postwar Phillips curve was more unfavorable than that of earlier periods; that is, the unemployment rate associated with wage stability ( $\overset{*}{W}$ = 0) was 8 per cent for the postwar period versus 5 per cent for the prewar period (1900–10 and 1920–29). Samuelson and Solow also made some conjectures (no equations are reported in the study) about the postwar trade-off in the United States between inflation and unemployment. They suggested that (a) a wage change of 2½ per cent a year (a figure roughly equal to average productivity growth) implies an unemployment rate of about 5.5 per cent and (b) a 3 per cent unemployment rate would most likely be accompanied by an annual inflation rate of 4 per cent to 5 per cent.

Bhatia [4], in a 1961 study, regressed percentage changes in average hourly earnings in U. S. manufacturing on the unemployment rate, the change in the unemployment rate, and percentage changes in consumer prices for the periods 1900–32 (excluding 1915–20), 1933–48 (excluding 1933–34 and 1942–48), and 1948–58. He found the unemployment rate to be significant (with its expected negative sign) for the first two periods but not for the postwar period. He also discovered that the change in unemployment was not a significant variable in any of the three periods, and that price changes explained wage changes better than the unemployment rate for all three periods. Bhatia interpreted his results as casting serious doubt on the general validity of the Phillips-Lipsey hypothesis.

The major finding of a 1963 study by Bowen and Berry [10] was that the long-term relationship between $\overset{*}{W}$ and $\dot{U}$ was significant, inverse, and quite stable in U. S. manufacturing, whereas the more familiar relationship between $\overset{*}{W}$ and U was quite unstable. This result is in direct conflict with Bhatia’s finding of an insignificant relationship between $\overset{*}{W}$ and $\dot{U}$ .¹¹ Both authors used the same time periods (but Bowen and Berry estimated a wage equation for the whole period 1900–58 as well as for the three subperiods mentioned in Bhatia’s study), so that the conflicting findings remain unexplained. Bowen and Berry argued that the instability of the Phillips curve was not surprising in view of the large institutional changes that had taken place in the United States over this 60-year period, such as the development of large industrial unions and varying degrees of structural unemployment. Like Phillips, they regard the change in the unemployment rate as a useful index of future conditions in the labor market; for example, unions will demand higher wages when unemployment is waning, and employers are likely to offer higher wages when unemployment is decreasing than when it is increasing. They also found evidence, as did Samuelson and Solow, to indicate that the Phillips curve in the United States had shifted upward (become more unfavorable) in the postwar period. A final point of interest that emerged from the studies by Bhatia and by Bowen and Berry was that the Phillips curve in the United States might be linear, in contrast to the observed nonlinear shape of the curve in the United Kingdom.¹²

In a later study (1966) of prices, wages, and productivity in the United States, Bodkin [8] estimated some wage equations of the Phillips variety (for the period 1899–1957) and obtained quite good results. All the explanatory variables (U, $\dot{U}$ , and $\overset{*}{P}$ ) were highly significant and carried the expected signs. Like all previous investigators, Bodkin found evidence of significant money illusion on the part of wage earners; that is, the coefficient on cost of living changes $(\overset{*}{P})$ was about 0.6. Using the familiar assumption that price changes equal wage changes minus productivity changes ( $\overset{*}{P}$ = $\overset{*}{W}$ − $\overset{*}{Q}$ ), Bodkin was able to derive some steady-state trade-off estimates between inflation and unemployment. Bodkin’s trade-off curve, which is considerably flatter than that of previous investigators, suggested that at 3 per cent unemployment the rate of inflation would be about 1.7 per cent per annum. The relative flatness of this relationship is indicated by Bodkin’s calculation that price stability implied an unemployment rate of almost 18 per cent.

The Phillips-Lipsey hypothesis was applied to Canadian data in a study by Kaliski [42]. The two time periods under study were 1921–39 and 1945–58. In the basic model, percentage changes in money wage rates (or in average weekly earnings) were regressed on the unemployment rate (expressed in nonlinear form as U⁻¹ + U⁻²), the change in the unemployment rate $(\dot{U})$ , and percentage changes in the cost of living $(\overset{*}{P})$ . As in the studies for the United States, Kaliski found that the Phillips curve was unstable over time. All three independent variables worked well for the postwar period, but only price changes were significant in the wage equation for the interwar period. The coefficient on price changes was again found to be less than 1 (it was about 0.6 in the equation for the postwar period). On the basis of his estimated wage equation (for the postwar period), Kaliski concluded that a 3 per cent unemployment rate in Canada was consistent with a 4½ per cent annual increase in money wage rates.

An interesting cross-country comparison of the Phillips-Lipsey hypothesis was made in a 1964 study by Klein and Bodkin [44]. They regressed changes in money wage rates (W_t − W_t−₁) on an average of past and current unemployment rates, lagged changes in consumer prices, and a time trend. The regression period was 1952–59. When this regression was fitted to quarterly data for Australia, Belgium, Canada, France, Italy, Japan, the Federal Republic of Germany, and the United States, all the overall correlations were high (R² > 0.75) except for France. All coefficients except those for the French and Japanese price changes were statistically significant with the expected signs. The relationship between wage changes and the unemployment rate was always inverse except for Italy.¹³ Klein and Bodkin found that the unemployment rate associated with an annual wage change of 2.5 per cent (assuming that $\overset{*}{P}$ = 0) was highest for the United States (5.6 per cent), Canada (5.7 per cent), and Belgium (4.5 per cent). For other countries (except Italy, where the estimated equation makes little sense), the corresponding unemployment rate was less than 3 per cent. Although some of these differences among countries were no doubt due to varying definitions of unemployment, Klein and Bodkin concluded that wages in the United States and Canada, compared with other countries, were relatively insensitive to the level of unemployment. This, however, does not conflict with their finding that the Phillips-Lipsey hypothesis about the trade-off between changes in money wage rates and the unemployment rate seems to have wide applicability.

The general findings of these early trade-off studies based on the Phillips hypothesis can be summarized as follows: (a) there did seem to be a significant inverse relationship between percentage changes in money wage rates and the unemployment rate, but this relationship was not very stable over time, at least in the United States, Canada, and the United Kingdom; (b) cost of living changes had an important effect on wage changes, but only part of these cost of living changes (roughly one half) appeared to be reflected in changes in money wage rates; and (c) changes in the unemployment rate may also have had a significant inverse relationship with the change in money wage rates, but the evidence here was not conclusive.

II. Extensions and Modifications of and Challenges to the Phillips Hypothesis

The addition of other variables to the wage function

Profits

To some observers, the Phillips demand-pull theory of money wage determination seemed to ignore some important factors in the wage bargaining process, especially with respect to organized labor markets where the classical supply/demand mechanism may operate very imperfectly. One of the factors most frequently advanced as an important determinant of changes in money wage rates is the profit rate. The general argument is that when profits are high, unions will press harder for wage increases, and the ability and willingness of employers to grant these wage increases will also be high. More particularly, it is claimed that when profits are high, it costs management relatively little to agree to higher wage demands because dividend and other financial requirements can easily be satisfied; that is, management’s “ability to pay” will be high. Also, if periods of high profits are periods of high demand, the firm’s danger of passing wage increases forward in higher prices will be relatively low. Similarly, when profits are high, unions will demand larger wage increases to maintain labor’s share in firm or industry income. For these reasons, the a priori expectation is for the change in money wage rates $(\overset{*}{W})$ and the profit rate (π) to be positively related.

One of the early proponents of this role of profits in money wage determination was Kaldor [41]. In his 1959 article, Kaldor accepted Phillips’s statistical findings but challenged the interpretation that Phillips gave them. He argued that Phillips’s results were also compatible with a bargaining theory of wage rates, that is, with the hypothesis that the rise in wage rates is a function of union bargaining strength, which, in turn, is closely related to the prosperity of industry. Thus, if periods of high profits are also periods of high and rising production and of low and falling unemployment, Phillips would incorrectly conclude that the unemployment rate is the strategic independent variable when, in fact, the key variable might well be profits. Given this hypothesis, Kaldor suggested that Phillips would probably have gotten better results if he had regressed wage changes on profits rather than on the unemployment rate.

Lipsey and Steurer [49] put Kaldor’s hypothesis to a series of empirical tests using U. K. data for the periods 1870–1913, 1926–38, and 1949–58. They estimated equations for $\overset{*}{W}$ using alternatively unemployment variables (U⁻¹ and U) and profit variables (the level and change in the profit rate, π and $\dot{π}$ , both lagged and unlagged). Their more important findings were (a) the correlation between unemployment and profits was much lower than Kaldor had thought (for example, for the period 1949–58, the simple correlation between U_t and π_t was 0.16) and (b) the hypothesis that profits explain wage changes better than unemployment was rejected for two of the three periods, 1870–1913 and 1949–58.

The case for including profits in the wage function would seem to rest on stronger empirical ground in the United States. Profits have been used both as an alternative and as a supplement to unemployment in explaining changes in money wage rates. Bhatia [5] found that both the profit rate (π) and the change in this rate ( $\dot{π}$ ) were significantly related to $\overset{*}{W}$ during the period 1948–59. Further, he discovered that profit variables explained $\overset{*}{W}$ better than did unemployment variables (U and $\dot{U}$ ) for this period: π and $\dot{π}$ explained about 80 per cent of the variance in $\overset{*}{W}$ whereas U and $\dot{U}$ explained only about 22 per cent.

When profit and unemployment variables are used in the wage equation, one allows both excess demand and bargaining factors to affect the percentage change in money wage rates; that is, conditions in both the labor market and the product market affect $\overset{*}{W}$ . Presumably, aside from possible collinearity between U and π, there would seem to be no reason why both variables cannot be used jointly to explain $\overset{*}{W}$ . In fact, two of the more widely discussed studies of postwar wage behavior in the United States employ just such a wage determination model.

The first of these studies is the 1964 article by Perry [57]. Perry attempted to explain percentage changes in money wage rates in U.S. manufacturing for the period 1947–60 (quarterly) by the following variables: the reciprocal of the unemployment rate, lagged percentage changes in consumer prices, the lagged profit rate, and the change in the profit rate, that is, ${\overset{*}{W}}_{t} = F (U_{t}^{- 1}, {\overset{*}{P}}_{t - 1}, π_{t - 1,} {\dot{π}}_{t}) .$ Perry’s model explained more than 85 per cent of the variation in $\overset{*}{W}$ , and all coefficients were significant at the 99 per cent probability level with the correct signs. The coefficient of $\overset{*}{P}$ was about 0.4, once again suggesting substantial money illusion by wage earners; however, the evidence also suggested that wage adjustments to cost of living changes were increasing over time. One important policy implication of Perry’s study is that the trade-off between inflation and unemployment will be more unfavorable the higher is the profit rate and the lower is the rate of productivity increase.¹⁴ For example, Perry suggested that at a profit rate of 11.8 per cent (the average π for 1947–60) and an annual productivity increase of 3 per cent, an unemployment rate of 6.4 per cent would be required to assure price stability. In contrast, if the profit rate were 10 per cent, and the rate of productivity increase were 3.3 per cent, the corresponding unemployment rate would drop to about 4.5 per cent.

The second study to use both unemployment and profits to explain wage changes is that of Eckstein and Wilson [24]. This study examined wage behavior in U. S. two-digit standard industrial classification (SIC) manufacturing industries over the period 1948–60. Eckstein and Wilson used two concepts in this study that are worth noting, namely, the wage round and the key-bargain (or spillover) hypothesis. Instead of using annual or quarterly observations on changes in money wages, Eckstein and Wilson divided the period 1948–60 into five wage rounds. The reasons for using wage rounds were (a) wage contracts between unions and employers vary from one to five years, (b) these contracts often cluster at certain points in time, and (c) the economic conditions prevailing and expected at the time of the contract negotiations play an especially important role in determining the outcome of the wage bargain. The key-bargain hypothesis merely argues that wage bargains in a number of key industries set the pattern for wage bargains in other industries; that is, $\overset{*}{W}$ in the key industries spill over into $\overset{*}{W}$ for the nonkeyindustries. Eckstein and Wilson tested their hypotheses by dividing the 20 manufacturing industries into two groups: a key-bargain group and nonkey-bargain group. For the key-bargain group, they regressed $\overset{*}{W}$ on the unemployment rate and the profit rate (and a constant). Although the regression contained only two degrees of freedom (five wage round observations on $\overset{*}{W}$ and three independent variables), R² exceeded 0.99 and both U and π were highly significant. For individual key-bargain industries, they found that $\overset{*}{W}$ regressions using group variables (the average value of the variable for the whole key-bargain group) performed better than the industry specific variables; this finding suggested that significant wage interdependence existed in this group. For each of the nonkey-bargain industries, they regressed $\overset{*}{W}$ (for seven wage rounds) on the industry unemployment rate, the industry profit rate, and key-bargain wage changes. Good results were obtained for 8 of the 11 industries in this group, and there was evidence of a significant spillover effect from wage changes in the key-bargain group.¹⁵

A study by Zaidi [88] of wage behavior in Canadian manufacturing suggested that both unemployment and profits were important determinants of wage changes.¹⁶ The independent variables in the wage equation were the reciprocal of the unemployment rate, the percentage change in consumer prices, and the profit rate (π); here, π was the ratio of total corporate profits before taxes to total wages and salaries in manufacturing. When this equation was fitted to annual data for the period 1947–62, more than 96 per cent of the total variance of $\overset{*}{W}$ was explained and all the variables were highly significant with the theoretically expected signs. The coefficient of $\overset{*}{P}$ was about one half. Like Perry, Zaidi concluded that the higher the profit rate and the lower the rate of productivity increase, the more unfavorable was the trade-off between inflation and unemployment. For example, Zaidi calculated that a 3 per cent annual rate of inflation was compatible with a 4 per cent unemployment rate if the profit ratio was equal to 0.37 (this was the average π for 1947–62) and the rate of productivity increase ( $\overset{*}{Q}$ ) was equal to 3 per cent. In contrast, if π = 0.31 and $\overset{*}{Q}$ = 4 per cent, a rate of inflation of 3 per cent could be obtained with an unemployment rate of only 2.9 per cent.

Changes in productivity

The role of profits in the wage equation has not gone unchallenged.¹⁷ One of the more well-known criticisms was provided by Kuh [46]. He argued that businessmen are unlikely to grant high wage increases simply because profits are high, since high profits may just be transitory; rather, profits may be a proxy for a more fundamental determinant of wages, namely, the marginal value productivity of labor. Kuh’s case for including marginal value productivity in the wage equation derives from classical employment theory, which argues that, in equilibrium, workers will be hired up to the point at which the money wage equals the marginal value product of labor. Kuh claims that even when unemployment is high, $\overset{*}{W}$ can rise if the value productivity of labor is increasing; however, he expects union bargaining power to be weaker when unemployment is high. To test his hypothesis, he estimated a wage equation in which the independent variables were real value added per employee man-hour (the productivity variable), the lagged change in consumer prices, and the lagged wage change. The model was fitted to quarterly U. S. data (for the period 1950 to 1967) for the private nonfarm sector and the sectors that manufacture durable goods and nondurable goods. Wage changes were alternatively defined as W_t − W_t−1 and as W_t − W_t−4. All variables turned out to be highly significant and carried the expected signs.¹⁸ Kuh compared his equation with two wage equations using unemployment plus profits (Perry’s model [57] and the Schultze-Tryon model [72]) and found the explanatory power and standard errors of estimate of his model to be superior.¹⁹ Also, in accordance with classical employment theory, he found a unitary long-run elasticity of wages with respect to value productivity. A final point of interest that emerges from Kuh’s study is that there may be two quite different price effects in the wage equation. The first is the effect of an increase in the firm’s product price, which raises the value productivity of labor and, in turn, wages. The second effect is the familiar cost of living adjustment in the wage bargain, which depends on changes in a more aggregate price index (the consumer price index).

Trade union aggressiveness

An alternative or supplement to using the unemployment rate or the profit rate to represent the balance of power in wage bargaining is to use some measure of trade union aggressiveness. An early empirical study of this type was Hines’s [30] 1964 article.²⁰ Hines argued that trade unions do affect the percentage change in money wage rates independently of the demand for labor. His index of trade union pushfulness (Hines’s term) was the rate of change of the percentage of the labor force that was unionized (ΔT); that is, trade union pushfulness would be highest when they were gaining new members rapidly. Using annual data for the United Kingdom, Hines regressed $\overset{*}{W}$ on ΔT for the periods 1893–1912, 1921–38, and 1949–61. The model explained $\overset{*}{W}$ very well for the interwar period, where U and $\dot{U}$ had previously not done well, and explained $\overset{*}{W}$ fairly well for the postwar period. Hines observed an upward shift in the slope of his wage function during the postwar period. He also estimated a second wage equation for the period 1921–61 (excluding war years) in which the independent variables were ΔT, T, $\overset{*}{P}$ , and U.²¹ He found the following: (a) the unionization variables were significant; (b) the price change variable was significant with a coefficient of about 0.6; and (c) the unemployment variable was insignificant.²² Hines suggested that, ceteris paribus, a unit change in the percentage of the labor force that was unionized would lead to a change of 1½ per cent in money wage rates.

The impact of unionization on the Phillips curve in the United States has been examined by Pierson [63] and by Ashenfelter and others [2].²³ Pierson divided U. S. manufacturing industries into strongly unionized and weakly unionized industry groups. She then estimated a wage equation of the Perry [57] variety for each of these groups on quarterly data for the period 1953–66. The coefficient on lagged price changes was found to be higher for the highly unionized group, suggesting that greater union strength is significantly associated with greater adaptation of wage changes to cost of living changes. Pierson also calculated some trade-offs between percentage changes in money wages and the unemployment rate. She found that greater union strength seemed to worsen the trade-off. At a 4 per cent unemployment rate, wage changes in the weak union group were 97 per cent of those in the strong union group, but at 5 per cent unemployment, the corresponding figure was only 84 per cent. Another finding of some interest was that the 1962–66 wage/price guideposts operated to offset the influence of union strength on $\overset{*}{W}$ , that is, the anti-inflationary impact of the guideposts was greatest in sectors with high unionization.

One of the important contributions made by Ashenfelter and others [2] is the construction of a simultaneous, three-equation model in which aggregate wage changes, aggregate price changes, and trade union growth are determined jointly. The simultaneous nature of the model is reflected by the inclusion of $\overset{*}{P}$ and ΔT as explanatory variables in the wage equation, ${\overset{*}{W}}_{t}$ and ${\overset{*}{W}}_{t - 1}$ as explanatory variables in the price equation, and $\overset{*}{P}$ as an explanatory variable in the equation for trade union growth.²⁴ The model was fitted to annual data for the U. S. manufacturing sector over the period 1914–63 and produced reasonable results. Aggregate wage changes were found to be positively related to trade union growth, price changes, and the ratio of work stoppages to union membership, and inversely related to the unemployment rate. The estimated coefficient on price changes in the wage equation was again substantially less than 1 (0.2 to 0.5, depending on the estimation method used). The solved reduced-form price equation from the model implied the following steady-state trade-offs between inflation and unemployment: (a) at U = 4 per cent and $\overset{*}{Q}$ = 2 per cent, and with all other exogenous variables assuming their mean values for the period 1950–60, the rate of price inflation was 3 per cent per annum; and (b) with $\overset{*}{Q}$ = 2.5 per cent, the unemployment rate consistent with price stability was about 6 per cent.²⁵

Threshold effects in cost of living changes

Recently, the hypothesis, advanced earlier by Phillips, that there is a threshold effect in the influence of cost of living changes on changes in money wage rates has been revived by Hamermesh [29] and by Eckstein and Brinner [22]. Using data from bargaining contracts of U. S. firms over the period 1948–67, Hamermesh found that small increases in the cost of living are not reflected in wage bargains. He reported that only in periods of relatively high rates of inflation do workers seek compensation for it by more rapid increases in negotiated wage rates. More specifically, Hamermesh found that the effect of $\overset{*}{P}$ on $\overset{*}{W}$ was greater when $\overset{*}{P}$ was greater than 2 per cent than when $\overset{*}{P}$ was less than 2 per cent. A rather weak effect was found for the influence of unemployment on $\overset{*}{W}$ , suggesting that the trade-off between these two variables was unimportant for negotiated wage changes. Hamermesh also made an argument for using wage rates rather than earnings in Phillips curve studies.²⁶

Eckstein and Brinner [22], in a recent study of inflation in the United States over the period 1955–70, also introduced a nonlinearity into the wage response to cost of living changes. More specifically, they found that as long as the rate of price inflation is below 2.5 per cent a year, the estimated coefficient on $\overset{*}{P}$ in the aggregate wage equation was about 0.5; however, when the rate of inflation exceeds 2.5 per cent for two consecutive years, then the price coefficient gradually rises to unity.²⁷ In fact, in large part because of this threshold cost of living effect, Eckstein and Brinner found that the wage/price mechanism in the United States becomes explosive at an unemployment rate of 4–4.5 per cent; that is, the long-run Phillips curve is virtually vertical at an unemployment rate of 4–4.5 per cent, and conventionally downward sloping at higher unemployment rates. Another finding of interest was that the poor combinations of inflation and unemployment experienced in the United States during the period of 1966–70 were due to particular historical circumstances (a period of excess demand, the abandonment of incomes policy, and the self-generating speed-up of the wage/price spiral once the fundamental conditions had gone sour) and did not indicate an unfavorable shift in the inflation/unemployment choices facing the economy.

Price and wage expectations and the expectations theory of the Phillips curve

The modifications to the Phillips curve reviewed earlier in this section qualify but do not challenge the conclusion that there is a long-run trade-off between inflation and unemployment. Recently, however, a number of writers, most notably Friedman [26] and Phelps [60], have argued that there is a temporary but not a permanent trade-off between inflation and unemployment.²⁸ It is their view that the temporary trade-off is a function of unanticipated inflation. In the long run when the actual rate of inflation comes to be fully anticipated, they expect the short-run Phillips curve to shift and the unemployment rate to return to its natural or normal level;²⁹ that is, the long-run steady-state Phillips curve is hypothesized to be a vertical line passing through the natural unemployment rate.³⁰ The expectations hypothesis also implies that attempts to hold the unemployment rate below [above] the natural rate will cause an upward [downward] acceleration of prices indefinitely.

In its simplest form, the expectations hypothesis as applied to wage determination can be written as ³¹

{\overset{*}{W}}_{t} = a_{0} + a_{1} U_{t} + a_{2} {\overset{*}{P}}_{t}^{e}

where ${\overset{*}{P}}_{t}^{e}$ is the expected rate of price inflation at time t.³² Empirical confirmation of the expectations hypothesis, at least with respect to competitive labor markets, requires that the estimated coefficient on ${\overset{*}{P}}_{t}^{e}$ be 1, for when a₂ = 1, then there is no long-run trade-off between inflation and unemployment.³³

The existing empirical evidence on the expectations hypothesis, while at this time still quite limited, suggests that the hypothesis can be rejected for the United States but not for Canada.³⁴ More specifically, empirical wage studies for the United States (using postwar data) by Turnovsky and Wachter [81], Gordon [28], Perry [59], and Holt and others [36] have found that the wage response to expected price changes is significant but is less than 1; that is, the coefficient a₂ is approximately 0.3 to 0.5. On the other hand, two recent studies of postwar wage behavior in Canada by Turnovsky [80] and Vanderkamp [84] have found that the wage response to expected price changes is not significantly different from 1 (a₂ ≈ 1), implying the absence of a long-run trade-off between inflation and unemployment there. Conclusions about the applicability of the expectations hypotheses in other countries await further empirical investigation.

Briefly summing up the results of those studies that have expanded the Phillips-Lipsey wage equation to accommodate new variables, it can be said that there is evidence, although it is not entirely conclusive, that at any given unemployment rate, the increase in money wage rates will be greater the higher are the profit rate, cost of living increases, labor productivity increases, and trade union aggressiveness. Since higher wage increases will, ceteris paribus, lead to higher price increases, this also implies that the higher are these variables the higher will be the rate of inflation at any given unemployment rate.³⁵ Also, where price expectations are fully reflected in money wage bargains, there will be no long-run trade-off between the rate of money wage inflation and unemployment. The available empirical evidence suggests that this condition has not been satisfied in the United States (and probably also not in the United Kingdom) but may well have been satisfied in Canada over the postwar period.

The simultaneous estimation of wage and price changes

One of the long-standing criticisms of single equation studies that regress changes in money wage rates on a set of variables that include price changes is that the relationship between wage changes and price changes is simultaneous: wage changes affect price changes just as price changes affect wage changes. The same criticism, of course, applies to single equation price studies that use wage changes as an independent variable. The consequence of simultaneity between $\overset{*}{W}$ and $\overset{*}{P}$ is that the estimated coefficients in the wage equation (or in the price equation) will be biased and inconsistent.³⁶ To overcome this problem, some writers have abandoned ordinary least-squares estimation of $\overset{*}{W}$ or $\overset{*}{P}$ in favor of more simultaneous methods, such as two-stage least squares or limited-information maximum likelihood. In addition, the interdependence between wage changes and price changes has become an important part of most econometric models of national economies.

The most popular method of treating the simultaneity between $\overset{*}{W}$ and $\overset{*}{P}$ has been to use a Phillips-type wage equation with a markup-type price equation and to estimate both equations by a method such as two-stage least squares. Assume that the structural wage and price equations take the following forms.

\begin{matrix} (1) & \overset{*}{W} = α_{0} + α_{1} U^{- 1} - α_{2} \dot{U} + α_{3} \overset{*}{P} \end{matrix}

\begin{matrix} (2) & \overset{*}{P} = β_{0} + β_{1} \overset{*}{W} + β_{2} C \overset{*}{M} - β_{3} \overset{*}{Q} + β_{4} {\overset{*}{P}}_{M}, \end{matrix}

where U⁻¹, $\dot{U}$ , $\overset{*}{W}$ , $\overset{*}{P}$ , and $\overset{*}{Q}$ are defined as before and where $C \overset{*}{M}$ and ${\overset{*}{P}}_{M}$ represent percentage changes in cost of materials and import prices, respectively. The estimation procedure requires only a few steps: (a) each of the endogenous variables (namely, $\overset{*}{W}$ and $\overset{*}{P}$ ) is regressed on all the exogenous (predetermined) variables (U⁻¹, $\dot{U}$ , $C \overset{*}{M}$ , $\overset{*}{Q}$ , and ${\overset{*}{P}}_{M}$ ) in the system; (b) the estimated (calculated) values of $\overset{*}{W}$ and $\overset{*}{P}$ (call them Ŵ and $\hat{P}$ ) from step (a) are then introduced into equations (1) and (2) in place of their actual values, so that the new equations become

\begin{matrix} (3) & \overset{*}{W} = α_{0} + α_{1} U^{- 1} - α_{2} \dot{U} + α_{3} \hat{P} \end{matrix}

\begin{matrix} (4) & \overset{*}{P} \end{matrix} = β_{0} + β_{1} \hat{W} + β_{2} C \overset{*}{M} - β_{3} \overset{*}{Q} + β_{4} {\overset{*}{P}}_{M};

(c) equations (3) and (4) are then estimated by ordinary least squares. In this way the interdependence between $\overset{*}{W}$ and $\overset{*}{P}$ is explicitly taken into account and the simultaneous equation bias is removed. This type of wage/price model also has two other features: (a) the only excess demand factor in the model is the unemployment rate, so that demand changes affect price changes only via their influence on wage changes (or other cost variables); and (b) as long as the product of the estimated coefficients of $\overset{*}{W}$ and $\overset{*}{P}$ (α₃ B₁) is less than 1 (and greater than zero), the wage/price spiral will not be explosive, that is, there will be a stable set of inflation/unemployment possibilities.

Two early studies of wage/price behavior in the United Kingdom, one by Klein and Ball [43] and the other by Dicks-Mireaux [18], are representative examples of the wage/price model described above. The former study covers the period 1948–57 (with quarterly data), while the latter covers the period 1946–59 (with annual data). The familiar inverse relationship between $\overset{*}{W}$ and U is confirmed in both studies, as is the two-way causation between $\overset{*}{W}$ and $\overset{*}{P}$ . Of particular interest in the Dicks-Mireaux study is the estimation of the wage and price regressions by both ordinary least squares (OLS) and two-stage least squares (TSLS). He found, as one would expect since $\overset{*}{W}$ and $\overset{*}{P}$ are positively related, that the OLS method gives higher coefficients on $\overset{*}{W}$ and $\overset{*}{P}$ than does TSLS, that is, OLS estimates of the coefficient of $\overset{*}{P}$ in $\overset{*}{W}$ regressions will have an upward bias. However, the bias of the OLS estimates was found to be quite small, which suggests that feedbacks between $\overset{*}{W}$ and $\overset{*}{P}$ were probably not too serious during this postwar period.³⁷

In a 1966 study, Vanderkamp [83] used a simultaneous wage/price model to derive estimates of the trade-off between inflation and unemployment in Canada. The study used quarterly data for the period 1947–62. Three estimating techniques were tried—OLS, TSLS, and full- information maximum likelihood (FIML). The discussion in the paper used the FIML estimates. There are separate wage regressions for the organized and unorganized sectors of the labor market. The regression for the organized sector took the form ${\overset{*}{W}}_{0} = f (U^{- 1}, \overset{*}{P}, \overset{*}{Q}),$ while that for the unorganized sector was ${\overset{*}{W}}_{U} = g (U^{- 1}, \dot{U}, \overset{*}{P}) .$ Vanderkamp was able to explain wage changes better in the organized than in the unorganized sector (R² = 0.89 versus R² = 0.52). The coefficient on $\overset{*}{P}$ in the wage equation was higher for the organized sector (but still less than 1); it will be recalled that Pierson [63] obtained similar results for the United States. The price change equation in the model regressed ${\overset{*}{P}}_{t} on {\overset{*}{W}}_{0}, {\overset{*}{W}}_{U}, {\overset{*}{P}}_{M}, and {\overset{*}{P}}_{t - 1} .$ All variables, except wage changes in the unorganized sector $({\overset{*}{W}}_{U}),$ were significant and the regression had very high explanatory power. Given the estimated wage and price equations, the following trade-off estimates were derived: (a) the unemployment rate compatible with price stability was 8 per cent (assuming that $\dot{U}$ = 0, ${\overset{*}{P}}_{M}$ = 0, $\overset{*}{Q}$ = 2 per cent a year); (b) at a 3 per cent unemployment rate, the annual rate of inflation was 1.8 per cent; and (c) at 2 per cent unemployment, the implied annual inflation rate was 3.2 per cent. Since Vanderkamp’s inflation/unemployment schedule was highly nonlinear, he found that small increases in unemployment produced high anti- inflationary payoffs when U was low (between 2 per cent and 5 per cent) but very small payoffs when U was high (greater than 5 per cent).

Prices and wages have also been estimated jointly in a number of studies for the United States. One of the interesting features of some of these studies is that the simple markup price equation has been modified to allow the markup (on variable costs) to vary with the state of excess demand in the product market. One of the first studies to incorporate this assumption was Schultze and Tryon’s [72] contribution to the volume on the Brookings model. The regression period was 1948 to 1960 (with quarterly data). The wage equation in the model was of the Perry type, that is, $\overset{*}{W} = f (U^{- 1}, π, \overset{*}{P})$ The explanatory power of the regression was quite good, and all variables were highly significant. At a 4 per cent unemployment rate (and assuming a normal profit rate (π) and $\overset{*}{P}$ = 0), their equation predicted a 5 per cent annual increase in wages in the manufacture of durable goods and 4.1 per cent increase in the manufacture of nondurable goods. The price equation in the Brookings model is a markup equation with the following properties: (a) prices are set as a markup on standard costs (costs at normal levels of operation), (b) temporary changes in costs (deviation of actual from standard costs) also affect prices but less than permanent changes, and (c) the markup factor varies with excess demand or excess supply (the markup is raised in expansions and lowered in recessions). The proxies for excess demand in the product market were the capacity utilization rate and an inventory disequilibrium variable. The fit of the price equation was quite good for durable manufacturing (R² > 0.9), and all variables were significant with the expected signs. No attempt was made to derive a trade-off between price inflation and unemployment.

At a recent conference on the econometrics of price determination, Hymans [38] provided a useful comparison of wage and price determination in three large econometric models of the United States. The three models were the Office of Business Economics (OBE) model, the FRB-MIT-Penn (FMP) model, and the DHL-Ill model of the University of Michigan.³⁸ Each model focuses on wage and price behavior in the private or nonfarm private sector of the economy during the period 1953–68 (quarterly). Simulations were also carried out for the period 1965–69. The wage equations in the three models are all of the Phillips-Lipsey variety with only slight modifications, that is, all use U⁻¹, $\dot{U}$ , and $\overset{*}{P}$ to explain $\overset{*}{W}$ . The wage equation had high explanatory power in each of the models. The estimated coefficient on consumer price changes was below unity in each model but its value differed substantially across models—it was 0.42, 0.57, and 0.77 in the DHL-III, FMP, and OBE models, respectively. The price equations in the three models are all of the variable markup variety, that is, prices are set as a markup on unit labor costs with the markup factor varying according to excess demand. The FMP model uses an unfilled orders variable to measure excess demand, while the OBE and DHL models use capacity utilization measures. The models also differ in that the OBE and DHL models include output per worker in the price equation (as one component of unit labor costs) whereas the FMP model uses only wage costs. Each of the models explained price behavior over the regression period quite well. In the simulation exercise for 1965-69, the FMP model performed best, followed by the DHL model.

Each of the three models was also simulated to produce the steady- state trade-off between inflation and unemployment implied by its estimated structure. The OBE trade-off curve was the steepest, while the DHL curve showed the greatest amount of curvature. The annual rate of inflation corresponding to a steady 4 per cent unemployment rate was 3.2 per cent for the DHL model, 3.7 per cent for the FMP model, and 3.9 per cent for the OBE model. At a steady 5 per cent unemployment rate, the annual rate of inflation dropped to about 2 per cent in each of the models. In contrast, at 3 per cent unemployment, the inflation rate ranged from 6 per cent to 8 per cent.

The general results of those studies that have taken a simultaneous approach to wage and price determination can be summarized as follows: (a) the relationship between wage changes and price changes does seem to run in both directions; therefore, unless price [wage] changes are lagged and do not overlap with wage [price] changes, the coefficients in the wage [price] equation will be biased and inconsistent if single equation estimating methods (OLS) are employed;³⁹ (b) the limited available evidence also suggests, however, that this simultaneous equations bias is not too serious, that is, TSLS produces coefficient estimates not very different from OLS; and (c) the most important determinants of wage and price changes in the simultaneous equation studies are generally the same as those in the single equation studies. More specifically, the inverse relationship between percentage changes in money wage rates and the unemployment rate has been confirmed for the United States, the United Kingdom, and Canada, among other countries.⁴⁰

Alternative measures of the excess demand for and the price of labor

A problem arises in any econometric model or equation when variables do not in fact measure what they are supposed to measure. This criticism has been made in a number of studies with respect to the unemployment rate and the change in money wage rates.

One of the early criticisms of the unemployment rate as a proxy for excess demand in the labor market was made by Dow and Dicks- Mireaux [19 and 20]. They argued that the excess demand for labor will be zero when the number of unemployed workers equals the number of job vacancies. Therefore, unemployment or vacancies alone will be an inaccurate measure of the excess demand for labor.⁴¹ Owing to frictional and structural unemployment, the unemployment rate will never fall to zero even when the demand for labor is very high; some workers will always be switching jobs, and there will always be some mismatching of job vacancies and unemployed workers owing to differences between skills required and those available and between wage aspirations and wages offered by employers. Also, the number of job vacancies will not be zero even when the demand for labor is very low because of imperfections and frictions in the labor market. Dow and Dicks-Mireaux therefore propose their own index of the pressure of demand for labor, which combines information on unemployment rates and job vacancy rates.⁴² In their 1959 article, they used this index of demand pressure, along with the change in retail prices, to explain changes in money wage rates (quarterly) in the United Kingdom for the periods 1946–56 and 1950–56. Both independent variables were significant, and the equation had high explanatory power.

More recently, Holt and others [36] have shown that the Phillips relation can be derived from a set of relationships in the labor market, one of which is the relationship between changes in money wage rates and the ratio of the vacancy rate to the unemployment rate; when this ratio is high, $\overset{*}{W}$ will be high, and vice versa. In a closely related article, MacRae and others [53] estimated wage equations with the ratio of vacancies to unemployment as the explanatory variable and obtained reasonable results for the United States, the United Kingdom, and Japan. The regression period was 1959–69 for the United States, and 1957–69 for the United Kingdom and Japan; quarterly data were used throughout. The estimated wage equations indicated that the sensitivity of wage change to labor market tightness was approximately the same in the United States and the United Kingdom but far higher in Japan.

Other criticisms of the unemployment rate as a proxy for excess demand are that it fails to account for: (a) a pool of unrecorded unemployment (known as the labor reserve, or hidden unemployment), which arises from deficient aggregate demand; (b) the underutilization of employed labor, which arises because labor is not a completely variable factor of production in the short run; and (c) changes in the age/sex composition of unemployment, which alter the degree of wage pressure associated with any given aggregate unemployment rate.

Unrecorded, or hidden, unemployment arises during periods of less than full employment because some groups in the labor force vary their participation rates in accord with the levels of aggregate demand and employment, that is, in accord with the probability of finding employment. More specifically, it has been found that secondary workers (teenagers, women, and older men) often drop out of the recorded labor force when they become unemployed (the so-called discouraged worker effect).⁴³ In contrast, the labor force participation of primary workers (prime-age men, 25–55 years old) does not seem to be related to labor market tightness, that is, they do not drop out of the labor force when they become unemployed. This, in effect, means that unless there is full employment, the recorded unemployment rate will overstate the degree of tightness in the labor market, because the recorded labor force will understate the size of the real labor force; that is, the recorded unemployment rate will always be lower (except at full employment) than the unemployment rate adjusted for hidden unemployment (labor reserves).

Simler and Telia [74] have used the concept of the labor reserve to explain the moderate changes in money wage rates that occurred in the United States during the period 1962–66. Earlier Perry [58] had attributed this wage slowdown to the imposition of the wage/price guideposts.⁴⁴ Simler and Telia pointed out that whereas the recorded unemployment rate fell from 6.5 per cent in 1961 to 3.7 per cent in 1966, the decline in the adjusted unemployment rate (U adjusted for labor reserves) was smaller, dropping from 8 per cent to 5.4 per cent. They therefore suggested that this labor reserve may have offset some of the upward wage pressure caused by the decline in the recorded unemployment rate. To test this hypothesis, they estimated a wage equation of the Perry type on quarterly data for the period 1953–64. The independent variables were U⁻¹, $\overset{*}{P}$ , π, $\dot{π}$ , and the difference between the reciprocals of the adjusted and recorded unemployment rates (U^*−1 − U⁻¹). All variables including the labor reserve variable were highly significant. In addition, the wage equation with labor reserves explained $\overset{*}{W}$ better (especially for the period 1962–64) than did the wage equation without labor reserves.⁴⁵

Underutilization of employed labor (hoarded labor) arises during recessions because employers are reluctant (owing to the fixed nature of hiring and training costs) to release trained and experienced workers, especially if the recession is expected to be only temporary. As Miller [54] has pointed out, hoarding of labor can be a substitute for holding a large inventory of finished goods. Also, the existence of contractual commitments between unions and employers constrains employee layoffs. For these reasons, labor can be regarded, in the words of Oi [55], as a quasi-fixed factor of production in the short run. Given this stickiness of employment with respect to changing demand conditions, it follows that the unemployment rate will be a lagging and imperfect indicator of excess demand (or supply) in the labor market.

A recent study by Taylor [78] for the United States includes an estimate of hoarded labor in the wage function. Taylor derived estimates of hoarded unemployment (U_n) and hidden unemployment (U_h) in U. S. manufacturing by applying the trend-through-peaks method on data for output per man-hour and for labor force participation rates of females. He then estimated a series of alternative wage equations for the period 1948–68 (quarterly) in which the recorded unemployment rate was compared with the adjusted unemployment rate (U adjusted for hidden and hoarded unemployment). The adjusted unemployment rate was found to be superior in all comparable equations, and it was always highly significant. Taylor also observed that whereas hidden unemployment had little effect on the performance of the unemployment variable in the wage equations, hoarded unemployment had a substantial effect.⁴⁶ Thus, the decision to raise wages may well be sensitive to the utilization of labor within the firm as well as to the excess demand for labor outside it.⁴⁷

Changes in the age/sex composition of unemployment (at any given unemployment rate) can also make the aggregate unemployment rate a less useful proxy for labor market tightness, because some types of worker exert a stronger influence on aggregate wage changes than do others. Whereas the official unemployment rate regards all unemployed individuals equally, it is well known that prime-age men work more hours on average and obtain higher average wages than do prime-age women or younger workers of both sexes. Thus, a given unemployment rate will exert less downward pressure on wages, the higher is the proportion of women and younger workers in unemployment.

Evans and Klein [25] in the Wharton model have used a wage equation that takes some account of the composition of unemployment. They used the difference between the unemployment rate for all workers and that for prime-group employees (men, ages 25–34) as their proxy for the excess demand for labor. Since the unemployment rate for prime-group employees (U*) is likely to be a sensitive and leading indicator of excess labor demand, they argued that the greater the difference between the two unemployment rates (U − U^*), the greater would be the upward pressure on wages.⁴⁸ The wage equation was tested on quarterly data (for 1948-64) for the sector in the United States that manufactures durable goods. All three independent variables— $\overset{*}{P}$ , lagged $\overset{*}{W}$ , and (U −U^*)—were significant, and the equation had respectable explanatory power.

The inflationary consequences of changes in the age/sex composition of unemployment have been more thoroughly investigated in a recent paper by Perry [59]. After demonstrating that the proportion of secondary workers (women, men over 65, and young workers) in the labor force and in unemployment increased in the United States between 1951 and 1969, Perry constructed a weighted unemployment rate that adjusts for differences in average hours worked and average wages paid among age/sex groups. Compared with the official unemployment rate, the weighted unemployment rate indicated a progressively tighter labor market in recent years relative to earlier periods, that is, the spread between the two unemployment rates increased from less than half a point early in the 1950s to a full point late in the 1960s. Perry also constructed a measure of the dispersion of unemployment among the same age/sex groups. In alternative wage equations on quarterly data for the period 1953–68, the weighted unemployment rate (in reciprocal form) and the variable for unemployment dispersion were significant with the expected signs, and the equations using these variables had higher explanatory power than those using the official unemployment rate ( ${\bar{R}}^{2}$ = 0.78 versus ${\bar{R}}^{2}$ = 0.66).⁴⁹ The coefficient on consumer price changes was again below unity, about 0.35. A proxy for hidden unemployment was tried in the wage equations, but it proved to be insignificant. Perry also derived some steady-state trade-offs between the rate of inflation (for both wage and price inflation) and the unemployment rate, which indicated that the current trade-off (1967–70) was more unfavorable than that of the mid-1950s.⁵⁰ More specifically, the annual rate of price inflation associated with a steady 4 per cent unemployment rate was estimated to be 4.5 per cent for the current period, versus 2.8 per cent for the mid-1950s. Further, Perry presented evidence that suggested that the unfavorable shift in the trade-off occurred because the labor market was tighter late in the 1960s than it was in the mid-1950s, at the same official unemployment rate.

Changes in the industrial or demographic composition of employment can similarly make the change in aggregate money wage rates a less useful proxy for the changing price of labor services.⁵¹ If no adjustment is made for these changes, then an increase in the ratio of employment in high-wage industries to employment in all industries or an increase in the ratio of prime-age male employment to all employment will increase $\overset{*}{W}$ quite independently of any change in the demand for labor. This point was well illustrated in two recent articles, one by Eckstein [21] for the United States and one by Braun [11] for the United Kingdom. Eckstein examined wage behavior in the United States for the sector that manufactures durable goods during the period 1950-60 (quarterly). He found that the most important determinant of $\overset{*}{W}$ was changes in the industrial mix of employment (defined as the change in the ratio of employment in the four highest-wage industries to total employment). Similarly, Braun found that after adjusting $\overset{*}{W}$ to reflect changes in the distribution of employment among industries and among men, women, and juveniles, there was less evidence than had previously been supposed to support the conclusion that the Phillips curve had shifted upward late in the 1960s (1967–70) in the United Kingdom.⁵²

It is clear that such factors as the vacancy/unemployment relationship, hidden unemployment, hoarded unemployment, and changes in the composition of both employment and unemployment can have an important influence on the relationship between the percentage change in money wage rates and the unemployment rate. The more these factors are changing over time, the less meaningful will be the trade-off between the rate of wage inflation and the official unemployment rate as an indicator of the relationship between the excess demand for labor and the price of labor services.

III. The Trade-Off Between Wage Inflation and Unemployment: A Comparison of Estimates from Different Studies

Since the existing empirical literature on the Phillips curve is by now rather substantial, at least for a few countries, it seems natural to inquire whether these studies suggest some consensus about the magnitude of the trade-off between the rate of wage inflation and the unemployment rate in these countries. Unfortunately, a meaningful comparison of trade-off estimates from different studies, both within and across countries, is made difficult by differences among studies with respect to time periods, degree of disaggregation, mathematical form of the relationships, estimating technique, definition of variables, and choice of independent variables.⁵³ Therefore, the most that should be expected from a comparison of trade-off estimates is an approximate picture of the past relationship between wage inflation and unemployment in the selected countries.

Table 1.

Some Representative Estimates of the Steady-State Trade-Off Between Wage Inflation and Unemployment in the United States, Canada, and the United Kingdom

¹D_S is a variable that measures changes in the distribution of output among manufacturing industries; D_S was assigned a value of 0.1359 for the calculations (its average value during the period 1961–65).

²D_IC is a dummy variable for the wage/price guideposts; it was assigned a value of zero.

³The expression (U^*−1—U⁻¹) was assumed to be equal to zero; U^*−1 is the reciprocal of the unemployment rate adjusted for labor reserves.

⁴ $\overset{*}{W}$ was set equal to ${\overset{*}{W}}^{- 1}$ for the trade-off calculations; D_IC was set equal to zero.

^⁵The profits variable was defined differently in this study.

⁶W_US, wage changes in the United States, were assumed to be equal to 3.2 per cent. $\overset{*}{W}$ was set equal to ${\overset{*}{W}}^{- 1}$ for the trade-off calculations.

⁷D_IC was set equal to zero.

⁸N is the change in the percentege of the labor force that was unionized; $\overset{*}{N}$ was assigned a value of zero.

⁸D_IC was assigned a value of zero; ${\overset{*}{P}}_{t}$ was set equal to ${\overset{*}{P}}_{t - 1}$ for the trade-off calculations.

Table 1.

Some Representative Estimates of the Steady-State Trade-Off Between Wage Inflation and Unemployment in the United States, Canada, and the United Kingdom

										Assumptions About
Investigator		Steady-State Percentage Wage Change Associated with Unemployment Rate Equal to					Regression Period	Data: Annual (A) or Quarterly (Q)	Form of Wage Change Equation	Profits	Rate of productivity increase
Investigator		1 per cent	2 per cent	3 per cent	4 per cent	5 per cent	Regression Period	Data: Annual (A) or Quarterly (Q)	Form of Wage Change Equation	(π)	$(\overset{*}{Q})$
United States
	Perry [57]			7.1	5.2	4.0	1947–60	Q	$\overset{}{W} = f (U^{- 1}, \overset{}{P}, \dot{π}, π)$	11.8	3.0
	Black and Kelejian [6]			5.3	4.1	2.9	1948–65	Q	$\overset{}{W} = f {(U, \dot{U}, \overset{}{P}, \overset{*}{Q}, D_{s})}^{1}$		3.0
	Pierson [63]			6.9	4.9	3.7	1953–66	Q	$\overset{}{W} = f (U^{- 1}, \overset{}{P}, π, D_{I C})^{2}$		3.0
	Simler and Telia [74]			6.2	4.8	4.0	1953–64	Q	$\overset{}{W} = f (U^{- 1}, \overset{}{P}, π, \dot{π}, U^{* - 1} - U^{- 1})^{3}$	11.8	3.0
	Bodkin and others [9]			5.4	4.3	3.8	1953–65	Q	$\overset{}{W} = f (U^{- 2}, \overset{}{P}, π, {\overset{*}{W}}^{- 1}, D_{I C})^{4}$	113.3 ⁵	3.0
Canada Zaidi [88]				6.9	5.0	3.9	1947–62	A	$\overset{}{W} = f (U^{- 1}, \overset{}{P}, π)$	0.37 ⁵	4.0
	Bodkin and others [9]			4.4	2.9	2.2	1953–65	Q	$\overset{}{W} = f (U^{- 2}, \overset{}{P}, π, {\overset{}{W}}_{U S}, {\overset{}{W}}_{- 1})^{6}$	97.75 ⁵	4.0
	Kaliski [42]			5.5	4.2	3.5	1946–58	A	$\overset{}{W} = f (U^{- 1}, \dot{U}, \overset{}{P})$		4.0
United Kingdom Bodkin and others [9]		13.6	5.5	2.9			1954–65	Q	$\overset{}{W} = f (U^{- 1}, \overset{}{P}, D_{I C})^{7}$		2.0
	Lipsey and Parkin [48]	4.4	2.7	1.0			1948–68	Q	$\overset{}{W} = f (U, \overset{}{P}, \overset{*}{N})^{8}$		2.0
	Smith [75]	7.0	2.3	0.8			1948–67	Q	$\overset{}{W} = f (U^{- 1}, \overset{}{P}, {\overset{*}{P}}_{- 1}, D_{I C})^{9}$		2.0

²D_IC is a dummy variable for the wage/price guideposts; it was assigned a value of zero.

³The expression (U^*−1—U⁻¹) was assumed to be equal to zero; U^*−1 is the reciprocal of the unemployment rate adjusted for labor reserves.

⁴ $\overset{*}{W}$ was set equal to ${\overset{*}{W}}^{- 1}$ for the trade-off calculations; D_IC was set equal to zero.

^⁵The profits variable was defined differently in this study.

⁶W_US, wage changes in the United States, were assumed to be equal to 3.2 per cent. $\overset{*}{W}$ was set equal to ${\overset{*}{W}}^{- 1}$ for the trade-off calculations.

⁷D_IC was set equal to zero.

⁸N is the change in the percentege of the labor force that was unionized; $\overset{*}{N}$ was assigned a value of zero.

⁸D_IC was assigned a value of zero; ${\overset{*}{P}}_{t}$ was set equal to ${\overset{*}{P}}_{t - 1}$ for the trade-off calculations.

Table 1.

Some Representative Estimates of the Steady-State Trade-Off Between Wage Inflation and Unemployment in the United States, Canada, and the United Kingdom

										Assumptions About
Investigator		Steady-State Percentage Wage Change Associated with Unemployment Rate Equal to					Regression Period	Data: Annual (A) or Quarterly (Q)	Form of Wage Change Equation	Profits	Rate of productivity increase
Investigator		1 per cent	2 per cent	3 per cent	4 per cent	5 per cent	Regression Period	Data: Annual (A) or Quarterly (Q)	Form of Wage Change Equation	(π)	$(\overset{*}{Q})$
United States
	Perry [57]			7.1	5.2	4.0	1947–60	Q	$\overset{}{W} = f (U^{- 1}, \overset{}{P}, \dot{π}, π)$	11.8	3.0
	Black and Kelejian [6]			5.3	4.1	2.9	1948–65	Q	$\overset{}{W} = f {(U, \dot{U}, \overset{}{P}, \overset{*}{Q}, D_{s})}^{1}$		3.0
	Pierson [63]			6.9	4.9	3.7	1953–66	Q	$\overset{}{W} = f (U^{- 1}, \overset{}{P}, π, D_{I C})^{2}$		3.0
	Simler and Telia [74]			6.2	4.8	4.0	1953–64	Q	$\overset{}{W} = f (U^{- 1}, \overset{}{P}, π, \dot{π}, U^{* - 1} - U^{- 1})^{3}$	11.8	3.0
	Bodkin and others [9]			5.4	4.3	3.8	1953–65	Q	$\overset{}{W} = f (U^{- 2}, \overset{}{P}, π, {\overset{*}{W}}^{- 1}, D_{I C})^{4}$	113.3 ⁵	3.0
Canada Zaidi [88]				6.9	5.0	3.9	1947–62	A	$\overset{}{W} = f (U^{- 1}, \overset{}{P}, π)$	0.37 ⁵	4.0
	Bodkin and others [9]			4.4	2.9	2.2	1953–65	Q	$\overset{}{W} = f (U^{- 2}, \overset{}{P}, π, {\overset{}{W}}_{U S}, {\overset{}{W}}_{- 1})^{6}$	97.75 ⁵	4.0
	Kaliski [42]			5.5	4.2	3.5	1946–58	A	$\overset{}{W} = f (U^{- 1}, \dot{U}, \overset{}{P})$		4.0
United Kingdom Bodkin and others [9]		13.6	5.5	2.9			1954–65	Q	$\overset{}{W} = f (U^{- 1}, \overset{}{P}, D_{I C})^{7}$		2.0
	Lipsey and Parkin [48]	4.4	2.7	1.0			1948–68	Q	$\overset{}{W} = f (U, \overset{}{P}, \overset{*}{N})^{8}$		2.0
	Smith [75]	7.0	2.3	0.8			1948–67	Q	$\overset{}{W} = f (U^{- 1}, \overset{}{P}, {\overset{*}{P}}_{- 1}, D_{I C})^{9}$		2.0

²D_IC is a dummy variable for the wage/price guideposts; it was assigned a value of zero.

³The expression (U^*−1—U⁻¹) was assumed to be equal to zero; U^*−1 is the reciprocal of the unemployment rate adjusted for labor reserves.

⁴ $\overset{*}{W}$ was set equal to ${\overset{*}{W}}^{- 1}$ for the trade-off calculations; D_IC was set equal to zero.

^⁵The profits variable was defined differently in this study.

⁶W_US, wage changes in the United States, were assumed to be equal to 3.2 per cent. $\overset{*}{W}$ was set equal to ${\overset{*}{W}}^{- 1}$ for the trade-off calculations.

⁷D_IC was set equal to zero.

⁸N is the change in the percentege of the labor force that was unionized; $\overset{*}{N}$ was assigned a value of zero.

⁸D_IC was assigned a value of zero; ${\overset{*}{P}}_{t}$ was set equal to ${\overset{*}{P}}_{t - 1}$ for the trade-off calculations.

I have calculated trade-off estimates between $\overset{*}{W}$ and U from a number of studies for each of the three countries under investigation—the United States, Canada, and the United Kingdom. These estimates appear in Table 1. They refer to the steady-state relationship between $\overset{*}{W}$ and U, that is, the $\overset{*}{W}$ associated with an unemployment rate that is constant over time. More specifically, the trade-off estimates were obtained under the following set of assumptions: (a) all rate of change variables (except $\overset{*}{Q}$ ) were set equal to zero ( $\dot{U}$ , $\dot{π}$ = 0), unless otherwise indicated; (b) all variables expressed in levels (except U) were assumed to take on their average values over the regression period, unless otherwise indicated; and (c) price changes were set equal to wage changes minus productivity changes, that is, $\overset{*}{P} = \overset{*}{W} - \overset{*}{Q} .^{54}$ For example, given an estimated wage equation of the form $\overset{*}{W} = a + b_{1} \overset{*}{P} - b_{2} U + b_{3} π,$ the steady-state solution for $\overset{*}{W}$ is given by

\overset{*}{W} = \frac{a - b_{1} \overset{*}{Q} + b_{3} π}{1 - b_{1}} - \frac{b_{2} U}{1 - b_{1}} .^{55}

Since a, b₁ b₂ and b₃ are available from the estimated wage equation, it is merely necessary to insert values for $\overset{*}{Q}$ , π, and U to calculate the steady-state trade-off between $\overset{*}{W}$ and U for various values of U. For the calculations in Table 1, the average rate of productivity increase $(\overset{*}{Q})$ was set equal to 4.0 per cent, 3.0 per cent, and 2.0 per cent for Canada, the United States, and the United Kingdom, respectively. Also, since the unemployment rate has been consistently lower (in the postwar period) in the United Kingdom than in either the United States or Canada, unemployment rates of 1–3 per cent were used for the U. K. calculations, while rates of 3–5 per cent were used for the U. S. and Canadian calculations.

Two interesting conclusions emerge from an examination of Table 1. First, although the studies for each country differ in many respects, the derived, steady-state trade-offs are quite similar within countries, especially for the United States and Canada.⁵⁶ While the studies included in Table 1 represent only a small sample of the many trade-off estimates for the three countries, the consistency of estimates in the table is encouraging. Second, an intercountry comparison of these Phillips curves suggests that the trade-off between wage inflation and unemployment is about equally unfavorable in the United States and Canada, and less unfavorable in the United Kingdom.⁵⁷ More specifically, the annual percentage change in money wage rates (in the steady state) associated with a 4 per cent unemployment rate would seem on the average of the postwar period (before 1967) to be about 4–5 per cent in the United States and Canada. In the United Kingdom, the same percentage change in money wage rates seems to have corresponded (over the same time period) to an unemployment rate of 1–2 per cent.

IV. Some Evidence on the Trade-Off Between Price Changes and Unemployment

Many of the studies discussed thus far in this review have been concerned primarily with the trade-off between wage changes and the unemployment rate. The trade-off that is generally considered to be of greater importance, however, is that between price changes and the unemployment rate. There are essentially three alternative approaches to calculating this latter trade-off. The first approach is to combine a wage equation of the Phillips-Lipsey type with the simple assumption that price changes equal wage changes minus changes in labor productivity. For example, if the wage equation indicates that a 3 per cent unemployment rate is associated with a 6 per cent wage increase, then assuming a 2 per cent increase in labor productivity, the associated rate of price inflation is calculated to be 4 per cent. While this approach offers obvious computational convenience, it is not likely to be very reliable, because the bulk of the empirical evidence on aggregate price determination (for example, see [22], [23], and [28]) suggests that price changes are not a function of changes in unit labor costs alone.⁵⁸ More specifically, such factors as changes in material costs, profits, import prices, and standard unit labor costs, as well as excess demand conditions in the product market, can also be expected to exert independent influence on price changes. Therefore, unless the price change assumption is modified to account for these factors, the single equation wage studies (cum the assumption that $\overset{*}{P} = \overset{*}{W} - \overset{*}{Q}$ ) are apt to be better indicators of the trade-off between wage changes and unemployment than of that between price inflation and unemployment.⁵⁹

The second approach to determining the trade-off between $\overset{*}{P}$ and U is to specify and estimate (by, for example, two-stage least squares) a simultaneous equations model for $\overset{*}{W}$ and $\overset{*}{P}$ , and then to solve this model (using the estimated parameters from the structural wage and price equations) for the reduced-form trade-off between $\overset{*}{P}$ and U. For example, if the structural equations for $\overset{*}{P}$ and $\overset{*}{W}$ are

\overset{*}{P} = a_{0} + a_{1} \overset{*}{W} + a_{2} C \overset{*}{M} + a_{3} \overset{*}{Q} + a_{4} E D

\overset{*}{W} = b_{0} + b_{1} U + b_{2} π + b_{3} \overset{*}{P},

where ED is a proxy variable for excess demand in the product market and where all other variables are defined as before, then the derived trade-off between $\overset{*}{P}$ and U is given by

\frac{\overset{*}{P} = a_{0} + a_{1} b_{0} + a_{1} b_{1} U + a_{1} b_{2} π + a_{2} C \overset{*}{M} + a_{3} \overset{*}{Q} + a_{4} E D}{(1 - a_{1} b_{3})} .

Using the estimated coefficients (a₀ … a₄, b₀ … b₃) and inserting average values for all exogenous variables for all exogenous variables $(π, C \overset{*}{M}, \overset{*}{Q}, and E D)$ except U, one can calculate the $\overset{*}{P}$ associated with any given U. This method will be an improvement on the first method to the extent that the estimated price equation provides a better explanation of $\overset{*}{P}$ than does the simple assumption that $\overset{*}{P} = \overset{*}{W} - \overset{*}{Q}$ .

The third approach to determining the trade-off between $\overset{*}{P}$ and U is to estimate the relationship between $\overset{*}{P}$ and U directly, that is, regress $\overset{*}{P}$ on U (and perhaps other variables). This third approach, like the first one, offers computational convenience but it also suffers from several deficiencies. It is necessary to first point out that an equation relating $\overset{*}{P}$ to U (among other variables) can be either a reduced-form price equation from a set of structural wage and price equations, or a structural price equation itself. If it is a reduced-form price equation, then it will suffer from all the familiar weaknesses of reduced-form estimation in cases where the structural wage and price equations are overidentified.⁶⁰ On the other hand, if it is proposed as a structural price equation, there are other shortcomings, at least with respect to the simple specification where $\overset{*}{P}$ is a function of U (and perhaps $\dot{U}$ ) alone. First, the unemployment rate is more properly a proxy for excess demand in the labor market rather than in the product market. Therefore, unless the excess demand for labor varies closely with the excess demand for products, the relationship between $\overset{*}{P}$ and U will probably be weaker than that between $\overset{*}{P}$ and a good proxy for excess demand in the product market (the ratio of unfilled orders to full capacity production, the ratio of inventories to shipments, etc.). Second, the absence of cost factors in the equation implies that such costs (wage, material, and capital costs) are a function of the unemployment rate. This assumption seems weak, at least with respect to nonwage costs. A better specification of the determinants of price changes should probably include both cost factors and excess demand factors, as, for example, in Eckstein and Fromm [23] and in Gordon [28]. In short, structural price equations that regress $\overset{*}{P}$ on U probably incur some specification error and may sacrifice some explanatory power in order to determine the relationship between two variables that are important policy targets.⁶¹

Since the empirical evidence from studies that calculate the trade-off between $\overset{*}{P}$ and U using the first two methods (outlined above) has already been discussed, we now turn to the empirical evidence from studies that regress $\overset{*}{P}$ on U directly.

In a 1968 study, Brechling [12] estimated some trade-offs between the percentage change in the U. S. GNP (gross national product) deflator $({\overset{*}{P}}_{G})$ and the unemployment rate on quarterly data for the period 1949–66. When ${\overset{*}{P}}_{G}$ was regressed on U (more precisely, on U_t−1, U_t−2;, U_t1, U_t+1, and U_t+2), the equation had relatively poor explanatory power (R² = 0.34). However, the addition of a variable for the change in agricultural prices markedly improved the equation’s explanatory power (R² = 0.8). The trade-off estimates that Brechling derived from his price equation suggested that a constant 3 per cent unemployment rate would produce a 3.3 per cent increase in prices in the short run and a 4.8 per cent increase in the long run. The average unemployment rate over the regression period was 5.0 per cent, and this implies, according to Brechling’s equation, an annual increase in prices of 2.6 per cent.

More recently, Holt and others [36] have estimated both static (short-run) and dynamic (long-run) trade-offs between ${\overset{*}{P}}_{G}$ and U for the United States for the period 1954–69 (using annual data). In the static model, ${\overset{*}{P}}_{G}$ was regressed on U⁻¹. The equation explained about 60 per cent of the total variance of price changes, and U⁻¹ was highly significant. The dynamic model merely adds lagged price changes $({\overset{*}{P}}_{G})_{t - 1}$ to the equation. Lagged price changes are included to represent the effects of past unemployment rates and expectations about future inflation rates. The dynamic (distributed lag) form of the price equation had higher explanatory power than the static form, and the lagged price change variable was highly significant. The derived trade-off estimates indicated that a 4 per cent unemployment rate was associated with a 3.1 per cent increase in prices in the short run and a 4.2 per cent increase in the long run (in the steady state).⁶² The steady-state inflation rates at 3 per cent and 5 per cent unemployment were 7.5 per cent and 2.3 per cent, respectively. These trade-off estimates, while based on very simple price change equations, are quite close to estimates obtained from some multiequation Iconometric models of the U. S. economy. For example, the inflation rate associated with a 4 per cent unemployment rate (in the steady state) was found to be 3.2 per cent, 3.7 per cent, and 3.9 per cent in the OBE, FMP, and DHL models, respectively.⁶³

One study that directly estimates the trade-off between price changes and unemployment for a number of industrial countries is the recent paper by Spitsäller [77]. He estimated price regressions in which the percentage change in the GNP deflator was regressed on the unemployment rate, the change in the unemployment rate, the percentage change in import prices, and the lagged dependent variable. The countries included in the study were Austria, Belgium, Canada, Denmark, France, Germany, Italy, Japan, the Netherlands, Sweden, the United Kingdom, and the United States. The regression period was usually 1955–68 or 1959–68 (using annual data). The results showed a significant relationship between ${\overset{*}{P}}_{G}$ and U⁻¹ for 11 of the 12 countries (Austria was the exception). On average, a nonlinear form for unemployment (U⁻¹) performed better than the linear form (U). The other independent variables were significant for some countries but not for others. The explanatory power of Spitäller’s price equation was quite good ( ${\bar{R}}^{2}$ > 0.7) for Belgium, Canada, Germany, Italy, and the United States, fair (0.7 > ${\bar{R}}^{2}$ > 0.5) for Denmark, the United Kingdom, and Japan, and relatively poor ( ${\bar{R}}^{2}$ < 0.5) for Sweden, France, and the Netherlands.

Spitäller also derived steady-state trade-offs between ${\overset{*}{P}}_{G}$ and U from his estimated price regressions; these trade-offs give estimates of the annual inflation rate associated with an unemployment rate kept constant over time and with $\dot{U}$ ${\overset{*}{P}}_{I}$ (import prices) = 0, and $({\overset{*}{P}}_{G})_{t}$ = $({\overset{*}{P}}_{G})_{t - 1}$ . Rates of unemployment in a range that covered each country’s past unemployment experience were used for the calculations. The more important conclusions that emerged from these calculations were (a) the unemployment rate consistent with price stability was 6–7 per cent for the United States, the United Kingdom, and France, and about 10 per cent for Canada, Germany, Sweden, and Japan;⁶⁴ (b) the rate of inflation associated with a 4 per cent unemployment rate was relatively high ( ${\overset{*}{P}}_{G}$ > 4 per cent) in the United States, Canada, and Denmark, relatively low (1.7 per cent < ${\overset{*}{P}}_{G}$ < 2.4 per cent) in Belgium and Italy, and extremely low ( ${\overset{*}{P}}_{G}$ < 1.7 per cent) in Sweden, Germany, France, the United Kingdom, and Japan;⁶⁵ and (c) of the 7 countries with apparently comparable unemployment data, the trade-off between inflation and unemployment appeared to be least unfavorable for Germany and Japan, more unfavorable for Sweden, France, and the United Kingdom, and most unfavorable for the United States and Canada.

Summarizing the rather limited evidence on the direct relationship between price inflation and the unemployment rate, it can be concluded that (a) there was a significant inverse relationship (a trade-off) between the rate of price increase and the unemployment rate in the United States, the United Kingdom, and Canada during the postwar period; (b) the extent of this trade-off was more unfavorable in the United States and Canada than in the United Kingdom (or in many other industrial countries); and (c) to limit inflation to a rate of 3 per cent per annum, it would be necessary on the basis of the postwar experience (post-1955) to accept an unemployment rate of approximately 4 per cent to 5 per cent in the United States, 3 per cent to 4 per cent in Canada, and 2 per cent to 3 per cent in the United Kingdom. Of course, for policymaking purposes it is desirable to have more precise estimates of the trade-off between inflation and unemployment, but in view of the changing nature of this trade-off over time, even these broad trade-off estimates should be taken cautiously.⁶⁶

V. Conclusions

In this paper an attempt was made to provide a reasonably comprehensive review of the econometric literature on the trade-off between inflation and unemployment for selected countries. The vast majority of the studies investigated suggested that such a trade-off does exist for Canada, the United Kingdom, and the United States (as well as for a number of other countries). However, it was also found that (a) this inverse relationship between the rate of increase of prices (or money wages) and the unemployment rate is considerably closer and stronger for some time periods than for others, indicating that this relationship is not very stable and (b) this relationship itself will be conditioned by a host of factors, such as profit rates, import prices, labor productivity, trade union aggressiveness, the vacancy/unemployment relationship, labor force participation rates, hoarding of employed labor, the industrial and demographic mix of employment and unemployment, and expectations about future wage, price, and unemployment conditions. Thus, while there is little question that, on average, a large increase (decrease) in the level of aggregate demand will lead to both an increase (decrease) in the rate of inflation and to a decrease (increase) in the rate of unemployment, the precise magnitude and timing of these price and employment responses are less certain.

Finally, it should be recognized that the relationship between inflation and unemployment can be altered by various economic policies.⁶⁷ Among the policy measures that might well lead to a lower rate of price or wage increases at any given unemployment rate are the following: a reduction in tariffs and import quotas, the repeal of retail price maintenance laws and minimum wage laws, legal measures to reduce racial and sexual discrimination in employment, increased tax and subsidy provisions for job retraining and greater labor mobility, the establishment of computerized job banks to yield better and faster matching of job vacancies and job applicants, and the establishment of wage/price guideposts to reduce the influence of excessive market power in wage and price decisions. Thus, the future trade-off between inflation and unemployment will be conditioned not only by the structure of the economy’s labor and product markets but also by the policies adopted to alter and improve the structure of these markets.

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Kuh, E., “A Productivity Theory of Wage Levels—An Alternative to the Phillips Curve,” The Review of Economic Studies, Vol. XXXIV (October 1967), pp. 333–60.
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Lipsey, Richard G., and J.M. Parkin, “Incomes Policy: A Re-appraisal,” Economica, New Series, Vol. XXXVII (1970), pp. 115–38.
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Lucas, Robert E., Jr., and Leonard A. Rapping, “Real Wages, Employment, and Inflation,” The Journal of Political Economy, Vol. 77 (September/ October 1969), pp. 721–754.
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MacRae, D., “Inflation and Unemployment in the United States: An Econometric Survey,” Working Paper 350-17, The Urban Institute (Washington, 1969).
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MacRae, C. Duncan, and Stuart O. Schweitzer, “Help Wanted Advertising, Aggregate Unemployment, and Structural Change,” in Proceedings of the Twenty-third Annual Winter Meeting, ed. by Gerald G. Somers, Industrial Relations Research Association (Madison, Wisconsin, 1970), pp. 87–96.
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MacRae, C. Duncan, and Stuart O. Schweitzer, and Charles C. Holt, “Job Search, Labor Turnover, and the Phillips Curve: An International Comparison,” in 1970 Proceedings of the Business and Economic Statistics Section, American Statistical Association (Washington, 1971), pp. 560–64.
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Miller, R.L., “The Reserve Labour Hypothesis: Some Tests of Its Implications,” The Economic Journal, Vol. LXXXI (1971), pp. 17–35.
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Parkin, Michael, “Incomes Policy: Some Further Results on the Determination of the Rate of Change of Money Wages,” Economica, New Series, Vol. XXXVII (1970), pp. 386—401.
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Perry, George L., “The Determinants of Wage Rate Changes and the Inflation-Unemployment Trade-Off for the United States,” The Review of Economic Studies, Vol. XXXI (October 1964), pp. 287–308.
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Perry, George L., “Wages and the Guideposts,” The American Economic Review, Vol. LVII (September 1967), pp. 897–904.
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Perry, George L., “Changing Labor Markets and Inflation,” Brookings Papers on Economic Activity, No. 3, 1970, ed. by Arthur M. Okun and George L. Perry, The Brookings Institution (Washington, 1970), pp. 411–48.
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Phelps, Edmund S., “Money-Wage Dynamics and Labor-Market Equilibrium,” The Journal of Political Economy, Vol. 76 (July/August 1968), Part II, pp. 678–711.
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Phillips, A.W., “The Relation Between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861-1957,” Economica, New Series, Vol. XXV (1958), pp. 283–99.
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Pierson, Gail, “The Effect of Union Strength on the U.S. ‘Phillips Curve’,” The American Economic Review, Vol. LVIII (June 1968), pp. 456–67.
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Rees, A., “The Phillips Curve as a Menu for Policy Choice,” Economica, New Series, Vol. XXXVII (1970), pp. 227–38.
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La relation inverse entre l’inflation et le chômage : une analyse des résultats empiriques dans certains pays sélectionnés

Résumé

Il s’est avéré très difficile, dans de nombreux pays, de concilier le plein emploi et la stabilité des prix. A en juger d’après les expériences antérieures, les responsables de la politique économique se heurtent au dilemme d’une relation inverse : les efforts pour accroître la production et l’emploi en augmentant le volume de la demande globale ont habituellement pour effet d’accroître les taux d’inflation, tandis que les mesures visant à réduire le taux de hausse des prix et des salaires conduisent le plus souvent à des taux de chômage plus élevés.

La présente étude analyse les ouvrages empiriques qui, depuis 1958, ont été consacrés à la relation inverse entre le chômage et l’inflation dans plusieurs pays. Ils portent essentiellement sur les études des prix et des salaires aux Etats-Unis, au Royaume-Uni et au Canada, mais examinent également plusieurs travaux qui évaluent l’effet compensatoire de l’inflation et du chômage au Japon, en France, en Italie, en République fédérale d’Allemagne, en Suède, en Belgique, en Australie, au Danemark et aux Pays-Bas.

L’étude comprend cinq parties. Dans la section I, l’auteur examine l’hypothèse initiale de Phillips, relative à la relation entre les variations des salaires nominaux et le taux de chômage, et les études effectuées sur les relevés statistiques du Canada, des Etats-Unis et du Royaume-Uni pour vérifier la justesse de cette hypothèse. La section II présente une étude des principaux prolongements et modifications de l’hypothèse de Phillips, qui comprend : 1) l’inclusion dans la fonction de salaire de variables comme les bénéfices, les variations de la productivité, les principaux accords de salaires, l’agressivité des syndicats, les variations du coût de la vie ainsi que l’évolution prévue des prix et des salaires; 2) l’évaluation concomitante des variations des prix et des salaires pour tenir compte de la marge d’erreur introduite par les équations simultanées dans les études sur les salaires à équation unique; et 3) des évaluations successives de la demande excédentaire de main- d’oeuvre et du coût de la main-d’oeuvre qui tiennent compte de facteurs comme le chômage occulte, le maintien d’effectifs en surnombre, les emplois vacants et les modifications de la composition de la main- d’oeuvre employée et en chômage par catégories démographiques et professionnelles. Dans la section III, l’auteur compare les équations de salaires de diverses études afin d’établir s’il existe une communauté de vues entre les experts quant à la relation inverse entre l’inflation des salaires et le chômage au Canada, au Royaume-Uni et aux Etats-Unis. La section IV présente une analyse succincte des études qui ont évalué directement la relation inverse entre le taux d’inflation des prix et le chômage. Dans la section V enfin, l’auteur tire les conclusions de la présente étude.

Les plus importantes de ces conclusions sont les suivantes : 1) une relation inverse non négligeable existait entre le taux d’accroissement des prix et le taux de chômage aux Etats-Unis, au Royaume-Uni et au Canada durant la période d’après-guerre; 2) le degré de cette relation inverse a été plus défavorable aux Etats-Unis et au Canada qu’au Royaume-Uni; 3) pour limiter l’inflation à un taux annuel de 3 pour cent, il faudrait, en se fondant sur l’expérience de l’après-guerre (après 1955), accepter un taux de chômage de l’ordre de 4 à 5 pour cent aux Etats-Unis et au Canada, et de 2 à 3 pour cent au Royaume-Uni; et 4) des évaluations plus précises de la relation inverse entre l’inflation des prix et le chômage, tout en étant souhaitables, ne semblent pas justifiées, étant donné le caractère changeant de cette relation avec le temps.

Relación de correspondencia entre la inflación y el desempleo: estudio de las pruebas econométricas para países seleccionados

Resumen

La conciliación del objetivo de pleno empleo con la estabilidad de precios ha sido muy difícil en muchos países. A juzgar por la experiencia, las autoridades se enfrentan con un dilema de relación de correspondencia: los intentos de aumentar la producción y el empleo mediante un aumento de la demanda agregada suelen tener por resultado tasas más altas de inflación, en tanto que los de reducir la tasa de aumento de los precios y salarios suelen redundar en tasas más altas de desempleo.

En este artículo se analiza la literatura empírica reciente (a partir de 1958) sobre la relación de correspondencia entre el desempleo y la inflación en algunos países. Se presta especial atención a los estudios sobre los precios y salarios de Estados Unidos, el Reino Unido y Canadá, aunque también se incluyen varios trabajos en que se ha estimado la relación de correspondencia entre la inflación y el desempleo en Japón, Francia, Italia, la República Federal de Alemania, Suecia, Bélgica, Australia, Dinamarca y los Países Bajos.

El estudio tiene cinco secciones. En la Sección I se estudia la hipótesis original de Phillips sobre la relación entre las variaciones de los salarios monetarios y la tasa de desempleo, y se examinan los estudios en que se ha tratado de verificar dicha hipótesis con datos sobre Canadá, Estados Unidos y el Reino Unido. La Sección II trata de las principales ampliaciones y modificaciones de la hipótesis de Phillips. Estos trabajos comprenden: 1) expansión de la función salarios a fin de incluir variables como los beneficios, las variaciones de la productividad, las principales negociaciones salariales, la agresividad sindical, las variaciones del costo de vida y las expectativas de los salarios y precios; 2) la estimación conjunta de las variaciones de los salarios y precios para tener en cuenta el sesgo de las ecuaciones simultáneas en los estudios sobre salarios con una sola ecuación, y 3) las variantes de medición de exceso de demanda de trabajo y el precio de los servicios del trabajo para tener en cuenta factores como el desempleo encubierto, el trabajo atesorado, las vacantes y las variaciones de la composición ocupacional y demográfica del empleo y el desempleo. En la Sección III, se comparan las ecuaciones de salarios de varios estudios, a fin de determinar si coinciden en cuanto a la relación de correspondencia entre la inflación de salarios y el desempleo en Canadá, el Reino Unido y Estados Unidos. En la Sección IV se describen algunos estudios en que se ha calculado directamente la relación de correspondencia entre la tasa de inflación de precios y el desempleo. En la Sección V se presentan las conclusiones del estudio.

Entre las conclusiones más importantes se cuentan: 1) en el período de posguerra ha existido una importante relación inversa (relación de correspondencia) entre las tasa de aumento de los precios y la tasa de desempleo en Estados Unidos, el Reino Unido y Canadá; 2) la magnitud de esta relación de correspondencia fue más desfavorable en Estados Unidos y Canadá que en el Reino Unido; 3) sobre la base de la experiencia de la posguerra (a partir de 1955), para limitar la inflación a una tasa del 3 por ciento anual sería preciso aceptar una tasa de desempleo del 4 al 5 por ciento aproximadamente en Estados Unidos y Canadá, y del 2 al 3 por ciento en el Reino Unido, y 4) aunque sería conveniente, no se justificaría realizar cálculos más precisos de la relación de correspondencia entre la inflación de precios y el desempleo porque varía con el tiempo.

In statistical matter (except in the resumes and resúmenes) throughout this issue,

Dots (…) indicate that data are not available;
A dash (—) indicates that the figure is zero or less than half the final digit shown, or that the item does not exist;
A single dot (.) indicates decimals;
A comma (,) separates thousands and millions;
“Billion” means a thousand million;
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A stroke (/) is used between years (e.g., 1962/63) to indicate a fiscal year or a crop year;
Components of tables may not add to totals shown because of rounding.

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Mr. Goldstein, economist in the Special Studies Division of the Research Department, is a graduate of Rutgers University and of New York University. He was formerly a Research Fellow in Economics at the Brookings Institution.

For more general surveys of the literature on inflation, price behavior, and wage behavior, the reader is referred to Bronfenbrenner and Holzman [13], Silberston [73], and Bodkin [8], respectively. The numbers in square brackets refer to items listed in the Bibliography, pp. 690–95.

As an example of other trade-offs, Eckstein and Fromm [23] found that stable U.S. manufacturing prices were consistent with a capacity utilization rate of only 82 per cent. Inventory and new orders disequilibrium variables were used to explain U.S. price changes by Schultze and Tryon [72] and Gordon [28], respectively. The relationship between changes in money wage rates and quit rates was examined by Behman [3], and more recently by Schultze [71].

For a good discussion of the different wage, price, and unemployment variables used in the wage and price studies of the United States, see MacRae [51], pp. 4–23.

See the recent paper by Black and Kelejian [7] for an analysis of the proper formulation of the dependent variable in the aggregate wage equation.

The definitions of and the data sources for $\overset{*}{W}$ , U, $\overset{*}{Q}$ , and π may vary somewhat from study to study and from country to country. The data also appear in both annual and quarterly forms and at various levels of aggregation. In most wage studies, $\overset{*}{W}$ is defined to exclude overtime pay and fringe benefits, and most usually it refers to the manufacturing sector; however, more comprehensive measures of labor compensation also have often been used in empirical studies. The unemployment rate (U) is usually defined as total unemployment as a percentage of the civilian labor force. When prices are used as an independent variable in an aggregate wage equation, $\overset{*}{P}$ is almost always the percentage change in the consumer price index. However, in aggregate price equations, the dependent variable can be the percentage change in either the consumer price index, the wholesale price index, or the GNP (gross national product) deflator. The percentage change in labor productivity ( $\overset{*}{Q}$ ) usually refers to the rate of increase of real output per man-hour in the economy. The profit rate (π) can take on a wide variety of definitions. Two of the more widely used measures are the ratio of profits (before or after taxes) to the total equity of stockholders (in manufacturing) and the ratio of total corporate profits to total wages and salaries in manufacturing. Unfortunately, owing to the large number of studies included in this review, a precise description of the variables used in each study cannot be given. The reader is therefore advised to consult the original studies if a more precise description of the variables is desired.

Actually, Phillips assumed that $\partial \overset{*}{W} / \partial \overset{*}{P}$ would be greater than zero only if the percentage change in prices reached some threshold; see page 652 on this point.

Two other examinations of Phillips’s results can be found in Routh [68] and in Knowles and Winsten [45].

In this article, Lipsey also develops a rather ingenious theoretical model to explain the relationship between $\overset{*}{W}$ and $\dot{U}$ In this model, $\dot{U}$ becomes a proxy for the dispersion or sectoral inequality of U. The important policy implication that emerges from this model is that if the relationship between $\overset{*}{W}$ and U is nonlinear, convex to the origin, and of identical slope for all sectors, then the $\overset{*}{W}$ associated with a given aggregate U will be higher, the greater is the sectoral inequality of U. The Lipsey model also implies that one needs to know the composition of U, as well as its level, to predict $\overset{*}{W}$ . Archibald [1], in a later article, estimated $\overset{*}{W}$ regressions for the United States and the United Kingdom in which the variance of U appeared as one of the explanatory variables. He found that the greater the geographical or industrial variance of U, the larger was $\overset{*}{W}$ at any given level of U. Similarly, Schultze [70] and Goldstein [27] have argued that changes in the industrial composition of aggregate demand, at any given level of aggregate demand, can affect the aggregate rate of price increase. For a statement of the necessary conditions for unemployment dispersion to adversely affect the aggregate Phillips curve, see Archibald [1] and Hines [32].

However, in the wage regression for the period 1923–57 (excluding the years 1940–47), the coefficient on $\overset{*}{P}$ was 0.69, which indicated that wage adjustments to cost of living changes were increasing over time.

An alternative explanation for a coefficient on $\overset{*}{P}$ of less than 1 is that wage earners are free of money illusion but do not have sufficient bargaining power to obtain full compensation for cost of living changes.

Although the two studies used slightly different definitions of $\overset{*}{W}$ and U, Bowen and Berry claimed that these differences were too small to explain the conflicting findings.

One possible explanation for the lack of curvature in the Phillips curve in the United States is that there are hardly any observations in the 0–3 per cent range of unemployment.

In a later study, Bodkin and others [9] found a significant inverse relationship between wage changes and the unemployment rate for Canada, the United States, the United Kingdom, France, and Sweden for the period 1954–65 (quarterly).

This conclusion follows because (a) wage changes are positively related to the profit rate and (b) price changes are assumed to be equal to wage changes minus productivity changes.

In a later paper, however, Eckstein [21] points out that pattern bargaining in key industries may be weakening owing to more diverse profit experience across industries. This suggestion is consistent with Ripley’s [67] finding that profit conditions (not wage changes or unemployment conditions) were the important cohesive factor in the key-bargain group.

Bodkin and others [9] also found that the profit rate had a significant positive effect on wage changes in Canada for the period 1953–65. The other significant independent variables were the unemployment rate, changes in consumer prices, wage changes in the United States, and lagged wage changes.

Bodkin [8] and Black and Kelejian [6] were unable to find a significant influence for profits in their wage functions for the United States (for the periods 1899–1957 and 1948–65, respectively).

Black and Kelejian [6] and Christian [15] have also found that changes in labor productivity have a significant positive effect on wage changes in U.S. manufacturing.

In a later article, Eckstein [21] challenged Kuh’s contention that his wage equation of the productivity type performs better than wage equations that use unemployment plus profits.

Also, see Holt [35] for a theoretical analysis of the influence of unions on wage determination.

In a recent article, Lipsey and Parkin [48] explained the percentage change in money wage rates in the United Kingdom (for the period 1948–68, quarterly) by using U, $\overset{*}{P}$ , and ΔT. The price change and unionization variables were highly significant, and the unemployment variable was close to significant.

In a later article, Hines [31] once again argued that his wage equation using unionization variables explained $\overset{*}{W}$ better than wage equations using unemployment variables.

To my knowledge, there are no studies that have tested the influence of unionization on the Phillips curve in Canada.

The rationale for including price changes in the equation for ΔT was that trade unions are likely to be gaining new members when prices are rising rapidly and workers are eager to maintain real wages without incurring the costs of mobility in the labor market. The trade union equation also included trade cycle variables and proxy variables for the social and political forces affecting ΔT.

Ashenfelter and others [2] argue against using the trade-off estimates derived from their reduced-form equations for policy forecasting, since the standard errors of forecast from these equations are in their opinion too large for practical use.

The argument is essentially that average hourly earnings are a poor measure of the price of labor for a bargaining theory of wage determination because earnings can change quite independently of any change in the excess demand for labor, owing to such factors as incentive payments (based on productivity changes), changes in skill-mix of employment over the cycle, and annual variation in the proportion of workers receiving wage increases negotiated in the particular year. The use of wage rates taken from negotiated contract settlements avoids these problems.

Eckstein and Brinner also found that inflationary expectations are built on about two years’ experience and, therefore, that with an effective wage/price program, it would be possible to restore normal expectations in about two years. They also calculated that without the new economic policies of August 1971, it would require an unemployment rate of 6 per cent maintained until 1975 to clear the system of the adverse effects of the recent inflation.

See the papers in the volume edited by Phelps [61] for a formal treatment of this view. Also, see Rees [64] for a careful critique of the expectations theory of the Phillips curve.

The rationale behind this hypothesis is explained clearly by Friedman [26]. He argues that an unanticipated rise in nominal demand will at first lead to a decline in real wages received, because product prices will typically rise faster than factor prices; however, real wages anticipated by employees will have increased, since they will have been evaluated at the old price level. This simultaneous fall ex post in real wages to employers and rise ex ante in real wages to employees will cause employment [unemployment] to rise [fall] temporarily. Over time, however, this ex post decrease in real wages will lead employees to press for higher nominal wages, and this will in turn lead to a rise in real wages. The rise in real wages will cause employment [unemployment] to fall [rise] until it returns to its former level (at the natural unemployment rate). See Phelps [60] for the development of a wage expectations model that stresses the expectations of employers.

The natural unemployment rate (the rate at which actual and expected price changes are equal) is claimed to be a function of the structural characteristics of the labor market (the rate and cost of labor mobility, the trend rate of increase of labor productivity, etc.) and is independent of the rate of inflation.

The expectations hypothesis as applied to price determination is often expressed as

\begin{matrix} (1) & {\overset{*}{P}}_{t} = a_{0} + a_{1} U \overset{*}{L} C + a_{2} E D + a_{3} {\overset{*}{P}}_{t}^{e} \end{matrix}

\begin{matrix} (2) & {\overset{*}{P}}_{t} = a_{0} + a_{1} U + a_{2} {\overset{*}{P}}_{t}^{e}, \end{matrix}

where ULC is the percentage change in unit labor costs, ED is a proxy for excess demand in the product market, U is the unemployment rate, and ${\overset{*}{P}}_{t}^{e}$ is the expected rate of price inflation at time t. Empirical confirmation of the expectations hypothesis is indicated by a coefficient on ${\overset{*}{P}}_{t}^{e}$ of 1. Using a price equation similar to equations (1) in this footnote (for the United States for the period 1947–66), Solow [76] found that the estimated coefficient on ${\overset{*}{P}}_{t}^{e}$ was substantially less than 1 (about 0.4).

where direct observations on price expectations are unavailable, $\overset{* e}{P}$ is usually generated as some distributed lag of actual past price changes. For a good presentation of several alternative hypotheses about how price expectations are formed, see Turnovsky [80]. Also, see Turnovsky and Wachter [81] for direct data (the Livingston survey) on price and wage expectations in the United States.

This can be seen clearly by considering the following simple, two-equation, wage/price model recently proposed (in a slightly different form) by Vanderkamp [84]

\overset{*}{W} = α_{0} + α_{1} U^{- 1} + α_{2} {\overset{*}{P}}_{t}^{e}

\overset{*}{P} = B_{0} + B_{1} \overset{*}{W}

Now make the following assumptions about the long run: (a) B1=1, all factor prices change at the same rate and are fully reflected in final prices (except for productivity increases −B₀); (b) ${\overset{*}{P}}^{e} = \overset{*}{P},$ expected price changes equal actual price changes; and (c) α₂=1, the wage response to expected price changes is 1. Given these assumptions, the steady-state, reduced-form trade-off for $\overset{*}{P}$ is given by

\overset{*}{P} = \frac{α_{0} + B_{0}}{1 - α_{2}} + \frac{α_{1} U^{- 1}}{1 - α_{2}} .

If α₂ (as predicted by the expectations hypothesis), then there is no trade-off between $\overset{*}{P}$ and U, because the coefficient on U⁻¹ (and on the constant term) is infinite.

In a recent study of wage behavior in the United Kingdom (for the period 1948–68), Parkin [56] found that the wage response to expected price changes was substantially less than 1; this finding implies that there is a long-run trade-off between inflation and unemployment there.

This conclusion follows for each of the above-mentioned variables except labor productivity changes, for which the net effect on the rate of inflation is ambiguous. On the one hand, a high rate of productivity increase should lead to higher wage increases, but, on the other hand, it also leads to lower unit labor costs, so that the net effect on prices is unclear.

See Johnston [40], pp. 231–36. An estimator, $\hat{β},$ is said to be biased if the expected value of that estimator does not equal the true value of the parameter (β), that is, if $E (\hat{β}) \neq β .$ An estimator is inconsistent if its bias persists for infinitely large samples.

Perry [57] and Eckstein and Brinner [22] also reported that the TSLS estimates of their wage equation were very close to the OLS estimates.

The three models are described in Hirsch [33], de Menil and Enzler [16], and Hymans and Shapiro [39], respectively.

If the explanatory price or wage variable is lagged so that it does not overlap with the dependent variable, then the wage/price system becomes recursive (rather than simultaneous) and the application of ordinary least-squares estimation is perfectly acceptable. However, if the wage variable $({\overset{*}{W}}_{t})$ is defined as $\frac{W_{t} - W_{t - 4}}{W_{t - 4}}$ and the price change variable is lagged one quarter (so that ${\overset{*}{P}}_{t - 1} = \frac{P_{t - 1} - P_{t - 5}}{P_{t - 5}}$ ), then simultaneity will still be present for quarters t−2, t−3, and t−4.

Watanabe [87], in a 1966 study for Japan, also estimated wage changes and price changes jointly and obtained results quite similar to those reported for other countries. The study used quarterly data for the period 1955–62. The wage equation was of the form $\overset{*}{W} = f (U, \overset{*}{P});$ the price equation was $\overset{*}{P} = g (\overset{*}{W}, \overset{*}{Q}) .$ Both regressions had good explanatory power, and the coefficients were significant with the expected signs. Differences between TSLS and OLS estimates were quite small. The unemployment rate estimated to be compatible with complete wage stability ( $\overset{*}{W}$ = 0) was 5.5 per cent; also, assuming that U=3 per cent and ${\overset{*}{P}}_{t - 1}$ = 1.5 per cent, the estimated $\overset{*}{W}$ was 10 per cent.

See MacRae and Schweitzer [52] for an empirical analysis of the inverse relationship between vacancies and unemployment in the United States.

The index of the pressure of the demand for labor (d) proposed by Dow and Dicks-Mireaux [19] is (m − u) when $u > (\frac{v}{s}), o r (\frac{v}{s} - m) w h e n u < (\frac{v}{s}),$ where u is the unemployment rate, v is the vacancy rate, s is the proportion of reported vacancies to true vacancies, and m is the amount of percentage unemployment to be attributed to maldistribution of the labor force (m is measured as the amount of unemployment at the point where $u = \frac{v}{s}$ ). When s = 1, d approximates $(\frac{v}{s} - u),$ the vacancy rate minus the unemployment rate.

See Dernberg and Strand [17]. Wachter [86], however, has recently demon-strated that the labor force participation of secondary workers responds to real wages and inflation as well as to excess demand conditions in the labor market; his labor supply equations also cast doubt on the estimates of hidden unemployment made by Simler and Telia [74] and others. Also, see Lucas and Rapping [50] for a neoclassical labor supply model that leads to a short-run, but not a permanent, trade-off between inflation and unemployment.

Alternatively, Black and Kelejian [6] have argued that the wage slowdown might be related to the especially mild changes in the industrial distribution of output that occurred during this period. They also found no significant influence for the wage/price guideposts on wage behavior.

Vroman [85] also found that the labor reserve affected the change in the money wage rates during the period 1962–66, but his estimate of the labor reserve was smaller than that of Simler and Telia. Eckstein and Brinner [22] have shown, however, that the hidden unemployment rate does not explain $\overset{*}{W}$ well (in the United States) in the period 1969–71.

Taylor hypothesized (and the empirical results supported this hypothesis) that when the degree of labor hoarding is high, $\overset{*}{W}$ will be low. The argument is that in periods of recession (periods of high labor hoarding), employer resistance to wage claims will be high (owing to low product demand) and trade union aggressiveness will be low.

Vanderkamp [84], in a recent wage study for Canada, came to the same conclusion. He used a productivity variable (the deviation in aggregate labor productivity from trend) as a proxy for excess demand for labor within firms in his $\overset{*}{W}$ equation and found it to be significant. The other explanatory variables in his $\overset{*}{W}$ equation were U⁻¹, $\dot{U}$ , expected price changes, and a nonlinear (threshold) cost of living index. The regression period was 1949–68 (with quarterly data).

The (U − U^*) variable will usually get larger during expansions and smaller during recessions.

The dependent variable in these wage equations was also adjusted to remove the effects of changes in the age/sex composition of employment, interindustry shifts in employment, and overtime pay.

Schultze’s [71] wage equations also indicate an unfavorable shift in the Phillips curve for this later period, but Eckstein and Brinner [22] find no evidence of such a shift.

Another criticism of money wage rates as the relevant dependent variable is that it is not a sufficiently comprehensive measure of labor costs to the entrepreneur. This argument claims that money earnings (wage rates plus overtime and other premium or fringe benefits) is the relevant cost variable. The difference between changes in hourly earnings and changes in hourly wage rates is often referred to as wage drift. Wage drift has received much more attention in the United Kingdom than in the United States. Klein and Ball [43] made wage drift a positive function of hours worked and labor productivity. Alternatively, Braun [11] related wage drift to the change in the number of unfilled vacancies over the preceding 12 months. Wage drift is likely to be a larger problem during expansions than recessions, because in expansions employers will be tempted to offer payments in excess of centrally negotiated wage rates in order to fill important job vacancies.

Braun [11] also argued that exceptional movements in the price of imported manufactures had a strong influence on the higher-than-expected wage increases during the period 1967–70.

For example, Bodkin and others [9] reported that the unemployment rate in the United Kingdom must be adjusted upward by a factor of 1.5 to make it comparable to the U. S. and Canadian unemployment definitions.

However, for the study by Bodkin and others [9] that used a lagged wage change variable in the wage function, the steady-state solution was obtained by setting ${\overset{*}{W}}_{t}$ equal to ${\overset{*}{W}}_{t - 1}$ and $\overset{*}{P}$ than does the simple assumption that $\overset{*}{P} = \overset{*}{W} - \overset{*}{Q}$ . Also, the steady-state solution in the study by Smith [75] was obtained by setting P_t = P_t−1 and $\overset{*}{P}$ than does the simple assumption that $\overset{*}{P} = \overset{*}{W} - \overset{*}{Q}$ .

This expression illustrates that: (a) at given values for $\overset{*}{Q}$ and π, $\overset{*}{W}$ is inversely related to U (the Phillips curve); and (b) at a given U, $\overset{*}{W}$ is positively related to π and inversely related to $\overset{*}{Q}$ (the family of Phillips curves). See Simler and Tella 74, P. 32.

Reuber [66] reached the same general conclusion in an earlier comparison of trade-off estimates for the same three countries.

Bodkin and others [9] found this trade-off (for the period 1953–65) to be most unfavorable for Canada, slightly less unfavorable for the United States, and substantially less unfavorable for the United Kingdom, pp. 260–67.

Also, the assumption $\overset{*}{P}$ than does the simple assumption that $\overset{*}{P} = \overset{*}{W} - \overset{*}{Q}$ implies that the nonwage components in prices vary in the same proportion as the wage components. See Brechling [121 for empirical evidence (for the United States) that suggests that the wage and nonwage components behave differently in response to changes in aggregate demand.

If the assumption that $\overset{*}{P}$ than does the simple assumption that $\overset{*}{P} = \overset{*}{W} - \overset{*}{Q}$ is suspect, then the calculated steady-state trade-offs between $\overset{*}{W}$ and U (see Table 1), which also utilize this assumption, are likewise suspect.

One weakness of reduced-form estimation in the case of overidentified models is that the reduced form ignores all the a priori information built into the model telling which variables appear in which equation. Equivalently, one can say that in overidentified models the reduced-form equation ignores the overidentifying restrictions of the model, and this is undesirable unless these restrictions are incorrect. Also, reduced-form estimation has a weakness for forecasting purposes when a structural change has occurred between the observation and prediction periods, since it cannot take advantage of this information; that is, one has to know the new structure of the model to obtain the relevant reduced- form parameters for the prediction period. See Christ [14], pp. 245–48 and 464–81 for a good discussion of these problems and for an analysis of the relative merits of several estimation methods for structural equations and reduced forms.

Another caveat to keep in mind in interpreting all estimated trade-offs between $\overset{*}{P}$ and U is that the unemployment rate does not cause price changes. Rather, both price changes and the unemployment rate are determined jointly by the level of aggregate demand, among other factors. Thus, as Holt and others [36] have pointed out, the Phillips curve is most appropriately viewed as a jointly determined relation rather than as either a structural or reduced-form relation.

The estimated price regression is of the form ${\overset{*}{P}}_{t} = a + b U^{- 1} + c {\overset{*}{P}}_{t - 1};$ the steady-state trade-off is given by the expression $\overset{*}{P} = \frac{a}{1 - c} + (\frac{b}{1 - c}) U^{- 1} .$

See pages 671–72 of this review for a description of these models.

The regression period was 1960–69 for the United States, 1955–67 for the United Kingdom, 1955–68 for France and Japan, 1959–68 for Canada and Sweden, and 1959–69 for Germany.

More specifically, the inflation rate associated with a 4 per cent unemployment rate was 5.7 per cent in the United States, 4.1 per cent in Canada, and 5.0 per cent in Denmark.

In particular, the trade-off estimates for Canada must be considered extremely tentative in view of the recent findings of Turnovsky [80] and Vanderkamp [84] (see Section II, p. 667) that there was no long-run money wage/unemployment trade-off during the postwar period.

With regard to such policy measures, see Holt and others [37], Tobin [79], and [82, pp. 83–90]. Also, policies that improve the functioning of labor and capital markets are desirable whether or not there is a long-run trade-off between inflation and unemployment. In the former case, such policies shift the Phillips curve inward toward the origin (in a favorable direction), while in the latter case, they lower the natural unemployment rate.

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IMF Staff papers: Volume 19 No. 3

Author:

International Monetary Fund. Research Dept.

Volume/Issue:: Volume 1972: Issue 003

Publisher:: International Monetary Fund

ISBN:: 9781451969290

ISSN:: 1020-7635

Pages:: 202

DOI:: https://doi.org/10.5089/9781451969290.024

Keywords
I. Early Tests of the Phillips Hypothesis
II. Extensions and Modifications of and Challenges to the Phillips Hypothesis
III. The Trade-Off Between Wage Inflation and Unemployment: A Comparison of Estimates from Different Studies
IV. Some Evidence on the Trade-Off Between Price Changes and Unemployment
V. Conclusions
BIBLIOGRAPHY
La relation inverse entre l’inflation et le chômage : une analyse des résultats empiriques dans certains pays sélectionnés
- Résumé
Relación de correspondencia entre la inflación y el desempleo: estudio de las pruebas econométricas para países seleccionados
- Resumen
Publications of the International Monetary Fund

Table 1.

Some Representative Estimates of the Steady-State Trade-Off Between Wage Inflation and Unemployment in the United States, Canada, and the United Kingdom

										Assumptions About
Investigator		Steady-State Percentage Wage Change Associated with Unemployment Rate Equal to					Regression Period	Data: Annual (A) or Quarterly (Q)	Form of Wage Change Equation	Profits	Rate of productivity increase
Investigator		1 per cent	2 per cent	3 per cent	4 per cent	5 per cent	Regression Period	Data: Annual (A) or Quarterly (Q)	Form of Wage Change Equation	(π)	$(\overset{*}{Q})$
United States
	Perry [57]			7.1	5.2	4.0	1947–60	Q	$\overset{}{W} = f (U^{- 1}, \overset{}{P}, \dot{π}, π)$	11.8	3.0
	Black and Kelejian [6]			5.3	4.1	2.9	1948–65	Q	$\overset{}{W} = f {(U, \dot{U}, \overset{}{P}, \overset{*}{Q}, D_{s})}^{1}$		3.0
	Pierson [63]			6.9	4.9	3.7	1953–66	Q	$\overset{}{W} = f (U^{- 1}, \overset{}{P}, π, D_{I C})^{2}$		3.0
	Simler and Telia [74]			6.2	4.8	4.0	1953–64	Q	$\overset{}{W} = f (U^{- 1}, \overset{}{P}, π, \dot{π}, U^{* - 1} - U^{- 1})^{3}$	11.8	3.0
	Bodkin and others [9]			5.4	4.3	3.8	1953–65	Q	$\overset{}{W} = f (U^{- 2}, \overset{}{P}, π, {\overset{*}{W}}^{- 1}, D_{I C})^{4}$	113.3 ⁵	3.0
Canada Zaidi [88]				6.9	5.0	3.9	1947–62	A	$\overset{}{W} = f (U^{- 1}, \overset{}{P}, π)$	0.37 ⁵	4.0
	Bodkin and others [9]			4.4	2.9	2.2	1953–65	Q	$\overset{}{W} = f (U^{- 2}, \overset{}{P}, π, {\overset{}{W}}_{U S}, {\overset{}{W}}_{- 1})^{6}$	97.75 ⁵	4.0
	Kaliski [42]			5.5	4.2	3.5	1946–58	A	$\overset{}{W} = f (U^{- 1}, \dot{U}, \overset{}{P})$		4.0
United Kingdom Bodkin and others [9]		13.6	5.5	2.9			1954–65	Q	$\overset{}{W} = f (U^{- 1}, \overset{}{P}, D_{I C})^{7}$		2.0
	Lipsey and Parkin [48]	4.4	2.7	1.0			1948–68	Q	$\overset{}{W} = f (U, \overset{}{P}, \overset{*}{N})^{8}$		2.0
	Smith [75]	7.0	2.3	0.8			1948–67	Q	$\overset{}{W} = f (U^{- 1}, \overset{}{P}, {\overset{*}{P}}_{- 1}, D_{I C})^{9}$		2.0

²D_IC is a dummy variable for the wage/price guideposts; it was assigned a value of zero.

³The expression (U^*−1—U⁻¹) was assumed to be equal to zero; U^*−1 is the reciprocal of the unemployment rate adjusted for labor reserves.

⁴ $\overset{*}{W}$ was set equal to ${\overset{*}{W}}^{- 1}$ for the trade-off calculations; D_IC was set equal to zero.

^⁵The profits variable was defined differently in this study.

⁶W_US, wage changes in the United States, were assumed to be equal to 3.2 per cent. $\overset{*}{W}$ was set equal to ${\overset{*}{W}}^{- 1}$ for the trade-off calculations.

⁷D_IC was set equal to zero.

⁸N is the change in the percentege of the labor force that was unionized; $\overset{*}{N}$ was assigned a value of zero.

⁸D_IC was assigned a value of zero; ${\overset{*}{P}}_{t}$ was set equal to ${\overset{*}{P}}_{t - 1}$ for the trade-off calculations.

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Abstract

I. Early Tests of the Phillips Hypothesis

II. Extensions and Modifications of and Challenges to the Phillips Hypothesis

The addition of other variables to the wage function

Profits

Changes in productivity

Trade union aggressiveness

Threshold effects in cost of living changes

Price and wage expectations and the expectations theory of the Phillips curve

The simultaneous estimation of wage and price changes

Alternative measures of the excess demand for and the price of labor

III. The Trade-Off Between Wage Inflation and Unemployment: A Comparison of Estimates from Different Studies

IV. Some Evidence on the Trade-Off Between Price Changes and Unemployment

V. Conclusions

BIBLIOGRAPHY

La relation inverse entre l’inflation et le chômage : une analyse des résultats empiriques dans certains pays sélectionnés

Résumé

Relación de correspondencia entre la inflación y el desempleo: estudio de las pruebas econométricas para países seleccionados

Resumen

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Balance of Payments Yearbook

Direction of Trade

International Financial Statistics

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