Inflationary Expectations and the Trade-Off Between Unemployment and Inflation in the United States

Erich Spitäller

doi:10.5089/9781451969382.024.A006

Author:

Erich Spitäller

Erich Spitäller https://isni.org/isni/0000000404811396 International Monetary Fund

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Publication Date:: 01 Jan 1975

eISBN:: 9781451969382

Language:: English

Keywords:: SP; price equation; price change; wage-price system; price movement; short-run price effect; Inflation; Unemployment; Unemployment rate; Threshold analysis; Labor markets

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For some 15 years, from the mid-1950s to the late 1960s, the record of prices and unemployment in the United States supports the notion of a trade-off between unemployment and inflation, implying that unemployment can as a rule be reduced only at the expense of rising inflation unless structural conditions in labor and product markets are changed or direct controls are brought to bear on wages and prices. In recent years, however, as the United States has been confronted with high unemployment and inflation simultaneously, this trade-off seemed not only to have worsened but, at times when both unemployment and inflation were rising, seemed no longer to exist. While there is evidence that the response of prices to unemployment is delayed, so that relatively high rates of unemployment and inflation may temporarily coexist, the lag involved has been no longer than six months on average and it is implausible that it would have lengthened sufficiently to account for the persistence of high unemployment and inflation in the years 1970 and 1971. Rather, the explanation appears to lie elsewhere. The literature has referred to changes in the demographic composition of unemployment—raising the unemployment rate that corresponds to a given degree of demand pressure—and to influences not necessarily associated with unemployment though affecting its trade-off against inflation. Among these influences are differential reactions of wages to increases of different magnitude in the cost of living and the role of expectations with respect to inflation.1

Abstract

These and other influences may alter any observed dependence of current price movements on past ones. This paper shows that an increase in that dependence has occurred, thus explaining the recent concurrence of high unemployment and inflation. The paper first presents a model of price behavior, based in part on an expectations hypothesis allowing for an inflationary process that is set in motion as price increases reach and exceed a certain level and which thereby raises the dependence of current price movements on past ones. The model is then empirically tested, and the implications of the results for the trade-off between unemployment and inflation are assessed in the short run as well as in the steady state.

I. The Price Equation

A model explaining movements in the general price level of an economy may be constructed in a number of ways differing to a greater or lesser degree at various stages of construction. In the corresponding estimating equations, however, these differences may no longer be apparent, and the model that is finally estimated may be consistent with more than one hypothesis. At the same time, where the structural model contains unobservable variables, any one of them may be expressed by one of several proxies and the model may be consistent with more than one estimating form. It will be seen that both of these considerations apply to the price equation presented and estimated in this paper.

Recent empirical work on price and wage behavior in industrial countries has identified several important determinants of this behavior. In particular, the dependence of price movements on factors such as productivity developments, changes in costs of factor inputs, and excess demand in the product market has been assessed, while wage movements have been explained in terms of productivity, excess demand in the labor market, and inflationary expectations.² Accordingly, the following price and wage equations, here written in linear form, are considered:

\begin{matrix} G \overset{*}{P} = a_{11} \bar{\overset{*}{P}} + a_{12} \overset{*}{W} + a_{13} + \overset{*}{K} + a_{14} \overset{*}{M} + f (DP) & (1) \end{matrix}

and

\begin{matrix} \overset{*}{W} = b_{11} \bar{\overset{*}{P}} + b_{12} G {\overset{*}{P}}^{e} + h (DL) & (2) \end{matrix}

where GP stands for the gross national product (GNP) deflator and P for productivity; W, K, and M refer to the costs of labor, capital, and raw material inputs; and DP and DL are measures of excess demand in product and labor markets. An asterisk over a variable indicates its rate of change from the preceding period, a bar over a variable refers to its trend value, and the superscript e on $G \overset{*}{P}$ denotes expected price changes.

the Phillips curve

The Phillips curve suggests both a measure of excess demand and the form in which it should enter the wage equation. The measure is the rate of unemployment, and its functional form involves a nonlinearity that may be represented by its reciprocal. In addition, the theory behind the Phillips curve allows for the reaction of wages to the speed at which excess demand increases or decreases, which is reflected in the rate of change in the unemployment rate. This study uses the unemployment rate as a measure of excess demand not only in the labor market but also in the product market—and therefore not only in the wage equation but also in the price equation. In view of the overwhelming share of labor costs in total value added in the economy as a whole, it may be defensible to abstract from inputs other than labor and to drop capital and raw material costs from the price equation. With these modifications and the use of the unemployment rate as a measure of excess demand, the price and wage equations (1) and (2) may be rewritten as

\begin{matrix} G \overset{*}{P} = a_{11} \bar{\overset{*}{P}} + a_{12} \overset{*}{W} + a_{15} U_{- i}^{- 1} + a_{16} \overset{*}{U} & (3) \end{matrix}

and

\begin{matrix} \overset{*}{W} = b_{11} \bar{\overset{*}{P}} + b_{12} G {\overset{*}{P}}^{e} + b_{13} U_{- i}^{- 1} + b_{14} \overset{*}{U} & (4) \end{matrix}

where i is the lag with which changes in prices and wages respond to the level of unemployment. The signs of the coefficients a₁₂, a₁₅, b₁₁, b₁₂, and b₁₃ are all expected to be positive, while negative signs are expected on the coefficients a₁₁, a₁₆, and b₁₄. Substitution of the wage equation (4) into the price equation (3) yields a price equation in reduced form:

\begin{matrix} G \overset{*}{P} = (a_{11} + a_{12} b_{11}) \bar{\overset{*}{P}} + (a_{15} + a_{12} b_{13}) U_{- i}^{- 1} + (a_{16} + a_{12} b_{14}) U^{*} \\ + a_{12} b_{12} G {\overset{*}{P}}^{e} & (5) \end{matrix}

In this equation the composite coefficient of the trend growth in productivity $\bar{\overset{*}{P}}$ is the only coefficient whose components carry opposite signs reflecting the dual effect of productivity increases on prices, which they lower directly but raise indirectly through their effect on wages. The sign of that coefficient depends, therefore, on the relative magnitudes of these components.

The trend growth in productivity may be absorbed into a constant term, unemployment may be assumed to be determined outside the wage-price system considered here, and expected price changes may be approximated by a function of past price movements. The formulation of expectations is ordinarily assumed to involve extrapolative or adaptive processes.³ Any lag structure that might apply is here approximated by a one-period lag. Since the empirical analysis relies on annual data, a closer study of the lag structure, which should be based on quarterly observations, is precluded.

inflationary expectations

While the assumption that expected price changes are related to past price movements is retained, a threshold effect is introduced which allows for a change in the slope of the relation. The effect applies as past price increases reach and exceed a certain level—causing the degree of money illusion in the economy to decline and, as a consequence, causing inflationary expectations to rise. In turn, the change in expectations will lead to anticipatory wage and price adjustments, and inflation will accelerate. This implies an increased dependence of current price movements on lagged ones in a price equation based on equation (5) but containing a proxy for inflationary expectations. Such a price equation may therefore be written as:

\begin{matrix} G \overset{*}{P} = α_{0} + α_{1} U_{- i}^{- 1} + α_{2} \overset{*}{U} + α_{3} G {\overset{*}{P}}_{- k} & (6) \end{matrix}

where

\begin{array}{l} α_{1} = a_{15} + a_{12} b_{13} > 0, \\ α_{2} = a_{16} + a_{12} b_{14} < 0, and \\ α_{3} = a_{12} b_{12} > 0. \end{array}

The constant α₀ reflects the constant trend growth in productivity, and $G {\overset{*}{P}}_{- k}$ is the proxy for inflationary expectations, where the subscript — k indicates a lag of k periods.⁴

The principal hypothesis explored in this paper can now be restated in terms of equation (6) as follows: the coefficient α₃ will be lower for values of $G {\overset{*}{P}}_{- k}$ below a certain threshold level than for values of $G {\overset{*}{P}}_{- k}$ that are equal to the threshold level or exceed it.

The hypothesized increase in the coefficient α₃ as past price changes reach and exceed the threshold level may be represented by their interaction with a dummy variable, D_m. On the assumption that the threshold would lie at a rate of price increase within the range of 3 to 5 per cent, its exact location can be determined by letting the dummy variable take the value of unity whenever price changes in the past were equal to or in excess of m, and the value of zero otherwise, where m refers to the alternative amounts of 3.0, 3.25, 3.50, …, 4.75, and 5.0 per cent. Inclusion of this modification in equation (6) yields a new price equation:

\begin{matrix} G \overset{*}{P} = α_{0} + α_{1} U_{- i}^{- 1} + α_{2} \overset{*}{U} + α_{31} G {\overset{*}{P}}_{- k} + α_{32} D_{m} G {\overset{*}{P}}_{- k} & (7) \end{matrix}

where D_m = 1 when $G {\overset{*}{P}}_{- k} \geq m$ , and D_m = 0 when $G {\overset{*}{P}}_{- k} < m$ . Comparison with equation (6) shows that α₃₁ + α₃₂D_m = α₃. As long as past inflation $G {\overset{*}{P}}_{- k}$ does not reach the threshold level (m) the composite coefficient α₃ on $G {\overset{*}{P}}_{- k}$ will be equal to α₃₁; but, assuming α₃₂ to be positive, α₃ will rise to α₃₁ + α₃₂ as soon as $G {\overset{*}{P}}_{- k}$ reaches and exceeds the threshold level.

Several questions arise with regard to the hypothesized threshold effect. These bear on (1) the location of the threshold, (2) the lowest unemployment rate that is still consistent with price increases below the threshold rate, and (3) the inflationary process set in motion as price increases reach and exceed that rate.

On the assumption that the location of the threshold can be determined, the lowest unemployment rate consistent with price increases below it can be derived from the trade-off curve between unemployment and inflation, provided that such a curve exists at least over the range of those price increases. The inflationary process that is set in motion as price increases reach and exceed the threshold will either worsen the trade-off or, when the coefficients on past price behavior sum to unity, the long-run relation between unemployment and inflation will become a straight line, precluding a trade-off. Equation (7) may be used to illustrate these alternative cases, where the sum of the two coefficients α₃₁ and α₃₂ is less than unity or exactly equal to unity (still always assuming that α₃₂ is positive). The long-run steady-state relation between unemployment and inflation is obtained by rewriting equation (7) without time subscripts and assuming no change in unemployment:

\begin{matrix} G \overset{*}{P} = \frac{1}{1 - α_{31}} [α_{0} + α_{1} U^{- 1}], for price increases below the & (8) \end{matrix}

threshold rate (D_m = 0, α₃₁ < 1); and

\begin{matrix} G \overset{*}{P} = \frac{1}{1 - α_{31} - α_{32}} [α_{0} + α_{1} U^{- 1}], for price increases at or & (9) \end{matrix}

above the threshold rate (D_m = 1, α₃₁ < (α₃₁ + α₃₂) < 1).

A comparison of equations (8) and (9) shows that the trade-off between unemployment and inflation worsens as price increases reach and exceed the threshold.

If α₃₁ and α₃₂ were, to approach closely to unity, equation (9) could not hold, because the fraction on the right-hand side would tend toward infinity; the rate of price change would then not vary continuously with the rate of unemployment. In these circumstances, equation (7) can be solved for the “natural rate of unemployment” (U_N), the only rate of unemployment consistent with a given finite rate of continuous price increase or decrease:

U_{N} = \frac{- α_{1}}{α_{0}}, D_{m} = 1, α_{31} < (α_{31} + α_{32}) = 1.

On the assumption that the direct negative effect of productivity on prices is greater than its indirect positive effect, α₀ is negative and the natural unemployment rate is a positive number.⁵

wage and price controls in 1971–72

The following empirical section provides answers to the questions raised. In particular, it determines for the United States the location of the threshold and the lowest unemployment rate that is still consistent with price increases below it and examines the inflationary consequences of price increases above it. Before estimating the price equation for the United States, however, it is necessary to consider a modification relating to any effects that the wage and price controls in 1971 and 1972 may have had on wage and price developments. The first phase of controls began on August 15, 1971—Phase I, with a freeze on nearly all wages, prices, and rents lasting three months. In October, Phase II was initiated, and programs were announced to replace the freeze by November 14 and to last throughout 1972.⁶ The controls are not examined here in any detail but are merely included in the price equation in the form of a shift dummy allowing for the possibility that they have dampened inflation. Estimation of the equation is based on annual data for the years 1957 to 1972 inclusive. The shift dummy takes the value of unity in the last year of this period and the value of zero in all other years, on the assumption that any effects of the controls would show in the rate of inflation for 1972.

II. Empirical Results

In the estimated price equation, the general price level in the United States is represented by the GNP deflator. The following equation, fitted over the period 1957–72, was obtained:

\begin{matrix} G \overset{*}{P} & = & \underset{(7.25)}{- 2.19} + \underset{(9.83)}{16.09} U_{- 1}^{- 1} - \underset{(3.85)}{1.23} \overset{*}{U} + \underset{(5.87)}{0.53} G {\overset{*}{P}}_{- 1} & (11) \\ + \underset{(3.38)}{0.17} D_{m} G {\overset{*}{P}}_{- 1} - \underset{(3.12)}{0.90} CD \\ {\bar{R}}^{2} & = & 0.98, D - W = 2.80, \bar{SE} = 0.21 \end{matrix}

where

figures in parentheses are t-ratios

As shown in Chart 1, equation (11) traces the price developments over this period very well. All explanatory variables in the equation are significant and carry the expected signs. The level of unemployment, in reciprocal form, affects inflation with a lag of half a year, while its rate of change affects inflation concurrently.⁸ Controls were apparently successful, reducing the rate of price increases from 1971 to 1972 by almost 1 percentage point.⁹ With regard to the location of the threshold, no statistical support was obtained (in tests not shown) for the assumption that it lies below 4 per cent, but it appears from equation (11) that once price increases reach or exceed 4 per cent annually the hypothesized change in slope is observable. Equation (11) suggests that this involves an increase from 0.53 to 0.70 in the coefficient on past price changes. It is conceivable that further threshold effects would hold at larger or smaller intervals as inflation continues to rise. To test for this possibility, the interaction of past inflation with additional dummy variables could be examined, identifying instances of larger and still larger price changes. The relation between current and past price changes could also be represented by an exponential function. The present analysis does not test for either of these possibilities. Extension of the analysis to the case of successive threshold effects would run into problems of multicollinearity and would in any case be more useful in a model based on semiannual data, while the fitting of an exponential function would place emphasis on a hypothesis that is an alternative to that of the threshold effect examined here.

Chart 1.

United States: Actual and Computed Annual Percentage Change in the Gross National Product Deflator, 1957–72

Citation: IMF Staff Papers 1975, 003; 10.5089/9781451969382.024.A006

steady-state and short-run relations between unemployment and inflation

Equation (11) does not distinguish among the causes that may lead to price increases above the threshold level; it merely implies that expectations change and inflation accelerates when past inflation reaches or exceeds 4 per cent.¹⁰ One such cause may be a reduction in unemployment, since the equation implies a trade-off between unemployment and inflation. It appears, therefore, that reduction of unemployment below a certain level can set in motion the process of inflation implied by the threshold effect, with the result that the trade-off worsens. The point at which this happens may be inferred from the equation by computing the lowest rate of unemployment that can be maintained in the long run without causing inflation to rise to a rate of 4 per cent.

The lowest unemployment rate consistent with inflation below the threshold is computed by assuming $G \overset{*}{P}$ in equation (11) to lie just below 4 per cent, setting the rate of change in the unemployment rate $(\overset{*}{U})$ equal to zero, dropping time subscripts from all variables, and solving for the rate of unemployment (U). The unemployment rate derived in this way is about 4 per cent. The implications of the threshold effect for the long-run steady-state relation between unemployment and inflation are illustrated in Table 1, where the relation that allows for the process of inflation attributable to this effect is contrasted with the relation that would prevail in its absence. It appears from the table that keeping unemployment at levels of 4 per cent and below would, under present structural conditions in labor and product markets, involve considerable costs in terms of price stability.

Table 1.

United States: Steady-State Relation Between Unemployment and Inflation and the Impact of the Threshold Effect

(In per cent)

Table 1.

United States: Steady-State Relation Between Unemployment and Inflation and the Impact of the Threshold Effect

(In per cent)

Levels of Unemployment (A)	Rates of Inflation with Threshold Effect		Threshold Effect (B) – (C)
Levels of Unemployment (A)	Included (B)	Excluded (C)	Threshold Effect (B) – (C)
6.0	1.0	1.0	—
5.5	1.6	1.6	—
5.0	2.2	2.2	—
4.5	2.9	2.9	—
4.0	3.9	3.9	—
3.9	6.8	4.0	2.8
3.5	8.6	5.1	3.5
3.0	11.1	6.8	4.3
2.5	14.7	9.0	5.7
2.0	20.1	12.5	7.7

Table 1.

United States: Steady-State Relation Between Unemployment and Inflation and the Impact of the Threshold Effect

(In per cent)

Levels of Unemployment (A)	Rates of Inflation with Threshold Effect		Threshold Effect (B) – (C)
Levels of Unemployment (A)	Included (B)	Excluded (C)	Threshold Effect (B) – (C)
6.0	1.0	1.0	—
5.5	1.6	1.6	—
5.0	2.2	2.2	—
4.5	2.9	2.9	—
4.0	3.9	3.9	—
3.9	6.8	4.0	2.8
3.5	8.6	5.1	3.5
3.0	11.1	6.8	4.3
2.5	14.7	9.0	5.7
2.0	20.1	12.5	7.7

The steady-state analysis of inflation and unemployment provides no information regarding the short-run price effects of consecutive changes in unemployment. In particular, it does not permit any inference about the amount and duration of unemployment required to dampen inflation attributable to low unemployment and the nonlinear relation between current and past price movements. However, the lagged response of prices to unemployment, the dependence of current price changes on their lagged values, and the modification of this dependence through the process set in motion as inflation reaches and exceeds the threshold level all indicate that during a cyclical upturn, when unemployment is successively reduced, the short-run relation between unemployment and inflation may lie below the corresponding steady-state relation. Similarly, during a cyclical downturn, the reverse may apply. Unemployment and inflation can therefore be expected to rise simultaneously in the initial phases of a downturn, and in a renewed upturn both can be expected to decline, at least for some time. Some short-run simulation results were derived from equation (11) and are reported in Table 2, showing the relation between unemployment and inflation under conditions of decreases and increases in unemployment. Specifically, it is assumed that unemployment declines initially from a previously steady level of 6 per cent to 3 per cent, returns subsequently to 6 per cent, and finally falls to 3 per cent. All changes in unemployment occur at a rate of ½ percentage point annually. The rates of inflation that correspond to these movements in unemployment are calculated both with and without the acceleration of inflation attributable to the threshold effect.

Table 2.

United States: Hypothetical Short-Run Relation Between Unemployment and Inflation and the Impact of the Threshold Effect

(In per cent)

Table 2.

United States: Hypothetical Short-Run Relation Between Unemployment and Inflation and the Impact of the Threshold Effect

(In per cent)

		Rates of Inflation with Threshold Effect
Period	Levels of Unemployment(A)	Included (B)	Excluded (C)	Threshold Effect (B) – (C)
Initial path
0	6.0	1.0	1.0	—
1	5.5	1.1	1.1	—
2	5.0	1.4	1.4	—
3	4.5	1.9	1.9	—
4	4.0	2.5	2.5	—
5	3.5	3.3	3.3	—
6	3.0	4.3	4.3	—
Final path
7	3.5	6.0	5.3	0.7
8	4.0	6.4	5.0	1.4
9	4.5	6.2	4.3	1.9
10	5.0	5.6	3.6	2.0
11	5.5	4.8	2.8	2.0
12	6.0	4.0	2.1	1.9
13	5.5	2.7	1.7	1.0
14	5.0	2.3	1.8	0.5
15	4.5	2.4	2.1	0.3
16	4.0	2.8	2.6	0.2
17	3.5	3.4	3.4	—
18	3.0	4.4	4.4	—
19	3.5	6.0	5.3	0.7
20	4.0	6.4	5.0	1.4
21	4.5	6.2	4.3	1.9
22	5.0	5.6	3.6	2.0
23	5.5	4.8	2.8	2.0
24	6.0	4.0	2.1	1.9
25	5.5	2.7	1.7	1.0
26	5.0	2.3	1.8	0.5
27	4.5	2.4	2.1	0.3
28	4.0	2.8	2.6	0.2
29	3.5	3.4	3.4	—
30	3.0	4.4	4.4	—

Table 2.

United States: Hypothetical Short-Run Relation Between Unemployment and Inflation and the Impact of the Threshold Effect

(In per cent)

		Rates of Inflation with Threshold Effect
Period	Levels of Unemployment(A)	Included (B)	Excluded (C)	Threshold Effect (B) – (C)
Initial path
0	6.0	1.0	1.0	—
1	5.5	1.1	1.1	—
2	5.0	1.4	1.4	—
3	4.5	1.9	1.9	—
4	4.0	2.5	2.5	—
5	3.5	3.3	3.3	—
6	3.0	4.3	4.3	—
Final path
7	3.5	6.0	5.3	0.7
8	4.0	6.4	5.0	1.4
9	4.5	6.2	4.3	1.9
10	5.0	5.6	3.6	2.0
11	5.5	4.8	2.8	2.0
12	6.0	4.0	2.1	1.9
13	5.5	2.7	1.7	1.0
14	5.0	2.3	1.8	0.5
15	4.5	2.4	2.1	0.3
16	4.0	2.8	2.6	0.2
17	3.5	3.4	3.4	—
18	3.0	4.4	4.4	—
19	3.5	6.0	5.3	0.7
20	4.0	6.4	5.0	1.4
21	4.5	6.2	4.3	1.9
22	5.0	5.6	3.6	2.0
23	5.5	4.8	2.8	2.0
24	6.0	4.0	2.1	1.9
25	5.5	2.7	1.7	1.0
26	5.0	2.3	1.8	0.5
27	4.5	2.4	2.1	0.3
28	4.0	2.8	2.6	0.2
29	3.5	3.4	3.4	—
30	3.0	4.4	4.4	—

The illustrations reveal several significant properties of the short-run relation between unemployment and inflation in the example at hand. First, the short-run relation lies below the steady-state relation in a cyclical upswing and above it in a cyclical downturn. Second, the increase in unemployment from 3 to 4 per cent over a two-year period is accompanied by a rise in the rate of inflation and the renewed decline in unemployment from 6 to 5 per cent by a decline in this rate. Third, if unemployment continues to move in the pattern assumed for this illustration, the corresponding price movements will eventually describe an unchanged path, as shown in Table 2.

The steady-state and short-run relations between unemployment and inflation recorded in Tables 1 and 2 are also shown in Chart 2. In the chart, the short-run relation is superimposed on the steady-state relation and describes a time path. In contrast, the steady-state relation is the collection of points that represent trade-offs between inflation and alternative steady levels of unemployment; therefore, it does not describe a time path.

Chart 2.

United States: Steady-State and Short-Run Relations Between Unemployment and Inflation and the Impact of the Threshold Effect

Citation: IMF Staff Papers 1975, 003; 10.5089/9781451969382.024.A006

Chart 2 illustrates, perhaps better than the tables, the process of inflation implied by the hypothesized threshold effect and the difference it makes both in the short run and the steady state. In the short run, the relations between unemployment and inflation, including and alternatively excluding the threshold effect, coincide during the first round of reductions in unemployment from the initially steady level of 6 per cent to a level of 3 per cent and describe different paths only subsequently. In contrast to the short-run relation, which illustrates the worsening of the trade-off between unemployment and inflation in successive periods, the upward shift in the steady-state relation represents the cumulative effect on the trade-off of a decline in unemployment below 4 per cent and an increase of inflation to 4 per cent. The cumulative effect over time is shown in Chart 3. The chart illustrates the effect on inflation over time as unemployment is reduced from a level that has been kept steady at 4 per cent to a slightly lower level, just enough for the threshold effect to apply, which is maintained thereafter. While Table 1 and the steady-state relation in Chart 2 show that such a one-time change in unemployment involves an increase in inflation from 3.9 to 6.8 per cent, Chart 3 shows that this increase takes some ten periods to materialize.

Chart 3.

United States: Cumulative Threshold Effect Over Time ¹

Citation: IMF Staff Papers 1975, 003; 10.5089/9781451969382.024.A006

¹ The illustration in this chart corresponds to the upward shift in the steady-state relation between unemployment and inflation of Chart 2, and it shows the time path of this shift.

reliability of the coefficient on expectations

While the results support the hypothesis of a threshold effect in the forming of expectations, the related increase in the coefficient on past price behavior to a level of 0.70 falls short of unity, to which it is in theory constrained in the long run. Since a unitary coefficient involves implications for the trade-off between unemployment and inflation that differ from those of a coefficient that is lower, a test is applied to establish whether the sum of the coefficients on past price behavior in the estimated price equation is in the statistical sense significantly smaller than unity.

The result of such a test is affirmative, and the accuracy of the estimated coefficient summing to 0.70 seems therefore reasonably assured.¹¹

All the same, some questions still remain regarding the existence of additional thresholds and the quality of the proxy for inflationary expectations. The possibility of full anticipation of future inflation cannot be excluded, although the evidence presented here does not support it. It may be that additional threshold effects apply at higher rates of inflation and that past price behavior does not capture in their entirety expectations held about inflation in the future.

As already mentioned, the equation used for estimation may be consistent with still other hypotheses than those that were considered in Section I, while, conversely, some of these hypotheses could have been represented in alternative ways. For example, inflationary expectations may affect prices directly rather than only through their impact on wages as hypothesized; and excess demand in the product market may be measured by other variables than the rate of unemployment.

III. Conclusions

This paper presents and tests a price equation which contains, among other arguments, a proxy for inflationary expectations allowing for a threshold effect. In the first section the implications of this effect for the trade-off between unemployment and inflation are analyzed, making alternative assumptions about the size of the coefficient on past price movements, which serve as proxy. In the second section the price equation is estimated for the United States over the period from 1957 to 1972 inclusive, using annual data. The empirical results confirm the hypothesis of a threshold effect which apparently applies as inflation reaches and exceeds a rate of 4 per cent. At this rate the dependence of current price movements on past ones rises, as demonstrated by the increase from 0.53 to 0.70 in the coefficient on past price changes. Even the latter value appears, on the basis of a statistical test, to be significantly different from unity.

With regard to the trade-off between unemployment and inflation, there is evidence that unemployment must not be lowered to 4 per cent or below if the threshold effect on inflation is to be avoided, unless structural conditions in labor and product markets are changed.

The results also show that the price equation, including the threshold effect, is capable of explaining not only a worsening of the trade-off between unemployment and inflation but even a situation where rising unemployment and rising inflation occur simultaneously (as was the case in the years 1969 and 1970 when inflation accelerated from 4.8 to 5.4 per cent and unemployment rose from 3.5 to 4.9 per cent). Furthermore, the results of the simulation exercise performed in this study, and illustrated in Table 2 and Chart 2, demonstrate that the equation can also accommodate a situation where the trade-off is substantially improved, although such improvement would be temporary rather than permanent, and it even appears that decreasing inflation would be consistent with reductions in unemployment, at least for some time.

Mr. Spitäller, economist in the Special Studies Division of the Research Department, is a graduate of the University of Graz, Austria, and of the School of Advanced International Studies of the Johns Hopkins University, Washington, D. C.

See Morris Goldstein, “The Trade-Off Between Inflation and Unemployment: A Survey of the Econometric Evidence for Selected Countries,” Staff Papers, Vol. 19 (November 1972), pp. 647–95, for a review of the literature. See also Otto Eckstein, editor, The Econometrics of Price Determination, a volume of papers from the Conference on the Econometrics of Price Determination, Board of Governors, Federal Reserve System (Washington, June 1972).

See James Tobin, “The Wage-Price Mechanism: Overview of the Conference,” in The Econometrics of Price Determination, edited by Otto Eckstein, Board of Governors, Federal Reserve System (Washington, June 1972), pp. 5–15; and Morris Goldstein, op.cit.

Extrapolative expectations may take the form of ${\overset{*}{P}}^{e} = β \overset{*}{P} + γ (\overset{*}{P} - {\overset{*}{P}}_{- 1}), β \leq 1, γ \geq 0,$

where ${\overset{*}{P}}^{e}$ is the rate of change in prices expected for the future at time t, and an asterisk indicates the rate of change from the previous period. If γ is equal to zero, expectations are approximated by current price changes unless β is equal to unity, in which case expectations are static.

A distributed lag pattern provides another formulation of extrapolative expectations; it may be written as

${\overset{*}{P}}^{e} = Σ_{k = 0}^{m} λ_{k} {\overset{*}{P}}_{- k}$

where λ is a weight, Σ_kλ_k = 1, and k indicates the length of the lag.

Adaptive expectations may be represented by

${\overset{*}{P}}^{e} = δ {\overset{*}{P}}_{- 1}^{e} + θ (\overset{*}{P} - {\overset{*}{P}}_{- 1}^{e}), δ < 1, 0 < θ < 1.$

See Stephen J. Turnovsky and Michael L. Wachter, “A Test of the ‘Expectations Hypothesis’ Using Directly Observed Wage and Price Expectations,” Review of Economics and Statistics, Vol. 54 (February 1972), pp. 47–54.

Price equations of this form were estimated for the United States and other industrial countries, in Erich Spitäller, “Prices and Unemployment in Selected Industrial Countries,” Staff Papers, Vol. 18 (November 1971), pp. 528–67.

However, even if the coefficients on past price movements summed to unity, a trade-off between unemployment and inflation exists in the short run. It can be seen from equation (7) that the rate of inflation then equals the past rate plus a constant plus a factor that depends on the rate of unemployment (as well as on its rate of change): $\begin{matrix} G \overset{*}{P} = G {\overset{*}{P}}_{- 1} + α_{0} + α_{1} U_{- i}^{- 1} + α_{2} \overset{*}{U} & (7 a) \end{matrix}$

For a description of the controls during Phases I and II, see “The Annual Report of the Council of Economic Advisers: Chapter 2. Inflation Control Under the Economic Stabilization Act,” in the Economic Report of the President (U.S. Government Printing Office, Washington, January 1973), pp 51–70.

Because of the inclusion of the lagged dependent variable in equation (11), the Durbin-Watson statistic is biased and does not therefore test reliably for absence of autocorrelation in the residuals. An alternative test developed by Durbin, the h-test, provides better information. However, this test applies to large samples and can only be indicative when applied to equation (11). The value of h for this equation is 1.65, indicating that autocorrelation is absent since the hypothesis of zero autocorrelation is rejected at the 5 per cent level if h > 1.645. See J. Durbin, “Testing for Serial Correlation in Least-Squares Regression When Some of the Regressors Are Lagged Dependent Variables,” Econometrica, Vol. 38 (May 1970), pp. 410–21.

The dependence of $G \overset{*}{P}$ on $U_{- 1}^{- 1}$ involves a lag of half a year because the observations for the rates of price change and unemployment are centered at year-end and mid-year, respectively.

This finding is consistent with the conclusions of a study that analyzes the effectiveness of the controls in detail. See Barry Bosworth, “Phase II: The U.S. Experiment with an Incomes Policy,” Brookings Papers on Economic Activity, No. 2 (1972), pp. 343–83.

The acceleration of inflation refers here to the rise in the elasticity of inflationary expectations with respect to past rates of price change as a result of the threshold effect and not to the acceleration that is merely attributable to higher rates of past inflation.

The hypothesis that the sum of the coefficients on past price behavior, over the range where the threshold effect applies, differs significantly from unity at the 5 per cent level is confirmed if $\frac{1 - 0.70}{SE (0.53 + 0.17)} > 2.2$

where SE is the standard error and 0.53 and 0.17 are the relevant coefficients. The denominator of this expression is computed as the square root of the sum of the variances of the coefficients plus twice their covariance. This yields $\frac{0.30}{\sqrt{0.0038}} = 5$ and the hypothesis is therefore confirmed.

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IMF Staff papers: Volume 22 No. 3

Author:

International Monetary Fund. Research Dept.

Volume/Issue:: Volume 1975: Issue 003

Publisher:: International Monetary Fund

ISBN:: 9781451969382

ISSN:: 1020-7635

Pages:: 292

DOI:: https://doi.org/10.5089/9781451969382.024

Keywords
I. The Price Equation
II. Empirical Results
- steady-state and short-run relations between unemployment and inflation
- reliability of the coefficient on expectations
III. Conclusions

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Chart 1.

United States: Actual and Computed Annual Percentage Change in the Gross National Product Deflator, 1957–72

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Chart 2.

United States: Steady-State and Short-Run Relations Between Unemployment and Inflation and the Impact of the Threshold Effect

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Chart 3.

United States: Cumulative Threshold Effect Over Time ¹

Table 2.

United States: Hypothetical Short-Run Relation Between Unemployment and Inflation and the Impact of the Threshold Effect

(In per cent)

		Rates of Inflation with Threshold Effect
Period	Levels of Unemployment(A)	Included (B)	Excluded (C)	Threshold Effect (B) – (C)
Initial path
0	6.0	1.0	1.0	—
1	5.5	1.1	1.1	—
2	5.0	1.4	1.4	—
3	4.5	1.9	1.9	—
4	4.0	2.5	2.5	—
5	3.5	3.3	3.3	—
6	3.0	4.3	4.3	—
Final path
7	3.5	6.0	5.3	0.7
8	4.0	6.4	5.0	1.4
9	4.5	6.2	4.3	1.9
10	5.0	5.6	3.6	2.0
11	5.5	4.8	2.8	2.0
12	6.0	4.0	2.1	1.9
13	5.5	2.7	1.7	1.0
14	5.0	2.3	1.8	0.5
15	4.5	2.4	2.1	0.3
16	4.0	2.8	2.6	0.2
17	3.5	3.4	3.4	—
18	3.0	4.4	4.4	—
19	3.5	6.0	5.3	0.7
20	4.0	6.4	5.0	1.4
21	4.5	6.2	4.3	1.9
22	5.0	5.6	3.6	2.0
23	5.5	4.8	2.8	2.0
24	6.0	4.0	2.1	1.9
25	5.5	2.7	1.7	1.0
26	5.0	2.3	1.8	0.5
27	4.5	2.4	2.1	0.3
28	4.0	2.8	2.6	0.2
29	3.5	3.4	3.4	—
30	3.0	4.4	4.4	—

$G \overset{*}{P}$	=	annual per cent change in the GNP deflator
U	=	average annual rate of unemployment in per cent and $\overset{*}{U}$ its rate of change divided by 100
D_m	=	1 for $G {\overset{*}{P}}_{- 1} \geq 4$ and zero otherwise
CD	=	control dummy with the value of unity in 1972 and zero in all other years
${\bar{R}}^{2}$	=	coefficient of determination adjusted for degrees of freedom
D-W	=	Durbin-Watson statistic⁷
$\bar{SE}$	=	standard error of the estimate adjusted for degrees of freedom.

$G \overset{*}{P}$	=	annual per cent change in the GNP deflator
U	=	average annual rate of unemployment in per cent and $\overset{*}{U}$ its rate of change divided by 100
D_m	=	1 for $G {\overset{*}{P}}_{- 1} \geq 4$ and zero otherwise
CD	=	control dummy with the value of unity in 1972 and zero in all other years
${\bar{R}}^{2}$	=	coefficient of determination adjusted for degrees of freedom
D-W	=	Durbin-Watson statistic⁷
$\bar{SE}$	=	standard error of the estimate adjusted for degrees of freedom.

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Abstract

I. The Price Equation

the Phillips curve

inflationary expectations

wage and price controls in 1971–72

II. Empirical Results

steady-state and short-run relations between unemployment and inflation

reliability of the coefficient on expectations

III. Conclusions

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