A Model of Inflation and Its Performance in the Seven Main Industrial Countries, 1958-76
  • 1 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

ERICH SPITÄLLER *

Abstract

ERICH SPITÄLLER *

ERICH SPITÄLLER *

A number of subjects in economics would appear to have been worked over so thoroughly that any new attempt to address them is likely to be suspect of treading old ground and rehearsing familiar arguments. This is certainly true of inflation. The literature abounds in studies of wage and price movements, and to undertake yet another study in this area requires justification. On a general level this is easily done: identifying the causes of inflation is a perennial and elusive problem, requiring frequent re-examination. Recent developments bear this out. Together with the relatively high levels of unemployment, inflation has been and continues to be among the main preoccupations of economic authorities in many countries. At the same time, the view is spreading that in the 1970s the process of inflation has undergone a number of structural changes and is therefore different from what it was in earlier years. Coincidentally, a rapidly growing body of literature has developed a new—although seriously contested—approach to the analysis of inflation, combining the so-called aggregate supply theory of Friedman and Phelps with the application of “rational” expectations to the labor market. The attention that this approach has attracted makes it necessary that any new study of inflation take it into account.

This paper is organized along the following lines. The theoretical section develops a model explaining price changes and discusses its properties with reference to recent work on inflation. The empirical section presents results from the estimation of reduced form price equations for the seven main industrial countries—Canada, France, the Federal Republic of Germany, Italy, Japan, the United Kingdom, and the United States—based on data from 1958 to 1976. The concluding section summarizes some of the distinctive features of the model and the main empirical findings.

I. A Model of Price Changes

In this section, factors affecting price changes are analyzed with reference to a number of structural relationships. These relationships are examined both for their implications regarding the inflation process and for the long-run equilibrium properties of reduced form solutions that may be derived. Some observations on the probable effectiveness of stabilization policies are made in the course of the discussion. On a general level, these relationships involve (i) price and wage equations, (ii) expectations schemes that relate to inflation and money growth in the short run and the long run, (iii) a linkage between measures of disequilibrium in different markets, and (iv) a linkage between these disequilibrium measures and growth in real income. Specifically, the rate of change in the general price level, P*—here to be understood as the deflator of total domestic demand—is expressed as a weighted average of corresponding rates of change in domestic prices, Pd* and in foreign prices and the exchange rate, Pf* and E*:

P*=a10Pd*+(1a10)[Pf*+E*](1)

where an asterisk denotes the percentage change in a variable, where a10 and (1 –a10) refer to the weights of domestic and foreign components in total demand, and where Pf*+E* serves as proxy for the percentage change in (PfE).

The rate of change in the domestic price level depends on the trend growth in productivity, Q¯* the rate of change in the wage rate, W* the output gap in the product market represented by the deviation of actual output from its capacity level, Y/Ȳ,1 both in real terms, and on the rate of change in the local currency price of competing imports, [Pf*+E*]. For simplicity, the value of foreign prices is assumed to be the same as in equation (1)

Pd*=a11Q¯*+a12Wk*+a13YY¯e+a14[P*f+E*]m(2)

a12, a14 > 0 a11 < 0 a13 ≷ 0

A bar over a variable refers to its trend value, and the subscripts k, ℓ, and m denote lags of different lengths.

The sign of the coefficient on the output gap, Y/Ȳ is ambiguous because its relationship to inflation involves two opposing influences, namely, an increase in demand pressure and a fall in actual unit costs. The former tends to raise inflation, while the latter tends to reduce it. Two points may be made in this connection. First, in considering an increase in the output gap, for example, it is well to distinguish between the effect of this increase, on the one hand, and the effect of the resulting higher level of capacity utilization per se, on the other hand. The increase is potentially deflationary in effect, while the effect of the higher level is likely to be inflationary. In the term a13 (Y/Ȳ)-l the two effects of the level of the gap and its change are combined, since Y/Ȳ may be approximated by

a13(Y/Y¯)=a131(Y/Y¯)m+a132Δ(Y/Y¯)n(2)

The coefficient a13 is then composed of the positive coefficient on the level of the gap and the negative coefficient on its change. Depending on the relative magnitudes of these coefficients, their composite may be either positive or negative in sign. Second, it could be argued, for example—although no distinction is introduced in equation (2)—that the inflationary effect of a rise in the gap would dominate whenever an economy moves along the steeper portion of its Phillips curve, say, whenever the value of the gap exceeds unity, but that the deflationary effect would be stronger along the flatter part of the curve where the value of the gap lies below unity.2

In the wage equation, the rate of change in the wage rate is a function of the trend growth in productivity, short-run inflationary expectations, Pe*(s), and the lagged unemployment rate, Ui

W*=b11Q¯*+b12Pe*(s)+b13Ui(3)

b11, b12 > 0 b13 < 0

The specification of price and wage equations given in equations (2) and (3) has been generally accepted in the literature and has found broad empirical support. For example, the use of standard unit labor costs in the price equation is common practice, reflecting the view that trend growth in productivity is more important in the context of wage negotiations than are fluctuations in productivity, even though they too have been shown to affect price movements.3 Similarly, the use of the output gap as a measure of demand pressure is widespread. The wage equation represents an expectations-augmented Phillips hypothesis whereby it may be noted that the expectations refer to inflation in the general price level. This implies that wage earners attempt to protect their purchasing power against price changes in both domestically produced and imported goods and services.

Inflationary expectations are represented here in a manner that distinguishes between the short run and the long run. In the long run, it is assumed that

Pe*()=Me*()Y¯*(4)

where Pe*() and Me*() are the expected long-run rates of change in the general price level and in the money stock, and where Y¯* is the long-run trend growth in real output. Over the short run, inflationary expectations are approximated by

Pe*(s)=d10Pe*(β)+(1d10)[Pe*(β)P*]j(5)
4

0 < d10 < 1

Expected long-run changes in the money stock are assumed to be proportional to corresponding changes expected for the short run,

Me*()=g10Me*(s)0<g10<1(6)

Short-run expectations are generated by an adaptive process

Me*(s)Me*(s)1=λ[M*(s)Me*(s)1]0<λ<1(7)

that implies that changes in expectations from one period to the next are adjusted for error.

Considering the model specification up to this point, and recalling the potentially dual role of the output gap in the inflation process, the following applies regarding the effectiveness of stabilization policies. When the productivity effect of the output gap dominates, fiscal expansion would not increase inflationary pressures but would reduce them. This would, however, be a temporary effect, since a higher level of capacity utilization would imply a lasting higher rate of inflation. By contrast, monetary expansion would not necessarily have the same effect, since it also raises inflationary expectations. The net effect of monetary policy on inflation would therefore be larger than that of fiscal policy, even if the direction of both effects proved to be the same. Conversely, monetary stabilization would be relatively more effective when output is above capacity and when the demand pressure effect of the output gap dominates. Monetary contraction would reduce inflation via a decrease in both inflationary expectations and demand pressure, while fiscal contraction would operate through this latter channel only.

The remaining relationships of the model comprise (i) a definition of capacity output, Ȳ, (ii) an identity relating the output gap, Y/Ȳ to the rate of change in real output, Y*, and (iii) a relationship between the output gap and unemployment. Capacity output is defined as

Y¯=aebtb>0(8)

where e is the exponential operator, b is a growth rate, and t is a time trend. The link between Y/Ȳ and Y* may be written as

YY¯=(Y*+1)(YY¯)1eb(9)

and is an identity.5 What equation (9) indicates is that the output gap during any period may be expressed in terms of two variables, namely, the percentage change in actual output from the preceding period and the then prevailing gap, multiplied by a constant. The form of the equation indicates that the current gap, Y/Ȳ, will be the higher, the higher is its past value relative to the ratio of current capacity to past capacity—given by eb, which equals (Ȳ/Ȳ-1)—and the higher is the percentage of growth in actual output, Y*. The link between levels of demand pressure in goods and labor markets is represented by a linear approximation

U=c0+c11(YY¯)c0>0,c11<0(10)

where the inclusion of the constant term, c0, allows for the possibility that some of the unemployment observed at any time is frictional or hard core in nature, and does not respond systematically to demand pressure in the goods market.6

The model is summarized in Table 1. Two features are worth emphasizing at this stage. The first relates to the mechanism of inflation. It will be seen that the model incorporates a trade-off between unemployment and inflation, subject to qualifications. The second bears on the ability of the model to yield a relationship between the difference in actual and expected rates of inflation, on the one hand, and the deviation of output from its trend value, on the other hand, a relationship that is central to much of the recent literature on the determination of output and price fluctuations.

Table 1.

Summary of the Model of Price Changes1

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The ten endogenous variables are P*,P*d,W*,YY¯,Y¯,U,Pe*(),Pe*(s),Me*(), and Me*(s). The exogenous variables are P*f,E*,, and Y*. Argy (1977 b) has developed a model of output changes in which the rate of inflation is exogenous. A study on the joint determination of changes in output and prices has been prepared, Argy and Spitäller (1978). Symbols used: P = general price level, that is, deflator of total demand; Pd = domestic price level, that is, deflator of demand for domestic goods; Pf = price level of foreign final goods; E = exchange rate expressed as the local currency price per unit of foreign currency; Q = productivity; W = wage rate; Y = real output; Ȳ = capacity output; U = unemployment rate; M = nominal stock of money. The superscript e stands for expectations about a variable, but in equations (8) and (9), e is the exponential operator. An asterisk denotes the percentage change in a variable, and a bar above a symbol refers to its trend value. The subscripts, i, j, k, ℓ, and m denote lags. However, in equations (4)-(6), (ℓ) refers to the long run and (s) to the short run. Equation (8) does not allow for the relative deceleration in output growth in the 1970s. For a different representation of “potential” output, see, for example, Ripley (1976), who defines potential output in terms of a geometric moving average.

As long as the demand pressure effect of a rise in the output gap dominates, a trade-off exists. If, however, the productivity effect is the decisive influence instead, the trade-off would be suspended for some time, depending on the difference in length of the lag on the gap, ℓ, on the one hand, and of the lags on wage changes, k, and on the unemployment rate, i, on the other hand. It might therefore happen that the concurrent relationship between inflation and unemployment would be positive, contrary to the trade-off concept, but that the longer-run relationship would be consistent with the concept. Again, it would make a difference whether the output gap rose once and for all, or kept rising at an increasing rate. In this latter instance, the suspension of the trade-off could last longer than in the former instance. Another influence that has been important, and that may well obscure this tradeoff, is the movement of import prices. If competition between domestic goods and imports is very strong, rising import prices may overwhelm the deflationary impact of declining demand pressure so that inflation would accelerate in the face of rising unemployment.

As regards inflation in the general price level, P, and its trade-off against unemployment, much the same arguments apply that hold with respect to inflation in domestic prices, Pd, simply because they are a component of P. However, the significance of import price changes may be increased, since they now enter not only indirectly through their effects on Pd but also directly as a component of P.7 Consequently, the implications of import price changes for the unemployment versus inflation trade-off may become more far-reaching than before. Accordingly, the effectiveness of price stabilization measures under a fixed exchange rate may be impaired even in the short run before arbitrage in the goods market has established purchasing power parity and increased domestic inflation to the level prevailing abroad.

By contrast, under a flexible exchange rate system, inflation in the domestic and general price levels is equal, the trade-off between unemployment and inflation is restored, and the effectiveness of stabilization is enhanced. This is true as long as purchasing power parity determines the change in the exchange rate, which adjusts to remove the difference between inflation in domestic and foreign prices, E*=P*dP*f. Substituting this expression in equation (1) yields the equality P*=P*d. It is conceivable that this equality would not hold in the short run where the exchange rate may be assumed to be determined on the markets for financial assets.8 To the extent, therefore, that the short-run exchange rate would deviate from its longer-run value, inflation would be transmitted from abroad and the effectiveness of stabilization could be impaired even under a flexible exchange rate system.

With regard to the second feature of the model to be emphasized—its ability to relate the difference in actual and expected inflation to the deviation of unemployment from its “natural” rate—this ability may be demonstrated with reference to the price and wage equations (2) and (3), the link between demand pressure in goods and labor markets in equation (10), and a definition of the “natural” unemployment rate. Defining the natural rate as the rate prevailing at capacity output, where the value of the output gap equals unity, the link between the two may be written, analogous to equation (10), as

Un=c0+c11(Y¯Y¯)(10)

Subtracting equation (10’) from equation (10) yields

UUn=c11(YY¯Y¯)(10)

which is also

YY¯=1c11(UUn)+(Y¯Y¯)(10)

This expression may be combined with the solution of the price and wage equations (2) and (3) for the rate of inflation in the domestic price level, P*d, to result in

P*dPe*(s)=α+αc11(UUn),(11)α=b13c11+a13>0

or,

P*dPe*(s)=α+α(YY¯Y¯)(12)

where it is assumed that a12, b11, and b12 equal unity—absence of money illusion—a11 equals –1, and where the component of unemployment that does not vary cyclically, c0, is disregarded. In addition, all lags are assumed to be zero and the price of imports is left out of consideration. From equations (11) and (12), it appears that in equilibrium where the “natural” rate of unemployment and the “normal” level of output prevail, and where α is zero, actual and expected rates of inflation are the same.

The fact that the relationships in equations (11) and (12) can be derived from the model as special cases implies its consistency with the aggregate supply theory on which much recent work on inflation is based.9 However, this consistency is assured on a formal level only and does not extend to the substance of the theory, as the following remarks show. Friedman and Phelps, who developed the new aggregate supply theory, and the authors in their wake argue that unemployment can deviate from its natural level only as a result of unanticipated inflation.10 Suppose, for example, that inflation rises as a result of monetary expansion. Suppose, further, that workers do not perceive the full extent of this inflation and claim wage increases only in line with their inflationary expectations. On account of the unanticipated inflation, real wages fall, leading to an increase in employment and output and a decline in unemployment below its natural rate. In the long run, however, such a decline cannot last, because faulty perception cannot persist and unemployment will revert to its natural rate. Clearly, in the context of the present model, this line of argument is not requisite to derive equations (11) and (12), whatever the merits of the argument. What their derivation does demonstrate is that different hypotheses about the inflation process can give rise to similar formulations.11

In all discussions of the inflation process, inflationary expectations play a crucial role; differences in view over how they are formed have far-reaching implications and lie at the core of most controversies. The new aggregate supply theory has been complemented by the hypothesis of rational expectations, which, in turn, relies on the assumption of efficient markets.12 In accordance with this hypothesis, workers have complete knowledge of how the economy works and expect the same rate of inflation that would be forecast from an econometric model in which expectations are rationally formed, thus assuring internal consistency within the model. Any difference between actual inflation and expected inflation—the unanticipated component of inflation—is attributable exclusively to errors in information, which are presumed to be random. The introduction of the hypothesis removes the distinction between the short run and the long run, since, with actual and expected inflation being identical up to a random error, there are no lags in adjustment.13 Once this distinction is abandoned, purchasing power parity—usually assumed to apply in the long run—is implicitly assumed to hold at any time. A further consequence is that policies that are fully anticipated, for example, those that are announced or that follow a certain rule, have no effect on real output; only unanticipated policy changes affect real output.14

Finally, the assumption of rational expectations and the associated assumption of efficient markets bring out clearly an important implication of the new aggregate supply theory, namely, the purely voluntary nature of unemployment.15 If unanticipated inflation follows a random walk, so must the deviation of unemployment from its natural rate, which amounts to saying that unemployment data must be free of autocorrelation and that persistent, involuntary unemployment is excluded. Since the present model does not build on the tandem of the new aggregate supply theory and the rational expectations hypothesis, it is free of the underlying assumptions and consequences just described. Needless to say, this does not mean that the way in which expectations are formed here is not open to question, but the underlying assumptions are certainly less stringent.16

Some recent work on inflationary expectations has allowed for the direct effect of foreign price and exchange rate changes on expectations. This was done to accommodate the belief that these variables began to exert a greater influence on domestic inflation in recent years than before, at least in the short run. For example, domestic prices might adjust to foreign prices more quickly through changes in expectations and costs rather than through the slower mechanism of goods arbitrage. In the extreme case, prices would adjust before goods would move, assuring instant purchasing power parity.17 In the present model, changes in foreign prices and the exchange rate enter only as components of inflation in the general price level and as competitive influences on domestic prices.18 No allowance is made for any effect that they may have on inflationary expectations. However, monetary changes are assumed to have a direct impact on inflationary expectations.19

By substitution in equation (1) from the remainder of the model, a price equation in reduced form may be obtained in which the rate of inflation in the general price level is expressed in terms of a number of predetermined variables, including the gap or the rate of change in real output. The adaptive expectations scheme in equation (7)

Me*(s)Me*(s)1=λ[M*(s)Me*(s)1]

involves a geometric distributed lag model of the general form

Me*(s)=λΣk=0(1λ)kM*(s)k(7)

where k is a lag, or, written in lag operator form,

Me*(s)=λ1[(1λ)L]M*(s)(7)

where L is a lag operator. If one relies on this particular form of the adaptive expectations scheme, substitution yields the following price equation:

P*=a10[λβ10+λβ11M*k+λβ12M*jk+β13(YY¯)ik(1λ)β13(YY¯)ik1+β14(YY¯)(1λ)β14(YY¯)1]+(1λ)P*1+a10β16P*jk(1λ)a10β16P*jk1+a10β15MP*m+(1a10)MP*(1λ)a10β15MP*m1(1λ)(1a10)MP*1(13)

where MP* stands for the sum of foreign price changes and the exchange rate change, MP*=P*f+E*.

β10=(a11+a12b11)Q¯*a12b12Y¯*+a12b13c0<0β11=a12b12d10g10>0β12=a12b12(1d10)g10>0β13=a12b13c11>0β14=a130β15=a14>0β16=a12b12(1d10)<0

The equation states that the rate of inflation in the general price level is a function of the rates of change in the money stock, foreign prices, and the exchange rate, and a function of the output gap, and of its own lagged values, P*1 and P*jk.

Recourse to the linkage between the gap in output and its rate of change that is shown in equation (9) of the model makes it possible to derive a reduced form relationship that expresses the rate of change in prices in terms of corresponding changes in output, rather than the gap. Substitution from equation (9) in equation (13) yields:

P*=a10[λβ10+λβ11M*k+λβ12M*jk+β13(wY*)ik+β13wik(1λ)β13(wY*)ik1(1λ)β13wik1+β14(wY*)+β14w(1λ)β14(wY*)1(1λ)β14w1]+(1λ)P*1+a10β16P*jk(1λ)a10β16P*jk1+a10β15MP*m+(1a10)MP*(1λ)a10β15MP*m1(1λ)(1a10)MP*1(14)

Here the rate of inflation depends on the rate of change in money balances as before, on the rate of change in real output weighted by w, which is the lagged output gap, (Y/Ȳ)-1, relative to the ratio of current capacity to its lagged value, Ȳ/Ȳ-1, on w alone, and—also as before—on the rates of change in foreign prices and the exchange rate, and on its own lagged values, P*1 and P*jk.

In long-run equilibrium, actual and trend output are the same, Y = Ȳ, and a number of coefficients in the model are equal to unity, carrying a positive or negative sign, (λ,a10, a12, b11 and b12, d10 g10 are all equal to +1, and a11 equals –1) while others (a13, b13, and al4) are equal to zero. In these circumstances, the composite coefficients in equations (13) and (14) assume the values given in footnote 20.20 Both equations now read

P*=M*Y¯*(15)

This is what one would expect, and it may be observed that for a closed economy as well as for an open economy under either fixed or flexible exchange rates the expression in equation (15) reduces to the same quantity theoretic proposition, even though the reasons involved differ in the individual cases.21

II. Empirical Results

In estimating the model of price changes, the reduced form equations (13) and (14) provide the point of departure. Both equations, however, may be substantially simplified on the basis of a few assumptions. First, it is assumed that prices respond to changes in unit labor costs as and when these changes occur, which amounts to setting the lags k and equal to zero. Second, the response of wage inflation to demand pressure, (Y/Ȳ)-i, and the response of domestic price inflation to changes in the price of imported materials, MP*m, are assumed to involve the same geometric distributed lag pattern that was specified for expectations about short-run changes in the money stock in equation (7′). The beginnings of the lag distributions are given by the lag i, assumed to equal one, and the lag m, assumed to equal zero. Finally, the lag j on the deviation of inflation from its long-run expected value—which enters as one of the determinants of short-run inflationary expectations in equation (4)—is set equal to zero.22 Application of these assumptions to the reduced form equations (13) and (14) yields estimating equations of the following general form

P*=P*[constant,M*,YY¯,(YY¯)1,MP*,P*1](16)

and

P*=P*[constant,M*,wY*,(wY*)1,MP*,P*1](17)

The coefficients on all variables other than the current output gap, Y/Ȳ, or current output changes, wY*—which have an ambiguous effect on inflation, as argued earlier—are expected to be positive. As regards the coefficient on the lagged dependent variable in particular, its value will equal (1-λ). The size of this coefficient provides a measure of adjustment speed in the mechanics of the inflation process. A more rapid response of inflation to import price changes or to demand pressure, or a more rapid response of expectations about short-run money changes to actual money changes, all would tend to reduce the coefficient on the lagged dependent variable, while, at the same time, the coefficients on the lagged output gap and on changes in money and import prices would tend to rise.

Two questions come to mind that bear on the empirical aspects of the model. First, what is the appropriate method of estimation? Second, is it permissible to abstract from w where it enters equation (14) multiplicatively in the term wY*? It appears that straightforward application of ordinary least-squares (OLS) methods would yield inefficient and inconsistent parameter estimates, because the error terms are not serially independent. Instead, the model was estimated subject to a first-order autoregressive process.23

On the question of how to treat w—the lagged output gap relative to capacity growth—the answer may be determined on empirical grounds. To resolve the issue, two alternatives were considered in the estimation of the model: in one instance, output changes were weighted by the lagged gap and the resulting transformed variable was used in estimation, while in the other instance, w was ignored and unweighted output changes were used. A comparision of the results should indicate whether abstraction from w would appreciably alter results. In fact, the results were virtually identical, so that it was decided to retain only estimates involving unweighted output changes.

In the estimation, the rate of inflation, P*, is measured by the rate of change in consumer prices; output is industrial production in manufacturing; import prices are import unit values; and the money stock is expressed in terms of narrow money, M1.24 This applies to all countries in the sample except for Japan, where institutional characteristics make it preferable to define inflation in terms of wholesale prices and to define the money stock in terms of broad money, M2.25 Identically specified equations were estimated for all countries for the period 1958 through 1976. The percentage changes in variables are computed as overlapping quarterly changes between corresponding quarters of successive years. Quarter-on-quarter changes—which might have been considered instead—have “a bad signal-to-noise ratio because the quarterly changes are small in most of the period and rounding alone discards much of the information”26 it would also appear that the weight of measurement errors is relatively larger. At the same time, however, overlapping changes introduce a moving average process in the error term. It is assumed here that most of this process is taken into account through correction for first-order autocorrelation.

Two sets of results are reported in Table 2. One relies on the level of the output gap as a measure of activity. The other uses the percentage change in real output. Only the latter, however, involves both current and lagged values of the activity variable as indicated in the reduced form equations. Regarding the former set of results, the output gap enters the estimating equation in current form only. As the gap is measured as a four-quarter moving average, current and lagged values are very largely collinear, which may make it impossible to distinguish between their effects.

Table 2.

Seven Main Industrial Countries: Reduced Form Price Equations Showing Selected Regression Results, 1958-7611

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Symbols used: An asterisk over a variable refers to its percentage change between corresponding quarters of successive years; M stands for the money stock, Y for output, MP for import prices, and CP for consumer prices; ρ is the coefficient of autocorrelation, R¯2 and SEE are the coefficients of determination and the standard error of estimate, both adjusted for degrees of freedom; figures in parentheses are t-statistics. Significance at the 95 per cent confidence level is assured whenever t-ratios exceed 1.67.

M = M1

Y = industrial production in manufacturing

Ȳ = exponential growth trend in industrial production in manufacturing. The output gap Y/Ȳ is expressed as a four-quarter moving average. Equations using the potential output measure of Artus (1977) were also estimated, yielding results virtually identical to the ones reported here.

In all countries other than Japan, the dependent variable is the percentage change in consumer prices, and M refers to M1. By contrast, for Japan, the dependent variable is the percentage change in wholesale prices, and M refers to M2.

Taking the two sets of results together, the following observations may be made:

(i) Money changes appear to affect the rate of inflation in all countries except Italy, but even there results are plausible, if insignificant statistically.

(ii) The demand pressure effect on inflation as measured by the output gap is borne out for all countries other than France and Italy.

(iii) The demand pressure effect as measured by the lagged percentage change in output is borne out for Canada, the United Kingdom, and the United States. For Japan, this same effect appears to operate through the current rather than lagged output changes. For France, a similar tendency may be noted, but the effect is statistically not significant.

(iv) The deflationary productivity effect of current output changes is in evidence in the United Kingdom and the United States, and in Canada where this effect seems initially only to neutralize—rather than to dominate—any inflationary impact of output changes. It appears then that in these three countries the influence of an acceleration in the growth of real output is first deflationary, or nil, and then inflationary. For the Federal Republic of Germany, the evidence, although statistically insignificant, points in the same direction.27

(v) Import price changes are important determinants of consumer price changes in all countries except the Federal Republic of Germany, but more about this will be said later.

(vi) The speed of adjustment in the inflation process, as measured by the coefficient on the lagged dependent variable, seems generally low—Japan being the only exception. Whether or not this speed has gathered momentum in recent years remains to be seen at this stage.

The results from the price equations using the output gap as the activity variable may be used to derive the long-run effects of changes in money and import prices, and of the level of the output gap, on the rate of inflation in consumer prices. These effects are reported in Table 3 and are based on the results of equation (1) in Table 2.

A number of exogenous disturbances may have affected price developments at some points during the years under consideration. Incomes policies of one form or another, and strikes, count among such disturbances. As regards consumer price changes, one important type of disturbance would consist of exogenous changes in food prices emanating from the supply side. In fact, of the exogenous influences that were taken into account via the use of shift dummies—various episodes of incomes policy in the United Kingdom and the United States, inflationary consequences of control removal, the purported increase in the inflationary momentum in Italy following the “hot summer” of 1969, possible effects on inflation of the events in France in May 1968, and food price changes—only food price changes proved to have significantly affected developments in consumer prices.28

In taking the effect of exogenous food price changes into account, two shift dummy variables were constructed, allowing for instances when food prices rose abnormally rapidly relative to trend and for instances when they rose unusually slowly or fell. Equation estimates including these dummy variables are shown in Table 4. Japan is not included in the sample, since its rate of inflation is defined in terms of changes in wholesale prices.

Table 3.

Seven Main Industrial Countries: Long-Run Price Effects of Changes in Money and Import Prices and of the Level of the Output Gap1

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The effects shown in the first two columns represent long-run elasticities.

Generally, the coefficients on the exogenous changes in food prices are statistically significant. However, their inclusion in the model tends to reduce the statistical significance of the coefficients on the other explanatory variables for reasons that are not immediately apparent.

Two issues remain to be discussed: (i) the puzzling result that import price changes appear to have no effects on price changes in the Federal Republic of Germany—at least judging from the results in Table 2—although they affect price changes everywhere else; (ii) whether or not the speed of adjustment has risen in recent years. The apparent insen-sitivity of prices in the Federal Republic of Germany to import price changes has been noted by several authors.29 However, the evidence in Table 4 suggests that for the period 1958-76 as a whole, import price changes have a small but statistically significant effect on prices in that country, once the shift dummies representing exogenous food price changes are taken into account. In addition, judging from the estimate shown for the period 1958-69, import price changes were more important in those years than they have been more recently.

Two experiments were conducted to test for possible changes in the speed of adjustment in the inflation process. First, slope dummy variables were used to allow for a purported decline in the coefficient on the lagged dependent variable after 1970, and for a corresponding rise in the coefficients on the remaining variables capturing systematic influences. Second, the model of equation (2) in Table 2.was estimated for the subperiods 1958-69, 1970-76, and 1973-76. Results from the first experiment did not indicate that, at least tested in this manner, the assumption of a changed adjustment speed was warranted. However, the second experiment did suggest that the adjustment speed has risen since 1970, and again since 1973, even if this did not seem to be true for all countries in the sample. For example, the coefficient on the lagged dependent variable in estimates for Canada fell from 0.98 (1958—69) to 0.80 (1970-76) and again to 0.68 (1973-76); for the United States from 0.93 (1958-69) to 0.78 (1970-76) and then to 0.66 (1973-76); for the United Kingdom from 0.76 (1958-69) to 0.45 (1970-76); for Italy from 0.72 (1958-69) to 0.64 for 1973-76. No reliable estimates were obtained for France or the Federal Republic of Germany. Admittedly, the evidence is not compelling throughout, especially when one notes the general parameter instability in estimates over different periods, but it generally indicates that the inflationary mechanism has gathered momentum.30

Table 4.

Seven Main Industrial Countries: Reduced Form Price Equations and the Effects of Exogenous Changes in Food Prices1

article image

All symbols except F1 and F2 are the same as those in Table 2. F1 and F2 are shift dummies, representing exogenous changes in food prices. F1 equals unity whenever food prices rose abnormally rapidly, and zero elsewhere. F2 equals –1 whenever food prices rose unusually slowly or declined, and zero elsewhere.

III. Conclusion

On a theoretical level, the model developed in this study differs from other contributions in the literature in a number of respects, especially (i) in the way in which inflationary expectations are formulated, (ii) in allowing for the possibility of a “first negative, then positive” relationship between changes in prices and changes in output, (iii) in the way in which the level of imbalances in the goods market is related to the percentage change in output, and, perhaps also, (iv) in the way in which foreign price and exchange rate changes affect inflation. In the first instance, this means that any effect of changes in money on inflationary expectations, and thereby on inflation, is taken into account. In the second instance, the model accommodates a situation where the productivity effect of output changes on inflation is initially stronger than the demand pressure effect of these changes. The model is therefore consistent with stagflation or the coexistence of rising output and falling inflation, at least for some time. The output gap, the measure of imbalance in goods markets, and the rate of change in output are linked through an identity relationship. This contrasts with the more conventional way of introducing changes in output via a link with the level of unemployment. This level is related here to the level of the output gap. Foreign price and exchange rate changes are represented together by import price changes, and enter the model as components of the rate of change in the general price level and as competitive influences on domestic price changes, rather than in any other way.

The empirical results for the period from 1958 to 1976 as a whole are most satisfactory for Canada, the United Kingdom, and the United States. Results for France, Italy, the Federal Republic of Germany, and Japan are plausible in most respects, although the evidence is not as clear cut, and some issues remain unresolved. In addition, exogenous changes in food prices appear to have affected changes in consumer prices, although other exogenous disturbances were apparently not significant. Finally, results from estimation of the model over different periods tend to support the view that the speed of the inflation process has increased in recent years.

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*

Mr. Spitäller, economist in the External Adjustments 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. He was formerly on the staff of the Organization for Economic Cooperation and Development.

1

In view of the definition of the output gap as Y/Ȳ, references to an increase, or a fall, in the gap are to be understood throughout this paper as an increase or a fall in the ratio of actual output to capacity output.

2

Experiments were made using a slope dummy on the output gap. This dummy would carry the value of +1 or -1, depending on whether the value of the output gap exceeded or fell short of unity. No results consistent with these particular assumptions were obtained.

4

Together, equations (4) and (5) imply that expectations are formed “semirationally.” In the long run, expectations conform to price changes in long-run equilibrium. In the short run, expectations gradually adjust toward their long-run value. See, for example, Knight (1976), pp. 8-9, and Mathieson (1977), pp. 15ff.

5

This may be seen rewriting the right-hand side of equation (9) as (YY11+1)(Y1Y¯1)(Y¯1Y¯), which reduces to YY¯.

6

Equation (10) is one formulation of Okun’s Law used in his 1962 study; see Okun (1962). It embodies the restrictive assumption that all changes in the output gap necessarily involve changes in unemployment in the opposite direction.

7

For a discussion of the influence of import price changes in the inflation process relative to the import content of total demand, see Goldstein and Officer (1977).

8

For empirical support of this assumption, see Artus (1976) and Knight (1976); additional references may be found in Schadler (1977).

9

See the recent review by Gordon (1977 a). For a critique of empirical tests of the aggregate supply theory, see Arak (1977) for her comments on the work of Lucas (1973). She also obtains results that are inconsistent with the theory: in the United States, errors in price expectations do not bear a significant relationship to variations in output. For a reply to Arak’s criticism, see Lucas (1977).

11

Modigliani illustrates this difference in terms of the explanation that demand pressure (excess employment) causes inflation and the contrasting view that the unexpected component of inflation causes excess employment. See Modigliani (1977).

12

For a most comprehensive and penetrating assessment of the role of rational expectations in economic models, see Poole (1976).

13

See Poole’s comments on Lucas, in Poole (1976), p. 465; see also Argy (1977 c).

14

On both of these points, see Argy (1977 c); on the latter point, see also Barro (1977).

15

See, for example, Modigliani (1977) on this point.

16

The superiority of the rational expectations scheme is argued in Hamburger and Reisch (1976); for a critique, see Poole (1976). The empirical tests of this scheme by Fratianni (1977) and Korteweg (1977) are criticized by Argy (1977 a).

17

For the argument that import price changes affect inflationary expectations, see Laidler (1976 a; 1976 b). However, he finds that world price changes perform even better in this connection than do import price changes. On the role of world price changes, see also Genberg (1976).

18

Recent references to the effects of foreign price and exchange rate changes on inflation in general include Kwack (1974), Crockett and Goldstein (1976), Sweeney and Willett (1974; 1976), Dornbusch (1976), and Dornbusch and Krugman (1976).

19

The significance of monetary changes in the context of inflationary expectations is also pointed out in Towards Full Employment and Price Stability: A Report to the OECD by a Group of Independent Experts (1977), Ch. 2, pp. 108-10. See also Artus and Crockett (1977), Bilson (1978 a; 1978 b), Dornbusch (1976), and Dornbusch and Krugman (1976). These studies analyze the more indirect link of monetary changes and inflation. Monetary expansion would—through its effect on interest rates—bring down the exchange rate. As a result, inflationary expectations would rise and inflation would accelerate.

20

β10=Y¯*,β11=1,β12toβ16=0. In addition, since Y/Ȳ both current and lagged values of the output gap equal unity. As a result, w(Y*+1)=1 in equation (13), since

w(Y*+1)=(Y1Y¯1)(Y¯1Y¯)[YY11+1]=1,forYY¯
21

The proposition applies to a closed economy because domestic and general price levels are the same, and a10 therefore equals unity. It applies to an open economy under either fixed or flexible rates on account of purchasing power parity in equilibrium; under a fixed rate, inflation at home adjusts to inflation abroad, while under a flexible rate it is the exchange rate that adjusts. All the same, however, the long-run policy implications of equation (15) differ in individual cases. In a closed economy and in an open economy under a flexible rate, changes in money are exogenous, and the country can have the inflation that it wants. Under a fixed rate, inflation cannot be controlled by the domestic authorities because they can affect only the domestic component of base money, not its reserve component. None of this is new, and it is mentioned only to show that the reduced form equations derived in this paper are consistent in long-run equilibrium with the fundamental quantity theory.

22

The last term (1λ)(1a10)MP*1, which is identical in both equations (13) and (14), is suppressed.

23

The rationale for this may be briefly set out with reference to the adaptive process that expectations about changes in the money stock were assumed to follow. Recalling its lag operator form as given in equation (7″) but including this time an error term, that process reads

Me*=λ1[(1λ)L]M*+uuN(0,σ2)(18)

where the error term, u, is normally and independently distributed with zero mean and constant variance. Equation (18) can be written as

Me*=λ[1+(1λ)L+(1λ)2L2+(1λ)3L3+]M*+u(19)

which is

Me*=λM*+λ(1λ)M*1+λ(1λ)2M*2++u(19)

An equation the right-hand side of which is expressed as in (19′) may be estimated—after truncation—nonlinearly, subject to certain restrictions.

Equation (18) may be rewritten with linear parameters as

Me*=(1λ)M1e*+λM*+ν(20)

where ν = u–(l–λ)u-1

This new error term, ν, is serially correlated because it is subject to a first-order moving average process. The same is true of the error terms in the reduced forms of the model, since their derivation involves relations (18) and (20). Serial correlation in the error term poses a particular problem in a model that contains the lagged dependent variable among its arguments, like the reduced form equations considered here. The reason is that in the circumstances the standard assumption of independence of the error term is no longer warranted. This is demonstrated in equation (20) where both M1e* and ν are functions of u-1 and are therefore correlated. As a result, OLS methods would yield inconsistent estimators. Dhrymes suggests maximum likelihood methods conditional on those values of ρ and λ that minimize the standard error of the regression. See Dhrymes (1971) and also Johnston (1972). In this context, Rasche (1976) criticizes Laidler (1976 a) for using OLS methods without adjustment for serial correlation.

The moving average process ν = u–(1–λ)u-1 may be transformed into an autoregressive process, which may be written in the form of

v=u(1λ)v1(1λ)2v2(1λ)3v3(21)

Truncating after the first term, equation (21) may be written as

v=ρv1+ε(22)

where ρ is the coefficient of autocorrelation and ∊ is assumed to be an error term with zero mean and constant variance.

Hence, the reduced form equations of this paper are estimated subject to a first-order autoregressive process.

24

Inflation was measured in terms of consumer prices and output in terms of industrial production in manufacturing on grounds of the availability of data. Sufficiently long series on quarterly data of real gross domestic product—which might be considered a better measure of output in this context—are not available for all countries.

25

In Japan, the consumer price index reflects conditions in the traditional economy and does not move in line with economic activity in general. By contrast, wholesale prices are cyclically sensitive; authorities react to inflation as measured by the wholesale price index and not the consumer price index. Authorities can exert tight control over commerical bank lending, and changes in Ml have been an even better empirical indicator of money conditions than changes in M1. See Komiya and Suzuki (1977) and the comments by Krause (1977 b).

27

This is an impression that is supported to some extent by results from estimates that were obtained for different subperiods but that are not reported here in detail. For example, an estimate of the price change equation for the Federal Republic of Germany over the period 1958-69 reads:

CP*=0.98(2.13)+0.03M*(0.83)0.08Y*(1.82)+0.02Y*1(1.40)+0.11MP*(2.67)+0.53CP*1(4.38)

A similar pattern applies to Italy, but only in estimates using annual observations. An annual price equation for the years 1959-76 reads:

CP*=4.35(1.87)+0.23M*(2.89)0.04Y*(0.65)+0.15Y*1(1.97)+0.13MP*(5.47)+0.88CP*1(7.56)
28

No pretense is made of an in-depth analysis of these various disturbances. Their apparent insignificance in the present model cannot be considered definitive. Contrasting results may, for example, be found in the studies of wage movements in Modigliani and Tarantelli (1977) for Italy and in Spitäller (1976) for the other countries.

29

See Gatz (1963), Dornbusch and Krugman (1976), Emminger (1977), and Goldstein (1977). Dornbusch and Krugman suggest that the insignificance of import price changes may be attributable to arrangements in the European Economic Community, which tend to offset effects of exchange rate changes on the prices of agricultural imports. Gatz claims that—referring to the 1961 revaluations—reductions in the deutsche mark price are not passed on. In this vein, Goldstein finds some evidence of a ratchet effect—a proportionately larger effect of devaluations on inflation than of revaluations. Emminger points out that the experience in this connection has not been consistent with respect to different revaluation episodes.

30

The reasons for such a change in adjustment speed are not explored here. But this change has coincided with an acceleration of inflation in most countries. Khan (1977 a; 1977 b) found that—at least in situations of hyperinflation—the speed of adjustment varied in direct proportion to the rate of inflation. The desire for protection from the losses caused by progressive monetary erosion is offered as an explanation.