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, $\stackrel{*}{P}$—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, $\stackrel{*}{P_d}$ and in foreign prices and the exchange rate, $\stackrel{*}{P_f}$ and $\stackrel{*}{E}$:

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 $\stackrel{*}{P_f}+\stackrel{*}{E}$ serves as proxy for the percentage change in $(P_f\cdot E)$.

The rate of change in the domestic price level depends on the trend growth in productivity, $\stackrel{*}{\overline{Q}}$ the rate of change in the wage rate, $\stackrel{*}{W}$ 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, $[\stackrel{*}{P_f}+\stackrel{*}{E}]$. For simplicity, the value of foreign prices is assumed to be the same as in equation (1)

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

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, $\stackrel{*}{P^e}\left(s\right)$, and the lagged unemployment rate, U_–i

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

where $\stackrel{*}{P^e}\left(\ell \right)$ and $\stackrel{*}{M^e}\left(\ell \right)$ are the expected long-run rates of change in the general price level and in the money stock, and where $\stackrel{*}{\overline{Y}}$ is the long-run trend growth in real output. Over the short run, inflationary expectations are approximated by

0 < d₁₀ < 1

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

Short-run expectations are generated by an adaptive process

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, $\stackrel{*}{Y}$, and (iii) a relationship between the output gap and unemployment. Capacity output is defined as

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

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 e^b, which equals (Ȳ/Ȳ_-1)—and the higher is the percentage of growth in actual output, $\stackrel{*}{Y}$. The link between levels of demand pressure in goods and labor markets is represented by a linear approximation

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

¹The ten endogenous variables are $\stackrel{*}{P},{\stackrel{*}{P}}_d,\stackrel{*}{W},\frac{Y}{\overline{Y}},\overline{Y},U,\stackrel{*}{P^e}\left(\ell \right),\stackrel{*}{P^e}\left(s\right),\stackrel{*}{M^e}\left(\ell \right),$ and $\stackrel{*}{M^e}\left(s\right)$. The exogenous variables are ${\stackrel{*}{P}}_f,\stackrel{*}{E},$, and $\stackrel{*}{Y}$. 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; P_d = domestic price level, that is, deflator of demand for domestic goods; P_f = 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.

Table 1.

Summary of the Model of Price Changes¹

$\begin{array}{ccc}\stackrel{*}{P}=a_{10}{\stackrel{*}{P}}_d+(1-a_{10})[{\stackrel{*}{P}}_1+\stackrel{*}{E}]& 0<a_{10}<1& \left(1\right)\end{array}$

$\begin{array}{ccc}{\stackrel{*}{P}}_d=a_{11}\stackrel{*}{\overline{Q}}+a_{12}{\stackrel{*}{W}}_{-k}+a_{12}(\frac{Y}{\overline{Y}}{)}_{-\ell }+a_{14}[{\stackrel{*}{P}}_f+\stackrel{*}{E}{]}_{-m}& a_{12},a_{14}>0a_{11}<0,a_{13}\gtrless 0& \left(2\right)\end{array}$

$\begin{array}{ccc}\stackrel{*}{W}=b_{11}\stackrel{*}{\overline{Q}}+b_{12}\stackrel{*}{P^e}\left(s\right)+b_{13}{U}_{-i}& b_{11},b_{12}>0b_{13}<0& \left(3\right)\end{array}$

$\begin{array}{ccc}\stackrel{*}{P^e}\left(\ell \right)=\stackrel{*}{M^e}\left(\ell \right)-\stackrel{*}{\overline{Y}}& & \left(4\right)\end{array}$

$\begin{array}{ccc}\stackrel{*}{P^e}\left(s\right)=d_{10}\stackrel{*}{P^e}\left(\ell \right)+(1-d_{10})[\stackrel{*}{P^e}\left(\ell \right)-\stackrel{*}{P}{]}_{-j}& 0<d_{10}<1& \left(5\right)\end{array}$

$\begin{array}{ccc}\stackrel{*}{M^e}\left(\ell \right)=g_{10}\stackrel{*}{M^e}\left(s\right)& 0<g_{10}<1& \left(6\right)\end{array}$

$\begin{array}{ccc}\stackrel{*}{M^e}\left(s\right)-\stackrel{*}{M^e}(s{)}_{-1}=\lambda [\stackrel{*}{M}\left(s\right)-\stackrel{*}{M^e}(s{)}_{-1}]& 0<\lambda <1& \left(7\right)\end{array}$

$\begin{array}{ccc}\overline{Y}={ae}^{bt}& b>0& \left(8\right)\end{array}$

$\begin{array}{ccc}\frac{Y}{\overline{Y}}=(\stackrel{*}{Y}+1)(\frac{Y}{\overline{Y}}{)}_{-1}{e}^{-b}& & \left(9\right)\end{array}$

$\begin{array}{ccc}U=c_0+c_{11}\left(\frac{Y}{\overline{Y}}\right)& c_0>0,c_{11}<0& \left(10\right)\end{array}$

¹The ten endogenous variables are $\stackrel{*}{P},{\stackrel{*}{P}}_d,\stackrel{*}{W},\frac{Y}{\overline{Y}},\overline{Y},U,\stackrel{*}{P^e}\left(\ell \right),\stackrel{*}{P^e}\left(s\right),\stackrel{*}{M^e}\left(\ell \right),$ and $\stackrel{*}{M^e}\left(s\right)$. The exogenous variables are ${\stackrel{*}{P}}_f,\stackrel{*}{E},$, and $\stackrel{*}{Y}$. 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; P_d = domestic price level, that is, deflator of demand for domestic goods; P_f = 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.

View Table

Table 1.

Summary of the Model of Price Changes¹

$\begin{array}{ccc}\stackrel{*}{P}=a_{10}{\stackrel{*}{P}}_d+(1-a_{10})[{\stackrel{*}{P}}_1+\stackrel{*}{E}]& 0<a_{10}<1& \left(1\right)\end{array}$

$\begin{array}{ccc}{\stackrel{*}{P}}_d=a_{11}\stackrel{*}{\overline{Q}}+a_{12}{\stackrel{*}{W}}_{-k}+a_{12}(\frac{Y}{\overline{Y}}{)}_{-\ell }+a_{14}[{\stackrel{*}{P}}_f+\stackrel{*}{E}{]}_{-m}& a_{12},a_{14}>0a_{11}<0,a_{13}\gtrless 0& \left(2\right)\end{array}$

$\begin{array}{ccc}\stackrel{*}{W}=b_{11}\stackrel{*}{\overline{Q}}+b_{12}\stackrel{*}{P^e}\left(s\right)+b_{13}{U}_{-i}& b_{11},b_{12}>0b_{13}<0& \left(3\right)\end{array}$

$\begin{array}{ccc}\stackrel{*}{P^e}\left(\ell \right)=\stackrel{*}{M^e}\left(\ell \right)-\stackrel{*}{\overline{Y}}& & \left(4\right)\end{array}$

$\begin{array}{ccc}\stackrel{*}{P^e}\left(s\right)=d_{10}\stackrel{*}{P^e}\left(\ell \right)+(1-d_{10})[\stackrel{*}{P^e}\left(\ell \right)-\stackrel{*}{P}{]}_{-j}& 0<d_{10}<1& \left(5\right)\end{array}$

$\begin{array}{ccc}\stackrel{*}{M^e}\left(\ell \right)=g_{10}\stackrel{*}{M^e}\left(s\right)& 0<g_{10}<1& \left(6\right)\end{array}$

$\begin{array}{ccc}\stackrel{*}{M^e}\left(s\right)-\stackrel{*}{M^e}(s{)}_{-1}=\lambda [\stackrel{*}{M}\left(s\right)-\stackrel{*}{M^e}(s{)}_{-1}]& 0<\lambda <1& \left(7\right)\end{array}$

$\begin{array}{ccc}\overline{Y}={ae}^{bt}& b>0& \left(8\right)\end{array}$

$\begin{array}{ccc}\frac{Y}{\overline{Y}}=(\stackrel{*}{Y}+1)(\frac{Y}{\overline{Y}}{)}_{-1}{e}^{-b}& & \left(9\right)\end{array}$

$\begin{array}{ccc}U=c_0+c_{11}\left(\frac{Y}{\overline{Y}}\right)& c_0>0,c_{11}<0& \left(10\right)\end{array}$

¹The ten endogenous variables are $\stackrel{*}{P},{\stackrel{*}{P}}_d,\stackrel{*}{W},\frac{Y}{\overline{Y}},\overline{Y},U,\stackrel{*}{P^e}\left(\ell \right),\stackrel{*}{P^e}\left(s\right),\stackrel{*}{M^e}\left(\ell \right),$ and $\stackrel{*}{M^e}\left(s\right)$. The exogenous variables are ${\stackrel{*}{P}}_f,\stackrel{*}{E},$, and $\stackrel{*}{Y}$. 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; P_d = domestic price level, that is, deflator of demand for domestic goods; P_f = 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, P_d, 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 P_d 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, $\stackrel{*}{E}={\stackrel{*}{P}}_d-{\stackrel{*}{P}}_f$. Substituting this expression in equation (1) yields the equality $\stackrel{*}{P}={\stackrel{*}{P}}_d$. 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

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

which is also

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, ${\stackrel{*}{P}}_d$, to result in

or,

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)

involves a geometric distributed lag model of the general form

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

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

where $M\stackrel{*}{P}$ stands for the sum of foreign price changes and the exchange rate change, $M\stackrel{*}{P}={\stackrel{*}{P}}_f+\stackrel{*}{E}$.

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, ${\stackrel{*}{P}}_{-1}$ and ${\stackrel{*}{P}}_{-j-k}$.

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: