## Abstract

The empirical analysis in this paper of the factors underlying the recent acceleration of price inflation in Germany was made in order to see whether price expectations give a satisfactory explanation of recent price behavior in Germany. Specifically, the hypothesis is tested that price expectations exercise at least a partially independent influence on actual price behavior. The paper differs from earlier analyses in that it uses a method for quantifying price survey results to derive an explicit time series of price expectations. Section I describes the method used and shows the derived series of expected price increases. Section II tests several expectations hypotheses, and Section III presents an assessment of the influence of price expectations on actual price behavior in the recent past. Some conclusions are set out in Section IV.

The empirical analysis in this paper of the factors underlying the recent acceleration of price inflation in Germany was made in order to see whether price expectations give a satisfactory explanation of recent price behavior in Germany. Specifically, the hypothesis is tested that price expectations exercise at least a partially independent influence on actual price behavior. The paper differs from earlier analyses in that it uses a method for quantifying price survey results to derive an explicit time series of price expectations. Section I describes the method used and shows the derived series of expected price increases. Section II tests several expectations hypotheses, and Section III presents an assessment of the influence of price expectations on actual price behavior in the recent past. Some conclusions are set out in Section IV.

The pace of price inflation in Germany has recently accelerated strongly. In the case of industrial producer prices, the acceleration began with the first signs of a new upswing in the beginning of 1972. In earlier business cycles industrial producer prices showed a distinct pattern of at least slow rises, if not declines, during the downswing and even after the lowest point of the cycle was reached. Chart 1 shows the development of industrial producer prices during the cyclical downswings and at the beginning of upswings for the past three cycles. While the increase of the index of industrial producer prices during the downswing of the earlier two cycles, which lasted for over two years, amounted to about 2 percent, the increase in the last cycle, which was of a similar length, was of the magnitude of 8 per cent. Consumer prices rose at an annual rate of about 5 per cent in the first half of 1972 and then accelerated in the second half to an annual increase of about 8 per cent. Since the cost of living index plays a great role in public opinion and in the price expectations of the public, price development became a major concern for economic policy.

Analysis of price inflation has recently focused increasingly on the role of price expectations in influencing the rate of inflation. A general view has emerged that when the rate of expected price increases is high the implementation of effective stabilization policies becomes much more difficult.^{1} Accelerating price expectations could lead to higher wage demands to compensate for the anticipated price increases; and also in such a situation, it is much easier for enterprises to raise prices (even in the absence of excessive demand pressures). By the operation of such a mechanism, price expectations might have an impact on actual price behavior.

## I. Quantification of Price Expectations

Price expectations are not directly observable, but a great deal of qualitative information is available.^{2} German businessmen in industry ^{3} (in common with their counterparts in other countries of the European Economic Community) are asked on a regular basis whether they expect that their selling price will rise, stay about the same, or fall during the next three to four months.^{4} The results of such surveys are recorded as:

*a*= the per cent of responses indicating that prices are expected to rise (price increases)*b*= the per cent of responses indicating that prices are expected to stay about the same (stable prices)*c*= the per cent of responses indicating that prices are expected to fall (declining prices)

In order to make these results useful for obtaining a time series of expected prices, a method of quantifying these qualitative data has been developed.^{5}

### assumptions

(1) Each individual asked in the survey has a subjective probability function over the expected price change. It may vary across individuals and over time.

(2) If the expected price change is within a certain interval (—s, *+s)*, the individuals will answer that they expect prices will stay about the same.

(3) Since the number of individuals asked is large, the expected rate of price change over all individuals can be assumed as normally distributed (Chart 2).

**Germany: Density Function of Expected Rate of Price Changes Over All Individuals Asked**

Citation: IMF Staff Papers 1974, 001; 10.5089/9781451956375.024.A004

Key:*X =*random variable of expected rate of price change over all individuals

*X ~ N*(

*p*, σ

_{e}^{2}

*)*

*f(x)*= density function of the random variable

*X*

*p*

^{e}

*, σ*

^{2}

*=*mean and variance of the normal distributed random variable X

*a*= relative frequency of the expectation of price increases

*b*= relative frequency of the expectation of about stable prices

*c*= relative frequency of the expectation of declining prices

*a, b*, and

*c =*the results of the survey.

**Germany: Density Function of Expected Rate of Price Changes Over All Individuals Asked**

Citation: IMF Staff Papers 1974, 001; 10.5089/9781451956375.024.A004

Key:*X =*random variable of expected rate of price change over all individuals

*X ~ N*(

*p*, σ

_{e}^{2}

*)*

*f(x)*= density function of the random variable

*X*

*p*

^{e}

*, σ*

^{2}

*=*mean and variance of the normal distributed random variable X

*a*= relative frequency of the expectation of price increases

*b*= relative frequency of the expectation of about stable prices

*c*= relative frequency of the expectation of declining prices

*a, b*, and

*c =*the results of the survey.

**Germany: Density Function of Expected Rate of Price Changes Over All Individuals Asked**

Citation: IMF Staff Papers 1974, 001; 10.5089/9781451956375.024.A004

Key:*X =*random variable of expected rate of price change over all individuals

*X ~ N*(

*p*, σ

_{e}^{2}

*)*

*f(x)*= density function of the random variable

*X*

*p*

^{e}

*, σ*

^{2}

*=*mean and variance of the normal distributed random variable X

*a*= relative frequency of the expectation of price increases

*b*= relative frequency of the expectation of about stable prices

*c*= relative frequency of the expectation of declining prices

*a, b*, and

*c =*the results of the survey.

Under above assumptions, *a* (the per cent of people answering that they expect prices will rise) is equal to the probability that the random variable “expected rate of price change” (*X*) takes a value greater than *s*:

P(X > s)=a = 1 – F_{x}(s)

where *F*_{x}*(s*) is the value of the distribution function of the random variable (*X*) for the argument(*s*).

Similarly

b = P(–s < X < s)and

c=P(X < –s).

If these equations are solved, the result is an estimate for *p*^{e} and σ^{2}. Therefore, with this method a series can be derived for the mean of the expected rate of inflation *(p ^{e})*. This expected rate of inflation is solely derived out of qualitative data obtained from surveys conducted on a regular basis. Details of the derivation of the expected rate of inflation are shown in the Appendix.

Chart 3 shows the results of the quantification of the qualitative data as given in *Results of the Business Survey Carried Out Among Heads of Enterprises in the Community* (s is assumed to equal 2). The expected rate of price change of industrial producer prices is an annual rate of change, comparing quarters with the same quarters in the preceding year. In short, price expectations are shown to have a clear cyclical pattern and recently started to accelerate.

**Germany: Expected Rate ofChange of Industrial Producer Prices**

Citation: IMF Staff Papers 1974, 001; 10.5089/9781451956375.024.A004

**Germany: Expected Rate ofChange of Industrial Producer Prices**

Citation: IMF Staff Papers 1974, 001; 10.5089/9781451956375.024.A004

**Germany: Expected Rate ofChange of Industrial Producer Prices**

Citation: IMF Staff Papers 1974, 001; 10.5089/9781451956375.024.A004

## II. Formation of Price Expectations

Several hypotheses for expectations were tested. In general, it was assumed that expectations for the future depend on past experience.

### extrapolative expectations hypotheses

where

*t*+l), expressed at period *t*.

P_{t−i} is the actual rate of price increase in period (*t−i*)

This hypothesis assumes that the price expectations depend on the actual rate of inflation in the past.

A modification of the hypothesis in equation (1) would be:

where *b _{1}* reflects the expectations about the trend. If

*b*> 0, it is expected that the trend of the actual rate of inflation continues. The trend is extrapolated. If b

_{1}_{1}< 0, a change in the trend is expected.

### adaptive expectations hypotheses

The hypothesis in equation (3) makes an adjustment for some form of learning process. If the expected and the actual rate of inflation were equal in the preceding period, it is assumed that no adjustment of price expectations is made. If the expected rate of inflation differed from the actual rate, then price expectations for the next period are corrected accordingly.

A modification of equation (3) is:

For *b _{1} + b_{2}* = 1, this hypothesis is equal to equation (3)

^{6}

For *b*_{1} + *b*_{2}>1, even if the actual rate of inflation is equal to the expected rate in the preceding period, a rise of the rate of inflation is expected—that is, a trend taken into account.

Besides the assumption that the expected rate of inflation depends on past actual rates, it seems plausible that the individuals also would take into account past and expected cost increases, as well as past and expected demand pressure, in the formation of their price expectations. Therefore, such variables were also included in the tests of the formation of price expectations.

### results

In order to eliminate the substantial amount of “noise” in quarter to quarter rates of change of the variables, all rates of change were transformed into annual rates of change, comparing quarters with the same quarters of the preceding year. This, of course, has the disadvantage of overlapping successive rates of change.

The adaptive expectations hypotheses did not give satisfactory results. When past actual rates of inflation were used as the only explanatory variables, the hypothesis in equation (2) gave the best results:

^{7}

or

When, in addition to past actual rates of inflation, cost and demand pressure variables were used as explanatory variables, the best results were given by equation (6):

where *dp*_{t−1} is the value of the demand pressure variable at period *(t−* 1). As a proxy for the demand pressure variable *(dp)*, the deviation of capacity utilization from its medium-term average was used:

dp_{t}= (cu_{t}– mcu)

where *cu*_{t} represents capacity utilization in manufacturing, in period *t*:

The Durbin-Watson statistics in equations (5a), (5b), and (6) are not satisfactory. This is probably partly due to the use of overlapping rates of change and to the operation of other factors that are difficult to quantify, that cannot be explained sufficiently by demand pressure and most recent price developments, and that influence price expectations. Chart 4 shows the results of equation (6) in graphic form. As can be seen, the equation overestimates price expectations considerably in 1966, when the beginning of a sharp economic downswing occurred, and underestimates price expectations systematically at the end of 1971 and 1972, when a mild downswing and the beginning of an economic upswing occurred.

**Germany: Actual and Computed Expected Rates of Change of Industrial Producer Prices**

Citation: IMF Staff Papers 1974, 001; 10.5089/9781451956375.024.A004

**Germany: Actual and Computed Expected Rates of Change of Industrial Producer Prices**

Citation: IMF Staff Papers 1974, 001; 10.5089/9781451956375.024.A004

**Germany: Actual and Computed Expected Rates of Change of Industrial Producer Prices**

Citation: IMF Staff Papers 1974, 001; 10.5089/9781451956375.024.A004

In summary, it is evident that price expectations depend to a large degree on past experience, in particular on past rates of inflation and demand pressure (see equation (6)),

or

or more generally

## III. Price Expectations and Actual Price Behavior

The next step in the analysis was to assess the impact of price expectations on actual price behavior. For this purpose, a price equation ^{8} for industrial producer prices was estimated:

where

*p*= actual rate of price increase*c*= rate of cost increases*dp*= level of demand pressure*p*= rate of expected price increase^{e}

The basic hypothesis on the price mechanism, as shown in equation (8), relates the rate of price increase to cost increases, demand pressure, and price expectations. It should be noted that the explanatory variables are probably not independent of each other; in particular, it is plain that cost increases are not independent of demand pressure. But experience shows that there is a lag between those variables and that the relationship is not constant. On the other hand, it has already been shown (see equation (6)) that price expectations depend on past demand pressures. The purpose of the estimation process is to show which of the variables best explain the actual price development.

The price equation was estimated with the stepwise regression program of the Fund’s data processing division. Several cost and demand pressure variables—lagged and current—and involving linear and nonlinear transformations were used in the estimation process.^{9}

where

*p =*rate of change of industrial producer prices*wh*= rate of change of earnings per man-hour (industry)*p*_{fr}*=*rate of change of foreign raw material prices*p*= rate of change of price expectations^{e}*D*= dummy variable

The price index for industrial producer prices, as published in German sources, includes the turnover tax up to 1968. From 1968 on, after the introduction of the value-added tax (VAT), the price index excludes VAT. Therefore, in order to take account of the break in the series, a dummy variable (D) was introduced. It has the value of one for each of the four quarters of 1968 and zero otherwise. The estimation period is from the first quarter of 1965 to the third quarter of 1972.

equation (9) and Chart 5 show the result of the analysis. It is clear that price expectations have influenced actual price developments and that price expectations give a better explanation of price behavior in the period 1965–72 than any of the demand pressure variables that have been tested. Chart 6 suggests two reasons for this result. First, the lag between demand pressure and price expectations is not constant. While the time lag between *p*^{e} and *dp* was approximately one to two quarters throughout most of the observation period, it seems that price expectations have led demand pressure in the recent past. Second, the functional relationship between *dp* and *p*^{e} seems to be unstable. While the medium-term average of capacity utilization was consistent with a rate of growth of price expectations of about 1 per cent in 1966, this trade-off worsened by 1972 to more than 2.5 per cent. Taking this into consideration, it was not surprising to find that the price expectations variable explained most of the actual price movement.

**Germany: Actual and Computed Rates of Change of Industrial Producer Prices**

Citation: IMF Staff Papers 1974, 001; 10.5089/9781451956375.024.A004

Source: Estimates by Fund staff members.**Germany: Actual and Computed Rates of Change of Industrial Producer Prices**

Citation: IMF Staff Papers 1974, 001; 10.5089/9781451956375.024.A004

Source: Estimates by Fund staff members.**Germany: Actual and Computed Rates of Change of Industrial Producer Prices**

Citation: IMF Staff Papers 1974, 001; 10.5089/9781451956375.024.A004

Source: Estimates by Fund staff members.**Germany: Price Expectations and Capacity Utilization**

Citation: IMF Staff Papers 1974, 001; 10.5089/9781451956375.024.A004

Source: IFO-Institut für Wirtschaftsforschung,*IFO-Schnelldienst*, various issues, and calculations by Fund staff.

**Germany: Price Expectations and Capacity Utilization**

Citation: IMF Staff Papers 1974, 001; 10.5089/9781451956375.024.A004

Source: IFO-Institut für Wirtschaftsforschung,*IFO-Schnelldienst*, various issues, and calculations by Fund staff.

**Germany: Price Expectations and Capacity Utilization**

Citation: IMF Staff Papers 1974, 001; 10.5089/9781451956375.024.A004

Source: IFO-Institut für Wirtschaftsforschung,*IFO-Schnelldienst*, various issues, and calculations by Fund staff.

The results of the analysis can be summarized in two statements:

(1) There is empirical evidence that price expectations influence the actual rate of inflation (see equation (9));

or

(2) Price expectations depend to a large degree on past experience, on past rates of inflation, and demand pressures (see equation (6)),

or

Equations (10a) and (10b) combined give:

or more generally

## IV. Conclusions

This analysis suggests that the actual rate of inflation at any point in time depends directly on three principal and separable factors: (1) cost pressures, (2) the degree of capacity utilization, and (3) the rate of inflation experienced in the recent past through its effect on the formation of current price expectations. These conclusions, if valid, have important policy implications.

In a situation of accelerating inflation (the current situation in Germany), it may be very difficult to moderate the pace of inflation by applying demand management policies in conventional degree. For such policies it is unlikely to be sufficient, for example, to bring pressures on capacity down to some medium-term norm, because the analysis suggests that it is necessary not only to eliminate excess demand pressure but also to take additional action that will offset the inflationary pressure built up as a result of recorded past price performance. In other words, if demand management policy is being used, it has to be sufficient, inter alia, to break rising price expectations. The implication of this approach is that a “break” in such expectations may be achievable by demand management policies only at the cost of an unusually high degree of restrictiveness and an associated cost in unemployment.

However, the analysis suggests that, in a situation in which price expectations have been broken by such policies and the contemporary rate of inflation is thus acceptably moderate, it would be possible for unemployment to return to its earlier lower level, with restoration of demand management policies to the earlier single role of avoidance of excess demand pressure. In other words, very tight demand management policies in the short term may be a means of improving the unemployment-inflation trade-off in the medium term.

Another approach to the breaking of built-up price expectations would be the implementation of prices and incomes policies, possibly involving a wage-price freeze. Arguably, this approach could mitigate the degree of severity of restrictive demand management policies that would be required if inflationary expectations were to be broken by such measures alone, while offering a perhaps broadly similar prospect for an improvement in the unemployment-inflation trade-off in the medium term.

### APPENDIX Derivation of the Expected Rate of Inflation

Expressing the outcomes of the survey as a random variable (*X*), the distribution function for the subset of enterprises expecting prices to fall may be written as:

*F _{x}(–s)*, where the interval (–

*s*,+

*s*indicates the area where no price changes are expected.

#### Notation

*X =*random variable of expected rate of inflation over all individuals.*F*value of the distribution function of the random variable_{x}(–s) =*X*for the argument –s.*P(*probability that the random variable*X*< –s) =*X*takes a value smaller than –*s*.*a, b, c*= results of the survey, referring to the per cent of enterprises expecting prices to rise, stay the same, and fall.(–s, +.s) = sensibility interval.

*N*= standard normal distribution function._{z}*μ, σ*^{2}= mean and variance of the random variable*X*.*p*expected average rate of inflation.^{e}=

#### Derivation

By definition

and

Similarly

and

Finally

and

The standard normal distribution function (*μ* = 0, *σ*^{2} = 1) can be used to evaluate the distribution function for a normal random variable with arbitrary μ and σ

Now

t=−s, s

and

*μ = p*^{e}, the expected average rate of inflation.

where

and

where

so

solving for *σ* and *p ^{e}*

If

then

where

uandvare obtained from the table of the standard normal distribution function.a, b, andcrefer, respectively, to the percentage of enterprises expecting prices to rise, stay the same, or fall during any time period.

Assuming an arbitrary value for *s, p*^{e} can be computed from equation (21). The final result is surprising, since z can be derived without an assumption about the interval (–*s*, *+s*), and *p*^{e} is then only a linear transformation of *z*, with s as the scaling factor. If an assumption about the interval is made, a time series of the expected rate of price change can be obtained.

## BIBLIOGRAPHY

Commission of the European Community,

*Directorate-General for Economic and Financial Affairs,*(Brussels), various issues.*Report of the Results of the Business Surveys Carried Out Among Heads of Enterprises in the Community*Commission of the European Community,

(Brussels, November 1967).*The Harmonized Business Surveys in the Community: Principles and Methods*Deutsche Bundesbank,

(Frankfurt am Main), various issues.*Monthly Report*Deutsche Bundesregierung,

(February 1973).*Jahreswirtschaftsbericht 1973*Goldstein, Morris, “The Trade-Off Between Inflation and Unemployment: A Survey of the Econometric Evidence for Selected Countries,”

, Vol. 19 (November 1972), pp. 647–98.*Staff Papers*Grätz, Wilfred, and Adalbert Knöbl,

*“Erwartungswerte in der Ökonomie, Investitionsund Preiserwartungen, Quantifizierungsmethode,”*, Nr. 70 (Institut für Höhere Studien, Vienna, July 1972).*Forschungsbericht*IFO-Institut für Wirtschaftsforschung,

(Munich), various issues.*IFO-Schnelldienst*Nordhaus, W.D., and W.A.H. Godley, “Pricing in the Trade Cycle,”

, Vol. 82 (September 1972), pp. 853–82.*Economic Journal*Organization for Economic Cooperation and Development,

(Paris, June 1971).*Economic Surveys: Germany*Parkin, M., “Incomes Policy: Some Further Results on the Determination of the Rate of Change of Money Wages,”

, Vol. 37 (November 1970), pp. 386–401.*Economica*Roussens, Stephen W., ed.,

(New York University, 1968).*Proceedings of a Symposium on Inflation: Its Causes, Consequences and Control*Sachverständigenrat zur Begutachtung der gesamtwirtschaftlichen Entwicklung,

(Bonn, November 1972).*Jahresgutachten 1972*Siebert, Calvin D., and Mahmoud A. Zaidi, “The Short-Run Wage-Price Mechanism in U. S. Manufacturing,”

, Vol. 9 (September 1971), pp. 278–87.*Western Economic Journal*Spitäller, Erich, “Prices and Unemployment in Selected Industrial Countries,”

, Vol. 18 (November 1971), pp. 528–69.*Staff Papers*Solow, R.M.

(Manchester University Press, 1969).*“Price Expectations and the Behavior of the Price Level*Statistisches Bundesamt,

(Wiesbaden), various issues.*Wirtschaft und Statistik*

^{}*

Mr. Knöbl, an economist in the Central European Division of the European Department, is a graduate of the Hochschule für Welthandel, Vienna, and was a scholar at the Institute for Advanced Studies and Scientific Research, Vienna.

^{}1

This view has been variously expressed in the German Government’s *Annual Economic Report*, *1973*, in the reports of the German Council of Economic Experts, and in the Deutsche Bundesbank’s *Monthly Report* (Frankfurt am Main), various issues.

^{}2

The Directorate-General for Economic and Financial Affairs of the Commission of the European Community publishes the *Report of the Results of the Business Surveys Carried Out Among Heads of Enterprises in the Community* (Brussels).

^{}4

The conduct of the surveys and the presentation of results are described in detail in: Commission of the European Community, *The Harmonized Business Surveys in the Community*: *Principles and Methods* (Brussels, November 1967).

^{}5

The method was developed in collaboration with two Austrian colleagues. Details are given in Wilfrid Grätz and Adalbert Knöbl, “Erwartungswerte in der Ökonomie, Investitions- und Preiserwartungen, Quantifizierungsmethode,” *Forschungsbericht*, Nr. 70 (Institut für Höhere Studien, Vienna, July 1972). At about the same time, basically the same method was developed by J. S. Carlson and M. Parkin. The method was presented at the Fund by Mr. Parkin in September 1972.

^{}6

Rearranging equation (3) shows: *b _{0}*=

*b*, it follows that

_{2}*b*+

_{1}*b*=1 and equation (4) corresponds to equation (3).

_{2}^{}7

The numbers below the coefficients are the T-ratios. *D-W* the Durbin-Watson statistics,

^{}8

Solow tested basically the same price equation for the United States and the United Kingdom, but he did not have an observed series of price expectations available. Therefore, p^{e} was created by use of the adaptive expectations hypothesis. See R. M. Solow, *Price Expectations and the Behavior of the Price Level*, (Manchester University Press, 1969).