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Clusters and Loops of the German

Phillips Curve

Quaas, Georg and Klein, Mathias

Universit¨t Leipzig

a

05. June 2010

Online at http://mpra.ub.uni-muenchen.de/23094/

MPRA Paper No. 23094, posted 06. June 2010 / 10:23

Clusters and Loops of the German Phillips Curve

Georg Quaas / Mathias Klein (University of Leipzig)

The Phillips Curve is one of the greatest findings in economics. This widely shared

assessment may well be the reason for its presence in almost any textbook on macroeconomics. A short description of what the statistician and economist Alban William Housego Phillips (* New Zeeland 1914; † Australia 1975) has discovered is often followed by an elaborated account of the modifications, critiques and extensions which arose in the course of the cognitive process that was triggered by Phillips (1958). In this way, his achievement appears belittled if not obsolete. For instance, Blanchard and Illing (2009, p. 255) write with a reference to the data of the German economy: „Nach 1970 bricht der stabile Zusammenhang zwischen Inflation und Arbeitslosigkeit weitgehend zusammen.“ 1

**For the time after this “break-down” Dieckheuer (2003, p. 355) states:**

„Und auch in empirischen Untersuchungen kam man jetzt immer häufiger zu dem Schluss, dass der mit der (einfachen) Phillipskurve beschriebene stabile Zusammenhang zwischen Inflationsrate und Arbeitslosenquote für viele Industriestaaten nicht bestand.“ 2 Similar assessments which often sound like a falsification (refutation) of Phillips’ discovery can be found easily. A modified Phillips Curve is said to have replaced the

**original relationship:**

„Die alte Phillips-Kurve wurde gerettet, indem sie durch zwei Kurven ersetzt wurde:

(1) eine kurzfristige, um Erwartungen erweiterte Phillips-Kurve, die der alten ähnlich ist, sich aber bewegen kann, und (2) eine langfristige Phillips-Kurve, die immer senkrecht verläuft“ 3 (Burda and Wyplosz, 2009, p. 386).

From the point of view of critical rationalism one ought to speak of totally different relationships with each of these modifications. However, considering the extensive literature we shall follow the tradition and use the term modifications.

English translation by the authors: “After 1970 the stable relationship between inflation and unemployment widely broke down.” English translation by the authors: “And also in empirical studies one came more and more to the conclusion that in most industrialized countries the stable relationship between inflation rate and unemployment rate, which could be described with the (simple) Phillips Curve, did not exist.” English translation by the authors: “The old Phillips Curve was recovered by replacing it with two curves: (1) one short-term curve including expectations which is similar to the old one but can shift and (2) a long-term Phillips Curve that always runs vertical.”

1. Definition of three different versions

1.1. The original Phillips Curve Phillips discovered – not without preliminary theoretical considerations – a statistical interrelation, more precisely: a negative, nonlinear relationship between the annual rate of change of money wage rates (y) and the annual unemployment rate (x). The empirical basis of his study consisted of data of the United Kingdom from 1861 to

1957. Based on the period 1861-1913 and verified with the periods 1913-1948 and 1948-1957, he set up an equation which generalizes his finding (Phillips, 1958, p.

290):

y + 0.9 = 9.638x-1.394. (1) In this formula, it is not the parameter values that are the main issue of the discovery – they were revised soon – but rather this “significant and very interesting relation” (Lipsey, 1960, p. 30) between the change of the average wage rate and unemployment, which can be characterized as statistical, nonlinear and negative.

Stressing the statistical nature of Phillips’ finding implies that equation (1) is thought to explain the central tendency of the data only. Other factors like the changes of the unemployment rate, of the consumption and of the import price index should be drawn on to explain the deviations from the central tendency (Phillips, 1958, p. 298;

Lipsey, 1960).

Two years later Samuelson and Solow replicated Phillips’ finding for the United States of America. They came to the conclusion that the same generalized relation could be observed for the US-American economy too. Due to the availability of data, they did not utilize the annual rate of change of the nominal wage rates, but instead utilized the average hourly wages in the manufacturing industry (Samuelson and Solow, 1960, pp. 187-194).

1.2. First modification of the Phillips Curve Samuelson and Solow went another step further and replaced the rate of change of wages by the inflation rate. 4 One reason for this modification was probably that they considered the wage-price spiral not empirically analyzable. Based on their post-war experiences with the American economy, they postulated a negative relationship

**between inflation and unemployment and called it:**

“our price-level modification of the Phillips Curve” (ibid., p. 192).

Both authors expected that their “Phillips Curve” would be shifted by fiscal or monetary policy arrangements. Furthermore, they drew the consequence that in the short-term there should be a “menu of choice” between the macroeconomic variables “inflation” and “unemployment” (ibid., p. 193). However, they warn of doing explicit forecasts or even “guesses” for the long-term based on the Phillips Curve. In the cited article one cannot find any evidence for the thesis that those authors deduced a long-term “menu” as a guideline for policy makers, which enabled them to choose between the two evils of inflation and unemployment (Hoover, 2010). Moreover, for Samuelson and Solow exists a one-way dependency whereupon unemployment For a theoretical derivation of this transformation see Steinmann (1973, p. 106). Its basic

affects the inflation in the short-term (Samuelson and Solow, 1960, p. 192) and not the other way around. For the conclusion that the modified Phillips Curve can be utilized in the contrary causality too (a high inflation rate that leads to a low unemployment rate), no evidence can be found in the last mentioned article. The postulated trade-off between inflation and unemployment means the following: If any economic measure produces lower unemployment, higher inflation has to be accepted.

1.3. Second modification of the Phillips Curve At the end of the 1960s the modified Phillips Curve increasingly faced criticism. The main critique consisted in the thesis that there could not be a long-term trade-off between a nominal variable (inflation) and a real variable (unemployment) (Phelps, 1967; Friedman, 1968; Phelps, 1968). Higher inflation leads to a higher inflation expectation, which again positively affects inflation. According to this view, the real wage and not the nominal wage represents the relevant price for the labour supply and labour demand, which are illustrated in the unemployment rate (Kösters and Hofmann, 1998, p. 160). The conclusion was that in the long-run the Phillips Curve has to be a vertical line (Abel and Bernanke, 2001, p. 445 or Mankiw, 2004, p. 786).

Only at times in which the average of the actual inflation and along with it the expected inflation would develop relatively steady, the relation postulated by Samuelson and Solow should be applied (Friedman, 1968, p. 9). Therefore, the second modification consisted in the addition of inflation expectations to the relation between inflation and unemployment.

**1.4. Other developments**

Further modifications could be seen in the alternative modeling of the formation of expectations. If, for example, the expected inflation is equal to the inflation of the previous period, it can easily be shown that unemployment does not affect the inflation but the change of the inflation rate. 5 According to Blanchard and Illing (2009, p. 257), „…diese Argumentation ist der Schlüssel zu den Geschehnissen seit den 70er Jahren“ 6. If this holds true for the German economy is now to be examined.

2. A pretest Table 1 shows the estimated results for linear regression equations with which the above described versions of the Phillips Curve can be formulated in a simplified form and statistically tested in an easy manner. The simplification consists in a linear approximation. It is legitimized as far as “there was only seldom strong evidence that unemployment exhibited a nonlinear influence” (Heilemann and Samarov 1990, p.

449). The parameters of the original Phillips Curve (PC0), its first (PC1) and second modification (PC2) as well as an alternative modeling of the expectation formation (PC3) are estimated by the method of ordinary least-squares (OLS). We utilize official annual data of the German Statistical Office (Statistisches Bundesamt) from 1952 to 2004 of the German Economy. The wage rates (w) are operationalized by gross wages and earnings in the numerator and the employees (native concept) in the denominator. In our view, effective wage rates are closer to the real situation on the labour market compared to negotiated wage rates. The “∆” stands here for the annual For the theoretically derivation see Blanchard and Illing (2009, p. 251-258). English translation by the authors: “…this argument is the clue that leads to an understanding of events since the 1970s.” 4 rate of change and the symbol “t” for the time. As an indicator for the inflation (π) we use the annual change of the consumer price index.

The structure of the table is now shortly illustrated by means of two examples. For the second modification of the Phillips Curve (PC2) the inflation rate π is determined by the unemployment rate and the lagged inflation rate (equates the inflation rate of the previous year) modeling inflation expectations. Of course, all estimated equations include a constant, which is not reported here. For an alternative modeling of the process of expectation formation (PC3) the change of the inflation rate (∆πt – the difference to the previous year) is explained mainly by the unemployment rate. In the equation PC3 the coefficient of the lagged inflation rate (see equation PC2) is fixed a priori at the value of one. As it is generally known, this relation is utilized to determine the NAIRU 7 (Blanchard and Illing, 2009, p. 258.).

The results: The signs of all parameters are theoretically plausible. The unemployment rate imposes a negative influence on the dependent variable while the lagged inflation rate has a positive impact.

The original Phillips Curve offers a relatively high adjusted R2 particularly with regard to the fact that the annual rate of change of money wage rates is explained by only one variable, namely the unemployment rate. According to this result, a one percentage increase of the unemployment rate would lead to a decrease of the change of the wage rates of 0.94 percentage points.

The first modification of the Phillips Curve according to the Samuelson and Solow approach shows a considerable lower adjusted R2 compared to the original Phillips Curve.

An improvement compared to the latter version of the Phillips Curve yields the second modification on the basis of the Friedman and Phelps considerations.

However, even this modification supplies worse results when compared to the original Phillips Curve.

The regression of the alternative modeling of the expectation formation comes up with serious problems. The only explanatory variable (the unemployment rate) has no Non-acceleration inflation rate of unemployment. 5 significant impact on the change of the inflation rate. The adjusted R2 is by far the lowest of all reviewed versions. Furthermore, with regard to the estimation of the second modification of the Phillips Curve, it must be stated that fixing the coefficient of the lagged inflation rate to the value 1 is not a realistic choice.

To this finding we have to add that from the beginning of the theoretical discussion of the “natural unemployment rate” their long-run variability was assumed. Therefore, it was not to expect to get a “good” estimation of the NAIRU for a period of 53 years.