# «Clusters and Loops of the German Phillips Curve Quaas, Georg and Klein, Mathias Universit¨t Leipzig a 05. June 2010 Online at ...»

Also, Table 3 shows the Root Mean Squared Percentage Error (RMSPE) that is based on the differences between actuals and baseline solutions, taken over the (centre of the) loops and over the movements separately, and this for all estimated approaches. Compared to the forecast accuracy of a comprehensive econometric model, the error values are high. The reader may take into account that we try to simulate short-term loops and movements by the help of average parameters estimated over 38 years. In general, we can observe that the errors for the movements are smaller than those inside the loops. But there are not only differences between the explanation of loops and of movements, but also between the explanation of different loops and explanation of different movements. Of course, the Phillips Curve approach with one variable only provides no explanation of any loop at all, because it provides a flat simulation curve. The simulation of a loop can be better or worse compared to a flat one depending on the extent of deviation from the observed data. Therefore, RMSPE has a limited scope for assessing the fit of the simulations. The astonishing fact is that all the different loops and movements can be simulated and in this sense explained by one equation model only.

In the equation of our eclectic approach the rate of change of money wage rates is explained by the unemployment rate (U), the annual rates of changes of the consumer price index (∆P), of the import prices (∆Pim), of the export prices (∆Pex), of the labour productivity (∆H), and of the profit rate (∆R). For all these variables a highly significant influence can be observed. Ninety-four percent of the total variance is explained. The results signalize the possibility of a first-order autocorrelation. On the other side, the values of the t-statistics are high enough for being taken seriously. 11 The single variable with the highest influence is productivity. Getting a share in productivity gains seems to play a more important role in the bargaining strategy of unions than getting a compensation for inflation – as far as it does play an important role. The productivity determination theory was ushered by Kuh (1967) as a proxy for profit. It turns out that the rate of change of productivity represents an important determinant, indeed, but it cannot replace profit as part of the single equation model.

There is a broad consensus that money wages are affected by prices reflecting living cost. On average, a change in consumer prices of one unit causes an increase of wages of about 0.54, suggesting that even though money wage bargains are made with a special attention to inflation, compensation is not complete (for similar results We have to note that between the varibales in the equation of the eclectic approach the problem of multicollinearity exists and therefore instability of the parameter could occur. 12 see for example Dicks-Mireaux and Dow, 1959, Hines, 1964 or Perry, 1964). This can be interpreted as a partial money illusion or, once again, as a limited effect of bargaining processes.

Surprisingly, the third place in importance is taken by the change of export prices. It reflects the special conditions of an export oriented economy (the “openness” index of Germany is more than 60 percent). Our interpretation of the positive sign of the parameter is simple and sounds plausible: A short-term change in export prices does not reduce immediately the quantity of exports, but enhances the revenue. This seems to be also profitable for employees.

The other side of the coin (of an open economy) are import prices. Because the influence of import prices on living costs is already included in our inflation index, we interpret this channel as follows: Higher import prices mean higher production cost for firms and this reduces the leverage for higher wages.

Changes of export and import prices are taken in this study as production-oriented prices; both are replacing GDP-deflator in this role.

Slightly more important for the explanation of changes of the wage rate in the eclectic approach is the standard variable of unemployment. Even though we introduced five other variables the unemployment rate has kept its significant influence. After several supply shocks and even during and after the German unification, the unemployment rate yields a reliable explanation of wage adjustments not only in the short, but also in the long-run.

The smallest parameter, albeit still significant, mirrors the negative influence of profit changes on wages. On the one hand this seems plausible because an increase of profits leads to the situation that less income can be distributed among the employees. On the other hand the negative impact of profits stands in opposition to some theoretically considerations (Kaldor, 1959, p. 293). The complex relationship can be described as follows: (i) profits and wages are exclusive shares of national income; (ii) growing national income results statistically in both, higher profits and higher wages; (iii) the higher the growths of profits the lower the enhancements of wages. The last point is what we found.

Lagged variables, especially for inflation, did not enhance the explained variance of our best fit regression equation. This seems to contradict the rules and experiences of wage bargaining in which inflation is one of the arguments that is made by union leaders for higher wages. Bargaining is a time consuming process and therefore a time lag should play a role in modelling the influence of the inflation rate. Speaking more exactly, it should be the expected inflation formed in one of the previous periods that plays a role in wage negotiations. Our finding could be interpreted as an indicator of the high ability of unionists in predicting inflation rates. If this were the case, it would be no outstanding skill: With a simple regression equation more than 90% of the next quarter’s inflation rate can be predicted. On the other side, inflation rate defined by the change of the price level, more exactly: of the index of the price development, includes as one factor the Paasche price index of the previous year, which can be interpreted as a crucial factor forming price and inflation expectations (for more on this point see next footnote).

13 Figure 2 and Figure 3 illustrate that the eclectic estimation equation can explain both the loops and the movements of the German Phillips Curve satisfactorily. 12 Table 3 shows that the RMSPE of the “best fit” approach is by far the lowest of all fitted equations inside the sum of all loops as well as for the sum of all movements. These results suggest the conclusion that the found estimation equation that determines the rate of change of money wage rates in the long-term can trace short-term deviations from the central tendency of these long-term movements too. In other words the curve in the long-run can be explained by the same variables as in the short-run.

6. Stability of the parameter estimates The reported estimations are based on the comparatively long period of 38 years.

The parameter values are averages with a high statistical significance due to the high number of 152 observations. We carried out simple stability tests under the leading question whether or not the same dependencies could be detected by the help of a regression analysis by OLS based on periods with a length of 10 years only. Figure 4 shows the estimates of all parameters of our best fit regression reflecting the most recent last 40 observations (10 years) for every quarter since 1981Q4 (so called “moving window”).

The positive influence of productivity changes on changes of the wage rate could be observed all the time, even after 2002 when it fell down considerably. The widely shared opinion of inflation as the central argument in wage setting bargaining shows up in parameter estimation only partially: more than half of the time the parameter was not statistically significant. The parameter of the inflation rate is below one all the time indicating a non-accelerating wage-price mechanism. With the exceptions of the crisis at the end of the 1980s, in the 1990s, and during the sluggish development in the first decade of this century, a change in export prices had fruitful consequences for wage earners. Apparently, difficult to detect for many researchers in the past, we found that higher changes of profits reduce the leverage of wage enhancements – of course, this is no big surprise. Import prices are interpreted here as wage reducing cost – the periods with deviant parameter values nearby zero or even with a positive sign show no statistical significance. The standard explanation of wage rate changes by unemployment holds for almost all the time; only during a short period after the German unification this relationship could not be detected by regression estimations using a ten-year moving window.

To econometricians of the past who had had the same best fit regression and data available as we did, periods in which one of the parameter values turned out to not be significant would have appeared as structural breaks because with one parameter in an equation less all parameter estimates would have changed. In general, the presence of changes in the parameter estimates is an indicator of an incomplete specification: there are changes in the determinants of wage rate changes that still cannot be explained. It reminds us that someone’s best fit equation cannot pass as the last word about the Phillips Curve. Consequently, we did not intend to present a new theory of macroeconomic wage determination, but went as far as possible with the old one and picked up the post signs to new approaches.

**7. Conclusion**

The assumption that Phillips’ original finding might still be of empirical relevance turns out to be true. Switching from a yearly to a quarterly data set of the German economy makes a more sophisticated analysis of the central tendency of the data and of its deviations possible. The three phenomena visible by a closer look at the data are (i) the negative, possibly non-linear central tendency of the data points in the long-run, (ii) a dozen loops that are the most salient deviation from the central tendency and (iii) movements between the loops. The hypothetical explanation of the loops by the cyclical up- and downturns of the economic development can be rejected as insufficient. Several versions of the Phillips Curve proposed in the literature proof the stable influence of the unemployment rate on the change of nominal wage rates, but are incapable to explain the loops. After completing a selection of historically recommended variables that turned out to be statistically significant in the regression analysis by the two indices of export and import prices the determination coefficient reaches 94 percent, the Durbin-Watson statistics improves and the corresponding 15 model solution follows the loops. In spite of the striking differences between the described phenomena, one regression equation model is sufficient to explain the loops, the movements between the loops and the long-term tendency of the German Phillips Curve.

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