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

Had we chosen shorter periods and let the estimations move over all dates we would have gotten better results. But the periods should not be too short. Considering that the concept of natural unemployment was proposed to measure the relationship of short-run changes of inflation as a function of deviations of the observed unemployment rate from the natural unemployment rate, it makes little sense to estimate the NAIRU based on periods with the length of one year or – even worse – a quarter of a year, although mathematical modeling may enable us to carry out this procedure (Borchert and Fröhling, 2001).

The comparatively best fit to the data has the original or unmodified Phillips Curve, and this was the reason to focus our research on the original finding which is to explain the rate of change of money wage rates by the help of the unemployment rate. We extended our analysis to quarterly data which are available from 1970Q1 to 2009Q4 and explored the visible deviations from the central tendency, especially such special phenomena like clusters and loops, which were already observed by Phillips.

**3. OLS or ML? A short remark to the estimation method**

There is no doubt that wages and prices are jointly dependent variables that affect each other. A comprising analysis of the circle “prices wages prices” requires a complete econometric model endowed with several equations, one of them addressing wages (Eckstein and Girola, 1978, p. 330, Lipsey and Parkin, 1970 or Parkin, 1970). Because wages depend (among other variables) on prices, and prices depend on wages, neither of them should be treated as an independent variable in an ordinary least squares regression. An estimation of the whole system of equations with, at best, the maximum-likelihood (ML) method would be appropriate. However, single equation estimates with OLS are widely used in econometric and forecasting literature, probably because of the technical difficulties inherent in the ML-estimation of models with, say more than, 15 equations. We have chosen OLS as the estimation method in the hope to give some advice for model building too. The main point is not OLS or ML, but that the focus of our analysis is laid to an analysis of single equations. It is well known that OLS and ML estimators of a one equation system are the same in value.

4. The Phillips Curve in Germany

salient features of Germany’s Phillips Curve: Periods in which the data cluster together alter with periods of moving data points from one cluster to another.

From a simple inspection of the data, some crucial questions arise. First, what can be considered as a short-term movement of data points contrary to a long-term movement? Of course, there is no other choice than to assess the whole period of 38 years as a long-term period. Taken this for granted, the observations conflict with the theoretical assumption of a vertical curve which should govern the spread of data in the long run. The vertical curve seems to be a theoretical construction only. As a matter of fact, Figure 1 shows by and large the same non-linear and negative relationship as central tendency of the data, which was discovered by Phillips.

Second, taking into account the flexible definitions of “short-term,” which can be found in textbooks, at least one thing can be said with certainty: a short-term period must be timely smaller than a long-term period. To avoid the slippery slope of skepticism, we decided to recognize the shortest observed period – the quarter – as the basic element of a short-term movement. Once again, on the rationale of these definitions, the observations conflict with the ruling dogma: The short-term movements, especially in the clusters, are often not like the one we have to expect according to the modern theory that the Phillips Curve as a whole is shifting. Third, the movements between the clusters, comprising often many quarters, have a negative slope of the same kind that Phillips found. Therefore, the next questions are 7 as follows: Where are the famous shifts located, which are claimed by modern theory allegedly to move the whole Phillips Curve up and down? Do the shifts happen between or in the clusters? How can it be that the shifts between the clusters often have a negative slope like the one in the clusters and like the whole Phillips Curve?

When we assume that the shifts are located in the clusters, why does Figure 1 show the same old loops and movements that were already part of Phillips’ discovery?

A closer look at the clusters discloses 12 loops (including double loops and one emerging loop at the end of the observation period, see Table 2), some of them with a left and others with a right turn around, among them the 4 examples depicted in Figure 2. The loops are mostly interrupted by periods of simple movements of different lengths.

Phillips suggested that these loops were a phenomenon which occurs more or less in every business cycle. In the phase of a cyclical upturn the actual rate of change of money wage rates were systematically higher and in a cyclical downturn systematically lower than the central tendency of the original Phillips Curve predicted (Phillips 1958, p. 290; Lipsey, 1960, p. 20). This fact was interpreted as the cyclical instability of the Phillips Curve (see Maneval, 1973, p. 91). Phillips also assumed that the possibility “of a time lag in the response of wage changes to changes in the level of unemployment” (Phillips, 1958, p. 293) could be a reason for the formation of the loops. If such a time lag exists the wage change in the actual period will be related to the lagged unemployment rate and not to the unemployment rate of the same period (ibid., p. 292). In his judgment such a time lag would lead to the loops in the diagrams showing the relationship between wage changes and unemployment. For Lipsey (1960, p. 23), structural differences in and dependencies between several product and labour markets of an economy produced the loops.

Other authors interpreted the emergence of the loops as the break-down of the original Phillips curve (Streit, 1972) – if it ever had existed.

9 Figure 3: Examples of simple Movements. UE: Unemployment Rate; WR_CH: Change of Nominal Wage Rate; Actuals: solid line; Baseline: broken line.

The German data show that both, the number of loops and the changing direction of their turn around, allow the conclusion that they have nothing to do with the few cyclical upswings and downswings the German economy has experienced (the first hypothesis made by Phillips).

In the search of a new explanation of the loops and the movements between the clusters (loops) we followed the standard method of (i) regressing the long-term movement and (ii) trying to explain the short-term deviations from the long-term tendency by special assumptions and regressions. It turns out that there is no essential difference between the explanation of the loops and the explanation of the movements between the clusters (loops). In the next part we will show that both can be explained by the same regression with about the same accuracy.

5. The estimation of different wage equations In the years after Phillips’ findings, several studies with the focus on additional exogenous variables for the explanation of the rate of change of wage rates were published. 8 Table 3 shows the estimation results for six different approaches of the determinants of the rate of change of money wage rates. The first five approaches were elaborated by Phillips (1958), Lipsey (1960), Eckstein and Wilson (1962), Perry (1964), and Kuh A summary of the results of different studies is delivered by Dicks-Mireaux and Dow (1959, pp. 169Eckstein and Wilson (1962, pp. 402-405) or Liebling and Cluff (1969). 10 (1967). The last estimation equation is an eclectic approach based on the ideas and findings of these and other authors. Also two variables which attracted (by now) in the listed literature only little interest namely the import prices and the export prices are implemented. 9 All equations were fitted by the method of ordinary least-squares to German data for 1972Q1-2009Q4. 10 The constants of the estimated equations are not reported.

The German unification was a shock that is mirrored in our regressor variables only partly: The process of integration of a population governed by a different wage regime into the West German economy needed several years, but the average wage rate was affected immediately. Therefore, we tested the influence of a dummy variable for the German reunification for all equations. This dummy equals the value one for 1991Q1-1991Q4 and zero for the rest of the observation period. In all fitted equation it has a significant negative impact on wages which varies from -9.19 to The dummy is part of all equations, but also not reported in the table.

For the nominal wage rates (WR) we use the reported quarterly average of the monthly labour costs per employee. The unemployment rate (U) is a moving average of four quarters of the number of unemployed per working force. As indicator for the inflation we utilise the percentage change of the consumer price index (P); the import prices and the export prices are treated accordingly and denoted by (Pim) and (Pex) respectively. The values for the productivity (H) equal the labour productivity per employee and the profit rates (R) are operationalized by property income related to the income of employees. A “∆” stands for the annual rate of change.

Table 3: Estimated values for different approaches of the determinants of the rate of change of money wage rates.

Own computations according to data from the German Statistical Office (Statistisches Bundesamt). The t-statistics are reported in parentheses below each parameter. One star * means significant on the 5%-level, **significant on the 1%-level and ***significant on the 1/10%-level. U: Unemployment rate; ∆U: Annual rate of change of the unemployment rate; ∆P: Annual rate of change of the consumer price index; ∆Pim: Annual rate of change of the import prices; ∆Pex: Annual rate of change of the export prices; H: Labour productivity; ∆H: Annual rate of change of the labour productivity; R: Profit rate; ∆R: Annual rate of change of the profit rate; RMSPE: Root Mean Squared Percentage Error. “a”: one period lagged sum of the one-quarter per cent changes in the consumer price index for periods t-1, t-2, t-3, t-4. “b”: one period lagged average annual profit rate over the last four quarters. “c”: annual rate of change of the average annual profit rate over the last four quarters.

In all equations the unemployment rate (U) has a highly significant negative influence on the rate of change of money wage rates. In four of the six estimation equations the consumer price index (∆P) is an exogenous variable and in three of this it shows a significant positive impact. In Lipsey’s equation the influence of the annual rate of change of the unemployment rate (∆U) is significant and positive. The profit rate (R) has in the Eckstein and Wilson equation and also in the Perry equation no significant impact on wages, but the annual rate of change of the profit rate (∆R) shows a significant influence in the Perry equation. For the Kuh approach, the level of labour productivity (H) has no significant impact on wages. The adjusted R2 of the first five estimation equations varies from 0.75 to 0.78. Furthermore, the Durbin-Watson statistic (D-W) signalizes that for all these “historical” approaches there is a problem with autocorrelations.