A simple plot of seasonal adjusted quarterly data between the change of nominal wage rates and the unemployment rate for the German economy shows a picture similar to that by which Phillips was inspired to his famous discovery, that there is a long-term tendency of a negative, non-linear relationship coupled with minor deviations from this tendency, which form so-called loops. At first sight, the Phillips Curve of Germany comprises clusters of data points and movements between these clusters. In spite of the striking differences of these phenomena, a model with one regression equation is sufficient to explain the loops, the movements between the loops and the long-term tendency of the German Phillips Curve. It might well be that the German Phillips Curve and the corresponding regressions are spurious, but an allegedly missing co-integration of wage rate changes and unemployment rate is not the argument that could be drawn on to sustain this scepticism. On the contrary, both variables are co-integrated. To get a more detailed insight into the relationship, the two variables are split into a trend and a cyclical component by the help of the HP-filter. The results of regression analyses applied to the separated components support Phillips’ hypothesis of a negative relationship between wage rate changes and the unemployment rate.Wages, Unemployment, Phillips Curve

Klein, Mathias

Quaas, Georg

English

Research Papers in Economics

Is the Phillips Curve of Germany Spurious? 
 
 
Georg Quaas / Mathias Klein 
 
 
It might well be that the German Phillips Curve (Figure 1) and the corresponding 
regressions (Table 1) are spurious. With “spurious” we mean a correlation, a partial 
correlation or a regression equation between two variables A and B, for instance 
between the change of the wage rate (A) und the unemployment rate (B), that does  
not indicate a causal relationship between A (the effect) and B (the cause) but is 
produced by another variable (i.e., by an underlying common cause (C), for instance 
by a country’s real economic activity). This scepticism about the causal essence of 
correlations and regressions can be extended to almost all important economic 
relationships, which are formulated by a stochastic equation and estimated by 
econometric methods, such as the well-known consumption function. The standard 
interpretation of this equation is that a one-unit change of disposable income causes 
a change of the amount of consumption equal to the parameter value of the marginal 
propensity to consume. This cannot only be regarded with sceptical distance, but is 
theoretically inverted by the Marxian interpretation that labour power’s consumption 
cost causes the amount of disposable income to be an indicator of its value on the 
labour market. Of course, the whole relation is controlled by a country’s economic 
activity – probably a common cause, not of the consumption function only, but also of 
the production function and of almost all other important econometric equations. 
Nevertheless, this scepticism has had almost no effect on the development of 
economic theory, like most of the critiques in the last fifty years testify (Dobusch, 
Kapeller 2009). 
 
This overall scepticism can be very productive when serving as a driving force in the 
search for a common cause of a special relationship. But as long as nothing has 
been found that serves as a reason for classifying a correlation as spurious, the 
hypothesis that the correlation or regression is indicating a causal relationship can be 
egitimized by the widely-shared Critical Rationalism as well as other schools of the 
philosophy of science (Outhwaite 1987).  
 
   2
The German Phillips Curve 
 
Quaas and Klein (2010) estimated in retro-respect several regressions that have 
been of historical importance as far as they influenced the development and 
consequently the shape of the modern macroeconomic theory on the price- and 
wage-setting process. They used data of the German economy from 1950 to 2004 
(old system of national accounts), and from 1970 to 2009 (new system of national 
accounts). The common feature of all tested regressions was a very stable 
relationship between the wage rate changes on the one hand and the unemployment 
rate on the other, which was the original finding of Phillips (1958).  
 
Phillips’ and especially Lipsey’s (1960) core theory that unemployment causes the 
wage rate to change cannot be refuted by the application of the argument that a 
nominal variable is not able to influence a real one (Phelps 1967), because the 
assertion here is that a real variable influences a nominal one. Moreover, Phillips’ 
core assertion is part of the modern theory on wage setting as far as unemployment 
still plays a crucial role in the wage-setting process. 
 
Nevertheless, very few people are adherents to old Phillips’ finding. Theoretical 
development has gone different ways, generalizing the experiences of stagflation and 
hyperinflation in certain periods of time and in certain countries. Meanwhile, a 
broader record of data is available, and those experiences might appear as statistical 
outliers. In some aspects, “the intellectual framework for analysing the inflationary 
process […] has come full circle and the Phillips curve is once again central in this 
framework”  (Gruen, Pagan, Thompson 1999, 253), at least for some of us. Accepting 
that there is no trade-off between inflation and unemployment in the long run does 
not affect Phillips’ original findings. In addition, it is a matter of fact that the data of the 
German economy can be displayed in a way that is very similar to the statistical 
relationship discovered by Phillips.   3
 
 
Figure 1: Germany’s Phillips Curve, Unification data smoothed. 
 
 
Statistical evidence is one thing, the theoretical interpretation another. We do not 
intend to present a new theory to explain the relationship between wage rate 
changes and unemployment. There are many approaches and explanations that can 
be found in the theoretical debate about the determinants of wages and prices 
(Eckstein, Wilson 1962; Kuh 1967; Streit 1972; Galí 2010). At the moment, we are 
concerned with two reproaches to our study (Quaas, Klein 2010) presented at the 
12th INFER Annual Conference 2010, which took place on 3-5 September at the 
University of Muenster (Westphalia, Germany).  
 
(i) It is likely that there is a high degree of multicollinearity among the explaining 
variables, in addition to the reported high degree of autocorrelation in the error term. 
Both render the estimated t-values as too high, and with them the significance of the   4
parameter estimations as too optimistic. As a consequence, the results should not be 
theoretically interpreted. 
(ii) The wage rate changes are likely of another type of time series compared to the 
unemployment rate with respect to stationarity. Therefore, the regression by which 
Quaas and Klein have explained clusters and loops of the German Phillips Curve 
was probably spurious, simply because the equation might be not consistent 
(Granger 1981). 
 
 
Are wage rate changes and unemployment rates co-integrated? 
 
If wage rate changes and the unemployment rate are not co-integrated, serious 
doubts can be cast on the causal interpretation of the Phillips Curve, especially on 
the regression explaining wage rate changes by the help of the unemployment rate 
(among other factors). As a matter of fact, the Augmented Dickey Fuller-test indicates 
stationarity for the wage rate changes and non-stationarity for the unemployment rate 
(Table 1). This fact and the high rate of autocorrelation and multicollinearity seem to 
be very good reasons to doubt the results reported by Quaas and Klein (2010).  This 
is a scepticism that could also be directed against many regression equations that 
are applied in many forecasting models of a country’s economy. Nevertheless, the 
argument should be taken seriously. 
 
In our view, the main point of the Phillips Curve is the hypothesis that there is a linear 
or curve linear inverse relationship between the changes of the wage rate and the 
unemployment rate – in the long run. If this is the case, both variables are necessarily 
different in nature with respect to stationarity. When unemployment rates are rising, 
the changes of the wage rate become smaller. By and large, this was the case in 
Germany until recently, but the picture of data points makes a judgement difficult 
(Figure 1). 
 
The following steps are undertaken to create a much clearer picture of the German 
Phillips Curve. 
 
 (i) We eliminated the effects of the German unification from the data by replacing the 
wage rate changes of 1990 by a moving average between 1989 (the old, smaller 
Germany) and 1991 (the united Germany).    5
 
(ii) We separated the long-term tendency from the cyclical component of the relevant 
time series by the help of the HP-filter.  
 
(iii) We regressed the long-term tendency separately from the cyclical component to 
see the different paths by which unemployment (UE) influences the change of the 
wage rate (WR_CH). 
 
The different curves are presented in Figure 2 and the results are reported in Table 1. 
 
 
 
Figure 2: Trend and Cycles of Wage Rate Changes (WR_CH) and of Unemployment 
Rate (UE). 
 
 
It turns out that the wage rate changes, and the inverse of the unemployment rate 
(taken in a simplified linear version) are both stationary and therefore co-integrated. 
In the long run, the lowering of wage-rate enhancements (changes) can be 
statistically explained by the rising unemployment rate.  
   6
 
Change of Wage Rates 
 
1 Total  2 Trend  3 Cycle 
  ADF 
Stats 
-2,46 
(-1,94) 
-3,35 
(-1,94) 
-6,16 
(-1,94) 
 -  -  Simple Best-Fit  Simple Best-Fit Simple Best-Fit 
Variable    \     Method    OLS ML OLS  ML OLS  OLS OLS OLS 
Unemployment Rate  0,10     
(-1,94) 
-0,92***
(-24,11)
-0,89 
(-24,11)
-0,60*** 
(-11,67) 
-0,58 
(-11,67) 
- -  - -  - -  - - 
Trend of  Unemployment 
Rate 
0,85     
(-1,94) 
  
    - -  - -  - -  - - 
A Constant minus Trend 
of Unemployment Rate, 
lagged 
-3,45     
(-1,94) 
  
   0,91***  
(47,43)
0,88***   
(44,84)   -  - 
Cyclical Component of 
Unemployment Rate 
-2,73     
(-1,94) 
  
   -  -   -0,52***   
(-10,89) 
-0,46***   
(-9,86) 
Inflation, lagged  -2,02 
(-1,94) 
  
0,30*** 
(3,75) 
0,22 
(3.75) 
     
Change of Import Prices, 
lagged 
-3,22 
(-1,94) 
  
-0,07** 
(-2,79) 
-0.13 
(-2.79) 
     
Change of Export Prices   -1,85     
(-1,94) 
  
0,17*** 
(4,35) 
0.18 
(4,35) 
- -  - -  - -  0,03***   
(5,19) 
Change of Productivity   -2,51     
(-1,94) 
  
0.31*** 
(5,04) 
0,20 
(5,04) 
- -  0,12***   
(3,84)    -0,02* 
(-2,30) 
Change of Profits  -4,41     
(-1,94) 
  
-0.04*** 
(-3,33) 
-0,13 
(-3,33) 
     
Adjusted R
2  - -  0,79  0,79  0,86  0,87 0,94 0,94  0,44  0,52 
Durbin-Watson Stats  - -  0,74  --  0,87  --  0,01  0,07 0,07 0,11 
Table 1: Estimation results for Wage Rate Changes, Trend and Cycles of Wage Rate 
Changes,  Maximum-Likelihood estimates are standardized.  
 
 
It could be argued that any falling (or rising) time series should also be capable of 
explaining the falling series of wage rate changes. Therefore, we put all theoretically 
relevant candidates of time series with a similar trend in the regression. It turned out 
that only the long-run tendency of the inflation rate is capable of replacing the 
unemployment rate as an explanation of wage rate changes. But this is no surprise,   7
because inflation has been considered a proxy of wage rate changes long before, 
namely since Samuelson and Solow (1960).  
 
 
Relevant determinants of wage rate changes 
 
A second result consists in another stable inverse (asymmetric) relationship between 
wage rate changes and the unemployment rate on the level of cyclical components of 
both time series. There is an exception of some years around the German unification, 
which does not fit into this scheme. Whereas in the regression of the long-term 
tendency, time lags can be introduced that correspond to the hypothesised causal 
order; time lags play almost no role in the explanation of the cyclical component. 
 
Quaas and Klein (2010) reported a best-fit regression that was capable of explaining 
clusters and loops of the German Phillips Curve. In Table 1 is reported which of the 
explaining variables plays a significant role on the level of the long-term tendency 
and on the level of the cyclical component. There is a short-term residuum (after 
subtracting the long-term tendency and the cyclical component) that cannot be 
explained by any of those variables. Interestingly, exactly this is the domain – the 
short run – where others hypothesise a relationship of the kind Phillips has proposed.      
 
In the best-fit regression, the single variable with the most (negative) influence is the 
unemployment rate. Although we include five other variables, the unemployment rate 
has kept its significant influence. This result could be an indication for a stable long-
run relationship between the unemployment rate and the changes of the nominal 
wages. The estimation results of the trend and the cyclical component confirm this 
observation, even though the cyclical component is not as well explained as the trend 
component. But this is in line with Phillips’ discovery of a long-term relationship. 
 
Besides the unemployment rate, the rate of change of labour productivity seems to 
be a further important variable for the wage-setting process. This variable keeps its 
significance in the equation of the cyclical and the trend component, while others lose 
their relevance (for example the inflation rate). 
   
In economic literature, 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   8
causes an increase of wages of about 0.30 about one year later. But inflation does 
not play a role in the determination of the trend or the cyclical component of the rate 
of change of wage rates.  
 
A variable that is important not only for wage changes in total but also for its cyclical 
component is the change of export prices. It reflects the special conditions of an open 
economy like the German one. The positive sign sounds plausible with the following 
background: A short-term change in export prices does not reduce immediately the 
quantity of exports, but enhances the revenue. This also seems to be profitable for 
employees. 
 
We also tested the influence of import prices, or more precisely, a one year lag of it. 
Because import prices have an influence on living cost, this information is already 
included in the inflation index, the interpretation of this channel is as follows: Higher 
import prices mean higher production costs for firms, and this reduces the leverage 
for higher wages. But the import prices have no significant influence on the trend or 
cyclical regression equations.  
 
The same is true for the influence of profit changes on wages. Profits have a 
significant negative influence on wage changes in total, but this does not hold for the 
trend or the cyclical component.    
 
In summary, the two variables that are significant in the explanation of the trend 
component of the wage changes are the (inverse of the) unemployment rate and the 
rate of change of productivity. For the cyclical component, it is the unemployment 
rate, the change of productivity and the rate of change of the export prices that are 
statistically significant.  
 
In Table 2, we put the variables in an order according to the standardized parameter 
values they received in the estimation of the best-fit equation. For instance, the single 
variable with the highest influence after unemployment was productivity.  
 
As can be seen in Table 2, there are only minor changes of the estimates based on 
standardised variables, and consequently only minor changes on the rank order of 
the variables compared to Quaas and Klein (2010).   9
 
Rank order  Quaas / Klein 2010 study  Present study 
1 Unemployment  Unemployment 
2 Productivity  Inflation 
3 Inflation  Productivity 
4  changes of export prices  changes of export prices 
5  changes of import prices  changes of import prices 
6  changes of profit  changes of profit 
Table 2: Corrected ranking of the variables according to their influence. 
 
 
Conclusion 
 
The problem of multicollinearity is reduced (Intriligator 1978, 267-268) when fewer 
variables are used in a regression. This reduction is necessary when trend and 
cyclical component of the Phillips Curve are explained separately. It turns out that 
this does not affect the decisive role the unemployment rate plays in the explanation 
of wage rate changes. Admittedly, autocorrelation is very high in the regressions on 
the level of the trend and of the cyclical component. Therefore, t-statistics may be 
misleading. As we said in the introduction, we cannot exclude that the reported best 
fit regression is spurious, but the allegedly missing co-integration of wage rate 
changes and unemployment rate is not a valid argument to sustain this scepticism.    
 
 
 
   10
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The Phillips curve in Australia,

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Is the Phillips Curve of Germany Spurious?

Is the Phillips Curve of Germany Spurious?

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