Validation of the modified Okun's law for Germany

In the upper panel of  figure 1, we present the evolution of the cumulative inflation (the sum of annual inflation estimates) in Germany. There are two curves as defined by the CPI and dGDP between 1970 and 2018. Both variables are normalized to their respective values in 1970. Since 1996, the dGDP curve is above the CPI one and this configuration we interpret as economic super-performance. This effect is likely related to the EU financial rules with the ECB in Frankfurt. In the past, Germany has weaker performance and the EU leadership made it a super-economy. In the middle panel, the inflation rates are shown for both variables. In the lower panel, we present the difference between the CPI and dGDP curves in the upper and middle panels. One can see that the difference between the cumulative curves has several quasi-linear segments. The change in the slope between these segments in most likely related to the multiple revision to the dGDP definition. We have already used this observation of the segmented character of the real GDP estimates in order to assess our Okun’s-law-like model of the link between the change in unemployment and the change in real GDP per capita. The years of breaks in the dGDP time series are not easy to estimate from the lower panel of Figure 1 and we allow the LSQR method to find these years when minimizing the RMS residuals.

  

Figure 1. Upper panel: The evolution of the cumulative inflation (the sum of annual inflation estimates) as defined by the CPI and dGDP between 1970 and 2018. Both variables are normalized to their respective values in 1970.  Middle panel: The dGDP and CPI inflation estimates. Lower panel: The difference between the CPI and dGDP curves in the upper and middle panels.    

 

As for other countries, we minimize the model residuals, i.e. determine the break years together with the regression coefficients. For Germany, the best fit model between 1971 and 2018 is as follows:

           du_p = -0.42dlnG + 1.50, 1970>t≥1984

du_p = -0.555dlnG + 0.700,  1985≥t≥1992

du_p = -0.450dlnG + 1.300,  1993≥t≥2006

du_p = -0.450dlnG + 0.400,            t≥2007     (1)

where du_p – one-year change in the (OECD) the unemployment rate, G – real GDP per capita (2011 prices). The break years are determined automatically. Figure 2 presents the measured and predicted rate of unemployment (upper panel), the model residual error (middle panel), and the regression of the measured and predicted time series. The overall fit (Rsq.=0.88) is more when excellent with the break years close to those expected from Figure 1. One of the largest model errors in the residual time series was observed in 1990. This is most likely related to the reunification and merging of two time series belonging to different economies. When this spike is excluded, the standard deviation falls from 0.99% to 0.76%, and Rsq increases from 0.88 to 0.92. 

 The modified Okun’s law linking the change in the unemployment rate and the change in the real GDP per capita is validated by new data for Germany for the period between 2010 and 2019.

  

Figure 2. Upper panel: The measured rate of unemployment in Germany between 1970 and 2018, and the rate predicted by model (1) with the real GDP per capita and the unemployment rate published by the MPD. Middle panel: The model residual: stdev=0.99%. When the 1991 reading is excluded, stdev=0.76%.  Lower panel: Linear regression of the measured and predicted time series. Rsq. = 0.88.