The modified Okun's law for France. Model validation with Rsq=0.98

 In the upper panel of Figure 1, we present the evolution of the cumulative inflation (the sum of annual inflation estimates) in France. There are two curves as defined by the CPI and dGDP between 1955 and 2018. Both variables are normalized to their respective values in 1955. Since 1985, the dGDP curve is above the CPI one and this configuration we interpret as economic underperformance. Also, we reported in this post that France has very low annual increment of the real GDP per capita. This effect is likely related to the EU financial rules. In the past, France and other European countries with underperforming economics forced price inflation in order to make exports more attractive due to lowering the exchange rate. 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 (e.g., imputed rent). 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 1955 and 2018. Both variables are normalized to their respective values in 1961.  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 in the previous posts, we minimize the model residuals, i.e. determine the break years together with the regression coefficients. For France, the best fit model between 1962 and 2018 is as follows: 

du_p = -0.134dlnG + 0.750, 1962>t≥1984

du_p = -0.255dlnG + 0.620,  1985≥t≥1999     

du_p = -0.520dlnG + 0.355,            t≥2000     (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.=0.98) is more when excellent with the break years close to those expected from Figure 1. One of the possible reasons is that France has a good set of methods and procedures to measure/estimate economic parameters. This approach does not avoid data incompatibility problems, however, and statistical analysis needs extra efforts to distinguish between actual economic structural breaks and ignorance of basic procedures. The importance of data quality is best illustrated by an example in Figures 3 and 4, where two GDP per capita estimates from the OECD and MPD are compared. One can see that these two agencies provide quite different estimates. The use of the MPD estimates would change the statistical model. We do not know whose estimates are more accurate, but the OECD time series gives excellent results.

  

Figure 2. Upper panel: The measured rate of unemployment in France between 1960 and 2018, and the rate predicted by model (1) with the real GDP per capita and the unemployment rate published by the OECD. Middle panel: The model residual: stdev=0.50%. Lower panel: Linear regression of the measured and predicted time series. Rsq. = 0.98. 

Figure 3. Comparison of the real GDP per capita estimates reported by the OECD and Maddison Project Database. Both time series are normalized to their respective levels in 1960. 

Figure 4. The ratio of the OECD and MPD real GDP per capita estimates between 1960 and 2018.