The link between unemployment and real economic growth in Spain

 

 

In our previous post, we revisited and validated the modified Okun’s law for Austria with new GDP and unemployment data for the years between 2010 and 2019. The revised model for Austria and other countries presented so far in this blog accurately describe the new data, i.e. the original model is validated. In order to reach the best fit between the measured and predicted unemployment rates, we introduce structural breaks related to the change in real GDP definition. To illustrate the breaks in the real GDP data (i.e. nominal GDP corrected for the price change) we compare price inflation estimates as defined by the GDP deflator and CPI. The latter is considered as a reference. It is also important that the goods and services in the CPI are also included in the GDP deflator, dGDP. In the past, the CPI and dGDP were almost equivalent and the deviation between them was forced by the introduction of such economic parameters as imputed rent in the 1970s. The experiments with the GDP deflator and nominal have been the essence of definitional activity ever since. The best is an enemy of good. Artificial breaks in the GDP and other economic variables make the work of researches very difficult.  

In this post, we revise the model for Spain and begin with the CPI and GDP deflator difference, which is used to reveal potential definitional breaks in the dGDP estimates. Obviously, such breaks in the dGDP create breaks in the real GDP per capita estimates, and thus, in the statistical estimates associated with our model. One has to find potential breaks and allow the model to compensate for corresponding disturbances and to provide unbiased statistical estimates of the defining parameters. There is another strong instrument in econometrics – dummy variables, which can explain the steps in many economic variables like labor force and unemployment. We do not use dummy variables in the model and achieve the best fit only with the structural breaks, i.e. the change in the coefficients of linear regression in the years of definitional revisions to the GDP deflator and nominal GDP. In that sense, our model becomes piecewise in order to match the changes in definition. It is like changing the speed from 105 km/h to 55 mph crossing the Canada/USA border, with physical speed not changing. 

In the upper panel of Figure 1, we present the evolution of the cumulative inflation (the sum of annual inflation estimates) as defined by the CPI and dGDP between 1970 and 2018 (the OECD data). Both variables are normalized to their respective values in 1970. The dGDP curve is close to the CPI before 1995 and then a significant deviation is observed. There is a low amplitude deviation between 1980 and 1990. After 1996, the deviation increases in amplitude, and the dGDP is first above the CPI curve and then dives below the CPI line in 2012.   In the middle panel, the rates of price inflation are shown for both indices. In the lower panel, we present the difference between the CPI and the dGDP cumulative inflation curves in the upper and middle panels. One can suggest the presence of breaks in 1979, 1985, 1995, 2007, and 2014. This is for the model to decide, however, when the breaks result in the bets LSQR fit.

      

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 curves in the upper and middle panels. One can observe the breaks in the difference between the cumulative curves. We suggest potential breaks in 1979, 1985, 1995, 2007, and 2014.  

In a modified model for Spain, we are looking for breaks near the years presented in Figure 1 and obtain the following intervals and coefficients:

 

du_p = -0.40dlnG + 2.11,  1995>t≥1970

du_p = -0.95dlnG + 2.03,  1996≥t≥2013                              

du_p = -0.50dlnG  - 2.10,            t≥2014     (1) 

where du_p – one-year change in the (OECD) the unemployment rate, G – real GDP per capita (2011 prices). The break years in Figure 2 are close to those estimated from the inflation curves in Figure 1, but not all potential breaks are used. The overall fit shown in the upper panel is excellent, as confirmed by the residual errors in the middle panel and the regression (Rsq=0.96) of the predicted and measured employment between 1973 and 2018. We retain in mind that the estimates of the unemployment rate are obtained in the surveys. The unemployment values are also corrected in the revisions to the unemployment definition. 

Considering the fall in real GDP growth caused by the COVI-19 pandemic one could expect that the rate of unemployment in Spain may increase according to equation (1) and probably will stay at an elevated level. Coefficient -0.5 in (1) predicts that a 1% decrease in real GDP per capita is converted to a 0.5% increase in the rate of unemployment. For Spain with its extremely high historical unemployment rate, this is a big problem.  

Figure 2. Upper panel: The measured rate of unemployment in Spain between 1970 and 2018, and the rate predicted by model (1) with the real GDP per capita published by the MPD and the unemployment rate reported by the OECD. Middle panel: The model residual: stdev=1.3%. Lower panel: Linear regression of the measured and predicted time series. Rsq. = 0.96.