There is a trade-off between the change in unemployment and employment. Figure 1 compares the change in the rate of employment (the employment/population ratio), de, and the rate of unemployment, du, in France. As expected, the change in the rate of unemployment is more volatile except the shift in the employment rate near 1982. This is a completely artificial break from 53.2% in 1981 to 55.3% in 1982, and we do not need to model it. All data sets on unemployment and employment have been retrieved from the U.S. Bureau of Labor Statistics.

Figure 1. The (negative) change in the rate of unemployment compared to the change in the rate of employment in France.

In this blog, we have already presented several empirical relationships predicting the employment/population ratio from the growth rate of real GDP per capita. This was a natural extension of Okun’s law for unemployment.

Here we estimate an employment/GDP model for France similar to Okun’s law. For France, the best-fit model has been obtained by the least-squares (applied to the cumulative sums):

de = 0.155dlnG– 0.65, t<1994

de= 0.25dlnG – 0.30, t>1993 (1)

where dlnG is the change rate of real GDP per capita at time t. Figure 2 shows the cumulative curves for the time series in (1). There is a structural break near 1994 which is expressed by significant shifts in slope and intercept. The employment/population ratio varies between from ~56%% in 1970 and 50.4% in 1992. The agreement is very good. Figure 3 present results of a linear regression with R2=0.91 for the period between 1971 and 2010.

Figure 2. The cumulative curves for the observed and predicted change in the employment/population ratio, de.

Figure 3. Linear regression of the measured and predicted curves in Figure 2.

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