We continue modeling the evolution of the employment rate in developed countries with Japan. In this study we use the trade-off between the change in unemployment and employment and Okun’s law. Figure 1 compares the change in the rate of employment (the employment/population ratio), de, and the rate of unemployment, du, in Japan. The change in the rate of unemployment is as volatile as that of unemployment and they differ drastically compared to the synchronized evolution of these variables in the U.S. That’s why we have failed to obtain a reasonable Okun’s law for Japan. As before, all data sets on unemployment and employment have been retrieved from the U.S. Bureau of Labor Statistics. The estimates of real GDP per capita have been retrieved from the database provided by the Conference Board.

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

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 Japan similar to Okun’s law. For Japan, the best-fit model has been obtained by the least-squares (applied to the cumulative sums):

det = 0.02dlnGt – 0.53, t<1978

det = 0.14dlnGt – 0.42, t>1977 (1)

where dlnGt 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 1978 which is expressed by a dramatic shift in slope and a slight break in intercept. The employment/population ratio varies between from 64%% in 1970 and 56% in 2010. The agreement is excellent. Figure 3 present results of a linear regression with R2=0.95 for the period between 1971 and 2010. We consider both variables as stationary ones over the long run despite the obviously negative trend since 1970.

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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