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 Canada. As expected, the change in the rate of unemployment is more volatile. We have retrieved all data on unemployment and employment from the U.S. Bureau of Labor Statistics.
Figure 1. The (negative) change in the rate of employment compared to the change in the rate of unemployment in Canada.
In one our previous posts we have estimated Okun’s law for Canada. It is instructive to estimate a model similar to Okun’s law for the employment/population ratio, e. For Canada, the best-fit model has been obtained by the least-squares (applied to the cumulative sums):
det = 0.40dlnGt – 0.70, t<1984
det = 0.56dlnGt – 0.76, t>1983 (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 1984 which is expressed by a significant shift in slope and a minor change in intercept. The employment/population ratio varies between from ~54.5% in 1971 and ~64.1% (!) in 2008. The agreement is very good. Figure 3 present results of a linear regression with R2=0.84 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.