Two
years ago we presented a parsimonious
model describing the evolution of employment/population ratio in Canada. In essence, this model is a modified Okun’s
law since there exists a trade-off between the change in unemployment and
employment. Yesterday,
we revisited the rate of unemployment in Canada based on a complimentary model
and found an extraordinary high fit between predicted and observed curves. (A
comprehensive description of both models also extended by examples in other
developed countries is presented in our paper “Modeling Unemployment And Employment In Advanced Economies: Okun’S Law
With A Structural Break”. )

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 slightly more volatile (also because of lower accuracy of measurements). 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.

Two
years ago we estimated several models of employment/population ratio,

*e*. For Canada, the best-fit model has been obtained by the least-squares (applied to the cumulative sums):*de*0.40

_{t}=*dlnG*0.67

_{t}–*, t<*1984

*de*0.44

_{t}=*dlnG*0.56

_{t}–*, t>*1983 (1)

where

*dlnG*is the change rate of real GDP per capita at time_{t}*t*. Figure 2 shows the cumulative curves for the time series in (1). We did not fix the initial value in 1971 and obtained it from the regression. There is a structural break near 1984 which is expressed by a slight shift in the slope of the regression line and a 0.11 change in the intercept term. Since the latter term is cumulated over years one can consider this change as a significant one. It makes a 1.1% employment change over 10 years. The break is needed because of the change to definitions and measurement procedures rather than actual break in the long-run link between*e*and*G*. In any case, functional dependence between these two variables stays untouched.
The
employment/population ratio varies between from ~54.5% in 1971 and ~64.1% (!) in
2008. The agreement between the actual and predicted curves in Figure 2 is excellent.
We added two readings for 2011 and 2012 which practically coincide. This observation
validates our original model and we will continue reporting on the evolution of
employment/population ratio in Canada.

Figure
3 present results of a linear regression with R

^{2}=0.88 for the period between 1971 and 2012. The standard error of the model is 0.82% which is chiefly related to the first ten years where measurements were rather crude.
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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