The beauty of science is the accuracy of prediction. It is difficult to
express the feelings of a researcher than new observations fit his predictions
based on a simple concept. It is especially
sweet when this concept is different from the mainstream one. I am sure that
economists never feel like that with all models flawed. Here, I present one of
many cases of accurate predictions based on the link between GDP and unemployment,
which is a modified Okun’s law in an integral form.

Canada provides an excellent set of macroeconomic data which can be
described by a few deterministic links with a high level of reliability and
confidence. We have retrieved real GDP (GK per capita) data from the Total Economic
Database and the rate of unemployment from the OECD. In
2012, we published a paper in
the Journal of Theoretical
and Practical Research in Economic Fields, where presented the first
version of the modified Okun’s law for developed countries including Canada. The
model was estimated till 2010 and used the data available in 2011. The original
model for Canada was also presented in this blog in 2011.
It’s time to revisit the model and its predictions.

Overall, the model is estimated using the LSQ technique to the integral
version of Okun’s law:

where

*u(t) = u(t*[_{0}) + bln*G/G*]_{0}*+ a*(*t-t*) (1)_{0}where

*u(t)*is the predicted rate of unemployment at time*t*,*G*is the level of real GDP per capita,*a*and*b*are empirical coefficients. For Canada, we estimated the model with a structural break allowed by data somewhere between 1980 and 1990. The best-fit (dynamic) model minimizing the RMS error of the cumulative model (1) is as follows:*du =*-0.28

*dlnG +*1.16

*, t<*1983

*-0.28*

du =

du =

*dlnG +*0.30

*, t>*1982 (2)

This model suggests no shift in the slope and a bigger change in the intercept around 1983. Figure 1 depicts the observed and predicted curves of the unemployment rate. Considering the accuracy of measurements for both involved variable the fit is excellent. The integral form of the dynamic Okun’s law (1) is characterized by a standard error of 0.67% for the period between 1971 and 2012. The average rate of unemployment for the same period is 8.12% with a standard deviation of the annual increment of 0.92%. Figure 2 shows that when the observed time series is regressed against the predicted one, R

^{2}=0.87. Here we do not test both time series for stationarity but presume that the rate of unemployment has to be a stationary time series in the long run.

One can suggest that the rate of unemployment has been driven by real economic growth and there is no much room for other macroeconomic variable to intervene. Personally, I admire the performance of this simple model and will keep reporting on it for Canada, but also for Spain, France, etc.

Figure 1. The observed and predicted rate of unemployment in the Canada between 1970 and 2010.

Figure 2. The measured time series is regressed against the predicted one. R

^{2}=0.87 with both time series likely to be stationary.
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