The Okun's integral law for Australia revisited

Three and a half years ago, I reported that Australia gives the best example of accurate quantitative prediction of unemployment in developed countries and therefore I felt satisfaction. Historically, we published a paper on Okun's in developed countries in the Journal of Theoretical and Practical Research in Economic Fields in 2012. We presented the first version of the modified Okun’s law for developed countries including Australia. The model was estimated before 2010 and we used only data available in 2011. Briefly, the model is estimated by the LSQ technique applied to the integral version of Okun’s law:
u(t) = u(t0) + bln[G/G0] + a(t-t0)   (1)
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. Essentially, our model says that the current level of unemployment is the integral effect of the historical growth in GDP per capita. Then the change in unemployment, du, is proportional to the growth rate in GDP per capita, whcih can be expressed as dlnG. This is the differential (dynamic) form of the Okun's law.
For Australia, we estimated an integral model with one structural break allowed by data somewhere between 1980 and 2000. The best-fit (dynamic) model minimizing the RMS error of the cumulative model (1) with the new data revision is as follows:
du = -0.69dlnG + 1.50, t before 1991
du = -0.45dlnG + 0.75, t after 1991 (2)

This is an update with new data for the years between 2012 and 2016 obtained from:  real GDP (GK per capita)  from the Total Economic Database, and the rate of unemployment from the OECD

Figure 1 depicts the observed and predicted curves of the unemployment rate. Statistically, the agreement is better than three years ago, when it was excellent. Figure 2 shows that when the observed time series is regressed against the predicted one, R2=0.88 (0.86 in 2013 and 0.84 in 2011).  The integral form of the dynamic Okun’s law (1) is characterized by a standard error of 0.7% for the period between 1975 and 2016. The average rate of unemployment for the same period is 7.0% with a standard deviation of the annual increment of 1.4%.  This is an extremely accurate prediction considering the accuracy of GDP (~1% per year) and unemployment (0.3% to 0.4%) estimates. The whole discrepancy is related to the measurement errors and thus the residual error shown in Figure 3 is an I(0) random process. 
The rate of unemployment depends on the cumulative change in real GDP per capita, as relationship (1) implies. To reduce the rate of unemployment in Australia, the rate of GDP (real per capita) growth must be above 1.7% per year.

I have to repeat it again and again. 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 exiting when this concept is different from the mainstream one. 

Figure 1. The observed and predicted rate of unemployment in Australia between 1975 and 2015. The regression line is red.

Figure 2. The measured time series is regressed against the predicted one. R2=0.88 with both time series likely to be stationary.

Figure 3. The residual error of the unemployment model. 

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