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)
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.