## 5/4/13

### The beauty of science II. Predicting the rate of unemployment in Australia

A few hours ago, I reported that Canada gives the best example of accurate quantitative prediction of unemployment in developed countries and therefore extreme satisfaction for a researcher. I changed my mind when revisited the case of Australia with new data - real GDP (GK per capita) data from the Total Economic Database and the rate of unemployment from the OECD. Two years ago, I presented a model based on data from the same sources and found relatively big discrepancy after 2000. In the new revision of the same data, this discrepancy have evaporated.

Historically, we published a paper 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 till 2010 and used the 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. For Australia, we estimated the model with a 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 1992

du = -0.45dlnG + 0.75, t after 1991 (2)

Originally, the model included the structural break neat 1995. With the new data the overall fit is better and the year of break moved to 1991, which is related to major revision of unemployment definition. The new model suggests a drop in slope and a big change in the intercept around 1991. Figure 1 depicts the observed and predicted curves of the unemployment rate. The agreement is very good. Figure 2 shows that when the observed time series is regressed against the predicted one, R2=0.86 (0.84 in 2011).  The integral form of the dynamic Okun’s law (1) is characterized by a standard error of 0.72% for the period between 1971 and 2012. The average rate of unemployment for the same period is 6.9% with a standard deviation of the annual increment of 1.9%.  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.

Figure 1. The observed and predicted rate of unemployment in Australia between 1971 and 2012.

Figure 2. The measured time series is regressed against the predicted one. R2=0.86 with both time series likely to be stationary.
Figure 3. The residual error of the unemployment model.

So, I have to repeat. 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.