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 the United Kingdom, we have estimated a similar model with a structural break somewhere between 1980 and 1990. The best-fit (dynamic) model minimizing the RMS error of the cumulative model (1) is as follows:
du = -0.63dlnG + 1.75, t<1988
du = -0.39dlnG + 0.63, t>1987 (2)
This model suggests a significant drop in slope and a big change in the intercept around 1988. (All coefficients are close to those for Australia.)
Figure 1 depicts the observed and predicted curves of the unemployment rate, the latter is predicted by (1) with coefficients from (2). The agreement is very good. Figure 2 shows that when the observed time series is regressed against the predicted one, R2=0.90. 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.
The integral form of the dynamic Okun’s law (1) is characterized by a standard error of 0.85% for the period between 1971 and 2010. The average rate of unemployment for the same period is 6.9% with a standard deviation of the annual increment of 1.07%.
One can suggest that the rate of unemployment has been driven by real economic growth and there is no room for structural unemployment. The will be no decease in the rate of unemployment if the growth rate of real GDP per growth does not exceed (0.63/0.39=) 1.63% per year.
Figure 1. The observed and predicted rate of unemployment in the UK between 1971 and 2010.
Figure 2. The measured time series is regressed against the predicted one. R2=0.90 with both time series likely to be stationary.