We have estimated a version of Okun’s law for the USA, France, Spain, Canada, Australia and the UK. We have applied a LSQ technique 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 Germany, 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 = -0.32dlnG + 1.19, t<1985
du = -0.43dlnG + 0.81, t≥1985 (2)
This model suggests a significant increase in slope and a big fall in intercept around 1985.
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, except the years between 2007 and 2009. The deviation is extremely high and unexpected. During the 2008/2009 recession, the rate of unemployment in Germany was decreasing what contradicts Okun’s law. Our model linking the rate of unemployment to the change in labor force has accurately predicted the observed fall in the unemployment rate.
Figure 2 shows that when the observed time series is regressed against the predicted one, R2=0.86. 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 0.57% for the period between 1971 and 2007 (2008 and 2009 excluded). The average rate of unemployment for the same period is 6.5% with a standard deviation of the annual increment of 0.83%.
Figure 2. The measured time series is regressed against the predicted one. R2=0.86 with both time series likely to be stationary.