u(t) = u(t0) + bln[G/G0] + a(t-t0) (1)
where u(t) is the rate of unemployment at time t, G is the level of real GDP per capita, a and b are empirical coefficients.
For Spain, we have a model estimated by a simple eye-fit. Here we re-estimate the model with a structural break somewhere between 1980 and 2000. The best-fit (dynamic) model minimizing the RMS error of the cumulative model (1) is as follows:
du = -0.406dlnG + 2.00, t<1995
du = -1.11dlnG + 1.54, t>1994 (2)
This model suggests a big shift in the slope and a smaller change in the intercept around 1995. Figure 1 depicts the observed and predicted curves. The agreement is very good, especially after 1995.
The cumulative form of the dynamic Okun’s law is characterized by standard error of 1.71% for the period between 1971 and 2010 (0.96% after 1995). The average rate of unemployment for the same period is 13.6% (14.6% after 1995) with a standard deviation of the annual increment of 2.12%.