In this paper, we question the stability of Okun's law, i.e. the empirical regularity that seems to hold between economic activity and unemployment. To this aim, we propose to build two complementary indicators of real rigidity, using the codependence methodology. The first one is a recursive estimation of Okun's coefficient, and the second one is a measure of persistence defined by the dimension of the dynamic structure. For the sample of OECD countries that we considered, it appears that only two of them (Italy and Belgium) present a high degree of such rigidities. The recursive analysis proves that all countries tend to be more flexible, confirming the movement towards more flexible labor markets. This analysis provides powerful tools for a better understanding of the dynamics within Okun's law.