Our paper seeks to gain insights into the effect of labor market institutions on the dynamics of the labor market during the diffusion process of new technologies. We develop an endogenous job destruction matching framework, with heterogeneous workers, where the segmentation of the labor market between workers having the required ability to do a technological job and the rest of the workers is endogenous. We show that the dynamics of this segmentation may follow a monotonous decreasing path or a non monotonous U-shaped path depending on the unemployment benefit system. If benefits are generous, we are in the U-shaped case, and therefore workers that previously had access to technological positions may be excluded from them at a given moment of time. Furthermore, generous labor market institutions lead to more unemployment inequality between the various segments of the labor market and also increase aggregate job instability