Adaptability, productivity, and educational incentives in a matching model

We study the connections between the labour market and the education sector in a matching framework with ex-post wage bargaining. Workers have multidimensional skills and the search market is segmented by technology. Education is a time-consuming activity and determines jointly the scope - or adaptability - and intensity - or productivity - of individual skills. We establish three main results. First, unemployment provides incentives to schooling by raising the need for adaptability. Second, private returns to productivity are below social returns, but no hold-up phenomenon is involved. Third, due to wage and congestion externalities, private returns to adaptability exceed social returns. As a consequence, both over- and under-education may take place in equilibrium.