This paper extends Pissarides (1990)'s matching model by considering two sectors (routine and manual) and workers' occupational choices, in the context of skill-biased demand shifts, to the detriment of routine jobs and in favour of manual jobs because of technological changes. The theoretical challenge is to investigate the reallocation process from the middle towards the bottom of the wage distribution. By using this framework, we shed light on the way in which labour market institutions affect the job polarization observed in the United States and Europe. The results of our quantitative experiments suggest that search frictions have non-trivial effects on the reallocation process and transitional dynamics of aggregate employment.