We show, theoretically and empirically, that the effects of technological change associated with automation and offshoring on the labor market can substantially deviate from standard neoclassical conclusions when search frictions hinder efficient assortative matching between firms with heterogeneous tasks and workers with heterogeneous skills. Our key hypothesis is that better matches enjoy a comparative advantage in exploiting automation and a comparative disadvantage in exploiting offshoring. It implies that automation (offshoring) may reduce (raise) employment by lengthening (shortening) unemployment duration due to higher (lower) match selectivity. We find empirical support for this implication in a dataset covering 92 occupations and 16 sectors in 13 European countries from 1995 to 2010.