Abstract

How are workers matched to firms when their skills are multidimensional, firms
a) differ in how they value each skill dimension in their production technology
as well as in their productivity; b) aggregate their workers’ skills to produce;
c) and optimally choose their size? When workers’ skills cannot be unpacked
and sold separately on skill-specific markets, the implicit price of each skill can
vary across firms and firms’ size is increasing in productivity. The equilibrium
wage function is shown to be log-additive in worker quality and a firm-specific
effect that reflects the firm’s aggregate skill-mix and equilibrium matching. When
individuals choose the amount of skills supplied to their firms or when skills can
be unpacked and purchased on markets (at a cost, thanks to new technologies
or increased outsourcing), firms reinforce their hires of skills in which they have
a comparative advantage yielding a more polarized matching equilibrium and a
flattened wage schedule. Generalist workers – endowed with a balanced set of
skills – are shown to benefit whereas specialists are negatively affected by markets
opening. We extensively discuss how skilled-biased technical change affects the
equilibrium outcomes. We also examine the empirical content of our theory.