  This paper proposes empirically tractable multidimensional matching models,
focusing on worker-job matching. We generalize the parametric model proposed by
Lindenlaub (2017), which relies on the assumption of joint normality of
observed characteristics of workers and jobs. In our paper, we allow
unrestricted distributions of characteristics and show identification of the
production technology, and equilibrium wage and matching functions using tools
from optimal transport theory. Given identification, we propose efficient,
consistent, asymptotically normal sieve estimators. We revisit Lindenlaub's
empirical application and show that, between 1990 and 2010, the U.S. economy
experienced much larger technological progress favoring cognitive abilities
than the original findings suggest. Furthermore, our flexible model
specifications provide a significantly better fit for patterns in the evolution
of wage inequality.
