  We investigate in this paper the theory and econometrics of optimal matchings
with competing criteria. The surplus from a marriage match, for instance, may
depend both on the incomes and on the educations of the partners, as well as on
characteristics that the analyst does not observe. Even if the surplus is
complementary in incomes, and complementary in educations, imperfect
correlation between income and education at the individual level implies that
the social optimum must trade off matching on incomes and matching on
educations. Given a flexible specification of the surplus function, we
characterize under mild assumptions the properties of the set of feasible
matchings and of the socially optimal matching. Then we show how data on the
covariation of the types of the partners in observed matches can be used to
test that the observed matches are socially optimal for this specification, and
to estimate the parameters that define social preferences over matches.
