In a static frictionless transferable utilities bilateral matching market
with systematic and idiosyncratic payo§s, supermodularity of the
match output function implies a strong form of positive assortative
matching: The equilibrium matching distribution has all positive local
log odd ratios or totally positive of order 2 (T P2). A particular
form of a preference for own type implies supermodularity of the
match output function. Other forms imply non-T P2 behavior. Local
odds ratios are not informative on whether a bilateral matching
market equilibrates with or without transfers. Using white married
couples in their thirties from the US 2000 census, spousal educational
matching obeyed T P2 except for less than 0.2% of marriages with
extreme spousal educational disparities. Using the T P2 order, there
were more positive assortative matching by couples living in SMSAís
than those who do not; but not more positive assortative matching in
2000 than in 1970. There were increases in speciÖc local log odds over
that period