Abstract:

Observable scalar rankings are widely used to compress complex information and guide allocation decisions, yet are often treated as portable summaries of behavior across environments. This paper evaluates the transportability of such rankings from search behavior to equilibrium matching and downstream outcomes. Using a randomized online-dating experiment that independently varies male height and income, we identify search-stage substitution patterns and construct behaviorally disciplined rankings separately by female height group, reflecting heterogeneity in substitution patterns across groups, and transport these group-specific rankings to nationally representative marriage data from the China Family Panel Studies (CFPS). We document four departures from commonly imposed scalar-index restrictions. First, substitution patterns vary across agents, rejecting a common ranking even within search. Second, a behaviorally identified one-sided ranking does not preserve equivalence of types in observed equilibrium matching: conditioning on the transported index fails to eliminate residual assortative sorting. Third, observed equilibrium allocation does not preserve the directional relationships implied by search-stage substitution patterns: while search implies compensating trade-offs between height and income, equilibrium sorting exhibits a positive height–income relationship, reflecting sorting on correlated characteristics. Fourth, additively separable outcome representations are rejected: the marginal effect of husband height on household income depends on wife height. These results show that behaviorally identified scalar rankings need not provide portable summaries across environments. Their ability to organize observed allocation is heterogeneous across groups and dimensions, and the relationships implied by search-stage substitution patterns may not be preserved when transported.