We study a matching model with heterogeneous agents, nontransferable utility and search frictions. Agents differ along a horizontal dimension (e.g. taste) and a vertical dimension (e.g. income). Agents' preferences coincide only in the vertical dimension. This approach introduces individual preferences in this literature as seems suitable in applications like labor markets (e.g. regional preferences). We analyze how the notion of assortativeness generalizes to integration or segregation outcomes depending on search frictions. Contrary to results from the purely vertical analysis, here, agents continuously adjust their reservation utility strategies to changing search frictions. The model is easily generalizable in the utility specification, the distribution of taste-related payoffs and the number of vertical types. Extreme utility specifications can be treated as a case of horizontal heterogeneity only.
matching horizontal differentiation marriage markets