Multidimensional Matching with a Potential Handicap: Smoking in the Marriage Market

We develop a two-dimensional matching model on the marriage market, where individuals are characterized by a continuous trait (e.g., socioeconomic status) and a discrete attribute (e.g., smoking status), and gains from marriage may be diminished by the discrete characteristic. We show that a stable match always exists but may fail to be pure, and we derive some general properties. We then further specify the model by assuming a quadratic surplus function. In that case, the stable match can be fully characterized in closed form. The model generates clear-cut conditions regarding matching patterns. Using CPS data and its Tobacco Use Supplements for the years 1996 to 2007, and proxing socioeconomic status by educational attainment, we …nd that these conditions are satis…ed. There are fewer “mixed”couples where the wife smokes than vice-versa, and matching is assortative on education within smoking types of couples. Among non-smoking wives those with smoking husbands have on average 0.14 fewer years of completed education than those with non-smoking husbands. Finally, we …nd that among smoking husbands those who marry smoking wives have on average 0.16 more years of completed education than those with non-smoking wives. Keywords: Marriage market, multidimensional matching, smoking, education. JEL Codes: D1, J1. We thank Bernard Salanié and Marco Francesconi, as well as participants at the Barcelona MOVE Family Conference 2011, Royal Economic Society Meetings 2012, Columbia University, University of Aarhus, and Universidad Carlos III, for helpful comments and suggestions. Financial support from the NSF (award # SES-1124277) is gratefully acknowledged. Ore¢ ce and Quintana-Domeque acknowledge …nancial support from the Spanish Ministry of Science and Innovation (ECO 2011-29751). The usual disclaimers apply.