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We develop a frictionless matching model under transferable utility where individualsare characterized by a continuous trait and a binary attribute. The model incorporatesattributes for which there are heterogeneous preferences in the population regarding theirdesirability, that is, the impact of the traits cannot be summarized by a one-dimensionalattractiveness index. We present a general resolution strategy based on optimal controltheory, and characterize the stable matching. We then consider education and smokingstatus, further specify the model by observing that there are more male than femalesmokers above each education level, and derive additional predictions about equilibriummatching patterns and how individuals with di§erent smoking habits ìmarry downî orìmarry upî by education. Using the CPS March and Tobacco Use Supplements for theperiod 1996 to 2003, we Önd that the hypotheses based on our model predictions are borneout in the data

Bidimensional Matching with Heterogeneous Preferences: Education and Smoking in the Marriage Market