Bidimensional Matching with Heterogeneous Preferences: Smoking in the Marriage Market

We develop a bidimensional matching model under transferable utility, where individuals are characterized by a continuous trait (e.g., socioeconomic status) and a binary attribute (e.g., smoking status).  The model is "truly multidimensional", in the sense that the impact of the traits cannot be summarized by a one-dimensional index.  We present a general resolution strategy based on optimal control theory, and characterize the stable matching.  We derive testable predictions about equilibrium matching patterns.  Using US data, we find that the observed marital sorting of smokers and non-smokers by education is consistent with our model.