We consider a parametric version of the two-sided matching model described in Roth and Sotomayer (1990). We develop the model for the analysis of matching data, where the data consist of pairs of individuals, with one individual from each of two distinct populations (for example employers and employees, or men and women). Individuals agree to form pairs based on utilities they have for one another, resulting in a stable set of matches between the two populations. We assume these utilities are linear combinations of observed characteristics of the individuals, plus an error term, and our goal is to estimate the coefficients of this linear function. We have found estimation of the parameters in such a model to be feasible via Markov chain Monte Carlo techniques, and we are beginning to use these techniques for simulation studies and data analysis.
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