  We argue that models coming from a variety of fields, such as matching models
and discrete choice models among others, share a common structure that we call
matching function equilibria with partial assignment. This structure includes
an aggregate matching function and a system of nonlinear equations. We provide
a proof of existence and uniqueness of an equilibrium and propose an efficient
algorithm to compute it. For a subclass of matching models, we also develop a
new parameter-free approach for constructing the counterfactual matching
equilibrium. It has the advantage of not requiring parametric estimation when
computing counterfactuals. We use our procedure to analyze the impact of the
elimination of the Social Security Student Benefit Program in 1982 on the
marriage market in the United States. We estimate several candidate models from
our general class of matching functions and select the best fitting model using
information based criterion.
