Lecture 5: Estimation of a One-to-One Transferable Utility Matching Model

Consider a single matching market composed of two large populations of, for concreteness, women and men. For each woman and man we respectively observe the discretely-valued characteristics Wi ∈ W = {w1,, . . . , wK} and X ∈ X = {x1, . . . , xL} .1 The K types of women and L types of men may encode, for example, different unique combinations of yearsof-schooling and age. While K and L are assumed finite, they may be very large in practice. Observationally identical women have heterogeneous preferences over different types of men, but are indifferent between men of the same type. Specifically female i’s utility from matching with male j is given by