  The problem of demand inversion - a crucial step in the estimation of random
utility discrete-choice models - is equivalent to the determination of stable
outcomes in two-sided matching models. This equivalence applies to random
utility models that are not necessarily additive, smooth, nor even invertible.
Based on this equivalence, algorithms for the determination of stable matchings
provide effective computational methods for estimating these models. For
non-invertible models, the identified set of utility vectors is a lattice, and
the matching algorithms recover sharp upper and lower bounds on the utilities.
Our matching approach facilitates estimation of models that were previously
difficult to estimate, such as the pure characteristics model. An empirical
application to voting data from the 1999 European Parliament elections
illustrates the good performance of our matching-based demand inversion
algorithms in practice.
