||This paper considers nonparametric identification and estimation of a generalized
Roy model that includes a non-pecuniary component of utility associated with each
choice alternative. Previous work has found that, without parametric restrictions
or the availability of covariates, all of the useful content of a cross-sectional
dataset is absorbed in a restrictive specification of Roy sorting behavior that imposes
independence on wage draws. While this is true, we demonstrate that it is also possible
to identify (under relatively innocuous assumptions and without the use of covariates)
a common nonpecuniary component of utility associated with each choice alternative.
We develop nonparametric estimators corresponding to two alternative assumptions under
which we prove identification, derive asymptotic properties, and illustrate small
sample properties with a series of Monte Carlo experiments. We demonstrate the usefulness
of one of these estimators with an empirical application. Micro data from the 2000
Census are used to calculate the returns to a college education. If high-school and
college graduates face different costs of migration, this would be reflected in different
degrees of Roy-sorting-induced bias in their observed wage distributions. Correcting
for this bias, the observed returns to a college degree are cut in half.