  We propose an optimal-transport-based matching method to nonparametrically
estimate linear models with independent latent variables. The method consists
in generating pseudo-observations from the latent variables, so that the
Euclidean distance between the model's predictions and their matched
counterparts in the data is minimized. We show that our nonparametric estimator
is consistent, and we document that it performs well in simulated data. We
apply this method to study the cyclicality of permanent and transitory income
shocks in the Panel Study of Income Dynamics. We find that the dispersion of
income shocks is approximately acyclical, whereas the skewness of permanent
shocks is procyclical. By comparison, we find that the dispersion and skewness
of shocks to hourly wages vary little with the business cycle.
