Recovering Latent Variables by Matching

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