Recovering Latent Variables by Matching

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. for this article are available online.

Automated summary

We propose an optimal-transport-based matching method to nonparametrically estimate linear models with independent latent variables. The method generates pseudo-observations from the latent variables and minimizes the Euclidean distance between the model's predictions and their matched counterparts in the data. Through analyzing panel data, we find that the dispersion of income shocks is approximately acyclical, whereas the skewness of permanent shocks is procyclical. Comparatively, the dispersion and skewness of shocks to hourly wages show little variation with the business cycle.