Recovering Latent Variables by Matching

TL;DR

This paper introduces an optimal-transport-based matching method for nonparametric estimation of linear models with latent variables, demonstrating consistency and practical effectiveness through simulations and real data analysis.

Contribution

It presents a novel nonparametric estimator using optimal transport to recover latent variables, with theoretical consistency and empirical validation.

Findings

Dispersion of income shocks is approximately acyclical.

Skewness of permanent income shocks is procyclical.

Wage shocks show little variation with the business cycle.

Abstract

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.