4.6 Article

Recovering Latent Variables by Matching

Journal

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume 118, Issue 541, Pages 693-706

Publisher

TAYLOR & FRANCIS INC
DOI: 10.1080/01621459.2021.1952877

Keywords

Factor models; Income dynamics; Latent variables; Matching; Nonparametric estimation; Optimal transport

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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.
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.

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