Low-Rank Approximations of Nonseparable Panel Models

TL;DR

This paper introduces estimation techniques for nonseparable panel models using low-rank matrix approximations, addressing computational challenges and bias correction, with applications to voter turnout analysis.

Contribution

It develops low-rank factor structure estimation methods for nonseparable panel models using matrix completion, including bias correction techniques.

Findings

Estimators are consistent in large panels.

Biases can be effectively corrected with matching and diff-in-diff methods.

Empirical application demonstrates practical usefulness.

Abstract

We provide estimation methods for nonseparable panel models based on low-rank factor structure approximations. The factor structures are estimated by matrix-completion methods to deal with the computational challenges of principal component analysis in the presence of missing data. We show that the resulting estimators are consistent in large panels, but suffer from approximation and shrinkage biases. We correct these biases using matching and difference-in-differences approaches. Numerical examples and an empirical application to the effect of election day registration on voter turnout in the U.S. illustrate the properties and usefulness of our methods.