Ridge Estimation of High Dimensional Two-Way Fixed Effect Regression

TL;DR

This paper introduces a ridge estimator for high-dimensional two-way fixed effect models with sparse bipartite networks, demonstrating convergence properties and practical applicability through simulations and wage data analysis.

Contribution

It develops a novel ridge estimation method for high-dimensional fixed effects models with sparse bipartite networks, including theoretical convergence results.

Findings

Bias and variance-covariance matrix converge to deterministic equivalents

Ridge parameters increasing with log network size improve estimation

Application to wage data demonstrates practical utility

Abstract

We study a ridge estimator for the high-dimensional two-way fixed effect regression model with a sparse bipartite network. We develop concentration inequalities showing that when the ridge parameters increase as the log of the network size, the bias, and the variance-covariance matrix of the vector of estimated fixed effects converge to deterministic equivalents that depend only on the expected network. We provide simulations and an application using administrative data on wages for worker-firm matches.