Ridge Estimation of High Dimensional Two-Way Fixed Effect Regression

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.