Uniform Inference in Linear Panel Data Models with Two-Dimensional Heterogeneity

This paper studies uniform inference in a linear panel data model when the slope coefficients may exhibit heterogeneity over both the individual and time dimensions and they can be correlated with the regressors. We propose a generalized two-way fixed effects (GTWFE) estimation procedure to estimate the model. To establish the asymptotic properties of the GTWFE estimators, we invert a number of large dimensional square matrices by approximating them with quasi-Kronecker structured matrices. We establish the asymptotic normality of our GTWFE estimators and show that their convergence rates depend on the unknown degree of parameter heterogeneity. To make a uniform inference on the common slope component, we propose a novel triple-bootstrap procedure to estimate the asymptotic variance. Simulations show the superb performance of our estimators and inference procedure. We apply our method to study the relationship between savings and investments, and find significant parameter heterogeneity along both the individual and time dimensions