Selective Multiple Testing: Inference for Large Panels with Many Covariates

Abstract

This paper proposes a novel testing procedure for covariate selection in large dimensional panels. Our procedure "selective multiple testing" adjusts for multiple testing in a panel with many units, where each unit can have test statistics for different covariates. Selective multiple testing provides correct false detection control while having higher power than existing approaches. We develop the inferential theory for a joint model where the covariates for each unit are selected with regularized estimators. We show how to control for family-wise error rates for data-driven hypotheses in large cross-sections. As an easy-to-use and practically relevant procedure, we combine selective multiple testing with a generalized LASSO, that allows us to incorporate priors. In an empirical study, we select a small number of asset pricing factors that explain a large cross-section of investment strategies. Our method dominates the benchmarks out-of-sample due to its better size and power. 

Keywords: panel data, high-dimensional data, LASSO, number of covariates, post-selection inference, multiple testing, adaptive hypothesis, step-down procedures, factor model

JEL Classification: C33, C38, C52, C55, G12