Inference for Large Panel Data with Many Covariates

TL;DR

This paper introduces Panel-PoSI, a new method for covariate selection and inference in large panel data with many covariates, controlling false discoveries and improving power over existing methods.

Contribution

It develops a novel inference procedure combining post-selection inference with multiple testing adjustments tailored for large panel datasets with many covariates.

Findings

Panel-PoSI controls family-wise error rates effectively.

The method outperforms benchmarks in out-of-sample asset pricing tests.

It identifies a small set of relevant factors explaining investment strategies.

Abstract

This paper proposes a novel testing procedure for selecting a sparse set of covariates that explains a large dimensional panel. Our selection method provides correct false detection control while having higher power than existing approaches. We develop the inferential theory for large panels with many covariates by combining post-selection inference with a novel multiple testing adjustment. Our data-driven hypotheses are conditional on the sparse covariate selection. We control for family-wise error rates for covariate discovery for large cross-sections. As an easy-to-use and practically relevant procedure, we propose Panel-PoSI, which combines the data-driven adjustment for panel multiple testing with valid post-selection p-values of 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.