  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.
