Scanning for Significance: False Discovery Control for Impulse Responses

Impulse response analysis builds economic narratives by scanning a large set of coefficients for significant effects. Pointwise inference ignores this multiplicity, so the false rejection rate grows unbounded with the response family. Simultaneous inference bounds the probability of even a single false rejection, which yields increasingly uninformative results as the family expands. Researchers are left to choose between overstating their evidence and understating it. We propose false discovery and false coverage control as a more appropriate target: bounding the expected share of false rejections among responses declared significant, with calibrated post-selection confidence intervals. Neither guarantee deteriorates as the response family grows, so researchers are not penalized for investigating thoroughly. The procedure integrates into standard VAR and local projection bootstrap workflows. Applications show that this inference strategy recovers effects lost under simultaneous bands while discarding fragile pointwise findings, in some cases materially altering the economic narrative.