We study whether the response of the economy to structural shocks changes at the zero lower bound. Monte Carlo evidence suggests that VARs have a limited ability to detect changes in impulse response functions at the ZLB compared to the standard environment with positive interest rates. This issue is confounded given the short sample lengths that characterize ZLB episodes. This is especially the case for timevarying parameter VARs, whose estimates are two-sided, and therefore tend to smooth changes across regimes. In contrast, fixed-coefficient VARs estimated by sub-sample exhibit greater power. Pooled estimates from panel VARs for six countries based on (long-run and) sign restrictions detect in several instances changes in the IRFs. This evidence is, however, weaker than it appears. Based on (long-run and) sign restrictions we find that prior and posterior IRFs are often close, so that the concern raised by Baumeister and Hamilton (2015) appears to be relevant. Evidence from a multivariate permanent-transitory decomposition of GDP shocks is markedly sharper. It points towards material changes in the IRFs: at the ZLB the IRFs of GDP and unemployment exhibit more inertia, the response of prices is flatter, and the responses of interest rates are weaker.