We propose to incorporate cross-sectional heterogeneity into structural VARs. Heterogeneity provides an additional dimension along which one can identify structural shocks and perform hypothesis tests. We provide an application to bank runs, based on microeconomic deposit market data. We impose i… dentification restrictions both in the cross-section (across insured and non-insured banks) and across variables (as in macro SVARs). We thus (i) identify bank runs, (ii) quantify the contribution of competing theories, and, (iii) evaluate policies such as deposit insurance. The application suggests substantial promise for the approach and has strong policy implications.