This paper empirically tests theories of bank runs. We use a structural panel VAR to extract runs from deposit market data. Identification exploits cross‐sectional heterogeneity in deposit insurance: we identify bank runs as adverse deposit market supply shocks hitting uninsured banks harder compared to insured. Conditional on a run, we study the behavior of uninsured banks with bad and good fundamentals. We find that both experience runs, but deposit outflows at the former are more severe. Panic effects, which affect all uninsured deposits alike, irrespective of fundamentals, dominate in the aggregate. Insured banks partially absorb the outflow of uninsured deposits.