We use the German Crisis of 1931, a key event of the Great Depression, to study how depositors behave during a bank run in the absence of deposit insurance. We find that deposits decline by around 20% during the run and that there is an equal outflow of retail and non-financial wholesale deposits from both ex-post failing and surviving banks. This implies that regular depositors are unable to identify failing banks. In contrast, the interbank market precisely identifies which banks will fail: the interbank market collapses for failing banks entirely but continues to function for surviving banks, which can borrow from other banks in response to deposit outflows. Since regular depositors appear uninformed, it is unlikely that deposit insurance would exacerbate moral hazard. Instead, interbank depositors are best positioned for providing “discipline” via short-term funding.