Do US Bank Failures Come in Clusters? Overdispersion in 3,520 FDIC Failures, 1934–2025, a Proof That Dispersion Grows With the Counting Window, and What 2023 Changed

If bank failures were independent rare events, annual counts would be Poisson and their variance would equal their mean. Using the FDIC BankFind list of 4,117 failures and assistance transactions from April 1934 to July 2026, I show that US bank failures are among the most overdispersed counts in economics. The 3,520 outright failures from 1934 to 2025 have an annual mean of 38.26 and a variance of 6,993.8, an index of dispersion of 182.8. Ten years hold 68.3% of all failures. I prove that for any mixed Poisson process the index of dispersion of counts over a window of m periods is 1 + m Var(λ)/E(λ), so dispersion rises linearly with the window when the failure rate moves slowly. The data match this: within 2008–2013 the monthly index is 5.0, and within 2014–2025 it is 1.3. A gamma mixing distribution gives a negative binomial with shape 0.4035 (0.4170 with the number of insured institutions as exposure), and the log-likelihood rises from −4,587.6 to −397.0. Annual counts are strongly persistent (correlation of log counts 0.858). The 2023 episode was different in kind: five failures, the fewest of any crisis year, but USD 532.2 billion of failed-bank assets in nominal terms, more than any year in the record.