The US Money Multiplier, 1959–2026: An Exact Decomposition Showing That the Reserve Ratio, Not the Currency Ratio, Explains Its Collapse and Partial Recovery

The textbook money multiplier writes broad money as M=mB with m=(1+c)/(c+r), where c is the currency–deposit ratio and r the reserve–deposit ratio. With monthly Federal Reserve data from January 1959 to September 2026 (M2, currency, monetary base), I construct c and r so that this identity holds exactly (maximum error 3.6×10⁻¹⁵), derive the elasticities of m with respect to each ratio, and prove that a two-factor Shapley split of Δln m is exact. The M2 multiplier rose from 5.68 in 1959 to a peak of 11.76 in February 1985, stood at 9.21 in August 2008, fell to 4.84 by January 2009 and to 2.82 in August 2014, and was 4.30 in September 2026. From August 2008 to September 2026 the base rose by 1.861 log points and M2 by only 1.098; the multiplier absorbed −0.763, of which −0.745 came from the reserve ratio and −0.018 from the currency ratio. Before 2008, annual base growth and M2 growth were essentially uncorrelated (correlation 0.029, 1960–2007), because movements in the multiplier offset 97% of base growth. The multiplier is an identity, not a behavioural constant, and its collapse after 2008 is the arithmetic of reserves that banks held rather than lent.