Free Banking as a Monetary Gauge

Selgin's Theorem -- that a free banking system operating on a fixed supply of commodity reserves acts to stabilize total nominal spending per year -- provides an analytical bridge between this alternative regime and conventional monetary theory. For a system of competing banks subject to stochastic spending decisions on the part of an interacting pool of depositors, I disaggregate Selgin's analysis according to transaction size, and examine the effect on the probability distribution for daily redemption demand at a representative bank. This leads to a generalized theorem involving nominal spending and total transaction number, which in turn suggests an econometric gauge that can assess current monetary policy by reference to a free banking-theoretic ideal. A simple equity/bond trading strategy derived from this gauge, and optimized using US historical data over 1983-2014, is seen to significantly outperform (in-sample) a static equity investment. I also discuss implications of this work for economic scenario generation in the context of portfolio theory and for the design of a cryptocurrency like bitcoin but that could be configured to stabilize more complicated macro variables like nominal spending, rather than money supply