In the 1920s, Irving Fisher extended his previous work on the Quantity Theory to describe how, through an early version of the Phillips Curve, changes in the price level could affect both output and unemployment. At the same time, Holbrook Working designed a quantitative rule for achieving price stability through control of the money supply. This paper develops a structural vector autoregressive time series model that allows these "classical" channels of monetary transmission to operate alongside, or perhaps even instead of, the nowmore-familiar interest rate channels of the canonical New Keynesian model. Even with Bayesian priors that intentionally favor the New Keynesian view, the United States data produce posterior distributions for the model's key parameters that are more consistent with the ideas of Fisher and Working. Changes in real money balances enter importantly into the model's aggregate demand relationship, while growth in Divisia M2 appears in the estimated monetary policy rule. Contractionary monetary policy shocks reveal themselves through persistent declines in nominal money growth instead of rising nominal interest rates. These results point to the need for new theoretical models that capture a wider range of channels through which monetary policy affects the economy and suggest that, even today, the monetary aggregates could play a useful role in the Federal Reserve's policymaking strategy.