This paper presents a model of finitely lived rational agents in which unanticipated innovations in the stock of fiat money affect real variables. An unanticipated inflation reduces the real value of the nominally denominated national debt, thereby reducing the crowding-out of capital and/or the tax burden. Both effects stimulate increased investment in capital, which leads to an increase in real output and wages in the following periods. In contrast with price-surprise models, these real effects occur even if the monetary innovation is instantly and perfectly observed by agents.

We ask whether the following observations may result from endogenously determined fluctuations in the money multiplier rather than a causal influence of money on output: (i) M1 is positively correlated with real output; (ii) the money multiplier and deposit-to-currency ratio are positively correlated with output; (iii) the price level is negatively correlated with output; (iv) the correlation of M1 with contemporaneous prices is substantially weaker than the correlation of M1 with real output; (v) correlations among real variables are essentially unchanged under different monetary-policy regimes; and (vi) real money balances are smoother than money-demand equations would predict.