Anticipation of future consumption: a monetary perspective

We adapt the (Sidrauski, 1967) monetary model to study the hypothesis of anticipation of future consumption. We assume that anticipation of future consumption affects an agent's instantaneous utility and that all effects of future consumption on current wellbeing are captured by the stock of future consumption. Monetary policy effectiveness is thereby reduced and a zero nominal lower interest rate (and thus the Friedman Rule) is destabilizing. Given this, we can derive a "just stable" equilibrium nominal interest rate with matching definitions for inflation and monetary growth. We demonstrate that these implied lower bounds match their historical analogues well.