Monetary feedback rules and equilibrium determinacy in pure exchange overlapping generations models

This paper considers a pure exchange overlapping generations model in which the money-growth rate is endogenous and follows a feedback rule. Different specifications for the monetary policy rule are analyzed, namely a so-called current, forward, or backward-looking feedback rule, depending on whether the monetary authority uses the actual, expected, or last observed values of the inflation rate to set the monetary policy. We study how the responsiveness of the policy rule with respect to inflation affects the determinacy of the monetary equilibrium. A policy rule is called aggressive (moderate) if it responds strongly (moderately) to inflation deviations from the target. We show how aggressive feedback rules, depending on the considered timing, can reinforce mechanisms that lead to indeterminacy or may lead the inflation rate to fluctuate around the monetary equilibrium at which monetary policy is aggressive. A leaning against the wind policy seems to be more desirable from an equilibrium determinacy point of view. On the contrary, a leaning with the wind policy could not be the recommended policy for the Central Bank.