Learning, the Stock Market and Monetary Policy

We investigate whether monetary policy defined as an interest rate rule should respond to stock prices fluctuations under the following two criteria: 1) the rule must guarantee a unique equilibrium and 2) the MSV representation of this unique equilibrium must be learnable in the E-stability sense. We conduct our analysis in a New Keynesian version of the Blanchard-Yaari "perpetual youth" model with risky equities. Stock prices fluctuations have real effects trough a demand channel since the dynamics of aggregate financial wealth is relevant for current aggregate consumption as well as for current inflation. We find that regardless of the timing of the rule, if the central bank reacts to the deviation of the stock price level from a target then the higher the reaction to this deviation, the higher should be the response to inflation in order to guarantee equilibrium determinacy and E-stability of the MSV representation. When instead the interest rate responds passively to changes in the stock price level, then the Taylor principle with respect to inflation is enough to guarantee E-stability and determinacy, regardless of the timing of the rule. Preliminary results show that the optimal monetary policy is also E-unstable. This can be overcome if private expectations about inflation, output gap and stock prices are observed and incorporated into an interest rate rule.