We explore the stability properties of interest rate rules granting an explicit response to stock prices in a New-Keynesian DSGE model populated by Blanchard-Yaari non-Ricardian households. The constant turnover between long-time stock holders and asset-poor newcomers generates a financial wealth channel where the wedge between current and expected future aggregate consumption is affected by the market value of financial wealth, making stock prices non-redundant for the business cycle. We find that if the financial wealth channel is sufficiently strong, responding to stock prices enlarges the policy space for which the rational expectations equilibrium is both determinate and learnable (in the E-stability sense of Evans and Honkapohja, 2001). In particular, the Taylor principle ceases to be necessary and also mildly passive policy responses to inflation lead to determinacy and E-stability. Our results appear to be more prominent in economies characterized by a lower elasticity of substitution across differentiated products and/or more rigid labor markets.
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