Inflation targeting, output stabilization, and real indeterminacy in monetary models with an interest rate rule

Central banks set the nominal interest rate to target inflation and stabilize output. In monetary models, monetary policy affects output directly via the wealth effect. I show that in these models, the response of the central bank to fluctuations in output may induce real indeterminacy even if the Taylor principle is satisfied. I find that the determinacy conditions depend on the interest elasticity of output and generally, the Taylor principle is neither necessary nor sufficient for determinacy. This is in stark contrast with the New Keynesian model where a sufficiently strong policy response to inflation or output usually ensures determinacy.