Is forward-looking inflation targeting destabilizing? The role of policy's response to current output under endogenous investment

We show that, with endogenous investment, virtually all monetary policy rules that set a nominal interest rate in response solely to expected future inflation induce real indeterminacy in models with (i) staggered prices, (ii) staggered prices and staggered wages, and (iii) staggered prices, staggered wages, and firm-specific capital. In (i), policy's response to current output can help significantly in ensuring determinacy with an infinite labor supply elasticity, but little with empirically plausible labor supply elasticity. In (ii), responding to output always helps a great deal, though under low price stickiness and without capital adjustment cost it may call for a moderate response to output in order to ensure determinacy for a wide range of response to inflation. In (iii), even a tiny response to output can always render equilibrium determinate for a wide range of response to inflation.