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Carlstrom and Fuerst (2007) ["Asset prices, nominal rigidities, and monetary policy," Review of Economic Dynamics 10, 256 - 275] find that monetary policy response to share prices is a source of equilibrium indeterminacy because an increase in inflation implies a high real marginal cost and low share prices in a sticky-price economy. The authors find that if the New Keynesian Phillips curve has a lagged inflation term caused by price indexation, this effect is weakened. Moreover, equilibrium indeterminacy caused by monetary policy response to share prices never arises if all the firms that cannot re-optimize their prices follow price indexation.
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