I study monetary policy in an estimated financial New-Keynesian model extended by behavioral expectation formation in the asset market. Credit frictions create a feedback between asset markets and the macroeconomy, and behaviorally motivated speculation can amplify fundamental swings in asset prices, that potentially cause endogenous, nonfundamental bubbles and bursts. Booms in asset prices improve firms financing conditions and are therefore deflationary. These features significantly improve the power of the model to replicate empirical key moments. A monetary policy that targets asset prices can dampen financial cycles and reduce volatility in asset markets (dampening effect). This comes at the cost of creating an additional channel through which asset price fluctuations transmit to macroeconomic fundamentals (spillover effect). I find that unless financial markets are severely overheated, the undesirable fluctuations in inflation and output caused by the spillover effect more than outweigh the benefits of the dampening effect.
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