Should monetary policy lean against housing market booms?

Should monetary policy lean against housing market booms? We approach this question using a small-scale, regime-switching New Keynesian model, where housing market crashes arrive with a logit probability that depends on the level of household debt. This crisis regime is characterized by an elevated risk premium on mortgage lending rates, and, occasionally, a binding zero lower bound on the policy rate, imposing large costs on the economy. Using our set-up, we examine the optimal level of monetary leaning, introduced as a Taylor rule response coefficient on the household debt gap. We find that the costs of leaning in regular times outweigh the benefits of a lower crisis probability. Although the decline in the crisis probability reduces volatility in the economy, this is achieved by lowering the average level of debt, which severely hurts borrowers and leads to a decline in overall welfare.