Optimal Implementable Monetary Policy in a DSGE Model with a Financial Sector

We build a simple New Keynesian DSGE model with a financial sector and examine if the Central Bank (henceforth CB)’s responding to the shocks originated in the housing market and/or the financial market is improving the social welfare. In order to do the analysis, we consider a Taylor-type rule and do simulations to find the coefficients of the rule that maximizes the social welfare, that is, a weighted average of the welfares of the patient and impatient households. Based on the simulations, we find that (i) the CB’s responding to the shocks originated in the housing market is improving welfare by small amounts, (ii) the CB’s responding to the shocks originated in the financial market is improving the social welfare significantly; more specifically, the social welfare increases by a factor of about four when the shocks are originated in the lending rate and it increases by more than 5 percent when the shocks are originated in the deposit rate.