In this paper we develop a DSGE model to analyze a macroprudential policy framework. We use it to describe the Hungarian economy and the key regulatory constraints implemented there: the loan-to-value and the debt-service-to-income caps imposed on mortgage borrowers and the minimum capital requirement imposed on banks. Our model is novel in the way it treats the borrowing caps as soft constraints, which makes it easy to analyze multiple non-redundant borrowing constraints. We also show an estimation strategy that involves a variation of impulse-response matching and accounts for the lack of historical data concerning the conduct of macroprudential policy, a common problem.