agents. However, in all these models, the financial friction is the only distortion in the economy. The question of how the pursuit of financial stability may affect macroeconomic stability is there- fore novel relative to this literature.
The third and final is a small, but growing literature that considers both macroeconomic and fi- nancial frictions at the same time. Benigno, Chen, Otrok, Rebucci, and Young (2011) analyze a fully specified new open economy macroeconomics 3-period model that features the same finan- cial friction analyzed here and Calvo-style nominal rigidities. The solution of the fully non-linear version of that model (i.e., without resorting to approximation techniques) shows that there is
a trade-off between macroeconomic and financial stability, but it is quantitatively too small to warrant the use of a second policy instrument in addition to the interest rate. Kashyap and Stein (2012) use a modified version of the pecuniary externality framework of Stein (2012) where the central bank has both a price stability and a financial stability objective. Similar to our findings, a trade-off emerges between the two objectives when the policy interest rate is the only instrument and it disappears when there is a second instrument (a non-zero interest rate on reserves, in their case). However, they do not model the price stability objective explicitly. Woodford (2012), in contrast, sets up a New Keynesian model with credit frictions, where the probability of a finan- cial crisis is endogenous (i.e., it is a regime-switching process that depends on the model vari- ables). Woodford characterizes optimal policy in this environment, showing that —under certain circumstances— the central bank may face a trade-off between macroeconomic and financial sta- bility. However, he does not explicitly model financial stability.
In contrast, in our paper, both the macroeconomic and the financial stability objective are well defined and each objective originates from a friction that we model explicitly. The interaction be- tween the macroeconomic and the financial friction delivers a stark trade-off between macroe- conomic and financial stability, that helps rationalize the role of monetary policy and macro- prudential policy (or the lack of thereof) in the run-up to the Great Recession in the United States.
The rest of the paper is organized as follows. Section 2 describes the model economy. Sections
3 and 4 characterize the decentralized and the socially planned equilibrium of the economy, re- spectively. In Section 5 we discuss the implications of our model in terms of the role played by U.S. monetary policy for the stability of the financial system in the run-up to the Great Recession. Section 6 concludes.
II THE MODEL
We include monopolistic banking and real interest rate rigidities in the pecuniary externality framework of Jeanne and Korinek (2010a). In Jeanne and Korinek (2010a)’s set up, consumers