Banking competition, collateral constraints and optimal monetary policy

We analyze optimal monetary policy in a model with two distinct financial frictions. First, borrowing is subject to collateral constraints. Second, credit flows are intermediated by monopolistically competitive banks, thus giving rise to endogenous lending spreads. We show that, up to a second order approximation, welfare maximization is equivalent to stabilization of four goals: inflation, output gap, the consumption gap between constrained and unconstrained agents, and the distribution of the collateralizable asset between both groups. Following both financial and non-financial shocks, the optimal monetary policy commitment implies a short-run trade-off between stabilization goals. Such policy tradeoffs become amplified as banking competition increases, due to the fall in lending spreads and the resulting increase in financial leveraging.