Optimal monetary policy with heterogeneous agents

We analyze optimal monetary policy under commitment in an economy with uninsurable idiosyncratic risk, long-term nominal bonds and costly inflation. Our model features two transmission channels of monetary policy: a Fisher channel, arising from the impact of inflation on the initial price of long-term bonds, and a liquidity channel. The Fisher channel gives the central bank a reason to inflate for redistributive purposes, because debtors have a higher marginal utility than creditors. This inflationary motive fades over time as bonds mature and the central bank pursues a deflationary path to raise bond prices and thus relax borrowing limits. The result is optimal inflation front-loading. Numerically, we find that optimal policy achieves first-order consumption and welfare redistribution vis-à-vis a zero inflation policy.