Optimal Monetary Policy with Heterogeneous Agents

Abstract

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.

Partial differential equation models in macroeconomics

“…As a result, these equilibrium allocations are in general suboptimal from the point of view of society as a whole. 2 Optimal allocations in heterogeneous agent models can be analysed along the lines of Nuño [19] and Lucas & Moll [20].…”

Should Monetary Policy Target Financial Stability?

“…However, if we consider ε π = 108 (half the benchmark number) and fix η Put = 1% and η LAW = 3.25% (the optimal values for ε π = 144), then the optimal rate cut is roughly 62bps, indicating that two and a half rate cuts could be justified to support the financial sector. Lower values of ε π may indeed be justified depending on the microfoundation for nominal rigidities (Nuño and Thomas (2016) consider a continuous-time New Keynesian model with Rotemberg pricing and argue for a much lower calibration of inflation costs).…”

Credibility and Monetary Policy

“…Other sources of time-inconsistency of monetary policy-that gives value to maintain the central bank's reputation -have been investigated as the stabilization bias. In addition, the inflation bias has been showed to arise due to multiple frictions: the steady-state distortion of monopolistic competition in the New Keynesian model and, among more recent contributions, the desire to redistribute wealth in the presence of nominal contracts in Nuno and Thomas (2017) or the inefficiently low steady state level of employment in the absence of private insurance as in Challe (2017).…”

“…In the standard New-Keynesian model, this inflation bias derives from the steady-state distortions of monopolistic competition. See alsoNuno and Thomas (2017) orChalle (2017) for alternative micro-foundations of this bias in the presence of incomplete markets. Alternatively, the stabilization bias due to cost-push shocks may produce the same kind of time-inconsistency.15 This equation can be micro-funded by a no-arbitrage condition when, at each date, risk-neutral households can choose to hold government bonds yielding a risk-free nominal return i t or real assets yielding a risk-free real return r. Without loss of generality, we assume that the return of the real asset is constant.…”