Should household inequality affect the conduct of monetary policy?

Inequality only has a moderate effect on optimal interest rate policy

McKay and Wolf, in this paper,  analyze a Ramsey problem in which the planner seeks to maximize a weighted sum of individual household utilities, which allows them to explore the role of changes in policymaker objectives. They derive a loss function, by applying a second order approximation, that adds to the usual output gap and inflation objectives a novel third term reflecting distributional concerns. Solving the optimal policy problem, they find that the optimal rule for any given policy instrument  contains three terms, trading off the policymaker’s ability to stabilize output, inflation, and consumption distribution. If, for example, interest rate movements do not affect consumption shares, then the Ramsey rule is in fact identical to the optimal dual-mandate rule; if, on the other hand, monetary policy has large redistributional effects, then distributional concerns may swamp price and output stability considerations.
Their main result is that the optimal interest rate target criterion is exactly the same as in a standard representative-agent environment.

The logic is as follows. Household heterogeneity only affects the model’s demand side (i.e., the “IS” curve). In the optimal policy problem, however, this demand side is a slack constraint: the policymaker can pick an output-inflation allocation subject to the Phillips curve, and then simply set nominal interest rates as necessary to generate aggregate demand consistent with the desired allocation. Household heterogeneity thus may matter for the path of the policy instrument, but not for optimal output and inflation outcomes.

Optimal Policy Rules in HANK
Authors: Alisdair McKay, Christian K. Wolf
From: Federal Reserve Bank of Minneapolis, MIT

Optimal policy should address distributional considerations

Dávila and Schaab in this paper develop a one-asset HANK economy with wage rigidity to study optimal monetary policy in heterogeneous-agent environments. To address the issue of how household heterogeneity affects the welfare impact of monetary policy, they suggest a “timeless Ramsey” approach to analyze three important dimensions of monetary policy design: 1) long-run policy, 2) time consistency and targeting rules, and 3) stabilization policy. They show that:

1. The optimal long-run policy under commitment leads to a zero inflation rate, while policy under discretion leads to an inflationary bias exacerbated by a novel redistribution motive: the planner has a time-inconsistent incentive to lower the real interest rate—thus overheating the economy—to redistribute towards indebted, high marginal utility households.
2. A planner must also adopt a new distributional target in addition to the standard inflation target in order to implement a time-consistent policy.
3. Divine Coincidence fails in heterogeneous-agent economies even in the absence of cost-push shocks due to the distributive pecuniary effects of interest rate policy.

If societies consider expanding central banks’ mandates in the future to include distributional considerations, they will also confront a new set of time consistency problems that may warrant a revision of the classical targeting framework.

Optimal Monetary Policy with Heterogeneous Agents: A Timeless Ramsey Approach
Authors: Eduardo Dávila, Andreas Schaab
From: Yale University, Columbia University