Optimal monetary policy and inequality

Optimal monetary policy with heterogeneous agents and nominal rigidities

In this paper, La’O and Morrison investigate how monetary policy should optimally respond to distributional concerns in an economy with heterogeneous households, nominal rigidities, and constrained fiscal instruments. The authors develop a dynamic general equilibrium model with the following features:

1. Heterogeneous households:
   – Households differ in type-specific, state-contingent labor productivity and initial firm ownership. Preferences are separable and iso-elastic, with complete markets allowing full insurance against idiosyncratic risk.
   – Labor earnings vary systematically across types, reflecting empirical evidence on countercyclical earnings inequality.
2. Firms and nominal rigidities:
   – Monopolistically competitive firms face sticky prices modeled as an informational friction. A fraction of firms set prices one period in advance, while others adjust flexibly.
   – Production uses a CES aggregator of intermediate goods, with equilibrium markups endogenously determined.
3. Policy framework:
   – The Ramsey planner jointly optimizes monetary and fiscal policy under commitment. Fiscal tools include linear taxes on consumption, labor income, sales, and profits, alongside uniform lump-sum transfers. Tax rates are restricted to be non-state-contingent, reflecting political constraints.
   – Monetary policy controls nominal aggregate demand, allowing state-contingent markups.
4. Analytical Approach:
   – The primal method (Lucas and Stokey, 1983) is used to characterize allocations directly, subject to implementability constraints. This approach disentangles the redistributive role of monetary policy from fiscal limitations.

Key findings:

• Proportional shocks and flexible-price optimality:
  When labor productivity shocks are proportional across households (relative productivities fixed), optimal monetary policy replicates flexible-price allocations by targeting price stability. Fiscal tools alone suffice for redistribution, as tax distortions have constant marginal costs/benefits across states.
• Relative productivity shocks and state-contingent markups:
  Under fluctuating relative productivities, monetary policy optimally deviates from flexible prices to target a state-contingent markup. This markup  covaries positively with labor income inequality: high inequality states warrant higher markups to compress the earnings distribution, and vice versa.
• Mechanism:
  By raising markups in high-inequality states, monetary policy reduces labor demand, lowering wages for high-productivity workers. This complements fiscal redistribution (uniform transfers funded by linear taxes), mitigating efficiency-equity trade-offs.
• Robustness to profit taxation:
  When profit taxation is constrained, heterogeneous firm ownership dampens but does not reverse the optimal monetary response. The markup’s sensitivity to inequality decreases if high-income households hold more equity, yet the pro-inequality covariance persists.

Conclusion

The study establishes a novel redistributive motive for monetary policy: when fiscal tools lack state contingency, markups should systematically respond to labor market inequality. This theoretical insight is quantitatively relevant, with implications for stabilizing inequality over the business cycle. The framework bridges Ramsey optimal taxation and New Keynesian models, highlighting the interplay between nominal rigidities and heterogeneity.

Optimal Monetary Policy with Redistribution
Authors: Jennifer La’O, Wendy Morrison
From: Columbia University, Federal Reserve Bank of Minneapolis

Optimal monetary policy with heterogeneous agents in an open economy

Acharya and Challe, in this paper, study optimal monetary policy in a Small Open Economy Heterogeneous-Agent New Keynesian (SOE-HANK) model with uninsured idiosyncratic risk and unequal bond market access. The authors develop a tractable SOE-HANK model with uninsured idiosyncratic income risk, a fraction of hand-to-mouth households, and incomplete markets for aggregate shocks. They use a CARA utility and normally distributed income shocks for analytical tractability and derive conditions for an “open-economy divine coincidence” result in SOE-HANK. Finally, they compare optimal policy in SOE-HANK to a representative agent (SOE-RANK) benchmark.

Key findings

• Under Cole-Obstfeld elasticities and acyclical income risk, optimal policy in SOE-HANK mimics SOE-RANK, implementing strict domestic price stability.
• With countercyclical income risk and realistic elasticities:
  – Optimal policy in SOE-HANK stabilizes output and exchange rates more than SOE-RANK.
  – This holds for both productivity and world interest rate shocks.
• The planner faces new tradeoffs between stabilizing inflation, output, and consumption inequality.
• Hand-to-mouth households amplify the real income channel of exchange rate fluctuations.
• Uninsurable risk generates inefficient fluctuations in within-group consumption inequality.

Conclusion

The paper shows how household heterogeneity introduces new considerations for optimal monetary policy in open economies, while nesting earlier results as special cases.

Inequality and Optimal Monetary Policy in the Open Economy
Authors: Sushant Acharya, Edouard Challe
From: Bank of Canada, Paris School of Economic