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Risk Capacity and Optimal Monetary Policy

Rui Sun

Abstract

We characterize optimal monetary policy when policy endogenously moves risk premia through redistribution across agents who differ in their willingness to bear risk. The analytical core is Marginal Risk Capacity, the covariance of monetary policy exposures with marginal propensities to take risk. This sufficient statistic governs this channel as MPCs govern the consumption channel. MRC enters the Ramsey criterion as a risk premium wedge that breaks divine coincidence, vanishes if and only if macroprudential tools are available, and generates a new inflation bias under discretion. Solving the Ramsey problem globally reveals a risk capacity trap where transmission collapses, and optimal policy preemptively prevents it.

Risk Capacity and Optimal Monetary Policy

Abstract

We characterize optimal monetary policy when policy endogenously moves risk premia through redistribution across agents who differ in their willingness to bear risk. The analytical core is Marginal Risk Capacity, the covariance of monetary policy exposures with marginal propensities to take risk. This sufficient statistic governs this channel as MPCs govern the consumption channel. MRC enters the Ramsey criterion as a risk premium wedge that breaks divine coincidence, vanishes if and only if macroprudential tools are available, and generates a new inflation bias under discretion. Solving the Ramsey problem globally reveals a risk capacity trap where transmission collapses, and optimal policy preemptively prevents it.
Paper Structure (82 sections, 16 theorems, 90 equations, 11 figures, 17 tables)

This paper contains 82 sections, 16 theorems, 90 equations, 11 figures, 17 tables.

Table of Contents

  1. Introduction
  2. General Framework
  3. Environment and Structural Properties
  4. MRC as a Sufficient Statistic
  5. Optimal Policy: The Risk Premium Wedge
  6. The Separation Theorem
  7. Time Consistency
  8. Welfare Decomposition: Orthogonality of MPC and MPR Channels
  9. Analytical Results in a Two-Period Environment
  10. Environment
  11. Risk Premium and Redistribution
  12. Marginal Risk Capacity
  13. Real Effects of Risk Premium Changes
  14. Welfare Decomposition: Two Orthogonal Channels
  15. Optimal Policy: The Risk Premium Wedge
  16. ...and 67 more sections

Key Result

Proposition 2

Under Assumptions ass:redistrib--ass:mpr_het, the effect of the interest rate on the economy's effective risk aversion is summarized by MRC: When $\mathrm{MRC}_t > 0$, a reduction in $i_t$ lowers effective risk aversion and compresses risk premia. Combined with Assumption ass:rp_real, MRC governs the risk premium channel of monetary transmission.

Figures (11)

  • Figure 1: The risk capacity trap
  • Figure 2: The Ramsey optimal policy function
  • Figure 3: Impulse responses to a monetary easing
  • Figure 4: Impulse responses to a negative productivity shock
  • Figure 5: Wealth distribution dynamics under Taylor rule versus Ramsey optimal policy
  • ...and 6 more figures

Theorems & Definitions (31)

  • Definition 1: Marginal Risk Capacity -- General
  • Proposition 2: General sufficient statistic
  • proof
  • Remark 1: Scope of the sufficient statistic
  • Proposition 3: General target criterion
  • Proposition 4: General separation
  • Proposition 5: General inflation bias
  • proof
  • Proposition 6: General decomposition
  • proof
  • ...and 21 more