Robust Monetary Policy

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Robust Monetary Policy

• Student Adam Altar Samuel
• Coordinator Professor Ion Stancu

2
Robust control

• Allows policymakers to formulate policies that
  guard against model misspecification.
• Provides a set of tools to assist decisionmakers
  confronting uncertainty.
• Allows private agents to express concern, or
  pessimism, when forming expectations.

3
Relevant literature

• Hansen and Sargent (1999, 2001, 2002, 2006)
• Svensson (1997)
• Dennis, Leitemo and Soderstrom (2004, 2005, 2006)
• Giordani and Soderlind (2004)

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Robust control problems

• can be solved using
• State space methods
• Structural methods
• Two distinct equilibria of interest
• Worst case equilibrium
• Approximating equilibrium

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Worst case equilibrium

• is the equilibrium that pertains when the
  policymaker and private agents design policy and
  form expectations based on the worst-case
  misspecification and the worst-case
  misspecification is realized

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Approximating equilibrium

• is the equilibrium that pertains when the
  policymaker and private agents design policy and
  form expectations based on the worst-case
  misspecification, but the reference model
  transpires to be specified correctly

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State space form

• (1)
• (2)
• where
• zt - vector of endogenous variables

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State space form

• ut vector of control variables
• et vector of white noise innovations
• vt1 vector of specification errors
• ? shadow price, inversely related to the budget
  for misspecification

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Structural form

• (3)
• (4)

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An empirical New Keynesian model

• Variables
• p inflation rate
• y output gap
• i interest rate
• ep supply shock
• ey demand shock

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Equations

• (5)
• (6)
• Objective function
• (7)

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Solution method

• The problem is, both in the nonrobust and in the
  robust case, a discrete time stochastic LQ
  problem.
• The optimal control is given by
• (8)
• where F is the optimal feedback matrix.

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Solution method

• In the nonrobust case
• In the robust case

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ResultsInflation responses to unit supply
shock Nonrobust Robust
15
ResultsOutput gap responses to unit supply
shock Nonrobust Robust
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ResultsInterest rate responses to unit supply
shock Nonrobust Robust
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ResultsInflation responses to unit demand
shock Nonrobust Robust
18
ResultsOutput gap responses to unit demand
shock Nonrobust Robust
19
ResultsInterest rate responses to unit demand
shock Nonrobust Robust
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Conclusions

• In the robust case, the optimal policy of the
  central bank is more activist than in the
  nonrobust case