How tough should you be Inflation targeting, fiscal feedbacks, and multiple equilibria

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How tough should you beInflation targeting,
fiscal feedbacks, and multiple equilibria

• Alexandre Schwartsman
• Unibanco

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The model structure

• Model consists of 2 blocks

• The reaction function block
• A minimalist inflation targeting model
• Phillips Curve
• IS function
• Loss function

• The fiscal/arbitrage block
• Explicit modeling of
• Arbitrage between sovereign and risk free debt
  instruments
• Relationship between domestic interest rates,
  fiscal policy and probability of default

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The reaction function block - 1

• Phillips curve
• IS function
• Loss function

Transmission mechanisms and efficacy usually
associated to parameters a, b
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The reaction function block - 2

• Modeling the exchange rate requires 2 assumptions
• Uncovered interest parity
• Mean reversal
• Thus, the current exchange rate behavior is given
  by

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The reaction function block - 3

• Reduced form for the Central Banks reaction
  function

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The fiscal/arbitrage block

• Assume 2 other assets, in addition to the local
  bond
• Risk-free bond with yield iUS
• Risky sovereign bond with yield i
• Risk neutral agents equate expected return
• where (1-l) is the probability of default

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Modeling the default risk - 1

• Primary surplus is random variable with support
  sL, sH
• Default rule if primary surplus is higher than
  real debt
• service s? (i-p)b, pay otherwise total default
• Zero probability of default
• 100 probability of default

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Modeling the default risk - 2

• Repayment probability can be expressed as a
  function of domestic interest rate

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Arbitrage

• The arbitrage equation then becomes

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Multiple equilibria and stability
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Comparison to standard case
Interest rates are higher than in standard case
(exogenous i) Fiscal feedback reduces efficiency
of monetary policy instrument
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Comparative statics
Fiscal policy
Risk-free rate
Usual transmission channels
Shocks
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Existence

• For simplicity assume primary surplus uniformly
  distributed

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Implication of inflation floor

• Setting the inflation target below the critical
  threshold implies no possible equilibrium

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Determinants of inflation floor

• Inflation floor depends essentially on 3
  determinants
• Primary surpluses
• Public debt
• Size of supply and demand shocks

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Unstable equilibrium properties

• Bad equilibrium associated to weaker currency
  due to higher interest rate differential

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Bizarre shock responses

• Responses to fiscal policy and shocks at odd with
  the data

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Saddlepath properties?

• Model does not have saddlepath properties, that
  is, Central Bank behavior is myopic (converges to
  stable equilibrium)
• If Central Bank were to choose the equilibrium,
  why would it choose the bad one?

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Extension

• Possibility of further equilibria, depending on
  primary surplus distribution (if second order
  condition fails)
• Stable high-interest rate equilibrium (C)

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Concluding remarks

1. Multiple equilibria, at least in this setting, do
   not seem to be the cause behind high real
   interest rate
2. Fiscal feedbacks, nonetheless, imply higher
   interest rates than standard exogenous interest
   rate case
3. Feedbacks depend on sensitivity of default
   likelihood to domestic interest rates, which is
   an empirical issue. Other forces may be at work
   (global risk aversion)
4. Future direction of research Central Bank
   reaction when output gap enters loss function
   possibility of further equilibria depending on
   the primary surplus distribution