Stabilizing Effects of Exchange Rate Band System

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Stabilizing Effects of Exchange Rate Band System

• Hitotsubashi University
• Eiji Ogawa

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Krugmans Honeymoon Effects

• Krugman (1991) discussed that the exchange rate
  band system has a honeymoon effects under an
  assumption that the exchange rate band is
  credible and there is no perceived probability of
  realignments.
• Bertola and Caballero (1992) pointed out that the
  exchange rate band system would increase the
  exchange rate fluctuations if it is not so
  credible that the monetary authorities keep the
  current boundaries.

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Repeated realignment model

• Bertola and Caballero (1992) formalized a
  repeated realignment model under a constant
  probability of realignments.
• Ogawa (1995) extended the model to build up a
  repeated realignment model under a variable
  probability of realignments.

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Assumptions in the models

• Symmetric two countries. The two economies have
  the same size and the same parameters
• Equilibrium in product markets under flexible
  prices.
• The economies are under full employments. Their
  GDP are given at full employment levels.
• No capital control. Capital movements are perfect
  between the two economies.
• Risk-neutral investors. Home currency denominated
  and foreign currency denominated financial assets
  are perfect substitutes.
• Economic agents have rational expectations by
  using an information set as of a current time t.

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A system of the model

• Domestic money market equilibrium
• Foreign money market equilibrium
• Exogenous real exchange rate
• Uncovered interest rate parity

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Exchange rate and fundamentals

• From equation (1.1) through (1.4), nominal
  exchange rate is derived
• Fundamentals f

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Probability process of the fundamentals

• Assume that without intervention in forex markets
  the fundamental level follows a Brownian motion
  process

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Assumptions of forex intervention

• The monetary authorities intervene in forex
  markets only at pre-specified points
  and ( a central
  parity applying up from the last realignment time
  0, a width between the central parity and
  both the boundaries).
• When the fundamental level reaches either of the
  boundaries at time T, the monetary authorities
  may either bring it back to the current central
  parity with probability or declare a new
  central parity with unchanged width and bring
  it to the new central parity with probability
  .

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Expected rate of change in exchange rate

• Exchange rate is a function of the current
  central parity and the fundamental level
• From Itos lemma, expected rate of change in
  exchange rate

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Exchange rate

• From eqs. (2.1) and (2.4),
• Exchange rate

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Continuity principle of rational speculation

• The exchange rate should not be expected to
  change at times when intervention is known to be
  imminent because rational market participants
  always take a chance of speculation and exploit
  expected capital gains.
• where R realignment, N non-realignment, a
  time immediately before an intervention, a
  time immediately after an intervention.

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(No Transcript)
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Fundamental level and central parity

• Immediately before the intervention
• Immediately after the intervention

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Assumption of an upward trend

• Substitute these values into eq. (2.8)
• Assume that the fundamental level has an upward
  trend. The floor is not effective ( ).

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Exchange rate fluctuations

• Exchange rate
• If , the exchange rate fluctuations are
  the same as flexible exchange rate system.
• If , the exchange rate fluctuations are
  smaller than flexible exchange rate system.
• If , the exchange rate fluctuations are
  larger than flexible exchange rate system.

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Signs of

• From eq. (2.11),

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Stabilizing or destabilizing effects of the
exchange rate band

• If an expected rate of change of central parity
  is smaller than the width of the band, the
  exchange rate is expected to come back into the
  band. (stabilizing effect)
• If the expected rate of change of central parity
  is larger than the width of the band, the
  exchange rate is expected to jump out of the
  band. (destabilizing effect)

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Realignments with a variable probability
Assumptions

• The probability of realignment varies over time
  in proportion to a shadow flexible exchange rate.
  
• The probability begins with an initial value
  in a realignment at time 0 when the monetary
  authorities set the fundamental level to a new
  central parity level.
• The probability reaches a unity when the shadow
  rate reaches the ceiling.

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Shadow flexible exchange rate

• From (1.13), shadow flexible exchange rate
• The probability gradually increases in proportion
  to the shadow flexible exchange rate and reaches
  a unity at time when the shadow
  flexible exchange rate reaches the ceiling.

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Probability of realignment

• We can formulate the probability at time t
  between the last realignment and next one
• Because the probability is related with
  , where

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Exchange rate under the variable probability

• Substituting eq. (2.15) into eqs. (2.10) and
  (2.11),

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Dynamics of (1)

• If the initial expected rate of change of central
  parity is smaller than the width of the band (
  ),
• starts with a negative value.
• It becomes zero at time
• After the time it turns to a positive value.
• The exchange rate band stabilizes the exchange
  rate fluctuations during the time the last
  realignment and the turning point. However, the
  exchange rates fluctuates more widely after the
  turning point.

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Dynamics of (2)

• If the initial expected rate of change of central
  parity is lager than the width of the band (
  ),
• starts with a positive value and it
  increases.
• Exchange rate fluctuates more widely immediately
  after the realignment under the exchange rate
  band system.

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Stabilizing effects of the exchange rate band
system

• How efficiently and how long the exchange rate
  band works to stabilize the exchange rate
  fluctuations depends on , which in turn
  depends on
• the initial probability of realignment
• the trend rate of fundamentals
• the rate of change of central parity
• the width of the band

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Stabilizing the destabilized exchange rate
fluctuations (1)

• If the monetary authorities decrease the rate of
  change of central parity, the expected rate of
  change of central parity is decreased. Speculator
  are discouraged to buy the foreign currency.
• If they widen the band, the gap between the
  expected rate of change of central parity and the
  width of the band is decreased. Speculator are
  discouraged to buy the foreign currency.

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Stabilizing the destabilized exchange rate
fluctuations (2)

• The monetary authorities may directly control the
  trend rate of fundamentals by their monetary
  policy, given the foreign monetary authorities
  behavior, in order to set the trend rate of
  fundamentals to zero.
• It is difficult for the monetary authorities to
  control directly the initial probability of
  realignment though they can control it indirectly
  through the trend rate of fundamentals.