Financial Crises

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Financial Crises

• Roberto Chang
• Rutgers University

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Introduction

• Financial crises and currency crashes have been a
  policy concern for a very long time
• However, economic theories that may explain them
  are relatively recent

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What do Recent Crises Look Like?
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• Crises refer to sudden changes in some
  variables (reserves, prices) and abandonment of
  some policies
• While dramatic, crises episodes do not seem to be
  completely chaotic
• The first economic model Krugman 1979

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First Generation Models
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Basic Example (Flood-Garber)

• Small Open Economy, Continuous Time
• Domestic Residents may hold domestic currency,
  and domestic and foreign bonds
• Initially, the central bank pegs the exchange
  rate at value S

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Assumptions on the Economy

• Money Demand Equation
• M(t)/P(t) a0 a1i(t)
• Purchasing Power Parity
• P(t) P(t)S(t) S(t)
• Uncovered Interest Parity
• i(t) i ?S(t)/S(t)
• (?S(t) dS(t)/dt)

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• Note that, while the exchange rate is fixed at S,
  i(t) i (by UIP) and
• M(t)/P(t) M(t)/S(t)
• M(t)/S
• a0 a1i
• So M(t) is fixed at S(a0 a1i)

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Central Bank Behavior

• The central bank pegs the exchange rate by
  standing ready to sell its reserves, R(t), for
  domestic currency at the fixed rate S
• This policy is feasible only if reserves are
  nonnegative. If reserves fall to zero, the
  central bank must abandon the peg. Then it is
  assumed that the currency floats.

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• CB balance sheet
• M(t) R(t) D(t)
• where D(t) credit to the government
• Observe that, if reserves are zero, M(t) D(t)
  (central bank always finances government needs)

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Evolution of Government Credit

• Flood and Garber assume for all t,
• ?D(t) µ gt 0
• (Hence D(t) D(0) µt)
• This completes the model

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Key Problem

• Fixed exchange rate and central bank financing of
  the government are incompatible. To see this,
  recall
• M(t) R(t) D(t)
• D grows, M is fixed, then R must be falling. But
  then R will be exhausted at some point

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• Krugmans crucial insight reserves will not fall
  smoothly to zero, but they will be exhausted in a
  final attack
• Why? If reserves fell to zero smoothly, then at
  the time of reserve exhaustion (call it z) the
  exchange rate would jump from S to S(z) gt S
  (show this!) But then the currency would be
  attacked at z-

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• This reasoning implies that, in equilibrium,
• S(z) S(z-) S
• This is used to solve for the rest of the model

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Solution

• In the floating era, the money demand equation
  reduces to
• M(t) bS(t) - c?S(t)
• for some constants b,c. We know M(t) D(t) then,
  so this is a differential equation in S with
  solution
• S(t) cµ/b2 D(t)/b

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• At attack time z, S(z) S and D(z) D(0) µz,
  so replacing in previous expression
• S cµ/b2 (D(0) µz)/ b
• i.e. z bS D(0)/ µ c/b
• R(0)/ µ c/b

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The Final Attack

• Prior to the attack,
• M(t) R(t) D(t) bS
• which must be true for t z- . Since D(z-)
  D(0) µz, this yields
• R(z-) bS (D(0) µz)
• cµ/b
• using the solution for z.

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Noteworthy Aspects

• Reserves fall smoothly for a while, then are
  exhausted in a final attack
• Crises are predictable the time of the attack
  and the fall in reserves are known in advance
• Key driving force inconsistent policy

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Some Weaknesses

• Obstfeld in practice, some governments seem to
  be able to borrow the reserves they need
• Abandonment of a fixed parity seems to be a
  government decision (ERM 1992 crises)

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Second Generation Models
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Obstfelds Logic Model

• Aggregate Supply
• y a(e w) u
• where y output, e exchange rate, w nominal
  wage, u a supply shock (logs)
• Wage setting
• w E e

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• Government chooses e to minimize
• ?(e e(-1))2 (y y)2/2 cZ
• ?x2 (y y)2/2 cZ
• where y gt 0 is a target value of y, and e(-1) is
  last periods exchange rate (so x e e(-1) is
  the devaluation rate) and Z is 0 if x 0, 1 if
  not.

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• Note that
• y a (e e(-1) e(-1)- w) u
• a (x e(-1)- Ee) u
• a (x Ex) u
• ? expectations of a larger devaluation tend to
  depress output

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Optimal Policy

• If there is no realignment, x 0, cZ 0 and the
  government loss is
• (Ex u y)2/2
• If x is chosen to be nonzero, it follows that the
  optimal devaluation policy is
• x (?/a)(aEx u y)
• with loss
• c (1- ?) (Ex u y)2/2

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• So a realignment is optimal if
• ?(aEx u y)2/2 gt c
• The governments optimal policy depends on Ex,
  the expectations of devaluation
• But such expectations depend on policy

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Solution

• Assume u is uniform on -m,m and look for an
  equilibrium in which the government devalues if
  and only if u gt u
• In such case,
• Ex Exuu Pruu Exugtu Prugtu
• Exugtu Prugtu

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• Prugtu follows from the assumption on the
  distribution of u, while Exugtu folloes from
• x (?/a)(aEx u y) ?
• Exugtu (?/a)(aEx Euugtu y)
• One derives a function (eq. 34 of paper)
• Ex d(u)

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• But recall that the largest shock consistent with
  no realignment must satisfy
• ?(aEx u y)2/2 c
• So u solves
• ?(ad(u) u y)2/2 c

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• Two equilibria, one with larger u and low
  expectations of devaluation, the other with low
  u and a large expected devaluation
• The intuition increased devaluation expectations
  raise the nominal wage, which make it more costly
  for the government to sustain the peg

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Recap

• Obstfelds approach placed heavy emphasis on self
  fulfilling expectations
• A crisis a switch from a good to a bad
  equilibrium
• Second generation models emphasized the
  governments decision to devalue and its
  interaction with macro variables

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• Unfortunately, neither first generation models
  nor second generation models seemed a good
  description of more recent crises in emerging
  markets, starting with Mexico 94.

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