appreciations and overvaluations - mit opencourseware€¦ · r.j. caballero (mit) appreciations...
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Appreciations and Overvaluations Macroeconomics IV
Ricardo J. Caballero
MIT
Spring 2011
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Introduction
Real exchange rate appreciations often refiect boom conditions, but they also stress important parts of the economy
Most economies experience episodes of this sort. Today, this is the case of commodity producing economies, emerging markets, as well as countries experiencing strong capital infiows
In this context the question arises whether there is a need for policyintervention
Here we present one framework to address such question(Caballero-Lorenzoni)
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Motivation: Appreciations
Episodes of large and persistent appreciations of real exchange rate
Many sources:
- Absorption of large capital infiows
- Infiation stabilization policies
- Exchange rate adjustments in trading partners
- Favorable price shock for commodity producers
- Discovery of natural resources (Dutch disease)
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Slow adjustment in recoveries
Persistent appreciations drains resources of export sector, lead todestruction/bankruptcies
May slow down export sector recovery once things turn around
Depressed input demand from consumers + depressed input demand from export sector
Real exchange rate overshooting
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RER overshooting
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Policy question
Is there a need to intervene to protect the export sector?
Does costly ex post adjustment justify intervention ex ante?
A: no
Add extra ingredient: financial constraint
A: in some cases
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Inter-temporal pecuniary externality
Suppose consumers reduce their demand for non-tradables in appreciation
Less destruction ex-ante and a faster recovery ex-post
Higher wages and real exchange rates ex post
Rational atomistic consumers ignore this effect
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Related work
’Dutch disease’(Corden, Krugman, Wijnbergen)
learning-by-doing, real externality
Broader problem: preventive measures during appreciations and current account deficits
ineffi cient current account deficits (Blanchard)
Financial development and the negative effects of macro volatility
exchange rate fiuctuations bad for liquidity constrained entrepreneurs (Aghion-Bacchetta-Ranciere-Rogoff, Aghion-Angeletos-Banerjee-Manova)
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Model
two goods: tradable T , non-tradable N
price of N (RER): pt
two countries: home, foreign
two groups in home country: consumers, entrepreneurs
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Preferences
Consumers: � � E ∑ βt θt log ctT + log ct
N
preference shock θt
Entrepreneurs and ROW: E ∑ βt ctT
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Shocks
First shift to θA , then shift to θD w.p. δ
θA > θD
D absorbing state
complete markets
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Endowments
Consumers sell 1 unit of labor inelastically
Entrepreneurs, period 0:
a0 tradable goods
n−1 production units
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Technology
Tradable sector
f of tradable good to create one production unit
(Leontief ) 1 production unit produces 1 tradable using 1 labor
(No mothballing) if production unit inactive → destroyed
Non-tradable sector
1 unit of labor produces 1 unit of NT
→ wages are equal to pt
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Financial constraint
No commitment on entrepreneurs’side
Portfolio of entrepreneurs: a(st+1 |st ) ≥ 0
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Equilibrium: consumers
Consumers’optimality + complete markets
Demand for NT
cN t = κ
θt pt
shock: persistent shift in demand for NT
κ endogenous depends on NPV of wages pt
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Equilibrium: export units and NT consumption
Market clearing in labor and goods market + Leontief:
n Nt + c
t = 1
Market clearing for used units + creation/destruction margin:
qt ∈ [0, f ]
nt > nt 1 implies q− t = f
nt < nt−1 implies qt = 0
qt price of used unit
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Characterization
Proposition Equilibrium is characterized by:
Phase A
p(st ) = pA > 1 q(st ) = 0
Phase D
p(st ) = pD ,j < 1 q(st ) = f
D, j : j-th period after reversal
Assumptions: θA /θD and n−1 suffi ciently large
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First Best — Phase A: Operational losses and option value
Cost of holding a unit:
pA − 1 > 0
Expected benefit:
βδf
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Phase D: Recovery
Cost of holding a unit:
f − (1 − pD,j ) > 0
Expected benefit:
βf
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First best (large a0)
Price pinned down by intertemporal margin on the supply side
Indifference between financial assets and physical capital
pfb A − 1 = βδf
f + pfb D − 1 = βf
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First best
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First best
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First best (continued)
Cutoff afb
If a0 ≥ afb financial constraint not binding
High wealth a0 needed for two reasons:
cover losses in A
cover investment costs in first period of D
(pA − 1)nA + δβaD ,0 = (1 − (1 − δ)β)a0
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Constrained equilibrium: Low a0
Prices no longer pinned down by intertemporal margin
Limited ability to exchange financial assets for physical capital
pA − 1 ≤ βδf
f + pD,j − 1 ≤ βf
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Entrepreneur’s problem: recursive setup
Equilibrium prices taken as given: q(st ) and p(st )
Individual state variables:
financial wealth a
physical capital n−
Lemma The value function V (a, n−; st ) takes the linear form
V � a, n−; st
� = ψ(st ) + φ(st )
� a + q(st )n− �
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Bellman equation
φ � � � st a t + q
�s
�
,
�n− =
e= max cT + s 1βE
�tφ( + )
�a(st+1) + q(st+1 )n
cT ,e ,n,a(.)
��s.t.
cT ,e + q(st ) · n + βE [a(s t t+1)] = (1 − p(s )) · n + a q(st + ) · n−
a(st+1) ≥ 0, n ≥ 0, cT ,e ≥ 0
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For physical capital (production units): �
st+1 φq st ( ) + p(st ) − 1
�= βE
�st )
�q
φ
� (
�s
� t+1 �
For securities:
φ �st � ≥ t+1 tφ
�s
�a �st+1 |s
�≥ 0
For consumption:
1 ≤ φ � � � � st cT ,e st ≥ 0
Optimality conditions
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Low a0
Limited funds a0
(pA − 1)nA + δβaD ,0 = (1 − (1 − δ)β)a0
keep resources for A
insure the recovery
Low a0 can bite in A, in D, both...
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Constrained appreciation
Units only pay back in state D
(pA − 1) φA = βδf φD ,0
φA ≥ φD ,0
If constraint is binding then
pA − 1 < βδf
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Constrained appreciation (continued)
Proposition
If a0 < aA then price is depressed pA < pfb A , destruction is bigger nA < nfb
A
Smaller appreciation, symptom of financial distress
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Constrained appreciation (continued)
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Overshooting
Proposition
If a0 < aD then overshooting:
pD ,0 < pfb D
pD ,j → pfb D
constrained recovery
f + pD,0 − 1 < βf
low wages help recovery of financially constrained firms →
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Overshooting (continued)
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Constrained equilibrium
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Back to consumers’demand
E ∑ tβ ptκ =
2E ∑ t β θt
Now κ depends on initial wealth of entrepreneurs
General equilibrium feedback
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Exchange rate policy
Exchange rate appreciation in A leads to
more destruction in A→
slower recovery in D→
Policy: Relieve pressure on demand for NT, increase nA, save units for the recovery
Q: Is this policy welfare improving?
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Policy instruments
no transfers between consumers and entrepreneurs
taxes on consumption of T/NT, rebated lump-sum to consumers
interventions with effects in this direction:
contractionary fiscal policy
policies to encourage savings
currency interventions/reserves management (?)
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Planner problem
Planner chooses:
state contingent path for cT (st ), cN (st )
Takes as given:
market clearing in labor market n(st N t ) = 1 − c (s )
entrepreneurs’optimality
Map n → T(.) p(.), a(.), c ,e (.)
maximize consumers’utility for fixed entrepreneurs’utility
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Perturbation
Increase nA locally, around CE
Effects on consumers’welfare (leaving entrepreneurs indifferent)
Result If constrained appreciation and overshooting then:
dUc > 0
dUe = 0
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Change nA locally, around CE
dUc = −θAu
� (1 − nA ) + pA λ + dnA
∂pA ∂pD ,0+λ
�nA + βδ nD ,0∂nA ∂nA
�
Perturbation (continued)
λ lagrange multiplier on consumers BC
first row zero (private FOC)
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Ineffi cient destruction
If constrained appreciation + overshooting (pA < pAfb and pD ,0 < pD
fb ) then
∂pA ∂pD ,0 nA + δβ nD ,0 = 1 − pA + βδf > 0 ∂nA ∂nA
total wage loss today = cost of saving an extra unit
total wage gain tomorrow = savings in investment costs
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If pD ,0 < pfb (overshooting) then: D
cT ,e dU ∂e D ,0 = = 0dnA ∂nA
Ineffi cient destruction (continued)
all extra funds tomorrow go to investment
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Constrained effi ciency
If no overshooting optimal policy is no intervention
∂pA ∂pD ,0 nA + δβ nD ,0 = 1 − pA < 0 ∂nA ∂nA
only wage losses today
then reduce nA?
no, the entrepreneur PC binding now
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Optimal policy
Optimal policy if no constrained appreciation? Intervention during recovery phase
still good
In general optimal to combine intervention in A and D
Hindrances:
real wage rigidities in recovery
nominal wage rigidities + peg
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Optimal policy (continued)
blue - CE, red - optimal policy
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Ex ante vs ex post: Three cases
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Three cases (continued)
First case, low a0 intervention in A is very effective
tax NT in A and subsidy in D
subsidy eventually vanishes
Second case, middle a0 intervention in A is effective but also leave some for D
ll intervention in D frontloaded a
Third case, high a0 intervention more effective in D
over-overshooting
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a0 and intervention (against CE)
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Implementation: tax on nontradable
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Persistence
How does δ affect the equilibrium, the incentive to intervene?
High δ: switch is very likely
small losses, easy to hedge
Low δ: switch is very unlikely
optimal to destroy many units also in first best, easy to hedge
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Persistence (continued)
shaded region - positive taxes
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Incomplete markets
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Conclusions
Appreciation can generate excessive destruction
For ineffi ciency, it is crucial that there is a constrained recovery
Trade-off wage cut in A v. faster recovery in D
Menu of intervention depends on initial conditions: more constrained entrepreneurs, more preventive policy
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14.454 Economic Crises Spring 2011
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