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Dealing with the Trilemma
Emmanuel Farhi, HarvardIván Werning, MIT
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Trilemma
1. Fixed exchange rates2. Independent monetary policy3. Free capital flows
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MotivationConstrained monetary policy...
fixed or de facto fixed exchange regimescurrency unions
Capital controls: regain monetary autonomy...Bretton Woods (Keynes-White)
Recent capital controls...developing countries and capital controls IMF blessingEurozone?
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GoalProvide characterization of optimal capital controls
nature of shocks?persistence of shocks?price rigidity?openness?coordination?
Emphasishot money, sudden stops (volatile capital flows)risk premium shocks
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Our ApproachOpen economy model
nominal rigidities: prices and wagesfixed exchange ratesoptimal policy
uncoordinatedcoordinated
Build on Gali-Monacelli (2005, 2009), Clarida-Gali-Gertler (2001)
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Related Literature
Calvo, MendozaCaballero-Krishnamurthy, Caballero-LorenzoniKorinek, Jeanne, Bianchi, Bianchi-MendozaMundel, Fleming, Gali-Monacelli , Schmitt-Grohe-Uribe, Boucekkine-Pommeret-Prieu
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SetupContinuum of small open economies
measure zerodifferent shocksotherwise identical
ExperimentsStart at deterministic steady stateOne-time unanticipated shock at t=0 (incomplete markets)No further shocks
i 2 [0, 1]
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HouseholdsFocus on one countryRepresentative household maximizes
subject to
1X
t=0
�t
"C1��
t
1� �� N1+�
t
1 + �
#
PtCt +Dt+1 +
Z 1
0Ei,tD
it+1di WtNt +⇧t
+ Tt + (1 + it�1)Dt + (1 + ⌧t�1)
Z 1
0Ei
t(1 + iit�1)Dit
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Differentiated GoodsConsumption aggregates
Ct =
"(1 � a)
1h C
h�1h
H,t + a1h C
h�1h
F,t
# hh�1
CH,t =
✓Z 1
0CH,t(j)
e�1e dj
◆ ee�1 CF,t =
✓Z 1
0C
g�1g
i,t di◆ g
g�1
Ci,t =
✓Z 1
0Ci,t(j)
e�1e dj
◆ ee�1
(country i and variety j)
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Price Indices
Differentiated Goods
Pt = [(1 � a)P1�hH,t + aP1�h
F,t ]1
1�h
PH,t =
✓Z 1
0PH,t(j)1�edj
◆ 11�e PF,t =
✓Z 1
0P1�g
i,t di◆ 1
1�g
Pi,t =
✓Z 1
0Pi,t(j)1�edj
◆ 11�e
(country i and variety j)
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LOP, TOT and RERLaw of one price
Terms of trade
Real exchange rate
St =PF,tPH,t
PF,t = EtP⇤t
Qt =EtP⇤
tPt
=PF,tPt
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Firms
Each variety:produced monopolistically technology
Different price setting assumptions:flexibleset one period in advance Calvo
Yt(j) = AtNt(j)
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Equilibrium
Goods market clearing
Labor market clearing
Price dispersion
Nt =YtAt
Dt
Dt =Z 1
0
✓PH,t(j)
PH,t
◆�e
Yt = (1 � a)Ct
✓QtSt
◆�h
+ aLtC⇤t Sg
t
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Household FOCsLabor supply
Euler
Consumption smoothing (Backus-Smith)
Capital controls
Cst Nf
t =WtPt
Ct = QtC⇤t Q
1st
b
✓Ct+1
Ct
◆�s
=1 + it
1 + pt+1
✓Qt+1
Qt
◆s
= 1 + tt
1 + it = (1 + i⇤t )Et+1
Et(1 + tt)
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Household FOCsLabor supply
Euler
Consumption smoothing (Backus-Smith)
Capital controls
Cst Nf
t =WtPt
Ct = QtC⇤t Q
1st
b
✓Ct+1
Ct
◆�s
=1 + it
1 + pt+1
✓Qt+1
Qt
◆s
= 1 + tt
1 + it = (1 + i⇤t )Et+1
Et(1 + tt)
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Trilemma
Wedge in UIP
Capital Controlsregain monetary autonomysecond best instrument
1 + it = (1 + i⇤t )Et+1
Et(1 + tt)
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Shocks1. Productivity2. Export demand 3. Foreign consumption4. Net Foreign Asset
5. Risk Premium Interest Rate (later)
{C⇤t }
{At}{⇤t}
NFA0
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Pricing
Flexible PricesRigid PricesOne-Period StickyCalvo
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Flexible Prices
Qt =h(1 � a) (St)
h�1 + ai 1
h�1
Nt =YtAt
C�st S�1
t Qt =e
e � 11 + tL
AtNf
t
max
1X
t=0
�t
"C1��
t
1� �� N1+�
t
1 + �
#
0 =•
Ât=0
btC⇤�st
⇣S�1
t Yt �Q�1t Ct
⌘
Yt = (1 � a)Ct
✓QtSt
◆�h
+ aLtC⇤t Sg
t
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without capital controls, i.e. constant trade is balancedincomplete markets = complete markets
non Cole-Obstfeld capital controls (Costinot-Lorenzoni-Werning)
Proposition (C-O, flex price).No capital controls at optimum.
Qt
Flexible Prices
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Rigid Prices
Qt =h(1 � a) (St)
h�1 + ai 1
h�1
Nt =YtAt
C�st S�1
t Qt =e
e � 11 + tL
AtNf
t
max
1X
t=0
�t
"C1��
t
1� �� N1+�
t
1 + �
#
0 =•
Ât=0
btC⇤�st
⇣S�1
t Yt �Q�1t Ct
⌘
Yt = (1 � a)Ct
✓QtSt
◆�h
+ aLtC⇤t Sg
t
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Rigid Prices
Qt =h(1 � a) (St)
h�1 + ai 1
h�1
Nt =YtAt
max
1X
t=0
�t
"C1��
t
1� �� N1+�
t
1 + �
#
0 =•
Ât=0
btC⇤�st
⇣S�1
t Yt �Q�1t Ct
⌘
Yt = (1 � a)Ct
✓QtSt
◆�h
+ aLtC⇤t Sg
t
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Rigid Prices
Nt =YtAt
max
1X
t=0
�t
"C1��
t
1� �� N1+�
t
1 + �
#
1 =h(1 � a) (1 )h�1 + a
i 1h�1
0 =•
Ât=0
btC⇤�st
⇣1 Yt � 1 Ct
⌘
Yt = (1 � a)Ct
✓11
◆�h
+ aLtC⇤t 1g
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Rigid Prices
Nt =YtAt
max
1X
t=0
�t
"C1��
t
1� �� N1+�
t
1 + �
#
0 =•
Ât=0
btC⇤�st (Yt � Ct)
Yt = (1 � a)Ct + aLtC⇤t
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Rigid Prices
Nt =YtAt
max
1X
t=0
�t
"C1��
t
1� �� N1+�
t
1 + �
#
0 =•
Ât=0
btC⇤�st (Yt � Ct)
Yt = (1 � a)Ct + aLtC⇤t
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Rigid Prices
Nt =YtAt
max
1X
t=0
�t
"C1��
t
1� �� N1+�
t
1 + �
#
0 =•
Ât=0
btC⇤�st (Yt � Ct)
Yt = (1 � a)Ct + aLtC⇤t
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Rigid Prices
Nt =YtAt
max
1X
t=0
�t
"C1��
t
1� �� N1+�
t
1 + �
#
0 =•
Ât=0
btC⇤�st (Yt � Ct)
Proposition. Tax on inflows has sign...1. same 2. opposite 3. opposite4. zero for NFA
At+1 �At
⇤t+1 � ⇤t
C⇤t+1 � C⇤
t
Yt = (1 � a)Ct + aLtC⇤t
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One Period Sticky
N0 =Y0A0
flexible price value function
NFA0 = �C⇤�s0 (Y0 � C0) + bNFA1
max
Y0
,C0
,W1
"C1�s
0
1 � s�
N1+f0
1 + f+ bV(NFA
1
)
#
Y0 = (1 � a)C0 + aL0C⇤0
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One Period Sticky
N0 =Y0A0
flexible price value function
Proposition.Positive initial tax on inflows
1. decrease in productivity2. increase in exports 3. increase in foreign consumption
⇤0
A0
C⇤0
NFA0 = �C⇤�s0 (Y0 � C0) + bNFA1
max
Y0
,C0
,W1
"C1�s
0
1 � s�
N1+f0
1 + f+ bV(NFA
1
)
#
Y0 = (1 � a)C0 + aL0C⇤0
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Permanent Shocksharder: shocks now affect V()
price adjustment makes permanent shocks more similar to temporary effects...... future shocks matter less (news shocks)
Proposition.Positive initial tax on inflows:
1. decrease in productivity2. increase in exports3. increase in foreign consumption 4. increase in wealth
LA
C⇤
NFA0
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cH
cF
openness
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cH
cF
openness
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cH
cF
openness
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cH
cF
openness
capitalcontrols
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Capital Controls
Second Best instrument...affects intertemporal spendingcan’t affect spending on H vs. F goods.......only indirectly through inflation
Capital controls flexible exchange rate with Local Currency Pricing (LCP)
⇡
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Calvo PricingPoisson opportunity to reset price
cost of inflationcapital controls affect inflation...... prudential interventions?
chosen optimally without coordination
Continuous time: convenient, initial prices givenAssume Cole-Obstfeld case: Log-linearize around symmetric steady state
tL
� = � = ⌘ = 1
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Planning Problem
pH,t = rpH,t � kyt � laqt
˙yt = (1 � a)(it � i⇤t )� pH,t + i⇤t � rt
˙qt = it � i⇤tZ
e�rt qtdt = 0
minZ
e�rthapp2
H,t + y2t + aqq2
t
idt
y0 = (1 � a)q0 + s0
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Planning Problem
pH,t = rpH,t � kyt � laqt
˙yt = (1 � a)(it � i⇤t )� pH,t + i⇤t � rt
˙qt = it � i⇤tZ
e�rt qtdt = 0
minZ
e�rthapp2
H,t + y2t + aqq2
t
idt
y0 = (1 � a)q0�s0
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Calvo Outline
Closed formsflexible pricerigid pricesclosed economy Limit
Risk premium shocks
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Numerical Exploration
Two experimentsA: terms of trade shockB: mean-reverting productivity shock (half-life 3.5 years)
Openness a 2 {0.4, 0.1}
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A: Terms of Trade
0 1 2 3 4 5�0.04�0.02
00.020.04
q
0 1 2 3 4 5�0.04�0.02
00.020.04
y
0 1 2 3 4 50
0.050.1
0.150.2
pH
0 1 2 3 4 5�0.01
0
0.01
0.02nx
0 1 2 3 4 5�0.1�0.05
00.05
0.1t = i � i⇤
1
↵ = 0.4
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A: Terms of Trade
0 1 2 3 4 5�0.06
�0.04
�0.02
0q
0 1 2 3 4 50
0.02
0.04
0.06y
0 1 2 3 4 50
0.050.1
0.150.2
pH
0 1 2 3 4 50
0.002
0.004
0.006nx
0 1 2 3 4 5�0.01
0
0.01
0.02t = i � i⇤
1
↵ = 0.1
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B: Productivity
0 1 2 3 4 5�0.04�0.02
00.020.04
q
0 1 2 3 4 5�0.04�0.02
00.020.04
y
0 1 2 3 4 5�0.2�0.1
00.10.2
pH
0 1 2 3 4 5�0.01
0
0.01
0.02nx
0 1 2 3 4 5�0.1�0.05
00.05
0.1t = i � i⇤
1
↵ = 0.4
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B: Productivity
0 1 2 3 4 5�0.06
�0.04
�0.02
0q
0 1 2 3 4 5�0.04�0.02
00.020.04
y
0 1 2 3 4 5�0.2�0.1
00.10.2
pH
0 1 2 3 4 50
0.002
0.004
0.006nx
0 1 2 3 4 50
0.010.010.020.02
t = i � i⇤
1
↵ = 0.1
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Risk Premia ShockRisk Premia ...
natural allocation...appreciationcurrent account deficit
equilibrium with no capital controls...(smaller) appreciation via inflation(same) current account deficitoutput and consumption boom
it = i⇤t + t + ⌧t
yt < 0
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Risk Premia Shock
0 1 2 3 4 5�0.4�0.3�0.2�0.1
0q
0 1 2 3 4 5�0.2�0.1
00.10.2
y
0 1 2 3 4 5�0.4�0.2
00.20.4
pH
0 1 2 3 4 5�0.1�0.05
00.050.1
nx and nx
0 1 2 3 4 5�0.2�0.1
00.10.2
s and s
0 1 2 3 4 50
0.050.1
0.150.2
t = i � i⇤ � y
Figure 7: Mean-reverting risk premium shock, a = 0.4.
85
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Rigid Prices
Stabilize CA: constantStabilize real exchange rate Lean against the wind......the more so, the more closed the economy
Proposition.
tt = �1 � a + 2a
1+f
1 � a + aq1�a
yt
1
nx
t
/nx
t
=aq
1�a
1 � a + aq1�a
< 1
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Closed Economy Limit
Lean against the wind (one-for-one)Perfectly stabilize economy......not true for other shocks
Proposition. tt = �yt
yt = pH,t = 0
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Risk Premia Shock
0 1 2 3 4 5�0.4�0.3�0.2�0.1
0q
0 1 2 3 4 5�0.2�0.1
00.10.2
y
0 1 2 3 4 5�0.4�0.2
00.20.4
pH
0 1 2 3 4 5�0.1�0.05
00.050.1
nx and nx
0 1 2 3 4 5�0.2�0.1
00.10.2
s and s
0 1 2 3 4 50
0.050.1
0.150.2
t = i � i⇤ � y
Figure 7: Mean-reverting risk premium shock, a = 0.4.
85
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Risk Premia Shock
0 1 2 3 4 5�0.4�0.3�0.2�0.1
0q
0 1 2 3 4 5�0.2�0.1
00.10.2
y
0 1 2 3 4 5�0.4�0.2
00.20.4
pH
0 1 2 3 4 5�0.04�0.02
00.020.04
nx and nx
0 1 2 3 4 5�0.2�0.1
00.10.2
s and s
0 1 2 3 4 50
0.020.040.060.08
0.1t = i � i⇤ � y
Figure 8: Mean-reverting risk premium shock, a = 0.1.
86
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Extensions
Flexible exchange ratesSticky WagesGovernment SpendingCoordination
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Flexible Exchange Rate
Lean against the wind... ...less than with fixed exchange rateNew: stabilize nominal exchange rate
Proposition.
tt = �ayyt �la
aqappH,t
pH,t 6= 0
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Sticky WagesAdd sticky wages (in addition to prices)
similar results: greater stickiness
Even with flexible exchange ratesperfect stabilization not possiblerole for capital controls emerges
Flexible exchange ratesgood, but not panacea
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Fiscal PolicyNow: fiscal policy (government spending)
Solution independent of openness
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CoordinationUp to now...
single country taking rest of world as givenNow, look at world equilibria...
without coordinationwith coordination
Beggar thy neighbor?
Coordination on what? Here...Fix labor tax at some levelCoordinate capital taxes
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Two cases:uncoordinated tax on labor (higher) coordinated tax on labor (lower)
Terms of trade manipulation...planner at uncoordinated tax: wants more outputstandard “inflation bias”
Coordination
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Coordination
Capital controlssame with or without coordination!
Gains from coordination...transition: uncoordinated capital controls restricts feasible aggregateslong-run: coincide
Overall: limited role for coordination
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ConclusionsProvided characterization of optimal capital controls
nature of shocksopennesspersistenceprice stickyness
Coordination?does not affect capital controls!limited role
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cH
cF
openness
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cH
cF
openness
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cH
cF
openness
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cH
cF
openness
capitalcontrols
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IMF’s Blessing“A recent discussion of this issue at the IMF Executive Board, focused on dealing with inflows [...] our views are evolving. In the IMF, in particular, while the tradition had long been that capital controls should not be part of the toolbox, we are now more open to their use in appropriate circumstances, although of course countries should be careful not to use them as substitutes for good macroeconomic policies.”
DSK, March 2011
“[...] while the issue of capital controls is fraught with ideological overtones, it is fundamentally a technical one, indeed a highly technical one. Put simply, governments have five tools to adjust to capital flows: monetary policy, fiscal policy, foreign exchange intervention, prudential tools, and capital controls. The challenge is to find, for each case, the right combination. This is not easy."
Olivier Blanchard, June 2011
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John Maynard Keynes“In my view the whole management of the domestic economy depends on being free to have the appropriate rate of interest without reference to the rates prevailing elsewhere in the world. Capital controls is a corollary to this.”
“[...] control of capital movements, both inward and outward, should be a permanent feature of the post-war system.”
“What used to be a heresy is now endorsed as orthodoxy."
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Eurozone Interest Rates
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Eurozone Trade Balance
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Eurozone Current Account