Dealing with the Trilemma

Emmanuel Farhi, HarvardIván Werning, MIT

Trilemma

1. Fixed exchange rates2. Independent monetary policy3. Free capital flows

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?

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

Our ApproachOpen economy model

nominal rigidities: prices and wagesfixed exchange ratesoptimal policy

uncoordinatedcoordinated

Build on Gali-Monacelli (2005, 2009), Clarida-Gali-Gertler (2001)

Related Literature

Calvo, MendozaCaballero-Krishnamurthy, Caballero-LorenzoniKorinek, Jeanne, Bianchi, Bianchi-MendozaMundel, Fleming, Gali-Monacelli , Schmitt-Grohe-Uribe, Boucekkine-Pommeret-Prieu

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]

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

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)

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)

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

Firms

Each variety:produced monopolistically technology

Different price setting assumptions:flexibleset one period in advance Calvo

Yt(j) = AtNt(j)

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

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)

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)

Trilemma

Wedge in UIP

Capital Controlsregain monetary autonomysecond best instrument

1 + it = (1 + i⇤t )Et+1

Et(1 + tt)

Shocks1. Productivity2. Export demand 3. Foreign consumption4. Net Foreign Asset

5. Risk Premium Interest Rate (later)

{C⇤t }

{At}{⇤t}

NFA0

Pricing

Flexible PricesRigid PricesOne-Period StickyCalvo

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

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

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

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

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

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

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

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

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

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

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

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

cH

cF

openness

cH

cF

openness

cH

cF

openness

cH

cF

openness

capitalcontrols

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)

⇡

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

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

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

Calvo Outline

Closed formsflexible pricerigid pricesclosed economy Limit

Risk premium shocks

Numerical Exploration

Two experimentsA: terms of trade shockB: mean-reverting productivity shock (half-life 3.5 years)

Openness a 2 {0.4, 0.1}

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

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

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

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

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

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

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

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

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

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

Extensions

Flexible exchange ratesSticky WagesGovernment SpendingCoordination

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

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

Fiscal PolicyNow: fiscal policy (government spending)

Solution independent of openness

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

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

Coordination

Capital controlssame with or without coordination!

Gains from coordination...transition: uncoordinated capital controls restricts feasible aggregateslong-run: coincide

Overall: limited role for coordination

ConclusionsProvided characterization of optimal capital controls

nature of shocksopennesspersistenceprice stickyness

Coordination?does not affect capital controls!limited role

cH

cF

openness

cH

cF

openness

cH

cF

openness

cH

cF

openness

capitalcontrols

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

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."

Eurozone Interest Rates

Eurozone Trade Balance

Eurozone Current Account