Dealing with the Trilemma

Emmanuel Farhi, HarvardIván Werning, MIT

BU/Boston Fed Conference on Macro-Finance Linkages

Trilemma

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

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.”

IMF’s Blessing“[...] 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 [...]”

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. "

Olivier Blanchard, June 2011

GoalOptimal monetary policy: well developed theoryDo the same for capital controls

nature of shockspersistence of shocksprice rigidityopennesscoordination

Emphasishot money, sudden stops (volatile capital flows)risk premium shocks

Related Literature

Calvo, MendozaCaballero-Krishnamurthy, Caballero-LorenzoniKorinek, Jeanne, Bianchi, Bianchi-Mendoza, Schmitt-Grohe-Uribe Mundel, Fleming, Gali-Monacelli

Setup

Continuum of small open economies fixed exchange ratedifferent 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 varietyproduced monopolistically technology

Yt(j) = AtNt(j)

UIPNo arbitrage (UIP)

Euler

b

✓Ct+1

Ct

◆�s

=1 + it

1 + pt+1

1 + it = (1 + i⇤t )Et+1

Et(1 + tt)

b

✓C⇤t+1C⇤

t

◆�s

=1 + i⇤t

1 + p⇤t+1

UIPNo arbitrage (UIP)

Euler

b

✓Ct+1

Ct

◆�s

=1 + it

1 + pt+1

1 + it = (1 + i⇤t )Et+1

Et(1 + tt)

b

✓C⇤t+1C⇤

t

◆�s

=1 + i⇤t

1 + p⇤t+1

(Backus-Smith)Ct = QtC⇤t Q

1st

✓Qt+1

Qt

◆s

= 1 + tt

Timing

Start at steady state t=-1At t=0

hit by unexpected shock (path for future)no insurance (incomplete markets)

Shocks1. Productivity2. Export demand 3. Foreign consumption (world interest rate)4. Net Foreign Asset

5. Risk Premium (later)

{C⇤t }

{At}{⇤t}

NFA0

Pricing

1. Flexible Prices2. Rigid Prices3. One-Period Ahead Sticky Prices4. Calvo Pricing

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

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, Transitory Shocks

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, Transitory Shocks

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

One Period Sticky, Permanent Shocks

harder: 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

Role of OpennessClosed economy limit

Perfect stabilization?No intervention: NoOptimal Capital Controls: Maybe

Depends ontype of shock: risk premium yesform of price rigidity

a ! 0

Calvo PricingPoisson opportunity to reset price

cost of inflationcapital controls affect inflation...... prudential interventions?

Continuous time: convenient, initial prices givenCole-Obstfeld case: Log-linearize around symmetric steady state

� = � = ⌘ = 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

Risk Premia ShockRisk Premia ...

natural allocation...appreciation, current account deficit

equilibrium with no capital controls...(smaller) appreciation via inflation(same) current account deficitoutput and consumption boom

it = i⇤t + t + ⌧tyt < 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

00.05

0.1nx 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: constantLean against the wind......more effective when economy more closed

Proposition.

1

⌧t = �1+⇥(1��)

1+⇥

1� ↵+ �✓1��

t

nxt/nxt = 1�1+⇥(1��)

1+⇥

1� �+ �✓1��

1

Proposition.

Closed Economy Limit

Lean against the wind (one-for-one)Perfectly stabilize economy......not true for other shocks

tt = �yt

yt = pH,t = 0

Risk Premium ↵ = 0.4

0 1 2 3 4 5�0.06

�0.04

�0.02

0

q

0 1 2 3 4 50

0.02

0.04

0.06y

0 1 2 3 4 50

0.05

0.1

pH

0 1 2 3 4 5�0.02�0.01

00.010.02

nx and nx

0 1 2 3 4 5�0.05

0

0.05

s and s

0 1 2 3 4 5�0.05

0

0.05

t = i � i⇤ � y

0 1 2 3 4 5�0.06

�0.04

�0.02

0

q

0 1 2 3 4 50

0.02

0.04

0.06y

0 1 2 3 4 50

0.05

0.1

pH

0 1 2 3 4 5�0.02�0.01

00.010.02

nx and nx

0 1 2 3 4 5�0.05

0

0.05

s and s

0 1 2 3 4 5�0.05

0

0.05

t = i � i⇤ � y

Figure 3: Mean-reverting risk premium shock, a = 0.4 (top) and a = 0.1 (bottom).

40

Risk Premium ↵ = 0.1

0 1 2 3 4 5�0.06

�0.04

�0.02

0

q

0 1 2 3 4 50

0.02

0.04

0.06y

0 1 2 3 4 50

0.05

0.1

pH

0 1 2 3 4 5�0.02�0.01

00.010.02

nx and nx

0 1 2 3 4 5�0.05

0

0.05

s and s

0 1 2 3 4 5�0.05

0

0.05

t = i � i⇤ � y

0 1 2 3 4 5�0.06

�0.04

�0.02

0

q

0 1 2 3 4 50

0.02

0.04

0.06y

0 1 2 3 4 50

0.05

0.1

pH

0 1 2 3 4 5�0.02�0.01

00.010.02

nx and nx

0 1 2 3 4 5�0.05

0

0.05

s and s

0 1 2 3 4 5�0.05

0

0.05

t = i � i⇤ � y

Figure 3: Mean-reverting risk premium shock, a = 0.4 (top) and a = 0.1 (bottom).

40

Proposition.

Flexible Exchange Rate

Lean against the wind... ...less than with fixed exchange rateNew: stabilize nominal exchange rate

tt = �ayyt �la

aqappH,t

pH,t 6= 0

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

Capital controlssame with or without coordination!

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

Overall: limited role for coordination

Coordination (Small )↵

Conclusions

Tight characterization of optimal capital controls...

nature of shocksopennesspersistenceprice stickinesscoordination

Eurozone Interest Rates

Eurozone Trade Balance

Eurozone Current Account

Recent Examples33

Figure 2. Evolution of Capital Controls

Sources: AREAER database; and authors’ calculations. Note: For indices of inflow and outflow controls, higher values indicate that the transactions are subject to more restrictions. For the tax and URR indices, higher values indicate that the regulation applies to more types of inflows.

Brazil

2000:01 2002:01 2004:01 2006:01 2008:01-15

-10

-5

0

5

Colombia

2000:01 2002:01 2004:01 2006:01 2008:01-4

-2

0

2

4

6

8

10

Thailand

2000:01 2002:01 2004:01 2006:01 2008:01-20

-15

-10

-5

0

5

10

15

Price-based inflow controlsOther inflow controlsOutflow controls

Korea

2000:01 2002:01 2004:01 2006:01 2008:01-35

-30

-25

-20

-15

-10

-5

0

5

Source: Baba and Kokenyne (2011; IMF)

Recent Examples

Source: Forbes et al (2011)

43