Fiscal Unions

Emmanuel Farhi, HarvardIván Werning, MIT

Currency Unions

Case for flexible exchange rates...Friedman (53)

Currency union...single monetary policy...can stabilize symmetric shockscannot stabilize asymmetric shocks

How to deal with asymmetric shocks?

Optimal Currency Area literature

factor mobility...Mundell (61)

openness...McKinnon (63)

fiscal integration....Kennen (69)

financial integration...Mundell (73)

Currency Unions

Optimal Currency Area literature

factor mobility...Mundell (61)

openness...McKinnon (63)

fiscal integration....Kennen (69)

financial integration...Mundell (73)

Currency Unions

This Paper

Mechanism design meets Keynesian economicsfiscal union as insurance in a currency unioncharacterize optimal arrangement

Dual role of transfersrisk sharingmacroeconomic stabilization

Key result: macro externality in insurance decisions

Within a currency union: social private

Fiscal and monetary unions go hand in handFiscal and financial integration not perfect substitutes

6=

This Paper

Implementation

Complete marketsmacro-prudential portfolio taxes

Incomplete marketsfiscal transfers

Implementation

Complete marketsmacro-prudential portfolio taxes

Incomplete marketsfiscal transfers

Households

U i(CiNT , C

iT , N

i; s)

Households

Country i households maximizes subject to

ZU i(Ci

NT (s), CiT (s), N

i(s); s)�(s)ds

ZDi(s)Q(s)�(s)ds 0

P iNTC

iNT (s) + PT (s)C

iT (s) W i(s)N i(s) + PT (s)E

iT (s)

+⇧i(s) + T i(s) + Di(s)

Households

Country i households maximizes subject to

ZU i(Ci

NT (s), CiT (s), N

i(s); s)�(s)ds

ZDi(s)Q(s)�(s)ds 0

P iNTC

iNT (s) + PT (s)C

iT (s) W i(s)N i(s) + PT (s)E

iT (s)

+⇧i(s) + T i(s) + Di(s)(1 + ⌧ iD(s))

Households

Country i households maximizes subject to

ZU i(Ci

NT (s), CiT (s), N

i(s); s)�(s)ds

ZDi(s)Q(s)�(s)ds 0

CiNT (s) =

✓Z 1

0Ci,j

NT (s)1� 1

" dj

◆ 11� 1

"

P iNTC

iNT (s) + PT (s)C

iT (s) W i(s)N i(s) + PT (s)E

iT (s)

+⇧i(s) + T i(s) + Di(s)(1 + ⌧ iD(s))

FirmsEach variety j of NT

produced monopolistically technology

price set one period in advance

Y i,jNT (s) = Ai(s)N i,j(s)

Government

Government budget constraint

Zero net international fiscal transfers

T i(s) = � iLWi(s)N i(s)� � iD(s)Di(s) + T̂ i(s)

ZT̂ i(s)di = 0

Equilibrium

Household FOCsFirm FOCGovernment budget constraintMarket clearing

CiNT (s) = Ai(s)N i(s)

ZCi

T (s)di =

ZEi

T (s)di

FOCsU iCT

(s)(1 + � iD(s))

Q(s)PT (s)=

U iCT

(s0)(1 + � iD(s0))

Q(s0)PT (s0)U iCT

(s)

PT (s)=

U iCNT

(s)

P iNT

�U iN (s)

W i(s)=

U iCNT

(s)

P iNT

.

P iNT = (1 + ⇥ iL)

⇤

⇤� 1

R Q(s)1+� i

D(s)W i(s)Ai(s) C

iNT (s)�(s)ds

R Q(s)1+� i

D(s)Ci

NT (s)�(s)ds

FOCs

U iCT

(s)

PT (s)=

U iCNT

(s)

P iNT

FOCs

U iCT

(s)

PT (s)=

U iCNT

(s)

P iNT

CiNT (s) = �i(pi(s); s)Ci

T (s)

pi(s) =PT (s)

P iNT

weak separability + homothetic

Alternative: Incomplete markets

Household budget constraint

Government budget constraint

Same implementability conditions!

P iNTC

iNT (s) + PT (s)C

iT (s)

W i(s)N i(s) + PT (s)EiT (s) +�i,j(s) + T i(s)

T i(s) = � iLWi(s)N i(s) + T̂ i(s)

openness

CNT

CT

openness

flex

CNT

CT

openness

flex rigid

CNT

CT

Planning Problem

Constrained Pareto frontier (weights )�i

ZCi

T (s)di =

ZEi

T (s)di

max

P iNT ,PT (s),Ci

T (s)

Z ZV i

✓Ci

T (s),PT (s)

P iNT

; s

◆�i⇡(s) di ds

Planning Problem

Constrained Pareto frontier (weights )�i

ZCi

T (s)di =

ZEi

T (s)di

U i

✓↵i(pi(s); s)Ci

T (s), CiT (s),

↵i(pi(s); s)

Ai(s)Ci

T (s); s

◆

max

P iNT ,PT (s),Ci

T (s)

Z ZV i

✓Ci

T (s),PT (s)

P iNT

; s

◆�i⇡(s) di ds

Optimality ConditionsProposition (Optimal Price Setting).Zero average labor wedge across states for each country:Z

�ip(s)C

iT (s)U

iCT

(s) ⇤ i(s)⇥(s) ds = 0

labor wedgeacross states for each country

across countries for each state

Optimality ConditionsProposition (Optimal Price Setting).Zero average labor wedge across states for each country:Z

�ip(s)C

iT (s)U

iCT

(s) ⇤ i(s)⇥(s) ds = 0

Proposition (Optimal Monetary Policy).Zero average labor wedge across countries for each state:Z

�ip(s)C

iT (s)U

iCT

(s) ⇤ i(s)⇥idi = 0

labor wedgeacross states for each country

across countries for each state

Optimal Risk Sharing

Standard risk sharing condition...... but with social instead of private marginal values

Fiscal and financial integration not perfect substitutes

Proposition (Optimal Risk Sharing).

V iCT

(s)

V i0CT

(s)=

V iCT

(s0)

V i0CT

(s0)

Optimal Risk Sharing

Standard risk sharing condition...... but with social instead of private marginal values

Fiscal and financial integration not perfect substitutes

Proposition (Optimal Risk Sharing).

U iCT

(s)

U i0CT

(s)

1 + ↵i(s)pi(s) ⌧

i(s)

1 + ↵i0 (s)pi0 (s)

⌧ i0(s)=

U iCT

(s0)

U i0CT

(s0)

1 + ↵i(s0)pi(s0) ⌧

i(s0)

1 + ↵i0 (s0)pi0 (s0)

⌧ i0(s0)

Two Implementations

Complete markets + macro-prudential portfolio taxes

Incomplete markets + fiscal transfers

⇥ iD(s) =�i(s)

pi(s)⇥ i(s)

T̂ i(s) = PT (s)(CiT (s)� Ei(s))

Two Implementations

Complete markets + macro-prudential portfolio taxes

Incomplete markets + fiscal transfers

⇥ iD(s) =�i(s)

pi(s)⇥ i(s)

T̂ i(s) = PT (s)(CiT (s)� Ei(s))

Non-Members

Outside currency union, same conditions, but...zero labor wedgesprivately and socially optimal risk sharing coincide no need for macro-prudential portfolio taxesfiscal unions replicate complete markets

Fiscal unions and currency unions go hand in hand

Moral Hazard

Up to now, no incentive issues

Introduce to capture concerns for moral hazard

Tradeoff insurance vs. incentives

More insurance in currency union (social vs. private)

Dynamic Model

Dynamic modelCalvo price settingall goods tradedopenness: home bias in preferencesfraction of HtM consumers with high MPCs (financially constrained)

Impulse Response (No HtM)

5% productivity shock

0 1 2 3 4 5-0.06

-0.04

-0.02

0Output gap

0 1 2 3 4 5-0.1

-0.05

0PPI inflation

0 1 2 3 4 5-0.06

-0.04

-0.02

0Output gap

0 1 2 3 4 5-0.1

-0.05

0PPI inflation

0 1 2 3 4 5-0.06

-0.04

-0.02

0Output gap

0 1 2 3 4 5-0.1

-0.05

0PPI Inflation

1

Optimal Transfers (No HtM)

NPV transfers/GDP: half-life of shock and openness5% productivity shock

02

46

810

00.2

0.40.6

0.810

0.01

0.02

0.03

0.04

1

Stabilization (No HtM)

Stabilization: half-life of shock and openness

02

46

810

00.2

0.40.6

0.810

0.2

0.4

0.6

0.8

1

1

Impulse Response (HtM)

0 1 2 3 4 5-0.06

-0.04

-0.02

0Output gap

0 1 2 3 4 5-0.1

-0.05

0PPI inflation

0 1 2 3 4 50

0.002

0.004

0.006Transfer

0 1 2 3 4 5-0.06

-0.04

-0.02

0Output gap

0 1 2 3 4 5-0.1

-0.05

0PPI inflation

0 1 2 3 4 50

0.01

0.02

0.03

0.04Transfer

0 1 2 3 4 5-0.06

-0.04

-0.02

0Output gap

0 1 2 3 4 5-0.1

-0.05

0PPI Inflation

0 1 2 3 4 50

0.05

0.1Transfer

1

5% productivity shock

Stabilization (HtM)

24

68

10

00.2

0.40.6

0.810

0.2

0.4

0.6

0.8

1

1

Stabilization: half-life of shock and openness

Optimal Transfers

24

68

10

00.2

0.40.6

0.810

0.04

0.08

0.12

1

NPV transfers/GDP: half-life of shock and openness5% productivity shock

Transfers vs. Other Instruments

Transfers vs. Other Instruments

Transfers vs. Other Instruments

Transfers vs. Other InstrumentsTransfers: better for more persistent shocks, more closed economies, more sticky prices, fraction of HtM improves for more transitory shocks and more flexible prices

Capital controls: better for more transitory shock, more closed economies, more flexible prices

Government spending: less sensitive to persistence, openness, stickiness, HtM

Redistribution and deficits: only with fraction of HtM, better for more transitory shocks, more closed economies, more flexible prices

Baseline calibration: transfers dominate all other instruments

ConclusionSpecial argument for fiscal unions in currency unions

Key determinants of optimal insurance arrangementasymmetrypersistenceopennessfinancial constraints (HtM)

Baseline calibration: transfers dominate domestic fiscal policy and capital controls