Mobility within Currency Unions

Emmanuel Farhi, HarvardIván Werning, MIT

Mobility and Adjustment

Regions in a currency union suffer shocksUS statesEurozone countries

Q: Mobility helps macroeconomic adjustment?

A: Mundell (61), OCA literature: YES!

Mundell and OCA

Broader question of macroeconomic stabilization of a currency union with nominal rigidities

Optimal Currency Areas (OCA): mobility (Mundell 61)openness (McKinnon 63)fiscal integration (Kennen 69)

Meade (57)

wage rigidities

This Paper

Formal model with nominal rigidities

revisit Mundell’s positive results

provide normative benchmark

This PaperMigration out of depressed regions

movers improve...... but regions? macroeconomic stabilization?

Effect on stayers?Too much or too little migration? Where?

Key insight: workers take not only their labor, but also their demandKey dimension: internal vs. external imbalances

Related LiteratureOCA: Mundell, McKinnon

Currency Unions: Farhi-Werning

Island models: Lucas-Prescott, Alvarez-Veracierto, Shimer, Alvarez-Shimer, ...

Trade models: Dornbusch, Fischer, Samuelson

Mobility Gains: Kennan

The Model

Price or Wage Rigidity?Wage rigidity prime suspectAre wages rigid?

Bewley...firms don’t cut wageswouldn’t help anyway! sales...

Price rigidity? Real rigidities? Interactions? In our models: wage and price rigidity similar!

Outline

Model 1: Internal Demand Imbalances

Model 2: External Demand Imbalances

Model 1 RegionsAgent types

Homogenous traded goodcompetitiveendowmentflexible price

Non-traded goods monopolistically competitiveproduced from local laborrigid price

i 2 I

j 2 J

Model 1 One period model

Price fixedEx post asymmetric shocks

preferencestechnologyendowments (wealth)

EitherUnanticipated shocksAnticipated but prices set before realization

Agents

Agents types total mass mass in region

µj

µi,j

U i,j = maxCi,j

T ,Ci,jNT ,Ni,j

U i,j(Ci,jT , Ci,j

NT , Ni,j)

PTCi,jT + PNT,iC

i,jNT WiN

i,j + EjT + Ti +

X

k2I

⇡j,k⇧k

i

j

AgentsRich location preference and mobility costs embedded in utility

Example

previous residence...

... plus mobility costs...

FirmsFinal non-traded good produced competitively

Each varietyproduced monopolistically technologyfixed price

Symmetry...

YNT,i =

✓Z 1

0YNT,i,l

1� 1" dl

◆ 11� 1

"

YNT,i,l = AiNi,l

PNT,i,l = PNT,i

YNT,i,l = YNT,i = AiNi

⇧i = (1� ⌧⇡,i)

✓PNT,i �

1 + ⌧L,i

AiWi

◆YNT,i

Government Regional budget balance

Alternativetransfers across regionsfiscal unions (Farhi-Werning 2012)

X

j2J

µi,jTi = ⌧L,iWiNi + ⌧⇡,i

✓PNT,i �

1 + ⌧L,i

AiWi

◆YNT,i

Equilibrium Without Free Mobility

Households optimizeFirms meet demand Government budget constraints holdMarkets clear

Equilibrium With Free Mobility

Households optimizeFirms meet demand Government budget constraints holdMarkets clear

Agents locate optimally

µi,j = 0 if U i,j < maxi02I

U i0,j

Additional Assumptions Profits fully taxed

Preferences over consumption and laborregion specific, not agent specificseparable between consumption and leisurehomothetic over consumption

⌧⇡,i = 1

Ti =PNT,iYNT,i �WiNi

µi

EquilibriumPer capita allocation...

Labor wedge

Ci,jT = ET

Ci,jNT = ↵i(pi)ET

N i,j = ↵i(pi)ET

Ai

⌧i = 1 +1

Ai

U i,jN

U i,jCNT

First bestBoomBust

ti = 0

ti < 0

ti > 0

Equilibrium

Movers out of depressed region better off... ... aggregate economic activity in currency union increases...... partial vindication of Mundell (1961)...... qualification: no impact on stayers

Intuition: move with your demand

Proposition (Per-capita allocations).Given , per-capita allocation of agents of type in region is independent of location decisions.

PT j

i

Social Optimum Indirect utility function

Restricted social planning problem given

Full social planning problem

V i,j(Ci,jT , pi) = U i,j

✓Ci,j

T ,↵i(pi)Ci,jT ,

↵i(p)

AiCT

◆

PT

W (PT ) = maxµi,j

X

i2I,j2J

�jµi,jV i,j

✓ET ,

PT

PNT,i

◆

X

i2I

µi,j = µj

maxPT

W (PT )

constrained efficient given monetary policy

constrained-efficient

Optimal Mobility

Intuitionno spillovers from mobility decisionsno need for government intervention

Proposition (Optimal mobility).Constrained efficient allocation given monetary policy are consistent with free mobility.PT

Optimal Monetary Policy

Monetary policystabilizes currency union on average both depressed and booming regions

Proposition (Optimal monetary policy).Constrained-efficient allocations satisfy

X

i2I,j2J

�jµi,j↵ipETU

i,jCT

⌧i = 0

Sticky Wages Sticky wages instead of sticky prices

Take as given (fixed)Either

rationing: equal sharing of labor within regionmonopolistic suppliers

All results go through unchanged!

Wi

Model 2

Each region produces different traded goodall goods tradable...... but allow home bias

Each traded goodproduced from local laborrigid price

Agents

Problem of agent of type living in region ij

Ui,j = maxCi,j

k ,Ni,jUi,j({Ci,j

k }, Ni,j)

Âk2I

PkCi,jk + WiNi,j + Ti + Â

k2Ip j,kPk

Rest of ModelKey differences

structure of demandno endowment good

Rest, same as before...firmsgovernmentequilibriumadditional assumptions: profit tax, preferences

Income in country iCountry i spending on k

... total income for k

Equilibrium

Ci,jk =

1

µi↵ikPi

PkYi

Ci,j =1

µi

Pi

P iYi

consumption index price index

N i,j =1

µi

Yi

Ai<latexit sha1_base64="LXs93bLTjyY/FUAGi1nMuMJP6l0=">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</latexit>

Structure of Demand

positive constant union-wide aggregate demandpinned down by monetary policy

Proposition (Structure of demand).

Exists { } such thatY ⇤i

Yi = �Y ⇤i

�

Equilibrium

As before...movers better off

Now...stayers also improve!

Simplest case: no home bias

Proposition (Per-capita allocations).Given per-capita consumption and labor allocation of agents of type in region depends on the equilibrium only through the sufficient statistic , to which it is inversely proportional.

j i�

µi

Social Optimum Restricted social planning problem given

Full social planning problem

X

i2I

µi,j = µjconstrained efficient given aggregate demand management

constrained-efficient

W (�) = maxµi,µi,j

X

i2I,j2J

�jµi,jU i,j

✓�Pi

P i

Y ⇤i

µi,�

Y ⇤i

Aiµi

◆

X

j2J

µi,j = µi

max�

W (�)

�

Optimal Mobility

Optimality condition for mobility

Inconsistent with free mobility

Proposition (Optimal mobility).Constrained efficient allocation given union-wide aggregate demand management are inconsistent with free mobility.

�

µi,j = 0 if U i,j � �i�j

< maxi02I

U i0,j � �i0

�j

�i = � +X

j2J

�j µi,j

µi�Pi

P i

Y ⇤i

µiU i,jC ⌧i

µi,j = 0 if U i,j < maxi02I

U i0,j

Optimal MobilityImpact on stayers’ welfareLabor wedge is sufficient statisticNot internalized by private agentsGovernment intervention required

not enough migrations out of depressed regionspotentially wrong destinations too

⌧i

Optimal Monetary Policy

Union-wide aggregate demand management stabilizes currency union on average

Proposition (Optimal monetary policy).Constrained-efficient allocations satisfy

X

i2I,j2J

�jµi,j Pi

P i

Y ⇤i

µiU i,jC ⌧i = 0

Sticky Wages

Once again, here...

Sticky price = Sticky wage

Looking aheadModel 3...

endowment and home biasnests model 1 and 2

Other extensions...heterogeneity: negative spillover on stayers? fixed factors: capitalprice/wage adjustmentsdynamicsother rationing rules?

ConclusionModel

costly mobilityprice/wage rigidities

Key insightmovers take demand for goods, not just labor supplypossible inefficiencies

Key dimensionstructure of demand

Appendix Slides

FirmsFinal non-traded good produced competitively

Each varietyproduced monopolistically technologyfixed price

Impliesoutputtotal profits

Yi =

✓Z 1

0Yi,l

1� 1# dl

◆ 11� 1

#

Yi,l = AiNi,l

Pi,l = Pi

Yi,l = Yi = AiNi

⇧i = (1� ⌧⇡,i)

✓Pi �

1 + ⌧L,i

AiWi

◆Yi

Government Each region must balance its budget

X

j2J

µi,jTi = ⌧L,iWiNi + ⌧⇡,i

✓Pi �

1 + ⌧L,i

AiWi

◆Yi

EquilibriumAs in model 1...

Two notions of equilibrium:equilibrium without free mobilityequilibrium with free mobility

Additional Assumptions Profits fully taxed and redistributed to local agents

Preferences of different agent types in a given region represent the same preference ordering

separable between consumption and leisurehomothetic over consumption

⌧⇡,i = 1

Ti =PiYi �WiNi

µi