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
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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