mobility within currency unions - bde
TRANSCRIPT
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Mobility within Currency Unions
Emmanuel Farhi, HarvardIván Werning, MIT
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Mobility and Adjustment
Regions in a currency union suffer shocksUS statesEurozone countries
Q: Mobility helps macroeconomic adjustment?
A: Mundell (61), OCA literature: YES!
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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
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This Paper
Formal model with nominal rigidities
revisit Mundell’s positive results
provide normative benchmark
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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
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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
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The Model
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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!
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Outline
Model 1: Internal Demand Imbalances
Model 2: External Demand Imbalances
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Model 1 RegionsAgent types
Homogenous traded goodcompetitiveendowmentflexible price
Non-traded goods monopolistically competitiveproduced from local laborrigid price
i 2 I
j 2 J
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Model 1 One period model
Price fixedEx post asymmetric shocks
preferencestechnologyendowments (wealth)
EitherUnanticipated shocksAnticipated but prices set before realization
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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
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AgentsRich location preference and mobility costs embedded in utility
Example
previous residence...
... plus mobility costs...
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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
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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
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Equilibrium Without Free Mobility
Households optimizeFirms meet demand Government budget constraints holdMarkets clear
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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
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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
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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
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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
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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
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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
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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
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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
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Model 2
Each region produces different traded goodall goods tradable...... but allow home bias
Each traded goodproduced from local laborrigid price
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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
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Rest of ModelKey differences
structure of demandno endowment good
Rest, same as before...firmsgovernmentequilibriumadditional assumptions: profit tax, preferences
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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>
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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
�
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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
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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 (�)
�
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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
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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
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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
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Sticky Wages
Once again, here...
Sticky price = Sticky wage
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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?
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ConclusionModel
costly mobilityprice/wage rigidities
Key insightmovers take demand for goods, not just labor supplypossible inefficiencies
Key dimensionstructure of demand
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Appendix Slides
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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
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Government Each region must balance its budget
X
j2J
µi,jTi = ⌧L,iWiNi + ⌧⇡,i
✓Pi �
1 + ⌧L,i
AiWi
◆Yi
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EquilibriumAs in model 1...
Two notions of equilibrium:equilibrium without free mobilityequilibrium with free mobility
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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