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A model of an optimum Currency Area
Lucas Antonio RicciResearch Department, International
Monetary Fund (2008)
Aim of this article
• Develops a model of the circomstances under which it is beneficial to participate in a currency area (CA in the following).
• CA : fixed exchange rate (ER) regime or single currency within an area, flexible ER with RoW.
• Mundell (61) : OCA if cost of relinquishing ER as an instrument of adjustment are outweighed by benefits of adopting single currency.
Interest of this paper
• The model attempts to capture most of the cost-benefit analysis in a monetary model of trade with nominal rigidities.
• simultaneous analysis of both the real and monetary aspects of the optimum currency area literature.
What we do today
1. Theoretical costs/benefits of adopting a single currency
2. Description of the model3. Shocks and adjustment under different
exchange rate regimes (flexible ER vs. CU)4. Cost/benefit analysis of a CU
1) Theoretical costs/benefits of adopting a CU.
1. Cost of adopting a CU Abandoning ER has a cost iff ER between 2
areas is an effective instrument of short run adjustment. Thas is to say :
- 2 areas face asymmetric shock ; - Domestic prices not fully flexible ;- Pass-through is not large ;- Adjustment through ER less costly than other
instrument.
1) Theoretical costs/benefits of adopting a CU.
2. Benefits of adopting single currency (Mundell, 61) :
• Elimination of transaction costs• Better performance of money as medium of
exchange and as unit account : - Elimination of relative price distorsions ; - Elimination of ER uncertainty.
1) Theoretical costs/benefits of adopting a CU.
2. Benefits of adopting single currency (next)• Important criterion : similarity of pre-union
inflation rates (Fleming, 71). - countries may have different Phillips curve. - Inflation as a tax instrument (Canzoneri &
Rogers) - « the advantage of tying one’s hands » BUT : some could loose
2) The Model
2.1) Structure and agent’s behavior2.1.1) Uncertainty, rigidities and timing of actions• Uncertainty arises from demand and monetary shocks• Wages are rigid• Extreme version of Phillips curve in price and employment:
flat at the marginal cost pricing below full employment, vertical once reached (labor supply is infinitely elastic at given wage until full employment is reached, taking wages as given, firms choose competitively optimal employment and prices).
2) The Model
2.1.2) Technology and specialization • Each country produces one traded good (A at home,
B abroad) and a non traded good (N, N*)
• Supplies of goods:
** **
NS LN
AS LA **
BS LB
** **
NS LN
2) The Model
2.1.3) PreferencesIndividuals gave Cobb-Douglas preferences over money,
traded goods and non traded goodsFor home :
s.t.
with tau Samuelson iceberg-type transaction cost.
1)1(* )'()( iiiii mNBAU
iiiiNiBiA mymNpBepAp '*
2) The Model
2.1.4) Shocks and monetary rulePossible inflationary bias of the monetary authorities introduced
through exogenous and anticipated ( ) increase in national money stocks
With redistribution of money across countries that equilibrates money market.
)1(0 WWS
)1(0 CUCU
CU MM
)1(0 MM FLEX
CU
),( *
2) The Model
2.2.1) Consumers behaviorMaximizing the consumers problem and aggregating
(for home):
And for money,
)( MYAp dA
)(* MYBep db
))(1( MYNp dN
))(1(' MYM
2) The Model
2.2.2) Firm’s behaviorDomestic and foreign firms maximize their profits.t. (for home) : For domestic country, either
Or :
LLLww NAS ;
LLLw
pw
p NAS
NS
A ;;
LLLw
pw
p NAS
NS
A ;;
2) The Model
2.2.3) Market’s equilibriumGoods market:
Money market:
)()()1( **** MYeMYYNpAp SN
SA
MY
1
2) The Model2.2.3) Market’s equilibrium (next)When goods and money markets are in equilibrium,
trade balance = 0
In flexible ER, determines the level of ER :
In a CU (e=1), determines the distribution of the world money stock, accross the countries, consistent with equilibrium :
011
**
****
MeMBepApTB d
Bd
A
***
*
)1(
)1(
M
Me
)1(
)1(*
**
*
M
M
2) The Model
2.2.4) Initial equilibrium
From market equilibrium, we get :
From zero profit condition:
000 MLwy
0
*0
*
*0
0
L
L
w
w
*0
0
0
0
0
0
*
*
*0
0*
;;N
B
N
A
B
A
p
p
p
p
w
w
p
p
3) Shocks and adjustment
3. Shocks and ajustment3.1) Flexible ERMoney stocks would change only because of the monetary
increase due to inflationary bias.
ER flexibility neutralizes prefectly any effect on nominal income of foreign monetary shocks and demand shocks to tradable.
*** 22ˆ
2ˆ
0ˆ
e
y
M
3) Shocks and adjustment
3.2) Currency Unione=1 and tau=1
Money supply changes not only because of inflationary bias, but also because of redistribution
0*0
0*0 )2(2
ˆ**
CUy
0*0
0 )22(ˆ **
CUM
3) Shocks and adjustment
3.3) Labor mobility as a form of adjustmentThe migration flow that would fully adjust the demand
shocks is
If partial labor mobility,
*
0*0
00 )( * dLL
dL
0*0
00*0*
))(1(22 **
qY CU
3) Shocks and adjustment
3.4) Fiscal federalism
tdY = - tdY* with
: change in income due to real shocks that is absorbed by tax scheme
Where n = 1 – epsilon - q
)1)(1(
)(
0*
0
0*
0
t
10
xN
Y CUCU
0*0
00*0*
)(22 **
3) Shocks and adjustment
3.5) Expected inflation and unemployment in the two ER regimes
Under flexible ER,
Under CU,
CE 2)( CuE 2)(
xCU CE )( xCuE )(
4) Cost-benefit analysis of a currency union
Loss function :
The 2 countries constitute an OCA if both expect positive gains from CU
)( TCuEH
02)1( CHFLEX
CUCU x
CH )1(
0)()2()1( CUxCNB
4) Cost-benefit analysis of a currency union
4.1) Adjustment cost component
We focus on the NB resulting from the adjustment cost in terms of inflation and unemployment.)2( xAC DNB
)2( xAC DNB
4) Cost-benefit analysis of a currency union
4.1.1) Monetary shocks
If real shocks are absent or fully adjusted, the adjustment cost component due to the monetary shocks is
)2)()()((2 ** 0*0
20
2*0
10
*0 DNBACM
4) Cost-benefit analysis of a currency union
4.1.2) Real shocks
If one neglects monetary shocks, the adjustment cost component due to the real shocks is
02)( 22210
*00 **
DnNBACR
4) Cost-benefit analysis of a currency union
4.1.3) Correlation between monetary and real shocks • A positive correlation between monetary shocks and
demand shocks to domestic tradables reduces variability of x, decreases adjustment cost of a CU : increases net benefits for home.
• A negative correlation increases the net benefit for the home country
Different levels of correlation between monetary and real shocks are associated with different advantages for either one country or the other.
4) Cost-benefit analysis of a currency union
4.2) The inflationary bias component
« the advantage of tying one’s hands »
4.3) Transaction costs
Increases with openess
0TCNB
)( CUIBNB
4) Cost-benefit analysis of a currency union
4.4) Openess
Effect unclear
