Sharing Money Creation in a Monetary Union*

Stephane Auray, Aurelien Eyquem,

Gerard Hamiache, and Jean-Christophe Poutineau

Abstract

This paper focuses on the way money creation is shared among the members of

the European Monetary Union. To address this issue, we construct a two-country

New Open Economy Macroeconomics model of an asymmetric monetary union with

an incomplete financial market and home bias in consumption. Two sharing rules

consistent with the current regulations of the European System of Central Banks

are examined. First, each participating National Central Bank supplies half of the

European Central Bank determined money creation in the monetary union. Second,

each National Central Bank adapts the national increase in money demand, under

the constraint that the total money creation in the union does not exceed the level

determined by the European Central Bank for the whole union. We adopt a linear-

quadratic procedure, and show that the current sharing rule, which ignores countries’

heterogeneity, is superior in terms of welfare. The key role of the current account is

emphasized. It proves an e!cient decentralized mechanism for allocation of money.

Keywords: Monetary Union, New Open Macroeconomics Economy, Sharing Rule.

JEL Classification numbers: E51, E58, F33, F41.

*Auray: GREMARS-EQUIPPE, Universite de Lille III, Domaine universitaire du Pont de Bois, B.P. 60149,59653 Villeneuve d’Ascq Cedex, France, and CIRPEE, Canada. E-mail: stephane.auray@univ-lille3.fr.Eyquem: CREM CNRS, Universite de Rennes 1 - 7, place Hoche, 35065 Rennes Cedex, France. E-mail:aurelien.eyquem@univ-rennes1.fr. Hamiache: GREMARS-EQUIPPE, Universite de Lille III, Domaine uni-versitaire du Pont de Bois, B.P. 60149, 59653 Villeneuve d’Ascq Cedex, France. E-mail: gerard.hamia-che@univ-lille3.fr. Poutineau: CREM CNRS, Universite de Rennes 1 - 7, place Hoche, 35065 RennesCedex, France. Ecole Normale Superieure de Cachan. E-mail: jean-christophe.poutineau@univ-rennes1.fr.We would like to thank the editor, Menzie Chinn, and two referees for insightful comments which led toa substantial revision of the paper. Useful input has been derived from discussions during presentationsat various conferences. We are indebted to Marjorie Sweetko for her excellent editing. The traditionaldisclaimer applies.

1

1. Introduction

In the European Monetary Union, money creation is shared on the basis of ho-

mogeneous treatment of its members (see “The Monetary Policy of the ECB,” 2nd

edition, January 2004, p. 72). This paper compares this current rule with a shar-

ing rule which takes account of national particularities. We consider two situations

that are consistent with the current regulations of the European System of Central

Banks (ESCB). First, each participating National Central Bank (NCB) supplies half

of the money creation determined by the European Central Bank (ECB) (and agents

are able to satisfy their money demand through money transfers within the union).

Second, each NCB accommodates the national increase in money demand, under the

constraint that total money creation in the union does not exceed the level determined

by the ECB for the whole union. We then evaluate the welfare gains associated with

these situations.

We address this issue in a two-country New Open Economy Macroeconomics

(NOEM) model of an asymmetric monetary union where two crucial assumptions

are made: financial markets are incomplete and there is home bias in consumption.

Further, it is worth noting that the following two assumptions are really borne out by

observations in practice.

(i) The incompleteness of financial markets allows agents to transfer wealth within the

union and restores the current account as an additional stationary external adjust-

ment channel. In a model with perfect risk-sharing, wealths are equal. When money

does not circulate in the monetary union, this implies that the net foreign assets are

stationary and, depending on parameter values, that the current account is balanced.

But when money circulates, introducing a di"erence in money demand and supply

patterns implies that money flows permanently a"ect net foreign assets.

(ii) Without home bias in consumption, agents have similar consumption baskets and

face similar consumer price levels and inflation rates; the current account is always

balanced and money demands are equal across the monetary union. In such a case,

there is no di"erence between a situation where the ECB supplies the amount of money

required in each country (which is the same in both countries) and a situation where

the ECB supplies the same amount of money to each NCB.

We assume that national economies are a"ected by asymmetric shocks, which is

in line with the findings of Camacho et al. (2006) among others, and that the estab-

2

lishment of the monetary union in Europe has not significantly increased the level of

co-movements across Euro-area economies. Union members may also di"er in terms

of nominal rigidities, which appears consistent with empirical contributions, such as

Alvarez et al. (2006).1 Adopting the linear-quadratic (LQ) procedure of Benigno and

Woodford (2006), we compute the optimal commitment monetary policy. Unfortu-

nately, this first best is not feasible given the set of constraints applied to the bank

policy, in particular the Harmonized Index of Consumer Price Index (HICP)2 based

measurement of inflation.

The main result of this paper is that the current sharing rule, which ignores

countries’ heterogeneity, is superior to the second sharing rule in terms of welfare.

This result is robust to a wide range of parameter combinations, and gains range from

0.05% to 0.26% of permanent consumption, depending on parameter values. Our

results show that the current account plays a key role by favoring smooth external

adjustment, since it provides the required quantity of money to national economies

while keeping the monetary union closer to its optimal monetary policy path.

The paper is organized as follows: Section 2 describes a two-country world that

forms a monetary union. Section 3 presents both the linear dynamics of the model and

the quadratic loss function. Section 4 focuses on the definition of di"erent monetary

policies compatible with ECB status. Section 5 compares the impact of these policies

in terms of welfare. Conclusions are o"ered in Section 6.

2. An Asymmetric Monetary Union

We assume a two-country monetary union sharing the same currency and which

delegates monetary policy to the Union Central Bank (UCB). In other words, gov-

ernments and NCBs implement the monetary policy decided by the UCB.3 Nominal

exchange rate issues are beyond the scope of this paper, being equal to one in our

model.4 Each nation is populated by N infinitely-living households, and an infinite

number of firms specialized in the production of di"erentiated goods. The financial

market between the two countries is incomplete and countries only trade one period

composite bond. The goods market is characterized by home bias in consumption

practices and a gradual adjustment of goods prices.

2.1 Households

In each country the number of infinitely-living households is normalized to one.

3

The representative household j ! [0, 1] of nation i ! {h, f} maximizes a welfare index

#it(j),

#it(j) =

!!

s=t

!s"tEt

"Ci

s(j)1"!

1 " "+

#

1 " $

#M i

s(j)P i

s

$1""

" N is(j)1+#

1 + %

%, (1)

subject to the budget constraint,

RtBit(j) + W i

t Nit (j) + $i

t(j) " T ig,t(j) = Bi

t+1(j) + P it C

it(j)

+ Pi,tACit(j) + M i

t (j) " M it"1(j) " T i

b,t(j), (2)

and the transversality condition, limT#!$T$=tR

"1$ Et

&Bi

T+1(j)'

= 0. The parameter

! = (1 + &)"1 is the subjective discount factor, Cit(j) is the consumption bundle

chosen by the representative agent, N it (j) is the quantity of labor of type j that

is competitively supplied to the firms of country i, " is the index of risk aversion,

and %"1 determines the Frischian elasticity. In Eq. (2), W it (j) is the nominal wage

corresponding to type j labor supplied in country i for period t, $it(j) =

( 10 $i

t(k, j)dk

is the profit paid by national firms to the representative national agent j, Bit(j) is the

holding of the composite one-period nominal bond at the end of period t " 1 paying

a gross nominal rate of interest Rt between periods t" 1 and t. In addition, T ib,t(j) is

a lump-sum transfer from NCBs to households and T ig,t(j) is a lump-sum tax paid by

household j to the national government of country i, P it is the consumer price index

in country i in period t. Finally, Pi,t is the producer price index in country i in period

t and ACit(j) represents portfolio adjustment costs.

We assume that households can trade a one-period composite financial asset. Buying

(resp. selling) bonds a"ects the individualized interest rate negatively (resp. posi-

tively), so that (i) agents have a strong incentive to return to their initial position

in the long run and (ii) agents belonging to a creditor country face lower nominal

interest rates than agents in a debtor country. As underlined by Schmitt-Grohe and

Uribe (2003), this assumption is a convenient way to balance the current account in

the long run. In this model, it is not possible to introduce asymmetries into the finan-

cial friction, since the premium paid by the debtor agent perfectly equates with the

premium received by the creditor agent. We assume the standard quadratic form for

portfolio adjustment costs,

ACit(j) =

'

2)Bi

t+1(j) " Bi(j)*2

,

4

where Bi(j) is the steady-state level of net foreign assets and ' is the portfolio adjust-

ment cost. Portfolio adjustment costs a"ect the Euler condition since,

Et

&P i

t+1Cit+1(j)

!'

= !Iit+1P

it C

it(j)

!, (3)

with, Iit+1(j) = Rt+1

)1 + 'Pi,t(Bi

t+1(j) " Bi(j))*"1. The value of ' a"ects the in-

tertemporal consumption choice described by Eq. (3). An increase in the cost of

bond trading reduces the sensitivity of wealth accumulation to a variation in interest

rate, as it becomes more costly to smooth consumption. The labor supply function is

standard since it depends on the level of consumption and on the real wage,

N it (j)

# =W i

t

P it C

it(j)!

.

The money demand depends on consumption and on the individualized nominal in-

terest rate, +M i

t (j)P i

t

,"

= #

+Iit+1

Iit+1 " 1

,Ci

t(j)!.

Shocks and nominal rigidity asymmetries between both countries induce di"erences in

the pattern of money demand, creating room for alternative monetary policies. The

Union System of Central Banks (USCB) can either address these di"erences or treat

countries identically, letting money circulate to provide the right amount of money in

the right place. In this paper, we assess the value of the latter decentralization mech-

anism and show that the second type of policy beats the first type in terms of welfare.

To do this, an incomplete financial market between the two countries is required. In

such a case, when the elasticity of substitution between home and foreign goods is

unitary, the terms of trade replicate the allocation of complete markets (see Cole and

Obstfeld (1991) and Corsetti and Pesenti (2001)). As a consequence, the assumption

of financial market incompleteness is neutral with respect to terms of trade adjustment

and weakly contributes to welfare losses in our framework. However, the incomplete-

ness of the financial market is a crucial modelling hypothesis since it allows agents

to transfer wealth within the union and restores the current account as an additional

stationary external adjustment channel. In a model with perfect risk-sharing, wealths

are equal. When money does not circulate in the monetary union, this implies that

the net foreign assets are stationary and, depending on parameter values, that the

current account is balanced. But when money circulates, introducing a di"erence in

5

money demand and supply patterns (M it (j) " M i

t"1(j) " T ib,t(j)) means that money

transfers permanently a"ect the net foreign assets and induce non-uniqueness of the

steady state and non-stationarity. Moreover, in the special case of $ = 1, assuming

perfect risk-sharing implies similar money demands, leaving no room for alternative

monetary policies.

Following Galı-Monacelli (2005) and Corsetti-Pesenti (2005), we assume home bias in

the consumption bundles. The aggregate consumption of consumer j living in country

i, Cit(j) and the companion consumption price index P i

t are,

Cit(j) =

)(%i

i (1 " (i)1"%i*"1

CiH,t(j)

1"%iCiF,t(j)

%i , P it =

-P i

H,t

.1"%i-P i

F,t

.%i ,

where (i !)0, 1

2

*represents the openness of the final goods market in country i

with (h + (f = 1 (see Corsetti (2006)). The consumption sub-indices are CiH,t(j) =

[( 10 Ci

H,t(k, j)!!1

! dk]!

!!1 , and CiF,t(j) = [

( 10 Ci

F,t(k, j)!!1

! dk]!

!!1 , where CiH,t(k, j) (resp.

CiF,t(k, j)) is the consumption of a typical final good k of home (resp. foreign)

country by the representative consumer j of country i and ) > 1 is the elastic-

ity of substitution between national varieties of final goods. The law of one price

holds and the corresponding prices of domestic and foreign goods in country i are,

P iH,t = PH,t = [

( 10 PH,t(k)1"&dk]

11!! and P i

F,t = PF,t = [( 10 PF,t(k)1"&dk]

11!! .

In a monetary union, the nominal exchange rate is constant. We consequently

define the real exchange rate as Qt = P ft

P ht

, which, after defining the terms of trade in

the monetary union as St = PF,t

PH,t, implies Qt = S1"2%h

t .

Finally, optimal variety demands are defined as,

CiH,t(k, j) = (1 " (i)

+PH,t(k)PH,t

,"&

S%it Ci

t(j), CiF,t(k, j) = (i

/PF,t(k)P i

F,t

0"&

S1"%it Ci

t(j).

We assume that countries are a mirror image of each other, so that (h = ( and (f

= 1 " (. Thus, a bias in favor of the national goods consumption in each country

requires that ( < 12 . Finally, the demand corresponding to portfolio costs writes as

ACit(j) = [

( 10 ACi

t(k, j)!!1

! dk]!

!!1 .

2.2 Firms

We normalize the number of firms to 1 in each economy. The representative firm

k ! [0, 1] of nation i ! {h, f} is the monopolistic provider of quantity Y it (k) of the kth

6

variety of final good in this economy according to, Y it (k) = Ai

tLit(k) where Ai

t+1 =

"iaAi

t + *it+1, and where *i

t+1 is iid. The marginal cost of firm k in country i ! {h, f}

writes,

$it(k) =

+(1 " +) P i

t (k) " W it

Ait

,Y i

t (k), (4)

with Y it (k) =

1Pi,t(k)

Pi,t

2"& 1Ch

i,t + Cfi,t + ACi

t

2where Ci

H,t =( 10 Ci

H,t(j)dj, CiF,t =

( 10 Ci

F,t(j)dj, and ACit =

( 10 ACi

t(j)dj. In Eq. (4), + is a subvention that compen-

sates for the distorting e"ects of monopolistic competition in the economy.5

Following Calvo (1983), we assume that in economy i ! {h, f}, a fraction-1 " ,i

.of

firms sets new prices each period, with an individual firm’s probability of re-optimizing

in any given period being independent of the time elapsed since it last reset its price.

Contrary to the typical mark-up behavior that would prevail in flexible price settings,

firms set higher prices according to the period during which they expect to be unable

to reset. Since households own firms, producers maximize the anticipated path of

profits per units of wealth, i.e.,

ArgmaxPi,t(k)

!!

v=0

-,i!

.vEt

3Y i

t+'(k)P i

t+'Cit+'(j)!

4(1 " +) Pi,t(k) " W i

t+v

-Ai

t+v

."156

,

implying,

P $i,t(k) =

)

() " 1) (1 " +)

7!v=0

-,i!

.vEt

3Y i

t+"(k)W it+v(Ai

t+v)!1

P it+"Ci

t+"(j)#

6

7!v=0 (,i!)v Et

8Y i

t+"(k)

P it+"Ci

t+"(j)#

9 .

Finally, aggregating among final firms and assuming behavioral symmetry of Calvo

producers, the average price of final goods in nation i ! {h, f} is,

Pi,t =)-

1 " ,i.P $

i,t(k) 1"& + ,iP 1"&i,t"1

* 11!! .

2.3 Authorities

In this model, fiscal policy is aimed at closing first order distortions, i.e, national

governments compensate for distortions on the goods market by taxing households to

finance support to firms,

: 1

0T i

g,t(j)dj + +

: 1

0Pi,t(k)Y i

t (k)dk = 0.

7

We assume that the USCB combines a UCB and two NCBs. The UCB controls

the nominal interest rate Rt+1 that endogenously determines the quantity of money

to be supplied in the union (see Beetsma and Jensen (2005)) and NCBs supply the

corresponding increase or decrease V it to their national economy, so that for i ! {h, f},

: 1

0T i

b,t(j)dj = V it ,

and,12V h

t +12V f

t = V ut = V u

t (Rt+1) .

Identical treatment of NCBs in the implementation process means that each provides

half of the money increase determined by the UCB.

2.4 General Equilibrium

Defining the aggregate supply as, Y it =

1( 10 Y i

t (k)!!1

! dk2 !

!!1, national goods mar-

kets clear according to,

Y ht = (1 " () S%

t Cht + (S1"%

t Cft + ACh

t ,

Y ft = (1 " () S"%

t Cft + (S%"1

t Cht + ACf

t .

Labor is immobile, thus for i ! {h, f},

N it =

: 1

0N i

t (j)dj =: 1

0Li

t(k)dk,

and the aggregate production function of country i ! {h, f} is, Y it DPi,t = Ai

tNit ,

where DPi,t =( 10

1Pi,t(k)

Pi,t

2"&dk is the dispersion of production prices in country i.

The equilibrium on the money market gives,

: 1

0M

dht (j)dj +

: 1

0M

dft (j)dj = M

dut ,

implying, by Walras law, the following equilibrium of the international financial mar-

ket, : 1

0Bh

t (j) +: 1

0Bf

t (j)dj = 0.

Finally, the aggregation of (nominal) national constraints for country i ! {h, f} yields

the following intertemporal equilibrium condition,

Bit+1 " RtB

it =

)PH,t

-Y i

t " ACit

." P i

t Cit

*"

)M i

t " M it"1 " V i

t

*. (5)

8

Equation (5) indicates that a country accumulates net foreign liabilities with respect

to the rest of the monetary union depending (i) on the di"erence between revenue

both from activity and from foreign liabilities already held and the amount of con-

sumption spending and (ii) on the value of the net money inflow with respect to the

level of money creation in this region. The latter component is traditionally neglected

in monetary union models, where the increase in national money supply exactly o"sets

the increase in money demand in the country, i.e. M it "M i

t"1 " V it = 0. Analytically,

(ii) describes money flows between union members and provides a way to compen-

sate for asymmetries in the provision of money caused by the adjustment of money

demand following asymmetric shocks. This dimension is crucial to our results, since

the possibility of trading money may justify the absence of a regional concern in the

implementation of monetary policy. Intuitively, Eq. (5) indicates that there may be

current account movements that even out money demand and money supply patterns.

3 A Linear-Quadratic Framework

We solve the model by applying standard linearization methods and define the

authorities’ loss function. The derivation of the optimal monetary policy is defined

as the minimization of a second order approximation utility-based welfare metric con-

strained by the model. Since the authorities’ loss function is quadratic, the model

does not need to be solved with a second order approximation.6

3.1 The Model in Log-deviation to the steady state

We firstly solve the model in log-deviation with respect to a symmetric steady

state. In the symmetric steady state Ai = A = 1, M i = M = 1 and V i = V = 0, #t

$ 0 for i ! {h, f}. To replicate the competitive flexible price equilibrium, we impose

that + = 11"& < 0. Then, Bi = B = 0, R = 1 + &, Y = C = N = 1, and PH = PF

= Ph = P f = PH(k) = PF (k) = P = W =1#"1

1(

1+(

221/". Applying the standard

linearization procedures, denoting xit as the log deviation of Xi

t , #t for i ! {h, f}

and defining ki =-

1 " ,i!. -

1 " ,i./,i, the model in log-deviation is summarized

in Table 1.7

9

Table 1: The model in log-deviation to the steady state

Global Households

"Et

&cit+1 " ci

t

'= (

1+( rt+1 " Et

&-i

t+1

'" 'bi

t+1

%nit + "ci

t = wit " pi

t

$-mi

t " pit

.= "ci

t "4

11+( rt+1 " '

bit+1(

5

Firms

-i,t = !Et {-i,t+1} + ki-wi

t " ait " pi,t

.

Goods markets equilibria

aht + nh

t = (1 " () cht + (cf

t + 2( (1 " () st

aft + nf

t = (1 " () cft + (ch

t " 2( (1 " () st

Definitions

pht = (1 " () pH,t + (pF,t pf

t = (1 " ()pF,t + (pH,t

-it+1 = pi

t+1 " pht -i,t+1 = pi,t+1 " pi,t

st = pF,t " pH,t qt = (1 " 2() st

Current accounts

bht+1 " (1 + &) bh

t = yht " ch

t " (st ")# 1+(

(

*1/" -mh

t " mht"1 " vh

t

.

bfs = "bh

s , #s = t, t + 1

3.2 The Model in Deviation with respect to the Natural Equilibrium

The optimal monetary policy at union level aims at reaching the e!cient equi-

librium. As is now standard in the literature, we consider the flexible price (corre-

sponding to ,i = 0) complete market equilibrium as the benchmark for the definition

of the optimal monetary policy of the UCB, as this situation corresponds to a zero

inflation rate for the monetary union. Considering ;xt as the natural log-deviation of

xt , ;xut = 1

2 (;xht + ;xf

t ) represents its average union wide value and ;xrt = 1

2 (;xft " ;xh

t )

represents its average relative value. National expressions can be obtained by applying

Aoki’s formulae, ;xht = ;xu

t " ;xrt and ;xf

t = ;xut + ;xr

t . Finally, we denote the variation

of a given variable xt by %xt = xt " xt"1. The corresponding natural values are

summarized in Table 2.

10

We define as <xt = xt";xt, the deviation of the corresponding variable from its log linear

natural equilibrium value. Letting $ = 1, the model in deviation from the flexible price

equilibrium writes,

<n rt = (1 " 2()<c r

t " 2((1 " ()<st, (6)

"Et{%<c ut+1} =

&

1 + &<rt+1 " Et

&-u

t+1

', (7)

"Et{%<c rt+1} = 'bh

t+1 "1 " 2(

2Et {-F,t+1 " -H,t+1} , (8)

-H,t = !Et {-H,t+1} + kh[(% + ")<c ut " %<n r

t " "<c rt + (<st], (9)

-F,t = !Et {-F,t+1} + kf [(% + ")<c ut + %<n r

t + "<c rt " (<st], (10)

%<st = (-F,t " -H,t) " %;st, (11)

<b ht+1 " (1 + &)<b h

t = <c rt " <y r

t " (<st + #1 + &

&(%<mr

t " <v rt ), (12)

%<m rt =

1 " 2(

2(-F,t " -H,t) + "%<c r

t " '

&%bh

t+1, (13)

<v ut = %<mu

t = - ut + "%<c u

t " 11 + &

%<rt+1. (14)

Table 2: The natural equilibrium

;yut = ;cu

t = (1+#)!+# au

t

;rt+1 = Et

8!(1+#)(1+()

((!+#) %aut+1

9

$%;mut = $;vu

t = !(1+#)(1+()((!+#) %au

t " !(1+#)((!+#)Et

&%au

t+1

'

;st = " 2(1+#)(1+2#)$)a

rt ;yr

t = 2)$(1+#)(1+2#)$)a

rt

;crt = (1"2%)(1+#)

!(1+2#)$) art ;nr

t = 2)$"1(1+2#)$)a

rt

.% = ( (1 " () /% = (1"2%)2+4!*$

2!

Here, variables are presented in terms of union, relative or national values, de-

pending on the role they play in the policy problem in the next section. Equation (6)

is the contraction of the relative expression of goods market equilibria within the union

(right-hand side) and the relative production function (left-hand side). Equations (7)

and (8) summarize the relative and union-wide expressions of Euler equations. Equa-

tions (9) and (10) are the modified expressions of the Phillips curves, obtained by

expressing marginal cost in terms of variables in deviation from natural equilibrium.

Equation (11) is the dynamic definition of terms of trade. Equation (12) describes

11

the dynamics of net foreign assets, which play a key role in our framework. Finally,

Eqs. (13) and (14) are the dynamic relative and union-wide versions of nominal money

demands.

3.3 The Authorities’ Loss Function

In this section we derive the loss function through a second order approximation

of the utility function We write this function as a quadratic function of endogenous

variables expressed in deviation from their natural paths. Stating # % 0, the global

welfare criterion assumes away monetary terms from the utility function.8 Using the

assumption of symmetry among agents and after some algebra, the welfare function

writes,

0uT = "C1"!

2

T!

s=t

!s"tEt {1s} + t.i.p + O-==*3

==., (15)

where, t.i.p gathers terms independent of the problem and where O-==*3

==.are terms

of order 3 or higher and where,

1s = ((1 " () (<st)2 +

)

2kh-2

H,t +)

2kf-2

F,t + (" + %) (<c ut )2 + " (<c r

t )2 + % (<n rt )2 .

The welfare measurement given by Eq. (15) takes into account the actualized inflation

and consumption gap rates in the monetary union. It also takes into account the

allocation of resources within the union via the relative consumption gap, the relative

e"ort gap and the terms of trade gap. The UCB takes Eq. (15) (with a reversed

sign) as its loss function. Note that the weights allocated to national inflation rates

are a"ected by the degree of price stickiness through the values of ki. Parameter ki

depends negatively on the degree of price rigidities, so that higher weights are given

to inflation rates when prices are stickier.

4 Monetary Policy

The UCB determines the monetary policy of the monetary union by minimizing

the union-wide welfare-based loss function using the model in deviation from the nat-

ural equilibrium. The corresponding first order conditions define a dynamic system

that characterizes the optimal path of the variables in the monetary union. As this

optimal policy cannot be implemented, this path will be kept as a benchmark for the

ranking of feasible monetary policies.

12

4.1 The Optimal Policy

Assuming that the UCB can commit for an infinity of periods, it adapts an optimal

monetary policy for the monetary union by minimizing the Lagrangian corresponding

to the optimal scheme,

L =7t=T

t=0 !tEt{1t

+2&1,t

)-H,t " !-H,t+1 " kh[(" + %)<c u

t " %<n rt " "<c r

t + (<st]*

+2&2,t

)-F,t " !-F,t+1 " kf [(" + %)<c u

t + %<n rt + "<c r

t " (<st]*

+2&3,t [(<st " <st"1) + (;st " ;st"1) " (-F,t " -H,t)]}.

The optimal path linked to the optimal policy is given by,

<c rt = <n r

t , (16)

)-ut + %<c u

t +-kh " kf

. -kh + kf

."1#

)

2(-F,t " -H,t) + %<c r

t

$= 0, (17)

)

2(-F,t " -H,t) + %<c r

t " &3,t

-kf + kh

.= 0, (18)

&3,t " !"1&3,t"1 = !"1.%<st"1 + !"1(<c rt"1, (19)

together with,

-H,t = !Et {-H,t+1} + kh ((% + ")<c ut " %<nr

t " "<c rt + (<st) , (20)

-F,t = !Et {-F,t+1} + kf ((% + ")<c ut + %<nr

t + "<c rt " (<st) , (21)

%<st = (-F,t " -H,t) " %;st. (22)

The existence and uniqueness of the equilibrium defined by Eqs. (16)-(22) are only

satisfied for symmetric nominal rigidities (i.e., for kh = kf ). As in the standard

literature, this path for endogenous variables implies,

<rt+1 = 0,

which means that the UCB targets the nominal interest rate to its natural value to

close both the union-wide inflation and the consumption gaps. This implies that

money creation is at its natural value, i.e., <mut " <mu

t"1 = <vut = 0, and that there

is no inflation, -ut = 0. However, this optimal policy is not fully feasible since the

path defined here implies too many variables and the UCB runs out of instruments

to implement it. Authorities have access to money creation and lump-sum taxes, not

13

su!cient to fully implement the e!cient equilibrium of the monetary union defined

by Eqs. (16)-(22). We therefore adopt this perfect situation as a benchmark for our

(feasible) policy analysis.

4.2 Feasible monetary policies and the concern for heterogeneity

We focus on policies setting the nominal interest rate at its natural level. Taking

the agenda for union-wide price stability as given for the UCB, we assume that it sets,

<rt+1 = %<mut = <v u

t = 0.

The corresponding quantity of money supplied at the union level is thus,

vut = ;v u

t =" (1 + %) (1 + &)

& (" + %)%au

t " " (1 + %)& (" + %)

Et

&%au

t+1

'. (23)

Secondly, monetary policy is implemented through NCBs. If the union system of

central banks has no concern for heterogeneity, the sharing rule for money creation in

the monetary union is,

vht = vf

t =12vu

t . (24)

Equation (24) represents the observed sharing rule adopted by the ECB according to

ESCB status. In this case, the dynamics of the current account is given by,

bht+1 " (1 + &)bh

t = yht " ch

t " (st " (#1 + &

&)(mh

t " mht"1 "

12vu

t ),

where the last element on the right-hand side expression reflects the decentralized

currency allocation mechanism analyzed previously.

However, if the USCB has a policy of heterogeneous response to shocks within the

union, the sharing of money creation is,

<v it = %<mi

t, (25)

for i ! {h, f}, with <v ht + <v f

t = 0, so that the policy responds exactly to the quantity

of money demanded in each country. In this case, the expression of the dynamics of

the current account becomes standard,

bht+1 " (1 + &) bh

t = yht " ch

t " (st.

We define two monetary policy regimes p ! {1, 2} , where p = 1 combines Eqs. (23)

and (24) and where p = 2 combines Eqs. (23) and (25). These policies are optimal in

14

terms of inflation-targeting (but are di"erent from the actual optimal monetary poli-

cy) when nominal rigidities are symmetric (see Benigno (2004)). Indeed, in the case

of heterogeneous nominal rigidities, setting <rt+1 = 0 does not imply -ut = 0. Figure 1

plots the Impulse Response Function (IRF) of union-wide inflation to a unit domestic

productivity innovation for di"erent asymmetric patterns of nominal rigidities.9 Figure

1 shows that -ut &= 0 and that the variance of union-wide inflation is a positive function

of nominal rigidity asymmetries. Since there is a negative relationship between the

union-wide inflation rate and the consumption gap dynamics when <rt+1 = 0 according

to Eq. (7), the variance of the union-wide consumption gap is a positive function of

asymmetries in the price-rigidities pattern.

Figure 1: Union-wide inflation IRF to a unit domestic productivity innova-

tion - sub-optimal policies

This implies a much higher response of the union-wide consumption gap linked to the

positive union-wide inflation rate by the union-wide Euler equation since <rt+1 = 0. As

a consequence, both policies yield some additional losses when nominal rigidities are

asymmetric, compared to when nominal rigidities are symmetric.

5 The Optimality of an Identical Treatment of NCBs

In this section, we examine the alternative policy regimes, p ! {1, 2}, on the basis

of their welfare implications. To this end, we simulate the model under alternative

15

policies and compute the average welfare distance to the optimal scheme defined by

Eqs. (16)-(22).10 We then obtain a permanent consumption loss (in %) for represen-

tative union-wide agents. Following Lucas (2003) and Beetsma and Jensen (2005), we

express this loss as (copt " cp), defined by,

copt " cp = 1001(" + %)"1 (1 " !)(0opt,T " 0p,T )

2 12

,

for p!{1, 2} and where T is the number of periods.

5.1 Calibration

We adopt a baseline calibration of the deep parameters of the model based on

standard values found in the literature. Following Beetsma and Jensen (2005), the

intertemporal elasticity of substitution is " = 2.5. The value of %"1 refers to Can-

zoneri, Cumby and Diba (2004) and varies between 0.05 and 0.33. For the baseline

case, we choose %"1 = 0.1. The elasticity of substitution across varieties determines

the average mark-up, which according to Rotemberg and Woodford (1997) is around

16-17%, implying ) = 7. We set the openness parameter to ( = 0.3 in the benchmark

calibration and, according to Faia [2006], we let it vary from 0.2 to 0.4. The parameter

controlling the nominal rigidities ranges, according to di"erent estimates, from 0.5 to

0.8. Following Canzoneri et ali. (2004), we set the baseline value at ,h = ,f = , = 0.7.

The portfolio cost parameter ' is set to 0.0007, in line with Schmitt-Grohe and Uribe

(2003). Remember that we set $ = 1 earlier in the paper. Other parameters are fairly

standard and we set ! = 0.99, # = 0.01, and std-*it

.= 0.7%. Finally, the persis-

tence parameter of productivity shocks is set to "a = 0.95, as in the standard RBC

literature.

5.2 Results

For various parameter combinations, Table 3 reports two permanent consumption

losses associated with asymmetric technology shocks, taking the complete financial

market flexible price situation as a benchmark. The first term (copt " c2) measures

the permanent consumption loss associated with the feasible monetary policy when

NCBs have the same per capita weight in the money creation process. The second

term (c2 " c1) measures the extra permanent consumption loss due to the di"erent

treatment of NCBs in the money creation process.

16

Table 3: Welfare analysis under symmetric nominal rigidities in percent of permanentconsumption loss - BC: Baseline calibration

BC " " "" 2.5 4 5 6

copt " c2 2.11 2.15 2.13 2.10

c2 " c1 0.09 0.06 0.05 0.05

( 0.3 0.2 0.25 0.35copt " c2 2.11 1.74 1.98 2.19

c2 " c1 0.09 0.26 0.16 0.05-,h,,f

.(0.70,0.70) (0.65,0.65) (0.75,0.75) (0.80,0.80)

copt " c2 2.11 1.64 2.81 3.86

c2 " c1 0.09 0.09 0.09 0.10

"a 0.95 0.8 0.9 0.99

copt " c2 2.11 8.14 5.14 0.26

c2 " c1 0.09 0.04 0.04 0.21

In the baseline case, the losses related to being unable to reproduce the optimal policy

are equivalent to a 2.11% drop in permanent consumption. For the baseline calibration,

our results also show that losses associated with a policy where NCBs are treated

di"erently are equivalent to a further permanent consumption drop of 0.09% compared

to the identical treatment policy. Nevertheless, since in all cases (c2 " c1) is positive,

treating NCBs identically when implementing non-optimal monetary policies improves

welfare. This result is robust to various combinations of parameters. Our results thus

show that the solution currently adopted in the European Monetary Union implies

sizeable welfare consumption-equivalent gains. Depending on parameter values, the

identical treatment of NCBs implies an equivalent rise in permanent consumption

ranging from 0.04% to 0.18%, with a value of 0.09% in the baseline calibration.

Welfare gains related to identical treatment are in line with most results encountered

in the literature. For example, Galı and Monacelli (2005), find that gains from an

optimal monetary policy are between 0.02% and 0.11% of permanent consumption.

Benigno (2004) finds that the optimal core-inflation monetary policy is equivalent to a

permanent consumption increase of 0.02% compared to the suboptimal HICP targeting

policy. Beetsma and Jensen (2005) find that the consumption-equivalent increase of

17

fiscal stabilization represents between 0.09% and 1.16% of permanent consumption.

Concerning the value of (copt " c2), our results range from 0.36% to 3.85%, in terms

of permanent consumption, which is consistent with the findings of Benigno (2001).

Figure 2: IRF to a unit domestic productivity innovation under alternative

policy regimes - OPT: Optimal monetary policy, CH: Monetary policy set

with concern for heterogeneity, NCH: Monetary policy set with no concern

for heterogeneity --,h, ,f

.= (0.70, 0.70)

Figure 2 reports the IRFs of the variables of interest. The two sharing rules di"er with

respect to relative consumption and terms of trade dynamics. These dynamics are

closer to the Pareto-optimal adjustment scheme if NCBs are treated identically. Since

these two variables directly a"ect the authorities loss function as given by Equation

(welfare), the welfare distance to the optimal situation in the monetary union is lower

when monetary policy is not concerned with regional factors. As already noted, the

identical treatment of NCBs implies that a greater role is given to the current account

as an e!cient decentralized mechanism to allocate money between union members, in

18

a situation where price rigidities imply suboptimal terms of trade adjustments.

As underlined above, the identical treatment of NCBs induces an international

money flow that provides money where needed in the monetary union. This net money

flow implies an accumulation of net foreign liabilities that contrasts with the standard

response of an accumulation of net foreign liabilities. As a matter of fact, the deficit

of the current account rises to 30% of GDP in our baseline calibration. This speeds up

both the consumption di"erential and terms of trade adjustments. Here, more money

is injected into the economy experiencing the technology shock. This, in turn, reduces

both deflation and the relative consumption di"erential. Finally, these two variables

return more quickly to the flexible price equilibrium, which reduces welfare loss in the

monetary union.

5.3 Sensitivity Analysis

A sensitivity analysis reveals that the Pareto-improving nature of this mechanism

is robust to various parameter combinations, while the size of the e"ect varies. An

increase in the parameter of risk aversion " from 2.5 to 6 reduces the value of the

consumption equivalent welfare gain of the current sharing rule from 0.09% to 0.05%.

As agents become more risk averse, they are less prone to use the current account

as a device to adjust asymmetric technology shocks, reducing the role of the current

account in the external adjustment. As the current account adjustment is closer to

that obtained when there is di"erent treatment of NCBs, the marginal reduction of the

consumption gap and of the terms of trade variability is lower. Therefore the welfare

gains associated with the identical treatment of NCBs are reduced.

A reduction in the home bias, for example an increase in the value of ( from 0.2

to 0.35, reduces the net permanent consumption gains associated with the identical

treatment of NCBs from 0.25% to 0.05%. The significant reduction of the Pareto-

improving nature of the equal sharing rule can be explained as follows. In this case,

aggregate consumption behavior becomes more homogeneous between countries, as

does money demand behavior. As a consequence, the economic implications of the

two money creation policies become more similar. In the extreme case where ( = 12 ,

both policies coincide. Thus, as consumption preferences become homogeneous in

the monetary union, identical treatment and di"erent treatment of NCBs become

isomorphic. Indeed, when ( = 12 , agents have similar consumption baskets (domestic

and imported goods are consumed in the same proportion) and face similar CPI price

19

levels and inflation rates. As a consequence, the current account is always balanced

and money demands are equal across the monetary union. There is no di"erence then

between a situation where the UCB supplies the amount of money required in each

country (which is the same in both countries) and a situation where the UCB supplies

the same amount of money to each NCB.

Following Baxter (1995) or Backus, Kehoe and Kydland (1992), we also investi-

gate the sensitivity of these results to situations where shocks become more permanent

("a ranking from 0.8 to 0.99). We show that, when "a increases, the welfare gains asso-

ciated with the identical treatment of NCBs increase. Here, as the identical treatment

of NCBs speeds up the adjustment of relative prices and relative consumption, the

monetary union returns more rapidly to the long-run equilibrium, which is better for

more permanent shocks. Note that a key feature of this sensitivity analysis for "a,

is that the distance between the actual equilibrium and the Pareto-optimal situation

diminishes from more than 8% (for "a = 0.8) to 0.26% (for "a = 0.99) of permanent

consumption. This is because, as shocks become more permanent, the economy must

adjust more rapidly to the new permanent situation, implying a quicker convergence

to the steady state, which remains the same independently of price-setting practices.

Thus there is a clear reduction in consumption loss compared to the optimal situation

and an increase in the optimality of the equal sharing rule.

Finally, our results are not significantly a"ected by the duration of prices as

long as pricing practices are symmetric. The only significant e"ect is the increase in

consumption loss as compared to the Pareto-optimal situation. When prices become

more rigid, the equilibrium moves further away from the flexible price equilibrium

and more weight is devoted to inflation in the welfare-based loss function. These two

aspects account for the increase of (copt " c2). Moreover, our results are robust to the

assumption of asymmetric nominal rigidities. Maintaining a constant average level of

nominal rigidities while the distance between ,h and ,f is variable, we have run similar

simulations and chosen not to report the results since they are very similar to those

already reported in Table 3. Since the assumption of asymmetric price rigidities implies

a higher dispersion of prices, results in this case feature additional losses compared to

a situation where nominal rigidities are symmetric.

20

6 Conclusion

This paper evaluates alternative sharing rules for the creation of money in an

asymmetric monetary union characterized by nominal rigidities, incomplete financial

markets and home bias in consumption. It shows that the identical treatment of

NCBs in a system of central banks such as the ESCB, leads to welfare gains. By

treating NCBs equally, the UCB relies on current account adjustments, which provide

an e!cient decentralized mechanism to allocate money where needed in the monetary

union.

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Notes

1. The particular problem of asymmetric nominal rigidities has already been ad-

dressed, using a di"erent approach, by Benigno (2004).

2. This HIPC is a compound average of the Consumer Price Index (CPI) of union

members with weights related to their respective share of Union total consumption.

3. In this paper, fiscal policy is strictly concerned with o"setting first-order distortions

related to monopolistic competition. Moreover, we assume lump-sum taxation. This

implies that fiscal policies do not interact with the decisions related to the design

of monetary policy. Indeed, Eyquem (2007) shows that the optimal design of fiscal

policies does not a"ect the design of the centralized optimal monetary policy. Debt

issues are beyond the scope of the paper. For insightful results concerning debt issues

in a monetary union, see Pappa and Vassilatos (2006).

4. See Corsetti and Pesenti (2005) for a discussion of nominal exchange rate policy in

NOEM models.

5. Indeed, monopolistic competition distorts the first-best allocation through mark-up

pricing and a lower output. As shown by Benigno and Woodford (2005), an optimal

subsidy policy restores the optimal perfectly competitive allocation.

6. Benigno and Woodford (2006) point out that using a first-order approximation to

the model leads to wrong optimal dynamics when the loss function is not quadratic. In

addition, they show that when the loss function can be expressed in a pure quadratic

fashion, the solution to the problem can be set in the convenient LQ form while

remaining valid.

7. Noting that price dispersion variations are of second order, the linear expression

of DPi,t writes dpi,t = 0. Furthermore, it should be remembered that the loglinear

expression for Rt+1 is dRt+1R = (

1+( rt+1. Finally, for Bit and V i

t , since B = V = 0, the

23

loglinear expressions of these variables need to be defined as bit = Bi

tPC and vi

t = V it

M .

8. This assumption is standard in NOEM models to prevent the inflationary bias in

optimal monetary policy. A full justification is provided in Devereux, Shi and Xu

(2005).

9. For instance, we choose the following patterns-,h, ,f

.= (0.50, 0.82),

-,h, ,f

.=

(0.55, 0.80),-,h, ,f

.= (0.60, 0.77) and

-,h, ,f

.= (0.65, 0.74). In all cases, the average

nominal rigidity in the union is , = 0.7, in line with most empirical studies.

10. Each welfare computation is averaged over 20 simulations. Each simulation is

characterized by the realization of a random and asymmetric productivity innovation

in each country at each period.

24