DBJ Discussion Paper Series, No.1205

The Stability of a Regionally Fixed Exchange Rate System:
Can Euro be Sustained by Austere Fiscal Discipline?

Masayuki Otaki(Institute of Social Science, University of Tokyo)

August2012

Discussion Papers are a series of preliminary materials in their draft form. No quotations,reproductions or circulations should be made without the written consent of the authors inorder to protect the tentative characters of these papers. Any opinions, findings,
conclusions or recommendations expressed in these papers are those of the authors and donot reflect the views of the Institute.

白紙The Stability of a Regionally Fixed Exchange Rate System:
Can Euro be Sustained by Austere Fiscal Discipline?
Masayuki Otaki
Institute of Social Science, University of Tokyo
Email: ohtaki@iss.u-tokyo.ac.jp
Phone: +81-3-5841-4952
7-3-1 Hongo Bunkyo, Tokyo, 113-0033, Japan
Abstract
This article considers under what conditions a regionally fixed exchange rate system
without a huge economy is sustainable. The euro area is a typical example. In general,
the euro area tends to be regarded as a currency area. However, the political power ofthe European Central Bank (ECB) is not strong enough to directly control thefiscal-monetary policy of each affiliate country. That is, the unification of central banks
within the area is not complete, and euro is not a currency area in the sense of Mundell(1961). It should be regarded as a regional fixed exchange rate system. Based on Otaki(2012-a), we construct an open economy Keynesian model under a fixed exchange rate
system with a dynamic neoclassical microeconomic foundation.
We obtained the following results. First, whenever a government’s tax-levying ability
is limited, austere fiscal policies are required to sustain the system. Second, the low
tax-levying ability has a negative effect on the economic welfare of that country becausesuch fragility limits its discretionary monetary policy.
Keywords: Dynamic Microeconomic Theory of Fixed Exchange Rate System, Euro as a
Regional Fixed Exchange Rate System without Exceptionally Economic Power,
Consequences of Austere Fiscal and Monetary Policies
JEL Classifications: F32, F33, F34, E24

1. Introduction
In this article, we consider whether a regional fixed exchange rate regime is asustainable system. This is not a trivial issue. The Bretton-Woods system, characterized
by a world-wide fixed exchange rate, rested on the overwhelming industrial andfinancial power of the U.S. Otaki (2012-b). Various sovereign risks that each country
faces are implicitly covered by the key-currency country (i.e., the U.S.).
However, euro includes no such exceptional country and the fixed exchange regime
is limited to a certain number of countries in the region. Therefore, we may regard euro
as a regional fixed exchange rate system characterized by a nominal exchange rate thatis fixed to unity with exchange rate adjustment prohibited.
Although euro seems to be a unified currency area, there is no such powerful entity
in reality. According to Mundell (1961), a currency area is identified with the unificationof the all central banks in the area. However, the power of the European Central Bank
(ECB) is rather restricted, and each affiliate country retains substantial discretionary
power over fiscal and monetary policy --- a situation that triggered the current Eurocrisis. Thus, the question of how viable euro is as a regional fixed exchange rate systemrather than a unified currency area is a potential topic for analysis.
With the adoption of a regional fixed exchange rate system, imbalances in thefiscal and current account become crucial problems in two senses. First, every country
without a strong tax-levying ability that seeks a full-employment equilibrium tends tolose her fiscal discipline and fall into unilateral default. Such current account deficits
are threat to her solvency, and she experiences much difficulty in sustaining the fixedexchange rate system.
Second, the viability of a regional fixed exchange rate system as a whole faces athreat when more countries are forced into a such one-sided debt default. That is, as theproblem of current account imbalances spread, every affiliate country (includingcreditor countries) faces serious conflicts of interest. Such conflicts raise questions
about the viability of the system as a whole, specifically because current accountadjustments by a change in the nominal exchange rate are per se infeasible.
Accordingly, some austere policies are inevitable for one-sided debtor countries.
However, the problem is how to harmonize such policies with the domestic equilibrium.
We face the problem of how to sustain a high-employment equilibrium in each debtor
country under austere policies.
Applying Otaki (2007, 2009) to this problem, we note that austere fiscal and current
account policies are compatible with a high-employment equilibrium within every
domestic economy. The reason is that a sufficiently higher tax levies with the1

implementation of austere policies, restores the maneuverability required for a
discretionary monetary policy. If austere policies lead to sufficiently high tax revenue tocompensate for the fiscal and current account deficits, the central bank in a one-sided
debtor country can increase the money supply, leading to a higher employment level
than in a liberal policy regime. Austere policies requiring a balanced budget increases s
economic welfare in every one-sided debtor country with a time lag between theimposition of fiscal discipline and implementation ofa discretionary monetary policy,.

This article is organized as follows. In Section 2, we construct a microeconomic andmonetary model that describes a regionally fixed exchange rate system in which theadjustment by the nominal exchange rate is prohibited. We deal with the normative
implications of austere policies required of one-sided debtor countries in Section 3.
Section 4 contains some brief concluding remarks.
2. The Model
2.1 Structure of the Model
We use the two-period overlapping generations model with money developed byLucas(1972) and Otaki (2007). A small country joins a regional fixed exchange rate
regime in which the nominal exchange rate is fixed at unity. The country is smallenough not to affect the aggregate demand and supply of the alliance as a whole. There
are differentiated goods[0,1] in this region. The country specializes in producing thespectrum of goods [0,  ] . The only production resource required is labor, theproductivity of which is assumed at unity.
Without a constraint on her fiscal discipline, this small country is tempted to use anunlimited amount of the common currency to acquire other countries’ goods. Therefore,
the regional fixed exchange rate alliance must impose fiscal discipline of each alliedcountry in advance.
Such an alliance can be described by the following two-stage game. In the firststage, each affiliate country determines the volume of tax collected to maintaining thealliance. In the second stage, each country supplies the common currency to thedomestic economy to maximize her economic welfare under the fiscal constraint
incurred by the first-stage game.
The order of the game is crucial. A commitment to levying proper tax is paramountimportance. The discussion will be clear if we consider the converse case. Currency
supply is determined first, followed by tax collection. In such a structure, a kind of thehold-up problem is invoked. Incentivized by unlimited currency supply, all affiliates
increase consumption, and go bankrupt. Since all candidates weave this tragic2

consequence into the decision on whether to participate in the system, such an allianceis never constituted. Even if it is realized, once the fiscal discipline of each affiliate issoftened, the alliance will immediately dissolve. Therefore, austere policies forone-sided debtor countries are desirable for the maintenance a regional fixed exchange
rate system without any exchange rate realignment.
2.2 The Mathematical Model
2.2.1

Optimization of Individuals

All individuals have the same lifetime utility function as
1

U (c1t , c2t 1 )  [c1t ]c [c2t 1 ]1 c   t  , cit   10 [cit ( z )]1 dz  1 ,
0  c  1,  1,
1

1

where cit denotes the aggregate consumption of individuals in the i -th stage of life

 t is adefinition function the value set to unity when he is employed and zero other wise. during period t . cit ( z ) is the consumption of good z of the same individual.
is the disutility of labor.
The aggregate demand function for good z is p ( z) ct ( z )   t  Pt 1Yt, Pt   10 [ pt ( z )]1 dz  1 , (1)Pt

where Yt is the nominal effective demand during period t . Aggregating these functions
over z , we obtain the lifetime budget constraint as

Yt   10 pt ( z )cit ( z )dz  Pc
t it  Pt 1cit 1.
i ,tMaximizing the lifetime utility function U with respect to (cit , cit 1 ) , we obtain thefollowing aggregate consumption function of the young generation as

ct  cyt ,where yt (2)Ytis the real disposable income in terms of the current goods.
Pt

Since the lifetime indirect utility derived from consumption h is expressed ashAYt, A  c c [1  c]1 c ,c 1 cPt Pt 1

the nominal reservation wage Wt R becomes

Wt R  A-1 Pt c Pt11c .

3(3)2.2.2

Optimization of firms

A firm maximizes its profit t ( z ) on pt ( z ) . We assume that the labor market

equilibrium is interior and some individuals are unemployed; hence the nominal
equilibrium wage is equal to the nominal reservation wage Wt R .
That is,max pt ( z ) [ pt ( z )  Wt R ]cit ( z ) .
Taking Equations (1) and (3) into consideration, we get the optimal pricing rule:pt ( z ) A1 Pt c Pt11c.
1   1

(4)

We must note that Equation (4) represents that the nominal money supply does notaffect the price level since the nominal stock of money does not appear in the equation.
It also implies that money is non-neutral in our model.
Aggregating Equation (4) over z , we obtain the equilibrium inflation rate  as1

  [ A 1[1   1 ]]1c .

(5)Thus, all countries within the alliance experience the same equilibrium inflation rate.
2.2.3

Government RoleThe government has two roles. First, it collects taxes and exports them in exchange
for the privilege of issuing the common currency. Second, it actually issues thecurrency to the domestic economy under the predetermined fiscal constraint in thefirst stage. The seigniorage obtained is assumed to be issued to individuals via
wasteful government expenditure.

Such activities are described by the followingequations.

T  E, E  M ,(6)where E and M denote the real export and import, respectively.1 The second equality
expresses the fiscal discipline from the regional fixed rate alliance. That is, to maintainthe alliance, the inflow and outflow of the common currency should be equalized.
2.2.4

Market Equilibrium

There are two kinds of market: the aggregated goods market and labor market. Thelabor market is in an interior equilibrium (imperfect-employment equilibrium) whenthe nominal equilibrium wage is equal to the nominal reservation wage as

For simplicity, we consider that private sector exports without corresponding taxation.
However, it is not difficult to introduce taxation, and our assumption does not lose theessence of the theory with this additional factor.
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aforementioned. Using Equation (6), the equilibrium conditions for the aggregate goods
market can be written asy  c[ y  T ]  m  T  [1   ] c[ y  T ]  m  y  T B  T  [1   ] c[ y  T ]  m  T 

1m  0, (8)1  c

m, (7)1  c

where B is the real current account surplus and m the real money supply.
Equation (7) represents the equilibrium condition for the aggregate goods market. The
first term is the total consumption of the young generation. The second term
corresponds to the sum of the old generation’s total consumption and government
expenditure financed by seigniorage. The third term is the export (equivalently
collected tax). The final term is the aggregate import. It consists of the younggeneration’s import [1   ]c[ y  T ] and the old generation’s import [1   ]m .
Equation (8) depicts the fiscal discipline imposed. To avoid a current accountimbalance, the policy variables (T , m) are constrained by the equation.
By these equations, the real GDP y and the tax levied T or the real money supply

m is determined. These two equations describe the regional fixed exchange rate system
excluding the possibility of the nominal exchange rate realignment as a whole.
2.3 Comparative Statics for Austere Policies
Eliminating m from Equation (7) by using Equation (8), we obtainy T T.
1(9)

Equation (9) has an important policy implication. Strengthening the austere policy (i.e.,increasing tax) raises the disposable income y  T , although it seems counterintuitive.
Such a consequence comes from the fact that the austere policy allows abundantliquidity supply for the domestic economy. As indicated in Equation (8), under theconstraint of a current account equilibrium, the government’s superior tax-collection
ability ensures a sufficient real money supply m . Since the old generation’s propensityof expenditure as regarads domestic goods is  and the corresponding multiplier isand the tax/export does not increase the real disposable income y  T (note that1
a balanced-budget multiplier is unity), only an increase in money supply can upturn thedomestic economy. An austere policy is required for this purpose.
3. Welfare Implications of Austere Policies
5From the indirect lifetime utility function h , the social economic welfare h* can bewrittenh*  T, 1cwhere  is the real profit in terms of current goods. By Equations (1) and (4), we obtainh*  1 y  T 1c(10)By Equations (9) and (10), as long as goods are sufficiently differentiated and  takes alower value, social economic welfare is an increasing function of T . Thus, as the realcurrency supply, which is regulated by the austere policy, becomes abundant, theeconomy can attain higher efficiency.
4. Concluding Remarks
We have discussed the general properties of a regional fixed exchange alliancewithout nominal exchange rate realignment. The results obtained are as follows.
First, austere policies for a one-sided debtor country such as the requirement ofbalanced current account can upturn the economy with time lag between the additionaltax imposition and easing of the monetary policy can be neglect. In other words, austerepolicies can restore the strength of the alliance and allow for the establishment of adiscretionary monetary policy for the one-sided debtor country, at least in the long run.
However, we must note that the order of the game is crucial. Committing fiscal
discipline should have the first priority. Whenever an easy monetary policy prevails, ahold-up problem is invoked and the alliance never becomes sustainable.
Second, austere policies improve economic welfare and upturn the business of theeconomy. The reason is that monetary expansion becomes feasible with theestablishment of fiscal discipline. This expansion upturns the economy via themultiplier process. This increases the social surplus (earnings), and improves socialwelfare.
References[1] R. E. Lucas, Jr. ``Expectations and the Neutrality of Money,’’ Journal of Economic

Theory 1972, Vol. 4, pp. 103-124.
[2] R. A. Mundell, ``A Theory of Optimum Currency Areas.’’ American Economic Review
Vol. 51, 1961, pp. 657-665.
[3 ]M. Otaki, ``The Dynamically Extended Keynesian Cross and the Welfare-Improving
Fiscal Policy,’’ Economics Letters, 2007, Vol. 96, pp.23-29.
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[4] M. Otaki, ``A Welfare Economics Foundation for the Full-Employment Policy,’’Economics Letters, 2009, Vol. 102, pp. 1-3.
[5] M. Otaki, ``A Keynesian Model of a Small Open Economy under a Flexible Exchange
Rate System,’’ Theoretical Economics Letters, 2012-a, Forthcoming.
[6] M. Otaki, ``How a Key Currency Functions as an International Liquidity Provision
and Insurance System, ’’ Paper Presented at the 8th Conference of Asia Pacific EconomicAssociation, 2012-b.

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