Non-Ricardian fiscal policies in an open monetary union.
Date: 2003-09-09
Institutions: Directorate-General for Economic and Financial Affairs
Subjects: economic policy, fiscal policy, monetary policy, monetary union, price index

EUROPEAN COMMISSION

DIRECTORATE-GENERAL FOR ECONOMIC
AND FINANCIAL AFFAIRS

ECONOMIC PAPERS

http://europa.eu.int/comm/economy_finance

N° 169 - April 2002

Non-Ricardian fiscal policies
in an open monetary union

by

Javier Andrés, Fernando Ballabriga,
and Javier Vallés

Non-Ricardian fiscal policies
in an open monetary union *
by
Javier Andrés, Fernando Ballabriga,
and Javier Vallés

ECFIN/229/02-EN

This paper only exists in English.

©European Communities, 2002

* We acknowledge comments from M. Canzoneri, J. Galí, P. Teles, C. Nielsen, D. López-Salido, J. Viñals
and participants at the Banco de España seminar.

Non-Ricardian Fiscal Policies in an Open
Monetary Union∗

Javier Andrés †

Fernando Ballabriga ‡

Javier Vallés§

January 2001

Abstract

The ﬁscal theory of the price level has challenged the conventional view
that monetary factors drive prices and exchange rates and has also pro-
vided a rationale for ﬁscal restrictions in a monetary union. This paper
extends the main results of this theory in the context of an open mone-
tary union model. First, it analyzes solutions to the indeterminacy of the
exchange rate, some of which have non-standard macroeconomic implica-
tions. Second, it shows in a calibrated model the consequences for the
monetary union of ﬁscal misdirection in one its members.

JEL classiﬁcation: E31, E63, F42, H3
Keywords: Non-Ricardian ﬁscal policies, exchange rate and price level de-

termination, inﬂation dynamics, monetary union.

∗We acknowledge comments from M. Canzoneri, J. Galí, P. Teles, C. Nielsen, D. López-Salido, J.

Viñals and participants at the Banco de España seminar..

†Departamento de Análisis Económico, Universidad de Valencia, and Banco de España; Avda

dels Tarongers, 46022 Valencia. Javier.Andres@uv.es.

‡ESADE; Av. Pedralbes 60-62, 08034 Barcelona. Fernando.Ballabriga@cec.eu.int.
§Research Department, Banco de España; Alcala 50, 28014 Madrid. Valles@bde.es.

1. Introduction

Fiscal behavior has been of central interest in the European Monetary Union
process. The concern with macroeconomic stability led ﬁrst to the imposition
of speciﬁc ceilings on the public debt and deﬁcits of candidate States as a pre-
condition for joining the Union. Once the Union was formed, the Growth and
Stability Pact imposed an even tighter ﬁscal discipline on Member States. How-
ever, although price stability is perceived as desirable, its connection with ﬁscal
restrictions is controversial. In fact, the most widely held view seems to be that
price stability can be achieved with an independent central bank and a credi-
ble monetary policy, whereas ﬁscal policy needs to be more ﬂexible to confront
asymmetric shocks within the union.1

That view is questioned by the ﬁscal theory of the price level on two grounds.
First, there is no reason why central bank independence per se should guarantee
ﬁscal discipline. Second, if tax and spending decisions are taken by the public
sector without regard for their eﬀects on the present value of net surpluses, an
independent central bank with a clear anti-inﬂationary objective may not be suf-
ﬁcient to guarantee price stability. Macroeconomists have long recognized the
connection between ﬁscal and monetary decisions induced by the fact that the
government has two sources of revenue, taxes and seignorage, which allow it to
achieve public sector solvency through alternative coordination schemes. This
connection imposes limits on the eﬃcacy of monetary policies (Sargent and Wal-
lace (1981)). The ﬁscal theory of price determination takes that interaction one
step further. According to this approach, monetary policy determines the ex-
pected inﬂation rate but, to the extent that the price level may be determined by
the government’s ﬁscal stance, ﬁscal shocks may determine the observed (ex-post)
inﬂation rate at each period of time.

The implications of the ﬁscal theory of the price level for a monetary union
were ﬁrst analyzed by Woodford (1996) and Sims (1997) and later on extended by
Bergin (2000). In Bergin’s model, the monetary union is itself a closed economy,
so that important issues, like that of exchange rate determination, are left out.
In this paper, we look at the case of an open monetary union in a model in which
there are three ﬁscally independent authorities and just two currencies. Our aim
is twofold: ﬁrst we revisit the issue of the determination of the exchange rate of
the monetary union vis-à-vis the rest of the world, and second we explore the
spillover eﬀects of ﬁscal shocks in one of the countries of the monetary union.

1 See, for example, Eichengreen and Wyplosz (1998).

1

In section 2 we show how the indeterminacy of prices and exchange rates may
be avoided in a multi-country setting with pegged interest rates, if some of the
countries involved follow non-Ricardian ﬁscal policies. Nominal determinacy is
achieved provided that there is incomplete risk sharing among the countries. This
extends the analysis of exchange rate indetermination made by Dupor (2000).
Although the conditions for a unique equilibrium are very demanding, we ﬁnd
that a wide range of combinations of risk sharing and policy rules generate such a
result in a multi-country model. Furthermore, some of these policy combinations
have non-standard economic implications.

In section 3 we simulate the eﬀect of ﬁscal shocks in some cases of special
interest for policy purposes, against the background of the standard monetary
(Ricardian) model. The benchmark case is one in which monetary policy is loose
within the union and tight in the rest of the world, and one of the countries
belonging to the union follows a non-Ricardian ﬁscal policy. This is the open
economy counterpart of the non-Ricardian regime that has received more attention
in the literature. We ﬁnd that ﬁscal shocks in that country may aﬀect other
countries unless the exchange rate adjusts; this adjustment does not take place in a
monetary union, which allows this contagion to operate at full strength. Moreover,
the instability in the union is largely independent of the ﬁscal behavior in the other
countries of the union and of the tightness of the monetary policy exerted by the
central bank. But this case is not the only departure from the Ricardian world
in which a unique equilibrium exists. Other policy combinations may also yield
uniqueness and are of interest since they involve diﬀerent conditional correlations
among macroeconomic variables.

2. Nominal determinacy in an open monetary union

2.1. The model

Let us consider a two-country model with two independent monetary authorities
(countries 1 and 2), in which one of the countries is a monetary union with one
currency and two independent ﬁscal authorities (1A and 1B). Seignorage within
the union is split on equal grounds between its members and there is perfect capital
mobility. We assume complete risk sharing, which means that each country may
issue limitless amounts of debt as long as some other country is willing to hold
it, although this assumption will be relaxed later. We leave aside the analysis of
the repercussions on the distribution of wealth and consumption across countries,

2

by assuming that the representative household consumes and produces goods in
both countries, and also holds assets according to their rate of return, regardless
of their currency of denomination. Goods must be purchased in each country
using of the currency of that country.

∈

1jt, BB

[0, 1]) chooses the vector cA

The setup of the model is in the spirit of Obstfeld and Rogoﬀ’s (1995),
which assumes monopolistic competition and sticky prices. The jth representative
1jt, c2jt, y1jt, y2jt,
consumer-producer (where j
BA
1jt, B2jt, M1jt, M2jt, P1jt and P2jt to maximize (2.1) subject to (2.2) -
(2.5). Individual outputs, y1jt, y2jt can be thought of as intermediate inputs of
two composite ﬁnal, goods y1t, y2t. As a consumer, each household purchases a
share of these composite ﬁnal goods in a perfectly competitive market, and as a
producer of intermediate goods she faces a ﬁnite elasticity demand curve for her
variety. Money and government bonds are deﬁned in terms of the home currency
in each case.

1jt, cB

M ax E0

∞

βt

t=0
X

(cjt)
σ
1

−




1

σ

−

(y1jt)γ

−

γ −

(y2jt)γ
γ

χ

+

M1jt
P1t
1

−

³

´
ε


cl
1jt+P2tc2jtet+

l=A,B
X

P1t

l=A,B
X

Bl

1jt+M1jt+etB2jt+etM2jt+P1t

1

ε
−

χ

1

ε
−

M2jt
P2t
1

³

−

ε 
´

(2.1)

τ l
1jt+etP2tτ 2jt

≤

+

l=A,B
X

P1jty1jt+etP2jty2jt+(1+R1t

1)

−

(Bl

1jt

1+(1+R2t
−

1)etB2jt
−

−

1+M1jt

1+etM2jt

−

1

−

l=A,B
X
P1tAC1jt

−

yijt = yit

; i = 1, 2

etP2tAC2jt

θ
−

−
Pijt
Pit ¶

µ
Pijt
Pijt

−

2

Ωi

yit ; i = 1, 2

¶

1 −

1
(1 + R1s)−

WjT = 0

!

3

ACijt =

φi
2

µ
T

1

−

Ã

s=0
Y

E0

lim
T
→∞

(2.2)

(2.3)

(2.4)

(2.5)

1js, BB

1jt + cB

1js, B2js (all that is needed is that BA

where cjt = cA
1jt + c2jt and M1js and M2js are non-negative for all s; the
assumption of complete risk sharing means that no such condition is imposed on
BA
1s+ B2 > 0). Equation (2.2) is
the ﬂow budget constraint of the jth consumer. Equation (2.3) is the demand for
product j in period t.2 Equation (2.4) is the producer’s adjustment cost function
of prices. Equation (2.5) is the transversality condition. Wealth is deﬁned in
country 1 currency as,

1s+ BB

Wjt+1 = (1 + R1t)

Bl

1jt + M1jt + (1 + R2t)et+1B2jt + et+1M2jt

(2.6)

l=A,B
X

Deﬁning Ωi as the steady state inﬂation in country i, the (symmetric aggregate
equilibrium) ﬁrst order conditions of the problem can be written as follows:

et (1 + R1t) Et

= (1 + R2t) Et

σ
c−
t+1

σ
t = β (1 + R1t) Et
c−

σ
c−
t+1

µ
P1t = P2tet

P1t
P1t+1 ¶

µ

σ
c−
t+1
P1t+1 ¶
M1t
P1t

σ
= c
ε
t

m1t =

m2t =

χ

1 +

·

µ

M2t
P2t

σ
= c
ε
t

χ

1 +

µ

1
ε

1
ε

1
R1t ¶¸
1
R2t ¶¸

et+1
P1t+1 ¶

(2.7)

(2.8)

(2.9)

(2.10)

(2.11)

·
2 To derive (2.3) we may think of two aggregators, one in country 1 and the other in country
2, who buy the diﬀerent varieties y1jt, y2jt, and produce two composite goods y1t, y2t. The ith
country aggregator (i = 1, 2) solves the following maximization problem:

µ

M ax
yijt

Pit

0
·Z

1

(yijt)

θ

−

1
θ dj

θ

1

−

θ

1

¸

−

0
Z

Pijtyijtdj

These demand functions, along with the zero-proﬁt condition for the aggregator, imply the
following aggregate price index for the ith country:

1

1

θ

−

Pit =

0
·Z

1

(Pijt)1
−

θ

¸

4

θy1t

(y1t)γ

1

−

σ
c−
t

−

−

σ
φ1y1tc−
t

£

¤
σ
+βφ1Ety1t+1c−
t+1

µ

P1t+1
P1t ¶ µ

θy2t

(y2t)γ

1

−

σ
c−
t

−

−

σ
φ2y2tc−
t

P1t
P1t

−

1 −

Ω1

+

¶

Ω1

= 0

(2.12)

¶
P2t
P2t

−

1 −

Ω2

+

¶

µ

µ

P1t
P1t
1 ¶ µ
−
P1t+1
P1t −
P2t
P2t

1 ¶ µ
−
P2t+1
P2t −

£

¤
σ
+βφ2Ety2t+1c−
t+1

¶

µ

Ω2

= 0

(2.13)

P2t+1
P2t ¶ µ
Equation (2.8) establishes that the law of one price holds, since there are no
restrictions on the movement of goods, which are perfect substitutes in consump-
tion; (2.7) captures the intertemporal substitution in consumption, whereas (2.10)
and (2.11) are the implied demands for both currencies. In a frictionless model,
the price level is an asset price which is determined only by the expectation of
future returns on holding money (expected inﬂation). By contrast, in this sticky
price model, equations (2.12) and (2.13) are the (new Keynesian) Phillips curves
relating inﬂation to the output gap in each country. Since both economies are
open, demand pressure is represented both by home production (yit) as well as by
world consumption (ct). The Phillips curve is positively sloped as long as there
are non-negligible costs of changing prices (φi 6
The symmetric aggregate equilibrium must satisfy three budget balance con-
straints (one for each independent ﬁscal authority) and the overall resource con-
straint of the economy,

= 0).

P1tgA

1t −

P1tτ A

1t =

1
2

µ

¶

(M1t

−

M1t

1) + BA
−

1t −

(1 + R1t

1) BA
1t
−

1

−

(2.14)

P1tgB

1t −

P1tτ B

1t =

1
2

(M1t

µ

¶
P2tτ 2t = M2t

M1t

1) + BB
−

1t −

−

(1 + R1t

1) BB
1t
−

1

−

M2t

1 + B2t

−

−

−

(1 + R2t

1) B2t

−

1

−

P2tg2t

−

ct + gA

1t + gB

1t + g2t = y1t + y2t

(2.15)

(2.16)

(2.17)

The deﬁnition of equilibrium is incomplete until the behavior of the monetary and
ﬁscal authorities is deﬁned. In the most common case of and exogenous money

5

supply and Ricardian ﬁscal policies, there is no unique equilibrium for prices. In
this case, the unique equilibrium for prices and the exchange rate is found by
assuming that the price level is bounded. If both central banks adopt a policy
of pegging the interest rate, the conditions for a unique nominal equilibrium are
more demanding.

2.2. Equilibria under complete risk sharing

Consider a situation of interest rate pegging, which we assume for the sake of
simplicity:

R1t = R2t = R > 0

(2.18)

To keep things simple, let us consider the perfect foresight equilibrium in the
ﬂexible price version of the model, in which φ1 = φ2 = 0.
In this case, the
supply curves are vertical in both countries, and ct, y1t and y2t are the solution
of (2.12), (2.13) and (2.17), which for constant values of git are also constant for
all t. Equations (2.9) and (2.7) imply et = et+1 and P1t
for all t.
P1t
Finally, the demands for real balances set the equilibrium value of m1t = m2t = m
and (2.14), (2.15) and (2.16) determine real debt. Thus, all real variables are
uniquely determined whereas the nominal values of P1, P2 and e are not. This is
the standard indeterminacy result associated with interest rate pegging shown by
Sargent (1987).

= P2t
P2t

= P
P

−

−

−

1

1

1

The ﬁscal theory of prices has been invoked in this type of environment to
obtain a unique value for the price level and (ex-post) inﬂation (Woodford, 1994).
This theory relies on the transversality condition of the household’s optimization
problem to obtain an additional condition that the price level must satisfy. This
can be easily seen in our model, under perfect foresight. Substituting the ﬁrst
order conditions (2.7), (2.8) and (2.9) in the government budget constraints (2.14),
(2.15) and (2.16), and adding them up, we obtain:

Wt = P1t

1t + θB
θA

1t + θ2t + ∆1tm1t + ∆2tm2t

+

Wt+1
(1 + R1t)

£

¤

where the surplus in each country is θl
g2t and
∆itmit represents the resources from seigniorage, with ∆it =
. Iterating
forward and applying the transversality condition (2.5) we obtain the following
condition that must be satisﬁed at any t:

gl
1t, l = A, B, θ2t = τ 2t

1t = τ l

Rit
1+Rit

1t −

−

³

´

6

Wt
P1t

=

1t+k + θB
θA

1t+k + θ2t+k + ∆1t+km1t+k + ∆2t+km2t+k

£

∞k=0

t+k
s=t

1

−

(1 + r1s)

¤

(2.19)

³Q
where (1 + R1s) = (1 + r1s)
and the real interest rate, (1 + rs), is equal to
the ratio of marginal utilities of consumption between s and s + 1 (discounted).
Under the assumption of interest rate pegging, this condition at any t, say t = 0,
looks like:

P
P1s+1
P1s

´

³

´

W0
P10

=

2∆m
β)
(1

∞

+

βt

1t + θB
θA

1t + θ2t

(2.20)

−

t=0
X
This expression means that the household transversality condition of bounded
wealth imposes one joint present value constraint on the ﬁscal behavior of the three
governments in the model. This present value constraint need not be satisﬁed by
each ﬁscal authority: all that is needed is that some government is willing to hold
limitless amounts of other country’s debt if necessary, so that the present value
of worldwide public sector surpluses suﬃces to pay back the outstanding debt.

£

¤

W0 is predetermined and ∆m is given by the monetary policy, but still this
condition may or may not pin down P10 depending on the way the governments
set their ﬁscal policies. To see this, assume that all three ﬁscal authorities in the
model design their ﬁscal policies as a constant surplus (θi for all t) whose size is
set as a function of the price level, such that the following relations hold for any
value of P10 and P20.

β)

(1

−

θl
∗1 =

Bl
1(

1)(1 + R) + 1

2M1(
−

1)

−

³

P10

1
2

¶

´

−

µ

∆m, l = A, B

β)

(1

−

θ∗2 =

¡

B2(

1)(1 + R) + M2(

−

P20

1)

−

−

¢

∆m

These policy reaction functions can be added to obtain the following expression
that also holds for any P10.

∗1 + θB
θA

∗1 + θ∗2 =

(1

β)W0

−
P10

−

2∆m

7

These policies (Ricardian policies) render (2.20) redundant and the transversality
condition cannot be used to select a unique level of prices. If some, or all, gov-
ernments set θi disregarding the present value constraint (i.e. any non-Ricardian
policy θi
= θ∗i ) the second term in the right-hand side of (2.20) is exogenous and
the transversality condition is satisﬁed only for a unique value of P10. This is the
basis of the ﬁscal theory of prices.

However, as Dupor (2000) has shown, non-Ricardian policies do not determine
a unique equilibrium in a two-country model. Even if there were a unique value of
P10 that satisﬁed (2.20), P20 and e0 would remain indeterminate. The explanation
of this indeterminacy is that the transversality condition implies a single present
value condition on aggregate debt. Debt in each country need not be bounded;
in other words, the possibility of one country issuing a limitless amount of debt
cannot be ruled out, as long as other countries become net lenders. One country’s
debt may be growing or falling without limit as long as the aggregate debt is not.3

2.3. Equilibria under incomplete risk sharing

The assumption of complete risk sharing among countries is a strong one, since
it may imply a substantial wealth transfer from countries with ﬁscal surpluses
to those with persistent deﬁcits. In the absence of compensatory payments (risk
insurance) this equilibrium can hardly be sustained. Let us assume instead that
there is incomplete risk sharing. This means that one country cannot accumulate
limitless amounts of other country’s debt, which imposes a lower bound for Bit.
Let us ﬁrst assume that there is risk sharing among the countries belonging to
the union (1A,1B) but not among those and country 2. This is represented by
the constraints,

(BA

1t + BB
1t)

0, B2t

≥

≥

∀

0,

t

(2.21)

which along with the transversality condition of the consumer’s problem, imply
the following necessary conditions for equilibrium,

E0

lim
T
→∞

T

1

−

Ã

s=0
Y

1
(1 + R1s)−

W1T = 0

!

(2.22)

3 Dupor (2000) shows that this result holds even if the substitutability of currencies is not

restricted.

8

6
lim
T
→∞
where W1t+1 = (1 + R1t)(BA

E0

T

1

−

1
(1 + R2s)−

W2T = 0

Ã
s=0
Y
1t + BB
1t) + M1t, W2t+1 = (1 + Rt)B2t + M2t.

!

(2.23)

Conditions (2.22) and (2.23) impose two present value constraints on govern-

ment balances that, under interest rate pegging, may be written as,

(2.24)

(2.25)

(2.26)

(2.27)

(2.28)

Now, if ﬁscal policies in both countries are non-Ricardian (i.e. θA
1t, θ2t are
exogenous), all nominal variables in the model are uniquely pinned down. In the
particular case in which current and future surpluses are expected to be constant,
we have P10, P20, e0 determined by:

1t, θB

W10
P10

=

∆m

β)

(1

−

∞

+

βt

1t + θB
θA

1t

t=0
X

+

¤

£
∞

βtθ2t

W20
P20

=

∆m

(1

β)

−

t=0
X

P10 =

P20 =

(1

−
∆m + θA

β)W10
1 + θB
β)W20
(1
∆m + θ2

−

1

e0 =

1

−

β)W20
(1
−
∆m + θ2 ¸

(1

−
∆m + θA

β)W10
1 + θB

1 ¸

·

·
It should be noticed at this point that the ﬁscal stance is not only important
insofar as it helps to determine prices and the exchange rate. When the central
bank follows a policy of pegging the money supply and the ﬁscal policy is Ricar-
dian, a tax cut today is oﬀset by an expected surplus rise at some point in the
future that would leave permanent income and consumption unaltered, and with
no eﬀect on prices. By contrast, under non-Ricardian ﬁscal policies, the response
of most macroeconomic variables to exogenous shocks diﬀers from what would be
obtained in the standard monetary equilibrium. Expressions (2.26) to (2.28) trace
out the eﬀect of ﬁscal shocks on prices and the exchange rate. For instance, a tax
cut in country 1B (reduction in θB
1 ) generates a rise in prices in country 1 and an
exchange rate depreciation. Nevertheless, to explore the conditional correlation
of variables under alternative shocks we have to move to a more general model
with more realistic policy rules. This is discussed at length in Section 3.

9

2.4. Alternative policy combinations and risk sharing assumptions

The last two subsections showed that, under interest rate pegging, Ricardian ﬁscal
polices produce the well known result of nominal indeterminacy, both for prices
and the exchange rate. Non-Ricardian policies, which serve to ﬁx a unique price
level in a closed economy, do not achieve the same in a multi-country model under
perfect capital mobility and complete risk sharing. Imperfect risk sharing, though,
allows to achieve nominal determinacy.4

In an open monetary union, however, the number of policy combinations that
may generate a unique equilibrium with the price level determined through the
intertemporal budget constraint is much larger than in the closed economy case.
Although we shall not describe all of them here, two might be of some interest.
First consider the following situation: the central bank in the monetary union ﬁxes
the money supply and both countries, 1A and 1B, follow Ricardian ﬁscal policies,
while country 2 pegs its interest rate and follows a ﬁscal policy of exogenous
In this case we would still have a unique equilibrium, but one with
surplus.
In particular, P2 would react to
diﬀerent properties to those discussed above.
shocks to θ2 while P1, which is now determined by the money demand in country 1,
would not respond to shocks to θ1; hence, the pattern of response of the exchange
rate would diﬀer from both the standard Ricardian and non-Ricardian regimes
discussed above.

A more striking case, also resulting in uniqueness of equilibrium, would be
one with the following policy combination: one of the countries belonging to the
union follows a non-Ricardian ﬁscal policy while the union’s central bank ﬁxes the
money supply and, simultaneously, country 2 pegs the interest rate and follows a
Ricardian ﬁscal policy. In a closed economy framework P20 would be indetermi-
nate while P10 would be over-determined. However, since these two countries are
connected through their goods and ﬁnancial markets, nominal variables would be
uniquely determined. Basically, the over-determination in country 1 is eliminated
since now there are two prices to be set: P10 and e; the purchasing power parity
condition then determines P20, thus removing the indeterminacy in country 2. It
goes without saying that in this case the international transmission of shocks is
diﬀerent from all the cases discussed above, with a predominant role for monetary
and ﬁscal shocks originating in country 1. This case will also be considered in
Section 3.

Notice further that all the above equilibria have been obtained in a model

4 Canzoneri, Cumby and Diba (1998) have noticed that result in a simpler environment.

10

under the assumption of incomplete risk sharing among countries. A diﬀerent
assumption about risk sharing would require alternative policies to generate a
unique equilibrium. For example, let us take the assumption of imperfect risk
sharing to the limit, imposing that countries 1A, 1B and 2 face some lower bound
limit for their debt. In such case the determination of nominal variables could not
be guaranteed:

1t, B2t
which implies, along with the transversality condition and (2.8), the following
relationships that P10, P20 and e0 must satisfy:

t
∀

≥

0,

BA

1t, BB

P10 =

¡

P10 =

¡
P20 =

(1
1
2

β)W A
10
−
∆m1 + θA
1

β)W B
(1
¢
10
−
∆m1 + θB
1
1
2
β)W20
(1
¢
∆m2 + θ2
P10
P20

−

e0 =

where P10, and thus the whole system, would be overdetermined, unless for ex-
ample only one of the countries belonging to the monetary union (1A or 1B) is
following a non-Ricardian policy. The bottom line is that our multi-country model
displays a variety of equilibria whose properties depend on the combinations of
risk sharing assumptions and policy schemes. Woodford (2000) has argued that
the US economy has gone through periods in which monetary policy was passive
and, nonetheless, prices were determined, which he interprets as evidence of un-
derlying non-Ricardian ﬁscal policies. His argument is a closed economy one, and
our results show that in an open economy a unique equilibrium can be obtained
with alternative non-Ricardian policy combinations.

3. The eﬀect of ﬁscal shocks under endogenous policy rules

This section explores the eﬀects of ﬁscal shocks in the open monetary union under
a more realistic environment in which both monetary and ﬁscal authorities react
to the state of the economy. First we discuss the stability of this model and later
on we calibrate it to analyze the eﬀects of shocks under alternative monetary and
ﬁscal regimes.

11

3.1. Stability of the model

As discussed previously, there are conditions under which a unique equilibrium
exists with all nominal and real variables uniquely determined. These conditions
require that either the monetary policy or ﬁscal policy, but not both, pin down
the price level. The eﬀects of ﬁscal shocks in the polar cases of interest rate
pegging and exogenous surplus have been analyzed in Section 2. However, purely
exogenous interest rates and government surpluses are an extreme form of policies
rarely seen in practice.

The recent literature has chosen to represent the behavior of monetary and
ﬁscal authorities by means of feedback rules, whereby policy instruments are cho-
sen to react to the level of some endogenous variable. Interest rate rules are well
known after the work of Taylor (1993 and 1999). He represents the policy reaction
function as an adjustment of the nominal interest rate to current inﬂation and
the output gap,5

P1t
P1t

R1t = δ10 + δ11

+ δ12

y1t + εR
1t

(3.1)

µ

R2t = δ20 + δ21

1 ¶
−
P2t
P2t
In these expressions, δ10 and δ20 are positive constants, which depend on the
steady state real interest rate. δ11 and δ21 capture the response of the nominal
rate to deviations of inﬂation from its target value. The response to deviations of
output from trend is captured by δ12 and δ22. Finally, εR
1t are monetary policy
innovations that produce unanticipated movements in the nominal interest rate.6
Similarly, Bohn (1998) has found empirical support for ﬁscal rules of the type,

b
y2t + εR
2t

1t, εR

+ δ22

1 ¶
−

(3.2)

µ

b

τ A
1t −

τ B
1t −

1t = αA
gA

10 + αA
11

1t = αB
gB

10 + αB
11

µ

µ

BA
1t
P1t

1
−
1 ¶
−
BB
1t
P1t

1
−
1 ¶
−

+ αA
12

y1t + ετ A
1t

+ αB
12

b
y1t + ετ B
1t

(3.3)

(3.4)

5 Alternatively, it may also respond to expected inﬂation, as in Clarida, Galí and Gertler

b

(2000).

6 These rules are identical to the standard Taylor rules of the form Rit =
yit where πit is the (net) inﬂation rate and Ωi its steady-state value.

δi2

δi0 + δi1 (πit

Ωi)+

−

e

b

12

B2t
P2t

1

−
1 ¶
−
12, αB

τ 2t

g2t = α20 + α21

+ α22

y2t + ετ
2t

(3.5)

−
Besides responding to a cyclical indicator (αA
(ετ A
debt as state variable, with coeﬃcients αA

1t , ετ B

1t , ετ

µ

12, α22), and to an innovation
2t), the surplus in each country reacts to the amount of real outstanding

b

11, αB

11 and α21 respectively.

In this section we return to the original setup in which producers act in a
monopolistic competitive environment and set prices whose adjustment is costly
(φs 6
= 0); its log-linear version appears in Appendix A. We assume that imperfect
risk sharing applies also within the monetary union.7 The path followed by the
endogenous variables in the model is driven by the dynamic behavior of real debt,
prices and consumption. Inspection of the log-linear model suggests that a subset
of parameters are of crucial importance to shape the dynamics of these variables:
β, δ11, δ21, αA
11, α21. The discount rate enters into the autorregressive process
of the system, whereas the other parameters determine the feedback from past
inﬂation into current inﬂation (δ11, δ21, through the eﬀect of monetary policy on
the excess demand) and from the stock of debt into future debt (αA
11, α21).
Existence of a unique equilibrium is not guaranteed, since there are plausible
parameter combinations for which the system (with six dynamic equations) has
either too many or too few eigenvalues outside the unit circle.

11, αB

11, αB

Given the large size of the system we have carried out the stability analysis
using a slightly simpliﬁed version; the details are described in Appendix B. The
parameter combinations that deﬁne the regions of non-equilibrium, indeterminacy
and unique equilibrium are a generalization of those obtained by Leeper (1991)
in a closed economy model, with exogenous output. 8 The critical values for the
relevant parameters are:

βδi1 ≶ 1, i = 1, 2

αl

i1 ≶ 1, i = 1, 2 and l = A, B

1
β−

−

Unlike the closed economy model, we now ﬁnd many other combinations that pro-
duce a unique nominal equilibrium, but which cannot be labeled either Ricardian
or non-Ricardian. Some of these combinations are described in the Appendix.
The cases that have received most attention in the literature in a closed economy
environment are the Ricardian and non-Ricardian regimes. A Ricardian regime
is deﬁned as one in which the monetary policy is active (βδi1 > 1), whereas ﬁscal

7We are imposing: BA
t.
8 See also Leith and Wren-Lewis (2000).

1t, BB

1t, B2t

≥

0,

∀

13

−

αl

policy adjusts to prevent real debt from exploding (i.e. ﬁscal policy is passive,
1
β−
i1 < 1). Non-Ricardian regimes have a unique equilibrium too, but mon-
etary policies hardly respond to inﬂation (βδi1 < 1), and it is ﬁscal policy that
1
pins down the level of nominal variables (i.e. it is active, β−

αl

−

i1 > 1).

Notice that a pure interest rate peg renders monetary policy unable to ﬁx the
level of prices. In equations (3.1) and (3.2) an interest rate peg is represented by
low values of δ11, δ21. Taylor (1999) has identiﬁed the post-Volcker US monetary
policy as one in which δi1 is well above 1, so that it has helped to stabilize
prices (i.e. active monetary policy). A similar logic applies to the degree of ﬁscal
response to the stock of debt, although in this case the benchmark value that
separates active and passive ﬁscal policies is αl
i1 ≈ 0. A purely exogenous ﬁscal
surplus (αl
i1 = 0) would make the stock of debt explosive, forcing an adjustment
of prices to prevent the economy getting onto such a path. Bohn (1998) obtains
evidence of such a ﬁscal reaction to the stock of debt that, although tiny, suﬃces to
characterize US ﬁscal policy as passive (in the sense of accommodating to prevent
the stock of debt from rising out of control).9

3.2. Calibration

The calibration sets most parameters at values that are common in the business
cycle literature. The utility function is assumed to be logarithmic in consumption,
and the discount rate is set at 0.994 to yield an implicit steady-state annual
real interest rate of 2.5% and an inﬂation rate of 1.5%.The income elasticity of
money demand is one and the interest elasticity is taken from Chari, Kehoe and
McGrattan (2000). The ratio of government consumption to output is 0.3. The
ratio m
y is set at 5%. The steady-state surplus is chosen to ensure that the debt-
to-output ratio is the one in Table 1. Finally, the slope of the Phillips curves
of all three countries is assumed to be the same, whith a value whith the
order of magnitude obtained in the literature ( Sbordone (1998)). Higher nominal
³
inertia would be represented by a lower elasticity of this curve.

θ
φΩ2

´

Aside from the possibility of diﬀerent policy regimes and from diﬀerences in
the ratio b
y , countries 1 and 2 are assumed to be symmetric in all respectss. The
calibration of the model is summarized in Table 1. The benchmark values for the
policy rules are displayed in Table 2.

9 Bohn’s results are consistent with those by Canzoneri, Cumbi and Diba (1999). Woodford
(2000) argues that these tests are not conclusive and that the possibility of non-Ricardian ﬁscal
policies in the US cannot be ruled out.

14

3.3. Fiscal Shocks

In this section we assess the relevance of some of the eﬀects discussed so far.
In particular we are interested in the response of inﬂation within the monetary
union and the exchange rate to a ﬁscal shock that takes place in country 1B. As
discussed above, the macroeconomic eﬀect of such a shock will depend mainly on
the combination of policies in all the countries.

Figure 1 compares the eﬀects of an expansionary ﬁscal shock in country 1B
under two diﬀerent policy combinations. The shock is formulated as an unex-
pected cut of 1% in the tax rate of that country. The starred line represents the
situation under what we call a Ricardian regime in both countries. The magnitude
of the ﬁscal authorities’ tax response to the level of debt is 0.05, the estimated
value found by Bohn (1998) for the US, whereas the monetary authorities follow
a Taylor rule. The continuous line is a non-Ricardian regime and corresponds
to the policy parameters described in Table 2. Country 2 follows a tight ﬁscal
(α21 = 0.05) and monetary policy (δ21 = 1.5), while in the monetary union coun-
try 1A also displays a strong ﬁscal response to the level of debt (αA
11 = 0.05),
whereas the deﬁcit in country 1B is virtually exogenous (αB
11 = 0.001); the mon-
etary authority of the union hardly responds to the level of inﬂation (δ11 = 0.1).
When the Ricardian regime prevails worldwide, consumption is determined by
permanent income, which is not aﬀected by tax changes; thus, a ﬁscal shock in
1B does not have inﬂation or output eﬀects. A temporary tax cut leads to a tem-
porary rise in real debt that returns to the steady state as a result of the response
of the surplus driven by the ﬁscal policy reaction function of that country.

Under a non-Ricardian regime the ﬁscal authority in 1B does not react to
the rise in the level of debt and another way of preventing a debt explosion is
needed. This is achieved by means of a sharp rise in the price level (and inﬂation)
of the union, as observed in the continuous line in the ﬁgure. This brings debt in
country 1B onto a path that asymptotically converges with its steady state. Also,
the reduction in the level of real debt in country 1A induces a reduction in taxes.
The interest rate rises as a result of the attempt by the monetary authorities in
the union to prevent the inﬂation increase. The implied fall in the real interest
rate induces a larger output eﬀect.

In the standard sticky price open macro model, a positive temporary ﬁscal
shock creates an excess demand for domestic goods relative to foreign goods that
generates a temporary exchange rate appreciation. Under the simulated Ricardian
regime this is limited by the immediate ﬁscal response. Surprisingly, in the non-
Ricardian regime the impact eﬀect is a currency depreciation, that is expected

15

to proceed further until the interest rate diﬀerential disappears. The expected
depreciation is consistent with the diﬀerence in the nominal interest rate across
countries, but the initial depreciation is somewhat counterintuitive.
It comes
about because of the purchasing power parity condition that ties P2 with (P1/e):
since P2 reacts very little, the exchange rate simply follows the path of P1.

This sequence of events is virtually independent of the response of the ﬁscal
authority in country 1A. To see to what extent country 1A could oﬀset the weak
response of taxes in 1B, we simulate the eﬀects of the same temporary tax cut
than before, but assuming that the ﬁscal rule of 1A is much more responsive to
its own debt: αA
11 = 1.0 (continuous line). Both impulse-responses are depicted
in Figure 2 and we see that they are almost identical in terms of the aggregated
variables. The only variables aﬀected are the paths of taxes and debt in country
1A.

Similarly, a stronger response by the union’s monetary authority is of little
help. Figure 3 compares two non-Ricardian regimes, one being again the bench-
mark case of Table 2 (represented here by the starred line) and the other assuming
that the central bank of the union sets a tighter inﬂation response, δ11 = 0.8 (con-
tinuous line). The eﬀects of the tax cut are qualitatively similar. With a tighter
monetary policy the price level increases by a similar amount but this increase is
more persistent. The only diﬀerence is to be found in the output response that is
now ﬂatter, mostly because of the ﬂat response of the real interest rate. In any
case, these results conﬁrm Woodford’s (1996) ﬁndings in the context of a closed
monetary union and have the implication that a suﬃcient degree of endogeneity
of surpluses is needed to bring all countries into a union-wide Ricardian regime
in which monetary policy can be held responsible for keeping prices stable.

To complete the picture, Figure 4 compares the eﬀects of the same tax cut
in country 1B in two non-Ricardian scenarios that diﬀer not merely in the size
of the parameters (as in Figures 2 and 3) but in the policy combinations them-
selves. Again, the starred line represents the responses of the variables in the
benchmark non-Ricardian case discussed so far. The continuous line represents a
policy combination that yields uniqueness at a worldwide level, although it would
have generated either overdetermination or indeterminacy if both countries were
closed economies.10 Under this parameterization, country 2 follows a loose mone-
tary (δ21 = 0.1) policy and a Ricardian ﬁscal one (α21 = 0.05), whereas monetary
policy is tight in country 1 (δ11 = 1.5) and ﬁscal policies diﬀer within the union:
country 1A is Ricardian (αA
11 = 0.001).

11 = 0.05) whereas country 1B is not (αB

10 This corresponds to the ﬁrst example in case 4 discussed in Appendix B.

16

There are four remarkable diﬀerences between the two cases: ﬁrst, the real inter-
est rate now increases, second, the ﬁscal shock in 1B is now much less inﬂationary
for the union as a whole, third, the tax cut now generates a recession in the union
and, ﬁnally, the exchange rate suﬀers a substantial appreciation, whereas it de-
preciated in the benchmark case. These two sets of impulse responses could lead
the observer to mistakenly interpret them as resulting from completely diﬀerent
shocks.

4. Conclusions

The ﬁscal theory of the price level has challenged the conventional view that
monetary factors drive prices and exchange rates and has also provided a rationale
for ﬁscal restriccions in a monetary union. This paper revisits the results of
this theory in the context of an open monetary union model. In contrast with
the closed economy, in this extended framework the discussion of equilibrium
determination becomes richer and more complex. A wider range of assumptions
on risk sharing and policy coordination schemes generate a unique equilibrium,
each with speciﬁc properties. Some of these combinations reproduce the results
obtained in the closed economy, but others display signiﬁcantly diﬀerent outcomes.

17

Appendix A: The log-linear model

Et

ct+1

−

1
ct = σ−

µ

b

b

R1
1 + R1 ¶
P1t =

R1t

−

b
P2t +

et

1
σ−

Et

Pt+1

³

b

−

Pt

´

b

R1
1 + R1 ¶

µ

R1t

R2
b
1 + R2 ¶

b
−
µ

R2t = Et
b

et+1

−

et

b

b
P1t =

M1t

−

c

b

M2t

−

P2t =

σ
ε

σ
ε

³

³

´

´

ct

b

ct

b

P1t

b
P2t

−

−

P1t

1 = β
−

b
P2t

1 = β
−

b

b

c
Et

b
P1t+1

³

³

b
P2t+1

Et

b

−

−

P1t

+

+

µ

µ

´

´

b
P2t

b

b

cσχ

− 

R1ε

M 1
P 1



³
cσχ

− 

R2ε

M 2
P 2

b
ε 

R1t

 b

´

R2t

ε 


θ (γ

³

1)

 b

´
y1t +

−
φ1Ω2

θ (γ

−
φ2Ω2

1 ¶
1)

2 ¶

b
y2t +

µ

µ

θσ
φ1Ω2
θσ
φ2Ω2

1 ¶

2 ¶

(A.1)

(A.2)

(A.3)

(A.4)

(A.5)

ct + εP
1t

(A.6)

b
ct + εP
2t

(A.7)

+

R1
Ω1

Ã

BA

1t −

³

b
A
B
1
P 1 !

BB

1t −

P1t

1
= β−

´

b

R1t

1

−

− Ã

b
P1t

1
= β−

BA
1t

1 −
−

P1t

+

³

b

M 1
A
1 !

2B

b

−

M1t

³

c

´

P1t

´

b

BB
1t

1 −
−

P1t

+

³
b
B
B
R1
1
Ω1
P 1 !

b
R1t

´

1

−

− Ã

b

³
M 1
B
1 !

2B

+

Ã

b
τ A
τ A
1t
1

+

¢

b

b
−

1

A
B
1
P 1 !

Ã

gA
1

gA
1t −

b

¡
M 1
A
1 Ω1 !
1

−

M1t

1

−

³

c

−

gB
1

gB
1t −

τ B
1

τ B
1t

− Ã

2B

B
B
1
P 1 !

Ã

P1t

(A.8)

´

b
+

¢

P1t

(A.9)

´

P1t

b

−

M1t

³

´

+

c
1

−

−

b
P2t

b

¡
M 1
B
1 Ω1 !
1

³

(g2

g2t

− Ã

2B

−

B2
P 2 ¶

M1t

b
1

−

−

b
τ 2t) +

τ 2

c

−

´

b

b

´

µ

b

18

b

−

B2t

³

b

P2t

1
= β−

B2t

´

b

³

b

+

R2
Ω2

B2
P 2 ¶

µ

R2t

b

M2t

M 2
B2 ¶ ³
1t + gB
gA
c
1

1

−

−
µ
ct + gA
c
1

P2t

−

−
µ
´
gB
g2t = y1
1t + g2
b

M 2
B2Ω2 ¶ ³
y1t + y2

M2t

y2t
c

1

−

−

P2t

´

b

R1
b

R1t = δ11Ω1
b

R2

R2t = δ21Ω2
b

³

P1t
b

P1t
b
−

1

−

P2t
b

P2t
b

1

−

−

+ δ12
b

y1t +

+ δ22

y2t +
b

εR
1t
b
εR
b
2t

´

τ A
1

τ A
1t −

gA
1

b
1t = αA
gA
11

τ B
1

b
τ B
1t −

b
1t = αB
gB
11

gB
1

³

A
B
1
P 1 !
B
B
1
P 1 !

Ã

Ã

b
BA
1t

b
1 −
−

³

b
BB
1t

1 −
−

´
P1t

1

−

b
P1t

1

−

b
+ αA
12

b
y1t +

ετ A
1t

+ αB
12

b
y1t +

b
ετ B
1t

´

´

b
τ 2t
τ 2

−

b
g2t = α21
g2

B2
P 2 ¶ ³

µ

b

b

b

1

−

−

b
P2t

b

+ α22

b
y2t +

b
ετ
2t

1

−

´

b

b

³

b
B2t

(A.10)

(A.11)

(A.12)

(A.13)

(A.14)

(A.15)

(A.16)

19

Appendix B: Stability analysis
In this appendix we calculate the regions of stability of the model, in the case
of incomplete risk sharing among all three countries (so that the independent
dynamics of all three debts matter).11 Further we make the following simplifying
assumptions:

c
y

= γ = 1, αA

12 = αB

12 = α22 = δ12 = δ22 = 0

After some manipulations, the dynamic representation of the linear version of the
model (disregarding exogenous variables) is,

ct+1

−

ct =

εy
σβ

c
y

µ

¶

b

b
π1t+1
−

π1t =

−

µ

ct +

·
1 + π
b
π

β
σ

δ11

µ

1
β2

−

εyc
βy

¶

¶ µ

ct +

¶ µ
1
β −

µ

π
1 + π

π1t

¶¸

b
π1t

1

¶

b
et+1

∆

−

b

b
et = β (δ11

∆

δ21)

−
1t = H A
bA
11
1t = H B
bB
11
b

bA
b
1t+1 −
bB
1t+1 −
b

π
1 + π

b
π1t + (βδ21

b
1) ∆

et

−

µ
ct + H A
12
ct + H B
12
b

¶
π1t + H A
b
14
π1t + H B
15
b

bB
1t
b

bA
1t

b

b2t+1

b
−

b
b2t = H21

ct + H22

b

b
π1t + H23∆

b
et + H26

b2t

(B.1)

(B.2)

(B.3)

(B.4)

(B.5)

(B.6)

b

et) and three pre-
in which there are three forward-looking variables, (
b
bB
, the H 0s, are
1t,
determined ones
functions of the parameters in the model, εy is the output elasticity in the price
b
1
αA
, H26 =
equation
β −

ct,
b
P1t
−
b
b
¢ ³
b
, H B
15 =

´
b
and, H A
14 =

π1t, ∆
b
P1t

¡
1
11 −

1
−
b
´
αB

b
. Also,

³
b
1)+σ)

b
1
β −

b
πt =

11 −

1+π
π

bA
1t,

b2t

θ((γ

b

1

−
φ1Ω2
1
. In matrix form:

´

³

´

³

´

1
β −

α21

1

³
−

³

´

∆

xt+1 = A

xt

where,

b

b

11 Under perfect risk sharing there would be either two (risk sharing among countries 1A
and 1B but not among 1 and 2) or one (risk sharing among countries 1A, 1B and 2) dynamic
equations, representing the time pattern of debt.

20

x0t =

ct

π1t ∆

et

bA
1t

bB
1t

b2t

h



εy
σβ

b
εy
´
−
β

b
³

b
1+π
π

β
σ
b

1
β2
b

δ11
b

−
1

i

π
1+π

0

´ ¡

¢

b

A =

¢ ³

³
1
β −
β (δ11
H A
12
H B
12
H22

δ21)

´
−

π
1+π

¡

¢

´ ¡

0
³
H A
11
H B
11
H21











0
(βδ21
0
0
H23

−

0

0

0

0

0

0



1) 0

0
14 0

0
0
15 0

H B
0

H A
0
0

H26











Given the form of the dynamic system, the characteristic roots do not depend

on the parameters H11, H12, H21, H22, H23. The eigenvalues of this system are:

z1 =

z2 =

z3 =

µ

µ

1
β −

1
β −
1
β −

µ

z4 = (δ21β

αA

11 −

1

αB

11 −

1

α21

1

¶

¶

¶

−
1)

−
1
β −

z5 =

z6 =

1
2 

µ



1
2 

µ

εy
σβ

+

1
β −

1

εy
σβ

+

− sµ

¶

2

1

¶

4

−

εy
σβ

+

1
β −

1

+

¶

sµ

εy
σβ

+

1
β −

1

2

¶

4

−

εy
σβ

εy
σβ

·

·

(δ11β

−

1)

¸





(δ11β

−

1)



¸

where z6 > 0 (provided that δ11 is not too large) and





sign (z5) = sign (δ11β

1)

−

The stability regions are a generalization of those in Leeper (1991), although
many more combinations are now possible.12 By way of illustration, the following

12 For the general case of δ21, δ22 > 0, the limits of the regions are slightly diﬀerent. In the

closed economy model, the benchmark value for δ1 is given by:

δ1 ≷

1
β −

1
εy µ

1
β −

1
¶ µ

δ2
1 + R

¶

Since the interest rate would respond to the output gap, a lower direct response to demand
shocks is required to stabilize prices, i.e. to achieve an active monetary policy

21

interesting cases arise:

1) Unique equilibrium under Ricardian policies: Ricardian regime. There is
only one possible combination that produces this result (z1, z2, z3 < 0, z4, z5, z6 >
0):

αA

11 >

1
β −

1, αB

11 >

1
β −

1, α21 >

1
β −

1, δ11β > 1, δ21β > 1

2) A unique equilibrium under non-Ricardian policies in all countries cannot

be obtained.

αA

11 <

1
β −

1, αB

11 <

1
β −

1, α21 <

1
β −

1, δ11β < 1, δ21β < 1

In this case there is no equilibrium since there are more unstable roots than non-
predetermined variables: z1, z2, z3, z6 > 0, z4, z5 < 0. A unique non-Ricardian
equilibrium can be obtained if we make:

either αA

11 >

1
β −

1 or αB

11 >

1
β −

1

in such a case P1 is determined by the budget constraint of the non-Ricardian
government.

3) Price levels are indeterminate whenever there are less unstable roots than

non-predetermined variables. One such case is: z1, z2, z4, z5 < 0, z3, z6 > 0, i.e.

αA

11 >

1
β −

1, αB

11 >

1
β −

1, α21 <

1
β −

1, δ11β < 1, δ21β < 1

4) Finally, there are other combinations which may produce a unique equilib-
rium without a clear Ricardian or non-Ricardian pattern. One example would be:
z1, z3, z5 < 0, z2, z4, z6 > 0, i.e.

αA

11 >

1
β −

1, αB

11 <

1
β −

1, α21 >

1
β −

1, δ11β > 1, δ21β < 1

In this parameter combination, country 2 is in a situation in which monetary
policy hadly responds to the level of inﬂation, whereas the ﬁscal authority reacts
quickly and strongly to prevent the level of debt from exploding. With this pol-
icy scheme, the price level in country 2 would not be uniquely determined in a
closed economy framework (i.e., this economy on its own would display price level

22

indeterminacy). Country 1 is in a diﬀerent situation: since the ﬁscal authority
of country 1B lacks discipline, the price level has to adjust to prevent bB
1t from
exploding, but at the same time, an aggressive monetary reaction function is at
work to determine the level of P1t . Thus, there would be no equilibrium in a
closed economy framework (i.e., this economy on its own would display price level
over-determination). Nevertheless, in the open economy context, this combina-
tion of policies helps to determine two nominal variables whereas the third one is
determined by the PPP condition.

Another interesting example would be: z1, z2, z5 < 0, z3, z4, z6 > 0, i.e.

αA

11 >

1
β −

1, αB

11 >

1
β −

1, α21 <

1
β −

1, δ11β > 1, δ21β < 1

In this case country 1 is in a Ricardian regime, so that P1 is determined by the
stance of monetary policy in that country. Since country 2 is non-Ricardian, P2
is ﬁxed by the present value of this country’s surpluses.

23

5. References.

Bergin, P., [2000], ”Fiscal solvency and price level determination in a monetary
union”, Journal of Monetary Economics, 45,3 , 657-680.

Bohn, H. [1998], ”The behavior of U.S. public debt and deﬁcits”, Quarterly

Journal of Economics, 113, 949-964.

Canzoneri, M., R. Cumby and B. Diba., [1999], ”Is the price level determined

by the needs of ﬁscal solvency?”, Working Paper, Georgetown University.

Canzoneri, M. R. Cumby and B. Diba, [1998], ”Fiscal discipline and the ex-

change rate regimes”, CEPR discussion Paper, 1899.

Chari, V.V., P. J. Kehoe and E.R. McGrattan [2000], ”Sticky price models of
the business cycle: Can the contract multiplier solve the persistence problem?”,
Econometrica, 68, 1151-1179.

Clarida, R. J. Galí and M. Gertler, [2000], ”Monetary policy rules and macro-
economic stability: Evidence and some theory”, Quarterly Journal of Economics,
115, 147-180.

Dupor, B., [2000], ”Exchange rates and the ﬁscal theory of the price lev-

el”,Journal of Monetary Economics, 45, 3, 613-630.

Eichengreen, B. and C. Wyplosz, [1998], ”The stability pact: more than a

minor nuisance?”, Economic Policy, April.

Leeper, E., [1991], ”Equilibria under ’active’ and ’passive’ monetary and ﬁscal

policies”, Journal of Monetary Economics, 27, 129-147.

Leith, C. and S. Wren-Lewis [2000], ”Interactions between monetary and ﬁscal

policy rules”, The Economic Journal, 110, 93-108.

Obstfeld, M and K. Rogoﬀ’s [1995], ”Exchange rate dynamics redux”, Journal

of Political Economy, 103, 624-660.

Sargent, T. [1987], Dynamic Macroeconomic Theory, Harvard University Press
Sargent, T. and N. Wallace, [1981], ”Some unpleasant monetarist arithmetic”,

Quarterly Review, The Federal Reserve Bank of Minneapolis, Fall, 1-17.

Sbordone, A. [1998], ”Price and unit labor costs: A new test of price sticki-

ness”, IIES, Working Paper no. 653.

Sims, C., [1997], ”Fiscal foundations of price stability in open economies”,

Mimeo.

Taylor, J., [1993], ”Discretion versus policy rules in practice”, Carnegie Rochester

Conference on Public Policy, 39, 195-214.

Taylor, J., [1999], ”A historical analysis of monetary policy rules”, in J.B.

Taylor, ed., Monetary Policy Rules, Chicago: University Chicago Press.

24

Woodford, M., [1996], ”Control of the public debt: A requirement for price

stability?”, NBER Working Paper no. 5684

Woodford, M., [2000], ”Fiscal requirements for price stability”. Mimeo

25

TABLE 1
PARAMETER AND STEADY-STATE VALUES
Deﬁnition Value

σ
β
γ
θ
φΩ2
σ
ε
cσχ
Rεmε

R
P1
eP2
m
y

2gA
1
y1
2gB
1
y1
g2
y2

2bA
1
y1
2bB
1
y1
b2
y2

1.0
0.994
2.0
0.12
1.0
0.4

1.01
1.0
0.05

0.30

0.30
0.30

0.6

1.0
0.5

Parameter values
Risk aversion
Discount Rate
Elasticity of disutility of eﬀort
output elasticity of inﬂation
Consumption elasticity of money demand
Interest rate elasticity of money demand
Steady-state values

Nominal interest rate
Real exchange rate
Money to output ratio
government consumption to output ratio
Country 1A

Country 1B
Country 2
Debt to output ratio
Country 1A

Country 1B
Country 2

26

TABLE 2
POLICY RULES: A NON-RICARDIAN REGIME

Fiscal Rule
BA
1t = αL
gL
1t
i1
P1t

1

1

−

−

τ L
it −

+ αL
i2

y1t

³

´
Country 2

Interest Rate Rule
Rit = δi1

Pit

+ δi2

yit

Pit

1

−

³

´

b

Country 1 Country 2
b

Country 1

0.05
0.001
0.00

αA
11
αB
11
αL
12
α21
α22

0.1
0.5

δ11
δ12

δ21
δ22

0.05
0.00

1.5
0.5

27

Figure 1 

An asymmetric positive fiscal shock in the monetary union 

0.02

0.04

0.02

1
e
t
a
r

.
t
n

i

0

0

0.06

1
n
o

i
t

a

l
f

n

i

0.04

0.02

0

0

5

10

15

20

5

10

15

20

A
1

t

b
e
d

0.02

0

-0.02

-0.04

5

0

A
1
s
e
x
a
t

0
x 10

-3

5

10

15

20

-5

0

5

10

15

20

1
t
u
p
t
u
o

0.01

0

0

0.06

t

e
a
r

.
x
e

0.04

0.02

0

0

0.04

0.02

0

B
1

t

b
e
d

-0.02

0

0.1

B
1
s
e
x
a
t

0

-0.1

0

5

10

15

20

Non-Ricardian regime 

Ricardian regime 

5

10

15

20

5

10

15

20

5

10

15

20

 
 
 
 
 
 
 
 
 
An asymmetric positive fiscal shock in the monetary union: 
A non-Ricardian regime 
0.02

Figure 2 

5

10

15

20

5

10

15

20

A tighter fiscal rule 

A loose fiscal rule 

5

10

15

20

5

10

15

20

1
t
u
p
t
u
o

0.01

0

0

0.06

t

e
a
r

.
x
e

0.04

0.02

0

0

0

B
1

t

b
e
d

-0.005

-0.01

0

0

B
1
s
e
x
a
t

-0.05

-0.1

0

5

10

15

20

5

10

15

20

5

10

15

20

5

10

15

20

0.04

0.02

1
e
t
a
r

.
t
n

i

0

0

0.06

1
n
o

i
t

a

l
f

n

i

0.04

0.02

0

0

0.02

0

-0.02

A
1

t

b
e
d

-0.04

0

0.1

A
1
s
e
x
a
t

0

-0.1

0

 
 
 
 
 
 
 
 
 
Figure 3 

An asymmetric fiscal shock in the monetary union: 

A non-Ricardian regime 

0.02

0.04

0.02

1
e
t
a
r

.
t
n

i

0

0

0.06

1
n
o

i
t

a

l
f

n

i

0.04

0.02

0

0

0

5

10

15

20

5

10

15

20

A
1

t

b
e
d

-0.02

-0.04

5

0

A
1
s
e
x
a
t

0
x 10

-3

5

10

15

20

-5

0

5

10

15

20

1
t
u
p
t
u
o

0.01

0

0

0.2

t

e
a
r

.
x
e

0.1

0

0

0

B
1

t

b
e
d

-0.005

-0.01

0

0

B
1
s
e
x
a
t

-0.05

-0.1

0

5

10

15

20

A tighter monetary rule 

A loose monetary rule 

5

10

15

20

5

10

15

20

5

10

15

20

 
 
 
 
 
 
 
 
 
An Asymmetric positive fiscal shock in the monetary union: 

Figure 4 

Alternative non-Ricardian regimes 

0.02

0.04

0.02

0

1
e
t
a
r

.
t
n

i

-0.02

0

0.06

1
n
o

i
t

a

l
f

n

i

0.04

0.02

0

0

0

5

10

15

20

5

10

15

20

A
1

t

b
e
d

-0.02

-0.04

5

0

A
1
s
e
x
a
t

0
x 10

-3

5

10

15

20

-5

0

5

10

15

20

1
t
u
p
t
u
o

0

-0.02

0

0.2

t

e
a
r

.
x
e

0

B
1

t

b
e
d

-0.2

0

0.04

0.02

0

-0.02

0

0.1

B
1
s
e
x
a
t

0

-0.1

0

5

10

15

20

Non-Ricardian regime 1 

Non-Ricardian regime 2 

5

10

15

20

5

10

15

20

5

10

15

20