The aim of this research is to study the effect that fiscal limitations have on the
macroeconomic dynamics in EMU. Governments which stumble upon fiscal limits fail to collect
taxes necessary to finance spending, given the level of public debt. This scenario unravels in
today’s Europe, where for many countries the scope of raising extra tax revenues via increases in
tax rates is limited1, forecasts for future rates of economic growth are grim, public debt
obligations are vast and the adversity of demographic trends suggests that aging-related
expenditures will rise substantially in the next 50 years2 and cause government’s surpluses to
diminish even further.
This section introduces a two-country model of EMU, where government of one country
(country 1) faces such limitations and runs “active” fiscal policy, whereas government of the
other country (country 2) adjusts fiscal surpluses in line with debt sustainability criteria.
Therefore, fiscal surpluses of country 1 evolve exogenously, depending on the level of nominal
debt, while surpluses of country 2 are set endogenously in accordance with a stochastic process.
The key assumption here is that agents’ portfolios consist of bonds provided by different
governments. Due to this assumption, when country 1 issues additional debt without generating
expectations of the corresponding increases in future fiscal surpluses, a union-wide wealth effect
emerges.3 The overall effect that fiscal policy of country 1 has on prices, interest rates and debts
in EMU will depend on ECB’s policy choices and fiscal policy, conducted by fiscally prudent
government.
Note that in the model behavior of fiscally imprudent government is set exogenously and
rational agents are aware of the characteristics of the underlying process. This assumption is not
counterintuitive, since the behavior of member governments in EMU is bound by Maastritch
Treaty, and even though European governments generally fail to fulfill its’ limitations, they still
cannot set their fiscal surpluses independently to maximize wealth of their subjects.
Distinctive feature of this analysis is that it does not presuppose that the non-Ponzi game
conditions hold for each stock of debt individually. Alternatively, this framework only requires
that the overall portfolio must be sustainable so the Ponzi schemes are not excluded. Equilibrium
with Ponzi schemes in this model corresponds to the scenario in which fiscally prudent
governments conduct excessively restrictive fiscal policy. In this case the overall level of debt in
the EMU may remain sustainable, regardless of fiscal policy conducted by the fiscally imprudent
government. Generally, if member governments raise taxes in excess of the amount needed to
insure sustainability of individual debts, an equilibrium fraction by which the fiscally imprudent
government defaults diminishes. This occurs because rational agents hold bonds issued by all
governments within their portfolio – thus, rationality only requires sustainability of the whole
portfolio, whereas individual debts may be unsustainable. Equilibria with Ponzi schemes may be
interpreted as case when eurobonds are issued.
The model
Governments of each country collect lump-sum taxes, pay transfers and issue debt. Fiscal
surplus of country i are defined as a difference between taxes collected and transfers paid:
 i ,t  zi ,t  si ,t
(1)
Country 1
1
See Trabandt, Uhlig (2009) who sowed that over the past 20 years European economies have drawn closer to the
peaks of their respective Laffer curves
2
According to IMF (2009), the net present value of these promised expenses is averaging 409% of GDP across the
advanced G-20 countries, meaning that the transfers are not backed by tax revenues
3
This assumption was introduced in Woodford (1995). The wealth effect is present if fiscally imprudent
government refuses to default
Surpluses of country 1 follow an AR(1) process:
s1,t  s1   ( s1,t 1  s1 )   t ,
where   1 ,  t
(2)
iid (0,  2 ) , s1 is a steady state value of fiscal surpluses in country 1.
In each period it is possible for the government of country 1 to default on its debt obligations.
Following Uribe, the fraction by which it defaults in period t is given by  t . Therefore, the
dynamic budget constraint for government 1 states that in each period:
B1,t
Pt
Rt 1 B1,t 1 (1   t )

where
Pt
 s1,t
(3)
B1,t is the value of nominal debt obligations of government 1 in period t.
Country 2
Now consider fiscal policy of the second country. Assume that surpluses depend on the
level of nominal debt obligations and evolve endogenously:
s2,t  s2   (
B2,t 1
 b2 )
Pt 1
(4)
To insure sustainability, suppose that

1

 1 . Government of the second country does
not encounter any debt-repayment issues and, hence, the interest on its debt is risk free. In this
regard, the dynamic budget constraint of government 2 is given by:
B2,t
Pt

Rt f1B2,t 1
Pt
 s2,t ,
(5)
f
where R is a risk free gross interest rate, B2,t is the value of nominal debt obligations of
government 2 in period t.
Consumer’s problem
The representative agent, who lives in country j, solves the following utility maximization
problem:

E0   t u(c j ,t )  max
(6)
t 0
subject to:
c j ,t 
Et rt 1D j ,t 1
Pt
 s j ,t  y j ,t 
D j ,t
Pt
(7)
lim Et qt  j Dt  j  0
j 
(8)
qt  j  rt rt 1...rt  j
Here, D j ,t is the value of contingent claims in period t, which depends on the state of the
world. Uncertainty arises due to first country’s imprudence: because there is a possibility tat
country 1 might default on its debt, the value of assets in period t+1 is unknown in period t.
Et rt 1 is a price of the contingent claims, y j ,t is the income of a resident of country j, s j ,t are
taxes collected in country j net of transfer payments, c j ,t is consumption.
First order condition for this problem states that:
u(c j ,t )  
1
P
Et t u(c j ,t 1 )
rt Pt 1
(9)
Equilibrium
In equilibrium goods and financial markets should clear. For simplicity consider an
endowment economy, where y1,t , y2,t are endowments given to residents of countries 1 and 2
respectively. Assume the sum of endowments is constant over time:
y1,t  y2,t  y
(10)
Therefore, in equilibrium:
с1,t  с2,t  y .
(11)
Since agents hold bonds issued by each government, in equilibrium overall demand for
financial assets must equal supply, provided by both governments:
B1,t  B2,t  D1,t  D2,t
(12)
Here, the expected payoff of a bond issued by the first government is Rt Et (1   t 1 ) .
f
Bonds issued in the second country pay Rt , which is risk free. In equilibrium it must be equally
profitable to hold each asset—therefore, from the first order condition it can be obtained that for
both assets, Euler equations must hold:
u(c j ,t )   Rt Et (1   t 1 )
u(c j ,t )   Rt f Et
Pt
u(c j ,t 1 )
Pt 1
Pt
u(c j ,t 1 )
Pt 1
(13)
(14)
For simplicity suppose utility is quadratic, so that marginal utility is linear:
a
u (c j ,t )  c j ,t  c 2j ,t .
2
(15)
By adding up Euler equations specified by (13) for j  1, 2 , the following relation for the
risky interest rate can be derived:
1   Rt Et (1   t 1 )
Pt
Pt 1
(16)
Similarly, for the risk free interest rate the following relation must hold:
1   Rt f Et
Pt
Pt 1
(17)
Equilibrium default rate
Following Uribe (2006), in equilibrium the fraction of debt by which country 1 defaults in
each period can be calculated. Multiplying the dynamic budget constraint of country 1 by
PR
t t (1   t 1 ) and iterating forward, the following relation is obtained:
j
B1,t  j Rt  j (1   t  j 1 )  ( Rt h (1   t h1 )) Rt 1 B1,t 1 (1   t ) 
h 0
j
j
h 0
k h
(18)
  ( Rt k (1   t k 1 )) Pt h ( s1,t h )
Dividing the equation by Pt  j 1 and applying an equilibrium condition (17) gives:
B1,t  j
Pt  j 1
Rt  j (1   t  j 1 )    j 1 Rt 1
Multiplication by

j 1
B1,t  j
Pt  j 1

j 1
B1,t 1
Pt
j
(1   t )    h j 1 ( s1,t h )
(19)
h 0
provides:
Rt  j (1   t  j 1 )  Rt 1
B1,t 1
Pt
j
(1   t )    h ( s1,t h )
(20)
h 0
The technique presented here was applied in Uribe (2006) and the above result is similar to
the one derived within the framework introduced in the paper. However, since Uribe addresses a
one-country case, the transversality condition from the consumer’s problem guarantees that the
non-Ponzi game condition is also fulfilled. However, in the model presented here transversality
only binds behavior of the whole portfolio. Therefore, although the non-Ponzy game condition
must hold for the joint sum of assets, it does not have to hold for each asset individually. In other
words, agents’ maximization allows Ponzi schemes, provided that the counterparty is prudent
enough.
If the government of country 1 is allowed to conduct such policy so Ponzi games are not
excluded, further restrictions are needed to specify equilibrium default rate. Suppose that Ponzi
games are allowed. In that case transversality restricts behavior of the whole portfolio:

B
B 
lim  j 1 Et  Rt  j (1   t  j 1 ) 1,t  j  Rt f j 2,t  j   0
j 
Pt  j 1
Pt  j 1 

(21)
Analogously to derivation of equation (20), intertemporal relation between debt of country 2 and
its sum of surpluses can be obtained:
 j 1
B2,t  j
Pt  j 1
R f t  j  R f t 1
B2,t 1
Pt
j
   h ( s2,t h )
(22)
h 0
Adding up equations (20) and (22) and imposing j   , equilibrium default rate can be
specified:

B2,t 1 
h
R t 1
  Et  ( s2,t h )   Et  h ( s1,t h )
Pt
h 0
h 0
 1
Rt 1 B1,t 1 / Pt
f
 tUR
(23)
From equation (23) it follows that increases in fiscal surpluses of both countries lead to
reductions in equilibrium default rate of country 1. If Ponzi schemes are not allowed, the value
of future surpluses in each country must exactly match the value of its debt obligations due to the
restriction:

B 
lim  j 1 Et  Rt  j (1   t  j 1 ) 1,t  j   0
j 
Pt  j 1 

(24)
In this case equation (23) assumes the form of the relation presented in Uribe (2006), hence the
analysis is similar to a one-country case:


  1  h 0
R
t
h
Et ( s1,t h )
Rt 1 B1,t 1 / Pt
(25)
Here, the equilibrium default rate is solely determined by the fiscal policy conducted by the
government of country 1. Fraction  tR increases when expected surpluses are being reduced.
This result is intuitive: whenever the surpluses decrease, probability of country 1 ever paying off
reduces, forcing country 1 to default. On the other hand, if the present value of expected
surpluses coincides with the value of debt, first country doesn’t need to default. Therefore,
default happens whenever debt is not backed by the expected future surpluses.
Now reconsider more general case where non-Ponzi game conditions do not have to hold
for each debt individually, so that equilibrium default rate is determined by (23). If the sum of
discounted surpluses in country 2 exceeds the value of its debt obligations, the equilibrium
fraction  tUR turns out to be smaller than  tR . In other words, when country 2 conducts
excessively prudent fiscal policy, the other country defaults by a smaller fraction. Therefore, this
analysis suggests that fiscally prudent government can potentially suppress instability, caused by
debt repayment issues faced by other governments in the union.
To identify equilibrium further specification is required. In this regard the next section
reviews four possible policy regimes. The first two regimes address the case in which there are
two separate non-Ponzi game conditions for each government. The regimes differ by a restriction
imposed on the default rate: in one case default is allowed, in the other it is not. Regimes 3 and 4
cover the general case with a portfolio non-Ponzi game condition. The latter regimes differ in the
same manner as the first two.
Separate NPG conditions
Joint NPG condition
Default is allowed
Regime 1
Regime 3
Default is not allowed
Regime 2
Regime 4
Table 1: the four regimes
Regime 1: Two NPG conditions, default is allowed
In this regime an equilibrium default rate is determined by equation (25). This case is
similar to the one reviewed in Uribe (2006). By assumption the evolution of surpluses in country
1 is determined by an AR(1) process, specified by equation (2). Application of this proposition to
equation (25) results in the following relation for the equilibrium default rate:
t  1 
s1,t (1   )  s1 (1   ) 
(1   )(1   ) Rt 1B1,t 1 / Pt
(26)
This relation does not fully determine an equilibrium default rate because it contains an
endogenous price level in period t. In equilibrium a higher Pt is associated with greater fraction
 , because the real value of debt decreases as prices go up. Therefore, with inflation targeting
the real value of government debt remains substantial, which leads to partial default. More
specifically, if ECB sets interest rates according to the Taylor rule, inflation target can be
achieved, but country 1 will be forced to default4. To illustrate this idea, consider the Taylor rule:
Rt  R *  (
Pt
  *)
Pt 1
(27)
with   1 to insure “active” monetary policy. As in Uribe (2006), it is possible for the ECB
to achieve  t   * by setting Rt  R*   * /  . In this case equilibrium default rate is given by:
t  1 
s1,t (1   )  s1 (1   ) 
(1   )(1   ) Rt 1B1,t 1 / Pt 1
*
(28)
or more generally by:

t  1 

h 0
h
Et ( s1,t h )
Rt 1B1,t 1 / Pt 1
*
(29)
Consequently, in this regime it is possible to maintain low inflation, but at a cost of
sovereign defaults. The lower is inflation target, the higher becomes a fraction by which fiscally
imprudent government defaults. In other words, when ECB pursues low inflation goal, the real
value of government’s obligations is substantially high, which means that greater surpluses are
4
This reasoning follows Uribe (2006)
needed to ensure debt sustainability. Thus, as surpluses of country 1 evolve exogenously, this
policy results in a higher default rate for country 1.
Regime 2: Two NPG conditions, default is not allowed
This regime presupposes that the fiscal authority withholds sovereign defaults, even though
fiscal policy does not adjust to changes in the debt level. In that case equation (25) reduces to the
well-known relation studied within the Fiscal Theory of Price Level:
Pt 
Rt 1 B1,t 1


h 0
h
(30)
Et ( s1,t h )
The numerator is predetermined in period t; the denominator is set exogenously due to
the preliminary assumptions. Therefore, unlike equation (25), equation (30) is an equilibrium
condition, which uniquely identifies the price level in period t.
From equation (30) it follows that the overall price level increases whenever expected future
surpluses in country 1 fall. Intuitive underpinning of this result stems from the fact that when
fiscal policy is “active”, ricardian equivalence is violated. Since current decreases in the amount
of collected taxes are not associated with the future rises in the tax rates, whenever taxes
decrease, consumers of country 1 feel wealthier and spend more, boosting aggregate demand and
pushing prices upward. Similarly, high levels of debt issued by country 1 and held by consumers
of each country are associated with greater wealth. This occurs because the accumulation of debt
by country 1 is not followed by expectations of corresponding future increases in taxes.
Consequently, higher levels of B1,t 1 and interest paid on these bonds result in greater spending
and substantial inflation. It follows that in such regime the price level in the EMU is determined
entirely by the fiscal policy conducted in country 1.
A crucial feature of this regime is that with such policy mix the ECB cannot afford
aggressive inflation targeting. Note that if both monetary and fiscal policies pursue their own
goals ignoring debt sustainability issues, debt dynamics become explosive. This occurs because
of the wealth effect that originates from fiscal policy activeness, creating an upward trend in
inflation and inflation expectations If ECB is committed to its original objective, it attempts to
flatten this trend by imposing higher interest rates. This sequence inevitably leads to an increase
in the operational deficit, so the “active” government has to issue more bonds, producing even
larger wealth effect, and so on. Therefore, doubly active policy results in unsustainable debt and
substantial inflation. This suggests that in times of fiscal stress aggressive inflation targeting
boosts public debt and actually leads to higher inflation. Hence, the presence of fiscal limits
significantly alters the effect of the ECB’s policy.
If ECB refrains from aggressive inflation targeting, sovereign crisis is mitigated through
real depreciation of the debtor’s obligations. Note that since the price level is common across
EMU, its appreciation devalues all sovereign debts nominated in euro. Consequently, this setup
results in lower real value of country 2’s debt. Given that country 2 implements “passive” fiscal
policy, with lower debt it can afford to reduce taxes and encourage its residents to consume
more5.
Regime 3: Joint NPG condition, default is allowed
5
This effect was discussed in Leeper, Walker (2010)
In this regime it is assumed that the governments are allowed to create Ponzi schemes.
However, agents’ rationality implies that the portfolio must satisfy transversality. Therefore,
Ponzi schemes can exist only when there are governments that conduct excessively prudent
fiscal policy, backing the joint portfolio. Preceding analysis suggests that with such policy mix
the default rate is determined by equation (23):
t  1 
R f t 1

B2,t 1 
  Et  h ( s2,t h )   Et  h ( s1,t h )
Pt
h 0
h 0
Rt 1 B1,t 1 / Pt
(23)
As noted earlier, if fiscal policy of country 2 responds only to changes in the level of debt
of country 2, equation (23) reduces to equation (25) and properties of this regime become
qualitatively similar to those of regime 1. However, if fiscal policy conducted in country 2 is
sensitive to changes in the level of B1 , the numerator of the right-hand side of equation (23)
becomes endogenous. Thus, not only it is possible to maintain low inflation in this regime, but
the solution with both low inflation and low default rate is also feasible. However, such policy
implies redistribution of wealth from residents of country 2 towards residents of country 1. In
other words, to offset inflationary consequences associated with wealth effects, it is necessary to
restrain aggregate demand; to do so, government of country 2, which does not face fiscal limits,
must raise taxes. Therefore, to ensure low inflation and debt sustainability consumption of
residents of country 2 must be sacrificed. Clearly, it is politically difficult to implement such a
policy.
Regime 4: Joint NPG condition, default is not allowed
This regime is not similar to regime 2, thus the results obtained within the FTPL
framework do not necessarily hold. With the restriction on
following relation:
Rt 1 ( B2,t 1  B1,t 1 )  j
   Et ( s1,t  j  s2,t  j )
Pt
j 0
 t , equation (23) transforms into the
(31)
Note that since default is no longer allowed, interest rates for both debts become risk free
and should be identical to rule out arbitrage.
If government of a fiscally prudent country sets surpluses to insure sustainability of its
own debt and does not respond to changes in B1 , this regime reduces to the FTPL scenario,
reviewed within regime 2. If this is the case, FTPL results are valid: namely, with prices being
determined by fiscal policy of country 1, aggressive inflation targeting leads to faster debt
accumulation and inflationary consequences which spread across the union. Therefore, to
exclude explosive paths ECB has to conduct “passive” policy, for instance, implement Rt  R *
. With such policy mix, consequents of country 1 stumbling upon a fiscal limit would be spread
evenly across EMU through common price level, given by (32):
Pt 
(1   )(1   ) Rt 1B1,t 1
st (1   )  s (1   ) 
(32)
However, if country 2 adjusts its fiscal policy in line with joint portfolio sustainability
criteria, the present value of its surpluses exceed the real value of debt. In other words, overall
portfolio is always sustainable if surpluses of country 2 evolve according to (33):
s2,t  s  ˆ (
where ˆ 
1

B1,t 1  B2,t 1
Pt 1
 b1  b2 )
(33)
 1, b1  b2 is a steady state value of total debt.
Hence, the implied price level would be smaller than in case country 2 does not account
for foreign debt repayment issues. But once again, such policy involves redistribution of wealth
towards residents of fiscally imprudent country, which makes this policy choice unfavorable for
the voters of country 2. If the agreement is reached, in total fiscal policy would be “passive” and
it is still possible to target inflation and maintain  t   * , as in the case with no fiscal limits
suggested by the monetarist approach.
Summary
Maastritch Treaty grants ECB independency from fiscal needs of individual governments,
which should lead to lower inflation, provided that fiscal policy is “passive” (see Rogoff (1985)).
However, currently many member governments face fiscal limitations or they are expected to
face them in the future, so their ability to conduct “passive” fiscal policy is debatable. The
presented analysis suggests that under different circumstances aggressive inflation targeting may
lead to different outcomes in terms of overall inflation and individual debt sustainability (see
table 2).
For instance, suppose that the fiscal authority, which is bound by fiscal limits, is expected
to refrain from defaulting at all times. In this case aggressive inflation targeting may result in
explosive debt dynamics and substantial inflation. This occurs because high levels of debt issued
by fiscally imprudent government and held by consumers of each country imply higher levels of
wealth since the debt is not backed by expectations of extensive future taxation. Therefore,
increases of debt holding generate wealth effect, which boosts spending and gives rise to
inflation hikes. If ECB sets interest rates in accordance with the Taylor rule, this process will be
followed by increases in interest rates, which will inflate operational deficits further and cause
fiscally imprudent governments to issue more debt. As a result, such policy mix leads to even
larger wealth effects and instigates explosive inflation.
One way to avoid this outcome is to refrain from aggressive inflation targeting and set
interest rates more or less independently of the inflation dynamics. In this case the emerging
wealth effects will be smaller and inflation will remain stable, although the price level will be
rather high. Within this scenario, inflation dynamics is determined by fiscal policy conducted by
the fiscally imprudent government and inflationary consequences of that policy are spread across
the whole union.
Another way of excluding hyperinflation is to allow defaults. In presence of defaults
wealth effects are mitigated: even though increases in debt levels are not backed by expectations
of future rises in taxes, there is a chance that the debts will not be repaid and this probability
increases with the actual debt level of a fiscally imprudent government. Therefore, equilibrium
with defaults and low inflation and “active” monetary policy is feasible.
Finally, to offset inflationary consequences associated with wealth effects, fiscally
prudent government can restrain aggregate demand by additionally increasing taxes paid by their
subjects. Such policy allows for equilibria with low inflation and no defaults. However, it
implies redistribution of wealth from residents of prudent countries towards residents of fiscally
imprudent ones and, therefore, is beneficial for the latter.
Explosive inflayion
Default
No deault
Table 2
 “passive” monetary
policy
 “active” monetary
policy
Moderate inflation (FTPL) Low inflation (  t   * )
not reviewed
 “active” monetary
policy
 “passive” monetary
policy
 “passive” monetary
policy
 fiscal policy in
country 2 is
excessively prudent
(redistribution of
wealth)
 separate NPG do
not hold