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Venice Summer Institute 2014
Venice Summer Institute
July 2014
REFORMING THE PUBLIC SECTOR
Organiser: Apostolis Philippopoulos
Workshop to be held on 25 – 26 July 2014 on the island of San Servolo in the Bay of Venice, Italy
FISCAL POLICY SUSTAINABILITY IN THE GIPS:
NEW EVIDENCE FROM NON-LINEAR MODELS
WITH STATE-VARYING THRESHOLDS
Roberto De Santis, Gabriella Legrenzi and Costas Milas
CESifo GmbH • Poschingerstr. 5 • 81679 Munich, Germany
Tel.: +49 (0) 89 92 24 - 1410 • Fax: +49 (0) 89 92 24 - 1409
E-Mail: [email protected] • www.cesifo.org/venice
Fiscal Policy Sustainability in the GIPS: New
Evidence from Non-Linear Models with
State-Varying Thresholds
Roberto De Santis
European Central Bank
Gabriella Legrenzi
Keele University, CESifo and Rimini Centre for Economic Analysis
Costas Milas
Liverpool University and Rimini Centre for Economic Analysis
December 6, 2013
Abstract
We introduce non-linear sustainability tests conditional on endogenously estimated state-varying thresholds. These thresholds vary with
…scal disequilibria, the economic cycle and …nancial market conditions.
Applied to …scal policies pursued by the GIPS, our empirical results provide evidence of threshold behavior in terms of large versus small budgetary imbalances. Financial market pressure relaxes the de…cit-to-GDP
threshold for adjustment in Ireland and Spain and reduces the threshold
for Portugal.
JEL Classi…cation: H63, H20, H60, C22.
Keywords: sovereign debt sustainability, European debt crisis, nonlinear models, GIPS.
The views expressed in this paper are those of the authors and do not necessarily re‡ect
those of the ECB or the Eurosystem. Previous versions of this paper have been presented at
the European Central Bank Public Finance Workshop on "The Political Economy of Fiscal
Adjustment in Europe" (European Central Bank, October 2013), the Rimini Centre for Economic Analysis 2nd Time Series Workshop (Rimini, 2013), the 15th ZEW Summer Workshop
on “Current Fiscal Policy Challenges in Europe” (Mannheim 2013), the International Finance
and Banking Society Annual Congress (Valencia 2012) and the CESifo Workshop in Public
Sector Economics (Munich 2012). We thank Cinzia Alcidi (Centre for European Policy Studies), Hashem Pesaran (University of Southern California), Cláudia Rodrigues Braz (Banco de
Portugal) and seminar participants for useful feedback and suggestions. The usual disclaimer
applies. Financial support from CESifo and ZEW is gratefully acknowledged.
1
1
Introduction
The recent …nancial crisis has exposed fundamental weaknesses in the European
Monetary Union, commanding extraordinary measures to provide …nancial support to four peripheral Eurozone countries, namely Greece, Ireland, Portugal
and Spain (GIPS)1 , known under the acronym of GIPS. Further, all GIPS (as
most EU countries) are currently undergoing an excessive de…cit procedure,
following the 2009 Council Decision on the existence of an excessive de…cit,
with a deadline for corrective action in 2014 (2015 for Ireland)2 . As the GIPS
economies, taken together, account for around 17% of Eurozone’s GDP, concerns
over the sustainability of their …scal policy have the potential of destabilizing
the whole Eurozone and endangering the credibility of the common monetary
policy. With this in mind, a comprehensive analysis of …scal policy sustainability in the GIPS has become a pressing policy issue in an attempt to monitor
the …scal health of the Eurozone area.
Existing literature on the sustainability of sovereign debt within the Eurozone not only provides ambiguous conclusions, but also focusses on the long-run
properties of the …scal variables, overshadowing the year-to-year adjustments of
the …scal policy variables, which might be relevant in ensuring the credibility of
a sustainable path of …scal policy. A further drawback of existing sustainability tests in the literature relies on the implicit assumption of linear adjustment
1 Greece, which was bailed-out twice (for e110bn in 2010 and then again for e109bn in 2011)
negotiated, in February 2012, a new e130bn rescue package involving a voluntary haircut of
some 53.5% on the face value of its bonds held by the private sector. Eurozone ministers agreed
(in November 2012) to cut Greece’s debt by a further e40bn. Ireland was bailed-out for e85bn
in November 2010. Portugal was bailed-out for e78bn in May 2011. Spain was granted, in July
2012, …nancial assistance from the European Financial Stability Facility (EFSF) for e100bn.
In September 2012, EFSF was replaced by the European Stability Mechanism (ESM).
2 Greece had already been subject to the same procedure in 2004, concluded in 2007 with
a Council Decision abrogating the existence of an excessive de…cit. Similar conclusions were
held for the previous two Portugal’s procedures (2002-2004 and 2005-2008), whilst Spain and
Ireland do not have a previous record of excessive de…cit procedures.
2
of …scal policy variables to correct budgetary disequilibria. This is in contrast
with political economy models, arguing that …scal adjustments are non-linear in
the sense that …scal policy authorities only correct …scal imbalances when they
become "too large".
Very few non-linear studies on the …scal sustainability in the Eurozone area
have recently started to emerge. Such literature, nevertheless, restricts the
…scal adjustment to follow the same process during "good" and "bad" times,
and consequently, might prove inadequate to understand the currently weak
economic environment over which …scal adjustments take place. Further, nonlinear models have generally been based on exogenously created state-invariant
thresholds. Such modelling is potentially inadequate in capturing the behavior
of …scal policy authorities that might opt for re-adjusting their target given the
changing state of the economy and …nancial market conditions.
We contribute to the literature by introducing non-linear sustainability tests
conditional on endogenously estimated state-varying thresholds. These thresholds vary with the sign and magnitude of …scal disequilibria, the economic cycle
and …nancial market conditions. This paper is organized as follows. Section
2 provides the theoretical background to sustainability testing and reviews the
existing literature on the sustainability of the GIPS …scal policy. Section 3 reports our long-run sustainability analysis. Section 4 presents our analysis of
the year-to-year adjustments of the …scal variables with emphasis on di¤erent
phases of the economic cycle and during …nancial crises. Section 5 concludes
and provides some directions for further research.
3
2
The Government’s Intertemporal Budget Constraint and the Sustainability of the GIPS Sovereign Debt
A given government’s …scal policy is considered sustainable if no-Ponzi games
are enacted, where new debt is issued to pay interest on the old debt. The
theoretical background to existing sustainability tests is provided by the government’s intertemporal budget constraint (IBC), derived below.
The single period nominal budget identity of the government sector, for
period t, can be written as:
Gt + Rt Bt = Tt + Bt+1
Bt
(1)
The left-hand side of the identity consists in the sum of non-interest government expenditure, Gt ; and interest payments on the outstanding debt, Rt Bt :
These outlays need to be …nanced by the right hand side variables, represented
by the tax revenues, Tt , and the issue of new debt, (Bt+1
Bt ) (see, e.g. Walsh
(2010) and Bohn (1988) )3 .
As policy debates are usually conducted by considering the …scal variables
as GDP ratios, we divide the above by the nominal GDP, Pt Yt , where Pt is the
price level and Yt is the real GDP, obtaining:
Rt B t
Tt
Bt+1 Pt+1 Yt+1
Gt
+
=
+
Pt Yt
Pt Yt
Pt Yt
Pt Yt Pt+1 Yt+1
Bt
Pt Yt
(2)
By letting lowercase letter to denote the corresponding variables in real to
GDP terms (i.e. gt
Gt
Pt Yt ,
bt+1
Bt+1
Pt+1 Yt+1 ;
and similarly for the other vari-
ables), we obtain:
3 A further revenue channel is constituted by surprise in‡ation, which lowers the real value
of the government’s outstanding debt, as well as seigniorage.
4
gt + Rt bt = tt + bt+1
Letting
t+1
Pt+1 Pt
Pt
and
Yt+1 Yt
Yt
t+1
GDP growth rate respectively, then
Pt+1 Yt+1
Pt Yt
Pt+1
Pt
bt
(3)
be the in‡ation rate and the real
= (1 +
t+1 )
and
Yt+1
Yt
= 1+
t+1
:
Substituting this in the above, we obtain:
bt+1 =
(1 +
1 + Rt
t+1 ) 1 +
bt
(1 +
t+1
1
)
1+
t+1
(gt
tt )
(4)
t+1
For the rest of the anaysis, to simplify the debt dynamics, we assume a
time-invariant interest rate, in‡ation rate and nominal growth rate4 .
When 0 <
1+R
(1+ )(1+ )
< 1, the debt dynamics is described by a stable dif-
ference equation, which can be solved backwards by successive substitution,
obtaining:
bt+n =
1 + Rt
(1 + t+1 ) 1 +
t+1
!n
n 1
bt +
X
1
(1 + )(1 + ) s=0
1+R
(1 + )(1 + )
n s 1
(gt+s
(5)
Given that
lim
n!1
1 + Rt
(1 + t+1 ) 1 +
t+1
!n
bt = 0;
(6)
a non-explosive debt-to-GDP ratio can be obtained even in presence of
permanent primary de…cits. This happens because the interest rate is below
the nominal growth rate of the economy, which is therefore bene…tting from a
"growth dividend".
The case
1+R
(1+ )(1+ )
> 1, represents an unstable di¤erence equations, which
can be solved forward:
4 For an analysis allowing for time-varying interest rates, in‡ation rate and growth, see
Polito and Wickens (2007).
5
tt+s ) :
bt =
(1 + ) (1 + )
1+R
n
bt+n
n 1
1 X
1 + R s=0
(1 + ) (1 + )
1+R
s
(gt+s
tt+s ) (7)
In order to avoid Ponzi games, where the government "bubble" funds its
expenditures, by …nancing old debt that matures with the issue of new debt, we
need to impose the following transversality condition:
lim
n!1
(1 + ) (1 + )
1+R
n
bt+n = 0:
(8)
The government’s IBC is consequently met when the present value of all
current and future surpluses (i.e. the left hand side of the equation) covers the
outstanding debt:
bt =
1
1 X
1 + R s=0
(1 + ) (1 + )
1+R
s
(gt+s
tt+s )
(9)
The origins of the empirical testing of the IBC and the sustainability of public
…nances trace back to the seminal contribution by Hamilton and Flavin (1986),
who explicitly test for a bubble term in the US debt dynamics. Studies on the
US debt (see e.g. Trehan and Walsh, 1991, Hakkio and Rush, 1991, Quintos
1995) have further developed the empirical methodology based on the timeseries properties of the debt series and/or cointegration between …scal revenues
and outlays5 . Such focus on the long-run, nevertheless, overshadows the yearto-year adjustments of …scal variables, which, in turn, could provide further
relevant information on the conduct of …scal policy-makers.
Recent contributions by Bohn (1998, 2007) have cast some doubts on the effectiveness of such approaches, introducing instead a model-based methodology
5 The equivalence between the cointegration tests (between with-interest government outlays and revenues) and the unit root tests is discussed in Afonso (2005).
6
which relies on the estimation of a …scal reaction function. A su¢ cient condition
for …scal policy sustainability within such model rests on a positive and statistically signi…cant feedback of the primary budget surplus to debt increases. On
the other hand, Woodford (1998) and Canzoneri et al. (2001) point to an identi…cation problem within the …scal reaction function, as it could also represent
the behavior of the public debt, anticipating a surplus shock in a non-Ricardian
regime, where the primary surplus follows instead an arbitrary process, as opposed to correcting budgetary disequilibria to ensure …scal sustainability.
Existing empirical literature on the sustainability of …scal policy in the GIPS
has failed to provide unambiguous results. Afonso (2005), based on the cointegration between general government revenues and expenditures, shows that the
public …nances of all GIPS (and most of the remaining Eurozone countries) are
unsustainable since they fail to satisfy the government’s intertemporal budget
constraint. Arghyrou and Luintel (2007) show that the public …nances of Greece
and Ireland are sustainable, Greiner et al. (2007) provide evidence in favour of
long-run sustainability of the Portuguese …scal policy based on the estimation
of a …scal reaction function. Santos and Silvestre (2002) show that the Irish and
Portuguese public …nances are unsustainable. Ballabriga and Martinez-Mongay
(2005) …nd a positive response of primary balances to increases in public debt
in the EU, pointing to sustainable …scal policies. A similar result is obtained
by Afonso and Jalles (2012) within a panel data analysis, and Afonso and Raut
(2010), showing that the EU public …nances are jointly sustainable.
It should also be noted that existing literature on the GIPS is implicitly
based on the assumption of a linear adjustment of …scal variables. This means
that …scal authorities are expected to correct every budgetary imbalance (no
matter if positive or negative, large or small), adopting the very same correction
7
mechanism.
This is in sharp contrast with political economy models, such as Bertola
and Drazen (1993), arguing instead that the process of …scal adjustment is
non-linear, in the sense that …scal policy authorities only correct …scal imbalances when they become too large. Their motivation relies on the di¢ culties
in reaching the necessary consensus for …scal retrenchment, and complementary
evidence is found in Alesina and Drazen (1991).
A further drawback of the linear approach is that linear cointegration tests
have low power in detecting threshold cointegration (see, e.g. Kapetanios et al.
2003). As a consequence, applied to our …scal policy set up, traditional linear
tests might mistakenly suggest that given countries are on a unsustainable …scal
policy path, whereas in fact their intertemporal budget constraint holds with
corrections only taking place beyond a particular threshold.
Most recent literature introduces possible non-linearities in the analysis of
…scal sustainability. Bajo-Rubio et al. (2006) adopt a threshold cointegration
approach to show that the Spanish public …nances are sustainable, based on
a …xed, state-invariant threshold; Mendoza and Ostry (2008) estimate cubic
…scal reaction functions for a panel of 56 countries, showing that higher debt
countries (in terms of the mean/median of the panel) fail the sustainability test.
A similar result is obtained by Theo…lakou and Stournaras (2012) for a panel
of EU countries exceeding the 60% Maastricht debt criterion and by Ostry et
al. (2010) who examine 23 advanced economies (including the GIPS).
Given the above discussion, we note that existing literature on GIPS sustainability is based on exogenously created, ad hoc or state-invariant thresholds, which might prove unrealistic given the (current) Eurozone crisis. In what
follows, we introduce an empirical model of …scal sustainability allowing for
8
endogenously determined state-varying thresholds.
3
Is the GIPS Sovereign Debt Sustainable?
3.1
The Long-Run Model
We initially address the issue of debt sustainability for the GIPS within a longrun model based on Quintos (1995) and Afonso (2005). To allow for potential
endogeneity of …scal variables, cointegration tests are performed by estimating a
Vector Error Correction Model (VECM; see Johansen, 1988, 1995) of the form:
yt =
k
X1
i
yt
i
+ yt
1
+
+ "t ;
(10)
i=1
where yt = [T AX=GDP; G=GDP ]0 : T AX=GDP is the general government
total revenues, G=GDP is the general government total outlays, both in GDP
ratios; "t
form
=
niid(0; );
0
, where
is a drift parameter, and
and
is a (p
p) matrix of the
are (p r) matrices of full column rank, with
containing the r cointegrating vectors and
carrying the corresponding loadings
in each of the r vectors. For each country, the lag length k is set as to minimize
the Akaike Information Criterion; the latter selects a lag length of k = 2 for all
countries. The test for cointegration is conducted in each case using Johansen’s
(1988, 1995) maximal eigenvalue ( -max) and trace ( -trace) statistics (with
critical values based on MacKinnon et al., 1999).
Such VECM analysis allows us to examine which …scal variable carries the
burden of …scal adjustments via weak exogeneity testing. This is particularly
important given the possibility of non-Keynesian e¤ects of spending cuts (as
opposed to tax increases), as discussed in Alesina and Ardagna (1998).
We use annual time series data over the 1960-2013 period for Greece, Ireland and Portugal. The dataset for Spain is available over the 1970-2013 period.
9
The source of our dataset is the Annual Macroeconomic Database of the European Commission (AMECO; for 2013, we use o¢ cial estimates provided by the
European Commission).6 Figure 1 provides a plot of the data.
Using a battery of unit root tests, preliminary analysis of T AX=GDP and
G=GDP suggests that all series are non-stationary in levels 7 . We now turn
our attention to the empirical results of the cointegration tests, which are reported in Table 1A. At the 5% level of statistical signi…cance, we fail to identify
the existence of a long-run relationship between …scal revenues and outlays for
Greece and Ireland and marginally for Portugal. For Spain, there is evidence
of cointegration using the -trace statistic. At the 10% level of statistical signi…cance, however, there is evidence of cointegration for Greece and Portugal
(using both the -max and -trace statistics) and evidence of cointegration for
Ireland and Spain (using the
-trace statistic). Looking at the cointegrating
vectors, we note that, for each of the GIPS, the estimated marginal response of
taxes to spending ( ) is lower than unity (the
estimates are 0.72 for Greece,
0.71 for Ireland and 0.80 for both Portugal and Spain). Given that outlays grow
at a faster rate than revenues, such a result, in presence of cointegration, points
to "weak form" sustainability of …scal policy as the country might experience
problems in marketing its debt (see on this, Afonso 2005, Quintos, 1995).
As an alternative to Johansen’s cointegrating approach, we report, in Table
1B, the Phillips and Ouliaris (1990) residual-based cointegration test. First we
regress T AX=GDP on a constant and G=GDP and then run a regression of the
estimated residuals on their own lag. We then calculate the Z(t) statistic which
tests the null hypothesis that the coe¢ cient on the lagged residuals is equal to
6 We use the following AMECO data series codes: URTG (tax revenues), UUTG (general
government outlays) and UVGD (nominal gross domestic product).
7 To save space, these results are not reported but are available on request.
10
one (this test is equivalent to testing the null hypothesis of no cointegration).
Our estimate is corrected for heteroskedasticity and autocorrelation in the residuals using the Newey-West (1987) covariance matrix estimator based on a lag
truncation parameter of one (results are robust to alternative lag truncation
parameter choices). From Table 1B, the Z(t) statistic (calculated at -8.40 for
Greece, -8.39 for Ireland, -16.50 for Portugal and -10.50 for Spain) rejects the
null hypothesis of no cointegration.
Under the assumption that cointegration exists, we can assess for each country the robustness of the
estimates using the dynamic OLS (DOLS) regression
of Stock and Watson (1993). In particular, we regress T AX=GDP on a constant,
G=GDP and
for the
(G=GDP ); we use a …xed lead and lag speci…cation equal to two
(G=GDP ) regressor (results are robust to alternative lead/lag speci…-
cations). The estimates are corrected for heteroskedasticity and autocorrelation
in the residuals using the Newey-West (1987) covariance matrix estimator (and
assuming a lag truncation parameter of one; results are robust to alternative lag
truncation choices). Stock and Watson (1993) and Hamilton (1994) point out
that under the assumption of cointegration, DOLS delivers asymptotically e¢ cient and asymptotically equivalent to maximum likelihood estimates obtained,
for example, via Johansen’s (1988, 1995) cointegration framework. Using the
DOLS regression,
is estimated at 0.69 (standard error= 0.04) for Greece, 0.63
(standard error=0.10) for Ireland, 0.77 (standard error=0.04) for Portugal and
0.80 (standard error=0.07) for Spain. These estimates are qualitatively similar to Johansen’s estimates reported in Table 1A (the DOLS estimate of 0.63
for Ireland is somewhat smaller but the 95% con…dence interval of (0.43, 0.83)
comfortably includes the 0.71 estimate based on Johansen’s methodology).
All in all, cointegration tests reported above indicate (marginal) evidence of
11
cointegration using Johansen’s tests and much stronger evidence of cointegration using the Phillips and Ouliaris (1990) test. Notice, however, that whatever
the test,
is estimated to be less than unity which provides evidence of "weak
form" sustainability for all countries. Turning our attention to the adjustment
coe¢ cients ( ) of the …scal variables (see Table 1A), we report that the
on
T AX=GDP is negative and in absolute value twice as high as its standard error;
this not the case for the adjustment coe¢ cient ( ) on G=GDP . Consequently,
we perform a weak exogeneity test for government’s outlays, via a Likelihood
Ratio (LR) test which is distributed as a
2
(1) under the null hypothesis of
a statistically insigni…cant adjustment coe¢ cient on G=GDP . The test computes
2
(1)=2.02 (p-value=0.15) for Greece,
2
land,
2
(1)=0.31 (p-value=0.57) for Portugal and
(1)=1.06 (p-value=0.30) for Ire2
(1)=1.53 (p-value=0.21)
for Spain, consequently failing to reject the null hypothesis. The implication
of the test is that GIPS’…scal policy authorities are shown to follow a spendand-tax model, where government spending is decided by the political process,
regardless of the needs of IBC sustainability, and the burden of correcting …scal
disequilibria is entirely left to the tax instrument. This is bound to result in a
serious detriment to the economy of the GIPS, not captured by the standard
sustainability tests.
3.2
The Evolution of GIPS Fiscal Sustainability
To gain further insight into the sustainability of the sovereign debt in the GIPS,
Figure 2 reports the recursively estimated
-max and
-trace test statistics
divided by their corresponding 5% critical values (values higher than one imply cointegration between government revenues and outlays) whereas Figure
3 plots the recursively estimated cointegrating vector +/-2*Standard Errors
12
(S.E.). Such recursive analysis provides useful information on the evolution of
the behavior of the GIPS’…scal policy authorities over time.
We turn our attention to Figure 2. For Greece, we notice a clear sustainability problem arising since 20048 . There is no evidence of sustainability for Ireland
over the entire sample. Spain’s sustainability problems trace back prior to its
Eurozone membership in 1999, whereas sustainability problems are recorded
for Portugal up until 2002. From Figure 3, the estimated marginal response of
taxes to spending for Greece increases in the run-up to its Eurozone membership
after which it drops markedly. For all countries, the estimated 95% con…dence
interval of the marginal response of taxes to spending fails to show support for
one-by-one movements between T AX=GDP and G=GDP .
Overall, our recursive estimates show a clear sustainability problem primarily in the case of Greece and Ireland (throughout most of the sample) whereas
sustainability for Portugal and Spain has improved following their Eurozone admission. This sustainability problem was apparent at the time of the successive
rulings of the European Council abrogating previous excessive de…cit rulings
(2005 for Portugal, 2007 for Greece, and 2010 for Ireland), pointing to some
ine¤ective monitoring from the EU. We also notice that admission to the euro
for Greece has coincided with a notable drop of the marginal response of taxes
to spending which further questions the sustainability of Greece’s …scal policies.
This latter result is in line with the …ndings of Bénétrix and Lane (2013), who
discuss the weak incentives to pursue sustainable public …nances within the Eurozone. The main message from the recursive linear cointegration tests is that
cointegration switches on and o¤ over time which raises the issue of non-linear
8 Notice that when the
-trace and -max tests diverge in inference, the -max test is
usually preferred as it has the sharper alternative hypothesis, see e.g. Enders (2010).
13
…scal adjustment; we address this in the next section.
4
Non-Linear Models with State-Varying Thresholds
As discussed in Section 1, a notable drawback of existing empirical evidence on
the GIPS is that it relies on linear models based on the implicit assumption of
a continuous and state-invariant …scal adjustment. In fact, the recursive linear
cointegration tests reported in the previous section suggest that cointegration
switches on and o¤ over time which (arguably) questions the assumption that
…scal adjustment is indeed linear. On the other hand, existing non-linear tests
for the GIPS are based on a …xed threshold and assume that …scal adjustments
are state-invariant, i.e. the same correction mechanism is applied regardless of
the state of the economy. In what follows, we estimate our …scal adjustment
models by relaxing the assumption of a …xed threshold. In addition, we examine
the behavior of …scal variables not only with respect to particular budgetary
thresholds, but also during di¤erent phases of the economic cycle and during
periods of …nancial market pressure. Such analysis provides further insight on
how "good" as opposed to "bad" times a¤ect the adjustment of …scal policies
pursued by the GIPS.
4.1
Non-Linear Adjustments of Fiscal Policy: General Government Revenues
To examine the issue of non-linear adjustment to …scal disequilibria in the dynamics of general government revenues, we proceed by considering a non-linear
model of the form
14
T AX
GDP
=
0 +( 11 CVt 1
+
12 gapt 1 ) t 1 +( 21 CVt 1
+
22 gapt 1 ) (1
t 1 )+ut ;
t
(11)
where CVt
T AX
GDP
and
refers to the deviations from the long-run relationship between
1
G
GDP
T AX
GDP
(i.e.
G
GDP
), gap is the output gap (that is, the gap
between actual and potential GDP as percentage of potential GDP; we plot this
in Figure 4 9 ), ut is a stochastic error term, ut
t 1
=1
s
[1 + exp(
(st
i:i:d: 0;
s
1
)=
st
1
2
u
)]
and
1
(12)
is the logistic transition function discussed in e.g. van Dijk et al. (2002)10 .
According to (11)-(12), tax policy exhibits regime-switching behavior which
depends on whether the transition variable, st
nously estimated threshold,
When (st
gapt
t
1
1
s
)!
is given by
s
and
12 ,
t
regimes. We make
of st
1 (Granger
s
s
t
and (1
t ),
respectively.
! 1. In this case, the impact of CVt
respectively. When (st
! 0. In this case, the impact of CVt
respectively. The parameter
is below or above an endoge-
, with regime weights
1, then
11
1,
1
and gapt
1
1
s
1
and
) ! 1, then
is given by
21
and
22 ,
> 0 determines the smoothness of the transition
dimension-free by dividing it by the standard deviation
and Teräsvirta, 1993).
9 The output gap series is available from the AMECO database (code: AVGDGP) and
starts in 1965; this restricts somewhat the estimation sample for the short-run models. As
an alternative measure, we used GDP detrended by a Hodrick-Prescott trend based on a
smoothing parameter
equal to 100 (suggested by Hodrik and Prescott, 1997, for annual
data). For robustness, we also considered the Ravn and Uhligh (2002) suggested value of
4
6.25, obtained from 1600 14 . As an alternative measure of the business cycle, we also used
annual GDP growth. Empirical results (available on request) were robust to these alternative
output de…nitions.
1 0 In
preliminary estimates we allowed for
T AX
GDP
t
to depend (both in a regime-switching
manner and by imposing common coe¢ cients) on its lag and the lagged value of
Results reported below show some (very) weak statistical e¤ect only from
Portugal only.
15
G
GDP
G
GDP
t 1
t
.
for
We consider two possible candidates for st
1:
CVt
1
and gapt
1.
In the …rst
case, we assess how taxes adjust to the deviations from the long-run relationship
between
T AX
GDP
and
G
GDP
. Since we estimate, for all countries,
CV
no clear interpretation of the threshold
CV
Notice, however, that CV
G
+ (1
) GDP
G
) GDP
CV
T AX G
GDP
=
in terms of a de…cit-to-GDP ratio.
G
GDP
T AX
GDP
=
< 1, there is
CV
G
) GDP
+ (1
=
T AX
GDP
CV
G
GDP
(1
.
Hence, we can recover the economic interpretation of the threshold in terms
of a de…cit-to-GDP ratio using the adjustment
CV
(1
G
) GDP
and employing,
for example, the sample average (or median) of the G=GDP series. Under the
assumption that the adjusted threshold is negative, we can assess how taxes
adjust in periods of a rising de…cit-to-GDP ratio as opposed to periods of a
falling de…cit-to-GDP ratio. On the other hand, using gapt
1
as the transition
variable allows us to assess whether taxes adjust di¤erently during periods of
economic downturns (when gapt
expansions (when gapt
1
>
gap
1
gap
<
) and during periods of economic
).
Assuming that …scal corrective action is dependent on a …xed threshold
might be too restrictive; rather, corrective action might vary with the pressure
arising from …nancial markets conditions. In this case,
CV
t
where
CV
0
=
CV
0
+
CV
1
is a …xed threshold and
f inpressuret ;
CV
1
(13)
is the state-varying component of
the threshold and the variable f inpressure is a composite measure of …nancial
turmoil/crisis (which draws heavily on Reinhart and Rogo¤, 2009), meant to
capture the pressure on …scal policy authorities arising from unfavorable market
conditions. This is a world …nancial crisis measure which takes into account
16
banking, currency, stock market, debt, and in‡ation incidences in the world.
For a given country in a given year, the index is bounded between zero and
…ve, emerging as the sum of the number of types of incidences the country
experienced. Therefore, the index takes the value of 0 if the country did not
experience any of the …ve incidences above and the value of 5 if it did experience
all …ve incidences. The index (plotted in Figure 5) pools together world’s 16
largest economies with country speci…c weights given by their relative GDP
share of the total GDP (based on Purchasing Power Parity)
In equation (13), a negative
CV
1
11 12
.
suggests that policymakers, possibly driven
by the fear of a deep and lasting recession in periods of …nancial pressure, might
be more willing to relax the threshold triggering a de…cit correction. On the
other hand, a positive estimate of
CV
1
signals that …nancial pressure strength-
ens the incentives for budgetary correction, possibly driven by the increasing
di¢ culties in marketing debt instruments.
We start by reporting in column (i) of Tables 2-5 linear tax revenues error
correction models for the GIPS. We also report, at the bottom of each Table,
the p-value of Hamilton’s (2001) -test, and the bootstrapped p-value (based on
1000 resamples) of the
A
and g-tests proposed by Dahl and González-Rivera
(2003). Under the null hypothesis of linearity, these are Lagrange Multiplier test
statistics following the
2
distribution. These tests are powerful in detecting
nonlinear regime-switching behavior like the one considered in our model. For all
countries, all three tests reject linearity, strengthening our argument in favour of
1 1 Chapter
16 of Reinhart and Rogo¤ (2009) describes the country speci…c indices in more detail; these are also available from the website of Carmen Reinhart
(http://www.carmenreinhart.com/data/). Country speci…c weights given by their relative
GDP share of the total GDP have been calculated for Argentina, Australia, Brazil, Canada,
China, France, Germany, India, Indonesia, Italy, Japan, Mexico, Russia, Turkey, UK and US.
1 2 To proxy …nancial market pressure, we also used the (i) spread between the 10-year yield
on each one of the GIPS and the 10-year yield on German bonds, and (ii) a 2 (and 3)-year
moving standard deviation of the spread but failed to …nd any signi…cant e¤ect.
17
non-linear modelling of …scal adjustments. We also report the Quandt-Andrews
breakpoint test for parameter stability (to run the test for the non-linear models,
we …x the threshold and
parameters to their estimated values); this test
suggests reasonable parameter stability for all estimated models.
We now turn our attention to the non-linear models. Column (ii) of Tables 25 reports the non-linear models (11)-(12) using CVt
1
as the transition variable.
Before turning our attention to country-speci…c results, we note (in column (ii)
of Tables 2-5) a common characteristic shared by all GIPS: …scal disequilibria are
corrected even when these are "low" (in which case there is arguably less pressure
for the GIPS to do so). However, as noted above, the estimated thresholds do
not have an economic interpretation in terms of a budget de…cit or surplus
13
.
We start our discussion with reference to Greece (see Table 2 (ii)). We apply the
threshold adjustment
CV
(1
G
) GDP
discussed above with
CV
= 5:093%,
= 0:72 and the sample average of 35.7% for the G/GDP ratio. Given this
information, we recover, in terms of a budget balance-to-GDP ratio, a threshold
estimate of -4.90%; using instead the 38.1% sample median of the G/GDP ratio,
we recover a threshold estimate of -5.58% (or, in terms of a de…cit, thresholds of
4.90% and 5.58%, respectively; we will follow the de…cit terminology for the rest
of the paper). We report strong correction adjustment when the de…cit exceeds
4.90% of national GDP, whilst corrective action is twice as slow when the de…cit
drops below the threshold. Notice also that only in the high de…cit regime, taxes
respond negatively to the output gap, suggesting some …scal irresponsibility in
the conduct of …scal policy, as the average tax rate decreases following above
1 3 For all countries, the unadjusted CV thresholds reported in Tables 2-5 are reasonably
close to the sample average (median) of the corresponding CV series. CV has a mean of 4.7
(median: 5.0) for Greece; a mean of 6.6 (median: 6.2) for Ireland; a mean of 2.9 (median: 3.4)
for Portugal and a mean of 4.1 (median: 4.3) for Spain.
18
trend growth.
Next, we turn to Ireland (see Table 3(ii)). Using
CV
= 6:254%,
= 0:71
and the sample average of 39.1% for the G/GDP ratio, we recover, in terms
of a de…cit, a threshold estimate of 5.10% (using instead the 40.4% sample
median of the G/GDP ratio, we recover a threshold estimate of 5.46%). In
sharp contrast to Greece, corrective action is statistically insigni…cant when
the de…cit exceeds 5.10% of GDP (the t-ratio on CVt
1
is "only" -1.20). On
the other hand, corrective action is statistically signi…cant when the de…cit
drops below 5.10% of GDP; we return to this issue below. The output gap is
insigni…cant in both regimes. Next, we turn to Portugal (see Table 4(ii)). Using
CV
= 3:564%,
= 0:80 and the sample average of 33.9% for the G/GDP ratio,
we recover, in terms of a de…cit, a threshold estimate of 3.22% (using instead
the 36.8% sample median of the G/GDP ratio, we recover a threshold estimate
of 3.80%). In line with Ireland, corrective action is statistically insigni…cant
when the de…cit exceeds 3.22% of GDP (the t-ratio on CVt
1
is "only" -1.15).
When the de…cit exceeds 3.22% of GDP, an improvement of economic conditions
(through an increase in the output gap) supports tax revenues (although the
impact is statistically weak). Using, for Spain (see Table 5(ii)),
CV
= 4:237%,
= 0:80 and the sample average of 36.8% for the G/GDP ratio, we recover,
in terms of a de…cit, a threshold estimate of 3.12% (using instead the 39.1%
sample median of the G/GDP ratio we recover a threshold estimate of 3.59%).
As in the case of Greece, corrective action is stronger when the de…cit exceeds
the estimated threshold; in this regime, the output gap exerts a positive (but
statistically weak) e¤ect.
Overall, the non-linear model allowing for the deviations from …scal equilibria as possible transition variable provides evidence of threshold behavior
19
in the conduct of …scal policy by Greece and Spain, in line with the theoretical predictions derived from political economy models. We also note that the
4.90% threshold for Greece is rather high, compared with the European Stability and Growth Pact (ESGP) criteria. Notice, however, that we do not …nd a
statistically signi…cant evidence that Ireland and Portugal correct …scal imbalances when their de…cits exceed the estimated thresholds. This …nding appears
counter-intuitive and calls for further investigation. A possible reason might be
that the non-linear model reported in column (ii) is inadequate in capturing the
…scal implications of the impact of a time-varying component in the threshold;
we return to this issue shortly.
Column (iii) of Tables 2-5 reports the non-linear models (11)-(12) using
the output gap as possible transition variable. The near zero estimates of the
threshold parameter suggest regime-switching with respect to positive versus
negative deviations from trend output. For Greece, the response of the average tax ratio to the output gap is statistically insigni…cant both during "good"
times (characterized by the regime where the output gap is positive) and "bad"
times (characterized by the regime where the output gap is negative). During "good" times, the error correction adjustment is slower than during "bad"
times. Also for Ireland, correction is stronger in "bad" as opposed to "good"
times. There is also some statistically weak evidence that the impact of the
output gap is positive during "bad" times. For Portugal, we provide evidence
of strong correction during both "good" and "bad" times, whilst the output
gap is statistically insigni…cant in both regimes. For Spain, correction occurs
only during "good" times and, in this regime, taxes respond positively to the
economic cycle. Overall the non-linear model using the output gap as transition
variable uncovers further interesting features of the …scal policies pursued by the
20
GIPS. The average tax rate for Greece and Portugal does not respond to the
economic cycle, whilst it responds positively to the cycle in Ireland during "bad"
times (notice, however, the weak evidence in statistical terms) and positively
in Spain during "good" times. These results suggest some degree of irresponsibility of …scal policy authorities in the GIPS. In "good" times, Greece, Ireland
and Portugal fail to exploit the improvement in economic activity to conduct
stronger adjustments. Consequently, tax adjustments are strengthened during
"bad" times, in an attempt to restore …scal discipline.
Column (iv) of Tables 2-5 reports the non-linear models (11)-(12) using
CVt
1
as the transition variable and introducing a time-varying threshold given
by equation (13). For Greece (see Table 2(iv)),
CV
1
is statistically insigni…cant.
For Ireland (see Table 3(iv)), we …nd a statistically negative
6:300%,
CV
1
=
2:748;
CV
1
. Given
CV
0
=
= 0:71, the sample average of 39.1% for the G/GDP
ratio and the sample average of 0.712 for …npressure t , we recover, in terms
of a de…cit, a threshold estimate of 6.99%14 . Hence, this model suggests that
during a …nancial crisis the Irish de…cit threshold is relaxed from 5.10% (implied
by Table 3(ii)) to 6.99%. Notice, however, that this model (which outperforms
the model in Table 3(ii)) provides some evidence of …scal correction when the
de…cit exceeds 6.99% of GDP. Indeed, the -0.210 point estimate on CVt
1
above
the 6.99% threshold suggests stronger adjustment than the -0.137 estimate on
CVt
1
below the 6.99% threshold; however, the t-ratio of -1.60 on the former
provides weak statistical evidence for this …nding. In the case of Portugal we
…nd a statistically positive
CV
0
= 3:500% and
CV
1
CV
1
. In particular (see Table 4(iv)), we estimate
= 1:911. Given
= 0:80, the sample average of
1 4 Notice that the 6.99% threshold estimate appears to be well-de…ned. Although it exceeds
the average of 5.12% for the Irish de…cit-to-GDP ratio over the sample period considered, 35%
of the sample values of the de…cit-to-GDP ratio exceed the 6.99% threshold.
21
33.9% for the G/GDP ratio and the sample average of 0.712 for …npressure t ,
we recover, in terms of a de…cit, a threshold estimate of 1.92%. Hence, this
model suggests that during a …nancial crisis the Portuguese de…cit threshold is
reduced from 3.22% (implied by Table 4(ii)) to 1.92%. Notice also that this
model, in contrast to the model in column (ii), identi…es statistically signi…cant
corrective action when the de…cit exceeds the 1.92% threshold. As in the case of
Ireland, we …nd a statistically negative
CV
0
= 4:511%,
CV
1
=
1:616;
CV
1
for Spain (see Table 5(iv)). Given
= 0:80, the sample average of 36.8% for the
G/GDP ratio and the sample average of 0.712 for …npressure t , we recover, in
terms of a de…cit, a threshold estimate of 4.00%. Hence, during a …nancial crisis,
the threshold estimate is relaxed from 3.12% (implied by Table 5(ii)) to 4.00%.
Overall, the introduction of the time-varying threshold is favored for Ireland,
Portugal and Spain; indeed, the model in column (iv) delivers a lower standard
error and a higher adjusted R2 . Financial market pressure relaxes the de…cit-toGDP threshold for adjustment in Ireland and Spain and reduces the threshold
for Portugal. Notice that also that for both Ireland and Spain (see Table 3(iv)
and Table 5(iv), the output gap e¤ect in the high de…cit regime is positive; for
Spain it is also much more statistically signi…cant. Therefore, by relaxing the
de…cit threshold (in an attempt to stave o¤ deep recessionary pressures) Ireland
and Spain rely on business cycle improvements to push up tax revenues (this is
not the case for Portugal where …nancial pressure reduces the threshold). Notice
also that this model reverses to some extent the counter-intuitive results of the
model in column (ii) for Portugal and Ireland as it shows signi…cant error correction for Portugal (when the de…cit exceeds 1.92% of GDP) and some weak
correction for Ireland (when the de…cit exceeds 6.99% of GDP). Amongst all
estimated models, the model in column (ii) delivers the best …t for Greece. The
22
model with the time-varying threshold component in column (iv) delivers the
best …t for Spain and Portugal, respectively. For Ireland, the model in Table
3(iii) which distinguishes between di¤erent phases of the economic cycle delivers
the best …t. All in all, our empirical results o¤er support to the earlier discussion of the long-run analysis in the sense that regime-switching with respect to
a "large" de…cit threshold corroborates the concerns about sustainability of the
public …nances largely for Greece and Ireland. To sum up, not only Ireland’s
de…cit threshold is "large", it also increases further as …nancial market conditions deteriorate. Greece’s threshold is also "large" but remains insensitive
to …nancial market conditions. Contrast this with Portugal and Spain both of
which have de…cit thresholds close to the 3% threshold dictated by the ESGP.
Deteriorating …nancial market conditions increase (on average) the threshold for
Spain from 3.12% to 4.00% and reduce the threshold for Portugal from 3.22%
to 1.92%. Both the 4.00% threshold for Spain and the 1.92% threshold for Portugal remain within one percentage point away from the 3% ESGP threshold
which arguably makes sustainability concerns for these countries less of an issue
compared to Ireland or Greece.
4.2
Government Outlays Models
Non-linear models were also considered for the adjustment of general government expenditure. Results, not reported for space considerations (but available
on request) are summarized as follows.
For all GIPS, own lags have a signi…cant and positive e¤ect on current spending, pointing to self-perpetuating spending growth dynamics. Budgetary disequilibria, on the other hand, are insigni…cant in explaining government spending
dynamics, as evidenced by the statistical insigni…cance of CVt
23
1.
Output gap
has a positive e¤ect for all countries; this points to a procyclical use of government spending. In statistical terms, the evidence is stronger for Greece (the
t-ratio on output gap is equal to 2.14) and much weaker for the remaining
GIPS (the t-ratio on output gap is equal to 1.30 for Spain, 1.20 for Portugal
and 1.10 for Ireland). We fail to …nd evidence of non-linear e¤ects in any of the
GIPS. These results further corroborate our earlier …nding of weak exogeneity
of government spending in the GIPS, as budgetary imbalances are corrected via
the tax instrument, and government spending is mainly determined by its past
history.
5
Conclusions and Directions for further Research
We consider the …scal policies of the GIPS, the four euro peripheral countries
which are supported …nancially by the so called "Troika" (that is, the European Commission, the European Central Bank and the International Monetary
Fund) in the aftermath of the …nancial crisis. Through formal IBC sustainability testing, we fail to identify robust evidence of a long-run relationship between
government outlays and …scal revenues. This is mainly an issue for Greece and
Ireland and casts some doubts on the e¤ectiveness of the monitoring mechanism currently in place by the European Commission. Further, we show that
…scal adjustment takes place using the tax instrument alone, with government
spending being weakly exogenous for all GIPS15 .
Allowing for non-linear corrections of …scal disequilibria, we provide evidence
of threshold behavior for the …scal authorities in the GIPS. Our endogenously
estimated thresholds for correction identify, for Greece and Ireland, a de…cit-to1 5 Legrenzi and Milas (2012) report weak exogeneity of G /GDP for Italy, which, together
with the countries considered in the current paper, form the GIIPS. Their work provides
evidence of non-linear …scal adjustment by considering square and cubic terms of the Italian
budget de…cit.
24
GDP ratio threshold well above the 3% ratio implied by the ESGP. Incidences of
…nancial crises have an impact on the estimated …scal threshold; this increases
for Ireland and Spain and becomes smaller for Portugal. By relaxing the de…cit
threshold (in an attempt to stave o¤ deep recessionary pressures) Ireland and
Spain rely on business cycle improvements to push up tax revenues.
Whilst, in principle, a threshold adjustment of the …scal variables would
point to non-explosive debt dynamics and therefore to a sustainable path of
…scal policy, …nancial markets have a point in questioning the credibility of such
policies. That is to say, in the presence of large debt/de…cits, …nancial markets
require high interest premia on government bonds, rendering more problematic
the servicing of the existing stock of debt; indeed, over the past three years, the
GIPS have faced high interest rate premia and have su¤ered successive sovereign
downgrades.
Looking at the e¤ects of the economic cycle, we show evidence of some
degree of …scal irresponsibility. Indeed, we …nd that …scal policy authorities in
Greece, Ireland and Portugal fail, in "good" times to exploit the improvement
in economic activity to raise their tax revenues. Consequently, during "bad"
times, corrections become more costly as tax adjustment becomes a priority in
an attempt to restore …scal discipline. For all GIPS, we document a procyclical
government spending. Announced policies in the GIPS to reduce government
spending seem, consequently, to be a step in the right direction, provided they
do not pose a risk to future growth prospects.
A full assessment of …scal policies during "good" and "bad" times, in conjunction with the e¤ects of political cycles should provide an interesting extension of this research. Further, the possibility of a "twin de…cit" and its consequences for the …scal policies in the GIPS has not been explicitly considered in
25
our analysis. We intend to address this important issue in future research.
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Table 1A: Johansen’s (1988, 1995) cointegration λ-trace and λ-max test statistics
Cointegrating λ-trace test
λ-max test
α on TAX/GDP (S.E.)
α on G/GDP (S.E.)
vector
(1,-β)’
Greece
(1, -0.72)’
14.29
12.87
-0.24 (0.07)
-0.19 (0.13)
Ireland
(1, -0.71)’
14.88
10.13
-0.11 (0.05)
0.19 (0.15)
Portugal
(1, -0.80)’
15.41
14.11
-0.19 (0.08)
0.06 (0.11)
Spain
(1, -0.80)’
16.65
9.71
-0.15 (0.08)
0.18 (0.10)
Notes: For each country we report the estimated cointegrating vector normalized on TAX/GDP and the
estimated λ-max and λ-trace statistics for the null hypothesis of zero cointegrating vectors. For each
country we also report the estimated adjustment coefficients α on TAX/GDP and G/GDP, respectively
(with standard errors in brackets).
MacKinnon et al (1999) 10% critical value for the λ-trace test: 13.42. MacKinnon et al (1999) 5% critical
value for the λ-trace test: 15.49.
MacKinnon et al (1999) 10% critical value for the λ-max test: 12.29. MacKinnon et al (1999) 5% critical
value for the λ-max test: 14.26.
Sample: 1960-2013 for Greece, Ireland and Portugal. Sample: 1970-2013 for Spain.
Table 1B: Phillips and Ouliaris (1990) residual based cointegration test
β
Z(t) test
Greece
0.68
-8.49
Ireland
0.50
-8.39
Portugal
0.76
-16.50
Spain
0.72
-10.50
Notes: For each country, the estimated marginal response β is based on the long-run regression of
TAX/GDP on a constant and G/GDP. We then regress the residuals of the long-run regression on their own
lag and calculate the Z(t) statistic which tests the null hypothesis that the coefficient on the lagged
residuals is equal to one. The test is equivalent to testing the null hypothesis of no cointegration. The Z(t)
test statistic is corrected for heteroscedasticity and autocorrelation using the Newey-West (1987)
estimator. We apply a lag truncation parameter of one (results are robust to alternative lag truncation
choices). The critical values for Z(t) are reported by Hamilton (1994) in Table B.9 (page 766): 10% critical
value=-3.07; 5% critical value=-3.37.
Sample: 1960-2013 for Greece, Ireland and Portugal. Sample: 1970-2013 for Spain.
31
Table 2: GREECE-OLS estimates of alternative error correction models for (TAX/GDP)
(i)
(ii)
(iii)
Linear model
Constant
CV t-1
gap t-1
(G/GDP) t-1
1.259 (4.08)
-0.186 (-3.27)
-0.029 (-0.41)
-0.120 (-1.10)
CV t-1
gap t-1
CV t-1
gap t-1
Logistic model
Logistic model
st 1  CVt 1
st 1  gapt 1
st 1  CVt 1
1.701 (4.80)
1.298 (3.37)
1.709 (4.46)
-0.131 (-1.13)
-0.125 (-1.11)
-0.112 (-1.13)
CVt-1 < 
Regime
gapt-1 < 
Regime
CVt-1 <  t
CV
gap
-0.486 (-3.18)
-0.223 (-2.12)
-0.242 (-2.63)
-0.076 (-0.87)
CVt-1 > 
Regime
gapt-1 > 
Regime
CV
-0.230 (-3.92)
0.037 (0.54)
5.093 (11.67)
 CV
 CV
(iv)
Logistic model
gap
-0.164 (-2.56)
-0.063 (-0.41)
10.00 (-)*
CV
Regime
-0.502 (-2.44)
-0.217 (-1.55)
CVt-1 >  t
Regime
-0.215 (-3.39)
0.026 (0.31)
CV
4.00 (-)*
-0.069 (-0.11)
 gap
 gap
20.30 (-)*
 0CV
5.200 (11.00)
 1CV
-0.981 (-0.86)
Diagnostics
Regression s.e.
R
2
Far (p-value)
Farch (p-value)
QA break (p-value)
2nd (p-value)
λ-test (p-value)
λA-test (p-value)
g-test (p-value)
1.10
0.16
1.02
0.21
1.08
0.13
1.05
0.17
0.87
0.68
0.30
0.95
0.01
0.00
0.01
0.88
0.63
0.20
0.84
0.83
0.66
0.20
0.90
0.87
0.62
0.50
0.83
R 2 is the adjusted coefficient of determination.
van Dijk et al. (2002) argue that the likelihood function is very insensitive to 
Notes: t-ratios in parentheses.
*Imposed value.
, suggesting that
precise estimation of this parameter is unlikely. For this reason, we run a grid search in the
range [0.1, 250] and fix the  parameter to the one that delivers the best fit of the estimated
models. Far is the Lagrange Multiplier F-test for 2nd order serial correlation. Farch is the 1st order
ARCH F-test. 2nd is a Chi-square test for normality. QA break is the p-value of the QuandtAndrews breakpoint test. We report the p-value of the maximum LR F-statistic using 15%
observation trimming, calculated using Hansen’s (1997) method. Sample: 1965-2013.
32
Table 3: IRELAND-OLS estimates of alternative error correction models for (TAX/GDP)
(i)
(ii)
(iii)
(iv)
Linear model
Constant
CV t-1
gap t-1
(G/GDP) t-1
0.893 (2.09)
-0.119 (-2.23)
0.036 (0.34)
-0.032 (-0.58)
CV t-1
gap t-1
Logistic model
Logistic model
Logistic model
st 1  CVt 1
st 1  gapt 1
st 1  CVt 1
1.070 (2.59)
1.547 (3.36)
1.174 (3.13)
-0.033 (-0.59)
-0.034 (-0.49)
-0.035 (-0.49)
CVt-1 < 
Regime
gapt-1 < 
Regime
CVt-1 <  t
CV
gap
-0.120 (-1.20)
0.113 (0.93)
-0.149 (-2.67)
0.265 (1.64)
CVt-1 > 
Regime
gapt-1 > 
Regime
CV
CV t-1
gap t-1
-0.132 (-2.67)
0.010 (0.05)
 CV
 CV
6.254 (3.94)
gap
-0.119 (-1.79)
-0.253 (-1.15)
11.10 (-)*
CV
Regime
-0.210 (-1.60)
0.310 (1.70)
CVt-1 >  t
Regime
-0.137 (-2.86)
-0.050 (-0.43)
CV
10.90 (-)*
-0.432 (-0.64)
 gap
 gap
25.38 (-)*
 0CV
6.300 (4.10)
 1CV
-2.748 (-2.03)
Diagnostics
Regression s.e.
R
2
Far (p-value)
Farch (p-value)
2nd (p-value)
QA break (p-value)
λ-test (p-value)
λA-test (p-value)
g-test (p-value)
1.45
0.14
1.41
0.15
1.35
0.20
1.38
0.17
0.11
0.68
0.15
0.25
0.01
0.02
0.01
0.18
0.28
0.49
0.20
0.40
0.77
0.29
0.20
0.19
0.30
0.50
0.19
R 2 is the adjusted coefficient of determination.
van Dijk et al. (2002) argue that the likelihood function is very insensitive to 
Notes: t-ratios in parentheses.
*Imposed value.
, suggesting that
precise estimation of this parameter is unlikely. For this reason, we run a grid search in the
range [0.1, 250] and fix the  parameter to the one that delivers the best fit of the estimated
models. Far is the Lagrange Multiplier F-test for 2nd order serial correlation. Farch is the 1st order
ARCH F-test. 2nd is a Chi-square test for normality. QA break is the p-value of the Quandt-Andrews
breakpoint test. We report the p-value of the maximum LR F-statistic using 15% observation
trimming, calculated using Hansen’s (1997) method. Sample: 1965-2013.
33
Table 4: PORTUGAL-OLS estimates of alternative error correction models for
(TAX/GDP)
(i)
(ii)
(iii)
Linear model
Constant
CV t-1
gap t-1
(G/GDP) t-1
1.895 (3.14)
-0.249 (-3.68)
0.070 (1.14)
0.215 (1.83)
Logistic model
Logistic model
st 1  CVt 1
st 1  gapt 1
st 1  CVt 1
1.626 (2.75)
1.788 (2.83)
1.484 (4.25)
0.204 (1.84)
0.209 (1.86)
0.205 (1.84)
CVt-1 < 
Regime
CV t-1
gap t-1
(iv)
Logistic model
CV
gapt-1 < 
Regime
gap
-0.241 (-1.15)
0.141 (1.65)
-0.338 (-3.06)
0.015 (0.17)
CVt-1 > 
Regime
gapt-1 > 
Regime
CV
CV t-1
gap t-1
-0.341 (-3.98)
-0.027 (-0.32)
 CV
 CV
3.564 (15.30)
gap
-0.305 (-2.55)
0.111 (0.73)
40.00 (-)*
CVt-1 <  t
CV
Regime
-0.321 (-2.71)
0.070 (1.07)
CVt-1 >  t
Regime
-0.411 (-3.73)
-0.169 (-1.18)
CV
15.00 (-)*
-0.408 (-0.77)
 gap
 gap
35.00 (-)*
 0CV
3.500 (12.80)
 1CV
1.911 (5.45)
Diagnostics
Regression s.e.
R
2
Far (p-value)
Farch (p-value)
2nd (p-value)
QA break (p-value)
λ-test (p-value)
λA-test (p-value)
g-test (p-value)
1.24
0.17
1.22
0.20
1.23
0.18
1.21
0.21
0.49
0.02
0.82
0.10
0.01
0.00
0.01
0.58
0.12
0.90
0.10
0.50
0.10
0.84
0.12
0.56
0.11
0.88
0.11
R 2 is the adjusted coefficient of determination.
van Dijk et al. (2002) argue that the likelihood function is very insensitive to 
Notes: t-ratios in parentheses.
*Imposed value.
, suggesting that
precise estimation of this parameter is unlikely. For this reason, we run a grid search in the
range [0.1, 250] and fix the  parameter to the one that delivers the best fit of the estimated
models. Far is the Lagrange Multiplier F-test for 2nd order serial correlation. Farch is the 1st order
ARCH F-test. 2nd is a Chi-square test for normality. QA break is the p-value of the QuandtAndrews breakpoint test. We report the p-value of the maximum LR F-statistic using 15%
observation trimming, calculated using Hansen’s (1997) method. Sample: 1965-2013.
34
Table 5: SPAIN-OLS estimates of alternative error correction models for (TAX/GDP)
(i)
(ii)
(iii)
Linear model
Constant
CV t-1
gap t-1
(G/GDP) t-1
1.214 (2.75)
-0.198 (-2.15)
0.134 (1.46)
0.030 (0.23)
CV t-1
gap t-1
(iv)
Logistic model
Logistic model
Logistic model
st 1  CVt 1
st 1  gapt 1
st 1  CVt 1
1.838 (2.40)
2.224 (4.55)
2.944 (5.01)
0.020 (0.13)
0.021 (0.23)
0.029 (0.15)
CVt-1 < 
Regime
gapt-1 < 
Regime
CV
gap
-0.358 (-2.10)
0.312 (1.57)
-0.074 (-0.92)
0.036 (0.32)
CVt-1 > 
Regime
gapt-1 > 
Regime
CV
CV t-1
gap t-1
-0.250 (-2.31)
-0.016 (-0.11)
 CV
 CV
4.237 (19.54)
gap
-0.160 (-2.61)
0.341 (2.10)
30.00 (-)*
CVt-1 <  t
CV
Regime
-0.311 (-2.28)
0.315 (2.14)
CVt-1 >  t
Regime
-0.291 (-3.49)
0.070 (0.76)
CV
54.00 (-)*
-0.181 (-0.55)
 gap
 gap
40.23 (-)*
 0CV
4.511 (11.50)
 1CV
-1.616 (-6.35)
Diagnostics
Regression s.e.
R
2
Far (p-value)
Farch (p-value)
2nd (p-value)
QA break (p-value)
λ-test (p-value)
λA-test (p-value)
g-test (p-value)
0.95
0.27
0.93
0.31
0.95
0.27
0.90
0.35
0.07
0.91
0.05
0.15
0.01
0.00
0.00
0.86
0.92
0.74
0.14
0.86
0.92
0.60
0.10
0.87
0.93
0.61
0.12
R 2 is the adjusted coefficient of determination.
van Dijk et al. (2002) argue that the likelihood function is very insensitive to 
Notes: t-ratios in parentheses.
*Imposed value.
, suggesting that
precise estimation of this parameter is unlikely. For this reason, we run a grid search in the
range [0.1, 250] and fix the  parameter to the one that delivers the best fit of the estimated
models. Far is the Lagrange Multiplier F-test for 2nd order serial correlation. Farch is the 1st order
ARCH F-test. 2nd is a Chi-square test for normality. QA break is the p-value of the QuandtAndrews breakpoint test. We report the p-value of the maximum LR F-statistic using 15%
observation trimming, calculated using Hansen’s (1997) method. Sample: 1970-2013.
35
Figure 1: TAX/GDP and G/GDP series for the GIPS, 1960-2013
56
70
52
48
60
44
40
50
36
32
40
28
24
30
20
16
20
60
65
70
75
80
85
G/GDP (Greece)
90
95
00
05
10
60
65
70
75
80
TAX/GDP (Greece)
85
90
95
00
05
10
00
05
10
G/GDP (Ireland)
TAX/GDP (Ireland)
52
48
48
44
44
40
40
36
36
32
32
28
24
28
20
24
16
12
20
60
65
70
75
80
85
90
95
00
05
10
60
TAX/GDP (Portugal)
G/GDP (Portugal)
65
70
75
80
85
G/GDP (Spain)
36
90
95
TAX/GDP (Spain)
Figure 2: Recursively estimated λ-max and λ-trace statistics divided by their 5%
critical value, 1985-2013
1.6
1.1
1.0
1.4
0.9
0.8
1.2
0.7
1.0
0.6
0.5
0.8
0.4
0.6
0.3
86
88
90
92
94
96
98
00
02
04
06
08
10
12
86
88
90
92
94
96
Trace-test (Greece)
Max-test (Greece)
98
00
02
04
06
08
10
12
04
06
08
10
12
Max-test (Ireland)
Trace-test (Ireland)
1.3
1.8
1.2
1.6
1.1
1.4
1.0
1.2
0.9
1.0
0.8
0.8
0.7
0.6
0.6
0.4
0.5
0.4
0.2
86
88
90
92
94
96
98
00
02
04
06
08
10
12
86
Trace-test (Portugal)
Max-test (Portugal)
88
90
92
94
96
98
00
02
Trace-test (Spain)
Max-test (Spain)
37
Figure 3: Recursive betas +/-2*S.E., 1985-2013
2.0
1.4
1.2
1.6
1.0
1.2
0.8
0.8
0.6
0.4
0.4
0.0
0.2
86
88
90
92
94
96
98
00
02
04
06
08
10
12
86
88
90
Recursively estimated beta+/-2*S.E. (Greece)
92
94
96
98
00
02
04
06
08
10
12
10
12
Recursively estimated beta+/-2*S.E. (Ireland)
1.1
1.1
1.0
1.0
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
86
88
90
92
94
96
98
00
02
04
06
08
10
12
86
Recursively estimated beta+/-2*S.E. (Portugal)
88
90
92
94
96
98
00
02
04
06
08
Recursively estimated beta+/-2*S.E. (Spain)
38
Figure 4: Output gaps for the GIPS
8
4
0
-4
-8
-12
-16
1965
1970
1975
1980
1985
1990
1995
2000
2005
00
05
2010
Output gap (Greece)
Output gap (Spain)
Output gap (Ireland)
Output gap (Portugal)
Figure 5: Financial pressure
2.0
1.6
1.2
0.8
0.4
0.0
60
65
70
75
80
85
90
95
Financial pressure
39
10