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CESifo, a Munich-based, globe-spanning economic research and policy advice institution 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. 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In Ben Bernanke and Julio Rotemberg, eds., NBER Macroeconomics Annual 1998. Cambridge, MA: MIT Press, 390–418. 30 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