Cost of Borrowing Shocks and Fiscal Adjustment

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Cost of Borrowing Shocks and Fiscal Adjustment Oliver de Groot, Fdric Holm-Hadulla, and Nadine Leiner-Killinger 2013-59 NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Cost of borrowing shocks and (cid:133)scal adjustment (cid:3) Oliver de Groot FØdØric Holm-Hadulla Nadine Leiner-Killinger Federal Reserve Board European Central Bank European Central Bank July 30, 2013 Abstract Docapitalmarketsimpose(cid:133)scaldisciplineongovernments? Weinvestigatetheresponses of (cid:133)scal variables to a change in the interest rate paid by governments on their debt in a panel of 14 European countries over four decades. To this end, we estimate a panel vector autoregressive (PVAR) model, using sign restrictions via the penalty function method of Mountford and Uhlig (2009) to identify structural cost of borrowing shocks. Our baseline estimation shows that a 1 percentage point rise in the cost of borrowing leads to a cumulativeimprovementoftheprimarybalance-to-GDPratioofapproximately2percentagepoints over10years,withthe(cid:133)scalresponsebecomingsigni(cid:133)cantlyevidentonlytwoyearsafterthe shock. We also (cid:133)nd that the bulk of (cid:133)scal adjustment takes place via a rise in government revenue rather than a cut in primary expenditure. The size of the total (cid:133)scal adjustment, however, is insu¢ cient to avoid the gross government debt-to-GDP ratio from rising as a consequence of the shock. Sub-dividing our sample, we also (cid:133)nd that for countries participating in Economic and Monetary Union (EMU) the primary balance response to a cost of borrowing shock was stronger in the period after 1992 (the year in which the Maastricht Treaty was signed) than prior to 1992. Keywords: Fiscal policy, Long-term interest rates, VARs, Sign restrictions JEL classi(cid:133)cations: C33, E43, E62, H60 (cid:3)We would like to thank A. Afonso, K.Bankowski, G.Callegari, J. Cimadomo, C. Giannitsarou, E. de Groot, W. Lemke, J.Roberts, M.Slavik, M. Trabandt, A.Tudyka, participants at a joint LSE and BoE macroeconomic workshop,atanECBseminarandattheRESannualconferenceforhelpfuldiscussionsandsuggestionsduringthe writing of this paper. Oliver would particularly like to thank the hospitality of the Fiscal Policy Division of the EuropeanCentralBankduringhisvisit. ThedatasetaswellasMatLabandRATScodetoreproducethe(cid:133)gures andtablesinthispaperareavailableathttp://sites.google.com/site/oliverdegroot/research. Correspondencevia oliver.v.degroot@frb.gov. Disclaimer: Theviewsexpressedaresolelythoseoftheauthorsanddonotnecessarily re(cid:135)ect those of the Federal Reserve Board or the European Central Bank.

... The [Irish] Government has today decided that an overall [(cid:133)scal] adjustment of e15 billion over the next four years is warranted ... The key reasons for the significant increase from the (cid:133)gure announced in Budget 2010 are lower growth prospects ... and higher debt interest costs. (Statement by the Irish Government, 26 October 2010).1 1 Introduction During the European sovereign debt crisis, sharp rises in yields on government bonds have been met with promises from governments to accelerate and expand their (cid:133)scal consolidation plans. Totheextentthepromisesareactedupon,thisbehaviourcanbeinterpretedasaformofmarketimposed (cid:133)scal discipline. Against this background, we examine empirically, over a long time series and across several European Union (EU) countries, the proposition that governments systematically respond to adverse shocks in their market borrowing rates by improving their (cid:133)scal positions. This question is relevant for two reasons. First, by providing estimates of past patterns in the response of EU governments to changes in their cost of borrowing, the current analysis can informviewsonhowthemedium-term(cid:133)scalstanceislikelytoevolve,insituationsinwhichthere is a re-pricing of government debt. Second, the paper provides a new perspective on the extent towhichitmaybeappropriatetorelyon(cid:133)nancialmarketstoreinforce(cid:133)scaladjustment. Tothe extent that markets provide discipline, it may be less important to establish formal rules, such as those recently adapted in the Stability and Growth Pact.2 The empirical analysis presented here may contribute to such an assessment by providing evidence on a critical link in the way (cid:133)nancial markets can provide (cid:133)scal discipline(cid:151)namely, whether market-induced changes in the cost of borrowing later a⁄ect the (cid:133)scal stance. In doing so, the paper addresses an issue that, to date, has received little attention in academic research. As pointed out by Bayoumi, Goldstein, and Woglom (1995), analyses of whether (cid:133)scal authorities are subject to market discipline should address two questions. First, do markets adjust the terms at which they lend to governments when (cid:133)scal positions change? Second, do governments adjust their (cid:133)scal positions when their cost of borrowing changes? A great deal of research has investigated the (cid:133)rst question in isolation.3 However, the hypothesis of market-induced (cid:133)scal discipline implies simultaneous responses of government bond market prices and (cid:133)scal policies, thus suggesting that the price and quantity of public debt are jointly determined. Yet, the causation from the cost of public debt service to (cid:133)scal policy decisions has received little attention in the empirical literature.4 This paper aims to bring some balance to the joint determination of (cid:133)scal variables and long-term interest rates by empirically assessing the response of (cid:133)scal policy to exogenous interest rate changes in a dynamic context. To motivate our empirical analysis, we present a simple model, in which the government of a small open economy optimally commits to a state-contingent path of government spending, labour taxes, and debt. The government is able to issue debt on capital markets, paying the world interest rate plus a risk premium. In this set up, an exogenous rise in the risk premium demandedbyinternationalinvestorsforholdingthisdebtgeneratesatighteningofthebudgetary 1http://www.(cid:133)nance.gov.ie/viewdoc.asp?DocID=6552&CatID=1&StartDate=01+January+2010 2For a discussion see, for example, Schuknecht, Moutot, Rother, and Stark (2011). 3Since the work of Evans (1985), there has been a large empirical literature on the e⁄ect of (cid:133)scal policy on long-term interest rates. Some of the more recent studies include Faini (2006), Ardagna, Caselli, and Lane (2007), Attinasi, Checherita, and Nickel (2009), Laubach (2009), Schuknecht, Von Hagen, and Wolswijk (2009) and Afonso and Rault (2011). 4The exception is Theo(cid:133)lakou and Stournaras (2012). They estimate a (cid:133)scal rule for a panel of European countries, and (cid:133)nd evidence in favour of including government bond yields in governments(cid:146)reaction functions. Their methodological approach is quite di⁄erent to that used here, as they estimate a single equation model. 1

path. However, the optimal speed and composition for budget tightening is dependent on the structural features of the economy. These model based simulations are then confronted with empirical estimates of the response of(cid:133)scalvariablestochangesinlong-terminterestrates. Tothisend, weuseavectorautoregressive(VAR)modelforapanelof14Europeancountriesandannualdatafrom1970to2011. The empirical analysis faces two important methodological challenges. First, because (cid:133)scal policy andthecostofborrowingarejointlydetermined,itisdi¢ culttoisolateexogenousmovementsin the cost of borrowing for governments. To overcome this challenge, we use the sign-restriction methodology of Mountford and Uhlig (2009) to identify several fundamental shocks that have beenwelldocumentedinthemacroeconometricliterature. Havingthusidenti(cid:133)edbusinesscycle and (cid:133)scal policy shocks, we treat any additional unexpected movements in long-term interest rates, orthogonal to the business cycle and (cid:133)scal policy shocks, as truly exogenous shocks to the cost of borrowing. Second, empirical estimates must respect the government(cid:146)s intertemporal budget constraint. We impose this restriction by keeping track of the nonlinear debt dynamics using the methodology of Favero and Giavazzi (2007). On this basis, it is possible to assess whether the (cid:133)scal response is su¢ cient to o⁄set the dynamics of rising debt generated by an increase in the cost of borrowing. We (cid:133)nd a statistically signi(cid:133)cant (cid:133)scal policy response to exogenous changes in the cost of borrowing. In our baseline estimations, a 1 percentage point rise in the cost of borrowing leads to a cumulative increase in the primary balance-to-GDP ratio of 2 percentage points after 10 years. However, the debt-to-GDP ratio is 1 percentage point higher 10 years after the shock, i.e. the budgetary response is insu¢ cient to compensate for the automatic debt-increasing e⁄ect of higher borrowing costs. The impulse responses reveal that the (cid:133)scal response is not immediate, with a signi(cid:133)cant consolidation appearing only two years after the shock. Almost all the adjustment takes place on the revenue side while primary expenditure remains broadly unchanged. Given the wide-ranging changes in the European (cid:133)scal framework over recent decades and their potential e⁄ect on economic policy in EU member states, we separate our panel into EMU and non-EMU countries and the periods pre- and post-1992 (which marks the signing of the Maastricht Treaty). Our estimates reveal that the sub-sample including the post-1992 EMU countries show a signi(cid:133)cantly stronger (cid:133)scal consolidation response following a rise in the cost of borrowingthanthepre-1992EMUsample. Apossibleinterpretationofthispatternisthatthose countries that eventually joined monetary union had an additional incentive to compensate for higher interest payments (which count against the Maastricht balance criterion) by tightening their stance with respect to other budget items. The rest of the paper proceeds as follows. Section 2 provides a simple theoretical framework to clarify the responses predicted by standard macroeconomic theory. Section 3 outlines the empirical methodology, in particular the identi(cid:133)cation strategy. Section 4 presents the results while Section 5 discusses policy implications and concludes. 2 Theoretical motivation In this section, we provide a stylized framework to analyze the responses of governments to an exogenous rise in the cost of borrowing. We use this model to illustrate the range of potential patterns of (cid:133)scal adjustment to shocks to the cost of borrowing. Based on these results, we test these implications in Section 4. The model is that of a small open economy populated by a large number of identical households and a benevolent government. Households have preferences over private and public consumption goods and hours worked and have access to incomplete international capital markets. The government can also borrow on international capital markets and has two (cid:133)scal instruments, distortionary taxes on labor income and public 2

consumption expenditure. The government sets its two policy instruments optimally under commitment. 2.1 Model The objective function of a representative household is max E 1 (cid:12)tu (1) 0 t ct;nt;bh t t=0 X subject to the intertemporal budget constraint c = bh rhbh +(1 (cid:28) )w n t t t t 1 t t t (cid:0) (cid:0) (cid:0) where u u(c ;n ;g ) v(c ;n )+w(g ) are preferences over private consumption, c , hours t t t t t t t t (cid:17) (cid:17) worked, n , and public consumption, g . The functional form for preferences over c and n t t t t follows Greenwood, Hercowitz, and Hu⁄man (1988), eliminating wealth e⁄ect on labour supply. Public consumption is additively separable. (cid:12) (0;1) is the subjective discount factor, w is t 2 the real wage and (cid:28) is the tax rate on labor income. Households issue debt, denoted bh, on t t international capital markets. The interest rate households face is denoted rh and is assumed t to be an increasing and convex function of both the aggregate debt-to-output ratio of the private sector, bh=y (where a tilde denotes an aggregate quantity and y is output) and the government debt-to-GDP ratio, bg=y: e bh b g rh rh t ; t;(cid:29)(cid:24) (2) t (cid:17) y y t t t ! e where (cid:29) captures the pass-through of the exogenous government cost of borrowing shock (to be described below) to the private sector(cid:146)s cost of borrowing. Production in the economy follows a linear technology, y = n , which implies that the real wage (before taxes) is constant and equal t t to one. The (cid:133)rst-order conditions of the household problem are u 1 = (cid:12)E 1;t+1 rh (3) t u t 1;t and u 2;t (1 (cid:28) )w = (4) t t (cid:0) (cid:0)u 1;t where u , for example, denotes the (cid:133)rst derivative of u with respect to its (cid:133)rst argument, c . 1;t t t In equilibrium, bh = bh. t t The government can levy taxes on labour income and issue debt in international capital markets to (cid:133)nanece public consumption, denoted g . The government(cid:146)s intertemporal budget t constraint is: g = b g r g b g +(cid:28) w n (cid:28) ((cid:28) (cid:28) )2 g (g g )2 (5) t t (cid:0) t (cid:0) 1 t (cid:0) 1 t t t (cid:0) 2 t (cid:0) t (cid:0) 1 (cid:0) 2 t (cid:0) t (cid:0) 1 where (cid:28) ((cid:28) (cid:28) )2 and g (g g )2 areconvexcostsofadjustingtaxratesandgovernment 2 t (cid:0) t (cid:0) 1 2 t (cid:0) t (cid:0) 1 expenditure, respectively. These reduced-form costs will play an important role in shaping the impulse responses to a cost of borrowing shock and generate paths for the primary balance that are able to match those in our empirical estimation in Section 4. These costs can be interpreted in three ways. First, they can be interpreted as actual administrative and compliance costs of changing the tax code or devising well-targeted government spending programmes.5 Even when and are high, the equilibrium deadweight (cid:28) g 5Papers such as Browning (1976) and Mayshar (1991) attempt to model and estimate these types of administrative and compliance costs. They estimate such costs to be of the order of one percent of tax revenues. However, applying this estimates for calibrating the values of and is not straightforward. (cid:28) g 3

costs remain economically small as the government optimally adjusts its (cid:133)scal instruments more gradually. Second, the adjustment costs can be thought of as capturing, in reduced form, the dynamics of distributional con(cid:135)icts between di⁄erent (cid:133)scal agents (or political parties) that have di⁄erent preferences over the mix of (cid:133)scal instruments. Tabellini (1986) showed that in this setting, the non-cooperative equilibrium would generate slower (cid:133)scal adjustment following shocks. Third,andourpreferredinterpretation,istheanalogywiththeliteratureonoptimalmonetarypolicyinertia. Aoki(2006)andWoodford(1999),forexample,showthatadjustingthemonetary policyinterestrategraduallyisoptimalwithoutimposinganypenaltyoninterestratevariations. As long as there is some friction due to which the policymaker cannot achieve its stabilization objectives independently in each period, optimal policy is history dependent. Providing a more fundamental model of this source of policy inertia, however, is left for future research. The interest rate on government borrowing, like that of the households, is assumed to be an increasing and convex function of both the (aggregate) private sector and government debt-to- GDP ratio. bh b g r g rg t ; t;(cid:24) (6) t (cid:17) y y t t t ! e In addition, the interest rate faced by the government is assumed to be stochastic, with an exogenous cost of borrowing shock denoted by (cid:24) , which follows an AR(1) process, (cid:24) = (cid:26)(cid:24) + t t t 1 (cid:16)" where " NIID(0;1). (cid:0) t t (cid:24) Closing the model requires two additional equations describing the behaviour of the government(cid:146)s two (cid:133)scal instruments. To do this, we assume that the government is benevolent and is able to commit to a time invariant (i.e. from the timeless perspective) optimal policy. The government therefore solves the following Lagrangian, which maximizes household utility subject to resource constraints and household(cid:146)s (cid:133)rst order equilibrium conditions: u +(cid:22) bh rh bh u2;tn c t 1;t t (cid:0) t (cid:0) 1 t (cid:0) 1(cid:0) u1;t t (cid:0) t ct;nt;bh t ; m bg t ; a gt x ;(cid:22) 1;t ;(cid:22) 2;t E 0 X 1 t=0 (cid:12)t0 B B B +(cid:22) 2;t 0 (cid:0) 2 (cid:28) u u b 2 1 g t ; ; (cid:16) t t (cid:0) (cid:0) r u u t g (cid:0) 2 1 ; ; 1 t t (cid:0) b g t 1 1 (cid:0) 1 2 + (cid:0) (cid:16) 2 1 g + (g t u u 1 2 (cid:0) ; ; t t (cid:17) g t n (cid:0) t 1 (cid:17) )2 (cid:0) g t 1 1 C C C (7) (cid:0) @ @ (cid:16) (cid:17) A A where(cid:22) istheLagrangemultiplieronthehouseholdbudgetconstraintand(cid:22) istheLagrange 1;t 2;t multiplier on the government budget constraint, with equations (4) and (11) substituted in. We alsoassumethatthegovernmenthasthesamesubjectivediscountfactor,(cid:12) astheprivatesector. The (cid:133)rst-order conditions are given in Appendix A, as are the functional forms for the utility function and interest rate equations (2) and (6). 2.2 Calibration Table1summarizesthecalibrationofthemodelandTable2summarizesthedeterministicsteady state around which a linear approximation of the model is taken. The calibration replicates several long-run averages in European data. For example, we achieve a debt-to-GDP ratio of both the private sector and the government of 50%, broadly in line with the sample average of 51:3%. Unlike small open economy models featuring a non-optimizing (cid:133)scal agent, the steady state debt-to-GDP ratio is uniquely pinned down in this model. In particular, it is pinned down in this model by the calibration of parameters (cid:30)ij and (cid:11)i with i;j g;h , where (cid:30)ij de(cid:133)nes 2 f g the response of the interest rate faced by i to a marginal change in the debt-to-GDP ratio of j, and (cid:11)i de(cid:133)nes the wedge between the steady state interest rate faced by i and the discount rate, (cid:12) 1. We set (cid:30)gg = (cid:30)hh = 0:05, which implies that a 1 percentage point increase in the debt- (cid:0) to-GDP ratio increases the cost of borrowing by 5 basis points. There is very little evidence on the response of longer-term interest rates to (cid:133)scal shocks for European countries, so we chose a value that matched the (cid:133)nding in Laubach (2009) based on US data. The cross-elasticities 4

Table 1: Calibration Symbol Description Value (cid:12) Subjective discount factor 0:95 (cid:27) Preference parameter 2 (cid:18) Preference parameter 1:8333 Preference parameter 1:0138 Government spending adjustment cost parameter various g Tax adjustment cost parameter various (cid:28) (cid:11)h;(cid:11)g Steady state interest rate discount 0:025 (cid:30)hh;(cid:30)gg Interest rate sensitivity parameter 0:05 (cid:30)hg;(cid:30)gh Interest rate sensitivity parameter 0 (cid:26) Cost of borrowing shock persistence parameter 0:8 Table 2: Deterministic steady state Symbol Description Value bh=y Private sector debt-to-GDP ratio 50% bg=y Government debt-to-GDP ratio 50% n Proportion of hours worked 25% g=y Government primary spending-to-GDP ratio 40% (cid:28) Tax rate 41:4% rh;rg Private sector and government cost of borrowing 2:76% (cid:30)hg = (cid:30)gh are set to zero. The steady-state interest rate is set below the household(cid:146)s subjective discount rate in order to induce a positive holding of debt by both the private sector and the government. Given (cid:30)gg and (cid:30)hh, achieving the 50% debt-to-GDP ratio required setting (cid:11)h and (cid:11)g at :0025. The preference parameters determine the number of hours worked. We therefore calibrate these parameters so that households work 25% of their time endowment. The weight on public consumption in the utility function is chosen to achieve a government primary spending-to- GDP ratio of 40%, which is consistent with the long-run average in our European data set. The adjustment cost parameters and do not feature in the steady state. We will conduct g (cid:28) sensitivityanalysiswithrespecttotheseparameters,aswellas(cid:29),thepassthroughofgovernment costofborrowingshockstotheprivatesector,whenanalyzingtheimpulseresponses. Themodel iscalibratedforannualdata, whichmeanswehave(cid:12) = 0:95and(cid:26) = 0:8, whichisapproximately equal to a persistence coe¢ cient of 0:95 in a quarterly model. 2.3 Impulse responses When the government faces a higher path of borrowing costs, it must, at some point, generate a higher primary balance path to preserve solvency. The government, however, faces two 5

important trade-o⁄s in choosing the optimal path of its two (cid:133)scal policy instruments to a cost of borrowing shock. The (cid:133)rst concerns the timing of adjustment. A sharp adjustment in the short-run can be costly due to the convex nature of the (cid:133)scal adjustment costs. However, a longer-term, more gradual adjustment means that the government will have to bear higher future interest rate payments. The second trade-o⁄ concerns the composition of adjustment. Cutting primary expenditures incurs both a deadweight cost of adjustment and a reduction in welfare due to the fall in public consumption, which directly enters households(cid:146)utility. Raising taxes also incurs a deadweight adjustment cost as well as causing an increase in the distortion in the labour market. However, the social planner is able to use the tax rate to shift part of the economy(cid:146)s debt burden from the government (which is facing a relatively higher cost of borrowing) to the private sector. Figures 1-3 show the impulse responses to an exogenous, unexpected 1 percentage point rise in the government cost of borrowing, under various calibrations of the model. In each (cid:133)gure, the grey background lines show the dispersion of responses that the model is able to generate within a given parameter space. Figure 1 highlights two calibrations: one without (cid:133)scal instrument adjustment costs and one with extremely high adjustment costs. The shape of the responses are interesting for two reasons. First, the response of the government debtto-GDP ratio is ambiguous. In the calibration without adjustment costs, the debt-to-GDP ratio immediately drops by 1 percentage point, while in the calibration with extremely high adjustment costs, the government debt-to-GDP ratio rises to 51.5 percentage points by the end of the 10 year horizon. Because the government makes only very gradual adjustments to its (cid:133)scalinstrumentsinthesecondscenario,theriseinthedebt-to-GDPratiooccurslargelybecause new debt issuance is used to cover higher interest payments. Without adjustment costs, the government cuts primary expenditure by 2 percentage points on impact, after which the level of primary expenditure is slowly rebuilt. This cut in primary expenditures translates into a fall in the primary expenditure-to-GDP ratio of almost 1 percentage point. The government also raises the tax rate on labour income by just over 0.1 percentage point. Since the real wage in this model is constant and equal to 1, the tax rate is always equal to the revenue-to-GDP ratio. The rise in the tax rates induces a reduction in labour supply and a consequent fall in output. The household smooths consumption by increasing borrowing. Figure 2 partly isolates the e⁄ect of the two (cid:133)scal instruments by varying the relative weight given to the two adjustment costs. In one of the highlighted responses, it is relatively more costly to adjust taxes, while in the other highlighted response it is more costly to adjust primary expenditure.6 With the intermediate calibration of the adjustment cost parameters in Figure 2 relative to Figure 1, the model generates hump-shaped responses of the (cid:133)scal instruments to cost of borrowing shocks, which is what we observe in our empirical analysis (see Section 4). Figures 1 and 2 had assumed zero pass through from the cost of borrowing shock to the private sector. Figure 3, instead, assumes that the household cost of borrowing is shocked 1-for-1 with the government cost of borrowing, thus leaving the exogenous component of the spread between government and household cost of borrowing unchanged (that is, in equation (2), (cid:29) = 1, rather than 0). This comparison highlights an adjustment mechanism that the social planner is able to exploit in the model. From a social planner(cid:146)s perspective, the debt of the household sector and the debt of the government are substitutes, and the social planner would like to shift the debt burden to the agent with the lowest cost of borrowing. The way the social planner is able to do this is by adjusting taxes. By increasing the tax rate, households reduce their supply of labour and smooth consumption by taking on more debt. Thus, raising 6TheassumptionofGreenwood,Hercowitz,andHu⁄man(1988)preferencesimpliesthatthereisnogovernment spending multiplierin thismodel. Had we used King,Plosser,and Rebelo (1988)preferencesinstead, the model would generate a positive government spending multiplier. However, we would also get a rise in output growth following a cost of borrowing shock. This is because a cost of borrowing shock acts like a wealth shock as it lowers the present value of future disposable income. Households will therefore react by supplying more labour which would generate a counterintuitive rise in output. 6

Figure 1: Cost of borrowing shock: extreme calibrations Output growth Gov. debt to GDP Interest rate on debt HH debt to GDP 1.5 1 0.4 0 1 0.8 0.2 0.1 0.5 % 0.2 .t.p 0 .t.p 0.6 .t.p 0 .p .p0.4 .p 0.3 0.5 0.2 0.4 1 0.2 0.4 0 5 10 5 10 5 10 5 10 Prim. exp. growth Prim. exp. to GDP Tax rate (also Rev. to GDP) Prim. bal. to GDP 1 0 0.2 0 0.8 0.2 % 1 .t.p .p 0.4 .t.p .p 0. 0 1 . 5 1 .t.p .p0 0 . . 4 6 0.6 0.05 0.2 2 0.8 1 0 0 5 10 5 10 5 10 5 10 Years Note: The grey background lines show the dispersion of responses for parameter combinations in the set (cid:8) 2 f v 2 (0;1); (cid:28) ; g 2 (0;5000). (cid:15) v = 0, (cid:28) = g = 0, (cid:4) v = 0, (cid:28) = g = 5000. Figure 2: Cost of borrowing shock: intermediate calibrations Output growth Gov. debt to GDP Interest rate on debt HH debt to GDP 1.5 1 0.4 0 1 0.8 0.2 0.1 0.5 % 0.2 .t.p 0 .t.p 0.6 .t.p 0 .p .p0.4 .p 0.3 0.5 0.2 0.4 1 0.2 0.4 0 5 10 5 10 5 10 5 10 Prim. exp. growth Prim. exp. to GDP Tax rate (also Rev. to GDP) Prim. bal. to GDP 1 0 0.2 0 0.8 0.2 % 1 .t.p .p 0.4 .t.p .p 0. 0 1 . 5 1 .t.p .p0 0 . . 4 6 0.6 0.05 0.2 2 0.8 1 0 0 5 10 5 10 5 10 5 10 Years Note: The grey background lines show the dispersion of responses for parameter combinations in the set (cid:8) 2 f v 2 (0;1); (cid:28) ; g 2 (0;5000). (cid:15) v = 0, (cid:28) = 5, g = 500, (cid:4) v = 0, (cid:28) = 500, g = 50. 7

Figure 3: Cost of borrowing shock: with and without pass-through Output growth Gov. debt to GDP Interest rate on debt HH debt to GDP 1.5 1 0.4 0 1 0.8 0.2 0.1 0.5 % 0.2 .t.p 0 .t.p 0.6 .t.p 0 .p .p0.4 .p 0.3 0.5 0.2 0.4 1 0.2 0.4 0 5 10 5 10 5 10 5 10 Prim. exp. growth Prim. exp. to GDP Tax rate (also Rev. to GDP) Prim. bal. to GDP 1 0 0.2 0 0.8 0.2 % 1 .t.p .p 0.4 .t.p .p 0. 0 1 . 5 1 .t.p .p0 0 . . 4 6 0.6 0.05 0.2 2 0.8 1 0 0 5 10 5 10 5 10 5 10 Years Note: The grey background lines show the dispersion of responses for parameter combinations in the set (cid:8) 2 f v 2 (0;1); (cid:28) ; g 2 (0;5000). (cid:15) v = 0, (cid:28) = 0, g = 5000, (cid:4) v = 1, (cid:28) = 0, g = 5000. taxes induces households to take on more debt. However, when the cost of borrowing for the household sector and the government rise proportionally, the social planner does not want the household to take on the higher burden of debt and it therefore does not increase the tax rate by as much. In Figure 3, the tax rate rises by only half as much when there is full pass through compared to when there is no pass through. This stylized model yields a set of empirical hypotheses on the patterns of (cid:133)scal adjustment to cost of borrowing shocks. Based on this model, we test our main hypothesis empirically in the next section. 3 Empirical methodology The subsequent subsections describe the data, estimation technique, and identi(cid:133)cation strategy we use to model the response of (cid:133)scal policy to cost of borrowing shocks. 3.1 Data OurbaselineempiricalmodelisaVARin(cid:133)vevariables: Thegovernmentprimaryexpenditure-to- GDPratio, governmentrevenue-to-GDPratio, GDPgrowthrate, in(cid:135)ationrate, andgovernment nominal cost of borrowing. The government(cid:146)s intertemporal budget constraint (involving these (cid:133)ve variables) is adhered to by keeping track of the government debt-to-GDP ratio, which enters the VAR as a lagged explanatory variable. The data covers an unbalanced panel of 14 European countries (Austria, Belgium, Germany, France, Finland, Greece, Ireland, Italy, Netherlands, Portugal, Spain, Denmark, UK and Sweden) at an annual frequency from 1970 to 2011. All the endogenous variables in the VAR are stationary as they have either been expressed in terms of growth rates or relative to GDP. Measuring the two (cid:133)scal variables as a ratio to GDPhastheaddedadvantagethatimpulseresponsesfortheprimarybalance-to-GDPratiocan be computed without approximation. A full description of the sources and construction of the 8

data series can be found in Appendix B. For the government(cid:146)s nominal cost of borrowing, we calculate an implicit interest rate using a measure of the government(cid:146)s total interest payments in a given period and its outstanding debt stock: interest payments t cob = 100 (8) t (cid:2) debt stock t 1 (cid:0) This measure for the cost of borrowing allows a direct mapping from the endogenous variables of the VAR to the government debt-to-GDP ratio that is the lagged explanatory variable in the VAR. We discuss this mapping in detail in the next subsection. The main drawback of this measure is that it represents the average cost of borrowing rather than the marginal cost of borrowing. The average and marginal cost of borrowing are only the same if the entire debt stock is re(cid:133)nanced every year. Since governments generally fund themselves at longer average maturities, a 1% rise in the marginal cost of borrowing will lead to a less than one-for-one rise in the average cost of borrowing.7 Yet, a temporary shock to the marginal cost of borrowing (assuming debt issuance patterns in terms of instruments, maturity etc. remain unchanged) has the same e⁄ect on the total cost of borrowing (i.e. the amount of tax revenue that is needed to service debt interest payments), independent of the maturity structure of the debt.8 While the marginal cost of borrowing may be conceptually preferable, (cid:133)nding a suitable measureisequallyproblematic. Sincegovernmentsborrowusingalargesetofdebtinstruments, any single bond(cid:146)s yield would be a poor proxy of the marginal cost of borrowing. We also have less historical data for bond yields in our sample since several of the countries did not regularly access capital markets for funding in the early part of our sample. We do, however, test for robustness along this dimension by including the 10-year government bond yield in a largerdimensioned VAR in Section 4. 3.2 Estimation The panel VAR we estimate takes the form: Y = A(‘)Y +F (‘)W +u u iid(0;(cid:6) ) (9) i;t i;t 1 i;t 1 i;t i;t u (cid:0) (cid:0) (cid:24) where Y is a G 1 vector of endogenous variables, W is an H 1 vector of predetermined i;t i;t (cid:2) (cid:2) variables, A(‘) and F (‘) are polynomials in the lag operator and iid means identically and independently distributed. Time is denoted by the subscript t = 1;:::;T and the country unit is denoted by the subscript i = 1;:::;N. We estimate a homogenous panel VAR in the sense that the coe¢ cient matrices A and F (where j denotes the lag) are independent of the country j j unit subscript i. We revisit this restrictive assumption in Section 4. In our baseline estimation, G = 5 and Y = [pe;v;g;(cid:25);cob] where pe is the government primary expenditure-to-GDP ratio, v is the revenue-to-GDP ratio, g is the GDP growth rate, (cid:25) is the in(cid:135)ation rate and cob is the government nominal cost of borrowing. We have one predetermined variable: H = 1 and W = d where d is the government debt-to-GDP ratio. All the variables are country- and time-demeaned to account for both country and time (cid:133)xed 7Supposewemodelthematuritystructureofdebtasacontinuumofcallableperpetuitybondswithstochastic calldatearrivingwithprobabilityp. Thestockofdebtevolvesasd =(1 p)d +dn,wheredn isnewlyissued debt. Theaveragecostofborrowingevolvesasia =(1 p)ia d t =d + (cid:0) imdn= t (cid:0) d 1 ,wh t ereim ist t hemarginalcost ofborrowing. The average maturity ofthe gover t nment (cid:0) (cid:146)s deb t t(cid:0)p 1 o t r (cid:0) tf 1 olio t is p t (cid:0) 1 t . T t he e⁄ect t on the average cost of borrowing for a change in the marginal cost of borrowing (evaluated at the steady state) declines as the average maturity increases:(@ia=@im) =p. t t jdt=d 8Usingthemodelin thepreviousfootnoteandsettingd =dand dn =pdfor tthen ia =(1 p)ia +pim. Let f im t g 1t=0 =i+(cid:27);i;i;:::. It is straight forward to show t that 1t=0 ( t ia t (cid:0) i)=(cid:27) 8 , which is t indepe (cid:0) nden t t(cid:0)o 1 f p, t t he average maturity of the debt. P 9

e⁄ects. The panel VAR is estimated with two lags of the endogenous variables and one lag of the predetermined variable.9 The inclusion of the government debt-to-GDP ratio as a lagged explanatory variable follows the method of Favero and Giavazzi (2007). The rationale for its inclusion is that it imposes the government intertemporal budget constraint on (cid:133)scal responses to shocks. As long as the estimated coe¢ cient vector, F , is non-zero, all the endogenous variables are able to respond to 1 the movements in the government debt-to-GDP ratio. Speci(cid:133)cally, the government debt-to- GDP ratio evolves as follows:b 1+cob t d = d +pe v +s (10) t t 1 t t t (1+g t )(1+(cid:25) t ) (cid:0) (cid:0) OneoftheadvantagesoftheFaveroandGiavazzi(2007)methodisthattheevolutionofthedebtto-GDP ratio in equation (10) is calculated recursively using the VAR(cid:146)s endogenous variables. However,themethoddoesgiverisetotwodi¢ culties. First,theintertemporalbudgetconstraint is a nonlinear function of the endogenous variables. Thus, when we generate impulse responses to shocks, the results will be sensitive to the initial debt-to-GDP ratio and the size of the shock. Second, in the (cid:133)scal accounts data the stocks and (cid:135)ows do not exactly tally and the residual is captured in the stock-(cid:135)ow adjustment variable, s. The inclusion of s in the endogenous vector, Y, would ensure that the debt-to-GDP ratio holds as an identity but would also increase the numberofcoe¢ cientswewouldneedtoestimate. Excludingsmeansthatthereisanadditional source of uncertainty in the model coming from the debt equation. Nevertheless, since it is not necessary to identify all the shocks in our system, we treat s as iid. We reconsider this t assumption when we conduct robustness exercises in Section 4. To draw inferences about (cid:8) = (A(‘);F (‘)) and (cid:6) , we employ a Bayesian approach, which u combines information from sample and priors. We employ commonly used di⁄use priors that allows us to bene(cid:133)t from Bayesian analysis without the di¢ culty of obtaining an informative prior. In particular, we employ a constant prior for (cid:8) and the Je⁄reys prior for (cid:6), P ((cid:6)) J / (cid:6) (G+1)=2, which means that P ((cid:8);(cid:6)) P ((cid:6)). The Bayes estimators are obtained via (cid:0) CJ J j j / Monte Carlo (MC) simulations. By sampling ((cid:8);(cid:6)) from the joint posterior distribution, we generate the Bayes estimates numerically. Let the OLS estimates of ((cid:8);(cid:6)) be (B;S). Under these assumptions, the posteriors are: (cid:6) IW (NTS) 1;NT GL HL (cid:0) Y W (cid:24) (cid:0) (cid:0) h 1 i vec((cid:8)) N vec(B);(cid:6) X 0 X (cid:0) (cid:24) (cid:10) h i where the posteriors of (cid:6) are drawn from an invers(cid:0)e Wis(cid:1)hart distribution, which takes as its arguments (NTS) 1 and degrees of freedom, NT GL HL where L and L are the (cid:0) Y W Y W (cid:0) (cid:0) numberoflagsY andW respectively. Theposteriorsof(cid:8)aredrawnfromanormaldistribution, where X is the matrix containing the right-hand side variables. To generate the error bands around our impulse responses, we ran 5000 MC iterations.10 3.3 Identi(cid:133)cation The estimated model, in its reduced form (equation (9)), lacks economic structure. This is becausetheerrors, u, thatresultfromaone-stepaheadforecastofthecorrespondingcomponent 9The choice of lag length is important due to the serial correlation in the maturity structure of government debt. As of 2010, the UK has the longest average maturity of debt of 13.7 years followed by Denmark with 7.9 years. Finland has the shortest average maturity with 4.3 years. The average maturity of debt across all the countries in our sample was 7 years (the data is from Faraglia, Marcet, and Scott (2011) who source the OECD and The Economist). Our choice of a VAR with 2 lags came from the use of standard lag length selection criteria. We considered VAR speci(cid:133)cations with lag lengths from 1 to 7. The Schwarz Bayesian Criterion indicated a single lag, the Hannan-Quinn Criterion indicated two lags while the Akaike Information Criterion indicated 7 lags. 10Increasing the number of runs to 10,000 does not signi(cid:133)cantly alter inference. 10

of Y are unlikely to be orthogonal innovations since (cid:6) is unlikely to be diagonal. To give u the model, and the shocks, economic structure, we must place some restrictions on the model that allow us to decompose the non-orthogonal innovations into orthogonal and economically interpretableshocks. WecandothisbychoosingamatrixB suchthatB(cid:6) B = I sincethenew u 0 shocks, " = Bu will satisfy E("") = I. These orthogonalized innovations have the convenient 0 propertythattheyareuncorrelatedacrossequations. Therearemanysuchfactorizationsof(cid:6) , u so the choice of method of orthogonalizing is not innocuous. The aim is to choose B such that the estimated model has a clear structural form with shocks, " that have a convincing economic interpretation. There are several commonly used methods to recover the structural form (i.e. identify shocks) in the literature. In this paper, we identify cost of borrowing shocks by making use of a methodology which imposes sign restrictions (see Faust (1998), Uhlig (2005), and Canova and Nicol(cid:243) (2002)) upon impulse responses.11 The central idea behind our identi(cid:133)cation strategy is that a cost-of-borrowing shock is a surprise change in the interest rate on government debt that is orthogonal to all other macroeconomic shocks. We do not want to impose any prior restrictions on the behaviour of the endogenous variables to a cost-of-borrowing shock. Instead, our identi(cid:133)cation strategy imposes sign restrictions that lead to the identi(cid:133)cation of a set of shocks that have been commonly studied in the macroeconomic literature. Any unexplained variation in our cost-of-borrowing variable that is orthogonal to these other macroeconomic shocks is then judged to be a costof-borrowing shock. If we were not to control for other macroeconomic shocks - (cid:133)scal policy shocks for example - it would be easy to end up confusing changes in the cost of borrowing due to supply shocks (surprise changes in the supply of government bonds) with changes in the level ofgovernmentborrowingduetodemandshocks(surprisechangesinthedemandforgovernment bonds). The theoretical model we presented in Section 2 is not rich enough to provide a robust set of sign restrictions to identify all the macroeconomic shocks that we wish to identify. The sign restrictions are therefore chosen from a wide reading of the macroeconomic literature to arrive at a set of sign restrictions that are as uncontroversial as possible. For two reasons, we also only impose sign restrictions on the responses of variables on impact. First, using impact sign restrictions in a model with annual data is analogous to the existing literature which usually imposes sign restriction for four quarters in a model with quarterly data. Second, the nonlinearity from the debt-to-GDP feedback severely complicates the identi(cid:133)cation strategy if sign restriction are imposed at further horizons. Rather than simultaneously identifying all the shocks, subject to the orthogonality restrictions, we identify the shocks sequentially via a penalty function following the method of Mountford and Uhlig (2009). Conceptually, for the (cid:133)rst shock to be identi(cid:133)ed, the penalty function method (cid:133)nds the set of parameter restrictions which minimize the sum of: x if x > 0 pf(x j ) = (cid:0) 100 j x if x j 0 , (11) j j (cid:26) (cid:0) (cid:20) across the sign restricted variables j = 1;:::;J where x is the impact response of variable j j (rescaled by the standard error of variable j). The function pf(:) rewards large impulse responses with the right sign (we assume in equation (11) that we are looking for a positive 11There are several alternative methods in the literature for identi(cid:133)cation in VAR models. Most of these methods use explicit (rather than implicit as in the case of sign restrictions) parameter restrictions. In general, thereduced-formmodelhasmorefreeparametersthanthestructuralmodel. Parameterrestrictionsaretherefore added to the reduced form model to enable the parameters of the structural model to be estimated. For early contributions to this literature, see Sims (1980), Blanchard and Watson (1986) and Sims (1986). The literature has followed either the use of short-run identifying restrictions, see Christiano, Eichenbaum, and Evans (1999), or long-run identifying restrictions, see Blanchard and Quah (1993). An alternative approach to the structural VAR literature has been the narrative (or natural experiment) approach of Romer and Romer (1989). 11

Table 3: Contemporaneous Identifying Sign Restrictions Primary Revenue GDP In(cid:135)ation Cost Variables: expenditure -to-GDP growth rate of -to-GDP rate borrowing Shocks: Aggregate demand (+) (+) (+) (cid:1) (cid:1) Cost-push ( ) (+) (cid:1) (cid:1) (cid:0) (cid:1) Primary expenditure (+) (+) (cid:1) (cid:1) (cid:1) Revenue (+) ( ) (cid:1) (cid:0) (cid:1) (cid:1) Cost of borrowing (+) (cid:1) (cid:1) (cid:1) (cid:1) Note: (+) or ( ) mean that the response of variable x to shock y on year of impact is restricted to be (cid:0) positive or negative, respectively. A blank space means no restriction has been imposed. response) more than small responses and punishes responses that go in the wrong direction. The second shock is then identi(cid:133)ed in the same way, with the additional restriction that it be orthogonaltothe(cid:133)rstshock. Therestoftheshocksareidenti(cid:133)edsimilarly. Theconsequenceof this sequential identi(cid:133)cation is that the penalty function ascribes as much movement as possible to the (cid:133)rst shock, then the second shock and so on. An overview of our identifying sign restrictions on the impulse responses is provided in Table 3. First, we identify an aggregate demand shock (row 1). The (+) symbols in the (cid:133)rst row indicate that an aggregate demand shock is anything that generates, on impact, a positive comovement between the growth rate of GDP, the in(cid:135)ation rate and the government revenueto-GDP ratio. The blank spaces in the (cid:133)rst row says that we are agnostic about how the government primary expenditure-to-GDP ratio and the government cost of borrowing respond, on impact, to an aggregate demand shock. The restriction on the movement of government revenue-to-GDP is crucial for identifying the government revenue shock later. While there is debate in the literature on the numerical estimate of the income elasticity of tax revenue, imposing procyclicality is, we think, uncontroversial. Since we associate aggregate demand shocks with the predominant cause of business cycle (cid:135)uctuations, we identify this shock (cid:133)rst. Second, weidentifyacost-pushshock. Ouridentifyingassumptionisthatthegrowthrateof GDPandthein(cid:135)ationrateshouldnegativelycomoveinresponsetoacost-pushshockonimpact. We also require the cost-push shock to be orthogonal to the aggregate demand shock. Third and fourth, we identify two (cid:133)scal policy shocks, a primary expenditure shock and a revenue shock. Both are identi(cid:133)ed by restricting the sign of the GDP growth rate response: GDP growth rate positively comoves with the government primary expenditure-to-GDP ratio for a primary expenditure shock and negatively comoves with the government revenue-to-GDP ratio forarevenueshock. The(cid:133)scalpolicyshocksareassumedtobeorthogonaltothetwo,preceding, businesscycleshocksbutwedonotrequirethatthetwo(cid:133)scalpolicyshocksbeorthogonaltoeach other. Again, without wanting to place any prior restrictions on the responses of endogenous variablestoacostofborrowingshock,weforceourselvestoidentifyfourcommonmacroeconomic shocksinordertorecoveracostofborrowingshockthatistrulyorthogonaltoother(cid:135)uctuations in the macroeconomy. A cost of borrowing shock, in our scheme, is therefore any unexpected movement in the cost of borrowing variable that induces a response of the other endogenous variables that is orthogonal to the response that the other four macroeconomic shocks generate. Anaturalconcernmayariseregardingtheorderinginwhichshocksareidenti(cid:133)ed. Howdoes the choice of ordering allow us, for example, to distinguish between shocks that are assumed to have the same e⁄ect on the same variables, such as the aggregate demand and primary expenditure shocks?12 The nature of the penalty function means that the shocks identi(cid:133)ed 12We are grateful to an anonymous referee for alerting us to this issue. 12

earlierarelikelytoaccountforalargershareoftotal(cid:135)uctuations. Itseemsreasonabletherefore to order the business cycle shocks ahead of the (cid:133)scal policy shocks. More importantly, however, while switching the order is important for the identi(cid:133)cation of these two shocks, we (cid:133)nd that the ordering of the (cid:133)rst four shocks has almost no e⁄ect on the identi(cid:133)cation and impulse responses of the shock of interest, namely the cost of borrowing shock. 4 Results Figure 4 presents the identi(cid:133)ed cost of borrowing shocks, which are, by construction, orthogonal to the preceding four shocks.13 It suggests that the variance of cost-of-borrowing shocks was signi(cid:133)cantly higher in the 1980s and early 1990s than the late 1990s and early 2000s, across Europe.14 Before commencing the formal analysis, it is useful to graphically inspect if the identi(cid:133)ed shocks actually coincide or precede periods that have been identi(cid:133)ed as entailing strong (cid:133)scal e⁄orts by certain governments. To this end, the shaded areas in Figure 4 denote periods of (cid:133)scal consolidation as identi(cid:133)ed by the narrative approach developed in Devries, Guajardo, Leigh, and Pescatori (2011). The two measures appear to be weakly correlated. Positive cost-of-borrowing shocks preceded the (cid:133)scal adjustment in Italy in the mid-1990s, Portugal in 1981, Finland in 1992 and Sweden in the end-1990s. The most striking omission is the apparent lack of (cid:133)scal adjustment following the cost of borrowing shocks in Portugal in 1990 and Spain in 1986. However, using an alternative measure of (cid:133)scal consolidations, Alesina and Perotti (1995) [Table 5. pp.218] record strong (cid:133)scal adjustments for Portugal in 1989 and Spain in 1986-87. 4.1 Baseline results Figure 5 displays the impulse responses to a temporary cost of borrowing shock over a 10year horizon. The responses have been normalized so that the cost of borrowing always rises by 1 percentage point. The initial level of the debt-to-GDP ratio will impact the impulse responses. In Figure 5, we initialize the debt-to-GDP ratio to 50% which is close to the sample mean. In Figure 6 below, we report sensitivity results to this choice of initial value. All the (cid:133)scal variables are measured in percentage points of GDP, while the interest rate and growth variables are measured in percent. The impulse responses reveal four key results. First, the shock generates a relatively persistent e⁄ect on the nominal cost of borrowing, which takes 4 years to halve. Second, it is revenues rather than primary expenditures that react to the cost of borrowing shock, with the revenue-to-GDP ratio 0.2 percentage points higher at the end of the 10 year horizon and the response of the primary expenditure-to-GDP remaining insigni(cid:133)cant throughout the 10 year horizon. Third, the (cid:133)scal policy adjustment is not immediate. The primary balance is unchanged on impact but still does not turn signi(cid:133)cantly positive until the second year following the shock. Fiscal adjustment between years 3 and 5 is fairly rapid before reaching peak adjustment in year 7. The cumulative change in the primary balance-to-GDP ratio reaches 0:19, 0:79 and 1:88 in years 2, 5 and 10 following the shock. Fourth, the (cid:133)scal adjustment is insu¢ cient 13We have relegated the identi(cid:133)ed aggregate demand, cost-push and (cid:133)scal policy shocks, as well as their corresponding impulse responses to Appendix C. Replication (cid:133)les for all the (cid:133)gures in this section, written in RATS code,isavailablefrom thecorrespondingauthor(cid:146)shomepage,http://sites.google.com/site/oliverdegroot/research 14Infact,thetimeseriesofidenti(cid:133)edcost-of-borrowingshocksinFigure4mightnotappearasonemightexpect, asweidentifynolargepositiveshocksforthecountriesstrugglingwiththecurrentsovereigndebtcrisis. Inpart, thisrelatestoourdiscussion(inSection3)ofthemarginalversusaveragecostofborrowingconcepts. Whilethe marginalcostofborrowing(proxiedby10yeargovernmentbondyields)forGreece,IrelandandPortugaletc. has increased sharply in recent years, their average cost of borrowing, which we use in this estimation, has moved by much less. The second explanation is that a considerable portion of the rise in governments(cid:146)cost of borrowing in recent years may have been driven by changes in governments(cid:146)primary de(cid:133)cits and debt, and have not been the consequence of unanticipated cost of borrowing shocks. 13

Figure 4: Identi(cid:133)ed Cost of Borrowing Shocks Austria Italy 5.00 5.00 3.00 3.00 1.00 1.00 1.00 1.00 3.00 3.00 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 Ireland Germany 5.00 5.00 3.00 3.00 1.00 1.00 1.00 1.00 3.00 3.00 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 Belgium Spain 5.00 5.00 3.00 3.00 1.00 1.00 1.00 1.00 3.00 3.00 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 Portugal UK 5.00 5.00 3.00 3.00 1.00 1.00 1.00 1.00 3.00 3.00 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 Finland Greece 5.00 5.00 3.00 3.00 1.00 1.00 1.00 1.00 3.00 3.00 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 France Sweden 5.00 5.00 3.00 3.00 1.00 1.00 1.00 1.00 3.00 3.00 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 Note: The y-axis measures the identi(cid:133)ed cost of borrowing shock with a unit standard deviation, the x-axis measures time in years. The error bands are generated by Monte Carlo integration, showing the 14th, 50th and 86th percentiles. The shaded areas are periods of (cid:133)scal consolidation identi(cid:133)ed by the narrative approach in Devries, Guajardo, Leigh, and Pescatori (2011). 14

Figure 5: Responses to 1 p.p.t. increase in cost of borrowing Primary expenditure to GDP ratio Inflation rate Primary balance to GDP ratio 0.3 0.1 0.25 0.2 0.05 0.2 0 0.1 0.15 0.05 0.1 0 0.1 0.05 0.1 0.15 0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 Revenue to GDP ratio C.o.B. (nominal) Cumulative p.b. to GDP ratio 1 0.3 2 0.8 0.2 1.5 0.6 0.1 0.4 1 0 0.2 0.5 0.1 0 0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 Output growth rate C.o.B. (inflation & growth adjusted) Debt to GDP ratio 1 2 0.15 0.8 1.5 0.1 0.6 0.05 1 0.4 0 0.5 0.2 0.05 0 0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 Note: The cost of borrowing shock is ordered (cid:133)fth and orthogonal to the business cycle and (cid:133)scal policy shocks. The y-axis is in percentage points, the x-axis is in years. The error bands are generated by Monte Carlo integration, showing the 14th, 50th and 86th percentiles. Responses have been normalized to a 1 percentage point rise in the cost of borrowing. The debt-to-GDP ratio is initially 0.5. to counteract the debt-increasing e⁄ect from the cost-of-borrowing shock over this time horizon. The debt-to-GDP ratio has rises by 1:3 percentage points in year 6 and falls slightly to 1:1% percentage points in year 10. The in(cid:135)ation and growth adjusted cost of borrowing response follows closely that of the nominal cost of borrowing response. This is because the responses of output growth and in(cid:135)ation are both either economically or statically insigni(cid:133)cant. The insigni(cid:133)cant response of output growth suggests that shocks to the governments(cid:146)cost of borrowing do not systematically a⁄ect private sector borrowing costs. 4.2 Initial conditions and debt feedback The addition of the governments(cid:146)budget constraint, in the form of the lagged debt-to-GDP ratio, generates a feedback mechanism in the vector autoregression model and potentially strong nonlinearities in the responses to shocks. In particular, we (cid:133)nd that the (cid:133)scal adjustment to a cost of borrowing shock is sensitive to the level of the debt-to-GDP ratio at the time of the shock. Figure 6 plots the median impulse responses of the primary expenditure-, revenue-, primary balance- and debt-to-GDP ratios to a cost of borrowing shock with two di⁄erent initial debt-to-GDP ratios, 20% and 140% respectively (and the baseline impulse responses plot in the background). Notice that this experiment is considering the response of our "representative" country being hit by cost of borrowing shocks when it(cid:146)s debt-to-GDP ratio is either cyclically high or cyclically low. Not until Figure 8 do we try and distinguish between the (cid:133)scal responses 15

Figure 6: Sensitivity to initial Debt-to-GDP ratio Primary balance to GDP ratio Primary expenditure to GDP ratio 0.3 20% 0.4 50% (Baseline) 0.2 140% 0.3 0.1 0.2 0 0.1 0.1 0 0 2 4 6 8 10 0 2 4 6 8 10 Debt to GDP ratio Revenue to GDP ratio 0.3 3 2.5 0.2 2 0.1 1.5 0 1 0.1 0.5 0 0 2 4 6 8 10 0 2 4 6 8 10 Note: Impulse responses to a cost of borrowing shock which raises the cost of borrowing by 1 percentage point. The y-axis is in percentage points, the x-axis is in years. The error bands are generated by Monte Carlo integration, showing the 14th, 50th and 86th percentiles. of countries with historically high and historically low debt-to-GDP ratios. This scenario analysis shows two interesting patterns. First, when a country(cid:146)s debt-to-GDP ratio is cyclically high at the onset of a cost of borrowing shock, it makes larger primary balance adjustments. The cumulative primary balance adjustment over 10 years is 3:6% of GDP when the debt-to-GDP ratio is 140%, relative to an adjustment of 1:9% when the debt-to-GDP ratio is 50%. Moreover, the median debt-to-GDP response peaks earlier in the 140% initial debtto-GDP ratio scenario than in the 50% initial debt-to-GDP ratio scenario. However, the peak change in the debt-to-GDP ratio is larger when the initial debt-to-GDP ratio is higher. Second, with a high initial debt-to-GDP ratio the (cid:133)scal adjustment comes both via primary expenditure cuts and revenue increases. Using the median responses, for the 50% initial debt-to-GDP scenario, 12% of the (cid:133)scal adjustment is via cuts in primary expenditure. For the 140% initial debt-to-GDP ratio scenario, primary expenditure cuts account for 43% of the (cid:133)scal adjustment. Since Bohn (1998), it has been common practice to describe the behavior of (cid:133)scal policy in terms of a (cid:133)scal reaction function, with the primary balance reacting to (cid:135)uctuations in output and debt. How much of the response of the primary balance to a cost of borrowing shock is a direct response to a change in the debt-to-GDP ratio, and how much is a reaction to a change in the cost of borrowing? To investigate this, we conduct to experiments, presented in Figure 7. The (cid:133)rst is to re-estimate the model, excluding the debt-to-GDP ratio as a lagged explanatory variable. The second is to restrict the coe¢ cients on the cost of borrowing for the primary expenditure and revenue variables to zero. The impulse responses are presented in Figure 7. The impulse response functions reveal two interesting results. First, the response of the primary balance to a cost of borrowing shock is still signi(cid:133)cantly positive, even in the absence of debt feedback. Second, in the absence of interest rate feedback, the adjustment of the primary 16

Figure 7: No debt and no interest rate feedback Primary expenditure to GDP ratio Primary balance to GDP ratio 0.3 No interest rate feedback Baseline 0.25 0.2 No debt feedback 0.2 0.1 0.15 0.1 0 0.05 0.1 0 0 2 4 6 8 10 0 2 4 6 8 10 Debt to GDP ratio Revenue to GDP ratio 0.3 2 0.2 1.5 0.1 1 0 0.5 0.1 0 0 2 4 6 8 10 0 2 4 6 8 10 Note: Impulse responses to a cost of borrowing shock. The y-axis is in percentage points, the x-axis is in years. The error bands are generated by Monte Carlo integration, showing the 14th, 50th and 86th percentiles. balance to a cost of borrowing shock becomes signi(cid:133)cantly positive with a longer lag. This suggests a (cid:133)scal reaction function does not only respond to the current debt-to-GDP ratio, but also(cid:133)nancialmarkets(cid:146)expectationsoffuturedebtdynamics,asproxiedbythecostofborrowing. 4.3 Heterogeneity across sub-samples Thus far, we have considered the 14 countries as a homogenous block, restricting the responses to a cost of borrowing shock to be the same across the sample. While we lack su¢ cient degrees of freedom to estimate the model for each individual country, we can attempt to explain potential heterogeneity by sub-dividing our sample along several dimensions. The key results are reported in Figure 8. The countries which comprise each sub-group are reported in Table 4. It is important to emphasize that these results are based on somewhat ad hoc sorting of countries into sub-samples, which may reduce their robustness. However, we think they are su¢ ciently interesting to warrant future research. The (cid:133)rst row of Figure 8 reports responses to a cost-of-borrowing shock for the 11 EMU countries,pre-andpost-1992. WeareinterestedinwhetherthesigningoftheMaastrichtTreaty (in 1992) - which binds countries to adhere to the Maastricht criteria, restricting government de(cid:133)citsanddebts-a⁄ectedthe(cid:133)scalresponsetocostofborrowingshocks. Inthepre-Maastricht period,thereisarelativelysmallpositiveprimarybalanceresponsetoacost-of-borrowingshock. By contrast, in the post-Maastricht period, the response of the primary balance is signi(cid:133)cantly larger. In fact, the rise in the primary balance is su¢ ciently strong to generate a fall of the debt-to-GDP ratio to 46.5%, below its initial value of 50%, at the end of the 10 year horizon. The second row of Figure 8 sub-divides the 14 countries based on a measure of political risk - the Political Constraint Index (POLCON) - developed by Henisz (2000). It attempts to measure "the ability of a government to craft a credible commitment to an existing policy 17

Table 4: Country Groupings c d A. Maastricht Treaty B. Political constraints C. Government indebtedness 1 Austria Yes Most 0.78 Most 51% 2 Belgium Yes Most 0.87 Most 98% 3 Germany Yes Most 0.83 Least 45% 4 France Yes Most 0.79 Least 39% 5 Finland Yes Most 0.78 Least 28% a 6 Greece Yes Least 0.36 Least 46% 7 Ireland Yes Least 0.75 Most 68% 8 Italy Yes Least 0.76 Most 67% 9 Netherlands Yes Most 0.83 Most 89% 10 Portugal Yes Least 0.62 Most 60% 11 Spain Yes Least 0.77 Least 50% b 12 Denmark No Most 0.78 Least 48% 13 UK No Least 0.74 Most 51% 14 Sweden No Least 0.76 Least 49% a b Note: Greece adopted the Euro in 2001. Denmark opted out of the Maastricht Treaty but remains in ERM c d II. Average value of the POLCON index, Henisz (2000), for the period 1970-94. Average government debt-to-GDP ratio for the period 1970-2011. regime" and prevent the "potential for arbitrary or capricious" policymaking, with a low score being more hazardous and a high score being more constrained. We take an average of the POLCON measure over the period 1970-1994 and split the sample of countries into a high and low grouping, using the median value in the sample as the threshold. The responses are robust to a 8-6 or 6-8 split of countries. The responses in Figure 8 for the two groups are supportive of the view that politically more constrained countries demonstrate more (cid:133)scal prudence. For example, the primary balance response of the low group is not signi(cid:133)cantly di⁄erent from zero, while the response of the high group is signi(cid:133)cant and positive. Interestingly, the rise in the primary balance for the high group countries is the result of a fall in primary expenditure following a cost-of-borrowing shock. Finally, the third row of Figure 8 sub-divides the 14 countries based on the historical indebtedness of the governments. Inference drawn from these impulse responses should be made with caution since there is a potential endogeneity problem, from the impulse responses, back to the groupings. The responses reveal that the primary balances of highly indebted countries do not respond to cost of borrowing shocks, while those for the less indebted countries do respond positively. Themediandebt-to-GDPratioofahighlyindebtedcountryrisesby2:7percentage points, while the debt-to-GDP ratio of a less indebted country is insigni(cid:133)cantly di⁄erent from its initial level, at the 10 year horizon. Note that this result is not in contradiction to the (cid:133)nding reported in Figure 6. The subsampleestimationrevealsthatcountriesthathave,onaverage,highdebt-GDPratiosalsodisplay weakresponsestocostofborrowingshocks. TheresultsfromFigure6, incontrast, suggestthat when a country experiences a cost of borrowing shock at a time when its debt-to-GDP ratio is high relative to what is normal for that country, the (cid:133)scal response to that cost of borrowing shock is also stronger relative to its normal response. 18

Figure 8: Heterogeneity across sub-samples A. Maastricht Treaty Primary expenditure to GDP ratio Revenue to GDP ratio Primary balance to GDP ratio Debt to GDP ratio 0.8 0 0 0 0.6 0.2 0.2 0.4 0.4 0.4 2 0.6 0.6 0.2 4 0.8 0.8 0 1 1 0 5 10 0 5 10 0 5 10 0 5 10 Legend: (cid:7) post-1992 period, (cid:4) pre-1992 period B. Political constraints Debt to GDP ratio Primary expenditure to GDP ratio Revenue to GDP ratio Primary balance to GDP ratio 0.4 3 0.5 0.5 0.3 0.2 2 0 0 0.1 0 1 0.1 0.5 0.5 0 0 5 10 0 5 10 0 5 10 0 5 10 Legend: (cid:7) 7 least politically constrained countries, (cid:4) 7 most politically constrained countries C. Government indebtedness Debt to GDP ratio Primary expenditure to GDP ratio Revenue to GDP ratio Primary balance to GDP ratio 0.8 0.8 4 0.6 0.6 0.3 3 0.4 0.4 0.2 0.2 0.2 2 0.1 0 0 0 1 0.2 0.2 0.4 0.4 0.1 0 0 5 10 0 5 10 0 5 10 0 5 10 Legend: (cid:7) 7 countries with least indebted governments, (cid:4) 7 countries with most indebted governments Note: Impulse responses to a cost of borrowing shock. The y-axis is in percentage points, the x-axis is in years. The error bands are generated by Monte Carlo integration, showing the 14th, 50th and 86th percentiles. 19

Table 5: 8-variable VAR sign restrictions Primary Revenue Stock- GDP In(cid:135)ation Cost Short Long Variables: expenditure -to-GDP (cid:135)ow growth rate of interest interest -to-GDP adj. rate borrowing rate rate Shocks: Aggregate demand (+) (+) (+) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) Cost-push ( ) (+) (cid:1) (cid:1) (cid:1) (cid:0) (cid:1) (cid:1) (cid:1) Primary expenditure (+) (+) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) Revenue (+) ( ) (cid:1) (cid:1) (cid:0) (cid:1) (cid:1) (cid:1) (cid:1) Monetary policy ( ) (+) (+) (cid:1) (cid:1) (cid:1) (cid:1) (cid:0) (cid:1) Stock-(cid:135)ow adj. (+) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) Cost of borrowing (+) (+) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) Note: (+) or ( ) mean that the response of variable x to shock y on year of impact is restricted to be (cid:0) positive or negative, respectively. A blank space means no restriction has been imposed. 4.4 Expanding the model The results presented thus far are the product of a (cid:133)ve-variable VAR. We next expand the model to include an additional three endogenous variables: the stock-(cid:135)ow adjustment in (cid:133)scal accounts,ashort-termnominalinterestrate,andalong-termnominalinterestrate. Theimpulse responses following a cost of borrowing shock are presented in Figure 9. As noted earlier, in the baseline analysis, we treated the stock-(cid:135)ow adjustment as an exogenousi.i.d. shockprocess.15 Hereweincludeitasanadditionalendogenousvariable. Oneofthe notable omissions from the 5 variable VAR was any discussion of monetary policy. Unanticipatedmonetarypolicyshocksa⁄ectinterestratesatboththeshortandthelongendoftheyield curve, Kuttner (2001). Including the short-term interest rate (3 month interbank rate) and a long-term interest rate (10 year government bond yield) allows us to identify a monetary policy shock, and ensure that the cost of borrowing shock we identify is orthogonal to the monetary policy shock. The identifying assumptions for the expanded model are shown in Table 5. The (cid:133)rst four shocks we identify are as before. The (cid:133)fth shock we identify is the monetary policy shock. A monetary policy shock is identi(cid:133)ed by a contemporaneous increase in the short and long rates and a fall in the in(cid:135)ation rate, as well as by it being orthogonal to the preceding four shocks. Almost by construction though (due to the orthogonality restriction), the in(cid:135)ation rate is unchanged on impact. The sixth shock is the stock-(cid:135)ow adjustment, and the seventh is the cost of borrowing shock. While before we identi(cid:133)ed the cost of borrowing shock simply by the orthogonality requirements to the preceding shocks, and the cost of borrowing rising, in this VAR, we identify the cost of borrowing shock as simultaneously increasing both the long rate and the nominal cost of borrowing. The responses in this expanded VAR are broadly similar to the (cid:133)ve variable VAR. The response of the primary balance is greater, rising to 0:5% of GDP at the end of the 10 year horizon. However, the rise in the debt-to-GDP ratio is also greater, with the median response reaching a maximum of 2:8 percentage points of GDP above baseline in year 6 following the shock. This is, in part, because the rise in the in(cid:135)ation and growth adjusted cost of borrowing is more persistent. Asone(cid:133)nalexperiment, wealsotesttherobustnessofourmeasureforthecostofborrowing. 15Thisstock-(cid:135)owadjustmentcaptures,amongotherthings,changesinthesizeofforeign-currencydenominated debt associated with a change in the exchange rate, (cid:133)nancial transactions in relation to government support to (cid:133)nancialistitutions,privatizationreceiptsandthepurchaseofassets. During(cid:133)nancialcrises,itcanthusbecome an important determinant of government debt developments. 20

As discussed in Section 3, (cid:133)scal adjustment is likely to be a factor both of the marginal cost of borrowing and the average cost of borrowing, and we conjectured a relationship between these two measures. In practice, the 10 year bond yield measure is only a proxy for the marginal cost of borrowing as governments can borrow using various bonds of di⁄erent maturities. Thus, an increaseinthe10yearbondyieldislikelytooverstatetheriseinthemarginalcostofborrowing, unless there is a level shift in the entire yield curve. In any case, in Figure 10, we report the impulse responses to a cost of borrowing shock where we identify the cost of borrowing shock only as a rise in the long-term bond yield. It is clear that the true nominal cost of borrowing only increases with a lag, and that it increases by less than the increase in the long-term bond yield.16 The result is a more modest (cid:133)scal response, with the primary balance not turning signi(cid:133)cantly positive until 7 years following the shock. Wehaveappliedseveraladditionalrobustnesscheckstoourestimates. Theseincludealtering the identifying sign restrictions for various shocks, altering the order in which some of the shocks are identi(cid:133)ed, and altering the de(cid:133)nition of some of the variables used. These additional robustness checks are available in the online appendix. 5 Conclusions This paper examines the response of (cid:133)scal variables to exogenous changes in the cost of public borrowing using a panel of European countries over four decades. Consistent with a simple theoretical model of (cid:133)scal behaviour, our results suggest that governments react to increases in the cost of borrowing by increasing their primary balances over several years. At the sample average, however, this response is not su¢ ciently strong to return the debt-to-GDP ratio to baselineovera10-yearhorizon. Theadjustmentisfoundtoonlybecomestatisticallysigni(cid:133)cant two years after the shock and to be generated mainly via the revenue side. At the same time, there is some tentative evidence that the magnitude of adjustment in response to a cost of borrowing shock is larger when the debt-to-GDP ratio is cyclically high. Also, the larger the adjustment, the more emphasis is placed on expenditure cuts relative to tax increases. When subdividing our sample, we (cid:133)nd that EMU countries in the period after the signing of the Maastricht Treaty show a signi(cid:133)cantly stronger budgetary response to cost-of-borrowing shocks than the same countries in the pre-Maastricht period. A possible interpretation of this patternisthatthosecountriesthateventuallyjoinedmonetaryunionhadanadditionalincentive tocompensateforhigherinterestpayments(whichcountagainsttheMaastrichtde(cid:133)citcriterion) by tightening their stance with respect to other budget items. Our results have important policy implications. The estimated average (cid:133)scal response suggests that market discipline can improve budgetary outcomes. Provided that (cid:133)nancial market participantssystematicallyandconsistentlysanctiondeteriorating(cid:133)scalpositionsthroughhigher interest rates, they may deter governments from building up imbalances. At the same time, experience since the start of EMU shows that the relationship between the (cid:133)scal (cid:147)health(cid:148)of a country and its borrowing rates can be subject to abrupt shifts, which renders (cid:133)nancial markets less reliable as an incentive mechanism for governments. Moreover, our estimates show that the budgetary response to market pressure tends to be delayed and alone is not su¢ cient to fully counteract its direct unfavourable e⁄ect on debt dynamics via rising interest payments. This in turn, suggests that further incentive mechanisms are needed to ensure that countries follow a (cid:133)scal reaction function aimed at restoring (cid:133)scal sustainability in a timely manner. Judging from our results, (cid:133)scal rules are an important complement to markets in this regard. 16Ifweusetheresponseofthecostofborrowinginyear1asourestimateofdiaverage=dimarginal thewegetan estimate of the average maturity of debt of 1=0:18 5:6 years. (cid:25) 21

Figure 9: Impulse Responses to a Cost of Borrowing Shock 8 variable VAR Primary expenditure to GDP ratio Inflation rate C.o.B. (inflation & growth adjusted) 1 5 variable VAR (Baseline) 0.2 8 variable VAR 0.2 0.8 0.1 0.6 0 0 0.4 0.2 0.1 0.2 0.4 0.2 0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 Revenue to GDP ratio C.o.B. (nominal) Primary balance to GDP ratio 0.5 1 0.4 0.2 0.8 0.3 0 0.6 0.2 0.4 0.1 0.2 0.2 0 0.4 0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 Cumulative p.b. to GDP ratio Stock flow adjustment Short term interest rate 0.5 3 0.3 2 0.2 0 1 0.1 0.5 0 0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 Debt to GDP ratio Output growth rate Long term interest rate 4 0.15 0.8 3 0.1 0.6 0.05 0.4 2 0 0.2 0.05 1 0 0.1 0.2 0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 Note: The cost of borrowing shock is ordered seventh and orthogonal to the business cycle, (cid:133)scal and monetary policy shocks. The y-axis is in percentage points, the x-axis is in years. The error bands are generated by Monte Carlo integration, showing the 14th, 50th and 86th percentiles. Responses have been normalized to a 1 percentage point rise in the cost of borrowing. The debt-to-GDP ratio is initially 0.5. 22

Figure 10: Impulse Responses to a 10yr Bond Yield Shock Cost of borrowing (nominal) Long term interest rate Primary balance to GDP ratio 1.5 1.5 0.2 1 1 0.1 0.5 0.5 0 0 0 0.1 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 Note: The cost of borrowing shock is ordered seventh and orthogonal to the business cycle, (cid:133)scal and monetary policy shocks. The y-axis is in percentage points, the x-axis is in years. The error bands are generated by Monte Carlo integration, showing the 14th, 50th and 86th percentiles. Responses have been normalized to a 1 percentage point rise in the 10 year bond yield. The debt-to-GDP ratio is initially 0.5. References Afonso, A. and C. Rault (2011). Long-run determinants of sovereign yields. Economics Bulletin 31(1). Alesina, A. and R. Perotti (1995). Fiscal expansions and adjustments in OECD countries. Economic Policy 10(21), 207(cid:150)248. Aoki, K. (2006). Optimal commitment policy under noisy information. Journal of Economic Dynamics and Control 30(1), 81 (cid:150)109. Ardagna, S., F. Caselli, and T. Lane (2007). Fiscal discipline and the cost of public debt service: Some estimates for OECD countries. The B.E. Journal of Macroeconomics 7(1), Article 28. Attinasi, M., C. Checherita, and C. Nickel (2009). What explains the surge in euro area sovereign spreads during the (cid:133)nancial crisis of 2007-09? ECB Working Paper Series 1131. Bayoumi, T., M. Goldstein, and G. Woglom (1995). Do credit markets discipline sovereign borrowers? Evidence from U.S. states. Journal of Money, Credit and Banking 27(4), pp. 1046(cid:150)1059. Blanchard, O. and D. Quah (1993). The dynamic e⁄ects of aggregate demand and supply disturbances: Reply. The American Economic Review 83(3), 653(cid:150)658. Blanchard,O.andM.Watson(1986).Arebusinesscyclesallalike? InThe American Business Cycle: Continuity and Change, pp. 123(cid:150)180. University of Chicago Press. Bohn, H. (1998). The behavior of US public debt and de(cid:133)cits. The Quarterly Journal of Economics 113(3), 949(cid:150)963. Browning, E. K. (1976). The marginal cost of public funds. Journal of Political Economy 84(2), pp. 283(cid:150)298. Canova, F. and G. Nicol(cid:243) (2002). Monetary disturbances matter for business (cid:135)uctuations in the G-7. Journal of Monetary Economics 49(6), 1131(cid:150)1159. Christiano, L. J., M. Eichenbaum, and C. L. Evans (1999). Monetary policy shocks: What have we learned and to what end? Volume 1, Part A of Handbook of Macroeconomics, pp. 65 (cid:150)148. Elsevier. Devries, P., J. Guajardo, D. Leigh, and A. Pescatori (2011). A new action-based dataset of (cid:133)scal consolidation. IMF Working Paper 11(128). Evans, P. (1985). Do large de(cid:133)cits produce high interest rates? The American Economic Review 75(1), 68(cid:150)87. 23

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A Model appendix The (cid:133)rst-order conditions of the government(cid:146)s problem in equation (7) are: u u u 2;t 11;t 21;t 0 = u +(cid:22) n 1 (12) 1;t 1;t u2 (cid:0) u t (cid:0) 1;t 1;t ! ! u u u u u u u u 21;t 2;t 11;t 2;t 2;t 1 21;t 2;t 11;t +(cid:22) 2;t u (cid:0) u2 n t (cid:0) (cid:28) u (cid:0) u (cid:0) u (cid:0) u2 1;t 1;t ! (cid:18) 1;t 1;t (cid:0) 1 (cid:19) 1;t 1;t !! u u u u u 2;t+1 2;t 21;t 2;t 11;t + (cid:12)E (cid:22) , (cid:28) t 2;t+1 u (cid:0) u u (cid:0) u2 (cid:18) 1;t+1 1;t (cid:19) 1;t 1;t ! u u u u bh 2 bhb g 0 = u +(cid:22) 2;t 12;t 22;t n 2;t +(cid:12)E (cid:22) rh t +rh t t (13) 2;t 1;t u2 (cid:0) u t (cid:0) u t 1;t+1 1;t n 2;t n2 1;t 1;t ! 1;t! (cid:18) t (cid:19) t ! u u u u u u u u u 22;t 2;t 12;t 2;t 2;t 2;t 1 22;t 2;t 12;t +(cid:22) 2;t u (cid:0) u2 n t + 1+ u (cid:0) (cid:28) u (cid:0) u (cid:0) u (cid:0) u2 1;t 1;t ! (cid:18) 1;t (cid:19) (cid:18) 1;t 1;t (cid:0) 1 (cid:19) 1;t 1;t !! b g bh b g 2 u u u u u +(cid:12)E (cid:22) r g t t +r g t + 2;t+1 2;t 22;t 2;t 12;t , t 2;t+1 1;t n2 2;t n (cid:28) u (cid:0) u u (cid:0) u2 t (cid:18) t (cid:19) (cid:18) 1;t+1 1;t (cid:19) 1;t 1;t !! u = (cid:22) 1+ (g g ) (cid:12) E (cid:22) (g g ), (14) 3;t 2;t g t t 1 g t 2;t+1 t+1 t (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:1)bh b g (cid:22) = (cid:12)E (cid:22) rh+rh t +(cid:12)E (cid:22) r g t , (15) 1;t t 1;t+1 t 1;tn t 2;t+1 1;tn t t (cid:18) (cid:19) bh b g (cid:22) = (cid:12)E (cid:22) rh t +(cid:12)E (cid:22) r g +r g t , (16) 2;t t 1;t+1 2;tn t 2;t+1 t 2;tn t t (cid:18) (cid:19) u c = bh rh bh 2;t n , (17) t t (cid:0) t (cid:0) 1 t (cid:0) 1 (cid:0) u 1;t t and u u u 2 g t = b g t (cid:0) r t g (cid:0) 1 b g t (cid:0) 1 + 1+ u 2 1 ; ; t t n t (cid:0) 2 (cid:28) u 2 1 ; ; t t (cid:0) u 2 1 ; ; t t (cid:0) 1 1 (cid:0) 2 g (g t (cid:0) g t (cid:0) 1 )2. (18) (cid:18) (cid:19) (cid:18) (cid:0) (cid:19) The functional form for the utility function and the two interest rate equations (2) and (6) are as follows: c t n(cid:18) t 1 (cid:0) (cid:27) 1 u u(c ;n ;g ) = (cid:0) (cid:0) +(cid:31)log(g ) (19) t t t t t (cid:17) 1 (cid:27) (cid:0) (cid:0)(cid:1) bh bh b g bg rh = 1=(cid:12) (cid:11)h+(cid:30)hh exp t 1 +(cid:30)hg exp t 1 +(cid:29)(cid:24) (20) t (cid:0) n (cid:0) n (cid:0) n (cid:0) n (cid:0) t t t (cid:18) (cid:18) (cid:19) (cid:19) (cid:18) (cid:18) (cid:19) (cid:19) bh bh b g bg r g = 1=(cid:12) (cid:11)g +(cid:30)gh exp t 1 +(cid:30)gg exp t 1 +(cid:24) (21) t (cid:0) n (cid:0) n (cid:0) n (cid:0) n (cid:0) t t t (cid:18) (cid:18) (cid:19) (cid:19) (cid:18) (cid:18) (cid:19) (cid:19) B Data appendix All the data we use is publicly available. The majority of the data is taken from AMECO, whichistheannualmacro-economicdatabaseoftheEuropeanCommission(cid:146)sDirectorateGeneral for Economic and Financial A⁄airs (DG ECFIN). Some of the interest rate series have been supplemented using data from the International Financial Statistics (IFS) database of the IMF. 25

All variables used in the PVAR were year and country demeaned to account for country speci(cid:133)c and time speci(cid:133)c (cid:133)xed e⁄ects (and the degrees of freedom in the estimated model appropriately adjusted). All AMECO codes are provided in brackets. GDPgrowthrate isthegrowthrateofGrossDomesticProductatconstantprices(OVGD). (cid:15) In(cid:135)ation rate is the growth rate of the GDP De(cid:135)ator (PVGD). (cid:15) Nominal short-term interest rate (ISN). This is usually a 3 month interbank rate. See (cid:15) the AMECO website for further details of the country speci(cid:133)c interest rates used for this measure. Forseveralcountries,datafromtheIFSIMFCountryTables,row60c(Treasury Bill Rate) has been used to supplement series for missing values in AMECO. Cost of borrowing in the benchmark estimation is the Implicit Interest Rate (AYIGD), (cid:15) which is calculated as the ratio of total interest payments in year t to the debt stock in period t 1. Alternatively we use the Nominal long-term interest rate (ILN). This is (cid:0) usually a 10 year government bond yield. See the AMECO website for further details of the country speci(cid:133)c interest rates used for this measure. For several countries, data from the IFS IMF Country Tables, row 61 (Government Bond Yield) has been used to supplement series for missing values in AMECO. Debt is General Government Consolidated Gross Debt (UDGG) as a ratio of GDP. (cid:15) Revenue is the sum of Revenue from Indirect Taxes (UTVG), Revenue from Direct Taxes (cid:15) (UTYG) and Social Contributions Received (UTSG) as a ratio of GDP. Primary expenditure is the sum of Expenditure on Bene(cid:133)ts (UYTGH), Expenditure on (cid:15) Wages(UWCG)andExpenditureonOther(whichisTotalCurrentExpenditureexcluding Interest (UUCGI) minus Expenditure on Bene(cid:133)ts and Wages) as a ratio of GDP. 26

C Preliminary results This appendix contains the identi(cid:133)ed shocks and impulse responses of the 4 shocks of the 5 variable PVAR that we identify before the shock of interest - the cost of borrowing shock. Due to space constraints, we plot the identi(cid:133)ed shocks only for a sub-set of the countries in our sample. Further details are available from the authors on request. The error bands around the identi(cid:133)ed shocks and impulse responses are generated by Monte Carlo integration, and we plot the 14th, 50th and 86th percentiles. The identi(cid:133)ed shocks have, by construction a standard deviation of 1. We have included shaded areas to identify periods of recession. The impulse responses have been normalized so that a variable of interest (see notes on each graph) rises by 1% on impact of the shock, and have been drawn using an initial value of the debt-to-GDP ratio of 50%. C.1 Aggregate demand shock The aggregate demand shock is identi(cid:133)ed (cid:133)rst, requiring GDP growth, in(cid:135)ation and government revenue-to-GDP ratio to rise on impact. The identi(cid:133)ed aggregate demand shocks are plotted in Figure 11. Due to the use of both time- and country-(cid:133)xed e⁄ects, the aggregate demand shocks correspond well with recessions which have been country speci(cid:133)c, and corresponds less well with synchronized periods of recession. For example, if we look at the 2008-2011 period, countries thatexperiencedrelativelymildrecessionsappeartohaveexperiencedpositiveaggregatedemand shocks. The impulse responses to an aggregate demand shock are plotted in Figure 12. A one percentage point increase in GDP growth increases the government revenue-to-GDP ratio by approximately 0.7 percentage points. With an average revenue-to-GDP ratio of 0:45, this means a 1% rise in the GDP growth rate leads to an approximate 2:6% increase in revenues.17 This elasticity is above the estimate used by the European Commission. However, Mertens and Ravn (2011) formulate an argument why the methodology used by the European Commission might generate a downwardly biased estimate (although they use US data in their example). While the e⁄ect on output growth is relatively short-lived, the rise in the government revenueto-GDP ratio is more persistent. The aggregate demand shock leads to a strong decline in the debt-to-GDP ratio, because the primary balance improves, and because the shock generates a large fall in the growth and in(cid:135)ation adjusted cost of borrowing for the government. Two years following the shock, primary expenditure begins to rise, generating a reversal of the primary balance. C.2 Cost-push shock The (negative) cost-push shock is identi(cid:133)ed second, requiring in(cid:135)ation to fall on impact and GDP growth and revenues to rise, while also being orthogonal to the (cid:133)rst shock. The identi(cid:133)ed cost-push shocks are plotted in Figure 13. These identi(cid:133)ed shocks correspond well with the existing literature, being more volatile for most countries in the pre-1990s part of the sample. The impulse responses to a cost-push shock are plotted in Figure 14. We get a similar rise in the government revenue-to-GDP ratio on impact from a 1% rise in the GDP growth rate, as under an aggregate demand shock. The improvement in the primary balance for debt-to-GDP dynamicsishowevero⁄setbyasharpriseinthein(cid:135)ationandgrowthadjustedcostofborrowing. While the nominal cost of borrowing falls moderately, the fall in in(cid:135)ation is more than twice the rise in output growth. 17Theelasticityofrevenueswithrespecttooutputis(cid:24)= (cid:1)R=R. Themodelprovidesthefollowinginformation: (cid:1)Y=Y (cid:1)Y=Y =0:01,(cid:1)(R=Y) 0:007andR=Y 0:45. Usingtheapproximation,(cid:1)(R=Y)=(R=Y) (cid:1)R=R (cid:1)Y=Y (cid:25) (cid:25) (cid:25) (cid:0) we can rewrite the elasticity as (cid:24) 1+ (cid:1)(R=Y)=(R=Y) =1+ 0:007=0:45 =2:6. (cid:25) (cid:1)Y=Y 0:01 27

Figure 11: Identi(cid:133)ed Aggregate Demand Shocks Germany Ireland 5.00 5.00 3.00 3.00 1.00 1.00 1.00 1.00 3.00 3.00 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 Spain Italy 5.00 5.00 3.00 3.00 1.00 1.00 1.00 1.00 3.00 3.00 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 France Portugal 5.00 5.00 3.00 3.00 1.00 1.00 1.00 1.00 3.00 3.00 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 Greece UK 5.00 5.00 3.00 3.00 1.00 1.00 1.00 1.00 3.00 3.00 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 Note: The y-axis measures the identi(cid:133)ed aggregate demand shock with a unit standard deviation, the x-axis measures time in years. The error bands are generated by Monte Carlo integration, showing the 14th, 50th and 86th percentiles. The shaded areas are periods of recession. Figure 12: Impulse Responses to an Aggregate Demand Shock Primary expenditure to GDP ratio Output growth rate C.o.B. (nominal) 1 1 0.8 0.4 0.8 0.6 0.3 0.6 0.4 0.4 0.2 0.2 0.2 0.1 0 0 0.2 0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 Debt to GDP ratio Revenue to GDP ratio Inflation rate 1 1 1.5 0 0.8 1 0.6 1 2 0.4 0.5 3 0.2 0 0 4 0.2 5 0.5 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 Note: The aggregate demand is ordered (cid:133)rst. The y-axis is in percentage points, the x-axis is in years. The error bands are generated by Monte Carlo integration, showing the 14th, 50th and 86th percentiles. Responses have been normalized to a 1 percentage point rise in the GDP growth rate. The debt-to-GDP ratio is initially 0.5. 28

Figure 13: Identi(cid:133)ed Cost-Push Shocks Germany Ireland 5.00 5.00 3.00 3.00 1.00 1.00 1.00 1.00 3.00 3.00 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 Spain Italy 5.00 5.00 3.00 3.00 1.00 1.00 1.00 1.00 3.00 3.00 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 France Portugal 5.00 5.00 3.00 3.00 1.00 1.00 1.00 1.00 3.00 3.00 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 Greece UK 5.00 5.00 3.00 3.00 1.00 1.00 1.00 1.00 3.00 3.00 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 Note: The y-axis measures the identi(cid:133)ed cost-push shock with a unit standard deviation, the x-axis measures time in years. The error bands are generated by Monte Carlo integration, showing the 14th, 50th and 86th percentiles. The shaded areas are periods of recession. Figure 14: Impulse Responses to a Cost-Push Shock Primary expenditure to GDP ratio Output growth rate C.o.B. (nominal) 1 0 0.8 0.8 0.05 0.6 0.1 0.6 0.15 0.4 0.4 0.2 0.2 0.2 0.25 0 0.3 0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 Debt to GDP ratio Revenue to GDP ratio Inflation rate 0.8 0 1 0.5 0.6 0.5 1 0.4 0 1.5 0.2 2 0.5 0 2.5 1 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 Note: The cost-push shock is ordered second and orthogonal to the aggregate demand shock. The y-axis is in percentage points, the x-axis is in years. The error bands are generated by Monte Carlo integration, showing the 14th, 50th and 86th percentiles. Responses have been normalized to a 1 percentage point rise in the GDP growth rate. The debt-to-GDP ratio is initially 0.5. 29

Figure 15: Identi(cid:133)ed Primary Expenditure Shocks Germany Ireland 10.00 10.00 6.00 6.00 2.00 2.00 2.00 2.00 6.00 6.00 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 Spain Italy 10.00 10.00 6.00 6.00 2.00 2.00 2.00 2.00 6.00 6.00 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 France Portugal 10.00 10.00 6.00 6.00 2.00 2.00 2.00 2.00 6.00 6.00 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 Greece UK 10.00 10.00 6.00 6.00 2.00 2.00 2.00 2.00 6.00 6.00 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 Note: The y-axis measures the identi(cid:133)ed primary expenditure shock with a unit standard deviation, the x-axis measures time in years. The error bands are generated by Monte Carlo integration, showing the 14th, 50th and 86th percentiles. The shaded areas are periods of recession. C.3 Primary expenditure shock The primary expenditure shock is identi(cid:133)ed (joint) third, requiring the primary expenditure-to- GDP ratio and the GDP growth rate to rise on impact, while also being orthogonal to the two business cycle shocks. The identi(cid:133)ed primary expenditure shocks are plotted in Figure 15. The series of identi(cid:133)ed shocks is dominated by Ireland in 2010. Due to interventions in the banking system, the Irish government recorded a primary de(cid:133)cit-to-GDP ratio of 28%. The results of the model are not sensitive to the inclusion of this single data point. TheimpulseresponsestoaprimaryexpenditureshockareplottedinFigure16. Thenominal cost of borrowing does not rise on impact, but does increase in the medium term, rising by a maximum of 10 basis points. This is broadly consistent with the (cid:133)ndings of Ardagna, Caselli, and Lane (2007). The 0:5 percentage point increase in the GDP growth rate corresponds to a government spending multiplier of 0:2, substantially below 1.18 Assuming total revenues are unchanged, the expansion in output can explain the reduction in the revenue-to-GDP ratio on impact of the primary expenditure shock. This ampli(cid:133)es the deterioration of the primary balance. Expansionary government spending also generates a rise in in(cid:135)ation. C.4 Government revenue shock The government revenue shock is identi(cid:133)ed (joint) third, requiring the revenue-to-GDP ratio to rise and the GDP growth rate to fall on impact, while also being orthogonal to the two business cycleshocks. Notethatwedonotrequirethetwo(cid:133)scalpolicyshockstobeorthogonal,although adding this extra orthogonality restriction does not materially alter the results in the Section 4. The identi(cid:133)ed government revenue shocks are plotted in Figure 17. The impulse responses to a government revenue shock are plotted in Figure 18. A 1 percentage point rise in the revenue-to-GDP ratio has a bigger impact on GDP growth than a 1 18Thegovernmentspendingmultiplieris(cid:24)= (cid:1)Y=Y. Themodelprovidesthefollowinginformation: (cid:1)(E=Y)= (cid:1)E=E 0:01, (cid:1)Y=Y 0:005 and E=Y 0:45. Using the approximation, (cid:1)(E=Y)=(E=Y) (cid:1)E=E (cid:1)Y=Y we can (cid:25) (cid:25) (cid:25) (cid:0) rewrite the elasticity as (cid:24) (cid:1)Y=Y = 0:005 =0:2. (cid:25) (cid:1)Y=Y+(cid:1)(E=Y)=(E=Y) 0:005+0:01=0:45 30

Figure 16: Impulse Responses to a Primary Expenditure Shock Primary expenditure to GDP ratio Output growth rate C.o.B. (nominal) 0.8 0.5 0.6 0.4 0.1 0.4 0.3 0.05 0.2 0.2 0 0.1 0 0.2 0 0.4 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 Debt to GDP ratio Revenue to GDP ratio Inflation rate 0.5 2 0.8 0.4 0.6 1.5 0.4 0.3 1 0.2 0.2 0 0.1 0.5 0.2 0.4 0 0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 Note: The primary expenditure shock is ordered (joint) third and orthogonal to the two business cycle shocks. The y-axis is in percentage points, the x-axis is in years. The error bands are generated by Monte Carlo integration, showing the 14th, 50th and 86th percentiles. Responses have been normalized to a 1 percentage point rise in the primary expenditure-to-GDP ratio. The debt-to-GDP ratio is initially 0.5. percentagepointfallintheprimaryexpenditure-to-GDPratio. GDPgrowthfallsby1:5percentage points on impact, implying a impact tax revenue multiplier of 2:1, which is substantially (cid:0) greater than 1.19 Again, by assuming that primary expenditure is unchanged on impact due (cid:0) to a government revenue shock, the fall in the denominator of the primary expenditure-to-GDP ratio can account for its rise on impact of approximately 0:7 percentage points. The size of the revenue multiplier means that the rise in the primary-balance to GDP ratio is smaller than the rise in the revenue-to-GDP ratio. In addition, the fall in GDP growth (and subsequent fall in in(cid:135)ation) generate a rise in the in(cid:135)ation and growth adjusted cost of borrowing, causing the debt-to-GDP ratio to rise in the response to a positive revenue shock. 19The tax revenue multiplier is (cid:24) = (cid:1)Y=Y. The model provides the following information: (cid:1)(R=Y) = 0:01, (cid:1)R=R (cid:1)Y=Y 0:015andR=Y 0:45. Usingtheapproximation,(cid:1)(R=Y)=(R=Y) (cid:1)R=R (cid:1)Y=Y wecanrewrite (cid:25)(cid:0) (cid:25) (cid:25) (cid:0) the elasticity as (cid:24) (cid:1)Y=Y = 0:015 = 2:1. (cid:25) (cid:1)Y=Y+(cid:1)(R=Y)=(R=Y) 0:01(cid:0)5+0:01=0:45 (cid:0) (cid:0) 31

Figure 17: Identi(cid:133)ed Government Revenue Shocks Germany Ireland 3.00 3.00 1.00 1.00 1.00 1.00 3.00 3.00 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 Spain Italy 3.00 3.00 1.00 1.00 1.00 1.00 3.00 3.00 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 France Portugal 3.00 3.00 1.00 1.00 1.00 1.00 3.00 3.00 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 Greece UK 3.00 3.00 1.00 1.00 1.00 1.00 3.00 3.00 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 Note: The y-axis measures the identi(cid:133)ed government revenue shock with a unit standard deviation, the x-axis measures time in years. The error bands are generated by Monte Carlo integration, showing the 14th, 50th and 86th percentiles. The shaded areas are periods of recession. Figure 18: Impulse Responses to a Government Revenue Shock Primary expenditure to GDP ratio Output growth rate C.o.B. (nominal) 0 0.1 1 0.05 0.8 0.5 0 0.05 0.6 1 0.1 0.4 0.15 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 Debt to GDP ratio Revenue to GDP ratio Inflation rate 0 4 1 0.1 3 0.8 0.2 2 0.3 0.6 0.4 1 0.4 0.5 0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 Note: The government revenue shock is ordered (joint) third and orthogonal to the two business cycle shocks. The y-axis is in percentage points, the x-axis is in years. The error bands are generated by Monte Carlo integration, showing the 14th, 50th and 86th percentiles. Responses have been normalized to a 1 percentage point rise in the government revenue-to-GDP ratio. The debt-to-GDP ratio is initially 0.5. 32