Fiscal consolidation in an open economy with sovereign premia

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1 Fiscal consolidaion in an open economy wih sovereign premia Aposolis Philippopoulos y (Ahens Universiy of Economics and Business, and CESifo) Peros Varhaliis (Ahens Universiy of Economics and Business) Vanghelis Vassilaos (Ahens Universiy of Economics and Business) June 5, 204 Absrac We welfare rank various ax-spending-deb policies in a New Keynesian model of a small open economy feauring sovereign premia and loss of moneary policy independence. When we compue opimized sae-coningen policy rules, our resuls are: (a) Deb consolidaion comes a a shor-erm pain bu he medium- and long-erm gains can be subsanial. (b) In he early phase of pain, he bes scal policy mix is o cu public consumpion spending and raise consumpion ax raes o address he public deb problem, while, a he same ime, cu capial ax raes o miigae he recessionary e ecs of deb consolidaion. (c) In he long run, he bes way of using he scal space creaed is o reduce capial and labor axes; he anicipaion of such reducions plays a key role in he recovery from scal consolidaion. (d) The scal auhoriies should also care abou he oupu gap. Keywords: Feedback policy, New Keynesian, Sovereign premia, Deb consolidaion. JEL classi caion: E6, F3, H6 Acknowledgemens: We hank Fabrice Collard, Harris Dellas and Dimiris Papageorgiou for discussions and commens. We have also bene ed from commens by seminar paricipans a he Universiy of Zurich, he CESifo Area Conference on Macroeconomics in Munich 203, he Ahens Universiy of Economics and Business, and he Bank of Greece. The rs auhor hanks he Bank of Greece for is nancial suppor when his paper sared. The second auhor is graeful o he Irakleios Research Program for nancing his docoral sudies. Any views and errors are ours. y Corresponding auhor: Aposolis Philippopoulos, Deparmen of Economics, Ahens Universiy of Economics and Business, Ahens 0434, Greece. el: aphil@aueb.gr

2 Inroducion Since he global crisis in 2008, and afer years of de cis and rising deb levels, public nances have been a he cener of aenion in mos eurozone periphery counries. Alhough several policy proposals are under discussion, a paricularly debaed one is public deb consolidaion. Proponens claim his is for good reason: as a resul of high and rising public deb, borrowing coss have increased, causing crowding ou problems and undermining governmen solvency. Opponens, on he oher hand, claim ha deb consolidaion worsens he economic downurn and leads o a vicious cycle. A he same ime, as members of he single currency, hese counries canno use moneary policy o couner he recession and/or moneize public deb. Thus, he only macroeconomic ool available is scal policy. Wha is he bes use of scal policy under hese circumsances? Is deb consolidaion bene cial? Should he deb raio be sabilized a is currenly hisorically high level or should i be brough down? If brough down, how quickly? Do he answers o hese quesions depend on which ax-spending policy insrumens are used over ime? 2 This paper welfare ranks various scal policies in ligh of he above. The seup is a raher convenional New Keynesian model of a semi-small open economy. By semi-small, we mean ha he ineres rae, a which he counry borrows from he world capial marke, increases wih he public deb-o-gdp raio. 3 We focus on a moneary policy regime in which he semi-small open economy xes he exchange rae and, a he same ime, loses moneary policy independence; his mimics membership in a currency union. Hence, he only macroeconomic ool lef is scal policy. Then, following mos of he relaed lieraure on deb consolidaion, we assume ha policy is conduced via simple and implemenable feedback policy rules. 4 In paricular, we assume ha public spending and ax raes on consumpion, capial income and labor income are all allowed o respond, among oher hings, o he gap beween acual public deb and arge public deb as shares of oupu, as well as o he gap beween acual and arge We will use he erms deb consolidaion, scal adjusmen and scal auseriy inerchangeably. 2 For a discussion of he radeo s faced by policymakers in he case of scal adjusmen, see e.g. he EEAG Repor on he European Economy (204). 3 For empirical suppor of his assumpion, see e.g. European Commission (202). See also e.g. Bi (200, 202). For he small open economy model and deviaions from i, see Schmi-Grohé and Uribe (2003). 4 See e.g. Coenen e al. (2008), Forni e al. (200), Canore e al. (202), Cogan e al. (203), Erceg and Lindé (202, 203), Almeida e al. (203) and Pappa e al. (204). Economeric sudies on he e ecs of deb consolidaion include e.g. Peroi (996), Alesina e al. (202) and Baini e al. (202). 2

3 oupu. 5 We experimen wih various policy arge levels depending on wheher policymakers aim jus o sabilize he economy around is saus quo (de ned as a soluion consisen wih he curren daa), or wheher hey also wan o move he economy o a new reformed long run (de ned as a soluion wih lower public deb han in he curren daa and wihou sovereign premia). In addiion, since we do no wan our resuls o be driven by ad hoc di erences in feedback policy coe ciens across di eren policy rules, we focus on opimized ones, namely, on simple and implemenable policy rules ha also maximize households welfare. In paricular, adoping he mehodology of Schmi-Grohé and Uribe (2004 and 2007), we compue welfaremaximizing rules by aking a second-order approximaion o boh he equilbrium condiions and he welfare crierion. The model is solved numerically using common parameer values and scal-public nance daa from he Ialian economy during We choose Ialy simply because i exhibis mos of he feaures discussed in he opening paragraphs above. I hus looks as a naural choice o quanify our model. Before presening our resuls, i is worh recalling ha here is no such a hing like "he" deb consolidaion. The macroeconomic implicaions of deb consolidaion depend heavily on which policy insrumen bears he cos in he early phase of auseriy and on which policy insrumen is expeced o reap he bene in he lae phase, once he deb burden has been reduced and scal space has been creaed. 6 The coss in he early phase are due o spending cus and/or ax increases, while he opposie holds once scal space has been creaed. Our resuls (see below) con rm all his. Hence, he choice of scal policy insrumens maers for lifeime uiliy and oupu. This choice also maers for how quickly public deb should be brough down: he more recessionary are he scal policy insrumens used during he early cosly phase, he slower he speed of scal adjusmen should be. Naurally, here is more choice when we allow for policy mixes (for insance, when he policy insrumen(s) used in he early cosly phase can be di eren from hose used in he lae phase of scal space) han when 5 For empirical suppor of such rules, see e.g. European Commission (20). There is a rich lieraure on moneary and scal feedback policy rules ha includes e.g. Schmi-Grohé and Uribe (2005 and 2007), Pappa and Vassilaos (2007), Leih and Wren-Lewis (2008), Baini e al. (2008), Kirsanova e al. (2009), Leeper e al. (2009), Bi (200), Bi and Kumhof (20), Kirsanova and Wren-Lewis (202), Canore e al. (202) and Herz and Hohberger (203). 6 See e.g. Leeper e al. (2009) and Davig and Leeper (20) on how he impac of curren policy depends on expecaions of possible fuure policy regimes. See also Coenen e al. (2008) in a model wih deb consolidaion. 3

4 we are resriced o use a single insrumen all he ime. 7 Our main resuls are as follows. Firs, irrespecively of he scal policy chosen, deb consolidaion is bene cial only if we are relaively far-sighed. For insance, in our baseline compuaions, deb consolidaion is welfare-improving only if we care beyond he rs en years. Deb consolidaion always comes a a shor-erm loss in boh welfare and oupu (especially when changes in scal policy insrumens are resriced o be close o heir hisorical average values). Thus, he argumen for, or agains, deb consolidaion involves a value judgmen. Neverheless, once he shor-erm pain is over, he gains from deb consolidaion ge subsanial over ime. Second, under deb consolidaion, he bes scal policy mix found is o make use of all available ax-spending insrumens during he early cosly phase of scal auseriy and o reduce capial and labor ax raes - which are paricularly disoring - during he lae phase of scal space. Acually, he anicipaion of such reducions plays a key role in he recovery from scal auseriy. During he early cosly phase, he assignmen of insrumens o inermediae arges should be as follows: cu public consumpion spending and raise consumpion ax raes o address he public deb problem, while, a he same ime, reduce capial ax raes in order o miigae he recessionary e ecs of auseriy. Labor ax raes should also be used (i.e. raised) o help wih he deb problem, if changes in public spending and consumpion axes are resriced. Therefore, as argued by Wren-Lewis (200), he choice of he policy mix is imporan. Third, during he phase of deb consolidaion, scal policy insrumens should, in general, reac o boh public deb imbalances and he oupu gap. The shor-erm recession becomes oo sharp if he scal auhoriies pay aenion o deb imbalances only. Thus, i is no righ ha paying aenion o he oupu gap undermines he e or of scal consolidaion. I is worh reporing ha, relaively o a closed economy, recession is exra cosly in a semi-small open economy, because a fall in oupu riggers a furher rise in he deb raio ha pushes up sovereign premia. Neverheless, i should be emphasized ha feedback reacion o deb imbalances is necessary for ensuring deerminacy. 7 In oher words, he debae abou he bene s and coss of each insrumen used for deb consolidaion is essenially a debae abou he size of he muliplier of each insrumen. See he discussion in he EEAG Repor on he European Economy (204). 4

5 Papers close o ours include Coenen e al. (2008), Canore e al. (202), Erceg and Lindé (203), Almeida e al. (203) and Pappa e al. (204). Bu mos of hese papers do no sudy opimized policy rules; hey a priori choose he speed/pace of adjusmen or, in oher words, wheher deb consolidaion should be fronloaded or no. Canore e al. (202) do sudy opimal policy bu hey impose ha all ax raes change by he same proporion; also, in heir model for he US, here is moneary policy independence. Therefore, as far as we know, here have no been any previous aemps o: (i) Welfare rank a relaively rich menu of ax-spending policy insrumens. (ii) Sudy how resuls depend on wheher he governmen simply sabilizes he economy from shocks, or also reduces public deb, wihin a semi-small New Keynesian open economy wih sovereign premia and wihou moneary policy independence. (iii) Search for he bes mix of scal acion. Acually, a message from our paper is ha he popular quesion "spending cus or ax rises?" could be replaced by he quesion "wha is he bes assigmen of insrumens o arges?". The res of he paper is as follows. Secion 2 presens he model. Secion 3 presens he daa, parameerizaion and he saus quo soluion. Secion 4 discusses how we work. Resuls are in Secion 5. A sensiiviy repor is in Secion 6. Secion 7 closes he paper. Model deails are in an Appendix. 2 Model Consider a semi-small open economy where, as said above, semi-small means ha he ineresrae premium is deb-elasic (see e.g. Schmi-Grohé and Uribe, 2003). On oher dimensions, our seup is he sandard New Keynesian model of an open economy wih domesic and impored goods feauring imperfec compeiion and nominal Calvo-ype rigidiies (see e.g. Gali and Monacelli, 2005 and 2008). The domesic economy is composed of N idenical households indexed by i = ; 2; :::; N, of N rms indexed by h = ; 2; :::; N, each one of hem producing a di ereniaed domesically produced radable good, as well as of moneary and scal auhoriies. Similarly, here are f = ; 2; :::; N di ereniaed impored goods produced abroad. Populaion, N, is consan over ime. 5

6 2. Aggregaion and prices 2.. Consumpion bundles The quaniy of variey h produced a home by domesic rm h and consumed by domesic household i is denoed as c H i; (h). Using a Dixi-Sigliz aggregaor, he composie of domesic goods consumed by each household i, c H i;, is given by:8 NP c H i; = [c H i;(h)] h= () where > 0 is he elasiciy of subsiuion across goods produced in he domesic counry and =N is a weigh chosen o avoid scale e ecs in equilibrium. Similarly, he quaniy of impored variey f produced abroad by foreign rm f and consumed by domesic household i is denoed as c F i; (f). Using a Dixi-Sigliz aggregaor, he composie of impored goods consumed by each household i, c F i;, is given by: " NP c F i; = f= # [c F i;(f)] (2) In urn, having de ned c H i; and cf i;, household i s consumpion bundle, c i;, is: c i; = c H i; c F i; ( ) (3) where is he degree of preference for domesic goods (if > =2, here is a home bias) Consumpion expendiure, prices and erms of rade Household i s oal consumpion expendiure is: c i; = P H c H i; + P F c F i; (4) where is he consumer price index (CPI), P H is he price index of home radables, and P F is he price index of foreign radables (expressed in domesic currency). 8 As in e.g. Blanchard and Giavazzi (2003), we work wih summaions raher han wih inegrals. 6

7 Each household s oal expendiure on home goods and foreign goods are respecively: P H c H P i; = N P H (h)c H i;(h) (5) h= P F c F P i; = N P F (f)c F i;(f) (6) f= where P H (h) is he price of variey h produced a home and P F (f) is he price of variey f produced abroad, boh denominaed in domesic currency. We assume ha he law of one price holds meaning ha each radable good sells a he same price a home and abroad. Thus, P F (f) = S P H (f), where S is he nominal exchange rae (where an increase in S implies a depreciaion) and P H (f) is he price of variey f produced abroad denominaed in foreign currency. A sar denoes he counerpar of a variable or a parameer in he res-of-he world. Noe ha he erms of rade are de ned as P F P H while he real exchange rae is de ned as SP. (= SP H ), P H 2.2 Households Each household i acs compeiively o maximize expeced lifeime uiliy given by: X E 0 U (c i; ; n i; ; m i; ; g ) (7) =0 where c i; is i s consumpion bundle as de ned above, n i; is i s hours of work, m i; is i s real money holdings, g is per capia public spending, 0 < < is he ime discoun rae, and E 0 is he raional expecaions operaor condiional on he informaion se. The period uiliy funcion is assumed o be of he form (see e.g. Gali, 2008): u i; (c i; ; n i; ; m i; ; g ) = c i; n + i; n + + m m i; g + g (8) where n ; m ; g ;,, ; are preference parameers. Thus, is a coe cien of ineremporal subsiiuion and is he inverse of Frisch labour elasiciy. The period budge consrain of each household i wrien in real erms is: 7

8 = P ( + c H ) c H i; + P F c F i; k r k P H k i; + e! i; + H x i; + b i; + m i; + S P fi; h + h 2 + ( n ) w n i; + R b i; + P S P f h i; SP P f h i 2 = + S P P m i; + Q fi; h l i; (9) where x i; is i s domesic invesmen, b i; is he real value of i s end-of-period domesic governmen bonds, m i; is i s end-of period real domesic money holdings, f h i; is he real value of i s end-of-period inernaionally raded asses denominaed in foreign currency, r k denoes he real reurn o he beginning-of-period domesic capial, k i;, e! i; is i s real dividends received by domesic rms, w is he real wage rae, R denoes he gross nominal reurn o domesic governmen bonds beween and, Q denoes he gross nominal reurn o inernaional asses beween and ; l i; are real lump-sum axes/ransfers o each household, and 0 c ; k ; n are ax raes on consumpion, capial income and labour income respecively. Small leers denoe real values, namely, m i; M i; ; b i; B i; ; fi; h F i; h P ; w W ; e! i; e i; ; l i; T i; l, where capial leers denoe nominal values. The parameer h 0 measures ransacion coss relaed o foreign asses as a deviaion from heir long-run value, f h i. The law of moion of physical capial for each household i is: 2 ki; k i; = ( )k i; + x i; k i; (0) 2 k i; where 0 < < is he depreciaion rae of capial and 0 is a parameer capuring adjusmen coss relaed o physical capial. Each household i acs compeiively aking prices and policy as given. Deails of he household s problem and rs-order condiions are in Appendix. These condiions include he demand for he rm s produc used below. 8

9 2.3 Implicaions for price bundles Given he above, he hree price indexes are: = (P H ) (P F ) () NP P H = [P H (h)] h= " NP P F = f= [P F (f)] # (2) (3) 2.4 Firms Each domesic rm h produces a di ereniaed good of variey h under monopolisic compeiion and facing Calvo-ype nominal xiies. Nominal pro s of rm h are de ned as: e (h) P H (h)y H (h) r k P H (h)k (h) W n (h) (4) All rms use he same echnology as represened by he producion funcion: y H (h) = A [k (h)] [n (h)] (5) where A is an exogenous sochasic TFP process whose moion is de ned below. Pro maximizaion by rm h is subjec o he demand for is produc: y H (h) = y H P (h) = c H (h) + x (h) + g (h) + c F H (h) = P H (h) y H (6) so ha, demand for rm h s produc, y H (h), comes from domesic households consumpion and invesmen, c H (h) and x (h), where c H (h) P N i= ch i; (h) and x (h) P N i= x i;(h); from h i P H he domesic governmen, g (h) = (h) g, and from foreign households consumpion, c F (h) P N i= cf i; (h). P H In addiion, following Calvo (983), rms choose heir prices facing a nominal xiy. In 9

10 paricular, in each period, each rm h faces an exogenous probabiliy of no being able o rese is price. A rm h, which is able o rese is price a ime, chooses is price P # (h) o maximize he sum of discouned expeced nominal pro s for he nex k periods in which i may have o keep is price xed. This objecive is given by: X X E k ;+k+k e n (h) = E k ;+k P # (h) y+k H (h) +k y+k H (h)o k=0 k=0 where ;+k is a discoun facor aken as given by he rm, y H +k (h) = (:) is he minimum nominal cos funcion for producing y H P # (h) P+k H y H +k and (h) a so ha 0 (:) is he associaed nominal marginal cos. Deails of he rm s problem and rs-order condiions are in Appendix Governmen budge consrain The period budge consrain of he governmen wrien in real erms is (deails are in Appendix 3): + P H g where d D P d + m = R S d + Q P P P P S ( ) d + m c ( P H c H + P F c F ) k (r k P H k + e! ) n w n l + g 2 [( ) d ( ) d] 2 (7) is he real value of end-of-period oal public deb and m is he end-of-period oal sock of real money balances. As above, small leers denoe real values, e.g. d D : Toal public deb, D, can be held by domesic privae agens, D ; as well as by foreign privae agens, ( ) D ; where he share 0 is reaed as a scal policy insrumen. 9 Also, since he governmen allocaes is oal expendiure among produc varieies h by solving an h i P H idenical problem wih household i, g (h) = (h) g. The parameer g 0 measures ransacion coss relaed o foreign liabiliies similar o hose of he household. In each period, one of he scal policy insrumens ( c, k, n, g ; l ; ; d ) adjuss o saisfy he governmen budge consrain (see subsecion 2.7 below). 9 Focusing on a single open economy, we do no model he behavior of foreign invesors. P H 0

11 2.6 Closing he model: he world ineres rae As is known, o avoid nonsaionariies, we have o depar from he benchmark small open economy model (see Schmi-Grohé and Uribe, 2003). Here, we do so by endogenizing he ineres rae faced by he domesic counry when i borrows from he world capial marke, Q. In paricular, we assume ha Q, namely, he gross nominal ineres rae beween and +, is an increasing funcion of he end-of-period oal public deb as share of oupu, when he laer exceeds a cerain hreshold. 0 D P HY H, In paricular, following Schmi-Grohé and Uribe (2003) and Chrisiano e al. (20), we use he funcional form: Q = Q + e D P H Y H d! (8) where Q is exogenously given, d is an exogenous hreshold value above which he ineres rae on governmen deb sars rising above Q and he parameer measures he elasiciy of he ineres rae wih respec o deviaions of oal public deb from is hreshold value. See subsecion 3. below for hese values. 2.7 Moneary and scal policy regimes To solve he model, we need o specify he exchange rae and he scal policy regimes. Concerning he exchange rae regime, since he model is applied o Ialy over he las decade, we solve i for a case wihou moneary policy independence. In paricular, we assume ha he nominal exchange rae, S ; is exogenously se (see subsecion 2.9 below) and, a he same ime, he domesic nominal ineres rae on domesic governmen bonds, R ; becomes an endogenous variable. 2 Concerning scal policy, we sar by assuming ha, along he ransiion, he residually deermined public nancing policy insrumen is he end-of-period oal public deb, D (see below for oher cases). 0 As said above, his raher common assumpion is suppored by a number of empirical sudies (see e.g. European Commission, 202). Alernaively, o model sovereign premia, we could appeal o he noion of a scal limi or o he noion ha defaul is a sraegic choice of he sovereign (see Corsei e al., 203). The value of d can be hough of as any value of deb above which susainabiliy concerns sar arising. As we repor below, our qualiaive resuls are robus o he exac value of d used. 2 This is similar o he modeling of e.g. Erceg and Linde (202). Recall ha in he popular case of exible, or managed oaing, exchange raes, S and R swich posiions, in he sense ha S becomes an endogenous variable, while R is used as a policy insrumen usually assumed o follow a Taylor-ype rule.

12 2.8 Fiscal policy rules Wihou room for moneary policy independence, only scal policy can be used for policy acion. Following Schmi-Grohé and Uribe (2007) and many ohers, we focus on simple rules, meaning ha he scal auhoriies reac o a small number of easily observable macroeconomic indicaors (as we repor below in secion 6, our main resuls do no change when we add more indicaors). In paricular, we allow he spending-ax policy insrumens, 3 namely, governmen spending as share of oupu, s g, and he ax raes on consumpion, capial income and labor income, c, k and n, o reac o he oupu share of he beginning-of-period public liabiliies as deviaion from a arge value, (l l), as well as o he curren oupu gap, y H y H, according o he simple linear rules: 4 s g s g = g l (l l) g y y H y H (9) c c = c l (l l) + c y y H y H (20) k k = k l (l l) + k y y H y H (2) n n = n l (l l) + n y y H y H (22) where variables wihou ime subscrips denoe policy arge values (de ned below), and q l 0 and q y 0, for q (g; c; k; n), are feedback policy coe ciens on public deb and oupu respecively. From he governmen budge consrain in subsecion 2.5 above, l as: l R D + Q S S ( )D P H yh is de ned where S S is he gross rae of exchange rae depreciaion beween and. 3 We focus on disoring policy insrumens, because using lump-sum ones o bring public deb down would be like a free lunch. 4 For similar rules, see e.g Schmi-Grohé and Uribe (2007), Bi (200) and Canore e al. (202). As said above, see European Commission (20) for similar scal reacion funcions used in pracice. 2

13 2.9 Exogenous variables and shocks We assume ha foreign impors or equivalenly domesic expors, c F, are a funcion of erms of rade, T T P F P H values:, where boh variables are expressed as deviaions from heir long-run c F c F = T T (23) T T where 0 < < is a parameer. The idea is ha foreign impors rise when he domesic economy becomes more compeiive. Regarding he oher res-of-he-world variables, namely, he exogenous par of he foreign ineres rae, Q, and he gross rae of domesic in aion in he foreign counry, H H, P H we assume ha hey are consan over ime and equal o Q = :03 (which is he daa average - see below) and for simpliciy H = a all : We se he exogenous gross rae of exchange rae depreciaion, S + S, a one, while, he oupu share of lump-sum axes/ranfers, s l, and he share of domesic public deb in oal public deb,, are se respecively a s l = 0:2 and = 0:6 a all, which are heir daa average values (see below). Finally, sochasiciy comes from TFP, which follows: log (A ) = ( a ) log (A) + a log (A ) + " (24) where 0 < a < is a parameer, " a N 0; 2 a and, as said above, variables wihou ime subscrip denoe long-run values. As we repor below, our main resuls do no change when we add exra shocks. 2.0 Decenralized equilibrium (given feedback policy coe ciens) We now combine all he above o presen he Decenralized Equilibrium (DE) which is for any feasible policy and, in paricular, for any feedback policy coe ciens. The DE is de ned o be a sequence of allocaions, prices and policies such ha: (i) households maximize uiliy; (ii) a fracion ( ) of rms maximize pro s by choosing an idenical price de ned as P # ; while a fracion jus se prices a heir previous period level; (iii) all consrains, including he governmen budge consrain and he balance of paymens, are sais ed; (iv) markes clear; 3

14 (v) policy makers follow he feedback rules as speci ed in subsecion 2.8. This DE is given he exogenous variables, fc F ; Q ; H ; ; s l ; ; A g =0, which have been de ned in subsecion 2.9, iniial condiions for he sae variables and he values of he feedback policy coe ciens in he policy rules. We end up wih a rs-order dynamic sysem of 33 equaions. Deails and he nal equilibrium sysem are in Appendix 4. To solve his sysem, we ake a second-order approximaion of he model around is seady sae. We sar wih he saus quo seady sae soluion in he nex secion. In urn, we will sudy ransiion dynamics and he opimal choice of feedback policy coe ciens along he ransiion o a new reformed seady sae. 3 Daa, parameerizaion and seady sae soluion This secion parameerizes he model by using he averages of scal and public nance daa from Ialy over and hen presens he resuling seady sae soluion. Recall ha, since policy insrumens reac o deviaions of macroeconomic indicaors from heir long-run values, feedback policy coe ciens do no play any role in he long-run soluion. 3. Daa and parameer values The sources of scal and public nance daa for Ialy are OECD and Eurosa. The ime uni is mean o be a year. The baseline parameer values, as well as he values of policy variables, are summarized in Table. 4

15 Table : Baseline parameer values and policy variables Parameer Value Descripion a 0:42 share of capial 0:9603 rae of ime preference 0:5 home goods bias parameer a home 3:42 parameer relaed o money demand elasiciy 0:04 rae of capial depreciaion 6 price elasiciy of demand inverse of Frisch labour elasiciy elasiciy of ineremporal subsiuion 0:5 home goods bias parameer abroad 0:5 price rigidiy parameer 0:05 risk premium parameer m 0:00 preference parameer relaed o real money balances n 7 preference parameer relaed o work e or g 0: preference parameer relaed o public spending d 0:9 hreshold value for public deb as share of oupu a 0:92 persisence of TFP a 0:07 sandard deviaion of TFP 0:9 erms of rade elasiciy of foreign impors 0:3 adjusmen cos parameer on physical capial g 0:3 adjusmen cos parameer on foreign public deb h 0:3 adjusmen cos parameer on privae foreign asses c 0:7 consumpion ax rae k 0:32 capial ax rae n 0:42 labour ax rae s g 0:22 governmen spending as share of GDP s l 0:2 lump-sum ransfers as a share of GDP 0:6 share of oal public deb held by domesic privae agens The value of he rae of ime preference,, follows from seing he gross nominal ineres rae a R = :043 (his implies a risk premium of.% over he German 0-year bond rae, which is he average value in he daa) and he long-run gross price in aion rae a =. The real money balances elasiciy,, is borrowed from Pappa and Neiss (2005). We employ convenional values used by he lieraure for he elasiciy of ineremporal subsiuion,, he inverse of Frisch labour elasiciy,, and he price elasiciy of demand,, which are all aken from Andrès and Doménech (2006) and Gali (2008). Regarding preference parameers in he uiliy funcion, m is chosen so as o obain a yearly seady-sae value for real money balances as raio of oupu equal o 0:46, n is chosen so as o obain yearly seady-sae labour hours equal o 0:27; while g is se a 0.. The price rigidiy parameer,, is se a 0:5 (as we repor below, we have experimened wih various values of and all key resuls remain 5

16 una eced). In our baseline parameerizaion, he criical value of he oupu share of public deb, above which sovereign risk premia emerge, d; is se a 0.9. This value is consisen wih evidence provided by e.g. Reinhar and Rogo (200) and Checheria-Wesphal and Roher (202) ha, in mos advanced economies, he adverse e ecs of public deb arise when i is around 90-00% of GDP. I is also wihin he range of hresholds for susainable public deb esimaed by he European Commission (20). In urn, he associaed sovereign premium parameer,, is se a 0.05, which, joinly wih he value of d, implies a seady-sae premium for Ialy over he German rae equal o.. These values are in line wih empirical ndings for OECD counries (see Ardagna e al., 2004). As we repor below in secion 6, our resuls are robus o changes in hese parameer values. Concerning exogenous variables, he persisence and sandard deviaion parameers of he TFP shock are se respecively a a = 0:92 and a = 0:07 (he value of a is similar o ha in Schmi-Grohé and Uribe, 2007, while he value of a is close o ha in Bi, 200, and Bi and Kumhof, 2009). As repored below, our resuls are robus o changes in hese values. Regarding he res-of-he world variables, H, Q and c F, we se heir long-run average values equal o H = ; Q = :03 and c F = 0:9c F, where 0:9 is calibraed o replicae he ne expor posiion found in he Ialian daa. In he baseline parameerizaion, in equaion (23) for foreign impors is se a 0.9. The long-run values of scal and public nance policy insrumens, c, k ; n ; s g ; sl ; are se a heir daa averages. In paricular, c ; k ; n are he e ecive ax raes on consumpion, capial and labor in he daa over Moreover, s g and s l ; namely, governmen spending and lump-sum ransfer paymens as shares of oupu, are se a heir average values in he daa, which are 0.22 and 0.2 respecively. Finally, ; he share of oal public deb held by domesic privae agens is se a 0:6; which is again is average value in he daa during he same period. 3.2 Seady sae soluion or he "saus quo" Table 2 presens he seady sae soluion of he model economy when we use he parameer values and he policy insrumens in Table. In his soluion, we rea oal public deb, d, 6

17 as he residually deermined public nance insrumen. In Table 2, we also presen some key raios in he Ialian daa whenever available. Noice ha mos of he solved raios are close o heir acual values. In paricular, noice he soluion for oal foreign deb as share of oupu, which is ( s)dt T T T f h y H = 0:36; is value in he daa is very close, around 0.35 (see Diz Dias, 200, for exernal deb saisics of he euro area). Also, he soluion for oal public deb as share of oupu, D P H y H, is., which is again close o he daa average,.09. This soluion will serve as a poin of deparure. Tha is, in wha follows, we depar from his soluion o sudy various policy experimens. This is why we call i he "saus quo" soluion. In his soluion, a lower public deb o oupu raio implies a lower sovereign premium and his leads o higher capial, higher oupu and higher welfare. This can raionalize he deb consolidaion policies sudied in wha follows. Table 2: Seady sae soluion (he "saus quo") Variables Descripion Seady-sae soluion Daa n hours worked w real wage rae.3 - r k real reurn o physical capial Q Q ineres rae premium T T c consumpion as share of GDP y H k physical capial as share of GDP y H T T f h y H privae foreign asses as share of GDP s d D P H y H oal public deb as share of GDP..09 ( s)dt T T T f h oal foreign deb as share of GDP y H Noe: Variables and shares are denominaed in domesic currency. 4 The role of policy and soluion sraegy In his secion, we explain he policy scenaria, how we model deb consolidaion and how we compue opimized feedback policy rules. Recall ha, along he ransiion pah, nominal rigidiies imply ha money is no neural so ha moneary policy and he exchange rae regime maer o he real economy. As said in subsecion 2.7, here we focus on xed exchange raes and loss of moneary policy independence. Also, recall ha, along he ransiion pah, di eren couner-cyclical policy rules can have di eren implicaions. Thus, our aim is o welfare rank di eren couner-cyclical scal policy 7

18 rules when here is no room for moneary policy. 4. Two policy scenaria Moivaed by he recen policy debae, we sudy wo scenaria regarding policy acion. In he rs, used as a benchmark, he role of policy is only o sabilize he economy agains shocks. For insance, say ha he economy is hi by an adverse emporary TFP shock, which, as he impulse response funcions reveal, produces a conracion in oupu, a rise in he public deb o oupu raio and a rise in he sovereign premium. Then, he policy quesions are which policy insrumen o use, and how srong he reacion of policy insrumens o deviaions from arges should be, in order o maximize household s welfare crierion (see subsecion 4.3 below). Noe ha, in his case, he policy arges in he feedback rules (9)-(22) are given by he seady sae saus quo soluion. In oher words, in his policy scenario, we depar from, and end up, a he saus quo soluion in subsecion 3.2 above, so ha ransiion dynamics are driven by shocks only. The second scenario is richer. Now he role of policy is wofold: o sabilize he economy agains he same shocks as above and, a he same ime, o improve resource allocaion by gradually reducing he public deb o GDP raio over ime. The policy quesions are as above excep ha, now, he policy arges in he feedback rules (9)-(22) are given by he seady sae soluion of he new reformed economy. In oher words, in his case, we depar from he saus quo soluion wih sovereign premia, bu we end up a a new reformed seady sae wih lower public deb and zero premia. Thus, now here are wo sources of ransiion dynamics: emporary shocks and he deerminisic di erence beween he iniial and he new reformed long run (see also Canore e al., 202). The nex subsecion provides deails for he deb consolidaion scenario. 4.2 Deb consolidaion We assume ha, in he reformed economy, he governmen reduces he share of public deb from 0% (which is is average value in he daa over he sample period and was also our saus quo soluion) o he arge value of 90%. Since, in our model, sovereign risk premia arise whenever public deb happens o be above he 90% hreshold, premia are also eliminaed once 8

19 such consolidaion has been achieved. Deb reducions can be accommodaed by adjusmens in he ax-spending policy insrumens, namely, he oupu share of public spending, and he ax raes on capial income, labour income and consumpion. I is widely recognized ha deb consolidaion implies a radeo beween shor-erm pain and medium-erm gain. During he early phase of he ransiion, deb consolidaion comes a he cos of higher axes and/or lower public spending. In he medium- and long-run, a reducion in he deb burden allows, oher hings equal, a cu in ax raes, and/or a rise in public spending. Thus, one has o value he early coss of sabilizaion vis-a-vis he mediumand long-erm bene s from he scal space creaed. I is also widely recognized ha he implicaions of scal reforms, like deb consolidaion, depend heavily on he public nancing policy insrumen used, namely, which policy insrumen adjuss endogenously o accommodae he exogenous changes in scal policy (see e.g. Leeper e al., 2009, and Davig and Leeper, 20). In he case of deb consolidaion, such implicaions are expeced o depend boh on which policy insrumen bears he cos of adjusmen in he early period of adjusmen and on which policy insrumen is expeced o reap he bene, once consolidaion has been achieved. Noice ha if lump-sum policy insrumens were available, he coss of scal adjusmen would be rivial. Given he above, o undersand he logic of our resuls, and following usual pracice in relaed sudies, we will sar by experimening wih one scal insrumen a a ime. This means ha we allow only one of he scal policy insrumens o reac o deb and oupu gaps during he ransiion phase and, a he same ime, i is he same scal policy insrumen ha adjuss in he long-run o close he governmen budge. Thus, we will sar by assuming ha he same policy insrumen bears he cos of, and reaps he bene from, deb consolidaion. In urn, we will experimen wih scal policy mixes, which means ha we can use di eren insrumens in he ransiion and in he long run. Speci cally, we work as follows. We rs compare he seady sae equilibria wih, and wihou, deb consolidaion. In urn, seing as iniial condiions for he sae variables, heir values from he soluion of he economy wihou deb consolidaion (in paricular, from he saus quo soluion in subsecion 3.2), we compue he equilibrium ransiion pah as we ravel owards he seady sae of he new reformed economy. This is for each mehod of public 9

20 nancing used. The feedback policy coe ciens of he insrumen(s) used along he ransiion pah are chosen opimally. The way we compue opimized feedback policy rules wih, or wihou, deb consolidaion is explained in he nex subsecion. 4.3 Opimized feedback policy rules Irrespecively of he policy experimens sudied, o make he comparison of di eren policies meaningful, we compue opimized policy rules, so ha resuls do no depend on ad hoc di erences in feedback policy coe ciens across di eren policy rules. The welfare crierion is household s expeced lifeime uiliy. To do so, we work in wo seps. In he rs preliminary sep, we search for he ranges of feedback policy coe ciens, as de ned in equaions (9-22), which allow us o ge a locally deerminae equilibrium (his is wha Schmi-Grohé and Uribe, 2007, call implemenable rules). If necessary, hese ranges will be furher resriced so as o give economically meaningful soluions for he policy insrumens (e.g. ax raes less han one and non-negaive nominal ineres raes). In our search for local deerminacy, we experimen wih one, or more, policy insrumens and one, or more, operaing arges a a ime. In he second sep, wihin he deerminacy ranges found above, we compue he welfaremaximizing values of feedback policy coe ciens (his is wha Schmi-Grohé and Uribe, 2005 and 2007, call opimized policy rules). The welfare crierion is o maximize he condiional welfare of he household, as de ned in equaion (26), where condiionaliy refers o he iniial condiions chosen; he laer are given by he saus quo soluion above. To his end, following e.g. Schmi-Grohé and Uribe (2004), we ake a second-order approximaion o boh he equilibrium condiions and he welfare crierion. As is known, his is consisen wih riskaverse behavior on he par of economic agens and can also help us o avoid possible spurious welfare resuls ha may arise when one akes a second-order approximaion o he welfare crierion combined wih a rs-order approximaion o he equilibrium condiions (see e.g. Gali, 2008, pp. 0-, Malley e al., 2009, and Benigno and Woodford, 202). In oher words, we rs compue a second-order accurae approximaion of boh he condiional welfare and he decenralized equilbrium, as funcions of feedback policy coe ciens, by using he perurbaion mehod of Schmi-Grohé and Uribe (2004) and, in urn, we use 20

21 a malab funcion (such as fminsearch.m) o compue he values of he feedback policy coef- ciens ha maximize his approximaion. In his exercise, as said above, if necessary, he feedback policy coe ciens are resriced o be wihin some prespeci ed ranges so as o deliver deerminacy and give meaningful values for policy insrumens. All his is wih, and wihou, deb consolidaion. 5 Resuls In his secion, we presen he main resuls. The emphasis will be on he case of he reformed economy bu, for reasons of comparison, we also presen resuls for he case wihou deb consolidaion. We sar by de ning he region of feeback policy coe ciens ha give local deerminacy. Recall ha, as said in subsecion 4. above, in he case of deb consolidaion, ransiion dynamics are driven boh by a emporary adverse supply shock and by changes in scal policy insrumens aiming a public deb reducion and eliminaion of sovereign premia over ime. 5. Deerminacy areas As is known, local deerminacy depends crucially on he values of feedback policy coe ciens. Our experimens show ha economic policy can guaranee deerminacy when scal policy insrumens (s g, c, k, n ) reac o public liabiliies beween criical minimum and maximum values, where hese values di er across di eren policy insrumens. In paricular, he ranges of scal reacion o public liabiliies are 0:06 < g l < :7, 0: < c l < 3:79, 0:3 < k l < 2:35 and 0:4 < n l < :58 for s g, c, k and n respecively. By conras, he values of q y; where q (g; c; k; n), measuring he reacion of scal policy insrumens o he oupu gap, have no been found o be criical o deerminacy. 5.2 Resuls wih deb consolidaion (one scal insrumen a a ime) Wihin he deerminacy ranges, we now compue opimized policy rules and he associaed macroeconomic oucomes under deb consolidaion. As explained in subsecion 4.2, o undersand how he model works, we sar wih one scal insrumen a a ime ( scal policy mixes 2

22 are sudied in subsecions 5.3 and 5.4 below) Policy reacion and welfare Welfare resuls, wih deb consolidaion, are repored in Table 3. The rs colunm liss he scal policy insrumen used, while he opimal feedback reacion of his insrumen o he deb and oupu gaps during he ransiion are in he second column. Seady sae uiliy, u, is repored in he hird column, while expeced discouned lifeime uiliy, E 0 V 0, is repored in he las column (below we also repor welfare di erences expressed in consumpion equivalens). We repor ha he resuling values of all insrumens used are well-de ned in all soluions and over all periods, meaning ha ax raes and public spending shares are beween zero and one and ha he nominal ineres rae is above zero (below, in subsecion 5.4, we also repor resuls for he case in which changes in policy insrumens are furher resriced). The resuls in Table 3 show ha, if we rank scal insrumens according o expeced discouned lifeime uiliy or seady sae uiliy, and we are resriced o use a single scal insrumen a a ime, hen capial and labor ax raes score beer han he consumpion ax rae or he share of public spending. This superioriy becomes clearer when he comparison is in erms of seady sae uiliy. Table 3 : Opimized policy rules and welfare wih deb consolidaion (one scal insrumen a a ime) scal insrumen opimal reacion o deb and oupu seady sae uiliy u expeced discouned lifeime uiliy E 0 V 0 s g g l = 0:63 g y = 0:0085 0: :4068 c c l = 0:4599 c y = 0 0: :5520 k k l = 0:482 k y = 0 0: :492 n n l = 0:2677 n y = 0:0692 0: :322 Noes: In all soluions, R, 0 < s g, c, k, n < a all : The resul ha capial and, in urn, labor axes are beer when he crierion is seady sae uiliy is no surprising; once public deb has been reduced, he mos e cien way of aking 22

23 advanage of he scal space creaed is o reduce paricularly disoring axes like capial and labor. This is consisen wih he Chamley-Judd normaive resul ha he long-run capial ax rae should be zero. A more ineresing resul is ha capial and labor axes remain superior even when he crierion is expeced discouned lifeime uiliy. Tha is, alhough now here is an ineremporal radeo, expecaions of cus in capial and labor axes in he fuure dominae over any oher shor-erm e ecs and his shapes he lifeime welfare ranking in Table 3. Therefore, when we are resriced o use a single scal policy insrumen all he ime, he common belief ha i is beer o use public spending for deb consolidaion (see e.g. European Commission, 20) is no con rmed in a semi-small open economy wih sovereign premia. 5 Erceg and Lindé (203) also nd ha labor axes are beer in he shor run of an open economy. Table 4 : Opimized policy rules and welfare wih deb consolidaion when he residual insrumen in he long run is lump-sum ransfers scal insrumen opimal reacion o deb and oupu seady sae uiliy u expeced discouned lifeime uiliy E 0 V 0 s g g l = 0:27 g y = 0: c c l = 0:4505 c y = k k l = 0:4007 k y = n n l = 0:2567 n y = 0: Noes: In all soluions, R, 0 < s g, c, k, n < a all : The fac ha expecaions of cus in capial and labor axes in he fuure play a key role in shaping expeced discouned lifeime uiliy is con rmed when we assume insead ha he scal space creaed by deb consolidaion is used o increase lump-sum ransfers, raher han o reduce disoring axes, a seady sae. In his case, wih rivial expeced bene s from deb consolidaion, consumpion axes and governmen spending score beer han capial and labor axes in erms of lifeime uiliy. Resuls for his case are repored in Table 4. Noice ha now, since lump-sum ransfers do no a ec he real allocaion, he seady sae soluion 5 By conras, in a closed economy wihou sovereign premia, public spending scores he bes in erms of expeced discouned lifeime uiliy. Tha is, ransiion e ecs dominae over seady sae e ecs. See Philippopoulos e al. (202). 23

24 is he same across di eren scal policy insrumens Public deb and oupu Inspecion of he opimal values of he feedback policy coe ciens in Table 3 reveals ha he reacion o he oupu gap should be much smaller in magniude han he reacion o public deb. In oher words, when we are rescriced o use one scal insrumen a a ime, he concern for deb consolidaion should more han o se he concern for oupu sabilizaion. As a resul, public spending should fall, while all ax raes should rise, over ime unil hey converge o heir new reformed seady sae values. 6 Figure shows he implicaions of he above policies for he pah of public deb as share of oupu. This is for each scal policy insrumen used. For insance, he coninuous line shows he case in which we use he oupu share of public spending, s g, as he sae-coningen insrumen; ha is, as repored in Table 3, row, s g reacs o public deb and oupu wih feedback coe ciens g l = 0:63 and g y = 0:0085 respecively, while all oher policy feedback coe ciens are se a zero, meaning ha he oher policy insrumens remain consan a heir seady-sae values (daa averages). In a similar manner, he oher lines show resuls when we use c ; k and n. As can be seen, deb sars a 0%, which is is saus quo value, and ends up a 90% a he new reformed long run. In he shor run, he economy is also hi by a emporary adverse shock ha reduces oupu and furher increases he deb-o-oupu raio bu evenually, hanks o scal reacion, deb sars falling owards is 90% hreshold. 7 Inspecion of Figure reveals ha he duraion of he deb consolidaion phase, or equivalenly he speed of deb reducion, varies depending on which scal insrumen is used. In his policy experimen, if we use he consumpion ax rae, c, i should ake around ve years only o bring deb down; if we use capial axes, k, around seven years; if we use public spending, s g, above 5 years; and, nally, i should ake abou 20 years, in he case of labor axes, n. In oher words, deb reducion should ake place a a much lower speed when we use public spending and especially labor axes. This is because hese wo insrumens, namely cus in public spending and rises in labor axes, are more recessionary han rises in consumpion and 6 The associaed impulse response funcions are available upon reques. 7 As also discussed in European Commission (202), consolidaions can lead o increases in he deb o oupu raio in he shor run. This is driven by "he denominaor e ec". 24

25 capial axes during he early phase of deb consolidaion. Tha consumpion axes are less disoring is well known (see e.g. Bi, 200). On he oher hand, he explanaion for capial axes is ha, in he very shor run, he capial ax base is inelasic. Namely, in he very shor run, capial axes ac like a capial levy on predeermined wealh and his is no so disoring in shor ime horizons. Figure : Pah of public deb as share of oupu s g τ c τ k τ n Years Figure 2 shows he implicaions of he above policies for he pah of oupu, again for each scal policy insrumen used. As can be seen, since i is opimal o reduce deb gradually when we use labor axes, he recession lass longer; his is he cos of gradualism. By conras, when we use he oher scal policy insrumens, i is opimal o engineer a deeper recession a impac, which is a he bene of a quicker recovery laer on. 8 Noice ha alhough he use of public spending, s g ; is paricularly recessionary in he shor run (his is also he case in Erceg and Lindé, 203), he associaed fall in oupu is no so prolonged as when we use labor 8 Our resuls imply ha, a impac, he use of governmen spending causes an oupu loss of around 7%, while he same loss is around 6.5% if we use capial axes, 5.3% if we use consumpion axes and only 3.2% if we use labor axes. We also repor ha hese dynamics are primarily driven by deb consolidaion; even if we swich o he adverse TFP shock, he opimized policy rules imply ha deb consolidaion leads o a shor erm recession, irrespecively of wheher here are adverse shocks or no a he same ime. 25

26 axes. 9 Figure 2 : Pah of oupu s g τ c τ k τ n Years 5.3 Resuls wih and wihou deb consolidaion ( scal policy mixes) So far, we have sudied one scal insrumen a a ime. In paricular, as discussed in subsecion 4.2 above, we have resriced ourselves o he case in which we use a single insrumen all he ime. Alhough his has helped us o undersand how he model works, i is oo resricive. Policymakers are free o use policy mixes. Therefore, we now sudy he richer case in which policymakers can use di eren insrumens in he ransiion and in he long run and, in addiion, hey can use all available scal insrumens a he same ime during he ransiion. Since feedback policy co ciens are chosen opimally, his can also ell us how o assign di eren policy insrumens o di eren inermediae policy arges. 9 Thus, if we use labor axes only, i is opimal o spread he cos of deb consolidaion over more periods. To undersand his, recall ha here we have an open economy disored by sovereign premia, where he laer furher rise when he deb-o-oupu raio rises, or equivaleny when oupu falls. Thus, a big drop in oupu would be exra cosly here. Since an increase in labor ax raes is paricularly recessionary, i is beer o go for a relaively mild use of labor axes a impac which comes a he cos of a prolonged recession. By conras, in a closed economy wihou sovereign premia, he shor-erm recession is much sharper when we use labor axes (see Philippopoulos e al., 202). 26