When Should Public Debt Be Reduced?

I M F S T A F F D I S C U S S I ON N O T E When Should Public Deb Be Reduced? Jonahan D. Osry, Aish R. Ghosh, and Raphael Espinoza June 2015 SDN/15/10

When Should Public Deb Be Reduced? Prepared by Jonahan D. Osry, Aish R. Ghosh, and Raphael Espinoza 1 Auhorized for disribuion by Olivier Blanchard DISCLAIMER: This Saff Discussion Noe represens he views of he auhors and does no necessarily represen IMF views or IMF policy. The views expressed herein should be aribued o he auhors and no o he IMF, is Execuive Board, or is managemen. Saff Discussion Noes are published o elici commens and o furher debae. JEL Classificaion Numbers: H63, H68 Keywords: Public deb; public invesmen; economic growh Auhors E-mail Addresses: josry@imf.org; aghosh@imf.org; r.espinoza@ucl.ac.uk 1 We hank Olivier Blanchard, Vior Gaspar, Jun Il Kim, and Thomas Sargen for helpful commens and discussions and Anne Lalramnghakhleli Moses for assisance. INTERNATIONAL MONETARY FUND

CONTENTS EXECUTIVE SUMMARY 1 INTRODUCTION 2 PUBLIC FINANCES AND GROWTH IN ADVANCED ECONOMIES: A SNAPSHOT 6 A PURE THEORY OF PUBLIC DEBT AND INVESTMENT 8 Opimal Fiscal Policy 8 A Deb Shock 10 Paying Down he Deb 12 STYLIZED FACTS 14 CONCLUSIONS 18 REFERENCES 22 BOXES 1. A Formal Model of Deb, Invesmen, and Growh 20 2. Opimal Fiscal Policy 21 FIGURES 1. Fiscal Space: Disance o Deb Limi 4 2. Advanced Economies: Fiscal Developmens and Growh 7 3. Dynamics Under Low, Medium, and High Iniial Deb 11 4. Advanced Economies: Poscrisis Deb, Public and Privae Invesmen, and Public Consumpion 16 TABLES 1. OECD Counries: Public Deb, and Public Invesmen and Consumpion 17 2. OECD Counries: Governmen Revenues and Real GDP Growh 17 INTERNATIONAL MONETARY FUND

EXECUTIVE SUMMARY Financial bailous, simulus spending, and lower revenues during he Grea Recession have resuled in some of he highes public deb raios seen in advanced economies in he pas 40 years. Recen debaes have cenered on he pace a which o pay down his deb, wih few quesions being asked abou he desirable level of public deb o which he economy should converge following a deb shock. While some counries face deb susainabiliy consrains ha leave hem lile choice, ohers are in he more comforable posiion of being able o fund hemselves a reasonable even excepionally low ineres raes. For hese counries, here is a very real quesion of wheher o live wih high deb while allowing he deb raio o decline organically hrough growh, or o pay i down deliberaely o reduce he burden of he deb. This paper considers opimal public deb and invesmen policy in he afermah of he global financial crisis. I absracs from rollover risks faced by counries ha are near heir deb limis, and also from shorer-run cyclical consideraions. I is no ha hese consideraions are unimporan for hey surely are a presen in a number of counries. Bu hey are no he dominan facors for counries ha are near full employmen and enjoy considerable fiscal space (even in some cases despie relaively high levels of public deb, as argued in our earlier IMF Saff Posiion Noe on his opic, Osry and ohers [2010]), a se of counries ha are also in need of policy advice. Under hese condiions, economic heory provides hree insighs. Firs, inheried public deb, hough accumulaed for good reasons, represens a deadweigh burden on he economy, dimming boh is invesmen and growh prospecs; a corollary is ha an economy ha has inheried a lo of public deb (for example, because of a financial crisis) will raionally choose o inves less in public capial han one wih a lower level of deb. Second, if fiscal space remains ample, policies o deliberaely pay down deb are normaively undesirable. The reason is ha for such counries, he disorive cos of policies o deliberaely pay down he deb is likely o exceed he crisis-insurance benefi from lower deb. In such cases, deb-o-gdp raios should be reduced organically hrough growh, or opporunisically when less disorionary sources of revenue are available. Third, public deb should be issued o smooh he axes necessary o finance lumpy expendiures. This acion yields a version of he golden rule whereby public invesmen is deb-financed and underaken o he poin ha social reurns equal he marke ineres rae, wih he wis ha he social reurn will iself be reduced by he need o raise disorive axaion on labor and capial o service he higher deb. Wha consiues a safe level of deb (or ample fiscal space, as defined in Osry and ohers [2010]) is, needless o say, very difficul o pin down precisely in pracice, and can never be esablished hrough some mechanical rule or hreshold. Sress esing public-secor balance shees is essenial o form judgmens a he counry level of wha consiues a safe public deb level. I may be helpful o hink of deb levels as falling ino hree zones: a green zone, in which fiscal space is ample; a yellow zone, in which space is posiive bu sovereign risks are salien; and a red zone, in which fiscal space has run ou. This paper is concerned wih green-zone cases. Reducing deb in such cases is likely o be normaively undesirable as he coss involved will be larger han he resuling benefis. INTERNATIONAL MONETARY FUND

INTRODUCTION High public deb in advanced economies is an imporan legacy of he global financial crisis, as is an erosion of he public capial sock (alhough his laer problem sared a couple decades ago, and applies o no only several advanced economies, bu also many emerging marke economies and low-income counries, in which infrasrucure bolenecks and deficiencies are a hindrance o economic developmen). The firs problem poins in he direcion of reducing public deb, while he second (given ha economic heory srongly suggess ha invesmen should be financed by deb raher han axes) poins o increasing i. This laer issue is especially rue a he curren juncure, given he very low level of real ineres raes and he exisence of demand shorfalls in a number of advanced economies. Why do we hink ha high public deb should be reduced? The main raionale is essenially one of risk managemen, he desire for addiional margins o cope wih unanicipaed or coningen risks. The opion value of lower deb is paricularly high if here are risks of caasrophic evens (an example would be a financial crisis in which a public backsop is essenial), in which he governmen would need o ramp up borrowing massively (he more so given he poliical and economic limis o raising axes sharply in a pinch). If deb is high when such a shock occurs, a heavy penaly may be exaced as sovereign risk premiums rise and, in exreme cases, a shuou from markes would ensue. In oher words, deb needs o be reduced oday o lower he poenial risk of a sovereign crisis omorrow. A second raionale for why high public deb needs o be brough down is he belief ha high public deb weighs on economic growh. While causaliy runs boh ways, an imporan causal channel is axaion: high public deb implies he need o disor economic aciviy (labor, capial) o service he deb (eiher hrough axaion or cus in producive spending), which dampens economic growh. A reasonable idea is ha laying he foundaion for susainable growh requires paying he upfron cos of reducing he deb oday. For counries wih a demand shorfall and infrasrucure gaps, bu wih high and risky levels of public deb, here is hus an eviden radeoff beween building up he public capial sock and conaining sovereign risks and laying he foundaion for fuure growh. An excepion o he dilemma would be if deb-financed public invesmen spending acually lowered he deb raio, as can occur if Keynesian effecs are large, he ineres burden is minuscule, and invesmen is super-efficien (he argumen is no fundamenally differen from he one pu forward by supplysiders in he 1980s, ha ax cus would raise GDP and governmen revenue so much ha he deb raio would fall). While hese condiions may be salien in some counries a presen, few consider hem o consiue a se of neural assumpions ha should guide public policy in general. More likely, he ypical case is one in which he lunch of a public infrasrucure buildup has o be paid for wih higher deb, and hus a judgmen formed abou he weigh o aach o he differen fiscal objecives in specific cases. 2 INTERNATIONAL MONETARY FUND

This is why debaes a presen seem focused on wha is he greaer prioriy: lowering public deb or building public infrasrucure. For counries wih low deb and big infrasrucure needs (and wih idle resources and facing low ineres raes), building infrasrucure should be he greaer prioriy. For counries wih significan risk of fiscal disress, i is unlikely ha hey could afford o ake he chance of going on a borrowing spree, no maer how large he public invesmen deficiencies. Bu wha abou less clear-cu cases? Wha abou counries wih high deb, bu no plausible risk of fiscal disress, wih some infrasrucure needs, bu ha are operaing near full employmen and normal levels of real ineres raes? Perhaps he larges economies are no in his siuaion oday, bu hese condiions are no far-feched, and have prevailed for many counries in he pas. Wha policy advice applies o such counries? To ge a his issue, one needs an analyical framework ha absracs from he consideraions ha have ended o drive recen debaes: Keynesian demand managemen and risk of fiscal crisis (concepually, hese can be added back ino he model, bu we wan o focus on a separae se of issues, which have no been explored much o dae). Our approach allows one o focus on how public deb, public invesmen and growh inerac in siuaions in which he economy may be near full employmen and here is ample fiscal space (which can occur, as argued in our earlier IMF Saff Posiion Noe, Osry and ohers (2010), even if here is subsanial public deb Figure 1). 2 Two quesions seem especially relevan in such a framework. The firs relaes o he normaive implicaions of high public deb iself. One implicaion migh be ha i should be paid down in a reasonable imeframe (no oo fas so as o open up an oupu gap, for example), no only because of maerial effecs of sovereign risk, bu also because he deb iself represens a burden in he classic public finance sense disorive axaion is needed o service i, undercuing he foundaion of fuure economic growh. A fiscal effor oday saves on he fiscal burden in perpeuiy, providing a benefi equal o he presen value of he smaller disorion. Agains his argumen is he increase in disorionary axaion oday (or during he imeframe of he fiscal effor), which is cosly. Does a sandard public-finance model yield a predicion of he relaive size of he gain and losses? And how does his predicion relae o how o handle he deb shock? A second issue concerns he impac of he deb shock on he warraned level of public invesmen. Higher deb, as jus menioned, requires higher disorive axaion for servicing. Such axaion is likely o reduce he produciviy of labor and capial (facors ha are complemenary o public capial), meaning ha boh oupu and public capial should be lower han in a siuaion in which here is less public deb. Thus, here are implicaions of public deb for warraned public invesmen and, in urn, for he growh pah of he economy. 2 The discussion of fiscal space in Osry and ohers (2010) has since been adoped by Moody s in heir assessmen of fiscal risks in advanced economies. Boh analyses highligh he exisence of wide gaps (margins of maneuver) beween curren deb raios and public deb limis (poins a which marke access is likely o be curailed or sharp rises in sovereign borrowing coss ake place) in a number of advanced and emerging marke economies. 3 INTERNATIONAL MONETARY FUND

Figure 1. Fiscal Space: Disance o Deb Limi (percenage poins) Norway Souh Korea New Zealand Hong Kong Luxembourg Ausralia Taiwan Province of Taiwan China Swizerland Denmark Singapore Israel Sweden Finland Finalnd Germany Unied Saes Neherlands Ausria Mala Canada Iceland Unied Kingdom Belgium France Spain Ireland Porugal Japan Ialy Greece Cyprus 0 0 0 0 58.8 171.7 167.9 165.1 158.1 156.6 151.1 149.8 145.3 132.6 124.3 116.9 115.2 105.5 246 241.1 228.1 224.5 222.9 214.5 209.5 202 196.7 193 191.1 188.8 0 50 100 150 200 250 Grave risk (0-40) Significan risk (41-69) Cauion (70-124) Safe(>124) Source: Moody s Analyics (esimaes as of May 2014, hps://www.economy.com/dismal/fiscal-space/defaul.aspx) based on mehodology developed in Osry and ohers (2010) and Ghosh and ohers (2013). Noe: Fiscal space is defined as he difference beween he deb limi and he acual deb-o-gdp raio. Our benchmark seup is a closed-economy represenaive-agen model of domesic deb, so we absrac from iner- and inrageneraional disribuion issues, as well as he inernaional ransfer problem. 3 The only purpose of public deb is o shif ineremporally he coss associaed wih disorionary. Despie he absracion of he formal framework or perhaps because of i we are able o draw several clear policy-relevan insighs. 3 In an open economy, paying down exernal deb involves a cosly ransfer of resources abroad, so he closedeconomy assumpion acually sacks he argumen agains living wih he deb. Noe ha, since he analysis here perains solely o sovereigns ha are firmly in he green zone of ample fiscal space, crisis risk is ruled ou regardless of wheher he economy is open or closed: inasmuch as he governmen may be less willing o make an exraordinary fiscal effor o honor is deb if held by foreigners raher han domesic residens, he size of he green zone could conceivably be narrower in he open economy conex. As o ax incidence, in an open economy in which capial is mobile, i would be very difficul o ax ha capial, bu his is economically very similar o he closed-economy case in which he opimal capial ax rae falls o zero afer he iniial period (as in Chamley [1986]). Essenially, in he closed economy, capial is ineremporally mobile (invesmen will no maerialize if capial is axed), while in he open economy, i is mobile across borders, wih he same resul (i is very difficul o ax). Thus, we do no see sharply differen messages as far as ax incidence is concerned. 4 INTERNATIONAL MONETARY FUND

Inheried public deb represens a deadweigh burden on he economy, reducing boh invesmen poenial and growh prospecs. Alhough he deb may have been incurred for good reasons, for a given sock of public capial, he higher he inheried deb, he poorer he economy (by he presen value of he disorionary coss of he axaion needed o service he deb). Efficiency dicaes ha he larger he inheried deb, and hus he higher he level of axaion, he lower will be boh public and privae invesmen, and he lower will be oupu growh. Higher-deb economies will raionally inves less in public infrasrucure han less-indebed economies. Where counries reain ample fiscal space, governmens should no pursue policies aimed a paying down he deb, insead allowing he deb raio o decline hrough growh and opporunisic revenues, living wih he deb oherwise. The reason is ha he deadweigh loss associaed wih inheried public deb represens a sunk cos so, absracing from rollover risk, here is lile purpose in paying i down by raising axes or cuing producive governmen spending (of course if here is scope o cu unproducive spending his should be pursued). Disoring your economy o deliberaely pay down he deb only adds o he burden of he deb, raher han reducing i. When fiscal space is limied, incurring his cos is likely o be normaively desirable given he crisis-insurance benefi. When space is ample which canno be esablished hrough some mechanical rule bu will generally require judgmens based on sress esing fiscal balance shees o wihsand exreme shocks he disorive cos of paying down he deb is likely o exceed he crisis-insurance benefi. Deb should be used o smooh he axes necessary o finance lumpy governmen expendiures. For public invesmen, his implies deb-financing of projecs whose social marginal produc earns a leas he marke ineres rae. The wis on he sandard golden rule is recognizing ha he addiional deb incurred will need o be serviced wih disorionary axaion of facors (labor, capial) ha may be complemenary o public capial, hereby reducing he reurn o he public invesmen. Thus, he social rae of reurn will need o be higher as he public deb increases: while he quaniaive impac on he required rae of reurn is likely o be small (in he order of a few basis poins), he cumulaive effec on he long-run sock of public (and privae) capial will no be negligible. For plausible parameers, an increase in public deb of 50 percen of GDP (roughly he order of magniude experienced by many advanced economies since 2007) would lower seady-sae oupu and consumpion by 2 percenage poins in perpeuiy (implying a presen value welfare loss of 30 percen of iniial consumpion), wih a similar decline in long-run levels of privae and public capial. I is a feaure of he framework adoped here ha higher public deb leads o lower invesmen, slower ransiional growh, and a lower long-run level of oupu: deb is bad for growh. Despie he clear causaliy, i does no follow ha once he deb has been accumulaed, i should be paid down o resore growh. On he conrary, where counries reain ample fiscal space, he cure 5 INTERNATIONAL MONETARY FUND

would seem o be worse han he disease he axaion needed o pay down he deb will be more harmful o growh han living wih he deb, and he reducion in sovereign risk ha would ensue is likely o be smaller han he disorive cos involved in paying down he deb. PUBLIC FINANCES AND GROWTH IN ADVANCED ECONOMIES: A SNAPSHOT The global financial crisis has resuled in sharp increases in advanced-economy public deb raios, on a scale unprecedened in peace ime. On average, deb rose from 53 percen of GDP a end-2007 o almos 80 percen by end-2012, while for he op quarile, deb now exceeds 100 percen of GDP (Figure 2, op panel). Corresponding o his increase were below-he-line operaions (mainly financial-secor resrucuring coss) ogeher wih marked deerioraions in primary balances, which swung from an average surplus of 2.1 percen of GDP in 2008 o a defici of 4.4 percen in 2009, before recovering parially by 2012 (Figure 2, middle panel). In urn, he deerioraion in primary balances corresponded mainly o he loss of revenues and he operaion of auomaic sabilizers during he Grea Recession; very lile represened discreionary simulus, and of ha, only a small fracion was invesmen in public infrasrucure. Thus, while he accumulaion of public deb was generally for good reasons (avering an economic or banking sysem collapse), he fac remains ha mos advanced economies have buil up large socks of deb bu have lile or no more public infrasrucure o show for i. Along wih he deerioraion of he public finances came he collapse of oupu growh. Real GDP growh in advanced economies urned sharply negaive in 2009, rebounded somewha in 2010, and has remained moderae hereafer. Across counries, many differen facors were a play in he iniial growh collapse, which cerainly canno be aribued o he rise in public deb (he causaliy was almos surely he oher way around). Bu longer erm, i becomes more plausible ha he rise in public deb may have effecs on invesmen and growh. I is noeworhy, for insance, ha projecions for 2017 a full decade afer he onse of he crisis sugges ha advanced economies will have barely half heir precrisis growh raes, and projeced growh for 2013 17 is srongly negaively correlaed wih end-2012 public deb raios (he correlaion is.41, and saisically significan a he 5 percen level). These developmens raise imporan policy quesions: will he rise in public deb dim invesmen and growh prospecs? If so, should governmens seek o pay down heir deb as soon as possible? Or should hey embark upon ambiious public infrasrucure programs o help resore growh, aking advanage of low ineres raes? Answering such quesions requires a formal framework based on public finance heory, o which we now urn. 6 INTERNATIONAL MONETARY FUND

Figure 1. Advanced Economies: Fiscal Developmens and Growh 1/ 120 Gross Public Deb (percen of GDP) 100 80 60 40 20 6 2006 07 08 09 10 11 12 13 14 15 16 17 18 19 Primary Balance (percen of GDP) 4 2 0-2 -4-6 -8 6 2006 07 08 09 10 11 12 13 14 15 16 17 18 19 Real GDP Growh (percen per year) 4 2 0-2 -4-6 2006 07 08 09 10 11 12 13 14 15 16 17 18 19 Sources: IMF, World Economic Oulook and Fiscal Monior daabases. 1/ Average, and upper and lower quariles. 7 INTERNATIONAL MONETARY FUND

A PURE THEORY OF PUBLIC DEBT AND INVESTMENT To analyze he normaive aspecs of public deb i is useful o absrac from iner- and inrageneraional disribuion issues as well as he inernaional ransfer problem, and focus on he siuaion where he deb is one ha we owe ourselves. 4 To yield policy insighs, he framework mus incorporae wo feaures: a leas par of governmen spending should be on producive public capial; and only disorionary axes should be available o finance spending. In such a seup, public borrowing does no relax he economy s flow resource consrain, and public spending necessarily crowds ou privae spending. The purpose of public deb is o shif he burden of axaion over ime so as o reduce is oal disorive cos. Opimal Fiscal Policy A formal model wih hese feaures is presened in Box 1. The represenaive agen chooses how much o consume and o work, as well as invesmen in physical capial and governmen bonds. The firs-order condiions characerizing behavior are sandard, and imply ha labor supply will depend on he afer-ax wage; he demand for governmen bonds will be a funcion of he ineres rae; and privae invesmen will depend on he afer-ax reurn on capial. The governmen mus decide how much o inves in public capial, how much of he public consumpion good o provide, wha axes o levy on wages and on he reurn o privae capial, and residually, how much o borrow (Box 2). Public deb is in he form of one-period bonds and here is no possibiliy of defaul. The governmen is benevolen in he sense ha i chooses is fiscal policy o maximize he represenaive agen s lifeime uiliy, subjec o he economywide resource consrain, is own budge consrain, and a feasibiliy consrain. The laer summarizes he agen s endogenous response o axaion and is ineremporal budge consrain. For insance, if he governmen axes wages more heavily, labor supply will be reduced, and his needs o be aken ino accoun in he governmen s opimizaion problem. If non-disoring axes were available, he feasibiliy consrain would never bind. The firs-order condiions characerizing opimal fiscal policy are analogous o hose of he represenaive agen, excep ha privae marginal uiliies and raes of subsiuion ge replaced by heir corresponding social quaniies. The laer differ from he privae counerpars because of he feasibiliy consrain (ha is, because only disorionary axes are available). Thus he public consumpion good should be provided o he poin ha is marginal uiliy equals he social marginal cos of is provision, and public invesmen should be underaken o he poin 4 In pracice, of course, i makes a grea deal of difference who is he we and who is he ourselves. The assumpion ha deb is held by domesic residens is plausible for advanced economies where, on average, more han wo-hirds of public deb is held by residens (ranging from abou 30 percen in France and Germany o 70 percen in he Unied Kingdom and he Unied Saes, and more han 90 percen in he advanced economy wih he highes deb raio, Japan). On he ransfer problem, see Keynes (1929). 8 INTERNATIONAL MONETARY FUND

ha he marginal produc of public capial equals he social marginal rae of subsiuion across periods. Taxes on labor and capial should be chosen such ha he marginal disuiliy of work is equal o he marginal social value of producing more oupu, and he marginal produc of privae capial is equal o he social marginal rae of subsiuion across periods. Alhough social marginal uiliies and raes of subsiuion differ from he privae quaniies because axes are disorionary, a key resul ha emerges from he formal opimizaion problem is ha he governmen s implied discoun rae will equal he marke ineres rae. (In essence, he wedge beween privae and social valuaions is consan over ime, and herefore does no affec he discoun rae. 5 ) As discussed nex, his has imporan implicaions for opimal deb policy. An illusraive baseline scenario is depiced in Figure 3 (solid line) where, for ease of exposiion, i is convenien o sar wih a case where here is no axaion of privae capial. Saring from a low level of public capial, he governmen invess, raising oupu and consumpion of boh he privae and public goods unil he seady sae is reached. 6 The economy hus follows a sandard neoclassical growh paern. (I would be sraighforward o add exogenous echnical change, in which case he economy would be consanly converging on a shifing raher han a unique seady sae, bu his is inessenial o he analysis here.) Turning o public deb dynamics, here is a sharp iniial increase in deb (especially when he saring level of deb is high, dashed lines), followed by more seady increases along he opimal pah. Since he disorionary coss of axaion are convex (ha is, increasing a an increasing rae) in he ax rae, minimizing he oal disorionary cos involves smoohing ax raes over ime. The reason deb is issued here is hus wo-fold: firs, public invesmen apers off over ime, implying a declining pah of invesmen expendiure; second, growh of he economy implies a larger ax base (wage income). Boh effecs mean ha i is opimal o defer paymen for governmen expendiure by issuing public deb. Indeed, i can be shown ha a golden rule obains whereby here is an approximae one-o-one correspondence beween public invesmen and cumulaive primary deficis. Thus public invesmen is largely deb financed, and underaken o he poin ha is marginal produc is equal o he marke ineres rae on public deb. This is he sandard golden rule for public invesmen, alhough i bears emphasizing ha he deb will need o be serviced using disorionary axaion on facors complemenary o public capial (for example, labor, privae capial), hus reducing he marginal produc of public capial. While he quaniaive impac on he required social rae of reurn is likely o be small, he cumulaive effec on he sock of public capial is non-negligible a higher values of inheried deb. 5 This resul, originally due o Chamley (1986) for he long-run and o Chari, Chrisiano, and Kehoe (1994) in he shor run for a CES (consan elasiciy of subsiuion) uiliy funcion, is akin o Lile and Mirrlees (1974) argumen ha, even in counries wih highly disored capial markes, world ineres raes can be used for discouning reurns in projec evaluaion. 6 Oupu declines slighly as he seady sae is approached because leisure is a normal good, so he represenaive agen works less as he economy becomes richer. 9 INTERNATIONAL MONETARY FUND

A Deb Shock Wih hese preliminaries, we can urn o our quesion of ineres: wha happens if here is an exogenous increase in public deb? (The increase is exogenous in he sense ha i does no correspond o higher public invesmen or provision of he public good, bu raher resuls from some exraneous even, such as he fallou from a financial crisis.) Concepually, here are hree possibiliies. Opimal policy could involve paying down he deb immediaely so ha, following he iniial period, he deb pah reurns o he baseline scenario; or i could involve paying down deb more gradually, so here is gradual convergence o he baseline scenario; or he economy could simply live wih he higher deb forever. A priori, i is far from clear which will obain. On he one hand, paying down he deb quickly involves high raes of axaion and correspondingly large disorionary coss; on he oher hand, never paying i down means servicing i forever, hus incurring he disorionary coss of axaion in perpeuiy. To see which is opimal, he model oulined in Box 1 is solved numerically, and he effec of an iniial deb shock simulaed. I urns ou ha he opimal policy involves living wih he deb forever, so he new pah of deb is essenially parallel o he baseline pah (Figure 3). To undersand why, recall he key resul from he opimizaion problem ha despie privae and social valuaions being differen, he governmen s discoun rae will equal he marke ineres rae. Suppose, in any period, he governmen is considering paying down $1 of public deb. If i does so oday, i incurs he disorionary coss of raising anoher dollar of revenue. If i defers repaymen o omorrow, he deb will have grown by he marke ineres rae, (1+r), and he cos will be he disorion associaed raising an addiional $(1+r). Bu he governmen discouns he fuure a precisely he marke ineres rae, so i gains nohing by paying down a dollar of deb oday. 7 Since he same argumen can be applied o any period, he governmen will jus live wih he original inheried deb. In fac, applying Rober Barro s (1979) ax-smoohing argumen, i can be shown ha axes will be se so as o achieve a consan disorionary cos; once he seady sae is achieved, his will imply consan ax raes and revenues, he laer equal o he ineres paymens on he deb (if axes were se any higher, deb would decline, so evenually axes would decline, violaing he ax-smoohing principle; if se any lower, deb would grow explosively, evenually requiring higher axes, which again would violae he ax-smoohing principle). 7 In his simple heurisic explanaion, he ineres rae is reaed as consan; in he acual opimizaion in Box 2, he governmen akes ino accoun he endogeneiy of he ineres rae o he privae secor s saving decision and is own fiscal policies. Since here is no possibiliy of defaul here, here is no risk premium. In a fuller model, he governmen would also need o consider ha, as deb rises and he deb limi is approached, so will he risk premium; he governmen would in his fuller seup ake his ino accoun in solving for is opimal fiscal program (consumpion, invesmen, borrowing, axaion). The heoreical analysis in Osry and ohers (2010) and Ghosh and ohers (2013) suggess ha he risk premium only rises appreciably close o he deb limi, and he empirical analysis in Acharya, Drechsler, and Schnabl (2014) implies only modes increases in he risk premium wih higher deb. Since he analysis in his paper is solely for counries wih ample fiscal space, hese consideraions are no incorporaed here. 10 INTERNATIONAL MONETARY FUND

Even hough i is opimal for he governmen o live wih he deb, his inheried deb is no wihou is (negaive) consequences. An economy ha inheris a sock of public deb is poorer by he presen value of he disorions associaed wih raising he revenue o service ha deb. Higher iniial deb requires higher axaion o service i. Higher ax raes lower labor supply, reducing he marginal produc of (privae and public) capial, wih correspondingly lower invesmen and oupu. Since he wo economies in he simulaions sar a he same level of oupu, average growh in he economy wih higher iniial deb mus be lower han average growh in he low-deb economy. Deb is hus bad for growh here, wih he causaliy running from higher deb leading o lower growh via he higher axaion required o service i. Figure 3. Dynamics Under Low, Medium, and High Iniial Deb (in percen of GDP) 1/ Public Deb Public Capial 140 110 120 100 100 90 80 80 60 40 70 20 60 0 0 2 4 6 8 10 12 14 16 18 20 50 0 2 4 6 8 10 12 14 16 18 80 Privae Consumpion 110 Oupu 70 100 60 90 50 0 2 4 6 8 10 12 14 16 18 20 80 0 2 4 6 8 10 12 14 16 18 20 Low deb Source: Auhors' calculaions Medium deb High deb 1/ All variables expressed in percen of iniial GDP of he low-deb scenario 11 INTERNATIONAL MONETARY FUND

Nor is his effec negligible. To pu he magniudes in perspecive, he simulaion assumes ha iniial deb is some 50 percen of GDP higher han in he baseline (ha is, 100 percen of GDP raher han 50 percen of GDP). As a resul, in he seady sae, consumpion, oupu, he capial sock, and invesmen are abou 2 percenage poins lower permanenly compared o he couner facual. A reasonable discoun raes, he presen value welfare cos of inheriing 50 percen of GDP higher deb is abou 30 percen of he iniial period consumpion. Paying Down he Deb The analyical framework implies ha i is beer o live wih high deb han o pay i down. In par, however, his is because he model does no incorporae rollover risk. In realiy, here is a rade-off: paying down he deb may be cosly, bu doing so lowers he likelihood of a funding crisis. In underaking he cos-benefi calculus, a firs quesion is how much more cosly would i be o pay down he inheried deb han o live wih i? For plausible parameers, paying down 5 percen of GDP (ha is, one-enh of he addiional inheried deb 8 ) in one year incurs a presen value welfare cos equal o abou 1 percen of GDP. 9 Bu hese coss are highly nonlinear: paying down 10 percen of GDP of he deb would imply a welfare cos equal o 2 3 percen of GDP, and paying down 20 percen of GDP would incur a cos of a leas 6 percen of GDP. Wha abou he benefi? This is very dependen on he level of he deb and he disance o he sovereign s deb limi ha is, he available fiscal space (as defined in our earlier IMF Saff Posiion Noe on fiscal space, Osry and ohers [2010]). If fiscal space is ample, he benefi in erms of lowering he probabiliy of crisis by reducing deb is likely o be small. Of course, in realiy, assessing when fiscal space is ample (as Moody s have done for he counries in he green zone of Figure 1 based on he mehodology of Osry and ohers [2010]) is no a mechanical exercise. In paricular, assessing wheher pernicious nonlineariies may begin o ake hold requires deailed sress esing of public secor balance shees and judgmens abou economic resilience in he face of exreme shocks. I may hus be helpful o hink in erms of counries falling broadly ino hree zones: a green zone in which fiscal space is ample and he poenial for a sovereign crisis negligible; a yellow zone in which space is posiive and perhaps even sizable bu where, especially given he likelihood ha markes may give lile warning of a deb limi (as shown in Osry and ohers [2010] and Ghosh and ohers [2013]), sovereign risks are salien; and a red zone, in which fiscal space has run ou. As deb rises, moreover, counries may ransiion across zones, and he cos-benefi calculus of wheher o pay down he deb or no will evolve, 8 Paying down less incurs a smaller cos, bu of course would conribue o correspondingly smaller crisisreducion benefis. 9 Of course, if we were hinking in erms of an open economy and exernal deb, he welfare cos of paying down 5 percen of GDP in exernal deb would be his disorionary cos (1 percen of GDP) plus he 5 percen ransferred o foreigners (so 6 percen). The cos of paying down he deb would hus be much larger in an openeconomy seing han in he one here. In ha sense, he closed-economy seing acually sacks he argumen agains living wih he deb (since he cos of repaying he deb is much lower in he closed-economy seing). 12 INTERNATIONAL MONETARY FUND

paricularly as he risk premium and borrowing coss begin o rise hrough he yellow zone. The model in his paper perains o counries in he green zone, bu he pracical applicaion would facor in where counries lie along he fiscal space coninuum. Empirically, i is difficul o pin down he probabiliy of a crisis le alone how much ha probabiliy falls as deb declines because sovereign deb crises in advanced economies are rare. A recen daabase (Baldacci and ohers [2011]) of negaive fiscal evens (sovereign defaul, deb resrucuring, spike in spreads, or high inflaion), however, can help. For an advanced economy wih 120 percen of GDP of deb, he likelihood of a negaive even is esimaed o be abou 2.6 percen per year: over a 20 year horizon, he expeced number of crises is 0.52, wih a very generous esimae of he oupu cos associaed wih hese evens (mos of which are no a full blown sovereign deb crisis) being approximaely 15 percen of GDP. 10 A deb of 120 percen of GDP, herefore, he expeced loss is 7.8 percen of GDP. Suppose deb is lowered o 100 percen of GDP. The corresponding likelihood of an even is 2.4 percen per year, yielding an expeced loss of 7.2 percen of GDP. 11 In oher words, he expeced benefi of reducing deb from 120 percen of GDP o 100 percen of GDP is only abou 0.4 0.6 percen of GDP or around oneenh of he welfare cos due o disorionary axaion. 12 The calculaion above is very much predicaed on he sovereign being sufficienly far from is deb limi (ha is, having ample fiscal space). Obviously, a or very near he deb limi (in he yellow zone, bu close o he red zone hreshold), here will be enormous gain from reducing deb before a crisis occurs. Thus he conclusion is no ha i is never worh reducing deb in order o lower he likelihood of crisis. Indeed, wih he precise locaion of he deb limi uncerain, here is insurance value in keeping fiscal space agains he possibiliy of fuure shocks ha increase he sovereign s deb (his would apply o counries in he yellow zone). Bu for counries ha have ample fiscal space (clearly in he green zone), he benefi of reducing deb 10 The oupu cos is calculaed as he undiscouned sum over he hree years subsequen o he even of he difference beween acual and precrisis rend GDP. This esimae is in line wih oher sudies for example, Surzenegger (2004); Borenszein and Panizza (2008); Levy-Yeyai and Panizza (2011), alhough a few papers for example, Furceri and Zdzienicka (2011); De Paoli, Hoggarh, and Sapara (2009) sugges a permanenly lower GDP level and hus larger coss. 11 An alernaive approach o esimaing he likelihood of crisis is o use he probabiliy implied by marke spreads. Simple regressions of governmen bond yields on deb (wih counry-fixed effecs and ime effecs) for a panel of advanced economies suggess ha an increase in deb of 10 percen of GDP would be associaed wih 20 basis poin higher spreads, so reducing deb from 120 percen of GDP o 100 percen of GDP would be associaed wih 0.4 percenage poins lower spreads. Acharya, Drechsler, and Schnabl (2014) obain very similar esimaes: in heir sudy, 20 percen of GDP higher deb would be associaed wih 40 basis poins higher CDS (credi defaul swap) spreads. 12 A slighly differen way of calculaing he benefi (in erms of reducing he expeced cos of crises) of lower deb is o consider he probabiliy ha a leas one crisis occurs over he planning horizon (say, 20 years). A deb of 120 percen of GDP, his probabiliy is 41 percen ( 100 (1 (1 0.026) ^ 20)), whereas a 100 percen of GDP, he corresponding probabiliy is 38.5 percen; again, herefore, he esimaed benefi is small (0.37 percen of GDP ( 100 ((0.41 0.38) 0.15)). 13 INTERNATIONAL MONETARY FUND

(by deliberaely running overall surpluses) is unlikely o exceed he cos of he necessary disorionary axaion. In such cases, deb-o-gdp raios should be reduced organically, hrough oupu growh, or opporunisically, when less disorionary sources of revenue such as privaizaion receips or royalies are available. Wihin he confines of he formal model, here are wo such sources of shor-run inelasic revenue: income from iniial holdings of public deb and income from he iniial sock of privae capial. Boh of hese sources will be inelasic in he shor run, bu highly elasic in he longer run (because agens can choose o save less in he form of governmen bonds or privae capial when hey expec he income o be axed heavily). Since here is no explici ax on he income from governmen bonds here, he axaion akes he form of very low perhaps negaive real ineres raes in he iniial period. In a moneary model wih sicky prices, his could be achieved by cuing nominal ineres raes as indeed has been he case in advanced economies since he global financial crisis where policy raes have been a hisoric lows and have even flired wih he zero-bound. Wihin he confines of he real model presened here, low real ineres raes mus be engineered by cuing axes on he more elasic ax base (labor), giving a fillip o oupu and consumpion in he iniial period, and hus reducing he rae of reurn payable on he inheried deb. 13 A similar phenomenon occurs when here is he possibiliy of axing capial income. In he iniial periods, when he capial sock is fixed (ha is, before i depreciaes), capial income is inelasic and is axaion largely non-disorionary. Accordingly, he opimal fiscal program calls for heavy axaion o reduce public deb. Very quickly, however, he privae capial sock becomes highly elasic (he anicipaion of axaion will lead o lower invesmen) and he opimal ax rae on capial falls o zero. 14 In an economy wih an iniially inelasic source of revenue, he governmen should opporunisically pay down some of he inheried deb; he greaer he inheried deb, he larger he amoun paid down hrough such axaion. STYLIZED FACTS Since he analyical framework used here is largely normaive, i canno be formally esed agains saisical evidence. Neverheless, i may be ineresing o examine he exen o which counries have been following he framework s prescripions, and wheher some is implicaions hold empirically. This secion summarizes some sylized facs regarding deb, privae and public invesmen, and oupu growh using wo bodies of daa: he shor span since he 2008 global 13 See Lucas and Sokey (1983), Deboroli and Nunes (2010, 2012), and Krusell, Marin, and Rios-Rull (2008). 14 As argued by Chamley (1986), models of opimal axaion generally imply zero axaion of privae capial in he long run because privae capial becomes a fully elasic source of revenue. 14 INTERNATIONAL MONETARY FUND

financial crisis, and a longer span covering he period 1960 2008. The advanage of he poscrisis daa is ha, during he crisis, several advanced economies experienced large increases in public deb ha were almos enirely unrelaed o public invesmen. The downside, of course, is ha much else was happening in hese economies, and i may be oo early o ell wha will be he medium- o long-run impac of he increase in public deb on growh. Wih his cavea in mind, Figure 4 (op panel) repors he correlaion beween he change in deb over he period 2009 11 and he change in public gross capial formaion in percen of GDP (measured as he average for he period 2009 11 relaive o average 2005 07). In general, counries ha experienced larger increases in public deb were also hose ha reduced public invesmen he mos, wih he associaion saisically significan a 5 percen level. 15 Of course, sovereigns ha experienced he larges increases probably had o do he mos bel-ighening as well, so he negaive correlaion beween rising deb and shrinking public invesmen is no much of a surprise. Bu i is unlikely o be only he governmen s budge consrain a play: public consumpion shows no such negaive relaionship in fac, he relaionship is marginally posiive, albei saisically insignifican (Figure 4, middle panel). This finding likely reflecs a pragmaic approach by governmens who find i poliically easier o cu invesmen han curren expendiure, especially during an economic downurn. Bu i is noeworhy ha he analyical framework developed here would carry he same implicaion as a normaive saemen: given he higher inheried deb, and he higher disorionary axaion required o service i, he reurn o and herefore he amoun of public invesmen will be lower. Moreover, again consisen wih he analyical framework, he negaive relaionship beween he increase in public deb and he decrease in economywide gross fixed-capial formaion holds even more srongly in he daa (Figure 4, boom panel). Turning o more sysemaic evidence, Table 1 repors regressions of public invesmen on curren or (five-year) lagged public deb using five-year, non-overlapping averages of hese variables for a sample of advanced economies over he period 1960 2008. Again, here is a srong negaive relaionship beween public deb and eiher curren or subsequen public invesmen (Table 1, columns 1 2). Bu no such negaive relaionship can be seen beween deb and public consumpion (Table 1, columns 3 4). Beyond he observaion ha an economy wih higher public deb should and will do less public invesmen, he analyical framework implies ha, in general, i is beer (for boh growh and welfare) o live wih high deb han o ry o reduce i hrough disorionary axaion. Table 2 repors sandard growh regressions (again using 5-year non-overlapping averages for Organisaion for Economic Co-operaion and Developmen [OECD] counries). Higher ax raes (measured as revenues in percen of GDP) are indeed associaed wih lower growh, conrolling 15 We are no claiming ha he mechanism emphasized by our model is he only facor a play here: poliical consrains, for example, would likely have played a role in deermining he cubacks in public invesmen. 15 INTERNATIONAL MONETARY FUND

Figure 4. Advanced Economies: Poscrisis Deb, Public and Privae Invesmen, and Public Consumpion 1.0 Change in Governmen Gross Capial Formaion vs. Change in Public Deb 0.5 y = -0.008**x + 0.14 R² = 0.15 0.0-0.5-1.0-1.5-30 -20-10 0 10 20 30 40 50 60 70 80 90 100 4.0 3.0 2.0 Change in Governmen Consumpion vs. Change in Public Deb y = 0.007x + 1.5 R² = 0.03 1.0 0.0-1.0-2.0-30 -20-10 0 10 20 30 40 50 60 70 80 90 100 4 2 0-2 -4-6 -8-10 -12-14 -16-18 Change in Gross Fixed Capial Formaion vs. Change in Public Deb y = -0.11***x - 1.1 R² = 0.40-30 -20-10 0 10 20 30 40 50 60 70 80 90 100 Sources:IMF and Organizaion for Economic Co-operaion and Developmen. Noe: Change in public deb (in percen of GDP) 2007 11 vs. change in Governmen Fixed Capial Formaion, Governmen Consumpion, Economywide Fixed Capial Formaion avg(2005 07) avg(2009 11). 16 INTERNATIONAL MONETARY FUND

Table 1. OECD Counries: Public Deb, and Public Invesmen and Consumpion VARIABLES (1) (2) (3) (4) Public Invesmen Public Invesmen Public Consumpion Public Consumpion Deb/GDP -1.896*** 6.075*** [-3.954] [5.196] Deb/GDP (-1) -2.264*** 4.251*** [-3.495] [4.520] Consan 4.808*** 4.878*** 14.83*** 16.01*** [20.83] [16.48] [27.90] [38.13] Observaions 229 211 274 247 R-squared 0.168 0.211 0.277 0.174 Number of counries 26 26 34 34 Noe: Robus -saisics in brackes. *** p<0.01, ** p<0.05, * p<0.1. Table 2. OECD Counries: Governmen Revenues and Real GDP Growh 1/ (1) (2) (3) (4) (5) (6) VARIABLES FE FE FE A-Bond IV insrumens: FE excl. inv incl. deb 2-sep collapsed VAT and SSC raes incl. deb wih VAT Gv revenues (percen of GDP) -0.0396** -0.0424** -0.0399* -0.0866** -0.423** [-2.106] [-2.349] [-1.756] [-2.207] [-2.306] Deb/GDP (-1) -0.00463-0.00559 0.0164 0.0175 [-0.718] [-0.341] [0.984] [1.463] Populaion growh 0.424 0.532* 0.536* 0.557* 1.424** 1.083* [1.587] [1.937] [1.892] [1.762] [1.974] [1.923] Iniial GDP -0.0386*** -0.0266*** -0.0219*** 0.00238-0.0848* -0.0698** [-5.450] [-3.744] [-3.014] [0.556] [-1.827] [-2.178] Terms of rade growh 0.0437 0.0459 0.0383 0.0682-0.118 0.154 [1.475] [1.411] [1.166] [1.014] [-0.962] [1.646] Terms of rade volailiy 2.22e-05-3.59e-05 2.88e-05-0.000415 0.00357-0.00103 [0.0868] [-0.128] [0.105] [-0.860] [1.412] [-0.918] Log(inflaion) -0.00728*** -0.00280-0.00419-0.00902-0.0249*** -0.0123*** [-3.214] [-1.099] [-1.611] [-1.674] [-2.679] [-3.340] Invesmen (oal, percen of GDP) 0.159*** 0.271** [4.388] [2.519] VAT rae -0.00657*** [-4.289] Consan 0.129*** 0.127*** 0.128*** 0.00906 0.890** 0.627** [6.902] [6.508] [4.643] [0.284] [2.186] [2.261] Observaions 233 240 227 222 70 107 R-squared 0.707 0.669 0.651 0.596 0.736 Number of counries 27 Number of insrumens 24 Hansen es p -value 0.235 A-B AR(1) es p-value 0.000840 A-B AR(2) es p-value 0.829 Noe: FE= fixed effecs; SSC= social securiy conribuion; VAT= value added ax 1/ Depdenden variable: Non-overlapping, five-year average real GDP growh, 1960 2008. Robus -saisics in brackes. *** p<0.01, ** p<0.05, * p<0.1. Coefficiens for ime and counry dummy variables no shown. 17 INTERNATIONAL MONETARY FUND

for he oher usual growh deerminans such as populaion growh, iniial per capia income, erms of rade shocks, inflaion, and invesmen (Table 2, column 1). 16 Par of his effec is hrough lower invesmen (again, as he framework would sugges); dropping invesmen, he negaive coefficien on axes becomes larger in absolue value (Table 2, column 2). Nor are hese resuls likely o be driven by reverse causaliy: if ax revenues are responding o GDP growh, hen he esimaed coefficien would be posiive; he finding of a saisically significan negaive coefficien mus herefore be in spie of raher han because of any possible endogeneiy. Moreover, using he Arellano-Bond esimaor or insrumening using value-added ax (VAT) or social securiy ax raes yields similar resuls (Table 2, columns 4 6). Finally, i is noeworhy ha when curren or lagged deb is included in he regression (in addiion o axes), he coefficien is negaive bu insignifican; inheried public deb may be bad for growh (since axes will need o be somewha higher o service he deb even if he governmen choose o live wih he higher deb), bu wha really kills growh is disorionary axaion o service he deb and, a foriori, o pay i down. CONCLUSIONS Advanced economies are facing some of he highes raios of public deb since World War II. For hose counries ha are no a imminen risk of losing marke access, curren policy debaes cener on he appropriae pace a which o pay down public deb. Those who believe ha deb is bad for growh favor a rapid reducion in indebedness, whereas hose who sress Keynesian demand managemen consideraions argue for a measured pace of consolidaion, perhaps wih a ramping up of public invesmen while ineres raes remain a hisoric lows. Somewha los in his debae is he possibiliy of simply living wih (relaively) high deb, and allowing deb raios o decline organically hrough oupu growh. The purpose of his paper is no o provide direc policy advice, bu raher o elici a debae on wheher governmens should acively seek o pay down public deb or simply live wih high deb. The analyical framework proposed here suggess ha his hird course, of living wih high deb, meris consideraion in counries where deb susainabiliy concerns are no pressing. Indeed, while deb may be bad for growh, i does no follow ha i should be paid down as quickly as possible, even absracing from Keynesian effecs on aciviy and oupu. A he same ime, higher deb may imply lower reurns o public capial han prior o he crisis, implying ha a scaling-back of invesmen plans would be appropriae. 16 Our resuls are very similar when esimaing a cross-secion regression of growh over he period 1978 2007. In such regressions, conemporaneous ax revenues are significan, whereas lagged ax revenues and lagged deb are no significan variables. However, he lieraure on he effec of axes on growh has been less conclusive, as underlined by Easerly and Rebelo (1993). Mendoza, Milesi-Ferrei, and Asea (1997) also found ha alhough axes affec invesmen, he effec on growh is no robus. 18 INTERNATIONAL MONETARY FUND

The main insighs may be summarized in hree guiding principles for hinking abou public deb and invesmen dynamics: Inheried public deb represens a deadweigh burden on he economy, reducing boh is invesmen poenial and is growh prospecs. Alhough he deb may have been incurred for good reasons, he higher he inheried sock, he poorer he economy (by he presen value of he disorionary coss of he axaion need o service he deb). Efficiency dicaes ha he higher inheried deb and corresponding axaion, he lower should be public and privae invesmen, and he slower will be oupu growh. When fiscal space is ample which can never be esablished hrough some mechanical procedure here is a case for simply living wih he deb, paying i down only opporunisically when non-disorionary sources of revenue are available and leing he deb raio decline hrough growh. The deadweigh loss associaed wih inheried public deb represens a sunk cos so, absracing from rollover risk, here is lile purpose in paying i down by raising axes or cuing oherwise-producive governmen expendiure. Living wih he deb in such circumsances represens he bes cos-benefi radeoff. Deb should be used o smooh he axes necessary o finance lumpy governmen expendiures. For public invesmen, his implies deb-financing of projecs whose social marginal produc earns a leas he marke ineres rae, bu recognizing ha he addiional deb incurred will need o be serviced wih disorionary axaion of facors ha may be complemenary o public capial, hereby reducing he reurn o public invesmen. This cumulaive effec on he sock of public capial is likely o be appreciable when public deb is high, implying high level of disorionary axaion. These are jus some guiding principles whose applicaion in any paricular case will need o ake accoun of counry-specific circumsances. Counries facing imminen risk of a curailmen of marke access, or ha need o re-esablish fiscal space agains he risk of coningen liabiliies or oher shocks, naurally do no have he luxury of living wih high deb. For ohers, he appropriae pace depends on he availabiliy of non- (or less) disorionary sources of ax revenue. And for hose counries in he forunae posiion of enjoying asse price booms, he message mus be ha hey should seize he opporuniy o pay down public deb. In sum, he appropriae response o high levels of public deb depends very much on he exen of available fiscal space and oher facors. There is no one-size-fis-all message: be i o pay down he deb o reduce he risk of a funding crisis or o live wih he deb, leing he deb raio decline organically hrough growh. Counries in he yellow and red zones in erms of fiscal space will no be in a posiion o live wih he deb. Bu nor is i he case ha counries wih ample space hose firmly in he green zone should rush o pay down heir deb. 19 INTERNATIONAL MONETARY FUND

Box 1. A Formal Model of Deb, Invesmen, and Growh The economy is closed, and is populaed by a single infiniely lived agen who maximizes: Max p u( c,, ) c. l, b, k l g 0 p L p 1 1 (1.1) s.. c k b (1 ) wl R k Yb (1.2) in which c, g,(1 l) are consumpion of he privae and public goods, and of leisure, respecively; L p w is he wage rae, axed a, R and Y are he reurns on privae capial, k, and bonds, b. Leing denoe he Lagrange muliplier on he budge consrain, he firs-order condiions are: u c, (1.3) ul, (1 ) w (1.4) u R c, u c, 1 Y (1.5) uc, The condiions for opimaliy are inuiive: (1.4) implies ha he agen will supply labor o he poin ha he marginal rae of subsiuion beween consumpion and leisure equals he aferax wage rae; condiion (1.5) equaes he ineremporal rae of subsiuion o he reurn on he governmen bond, which, by arbirage, mus also equal he reurn on privae capial. Finally, muliplying (1.2) by he Lagrange muliplier,, summing for all 0, using he p ransversaliy condiions (lim b k 0), and exploiing (1.3) (1.5) provides a convenien summary of he privae secor s behavior: p ( u c u l ) u ( Yb Rk ) c, l, c,0 0 1 0 1 (1.6) 0 p in which b 1 and k are he iniially inheried socks of governmen bonds and privae capial. In 1 urn, (1.6) consiues a feasibiliy consrain ha he governmen mus ake ino accoun in choosing is opimal fiscal policy. The simulaions shown in he figures assume a Cobb Douglas producion funcion g( ) p( ) (1 ) y k k l (1.7) 1 1, in which α = 0.33 and θ = 0.1 (hese, and oher parameers, are sandard from he lieraure). The uiliy funcion is iso-elasic: 1 c 1 l 1 c c (1 l) g uclg (,, ) (1 g)( c (1 c) ) g 1 1 1 c l g in which c 0.3; g 0.1; c 1; l 1; g 1 (his calibraion implies uiliy is logarihmic). Oher parameers are he discoun rae, 0.96, and he rae of depreciaion, 0.1. (1.8) 20 INTERNATIONAL MONETARY FUND

Box 2. Opimal Box 2. Opimal Fiscal Policy The governmen commis o a fiscal plan {,,, g g g b k } (in which 0 k is public capial) o maximize he agen s uiliy, subjec o he economywide resource consrain and he feasibiliy consrain ha summarizes privae secor behavior (Box 1 (1.6)). Formally: The opimal fiscal program is: Max g u( c,, ),,, l g b k g (2.1) 0 s.. c g k (1 ) k k (1 ) k F( k, k, l ) (2.2) p p g g g p 1 1 1 1 ( uc, c ul, l) uc,0( Yb 0 1 R0k 1) (2.3) 0 F F, u 0 (2.4) p k g k l, ll l, c, cc c, l, g { u ( u l u )} { u ( u c u )} F 1 (2.5) u ( u c u ) ( u ( u c u ))( F (1 )) 1 (2.6) c, cc, c, c, 1 cc, 1 1 c, 1 g k in which, are he Lagrange mulipliers on resource and feasibiliy consrains respecively. When axes are lump-sum, and hus non-disorionary, he feasibiliy consrain does no bind, so 0, in which case (2.5) (2.6) reduce o: u / u F 1 (2.7) l, c, l, ( u / u ) ( F (1 )) ( F (1 )) 1 (2.8) c, c, 1 k p g k Bu hese are jus he analogs o he represenaive agen s firs-order condiions, (1.4) (1.5). Condiion (2.7) equaes he marginal rae of subsiuion beween consumpion and leisure o he marginal produc of labor, implying from (1.4), ha he wage should be he marginal produc of labor. Condiion (2.8) saes ha privae and public invesmen should be underaken o he poin ha he respecive marginal producs equal he ineremporal rae of subsiuion, which, from (1.5), is he marke ineres rae. When only disorionary axes are available, however, 0, and he impac on he governmen s abiliy o raise revenues needs o be aken ino accoun. Therefore, social raher han privae marginal producs and raes of subsiuion mus be used, as in (2.4)-(2.6). For example, invesmen may yield a higher social reurn han he privae reurn because, by raising he marginal produc of labor, i makes i easier o raise labor axes. Neverheless, a key resul is ha, even wih 0, he implici discoun rae used by he governmen in is opimal fiscal program equals he marke ineres rae. This holds exacly in he case of iso-elasic uiliy, and approximaely oherwise. Subsiuing (1.8) ino (2.6), yields: ( u / u ) R F (1 ) F (1 ) (2.9) c, c, 1 k p g k Condiion (2.9) saes ha even hough axes are disorionary, he marke ineres rae equals he represenaive agen s discoun facor which is also he discoun facor used by he governmen in seing opimal policy (for example, when deciding wheher o repay deb or defer axaion). Finally, in period 0, he firs-order condiions (2.5) (2.6) are: { u ( u l u )} { u ( u c u u ( Yb Rk ))} F (2.10) p l,0 ll 0 l,0 c,0 cc,0 0 c,0 cc,0 0 1 0 1 l,0 0 These differ from heir period 1 u ( u c u u ( Y b R k )) ( u ( u c u ))( F (1 )) (2.11) p c,0 cc,0 0 c,0 cc,0 0 1 0 1 c,1 cc,1 1 c,1 g k p analogs by he erm u ( Yb Rk ),0 0 1 0 1 cc, which perains o he opimaliy, as discussed in he ex, of opporunisically axing inelasic ax bases income from he iniial socks of governmen bonds and of privae capial. 21 INTERNATIONAL MONETARY FUND

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