Department of Economics Athens University of Economics and Business

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1 Dearmen of Economics Ahens Universiy of Economics and Business WORKING PAPER no The ECB s olicy, he Recovery Fund and he imorance of rus: The case of Greece Vasiliki Dimakooulou, George Economides and Aosolis Philiooulos November 202 Πατησίων 76, Αθήνα. Tηλ.: econ@aueb.gr / 76, Paission Sree, Ahens Greece. Tel.: (+30)

2 The ECB s olicy, he Recovery Fund and he imorance of rus: The case of Greece Vasiliki Dimakooulou 2, George Economides 3 and Aosolis Philiooulos 4 November 20, 202 We hank Dimiris Malliarooulos, George Tavlas and Panos Tsakloglou for discussions and commens. We also hank Vanghelis Vassilaos for join work and discussions. V. Dimakooulou is graeful o he Sae Scholarshis Foundaion (IKY) for suoring her research co- nanced by Greece and he Euroean Union (Euroean Social Fund- ESF) hrough he Oeraional Programme «Human Resources Develomen, Educaion and Lifelong Learning» in he conex of he rojec Reinforcemen of Posdocoral Researchers - 2nd Cycle (MIS ), imlemened by he Sae Scholarshis Foundaion (IKY). Any views and errors are ours. 2 Ahens Universiy of Economics and Business 3 Ahens Universiy of Economics and Business, Hellenic Oen Universiy, and CESifo 4 Ahens Universiy of Economics and Business, and CESifo. Corresonding auhor: Dearmen of Economics, Ahens Universiy of Economics and Business, 76 Paission sree, Ahens 0434, Greece. el: , ahil@aueb.gr

3 Absrac This aer, using a microfounded macroeconomic model ha embeds he key feaures of he Greek economy, sudies he e cacy of he various olicy measures aken, a naional and EU level, o cushion he economic e ecs of he andemic shock. The aer aems o give quaniaive answers o quesions like: Wha are he e ecs of hese olicies and, esecially, wha are he imlicaions of he scal ransfers and grans from he Recovery Fund and he quaniaive olicies of he ECB, like he PEPP, for he Greek economy? Do hey helhe real economy and, if yes, by how much? Wha would have haened had hese measures no aken? How cosly will be he re-emergence of he fear of deb defaul and risk remia? JEL classi caion: E5, E6, F3. Keywords: Cenral banking, Fiscal olicy, Inernaional lending, Pandemic.

4 Inroducion The covid-9 andemic sruck Greece in early 2020 when i was jus saring o embark on a moderae growh ah afer many years of deression; Greece had already los more han 25% of is GDP during is sovereign deb crisis in Moreover, he andemic crisis found he counry wih limied scal sace; is ublic deb was already 80% of GDP in he end of 209 and mos of i (around 70%) was in he hands of Euroean Union (EU) ublic insiuions as a resul of he hree o cial scal bailous in he 200s. In an e or o sem he andemic, like mos governmens, he Greek governmen has been forced o ake exended lockdown measures which have reversed he growh dynamics of he Greek economy and, a he same ime, o ake severe scal simulus measures in order o couner he economic imlicaions of he andemic. A he same ime, Greece can bene from nancial suor from he Euroean Commission (EC) and he Euroean Cenral Bank (ECB). Regarding he EC, hrough he redisribuive ransfers of he Recovery Fund, i is aniciaed ha Greece will bene uo a ne amoun of 32 billion euros in he form of loans and grans; his amoun ranslaes o around 7:5% of he Greek GDP in 209 and can be used by he end of 2026 for invesmens and reforms. Regarding he ECB, he laer has decided no only o coninue he various olicy measures owards Greece since 2008 (suor of rivae banks hrough a full allomen lending olicy, he issuance of cross-border TARGET2 liabiliies o he Eurosysem (ES), ec), bu also o include Greek governmen bonds in is new asse urchase rogram, he so-called Pandemic Emergency Purchase Programme (PEPP), so as o suor heir rice and narrow bond sreads. In his aer, we ry o give quaniaive answers o he following quesions. Wha are he e ecs of hese olicies on he Greek macroeconomy? Do hey helhe real economy and, if yes, by how much? Wha would have haened had hese measures no aken? Wha will haen if he fear of deb defaul and risk remia re-emerge? Our vehicle of analysis is a medium-scale micro-founded DSGE model of a small oen economy ariciaing in a currency union like he ES. Paricular aenion is given o he nexus beween scal olicies and quaniaive moneary olicies in he conex of he ES. Regarding scal olicy, we feed he model wih a sending-ax olicy mix ha mimics he naional scal simulus adoed by he Greek governmen since he beginning of 2020, as well as wih he redisribuive funds from he EU s Recovery Fund in he form of loans and grans. Regarding moneary olicy, as imlied by he nancial saemens of he Naional Cenral Bank (NCB) of Greece, we assume ha he Greek NCB rovides credi o rivae banks a a olicy ineres rae, issues banknoes held by he non-bank ublic and ineres-bearing reserves held by rivae banks, ariciaes in he secondary marke for governmen bonds under he PEPP, receives a ne redisribuive dividend from

5 he ES, and issues TARGET2 liabiliies o oher NCBs in he ES as ar of is moneary base. This comlex olicy mix is embedded ino our DSGE model, which includes various real and nominal fricions yically used in he New Keynesian lieraure as well as some Greek-seci c characerisics. In our model, ineres rae olicy can have real e ecs because of nominal rigidiies, credi olicy can have real e ecs because of rivae banks borrowing consrains, and balance-shee or quaniaive moneary olicies can have real e ecs because of ransacion coss associaed wih nancial inermediaion as in e.g. Andrés e al (2004) and Cúrdia and Woodford (20), while, he issuance of new TARGET2 liabiliies can work as an exra nonmarke mechanism hrough which he counry borrows from oher counries in he ES as argued by Sinn (204). Our main resuls are as follows. The scal simulus of he Greek governmen and he nancial assisance rovided by he Recovery Fund and he andemic-relaed ECB olicies (e.g. PEPP) have heled he Greek economy o avoid he worse. In aricular, our baseline simulaions imly ha, wihou any olicy reacion, he fall in ouu in 2020 would be 2% relaive o 209 and would say below is 209 level for several years. By conras, wih he scal reacion and he EU assisance, he fall in 200 is 8.5% (which is close o 9% in he daa) and will rebound soon. Wihou nancial assisance from he Recovery Fund and he ECB, ha is, only wih he naional scal simulus, he fall in ouu would be 0.5% in 2020 and again he rebound would come laer. Acually, he role of EU insiuions is more imoran han he above numbers seem o imly. This is because one of he bene s ha Greece receives from membershi in hese sura-naional insiuions is he imor of credibiliy and, in aricular, he aniciaion of markes ha hese insiuions will se in, in one way or anoher, if somehing goes wrong in he fuure. To rovide a numerical examle of he bene s of imored credibiliy, we allow for fear of defaul on ublic deb and hence for sovereign risk remia; in aricular, we assume a 20% ex ane robabiliy of defaul during on Greek governmen bonds which is wihin he range exerienced by Greece during is sovereign deb crisis. The simulaed ahs of ouu and ublic deb-o-gdp under his hyoheical scenario imly ha he emergence of risk remia would make he recession much sharer and longer lasing and, a he same ime, he deb-o-gdp raio would skyrocke, even if domesic scal olicy reacs o ublic deb imbalances and he fear of defaul does no maerialize ex os. In oher words, rus is imoran and any shock ha riggers he loss of rus, and hence he re-emergence of risk remia and high ineres raes, will bring he Greek economy in a osiion similar o ha en years ago. In aricular, as is discussed below when we u our work in he conex of he lieraure on inernaional crises (see Lorenzoni (204) for a review), such a crisis erus when a counry wih weak fundamenals (like high ublic deb) is being hi 2

6 by an adverse domesic or exernal adverse shock. The crisis of he revious decade has augh us ha, in he case of Greece a leas, hese shocks can include a sudden oliical olarizaion ha signals oor growh rosecs, rolonged negoiaions wih EU insiuions, reors of insolvency by big raing agencies, ec. Our work di ers from he lieraure mainly because we are aware of no oher aers ha embed he currenly observed in racice nexus beween scal and quaniaive moneary olicies in a DSGE model of a eurozone counry ha receives nancial assisance from scal (see e.g. Recovery Fund) and moneary (see e.g. PEPP, TARGET2) EU insiiuions. Thus, we believe our work is more han a counry sudy. The model used here builds on he models develoed by Economides e al (202a, 202b). However, Economides e al (202a), as well as Paageorgiou and Tsiaras (202), have sudied he Greek sovereign deb crisis of he revious decade, while, Economides e al (202b) have sudied he Greek andemic crisis in a real model wihou moneary olicy. Balfoussia e al (2020) have also examined he Greek economy in he andemic bu heir focus is on he nancial secor raher han on he scal-moneary olicy nexus. The res of he aer is organized as follows. The model is resened in secion 2. Parameerizaion, daa and soluion for he year 209 are in secion 3. Secion 4 inroduces andemic scenaria. Secions 5, 6 and 7 resen soluions. Secion 8 closes he aer. An aendix conains algebraic and olicy deails as well as daa. 2 Model This secion consrucs a medium-scale micro-founded macroeconomic model for he Greek economy ha accommodaes he macroeconomic olicies observed in racice. We sar wih an informal descriion of he model. 2. Informal descriion of he model To caure he key feaures of he Greek economy, we add wo yes of fricions o a sandard small oen economy model. The rs ye includes real and nominal fricions commonly used by he quaniaive macroeconomic lieraure (see e.g. Uribe and Schmi-Grohé (207)). The second ye includes Greek-seci c feaures. The commonly used fricions include various yes of adjusmen coss, imerfec comeiion, nominal rigidiies, ec. The Greek-seci c feaures include a relaively deailed ublic secor wih ublic emloyees as a searae income grou, sae rms, roblems of By conras, here are several aers on his nexus in closed economy models for he US; see e.g. Sims and Wu (2020) and Chanda e al (202). 3

7 insiuional qualiy and nancial assisance from EU insiuions. In wha follows, we brie y inroduce he building blocks of he model. Households There are hree disinc yes of households, called caial owners, workers and ublic emloyees. Caial owners own rivae rms and banks and so receive heir ro s. They can also kee deosis a domesic and foreign rivae banks. Privae workers work in rivae rms. Public emloyees work in sae rms. All yes of households consume a domesic and a foreign good, rovide labor services, hold currency and are engaged in ren-seeking aciviies (he laer are discussed below). The hree yes of households are modeled in subsecion 2.2. Privae rms The domesic nal good is roduced by nal good rms ha ac comeiively using di ereniaed inermediae goods. The laer are roduced by inermediae goods rms which ac monoolisically à la Dixi-Sigliz and face nominal rigidiies à la Roemberg. Inermediae goods rms choose labor, caial and imored goods and also make use of roduciviy-enhancing ublic goods/services. On heir nancial side, hese rms can borrow from domesic and foreign rivae banks. There are also caial good rms ha roduce he caial demanded by inermediae goods rms. Any ro s generaed by rivae rms are disribued o caial owners. Firms are modeled in subsecion 2.3. Privae banks On he asse side, rivae banks make loans o rivae rms a home and abroad, hold ineres-bearing reserves a he NCB and buy domesic and foreign governmen bonds. On he side of liabiliies, hey receive deosis from savers, domesic and foreign, and loans from he NCB. To model he ro -maximizing behavior of rivae banks, and also accoun for he ossibiliy ha borrowing and lending akes lace in equilibrium, we ado he seu of Cúrdia and Woodford (20). 2 Wihin his seu, he di erence beween he di eren ineres raes (or he so-called asse ricing wedges) emerges as a resul of cosly nancial inermediaion. Any ro s generaed by rivae banks are disribued o caial owners. Banks are modeled in subsecion 2.4. Sae rms Sae rms use ublic emloyees, goods urchased from he rivae secor and ublic caial (he laer is augmened by ublic invesmen sending) o roduce a ublic good ha rovides uiliy-enhancing services o households and roduciviy-enhancing services o rms, where he associaed sending inus as shares of GDP, as well as he fracion of ublic emloyees in oulaion, will be se as in he daa. Sae rms are in subsecion 2.5. Naional cenral bank (NCB) in he Eurosysem (ES) On he side of asses, he Greek NCB makes loans o rivae banks and urchases 2 The model of Gerler and Kiyoaki (200) and Gerler and Karadi (20) is anoher oular model in his lieraure. We do no believe he aricular model of he banking secor is imoran o our resuls. We use he Cúrdia-Woodford model for is relaive simliciy. Walsh (207, chaer ) reviews his lieraure. 4

8 Greek governmen bonds in he secondary marke where hese bolds have been urchased by domesic and foreign rivae banks in he rimary marke. On he liabiliies side, he moneary base consiss of banknoes, reserves and cross-border TARGET2 liabiliies. These are he larges asse and liabiliy iems in he daa. In oher words, he NCB s sending is nanced by rining new banknoes held by rivae agens, by issuing reserves held by rivae banks and by issuing cross-border TARGET2 liabiliies according o he rules of he ES. The NCB also receives a ne ransfer from he ES, which reresens he di erence beween he moneary income aid by he Greek NCB o he common ool of he ES and he NCB s claim of ha common ool. Any ro s generaed by he NCB are in urn ransferred o is governmen. The NCB is modeled in subsecion 2.6.3, while moneary olicy deails during he andemic are discussed in subsecion 4.2. Treasury On he revenue side, he Treasury, or he governmen, axes households income and consumion as well as rms ro s, receives a ransfer from is NCB and issues bonds. The laer can be urchased by domesic rivae invesors/banks, foreign rivae invesors/banks and EU ublic insiuions (loans by, say, he ESM coun as ublic deb and he same alies o funds from he Recovery Fund in he form of loans). On he exendiure side, he Treasury sends on wages of ublic emloyees, governmen invesmen, governmen urchases of goods from he rivae secor, as well as ransfer aymens o households. The Treasury is modeled in subsecion 2.6.2, while scal olicy deails during he andemic are discussed in subsecion 4.2. Insiuions I is widely recognized ha Greece is a counry wih relaively oor insiuional qualiy. 3 An imoran asec of he laer is ren seeking which is broadly de ned as he engagemen of ineres grous wih he ublic secor aiming for exra riviliges a he exense of social welfare. Here, we will assume ha ren seeking akes he form of a social con ic over he disribuion of a share of governmen ransfers. In aricular, we will assume ha households devoe ime and energy o comee wih each oher for exra governmen ransfers in a Tullock-ye redisribuive cones. Thus, here weak insiuions are a roblem of collecive acion. The ren-seeking echnology is seci ed in subsecion 2.2. Modelling he economic imac of he lockdown Alhough he healh crisis has damaged he real economy in many ways (see e.g. Euroean Commission (2020)), here, similarly o e.g. Eichenbaum e al (2020) and Economides e al (202b), we assume ha he dro of economic aciviy is riggered by wo e ecs/shocks: (i) an adverse labor suly shock and (ii) an increase in ransacion coss associaed wih consumion. The rs channel caures he adverse e ec of he andemic on work hours and emloymen 3 See e.g. Angelooulos e al (2009), Masuch e al (208), Kollinzas e al (208) and Chrisou e al (202). 5

9 in general. The second channel aims a cauring he exra ransacion coss ha consumers face because of he same measures. In oher words, he rs channel oeraes hrough he suly side, whereas he second shock hrough he demand side of he economy. These shocks are modeled in subsecions 2.2 and 4.. Modelling deails will be rovided as we resen each building block of he above described model Households There are hree disinc yes of households, called caial owners, workers and ublic emloyees. Caial owners are indexed by he subscri k = ; 2; :::; N k, workers by he subscri w = ; 2; :::N w, and ublic emloyees by he subscri b = ; 2; :::; N b. Tha is, he oal oulaion is N = N k + N w + N b. Equivalenly, in erms of oulaion shares, n k N k n w N w N and nb N b N = nk n w. For simliciy, oal oulaion and is decomosiion o he hree grous is exogenous and ke consan over ime; ha is, we assume away occuaional mobiliy from one grouo anoher Households as caial owners Caial owners own he rms and banks and so receive heir ro s. They can also save in he form of deosis a domesic and foreign banks. Besides, like all oher yes of households, hey receive income from work, hold currency and are engaged in a ren-seeking comeiion for exra scal ransfers. Each caial owner, k = ; 2; :::; N k, maximizes discouned lifeime uiliy: X u (c k; ; u k; ; y g ) () =0 where c k; and u k; denoe resecively k s consumion and leisure ime, y g denoes he er caia quaniy of ublic goods/services rovided and roduced by he governmen, and 0 < < is a ime discoun facor. 4 Before we roceed, we make a remark abou unemloymen. By assuming markeclearing in he labor marke(s), any fall in ouu is obviously re eced in a fall in hours of work raher han in unemloyed eole. This is for simliciy. In earlier versions of he aer, we exerimened wih an exended version of our model ha allows for boh less hours of work and less emloyed eole whenever ouu haens o fall. In aricular, we have imlemened his by relacing he suly of labor funcion wih a wage rigidiy rule as in e.g. Blanchard and Gali (2007), and where any decrease in he demand for labor on he ar of rms is divided beween a decrease in work hours and a decrease in he number of working eole as in Ball and Romer (990). Since he main resuls are no a eced by his exension, we resen he version of he model wihou unemloyed eole. N, 6

10 For our numerical soluions, we will use he uiliy funcion (aking ino accoun he calibraion, our resuls do no deend on he funcional form used) : u (c k; ; u k; ; y g ) = log c k; + 2 log u k; + 3 log y g where 0 <, 2, 3 < are reference arameers wih =. Since here are wo goods, home and foreign, we de ne he consumion index: c k; = (ch k; ) (c f k; ) ( ) (2) where c h k; and cf k; denoe k s domesic and foreign consumion resecively and 0 < < measures he weigh given o he domesic relaive o he foreign good. The ime consrain of each k in each eriod is: l k; + s k; + u k; = (3a) where l k; and s k; are resecively k s e or ime allocaed o roducive work and ren seeking aciviies. The wihin-eriod budge consrain of each k wrien in real erms is: (+ c ) c h k; + f c f k; c +j h k; +e = ( y )wk l l k; + i k; + k; + j f k; +f e 2 j f 2 k; j f +m k; = +( + i d ) jk; h + ( + id ) e j f k; + m k; + +g r k (s k; ) + N k k (s k; ) + N w w (s w; ) + N b b (s b; ) (RS G r ) (3b) where is he rice of he domesic good, f is he rice of he foreign good exressed in domesic currency, is he counry s CPI seci ed below, is he CPI abroad, e is he nominal exchange rae where an increase means a dereciaion, is he real value of k s end-of-eriod deosis held a j h k; domesic banks earning a nominal ineres rae i d + in he nex eriod, jf k; is he real value of k s end-of-eriod deosis held a foreign rivae banks exressed in foreign rices and earning a nominal ineres rae i d + in he e nex eriod, 2 2 j f k; j f is a resource cos associaed wih banking abroad, m k; is he real value of end-of-eriod currency carried over by k from o +, w k is he real wage rae earned by caial owners, k; i is he dividend aid o each k by rivae rms ne of axes, k; is he dividend aid o each k by rivae banks ne of axes, and 0 c, y < are he ax 7

11 raes on consumion and income. Also, 0 < l measures he degree of resricions imosed by conainmen measures on work hours and c is a roxy for he exra ransacion coss ha consumers face because of he same measures (boh are similar o hose inroduced by Eichenbaum e al (2020)); hese exogenous sochasic variables are modeled in subsecion 4. below. The wo erms in he las line of (3b) are governmen ransfers. The rs one, g r, denoes a lum-sum ransfer ha is common across agens and indeenden of ren-seeking aciviies. The second one is an exra ransfer exraced by each k from he common ool, where he laer is he oal amoun of ublic sending earmarked for ransfers, G r. Tha is, only a fracion, 0 < ( RS), of G r is available o be disribued equally o everybody, while, he res, (RS G r ), is aken away by ren seekers, where he ren exraced by each individual deends on he e or ime allocaed by him/her o ren-seeking aciviies relaive o oal ren-seeking aciviies. 5 In oher words, he erm k (s k; ) is he fracion of N k k (s k; ) +N w w (s w;) +N b b (s b; ) he common ool exraced by each k in a Tullock (980) ye ren-seeking comeiion. Regarding he ren-seeking echnology, he ower coe cien,, is beween 0 and and measures how quickly diminishing reurns arise in ani-social aciviies, while he arameer k measures he e cacy of k s aggression. If k increases and/or decreases, agen k has a sronger incenive o devoe e or ime o ren seeking. 6 To give money a role, we use a cash-in-advance consrain like: m k; ( + c ) c c h k; + f c f k; (3c) Each k acs comeiively choosing fc h k;, cf k;, c k;, l k;, s k;, jk; h ; jf k; m k; g =0 subjec o he above. The rs-order condiions are in Aendix A Households as workers Workers are emloyed by rivae rms. They consume, work, hold currency and ariciae in ren-seeking aciviies. 5 Tha is, G r = Ng r + (RS G r ) = ( RS)G r + (RS G r ). This is as in e.g. Eseban and Ray (20), who call RS he degree of "ublicness" of he common ool, Angelooulos e al (2009), Chrisou e al (202), ec. In he calibraion secion below, we use an index of he degree of roery righs o quanify RS. 6 For similar ren seeking echnologies, see e.g. Murhy e al (99), Dixi (2004, chaer 5), Hillman (2009, chaer 2), Angelooulos e al (2009), Eseban and Ray (20), Economides e al (202a, 202b), Chrisou e al (202), ec. Noe ha our seci caion, seci cally, he di eren values of k, w and b, allows us o have asymmeries in equilibrium; namely, di eren yes of ren seekers can choose di eren allocaions and receive di eren wages even if hey aack he same ie and share he same references. 8

12 Each worker, w = ; 2; :::; N w, maximizes: X u (c w; ; u w; ; y g ) (4) =0 where variables are de ned as above in he caial owners roblem if we relace he subscri k wih he subscri w. As above, we use he uiliy funcion: u (c w; ; u w; ; y g ) = log c w; + 2 log u w; + 3 log y g and he consumion index: c w; = (ch w;) (c f w; ) ( ) (5) Also, as above, he maximizaion is subjec o he ime consrain: l w; + s w; + u w; = (6a) he budge consrain: ( + c ) c h w; + f c f w; c + m w; = +g r + = ( y )ww l l w; + m w; + w (s w; ) N k k (s k; ) + N w w (s w; ) + N b b (s b; ) and he cash-in-advance consrain: m w; ( + c ) c c h w; + f c f w; (RS G r ) (6b) (6c) where w w is he real wage rae of workers. Each w acs comeiively choosing fc h w;, c f w;, c w;, l w;, s w;, m w; g =0 subjec o he above. The rs-order condiions are in Aendix A Households as ublic emloyees Public emloyees are emloyed by sae rms. Like workers, hey consume, work, hold currency and are engaged in ren-seeking aciviies. Variables will be de ned as above in he workers roblem if we relace he subscri w wih he subscri b. 9

13 Each ublic emloyee, b = ; 2; :::; N b, maximizes: X u (c b; ; u b; ; ; y g ) (7) =0 As above, he uiliy funcion and he consumion index are: u (c b; ; u b; ; ; y g ) = log c b; + 2 log u b; + 3 log y g c b; = (ch b; ) (c f b; ) ( ) (8) Also, as above, he maximizaion is subjec o he ime consrain: he budge consrain: +g r + ( + c ) l b; + s b; + u b; = c h b; + f c f b; c + m b; = = ( y )wg l l b; + m b; + b (s b; ) N k k (s k; ) + N w w (s w; ) + N b b (s b; ) and he cash-in-advance consrain: m b; ( + c ) c c h b; + f c f b; (RS G r ) (9a) (9b) (9c) where w g is he real wage in he ublic secor while he res of he variables are de ned as in he worker s roblem. Each b acs comeiively choosing fc h b;, cf b;, c b;, l b;, s b;, m b; g =0 subjec o he above. 7 The rs-order condiions are in Aendix A Privae rms and roducion of rivae goods Privae rms are owned by caial owners. Following mos of he relaed New Keynesian lieraure, here are hree yes of goods roduced by hree associaed yes of rms. There is a single domesic nal good roduced by comeiive nal good rms. There are also di ereniaed inermediae goods used as inus for he roducion of he nal good. Each di ereniaed inermediae good is roduced by an inermediae goods rm ha acs as a monoolis in is own roduc marke à la Dixi-Sigliz facing Roembergye nominal xiies. Finally, comeiive caial good rms roduce caial used as an inu in he roducion of inermediae goods. 7 The choice of l b; can be hough as a choice of work e or. Allowing for a xed shif, or hours of work, in he ublic secor would no change our resuls o he exen ha ublic emloyees can sill choose he e or hey make while a work. 0

14 2.3. Final good rms There are N h nal good rms indexed by subscri h = ; 2; :::; N h. For noaional simliciy, we will se N h = N k, ha is, he number of nal good rms equals he number of heir owners. Each nal good rm roduces an amoun yh; h by using inermediae goods according o he sandard Dixi- Sigliz echnology: 2 3 N i yh; h = X 4 N i (yh i;) 5 (0) i= where yi; h denoes he quaniy of inermediae good of variey i = ; 2; :::; N i used by each nal good rm h and 0 is a arameer where =( ) measures he degree of subsiuabiliy beween inermediae goods. Each nal-good roducer h chooses inus yi; h o maximize real ro s: h; = y h h; N i X i= h i; N i y h i; () where is he rice of he nal good and h i; is he rice of inermediae good i. The rm maximizes is ro acing comeiively subjec o he above. The familiar in he Dixi-Sigliz lieraure rs-order condiion for inus is in Aendix A Inermediae goods rms There are N i inermediae goods rms indexed by he subscri i = ; 2; :::; N i. Since hey are owned and managed by caial owners, we again se N i = N k for noaional simliciy. These rms make invesmen and oher facor decisions facing caial adjusmen coss and Roemberg-ye rice adjusmen coss. New invesmen is nanced by reained earnings and loans from rivae banks. 8 Each rm s ne real dividend, i;, disribued o is owners, is (see Aendix A.5): i; = ( ) " h i; y h i; w w l w i; w k l k i; f m f i; 8 For simliciy, we assume ha rms do no issue shares bu simly disribue ne ro s o heir owners (he caial owners). Allowing for issuance of shares leaves our resuls unchanged o he exen ha we imose ha he number of shares is consan (say a one) before solving he rm s oimizaion roblem (his is as in e.g. McGraan and Presco (2005), Miao (204, chaer 4) and Uribe and Schmi-Grohé (207, chaer 4)). For richer roblems of he rm wih non-rivial cororae nance decisions and he Modigliani-Miller neuraliy resul, see e.g. Turnovsky (995, chaers 0 and ), Alug and Labadie (994, chaer 4), Auerbach (2002) and Gourio and Miao (200, 20). #

15 x i; k 2 ki; k i; 2 k i; 2 h i; h i; 2 y h i;+ + L h i; ( + i l ) L h i; + e L f i; ( + i l ) L f i; (2) where l w i; is labor services rovided by workers and used by rm i, lk i; is labor services rovided by caial owners and used by i, m f i; is imored goods used by each i, x i; is i s invesmen in caial goods and k i; is i s sock of caial goods used in roducion in he nex eriod (as we shall see below, he relaive rice of caial is ), L h i; and Lf i; are he real values of beginning-of-eriod loans received from domesic and foreign rivae banks resecively on which he rm ays a nominal ineres rae, i l, and i l, resecively in he curren eriod, 0 < a ro ax rae, k is a arameer measuring sandard caial adjusmen coss and is a arameer measuring Roemberg-ye rice adjusmen coss. 9 The law of moion of he rm s caial sock is: k i; = x i; + ( ) k i; (3) where he arameer 0 is he caial dereciaion rae. For he rm s roducion funcion, we ado he form: y h i; = A N g y g g; N i (k i; ) o + ( )(m f i; )o o A w li; w + A k li; k (4) where he arameer 0 measures he inensiy of caial, k i;, relaive o goods imored from abroad, m f i;, he arameer o > 0 is a measure of he degree of subsiuabiliy beween caial and imored goods, he coe cien a is he share of labor inus, he arameers A w and A k measure he relaive roduciviy of workers and caial owners resecively, A > 0 is TFP in he rivae secor and 0 is he conribuion of ublic goods/services er rm o rivae roducion. Firms are subjec o a working caial consrain. 0 Following e.g. Walsh (207,. 208) and Uribe and Schmi-Grohé (207), we assume ha rms have o nance a fracion of aymens o labor wih loans from domesic and foreign rivae banks: L h i; + e L f i; (ww l w i; + w k l k i;) (5) 9 Roemberg-ye coss associaed wih rice changes are assumed o be roorional o average ouu, y h i;, which is aken as given by each i. This is no imoran bu hels he smooh dynamics of he model. 0 We could assume di eren yes of consrains as in e.g. Gerler and Karadi (20) and Sims and Wu (2020). 2

16 where he arameer 0 measures he ighness of borrowing condiions. Each rm i maximizes he discouned sum of dividends disribued o is owners: X i; i; (6) =0 where, since rms are owned by caial owners, we will ex os osulae ha he rm s discoun facor, i;, equals he caial owners marginal rae of subsiuion beween consumion a and +. Each rm i chooses fli; w, lk i;, mf i;, k i;, L h i;, Lf i; g =0 o maximize is sream of dividends or ne ro s, as de ned in (2) and (6), subjec o he law of moion of caial (3), he roducion funcion in (4), he borrowing consrain in (5) and he inverse demand funcion for is roduc coming from he nal good rm s roblem. Deails and he rm s rs-order condiions are in Aendix A Caial good rms There are N c caial good rms indexed by he subscri c = ; 2; :::; N c. Since hey are owned by caial owners, we again se N c = N k for noaional simliciy. We assume ha caial good roducers acquire he dereciaed caial sock, choose invesmen aciviy and sell he laer o inermediae goods rms. Here, his roblem is modeled in he simles ossible way by assuming away adjusmen coss, so ha, in each eriod, each rm c maximizes is ro given by: 2 c; = Q x c; x c; (7) where x c; is he amoun of invesmen roduced and Q is he relaive rice of caial also known as Tobin s q. Here, wihou caial adjusmen coss, he rs-order condiion is simly Q = as assumed above. Also, he ro is zero in equilibrium. 2.4 Privae banks There are N rivae banks indexed by he subscri = ; 2; :::; N. Since hey are owned and managed by caial owners, we again se N = N k for noaional simliciy. In addiion o heir sandard role, which is he rovision of inermediaion beween lenders and borrowers by convering bank deosis ino loans o rms, we also allow rivae banks o hold ineresbearing reserves a he NCB and o urchase domesic and foreign governmen bonds. In oher words, on he asses side, we have loans o rivae rms, reserves held a he NCB and domesic and foreign governmen See e.g. Uribe and Schmi-Grohé (207,. 0-). 2 See also Miao (204, chaer 4), Günner (205), Uribe and Schmi-Grohé (207, chaer 4) and many ohers. 3

17 bonds, while on he liabiliies side, we have deosis from domesic and foreign households and loans from he NCB. Any ro s made by banks are disribued o caial owners. As i is he case in realiy, we assume ha here is a secondary marke for governmen bonds. In aricular, we assume ha, in he beginning of he curren eriod, he rivae bank can kee a fracion, 0, of he domesic governmen bonds urchased a, b ;, and sell he res, 0, o is NCB a a rice. Tha is, when i does he laer, he rivae bank receives he amoun ( ) b ; from he NCB and his is credied in is reserves accoun held a he NCB. The general idea behind such ransacions is ha hey reduce ossible risks and coss associaed wih holding bonds issued by a highly indebed governmen and also rovide exra liquidiy o rivae banks (see also below). 3 Each bank s ne real dividend, ;, disribued o is owners, is (see Aendix A.6): ; = ( ) [(+i l ) L ; +(+i b ) e f ; +(+i r ) m ; + +( + i b ) b ; + ( )b ; ( + i d ) j ; ( + i z ) z ; ()] L ; b ; e f ; m ; + j ; + z ; (8) where L ; are loans given o domesic and foreign rms (namely, L ; = L h i; + Lf i;, where Lf i; is loans demanded by foreign rms from domesic banks exressed in domesic rices) on which he bank receives a nominal ineres rae i l + one eriod laer, f ; is he real value of one-eriod foreign governmen bonds denominaed in foreign rices and acquired by each a on which he bank receives a nominal ineres rae i b + a + ;4 m ; is he real value of ineres-bearing reserves held a he NCB on which he bank earns a nominal ineres rae i r + a +, b ; is he real value of oneeriod domesic governmen bonds urchased by he bank a and earning 3 Sricly seaking, hese coss and risks aly more o long-erm bonds as sudied Andrés e al (2004) and in more deail by Chen e al (202). Long-erm bonds also allow he real reurn o hem o deend on he change in heir marke rice, in he sense ha he real reurn o inheried long-erm bonds increases no only wih he ineres rae bu also wih he increase in heir marke rice. However, o keehe model relaively simle, we work wih one-eriod mauriy bonds only. 4 This is denominaed in foreign currency. Tha is, if F ; is he nominal value for each agen k, he real value is f ; F ;. 4

18 a nominal ineres rae i b + a + if he bank kees hem or if he bank sells hem o is NCB in he secondary marke, j ; is deosis obained by domesic and foreign households (namely, j ; = jk; h + jf k;, where jf k; is deosis of foreign households a domesic banks exressed in domesic rices) on which he bank ays a nominal ineres rae i d + one eriod laer, z ; is loans from he NCB o he rivae bank on which he laer ays a nominal olicy ineres rae i z + one eriod laer and () caures real oeraional coss faced by banks. Also, is he ro ax rae as already de ned above. Real oeraional coss, (), are assumed o be increasing in he volumes of governmen bonds, loans given o rms and loans aken from he NCB, while hey are decreasing in he volume of reserves held a he NCB. 5 Tha is, () = (L ; ; b ; ; e f ; ; m ; ; z ; ). In our numerical soluions, we will use he funcional form: () = l 2 (L ; ) 2 + b 2 ( b ; ) 2 + f 2 (e f ; ) m 2 (m ; + ( )b ; ) 2 + z 2 (z ; ) 2 which roduces well-de ned demand and suly funcions for di eren asses and liabiliies. Noice above ha he bank s coss are a eced by credi oeraions in he secondary marke, in he sense ha, when he NCB urchases bonds in he secondary marke, rivae banks bonds are reduced and, a he same ime, heir reserves increase by he same amoun. Also noe, as is discussed in more deail below in subsecion 2.6., ha such ransacion coss roduce asse ricing wedges which in urn allow quaniaive moneary olicies o have real e ecs. This is on o of he real e ecs ha moneary olicy can have hrough nominal xiies like Roemberg ye in our model. Each rivae bank maximizes he discouned sum of dividends disribued o is owners: X ; ; (9) =0 where, since banks are owned by caial owners, we will ex os osulae ha he rm s discoun facor, ;, equals he caial owners marginal rae of subsiuion beween consumion a and +. Each bank chooses fl ;, b ;, f ;, m ;, z ; g =0 o maximize is sream of dividends, as de ned in (8) and (9). The bank s roblem is solved as in e.g. Cúrdia and Woodford (20) and Corsei e al (203). Deails and rs-order condiions are in Aendix A.6. 5 This is similar o e.g. Cúrdia and Woodford (20), where banks inermediae beween borrowers and lenders and he associaed inermediaion cos falls wih bank reserves held a he cenral bank. 5

19 2.5 Sae rms and roducion of ublic goods/services We now model he way in which sae enerrises roduce he ublicly rovided good/service. There are N g sae rms indexed by he subscri g = ; 2; :::; N g roducing a single ublic good/service. For noaional simliciy, we will se N g = N b, ha is, he number of sae rms equals he number of ublic emloyees. The cos of each sae rm g for roducing he ublic good is in real erms: w g l g; + h (g g g; + gi g;) + f m g g; (20) where l g; is labor services used by each sae rm g, g g g; is goods urchased from he rivae secor by each g, gg; i is invesmen made by each g, and m g g; is imored goods used by each g. The roducion funcion of each sae rm g is assumed o be similar o ha in he rivae secor: y g g; = Ag g (k g g; )og + ( g )(m g g; )og og (l g; ) 2 g g 2 g; (2) where 0 g measures he inensiy of ublic caial, k g g;, relaive o goods imored from abroad, m g g;, he arameer og > 0 is a measure of he degree of subsiuabiliy beween ublic caial and imored goods, he coe ciens 0 <, 2, 2 < measure he shares of he associaed facors in roducion and A g > 0 is TFP in he ublic secor. The sock of each sae rm s caial evolves over ime as: k g g; = ( g )k g g; + gi g; (22) where 0 < g < is he dereciaion rae of ublic caial. To secify he level of ouu roduced by each sae rm, y g g;, and hence he oal amoun of ublic goods/services rovided o he sociey, we obviously have o secify he amouns of inus, l g;, g g g;, mg g; and kg g; (or equivalenly gg;). i Exce from work hours or e or which is deermined by ublic emloyees (see heir roblem above), we will consider he case in which he values of hese inus are as imlied by he daa, meaning ha he oal number of ublic emloyees as a share of oulaion, as well as he associaed governmen exendiures (on ublic invesmen, ublic wages, goods urchased from he rivae secor and imored goods), as shares of GDP, are se as in he daa. Seci cally, we de ne g i g; = si nk y h i; n b, g g g; = sg nk yi; h, m g n b g; = h s m nk yi; h and w g f n b = sw n k y h i; n b l b;, where n b N b N he fracion of ublic emloyees in oulaion and s i, s g, sm and s w are resecively he GDP shares of governmen exendiures on invesmen, goods urchased from he rivae secor, imored goods and ublic wages; hese values will be se according o he daa (see secion 3). 6 is

20 2.6 Fiscal and moneary olicy This secion models searaely he Treasury and he Greek Naional Cenral Bank ariciaing in he Eurosysem (ES). This can hel us o undersand he menu of scal and moneary olicy insrumens available o olicymakers and how hese insrumens inerac wih each oher. Before we roceed formally, in he rs subsecion, we u our work in he conex of he lieraure on he nexus beween scal, ublic nancing and quaniaive moneary olicies Quaniaive moneary olicies and wha di ers in he ES As is well known, he massive exansion in cenral bank balance shees since he onse of he global nancial crisis has forced a re-examinaion of Wallace s (98) neuraliy roery according o which he cenral bank s balance shee, or quaniaive, olicies (which have o do wih he oal size of he cenral bank s balance shee and he mix of asses and liabiliies ha he cenral bank holds) do no have any real e ecs. However, as a resonse o hese massive quaniaive olicies, he lieraure has added various nancial fricions o he benchmark framework ha resul in asse ricing wedges and hereby dearures from Wallace s roery. Examles of such fricions, hrough which quaniaive moneary olicies a ec he real economy, include ransacion coss associaed he relaive sulies of di eren asses, borrowing consrains, marke segmenaion, limied marke ariciaion, moral hazard, ec (see e.g. Andrés e al (2004), Gerler and Kiyoaki (200), Gerler and Karadi (20), Cúrdia and Woodford (20), Benigno and Nisicò (207), Basseo and Sargen (2020), Sims and Wu (2000), while see e.g. Walsh (207, chaer ) for a rich review). Once we allow for such fricions, quaniaive moneary olicies can have scal and real imlicaions. In our model, as said above, his role is layed by he ransacion cos funcion () in he rivae bank s roblem. On o of his, as e.g. Sinn and Wollmershauser (202), Sinn (204, 2020) and Reis (207) have oined ou, in a currency union like he ES, 6 here can be exra, direc roues hrough which quaniaive moneary olicies can alleviae scal burdens and relax naional consrains, even in he absence of nancial fricions like he above. Seci cally, Reis (207, secion 0) has argued ha several of he ECB s olicies (like he SMP, he rovision of 6 For he olicy of he ECB, esecially since he global nancial crisis of 2008, see e.g. Whelan (202), Wylosz (202), Siber (202), Merler e al (202), Sinn (204), de Grauwe (206), Harmann and Smes (208), Brunnermeir and Reis (209), Rosagno e al (209, 202), Coenen e al (2020), Havlik and Heinemann (2020), Fabiani e al (202) and Lane (202). For he e ecs of ECB s olicies on asse rices and/or he macro economy in aricular, see e.g. Gibson e al (206, 209), Gambei and Musso (207), Quin and Trisani (207), Larkin e al (207), Moessner (208), Rosagno e al (209, 202), Coenen e al (2020) and many ohers. 7

21 ELA and he way ECB s dividends are re-allocaed o member-counries of he EZ) can belong o his caegory allowing for redisribuion of real resources among governmens and naions wihin he ES. A arallel, and holy debaed, lieraure (saring wih Sinn and Wollmershauser (202)) has argued ha he issuance of new TARGET2 balances can also work in a redisribuive way (TARGET2 balances, which are aricularly large in he case of he Greek NCB are discussed below). Bu one needs a formal crierion o judge wheher a quaniaive, or balance-shee, moneary olicy of he ES can lay a direc allocaive role: i can, if, once marke-clearing condiions, ec, have been aken ino accoun, his olicy insrumen remains as an iem in he economy s resource consrain, namely, in is balance of aymens. According o his crierion, one can show ha olicies, like redisribued dividends from he ES o he NCB beyond hose conribued by he NCB o he ES, bond urchases by he ES beyond hose urchased by he NCB and a a rice above he marke-rice, or he issuance of new TARGET2 liabiliies o he ES can, a leas in rincile, no only alleviae naional scal burdens bu also (since hey aear in he counry s balance of aymens) increase naional resources. This will be formalized below when we resen he balance of aymens The Treasury ( scal auhoriies) The Treasury, or he scal branch of governmen, uses revenues from various axes, he issuance of new bonds and a direc recei/dividend from he NCB o nance is various sending aciviies. This is sandard; we will only di er in who can hold Greek ublic deb so as o allow for he o cial bail ous during he sovereign deb crisis and he loans from he EU s Recovery Fund during he andemic crisis. Holders of ublic deb Le us de ne he real and er caia ublic deb a he end of eriod as d. We assume ha i can be held by hree di eren yes of crediors: domesic rivae agens/banks, foreign rivae agens/banks, and EU ublic insiuions. The laer refers o loans from he ESM and oher euro saes during he sovereign deb crisis and loans from he Recovery Fund during he andemic. Noice ha, in he end of 209, namely, jus before he eruion of he andemic crisis, as a resul of he hree o cial bailous in 200, 202 and 205, around 70% of Greek ublic deb was owned by EU ublic insiuions (see Aendix B. for he holders of Greek ublic deb over ime). Also recall ha cenral banks in he ES can buy governmen bonds in he secondary marke only (see nex subsecion). Therefore, d is decomosed o he hree above holders: d b d + e f g + e f eu (23a) 8

22 where, exressing hem as fracions of oal deb, we de ne: 7 b d d d (23b) e f g g d (23c) e f eu eu d (23d) where 0 d, g, eu are he fracions of Greek ublic deb held resecively by domesic rivae agens, foreign rivae agens and he EU, where d + g +eu =. If he olicy and res-of-he-world variables, g and, are exogenously given (hey will be se as in he daa), hen residually eu d = ( g eu ). 8 Budge consrain of he Treasury Using his noaion, he ow budge consrain of he governmen wrien in er caia and real erms is: g r + n b " w g lg g; + h g g g; + f gi g; + m g g; +( + i b ) d d + ( + i b ) e e g d + +( + i ) e e eu d d + T N + rcbg (24) where g r is ransfers (boh lum-sum and exraced via ren seeking as exlained above), n b [w g lg g; + h (g g g; + gi g;) + f m g g; ] is he cos of he inus used by sae rms, T N is ax revenues (de ned righ below) and rcbg is a direc ransfer from he NCB o he Treasury. The res of he erms caure ineres aymens on ublic deb where noice ha he ineres raes can vary deending on he ideniy of he credior. For insance, we assume ha when he governmen borrows from he (domesic and foreign) marke, is ays he marke ineres rae, i b, while, when he governmen borrows from he EU or he ES, i ays an exogenous and consan rae, i. Toal ax revenues in real and er caia erms are: T N c [n k c ( h c h k; + f c f k; ) + nw c ( h c h w; + f c f w; )+ 7 Tha is, if F g denoes he nominal value of oal ublic foreign deb exressed in foreign currency, f g F g is is er caia and real value N 8 We have also exerimened wih he case in which he bonds bough by he EU have more han one eriod mauriy so as o caure he longer mauriy of hese loans in realiy. We reor ha adding muli-eriod safe loans by he EU (and he associaed ineres raes) does no change our main resuls. Perhas his is because oimizing rivae agens are raional and forward-looking. # + 9

23 +n b c ( h c h b; + f c f b; )] + y [nk w k l l k; + n w w w l l w; + n b w g l l b; ]+ + n k [ h y h i; w w l w i; w k l w i; f m f i; ]+ + n k [( + i l ) L ; + ( + i b ) e f ; + ( + i r ) m ; + +( + i b ) b ; + ( )b ; ( + i d ) j ; ( + i z ) z ; ()] (25) One of he olicy variables mus follow residually o close he Treasury s budge consrain in (24). In our soluions below, since hey caure he eriod 209 and afer, his role will be layed by he end-of-eriod oal ublic deb, d, while he sending-ax olicy insrumens will be se as in he daa The Greek Naional Cenral Bank in he Eurosysem On he side of asses of he Greek NCB, we include loans o rivae banks and governmen bonds urchased in he secondary marke. In aricular, we allow he Greek NCB o urchase Greek governmens bonds in he secondary marke where hese bonds are in he hands of boh domesic and foreign rivae invesors/banks (his alies only o he eriod afer 209 and in aricular o he PEPP because Greek governmen bonds have been excluded from he PSPP which has been he bigges ar of he large-scale APP of he ES ha sared in 205). 20 On he side of liabiliies, we include banknoes, reserves and TARGET2 liabiliies o he ES. 2 These have been 9 By conras, beween 200 and 208, here was no marke for Greek governmen bonds. All borrowing was from EU ublic insiuions. 20 For simliciy, we assume away urchases of oher securiies (domesic and foreign) by he Greek NCB. Also we assume away urchases of Greek governmen bonds by oher NCBs in he ES or he ECB iself in he secondary marke. This is for simliciy bu also because, according o he rules of he ES, he ECB canno hold more han 0% of sovereign bonds of each member-counry. 2 As rs oined ou by Sinn and Wollmershauser (202) and Sinn (204), and also sudied by Whelan (204, 207), Peroi (2020) and many ohers, TARGET2 balances are ne bilaeral osiions vis-a-vis he ES, which means ha he NCB of a member counry ransferring money abroad records a TARGET2 liabiliy o he res of he ES, while he NCB of a member counry receiving money from abroad records a TARGET2 asse. These TARGET2 balances cancel each oher ou a aggregae ES level (his is by consrucion) and herefore do no aear in he consolidaed balance shee of he ES. However, hey do aear in he balance shees of individual NCBs and he ECB, in he sense ha hey 20

24 he larges (asse and liabiliy) iems in he nancial saemens of he Greek NCB a leas since 2008 (see Aendix B.2). Budge consrain of he NCB The budge consrain of he NCB linking changes in asses and liabiliies is in real and er caia erms: ( ) d d + ( ) e e g d + +n k z ; + n k ( + i r ) m ; + rcb g ( )(+i b ) d d +( )(+i b ) e e g d + +n k ( + i z ) z ; + n k m ; + m n; m n; + + T ARG + i MRO T ARG + mi (26) where n k z ; is he end-of eriod loans o rivae banks, n k m ; is he endof eriod ineres-bearing reserves held by rivae banks a he NCB, m n; denoes he end-of-eriod sock of banknoes in circulaion held by he nonbank ublic, 22 ( ) d d and ( ) g d are sovereign bonds having been urchased by domesic and foreign rivae banks resecively in he rimary marke in he as and reurchased in he curren eriod by he NCB in he secondary marke a a rice on which he NCB earns he marke ineres rae i b, 23 rcb g is he direc ransfer/dividend from he NCB o is own governmen (as said above, his is he NCB s balance-shee earnings rebaed o he Treasury), T ARG is he end-of-eriod sock of TARGET2 liabiliies o he ES on which he NCB ays he main re nancing oeraions ineres rae, i MRO +, in he nex eriod, and mi is he ne ener as an exra iem of liabiliies for a counry wih Inra-Eurosysem liabiliies like Greece (see e.g. Whelan, 204, Table 2) or as an exra iem of asses for a counry wih Inra-Eurosysem claims like Germany (see e.g. Whelan, 204, Table 3). Focusing on he Greek economy, since 2008, TARGET2 liabiliies have become a big ar of he moneary base creaed by is NCB in accordance wih he rules of he ES (see Aendix B.2 for daa). 22 Tha is, m n; = n k m k; + n w m w; + n b m b; a each. 23 For simliciy bu also for lack of daa, we assume he same fracion,, of governmen bonds urchased by he NCB from domesic and foreign rivae banks. See also below. 2

25 ransfer from ooling moneary income (i.e. he dividend received by he ES minus he dividend aid o he ES). 24 Noice ha, in our model, m n; +n k m ; +T ARG MB is he moneary base of he Greek NCB wihin he ES. To u he same hing di erenly, TARGET2 liabiliies o he ES are he di erence beween he moneary base and he amoun of money held by he non-bank ublic and rivae banks. Quoing Sinn (204,. 80), TARGET2 balances "re ec he amoun of cenral bank credi ha has been issued in excess of he liquidiy needs for ranscaions wihin he NCB s naional jurisdicions". The way in which hese cross-counry liabiliies are used will become clear below when we resen he counry s balance of aymens. One of he olicy variables mus follow residually o close he NCB s budge consrain in (26). In our soluions below, his role will be layed by he ransfer o he Greek Treasury, rcb g. Aendix A.7 resens he budge consrain of he consolidaed ublic secor (Treasury and he NCB seen as a single olicy eniy). 2.7 Balance of aymens To make he direc allocaive role of EU insiuions more ransaren, we resen he counry s balance of aymens. If we add uhe budge consrains of all agens above, we ge he balance of aymens (wrien in real and er caia erms): f n k c c f k; + nw c c f w; + nb c c f b; + nk m f i; + nb m g g; c f + 24 In oher words, rying o mimic he comlexiy of realiy, he moneary olicy insrumens are: (i) loans o rivae banks or he associaed nominal ineres rae; (ii) reserves held by rivae banks a he NCB or he associaed nominal ineres rae; (iii) non-ineres bearing currency held by he non-bank ublic for ransacion uroses; (iv) he amoun of bonds urchased in he secondary by he NCB or heir rice; (v) he ransfer o he Treasury; (vi) he nominal exchange rae; (vii) TARGET2 balances and he associaed nominal ineres rae and (viii) he ne ransfer o he ES. In a small oen economy ariciaing in he ES, (vi)-(viii) are aken as given and will be se as in he daa. Regarding (i)-(ii), we will assume ha he cenral bank ses he ineres raes (as in he daa) and banks decide he quaniies of loans and reserves. Regarding (iii), he cenral bank will accommodae he demand side. Regarding (iv), we simly asssume ha he NCB ses he rice of governmne bonds urchased in he secondary marke and we also se he resecive amoun as in he daa. Noe ha, sricly seaking, as in any marke, he NCB can se eiher he rice or he quaniy of bond reurchases. We could allow he rivae bank o choose he quaniy of bonds sold o he NCB given rices (i.e. o have an exra Euler condiion in he banks roblem), bu, since he arameerizaion is such so as o in down he amoun as i is in he daa, we refer for simliciy o rea boh he rice and he amoun as exogenously given o rivae banks. Also noe ha we do no consider oher moneary olicies like he relaxaion of collaeral requiremens, he exension of loan mauriy and forward guidance. 22

26 +n k e j f k; + nk f e 2 j f 2 k; j f + n k e f ; + n k L f i; +n k ( + i d ) j f k; + nk ( + i l ) e L f i; + + ( + i b ) + ( ) e e g d +( + i ) e e eu d = = n k + i d e j f k; + nk ( + i ) e f ; + +n k + i l L f i; + nk j f k; + e nk L f i; + g d + eu d + arg + i MRO P arg P + mi (27) Insecion of he balance of aymens con rms he redisribuive role ha he ES can lay a leas in rincile. This can be done by dividends from he ES beyond hose conribued by he Greek NCB o he ES (see he ne erm mi which can be osiive or negaive) and he issuance of new TAR- + i MRO P GET2 liabiliies (see he erm ( arg P arg )). 25 This is in addiion o o cial bond urchases by he EC (see he erm eu d ). All hese iems can be used, a leas in rincile, o nance rade de cis, o reay foreign deb or o nance invesmens abroad. In he case of Greece, as discussed in Aendix B.2, he laer has aken he form of caial igh o safey (during he counry s sovereign deb crisis of he revious decade) or he urchase of governmen bonds held by invesors abroad in he secondary marke by he Greek NCB (his has been haening since he eruion of he andemic under he ECB s PEPP). 26 Noe ha had we allowed for bond urchases by he ES beyond hose urchased by he NCB and a a 25 Had he economy been closed, or had we have a small oen economy wih a naional currency, his erm could no be resen in he balance of aymens. Here, i becomes ossible hanks o ariciaion in a currency union which means ha he money marke clears a currency union level, raher han a naional level wihin each jurisdicion, and ha he currency issued (euro) works like an "inernaional" currency a leas wihin he EZ. See Economides e al (202a) for furher deails. 26 See e.g. Fabiani e al (202) for recen economeric evidence ha TARGET2 balances ac as as auomaic sabilizer couneracing sudden sos in rivae caial in ows. 23

27 rice above he marke-rice, hese ransacions would have also aeared in he balance of aymens and hence could lay a redisribuive allocaive role similar o ha layed by eu d, mi and he change in TARGET2 liabiliies. 2.8 Macroeconomic sysem Marke-clearing condiions, he macroeconomic sysem and he lis of endogenous and exogenous variables are resened in deail in Aendix A.8. The sysem consiss of 58 equaions in 58 endogenous variables. This is given he ahs of he exogenously se variables whose values will be se as in he daa. Non-exlosive ublic deb dynamics usually requires a leas one of he exogenously se scal olicy insrumens o reac o he ga beween he ublic deb o GDP raio and a arge value. This is also he case in our model, esecially since he eruion of he andemic crisis. Wihou loss of generaliy, we sar by assuming ha his role is layed by governmen ransfers which are he leas disoring scal insrumen in his class of models. In aricular, we roose ha he GDP share of governmen ransfers, s r, follows a Taylor-ye reacion funcion: s r = s r + ( ) s r d d (28) y y where s r and d y are arge values for he GDP share of ransfers and he ublic deb o GDP raio resecively, 0 is a ersisence arameer and = 0 is a feedback olicy coe cien on ublic deb imbalances (all hese values are seci ed below in subsecion 3.). 2.9 How we are going o work In he nex secions, we will arameerize he model, resen he daa used and solve i numerically. In aricular, our quaniaive analysis will consis of he following ses. Firs, afer calibraing he model o daa averages from he Greek economy, we will ge a iniial seady sae soluion using daa of he year 209 for he model s exogenous variables. As we shall see, his soluion can mach reasonably well he main feaures of he Greek macroeconomy jus before he eruion of he andemic crisis and can hus serve as a dearure oin in wha follows. This will be in secion 3. In urn, in secion 4, we will secify he lockdown shocks and he olicies adoed during he andemic. In oher words, dearing from he iniial seady sae de ned as he year 209, ransiion dynamics will be driven by lockdown shocks and olicy reacions o hese shocks. Simulaion resuls will be reored in secions 5, 6 and 7. In our soluions hroughou he aer, we assume ha all his is common knowledge so ha we solve he 24

28 model under erfec foresigh by using a non-linear Newon-ye mehod imlemened in Dynare Calibraion, daa and soluion for he year 209 Subsecion 3. resens arameer values and he daa used. 28 Then, subsecion 3.2 will resen a soluion for he year 209 which was he las year before he burs of he andemic. 3. Calibraion and daa Regarding srucural arameers for echnology and references, mos of hem are calibraed on he basis of Greek annual daa, while, for he res, we use commonly emloyed values and hen check heir robusness. Unless oherwise saed, he eriod over which we use Greek macroeconomic daa o calibrae he model exends from 995 o 209. Parameer values, eiher calibraed or se, are lised in Table. We reor a he ouse ha our main resuls are robus o changes in hese baseline arameer values a leas wihin reasonable ranges. Saring wih reference arameers, rivae agens ime discoun facor,, is calibraed from he seady sae version of he Euler equaion for domesic deosis (equaion (S5) in Aendix A.8) by using he weighed average value of he real deosi rae of Greek rivae banks for households deosis during he years (i d = :33%; he daa are from he Bank of Greece). The resuling value is = 0:9869. The weighs given o rivae consumion and leisure, and 2, in he households uiliy funcion are calibraed, for given 3, from he seady sae versions of equaions (S2), (S3), (S2), (S3), (S20) and (S2) in Aendix A.8, using daa for he share of rivae consumion o GDP (0:6747), he labour income share (0:583), he ercenage of ime devoed o leisure (0:59236) and own calculaions for he e ecive income and consumion ax raes (0:3094 and 0:8537). 29 The obained values of and 2, by 27 We have also solved he model assuming ha exogenous variables follow, for examle, a random walk rocess and ha rivae agens nex eriod execed values are equal o heir curren values. We reor ha he main resuls are no a eced. 28 Our calibraion secion is based on Economides e al (202b). The main di erence is ha now we also have rivae banks and moneary olicy. 29 These are average values. The daa regarding he share of oal labor comensaion in GDP, he ercenage of ime devoed o leisure and he share of rivae consumion in GDP are from "The Conference Board Toal Economy Daabase" of Eurosa and our own calculaions. In wha concerns ren seeking, we assume ha his akes lace during hours a work where he laer are as in he daa, i.e. non-leisure ime includes boh roducive and unroducive e or. Also, following usual racice, we have de ned oal hours available on a yearly basis as = Finally, he series of he e ecive ax raes are based on our own calculaions using daa from Eurosa (deails on he sandard formulas used can be found in e.g. Kollinzas e al (208)). 25

29 assuming 3 = 0:05, are 0:5436 and 0:4064 resecively. We reor ha our main resuls are robus o changes in 3, namely, he weigh given o uiliy-enhancing ublic services, whose value is agnosic and is usually se beween 0 and 0: (see e.g. Baxer and King (993) and Baier and Glomm (200)). The degree of reference for home over foreign goods in consumion,, also known as home bias, is calibraed from he equilibrium exression e f = ( f ) 2 (see Aendix A.8), where e is he real exchange rae and is he raio of he rice level of he foreign imored good o he rice level of he domesically roduced good. Using annual daa for he average real e ecive exchange rae (:07450) and he average raio of foreign o domesic rices (:4243), he resuling value is = 0: Coninuing wih echnology arameers, in he roducion funcion of rivae goods, he exonen on labor,, is calibraed from he exression ( ) ( ) = 0:583, where 0:583 is he above menioned average labour income share in he daa and measures he conribuion of roduciviyenhancing ublic goods/services in rivae roducion. Following e.g. he early aer by Baxer and King (993), he recen work of Ramey (2020) and many ohers, we se equal o 0:05. This value for imlies ha, which is he exonen on he comosie CES erm including caial and imored goods, equals 0:387. The arameer measuring he inensiy of caial vis-avis imored goods,, is calibraed using daa for imored caial goods and gross xed caial formaion, boh as shares of GDP. We consider he sum of hese wo comonens o give oal invesmen in hysical caial, domesic and foreign, in he economy. Using as a roxy for he share of xed gross caial formaion over oal invesmen in hysical caial, we end u wih a value for equal o 0:504 (he same value of 0:504 will be used for g in he sae rm s roducion funcion discussed below). 3 Regarding he subsiuabiliy arameer in he rivae roducion funcion, o, is se a 0:5; which imlies an elasiciy of subsiuion beween caial and imored goods in rivae roducion of 2 (he same value of 0:5 will be used in he sae rm s roducion funcion below); noe ha his is a commonly used value for CES roducion funcions (see e.g. Sokey (996)). Finally, he work roduciviy arameers of caial owners and workers in he rivae roducion funcion, A k and A w, are se a 2 and resecively; his di erence roduces a skill wage remium around 2 which is wihin usual 30 The daa on he real e ecive exhange rae have been obained from he Federal Reserve Bank of ST. Louis, while, for he raio of foreign o domesic rices, as a roxy, we use he raio of foreign o domesic GDP de aor. Regarding he foreign GDP de aor, we have chosen o use he German one, whereas he daa for boh de aor, i.e. he Greek and he German one, are obained from Eurosa. 3 The daa regarding xed gross caial formaion are obained from AMECO, whereas, he daa for imored caial goods are obained from OECD. 26

30 ranges in he lieraure on income inequaliy (see e.g. Auor (204)). In he sae rms roducion funcion, he Cobb-Douglas exonens on ublic caial and ublic emloymen, and 2, are se resecively a 0:309 and 0:398, which corresond o average aymens for ublic invesmen and ublic wages, exressed as shares of oal ublic aymens o all inus used in he roducion of ublic goods (he daa are from Eurosa). In urn, he Cobb-Douglas exonen on goods urchased from he rivae secor, 2, follows residually and is 0:293. The caial dereciaion rae,, is se a 0:04. This value resuls from calibraing he seady sae version of equaion (S33) in Aendix A.8 by using annual daa for gross xed caial formaion and ne caial sock from AMECO. The same value will be used for he dereciaion rae of ublic caial. Boh he TFP arameers (in he rivae and in he ublic secor roducion funcions) are normalized a. In he ren-seeking echnology, ( RS) is se a he degree of roery righs in he daa. This is de ned as he average of hree sub-indices: "he rule of law", "regulaory qualiy" and "oliical sabiliy and absence of violence/errorism", which are hree indicaors commonly used for he consrucion of a measure of roery righs roecion (he daa are from he World Governance Indicaors) rescaled in he 0 o range (he higher he value, he beer he qualiy of insiuions). This gives RS = 0:464 for he degree of ublicness. The ower coe cien,, is assumed o be common for caial owners and rivae workers and is se a 0:5, while for ublic emloyees is se o 0:65. The e eciveness arameers of ublic emloyees, rivae workers and caial owners, b, w and k are se resecively a 3, 0:5 and :5 o re ec heir relaive oliical ower in ren exracion. This arameerizaion conribues o geing hours a work wihin daa averages and also makes ublic emloyees he main winners from ren exracion. As is widely recognized, in he Greek economy, he ower of ublic secor emloyees is bigger relaive o oher social grous (see e.g. Kollinzas e al. (208)), and his is caured by he choice of hese seci c values. We calibrae he ransacion cos arameer associaed wih caial changes in he rm s roblem so as he invesmen loss in erms of ouu o be around %. This obains for k = 0:45. However, we reor ha our main resuls are robus o changes in he value of k. The ransacion cos arameers associaed wih rivae ariciaion in he foreign marke for deosis, and j f, are se o 0:5 and 0:78 resecively, so as o ge deosis a foreign rivae banks equal o 0:25 of heir resecive deosis a domesic rivae banks (i.e. j f = 0:25 j h ). Following he economeric sudy by Dinooulos e al. (2020) for he Greek economy, we se he exors elasiciy, reresened by arameer in equaion (S53) in Aendix A.8, a 3:040; we reor however ha our main resuls are robus o changes in he value of. Coninuing wih he banking secor, we se he arameers in he cos 27

31 funcion of banks so as o mach daa for 209. In aricular, we se he cos arameers associaed wih rivae loans o rms, l, reserves, m, and loans rovided by he NCB, z, a 0:, 0:00003 and 0:35 so as o mach he GDP shares of Greek rivae banks loans o small and medium size enerrises (SMEs), reserves held a he NCB and loans by he NCB (he daa are from he websie of he Bank of Greece). We se he cos funcion arameer associaed wih domesic governmen bonds, b, a 0:022, o mach he average value of he real ineres rae in he daa (where he laer is he di erence of he nominal ineres rae on he 0-year Greek governmen bond and he in aion rae measured by he ercenage change of he Greek GDP de aor). 32 The oulaion fracions of ublic emloyees, n b, and caialiss or selfemloyed, n k, are se a 0:2 and 0:2 resecively, similarly o daa from OECD so ha he fracion of rivae workers, n w, follows residually a 0:6. For our baseline simulaions, we assume ha he shares in oal oulaion of nal good rms n h, inermediae goods rms n i, caial good rms (n c ) and rivae banks (n ), are all equal o he share in oal oulaion of heir owners, namely, he caialiss n k, ha is, n h = n i = n c = n = n k = 0:2. We also se n b = n g = 0:2, ha is, he share in oal oulaion of sae rms equals he share in oal oulaion of ublic secor emloyees. To se he Dixi-Sigliz arameer measuring imerfec comeiion in he roduc marke, #, we use informaion from Eggerson e al (204), who reor ha he gross marku in raded goods (recall ha we have raded goods only in our model) is around :7 in he erihery counries of he EZ (and :4 in he core counries). Thus, as in Eggerson e al (204, secion 3.7), we in down by argeing a seady sae gross marku of :7 and his gives # = 0:85 (noe ha his corresonds o 6:88 in he Eggerson e al funcional seci caion). We also se he arameer in he Roemberg-ye rice adjusmen coss,, o 3, which is a value wihin commonly used arameer ranges. 32 The daa are from Eurosa. 28

32 Table Baseline arameerizaion Parameer Descriion Value home goods bias in consumion 0:77 calibr weigh of consumion in uiliy 0:5436 calibr 2 weigh of leisure in uiliy 0:4064 calibr 3 weigh of uiliy-enhancing ublic services 0:05 calibr ime discoun facor 0:9869 calibr and g dereciaion rae of riv and ub caial 0:04 calibr ransacion cos in foreign deosi marke 0:5 calibr j f hreshold in foreign deosi marke 0:78 calibr A TFP in rivae secor s roducion funcion se A g TFP in ublic secor s roducion funcion se A k caial owners labour roduciviy 2 calibr A w workers labour roduciviy calibr share of labor in rivae roducion 0:63 calibr conribuion of ublic ouu o rivae roducion 0:05 se share of caial and imored goods in ublic roducion 0:309 calibr 2 share of labor in ublic roducion 0:398 calibr inensiy of rivae caial relaive o imored goods (rivae) 0:504 calibr o subsiuabiliy beween caial and imored goods (rivae) 0:5 calibr g inensiy of ublic caial relaive o imored goods (ublic) 0:504 calibr og subsiuabiliy beween caial and imored goods (ublic) 0:5 calibr coe cien in Roemberg-ye coss 3 se k caial adjusmen cos arameer 0:45 calibr l ransacion cos associaed wih bank loans o rms 0: calibr z ransacion cos associaed wih NCB loans o banks 0:35 calibr b ransacion cos associaed wih banks gov bonds 0:022 calibr m ransacion cos associaed wih banks reserves 0:00003 calibr 29

33 Table con. Baseline arameerizaion Parameer Descriion Value k e ciency of caial owners ani-social aciviy :5 calibr w e ciency of workers ani-social aciviy 0:5 calibr b e ciency of ublic emloyees ani-social aciviy 3 calibr RS degree of ublicness 0:464 daa k measure of diminishing reurns in ani-social aciviies of caialiss 0:5 se w measure of diminishing reurns in ani-social aciviies of workers 0:5 se b measure of diminishing reurns in ani-social aciviies of ublic emloyees 0:6 se exonen in he funcion of exors 3:040 se # subsiuabiliy beween inermediae goods 0:85 calibr n k share of ca owners in oulaion 0:2 daa n w share of riv workers in oulaion 0:6 daa n b share of ub emloyees in oulaion 0:2 daa n g share of sae rms in oulaion 0:2 se n i share of rivae rms in oulaion 0:2 se n c share of caial rms in oulaion 0:2 se n share of rivae rms in oulaion 0:2 se In addiion, o solve he model, we also need daa for he exogenous variables, namely, olicy insrumens and res-of-he-world variables for he year 209. Regarding sending-ax olicy insrumens, using daa from Eurosa and our own calculaions, we se s i, s g, sm, s w, c, y and, which are resecively he GDP shares of governmen sending on invesmen, goods urchased from he rivae secor, imored goods/caial, ublic wages, as well as he e ecive ax raes on consumion, income and cororae rofis, a 0:022; 0:077; 0:045; 0:7; 0:225; 0:354 and 0:273 resecively. In wha concerns he e ecive cororae ax rae, we use as a roxy he e ecive ax rae on caial income. In addiion, we se s r a 0:2 (in he average daa he resecive value is 0:207) o arge he seady sae value of he ublic deb o GDP raio as in he daa in he year 209 (around 80%). Regarding moneary olicy insrumens, using daa from ECB, we se i r, i z and i MRO, which are he ineres raes on reserves, bank loans and main re nancing oeraions a 0:5%, 0:25% and 0% resecively. Also, we se he raio of ES dividends o GDP, mi y, a 0:0002, which is he average value in he daa over (he daa are from he websie of he Bank of Greece). The fracions of Greek ublic deb in he hands of foreign rivae 30

34 agens/banks and EU insiuions, g and eu, as in subsecion above, are se a 0:596 and 0:7087 resecively as indicaed in he daa for 209 (see Aendix B. for deails and he evoluion of g and eu over ime). The ineres rae on EU loans, i, is se a %. Also, in he soluion for 209, we assume zero governmen bonds urchases in he secondary marke by he cenral bank ( = 0); his is because Greek governmen bonds became ar of he ES s asse urchase rogrammes afer he eruion of he andemic and in aricular under he PEPP rogram. Finally, in he feedback olicy rule equaion (28), he values of s r and d y are hose in he dearure year 209, while he ersisence arameer,, is se a 0:5, and he feedback coe cien arameer,, is se a 0:04 which is he lowes ossible value needed o ensure dynamic sabiliy a leas in our baseline simulaions. For he exogenous res-of-he-world variables, we se, for simliciy, domesic bank loans o foreign rms, L f i;, and deosis by foreign households a domesic banks, j f k;, a 0. The foreign lending rae, il, is se a 5:39%, which is he ineres rae on loans o Greek non- nancial cororaions, while he foreign deosi rae, i d, is se a :06%, which is he average annual rae of German rivae banks. 33 Finally, he ineres rae on foreign governmen bonds is calculaed from he seady sae version of equaion (S42) in Aendix A.8. For simliciy, we se he foreign governmen bond s rae equal o he domesic deosi rae, i b = i d, which imlies ha he domesic rivae banks do no hold foreign governmen bonds. Daa averages of olicy variables over he eriod , as well as olicy arameers, are resened in Table 2, while daa of foreign nancial variables are resened in Table Daa averages are calculaed over he eriod Daa are from Bundensbank and Bank of Greece. 3

35 Table 2 Policy variables ( ) and arameers Parameer Descriion Value s i ublic invesmen o ouu (%) 0:022 daa s g gov urchases from he riv secor o ouu (%) 0:077 daa s m gov sending on imors o ouu (%) 0:045 daa s w ublic wage bill/ouu (%) 0:7 daa s r gov ransfers/ouu (%) 0:2 calibr c e consumion ax rae 0:225 daa y e ecive income ax rae 0:354 daa e ax rae on caial income 0:273 daa eu share of oal ublic deb held by EU insiuions 0:7087 daa g share of oal ublic deb held by foreign banks 0:596 daa i r ineres rae on reserves 0:5% daa i z ineres rae on CB s loans 0:25% daa i MRO ineres rae on main ref oeraions 0% daa i ineres rae on EU loans % se CB s gov bonds urchases se ersisence arameer in he olicy rule 0:5 se feedback coe cien in he olicy rule 0:04 se Table 3 Res-of-he-world variables Variable Descriion Value j f k deosis of foreign agens 0 se L f i; loans o foreign rms 0 se i d foreign deosi rae (%) :06 calibr i l foreign lending rae (%) 5:39 calibr i b foreign gov bonds rae (%) :33 se 3.2 Soluion for he year 209 Using he above arameer values and daa of he year 209, he seady sae soluion of he model is reored in Table 4. In his soluion, variables do no change (so i can be hough as he "rend" of he Greek economy afer is sovereign deb crisis and before he burs of he andemic crisis) and all exogenous variables have been se as in he daa of he year 209. As can be seen, his soluion is in line wih acual daa in 209 and can hus rovide a reasonable dearure for he olicy scenaria sudied in he nex secions. In aricular, he soluion does a relaively good job a mimicking, for examle, he osiion of he counry in he inernaional caial marke, as well as he consumion-invesmen behavior of he rivae secor. 32

36 Table 4 Main variables in he soluion for he year 209 Variable Descriion Value c=y consumion/ouu 0:63 inv=y invesmen/ouu 0:5 b=y ublic deb/ouu :8 k=y caial/ouu 3: l=y rivae loans/ouu 0:9 d=y deosis/ouu 0:45 m =y reserves/ouu 0:05 z=y CB loans/ouu 0:04 m=y money/ouu 0:77 f =y rms ro s/ouu 0:8 c k consumion of caial owner 0:57 c w consumion of rivae worker 0:9 c b consumion of ublic emloyee 0:30 l k work hours of caial owner 0:24 l w work hours of rivae worker 0:49 l b work hours of ublic emloyee 0:3 u non-leisure ime 0:45 w k wage of caial owner : w w wage of rivae worker 0:55 w b wage of ublic emloyee 0:85 f = h raio of foreign o domesic rices 0:47 s k caialis s e or ime allocaed o ani-social aciviies 0:03 s w worker s e or ime allocaed o ani-social aciviies 0:0 s b ublic emloyee s e or ime allocaed o ani-social aciviies 0:8 i l ineres rae on loans (%) 5:39 i d ineres rae on deosis :33 i b ineres rae on governmen bonds (%) 2:35 4 Lockdown shocks and olicy scenaria sudied In his secion, we rs model he wo lockdown shocks, c and l, needed o rigger he andemic economic downurn, and hen de ne he olicy scenaria (facual and hyoheical) we will focus on. These shocks and olicies will drive he ransiion dynamics dearing from he iniial 209 soluion. 4. Modelling he lockdown shocks As in Economides e al (202b), we assume ha, in 2020, l and c changed by 5% relaive o heir value in he absence of lockdown e ecs (his value 33

37 is ) 34 and hen evolve according o he AR() rocesses: l = l l l l (29a) c = c c ( c ) c (29b) where l and c are ersisence arameers chosen so as he imac of he lockdown on economic aciviy o weaken gradually, wihou any governmen reacion, wihin four o ve years, whereas as said above l = c =. 4.2 Policy reacion o he andemic a naional and EU level We now discuss olicy resonses a naional and EU level. These resonses will hen be added formally o our model Fiscal olicy reacion a naional level We sar wih he main olicy measures adoed by he Greek governmen during 2020 and 202. In aricular, we assume ha he oal size of he naional scal simulus (i.e. labour income comensaion, ax discouns, increases in governmen sending, ec.) is as in he daa, ha is around 7.5% of GDP in 2020, and around 8% (esimaed) in he curren year of 202. Since we do no have deailed daa on he exac use of his scal simulus, we make he assumion ha i is equally used for ax discouns and sending rises. Seci cally, we assume ha he governmen makes a lum-sum ransfer aymen o all households so as o cover he reducion in heir labor incomes caused by he andemic shocks assumed above. In oher words, we add exra ransfers ino he budge consrains of he hree income grous, denoed as gk; con, gcon w; and gb; con resecively, ha are rovided in a lum-sum fashion and ake he form: gk; con = ( y ) w k l l k; (30a) g con w; = ( y ) w w l l w; gb; con = ( y ) w g l l b; (30b) (30c) On o of he above, we assume ha he Greek governmen rovides subsidies o rivae rms in an aem o mainain heir demand for labor during Seci cally, we assume ha he governmen subsidizes he 34 Tha is, l = 0:85 and c = :5 in The magniude of hese iniial Covid shocks is chosen so as o mach he size of he Greek recession in

38 labor cos by % in 2020 and by 3% in 202 (hese numbers are consisen wih announcemens made by he Greek governmen). We also assume ha he governmen increases emorarily is sending on ublic invesmen and governmen urchases from he rivae secor as shares o GDP, by ercenage oin in boh 2020 and 202. Finally, we assume ha he governmen cus emorarily he ax raes on income, consumion and cororae ro s by 2 ercenage oins in 2020 and by ercenage oin in 202. Before roceeding, we should oin ou ha all olicy changes hroughou he aer are nanced by adjusmens in he end-of-eriod ublic deb which, as said above, is he residual ublic nancing insrumen Financial assisance from he Recovery Fund In addiion o he above resonses, he Greek economy can bene from resources coming from he EU s newly esablished Recovery and Resilience Faciliy, whose aim, as said in he Inroducion, is o raise funds from rivae markes and new axes and hen allocae hem o member-counries deending on how much hey have been hur by he COVID-9 andemic. Greece can bene uo a ne amoun of around 32 billion euros in he form of grans and loans where he laer are rovided a non-marke ineres raes. The amoun of 32 billion euros ranslaes ino around 7:5% of he Greek GDP in 209 and should be used by he end of As has been decided by he EU, 40:63% (or 3=32) of he oal funds received will be in he form of loans received during (and hence hey will be added o he amoun of Greek ublic deb held already by EU insiuions as modeled in subsecion above) and he res will be in he form of grans (hese are cash ransfers ha are added as an exra iem o he budge consrain of he Greek governmen and hence of he counry s balance of aymens again from 202 o 2026). In our numerical simulaions, we will assume a ime-o-send lag regarding he acual use of hese amouns which means ha hey will be equally divided in each year beween 2022 and 2027 (i.e. one sixh in each year). Hence, he oal amoun of Greek ublic deb held by EU insiuions in each eriod since 209 evolves as: eu d = eu 209d :63% Re covery_f und (3) Regarding he way hese funds are used, we assume ha he Greek governmen uses half of hem o nance an increase in ublic invesmen, gg;, i governmen urchases from he rivae secor, g g g;, and imored caial goods, m g g;, which all of hem are used for he roducion of ublic goods/services (see secion 2.5 above), while, he oher half goes o ransfers. In aricular, we assume ha 25.29% of he 6 exra billion euros is used o nance ublic invesmen, gg;, i 48.58% of he 6 exra billion euros is used o nance governmen urchases from he rivae secor, g g g;, 26.3% of he exra 6 biilion euros is used o nance imored caial goods, m g g;, 35

39 while, he oher 6 exra billion euros are added o he ransfer aymens, g r Financial assisance from he ECB in he andemic Wih resec o moneary olicy, we assume ha ES kees he main olicy ineres raes a heir 209 levels, and, in addiion, ermis he issuance of new TARGET2 liabliies by he Greek NCB and urchases Greek governmen bonds in he secondary marke (boh are as in he daa). Regarding TARGET2 liabiliies, we assume ha from 2020 onwards hey reac o deb imbalances by following he feedback olicy rule: d arg = d arg + T ARG d d y y (32) P where d arg = arg P arg is he change in TARGET balances, is a ersisen arameer se a 0:5 and is a feedback olicy coe cien se a a low value, 0:05 (his arameerizaion hels us o ge a deb-o-gdp raio around 205% in 2020 which is close o he daa). Regarding urchases of Greek governmen bonds by he Greek NCB from domesic and foreign rivae banks in he secondary marke under PEPP, we assume, as in he daa, ha cumulaive urchases (he average mauriy of hese bonds is 8 years) are around 8.9 billion euros a he end of Januray 202, which ranslae o around 0% of he Greek GDP in 209, while, following he announcemens of he ECB, we assume ha he NCB will urchase a similar amoun of bonds in 202 and coninue hese urchases uo March In erms of modelling, his means ha he Greek governmen bonds reurchased by he Greek NCB from rivae banks a home and abroad is: ( ) d d + ( ) e e g d = By (33) where B is a arameer which is se a B = 0: in 2020 and 202, and a 0:025 in Finally, we assume ha he NCB buys governmen bonds in he secondary marke a a xed rice,, which is above he "shadow" marke-rice; in aricular, we se = :2 ( + i b 209 ), where ib 209 is he nominal ineres rae on governmen bonds in he 209 soluion Baseline scenaria Given he above, we nd i naural o sar wih wo baseline scenaria. The rs is he case wih he lockdown shocks only, assuming away any olicy 35 According o he ECB websie, he Governing Council will erminae ne asse urchases under he PEPP once i judges ha he COVID-9 crisis hase is over, bu in any case no before he end of March

40 reacion. This can hel us o undersand he economic consequences of he andemic had olicy no reaced a all. We label his S0. Second, he "acual" case wih he lockdown shocks and olicy reacion a boh naional and EU level as described above. We label his S. Resuls are reored nex. 5 Resuls for he baseline scenaria Grah illusraes he simulaed ah of GDP as % deviaion from is 209 value under S0 and S. In boh cases, he andemic-relaed shocks, l and c, ake he value of 0:85 and :5 resecively in 2020 and hen gradually reurn o heir re-covid value (i.e. ) according o (28a)-(28b). As said above, S0 describes wha would have haened wihou any olicy reacion o he economic consequences of he andemic (i.e. we kee all scal and moneary olicy variables consan a heir values in he iniial seady sae soluion of 209 and we only allow, as said above, governmen rnasfers o reac o deb-o-gdp raio for dynamic sabiliy reasons), while S mimics wha has been haening in realiy which means ha here is olicy reacion as ha in he daa and his is boh a naional and EU level (i.e. on o of S0, his incororaes he naional scal simulus, he funds from he Recovery Fund and accommodaive moneary olicy in he form of PEPP and TARGET2 s reacion o deb imbalances). As can be seen, under S0 (he black line), he economy would have los around 2% of is ouu in 2020 relaively o 209; o make i worse, he economy could no have managed o rebound in he years afer, in he sense ha GDP would remain below is 209 level for several years. By conras, under S (he blue line), he simulaed ouu loss in 2020 is limied o abou 8:5%, which is close o he daa; moreover, afer 2023, he GDP can be close o is re-crisis 209 level. 37

41 Grah : Real GDP under S0 and S (% deviaion of ouu from is 209 value) S0 S We also reor welfare (i.e. discouned lifeime uiliy) resuls in erms of consumion equivalens as in he olicy reform lieraure (see e.g. Lucas (990)). Vis-a-vis he iniial year, 209, S0 and S need welfare subsidies 6% and :5% resecively. Tha is, one would need a 6% ermanen increase in consumion in each eriod o comensae households from he economic consequences of he andemic shock had no olicy reacion aken lace, while, his is reduced o :5% hanks o he comrehensive olicy reacion ha has aken lace. Noice ha hese are non-negligible numbers. 36 Overall, hese resuls show he big vulnerabiliy of he Greek economy o shocks (boh suly and demand). They also imly ha olicy inervenion has been more han necessary. Grah 2 resens he simulaed ah of he ublic deb o GDP raio under S0 and S. Under boh S0 and S, his raio jums o around 205% in 2020, which is close o he daa (206%), and hen de-escalaes afer he imac year as he GDP rebounds. 37 On he oher hand, he increased scal 36 For comarison, Lucas (990) concludes wih a welfare gain beween 0.75 and.25% of consumion even if he reform sudied in his aer is radical (from he exising US ax srucure o an oimal Ramsey srucure wih zero caial axes over ime). 37 We reor ha a higher value of he feedback olicy coe cien T ARG, in he olicy rule hels he deb-o-gdp raio o sabilize faser a is 209 level. 38

42 cos of he naional simulus as well as he funds in he form of deb coming from he Recovery Fund imly a higher deb o GDP raio under S han under he no-olicy-reacion scenario S0, desie he smaller fall in GDP under he former. Tha is, as execed, he relaive small ouu loss under S comes a he cos of higher deb. Grah 2: Public deb o GDP under S0 and S (%) S0 S Wha would have haened wihou nancial assisance from he EU In his secion we erform wo counerfacual exerimens. We examine wha would have haened wihou nancial assisance from EU insiuions. To quanify he role of he ES, we rs consider wha would have haened wihou he new measures aken by he ES since 209. In aricular, relaive o S, we swich-o bond urchases under PEPP and he rise of TARGET2 liabiliies resuling from heir feedback reacion o rising ublic deb. This scenario is labelled S2. Second, on o of S2, we also swich o he resources coming from he Recovery Fund. In oher words, under his scenario, labelled S3, he Greek economy can only bene from he naional scal simulus adoed by he Greek governmen. Of course, in 39

43 boh S2 and S3, he economy coninues o bene from nancial assisance as in he re-covid years (see he 209 soluion). Grah 3 resens S2 (red line), S3 (green line) bu also includes S (blue line) and S0 (black line) for exosiional convenience. Comarison of S and S2 reveals he exra bene s of he new nancial assisance rovided by he ES. In aricular, wihou he laer (i.e. under S2), he ouu loss in 2020 would be 9:5% relaive o 209. I is imoran o reor here ha hese bene s would be even bigger if we increase he magniude and/or he duraion of he PEPP urchases, as well as heir rice. Higher bene s would also be delivered if we allow a sronger reacion of TARGET liabiliies o deb imbalances. Nex, if, on o of his, here were no scal assisance from he Recovery Fund eiher, hen he ouu loss in 2020 would be even bigger, 0:5%. Recall ha wih he full ackage (S), he loss is 8:5%. In addiion, noice ha he recession would las longer under boh S2 and S3. Regarding he welfare losses, always vis-a-vis he year 209, hese are 2:3% under S2 and 3:6% under S3; again, non-negligible. Grah 3: Real GDP under S0, S, S2 and S3 (% deviaion of ouu from is 209 value) S0 88 S S2 S Grah 4 resens he simulaed ah of ublic deb o GDP raio under scenaria S0, S, S2 and S3. As can be seen, wihou assisance from he EU and esecially from he Recovery Fund, he ublic deb o GDP raio would be higher and longer lasing relaive o he acual scenario S. 40

44 Grah 4: Public deb o GDP under S0, S, S2 and S3 (%) S0 S S2 S Summing u, he above resuls show how necessary he olicy reacion has been bu also con rm he imorance of nancial assisance from EU insiuions in crisis years. 38 Acually, he role of EU insiuions (Euroean Commission and ECB) is more imoran han wha Grahs -4 seem o imly a rs sigh. This is because one of he main bene s ha Greece receives from membershi in hese sura-naional insiuions is he imor of credibiliy and, in aricular, he aniciaion of markes ha hese insiuions will se in, in one way or anoher, if somehing goes wrong in he fuure. This is sudied nex. 7 The imorance of rus So far we have assumed away he fear of defaul on ublic deb and hence sovereign risk sreads. Acually, his is as in he daa. I is remarkable ha, since 209, desie he fall in economic aciviy and he big rise in ublic deb-o-gdp raios, even counries wih heavy ublic deb burdens, like Greece, have been enjoying very small bond sreads (excess yields) over he German Bund - a leas so far. For examle, a he days of wriing his 38 See Economides e al (202a) for a similar conclusion during he Greek sovereign deb crisis of he revious decade. 4

45 aer, he Greek governmen issues bonds wih a 0.9% ineres rae while is ublic deb is higher han 200% of GDP. We believe his haens for several reasons. One reason, as already said above, is he nancial assisance from he ECB (see e.g. PEPP) and he EC (see e.g. he Recovery Fund) and, erhas more imoranly, he signals of suor sen by hese EU insiuions if somehing goes wrong. Anoher comlemenary reason is he relaive oliical sabiliy in he heavily indebed counries combined wih coordinaion and rus beween EU leaders and naional governmens in he curren siuaion. All his has increased markes rus in he abiliy, or a leas he wilingness, of hese counries o reay heir debs, a leas so far. Bu, as he exerience of he Euroean deb crisis in he revious decade has shown, a mix of weak economic fundamenals, negaive shocks/news, and uncerainy over olicy reacion, can very easily change he siuaion for he worse (see also he review aer of Lorenzoni (204)). Inernaional crises are yically receded by weak economic fundamenals, like ersisen budge de cis and a large sock of ublic deb, ersisen curren accoun de cis and a large sock of foreign deb, an overvalued real exchange rae, oor qualiy of core insiuions, ec. 39 These imbalances se he sage for a crisis. Then, if a negaive shock his a counry wih such weak fundamenals, senimens can change, rus can be los, invesors will sar selling domesic asses, risk remia will emerge o comensae for he fear of defaul, deb burdens will rise as ineres raes rise, a recession will sar and all his can become a vicious cycle and an inernaional nancial crisis. Various shocks can work as riggers of he crisis, including unrealisic romises ha ignore he governmen s iner-emoral budge consrain; an insiuional deerioraion, fuelled by oliical olarizaion, ha signals bad growh rosecs; he loss of rus beween naional olicymakers and EU insiuions; a reor by an inernaional raing agency or organizaion exressing doubs abou deb susainabiliy; ec. 40 Moreover, he crisis can have di eren imlicaions deending on he abiliy of he oliical sysem o ake he necessary ses, he relaionshi beween crediors and debors or, in he case of Greece, he rus beween EU insiuions (he ECB and EC) and he Greek governmens (curren and fuure), ec. In oher words, in a crisis eisode, here can be many underlying causes, many riggers/shocks and many ossible olicy resonses, and all of hem shae he robabiliy of defaul or he ex ane defaul rae and hence he size of risk sreads. Hence, a formal model of he laer canno be bu selecive and incomlee. Which fundamenals, riggers/shocks and olicy reacions 39 The lieraure has exlored he role of such fundamenal variables in forecasing crises and deb defauls; see Lorenzoni (204, secion 6). 40 Or, in he case of he US in , he rigger was a decline in housing rices in 2006 ha a eced he shadow banking secor before being ransmied o he whole economy. 42

46 o include as argumens in he robabiliy funcion? 4 Given all his, o rovide a simle numerical examle of he consequences of risk remia, here we jus se i exogenously. 42 In aricular, we assume ha rivae agens fear ha he governmen and domesic rivae banks will arially defaul on heir obligaions 43 and we se his ex ane defaul rae a 20% during which is wihin he range observed in Greece during is sovereign deb crisis. 44 We add his fear of defaul scenario (labeled S4) o our baseline scenario S oher hings equal. Grah 5 and 6 lo he simulaed ahs of ouu and deb-o-gdp raio resecively under S4. We also include S for comarison. As can be seen, he emergence of risk remia makes he recession sharer and longer (see Grah 5) and, a he same ime, he deb-o-gdp raio skyrockes as long as ineres rae risk remia exis (see Grah 6) as a resul of a higher cos of borrowing and subsequenly higher ineres rae reaymens. Noe ha, even if defaul does no acually maerialize (i.e. he ex os defaul rae in he budge consrains is se a zero), he mere aniciaion of defaul increases he relevan ineres raes and his is enough o do he macroeconomic damage. Trus is imoran. 4 I is usual o assume ha his robabiliy deends only on he sock of ublic or exernal deb relaive o a hreshold value, and erhas on a shock wih an assumed disribuion funcion (see e.g. Corsei e al (203)). Bu, as Lorenzoni (204) oins ou, scal condiions are no always he main culri in hese eisodes. Corsei e al (203) also rovide a brief review of he lieraure on deb defaul. 42 See Kriwoluzky e al (209) who also se he defaul rae exogenously. Acually, hese auhors assume a richer robabilisic srucure (ha includes several oucomes in addiion o defaul) bu, on he oher hand, work wih a simler model. 43 The ex ane defaul rae adds new wedges o he Euler equaions of deosis and governmen bonds. The new macroeconomic sysem wih he ex ane defaul rae is resened in deail is Aendix A We reor ha we have also exerimened wih various endogenous seci caions according o which he ex ane defaul rae is a funcion of he ga beween he ublic deb o GDP raio and a hreshold value, and/or he degree of deerioraion of a core insiuional fundamenal like he roecion of roery righs. To he exen ha we calibrae he underlying arameers in he robabiliy funcion so as o accoun for he same rae as ha se exogenously, he resuls remain basically he same. We hus model he fear of defaul in he simles ossible way. 43

47 Grah 5: Real GDP under S and S4 (% deviaion of ouu from is 209 value) S S Grah 6: Public deb o GDP under S and S4 (%) S S

48 8 Closing he aer Greece had jus sared o recover from is sovereign deb crisis when, like mos counries, was hi by he andemic shock in early The olicy measures aken by he Greek governmen, he Euroean Commission (e.g. Recovery Fund) and he ECB (e.g. PEPP) have heled he counry o avoid he worse and reduce he economic downurn bu his has come a he cos of ublic nances. These days, wih a ublic deb above 200% of GDP (he imlicaions of which have been masked so far mainly by he nancial assisance and he imored credibiliy rovided by hese EU insiuions), he counry is vulnerable o economic and oliical shocks. As we showed, if somehing haens and he fear of deb defaul and risk remia re-emerge, he macroeconomic e ecs will be derimenal. One canno rely on he assumion of low risk remia. Alhough exogenous facors canno be conrolled for, he counry should a leas no reea he same misakes as during he sovereign deb crisis of he revious decade (esecially, oliical olarizaion and reform ineria boh of which creaed uncerainy, raised risk remia and all his led o a vicious cycle of recession and deb). Since he main resuls have already be wrien in he Inroducion, we close wih a ossible exension. Here we sudied a Eurozone erihery counry receiving assisance wihin a small oen economy model. I would be ineresing o develo a wo-counry model, wih a erihery and a core counry, and model he imlicaions of he Recovery Fund and he ECB s olicies, as hey are in he daa, for boh counries. 45

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56 Aendix A: Soluions A. Soluion of caial owners roblem Each k acs comeiively choosing fc h k;, cf k;, c k;, l k;, s k;, j h k;, jf k;, m k;g =0. The rs-order condiions include he de niion in (2) and he consrains in (3a-3c) in he main ex as well as: c k; = ( k; + k; ) ( + c ) c (Aa) 2 ( l k; s k; ) = k;( y )wk l (Ab) 2 ( l k; s k; ) = k (s k; ) (RS G r ) k; n k k (s k; ) + n w w (s w; ) + n b b (s b; ) (Ac) k; = k;+ ( + i d +) + (Ad) k; e + f e j f k: j f e + + = k;+ ( + i d +) + + (Ae) c h k; c f k; = ( ) f (Af) k; ( + c ) c k; k; = k;+ c h k; + f c f k; + (Ag) m k; = 0 (Ah) where k; and k; are he Lagrange muliliers associaed wih he budge and he cash-in-advance consrain resecively. I also follows from he above equaions ha he CPI is: = ( ) ( f ) 53

57 A.2 Soluion of workers roblem Each w acs comeiively choosing fc h w;, c f w;, c w;, l w;, s w;, m w; g =0. The rs-order condiions include he de niion in (5) and he consrains in (6a-6c) in he main ex as well as: c w; = ( w; + w; ) ( + c ) c (A2a) 2 ( l w; s w; ) = w;( y )ww l (A2b) 2 ( l w; s w; ) = w (s w; ) (RS G r ) w; n k k (s k; ) + n w w (s w; ) + n b b (s b; ) (A2c) c h w; c f w; = ( ) f (A2d) w; ( + c ) c w; w; = w;+ c h w; + f c f w; + (A2e) m w; = 0 (A2f) where w; and w; are he Lagrange muliliers associaed wih he budge and he cash-in-advance consrain resecively. A.3 Soluion of ublic emloyees roblem Each b acs comeiively choosing fc h b;, cf b;, c b;, l b;, s b;, m b; g =0. The rs-order condiions include he de niion in (8) and he consrains in (9a-9c) in he main ex as well as: c b; = ( b; + b; ) ( + c ) c (A3a) 2 ( l b; s b; ) = b;( y )wg l (A3b) 2 ( l b; s b; ) = b (s b; ) (RS G r ) b; n k k (s k; ) + n w w (s w; ) + n b b (s b; ) (A3c) c h b; c f b; = ( ) f (A3d) b; b; = b;+ + (A3e) 54

58 b; ( + c ) c c h b; + f c f b; m b; = 0 (A3f) where b; and b; are he Lagrange muliliers associaed wih he budge and he cash-in-advance consrain resecively. A.4 Soluion of nal good rms roblem Each nal good rm acs comeiively. The rs-order condiion for y h i; gives he demand funcion: h i; = y h i; y h h; (A4a) which in urn imlies from he zero-ro condiion: 2 XN i = 4 N i (h i;) i= 3 5 (A4b) Tha is, in a symmeric equilibrium, we will have yh; h = yh i;, h and h; = 0. = h i; A.5 Soluion of inermediae goods rms roblem The gross ro of rm i, denoed as gross i;, is de ned as sales minus he wage bill minus he cos of imored goods minus adjusmen coss associaed wih changes in caial and rices: gross i; h i; y h i; w w l w i; w k l k i; f m f i; k 2 ki; k i; 2 k i; 2 h i; h i; 2 y h i; (A5a) This gross ro is used for reained earnings, he aymen of cororae axes o he governmen, dividends o shareholders and ineres aymens for loans received from rivae banks. Thus, gross i; RE i; + h i; y h i; w w l w i; w k l k i; f m f i; + + i; + i l L h i; + i l e L f i; (A5b) 55

59 Purchases of new caial, i.e. invesmen, are nanced by reained earnings and new loans from rivae banks: L f i; [k i; ( )k i; ] RE i; +(L i; L i; )+ e Combining he above, we have as in he main ex: " # h i; ( i; ) yi; h w w li; w w k l k f i; m f i; [k i; ( )k i; ] 2 + L h i; ( + i l ) L h i; h i; h i; + e k 2 ki; k i; 2 k i; 2 y h L f i; i;+ ( + i l ) L f i; L f i; (A5c) (A5d) Therefore, each rm i maximizes he discouned sum of dividends disribued o is owners: X i; i; (A5e) =0 where, since rms are owned by caial owners, we will ex os osulae ha he rm s discoun facor, i;, equals he caial owners marginal rae of subsiuion beween consumion a and +, ha is i; k; k;0. The rs-order condiions for fli; w, lk i;, mf i;, k i;, L h i;, Lf i; g =0 are resecively: ( )w w + N i; w w = [( ) ( )y h i; + y h i; + k;+ k; ( )w k + N i; w k = [( ) + k;+ k; ( ) f = [( h + ( + )y h i;+ yi; h ] ( )( )Aw yi; h (A k li; k + Aw li; w ) (A5f) h ( )y h i; + h + ( + )y h i;+ ) 56 y h i; y h i; ] ( )( )Ak y h i; (A k l k i; + Aw l w i; ) (A5g) ( )y h i; + y h i;

60 + k;+ k; h + k ki; k i; k 2 ki;+ k i; h + ( + )y h i;+ ( )yi; h ] ( )(m f i; )o i h (k i; ) o + ( )(m f i; )o y h i; = k;+ + [ + ( k; +) + r+ k k ki;+ ki;+ ] k i; k i; (A5h) k;+ k; k;+2 k; h + ( + )r++ k h +2 h ( +2 )r+ k (A5i) + + N i; = k;+ ( + i l +) k; + (A5j) e + N i; e = k;+ ( + i l +) e + + k; + + (A5k) and we also have he comlemenary slackness condiion on he borrowing consrain: N i; L h i; + e L f i; (w w n w;e n w n k l w; + w k l k; ) = 0 (A5l) where N i; is i s mulilier associaed wih he borrowing consrain and r+ i; = ( )yh i;+ (k i; ) o i. h (k i; ) o +( )(m f i;+ )o Noice ha (A5j) and (A5k) joinly wih he Euler equaion for bank deosis in he savers roblem, reveals ha i l + can di er from id +, which is helful in he rivae banks oimizaion roblem ha follows below. A.6 Soluion of rivae banks roblem The gross ro of each bank, denoed as gross ;, is de ned as ne ineres income minus adjusmen coss associaed wih changes in asses and liabiliies: gross ; ( + i l ) L ; + ( + i b ) e f ; + ( + i r ) m ; + +( + i b ) b ; + ( )b ; 57

61 ( + i d ) j ; ( + i z ) z ; () (A6a) The gross ro is used o ay axes, dividends o shareholders, ;, and wha is lef is ne worh, n ; : gross ; gross ; + ; + n ; (A6b) where ne worh is de ned as asses minus liabiliies: n ; L ; + b ; + e f ; + m ; j ; z ; (A6c) Combining he above, we have as in he main ex: ; = ( ) [(+i l ) L ; +(+i b ) e f ; +(+i r ) m ; + +( + i b ) b ; + ( )b ; ( + i d ) j ; ( + i z ) z ; ()] L ; b ; e f ; m ; + j ; + z ; (A6d) We solve he roblem as in Curdia and Woodford (20). Thus, we se in each ime eriod: ( + i d ) j ; + ( + i z ) z ; = ( + i l ) L ; + +( + i b ) b ; + ( )b ; + (A6e) +( + i ) e f ; + ( + i r ) m ; so ha by leading i one eriod forward we have for he issuance of deosis a ime : j ; = ( + il + ) + L ; + ( + i b + ) + + b ; ( + )b ; ( + i d + )

62 +( + i + ) + e f ; + ( + i r + ) + m ; Combining he above, we have: ( + i d + ) + ( + i z + ) + z ; (A6f) ; = j ; + z ; L ; b ; e f ; ( ) h () where we use: (A6g) () = l 2 (L ; ) 2 + b 2 ( b ; ) 2 + f 2 (e f ; ) m 2 (m ; + ( )b ; ) 2 + z 2 (z ; ) 2 which can give well-de ned demand and suly funcions. Since rivae banks are owned by caial owners, we will ex os osulae ha he banks s discoun facor, ;, equals he caial owners marginal rae of subsiuion beween consumion a and +, ; k; k;0. The rs-order condiions for L ;, b ;, f ;, m ; and z ; are: + + k;+ k; ( +) l (L ; ) = ( + il + ) ( + i d + ) (A6h) + + k;+ k; ( +) b ( + b ; ) + = ( + ib + ) ( + ) ( + i d + ) + (A6i) + h + + ( +) k;+ k; m (m ; + + ( + )b ; ) 3 + ( + ) + + ( +) k;+ f e + + ( e + ( + i + + ) e + f ; ) = e k; + + ( + i d + ) + (A6j) + + ( +) k;+ m m ; + + ( k; + + )b ; 3 = ( + ir + ) ( + i d + ) (A6k) + + ( +) k;+ k; z (z ; ) = ( + i z + ) ( + i d + ) (A6l) 59

63 A.7 Budge consrain of he consolidaed ublic secor To he exen ha he ransfer/dividend from he NCB o is governmen, rcb g, is reaed as an endogenous variable, we can merge he budge consrain of he Treasury and he budge consrain of he NCB ino a single consrain, he budge ideniy of he consolidaed ublic secor (see e.g. Reis (207) and Benigno and Nisicò (207) for deails). Tha is, by also using he marke-clearing condiion for currency m n; = n k m k; + n w m w; + n b m b;, we ge (wrien in real and er caia erms): g r + n b " w g lg g; + h g g g; + f gi g; + m g g; # + h i + ( + i b ) + ( ) d d + h i + ( + i b ) + ( ) e e g d + +( + i ) +n k m ; ( + i r ) m ; + T ARG e e eu d d + T N + + m n; m n; + where all variables have been de ned above. n k z ; ( + i z ) z ; + ( + i MRO ) T ARG + mi (A7) 60

64 A.8 Marke-clearing condiions and he macroeconomic sysem A.8. Marke-clearing condiions Recall rs he de niions of oulaions and heir fracions. Tha is, N k + N w + N b = N, n k = N k N, nb = N b N, nw = N b N = nk n b. Recall also ha we have assumed for noaional simliciy N k = N h = N i = N and N b = N g. Then, we have he following marke-clearing condiions: In he markes for dividends ( rms and banks): N k k; i = N i i; = N k i; N k k; = N ; = N k ; In he labor marke for managerial services: N k l l k; = N i li; k = N k li; k (A8a) (A8b) (A8c) In he labor marke for ublic emloyees: N b l l b; = N g l g; = N b l g; (A8d) In he labor marke for rivae workers: N w l l w; = N i l w i; = N k l w i; (A8e) In he bank deosi marke: N j ; = N k j ; = N k j h k; + N k j f k; (A8f) where j f k; denoes he deosis of foreign households in domesic banks exressed in domesic rices and N k is heir resecive number. In he marke for domesic bank loans: N L ; = N k L ; = N k L h i; + N k L f i; (A8g) where L f i; is loans demanded by foreign rms from domesic banks exressed in domesic rices N k is heir resecive number. For simliciy we se N k = N k. Regarding sovereign bonds urchased by domesic rivae agens: n k b ; b d = d d (A8h) 6

65 In he money marke (currency): m n; = n k m k; + n w m w; + n b m b; (A8i) In he marke for he domesically roduced good: n k y h i; = n k c h k; + nw c h w; + n b c h b; + nk x k; + n b (g g g; + gi g;) + c f + (A8j) +n k k 2 2 kk; k k; k k; + n k 2 2 y h i;+ +n k ( l 2 (L ; ) 2 + b 2 ( b ; ) 2 + f 2 (e f ; ) m 2 (m ; + ( )b ; ) 2 + z 2 (z ; ) 2 ) (A8k) where c f denoes er caia exors o he res of he world. Since in a small oen economy his is an exogenous variable, we assume, following e.g. Lorenzoni (204,. 698), ha c f arameers. A.8.2 Macroeconomic sysem = f #, where ; # > 0 are Collecing all equaions, he macroeconomic sysem ha we solve numerically consiss of he following equaions: Caial owners c k; = (ch k; ) (c f k; ) ( ) (S) c k; = ( k; + k; ) ( + c ) c (S2) 2 ( l k; s k; ) = k;( y )wk l (S3) 2 ( l k; s k; ) = k (s k; ) (RS g r ) k; n k k (s k; ) + n w w (s w; ) + n b b (s b; ) k; = k;+ ( + i d +) + (S4) (S5) 62

66 k; e + f e j f k: j f e + + = k;+ (+i d +) + + (S6) c h k; c f k; = ( ) f (S7) k; ( + c ) c k; k; = k;+ c h k; + f c f k; + (S8) m k; = 0 (S9) Workers ( + c ) c w; = (ch w;) (c f w; ) ( ) (S0) c c h w; + f c c f w; + m w; ( y )ww l l w; + m w; + ( RS)g r + w (s w; ) (RS g r ) + n k k (s k; ) + n w w (s w; ) + n b b (s b; ) (S) c w; = ( w; + w; ) ( + c ) c (S2) 2 ( l w; s w; ) = w;( y )ww l (S3) 2 ( l w; s w; ) = w (s w; ) (RS g r ) w; n k k (s k; ) + n w w (s w; ) + n b b (s b; ) (S4) c h w; c f w; = ( ) f (S5) w; ( + c ) c w; w; = w;+ c h w; + f c f w; + (S6) m w; = 0 (S7) 63

67 Public emloyees ( + c ) c b; = (ch b; ) (c f b; ) ( ) (S8) c c h b; + f c c f b; + m b; = = ( y )wg l l b; + m b; + ( RS) g r + b (s b; ) (RS g r ) + n k k (s k; ) + n w w (s w; ) + n b b (s b; ) (S9) c b; = ( b; + b; ) ( + c ) c (S20) 2 ( l b; s b; ) = b;( y )wg l (S2) 2 ( l b; s b; ) = b (s b; ) (RS g r ) b; n k k (s k; ) + n w w (s w; ) + n b b (s b; ) (S22) c h b; c f b; = ( ) f (S23) w; ( + c ) c b; b; = b;+ c h b; + f c f b; + (S24) m b; = 0 (S25) Price indexes = ( ) ( f ) (S26) f = e h (S27) Privae (inermediae goods) rms y h i; = A n g y g g; n k " (k i; ) o + ( )(m f i; )o o A k ll k; + A w nw;e (S28) n w l l w; n k # ( )w w + N i; w w = [( ) ( )+ 64

68 + k;+ k; h + ( + )yi;+ h ( )( )A w yi; h yi; h ] (A k l l k; + A w nw;e n w l lw; ) n k (S29) ( )w k + N i; w k = [( ) ( )+ + k;+ k; h + ( + )yi;+ h ( )( )A k yi; h yi; h ] (A k l l k; + A w nw;e n w l lw; ) n k (S30) h + k ki; = k;+ + [ + ( k i; k; +) + r+ k + k 2 2 ki;+ + k ki;+ k i; k i; ki;+ k i; ] k;+ k; k;+2 k; h + ( + )r++ k h +2 h ( +2 )r+ k (S3) + ( ) f = [( ) h ( )+ + k;+ k; h + ( + )yi;+ h ( )yi; h ] ( )(m f i; )o i h (k i; ) o + ( )(m f i; )o y h i; (S32) i; ( ) k i; = x i; + ( ) k i; (S33) " # yi; h w w n w n k l l w; w k l f l k; m f i; [k k; ( )k k; ] k 2 kk; k k; 2 k k; 2 2 y h i;+ L h i; ( + i l ) L h i; + e L f i; ( + i l (S34) ) L f i; 65

69 + N i; = k;+ ( + i l +) k; + (S35) e + N i; e = k;+ ( + i l +) e + + k; + + (S36) N i; L h i; + e L f i; (w w n w;e n w n k l l w; + w k l l k; ) = 0 (S37) where r k k; = ( )yh i;+ (k k; ) o h (k i; ) o +( )(m f i;+ )o i. Privae banks ; j ; + z ; L ; d d e f ; m ; ( ) h (L ; ; d d ; m ; ; e f ; ; z ; ) (S38) j ; = ( + il + ) + L ; + ( + i b + ) + + d d ( + ) d d ( + i d + ) + + (S39) +( + i + ) + e f ; + ( + i r + ) + m ; ( + i d + ) + ( + i z + ) + z ; + k;+ + l (L ; ) = ( + il + ) + k; ( + i d + ) (S40) + k;+ + b ( + d d ) + = ( + ib + ) + + ( + ) + k; ( + i d + ) + (S4) + h + k;+ 3 + m m ; + + ( + ) d d + ( + ) + k; + k;+ + f e + + ( e + ( + i + + ) e + f ; ) = e + k; + + ( + i d + ) + (S42) 66

70 + k;+ + m m ; + + ( + k; + + ) d d 3 = ( + ir + ) ( + i d + ) (S43) where + k;+ + z (z ; ) = + k; ( + i z + ) ( + i d + ) (S44) n k j ; = n k j h k; + nk j f k; (S45) and where we use: n L ; = n k L ; = n k L h i; + n k L f i; (S46) (L ; ; d d ; m ; ; e f ; ; z ; ) = l 2 (L ; ) 2 + b 2 ( d d ) 2 + f 2 (e f ; ) 2 + Sae rms + m 2 (m ; + ( )b ; ) 2 + z 2 (z ; ) 2 y g g; = Ag g (k g g; )og + ( g )(m g g; )og og ( l l b; ) 2 g g 2 g; (S47) k g g; = ( g )k g g; + gi g; (S48) Consolidaed governmen budge consrain " # g r + n b w g l l b; + h g g g; + f gi g; + m g g; + + ( + i b ) + ( ) + ( + i b ) + ( ) +( + i ) ( g eu )d + e e g d + e e eu d = = d + T N + 67

71 + n k m k; + n w m w; + n b m b; (n k m k; + n w m w; + n b m b; ) + +n k m ; ( + i r ) m ; + arg Gross Domesic Produc (GDP) ideniy n k z ; ( + i z ) z ; + + i MRO P arg P + mi (S49) n k y h i; = n k c c h k; + nw c c h w; + n b c c h b; + nk x k; + n b (g g g; + gi g;) + c f + +n k k 2 2 kk; k k; k k; + n k 2 2 y h i;+ where c f +n k (L ; ; d d ; m ; ; e f ; ; z ; ) (S50) is exors o he res of he world (de ned below). Balance of aymens (economy s resource consrain) f n k c c f k; + nw c c f w; + nb c c f b; + nk m f i; + nb m g g; c f + +n k e j f k; + nk f e 2 j f 2 k; j f + n k e f ; + n k L f i; +n k ( + i d ) j f k; + nk ( + i l ) e L f i; + ( + i b ) + ( ) e e g d + +( + i ) e e eu d = = n k + i d e j f k; +nk ( + i ) e f ; +n k + i l + g d + eu d + arg +n k j f k; + e nk L f i; + i MRO P arg P + mi (S5) L f i; + 68

72 Tax revenues T N c [n k c ( h c h k; + f c f k; ) + nw c ( h c h w; + f c f w; )+ +n b c ( h c h b; + f c f b; )] + y [nk w k l l k; + n w w w l l w; + n b w g l l b; ]+ + n k " y h i; w w n w n k l l w; w k l l k; f m f i; # + (S52) + n k [( + i l ) L ; + ( + i b ) e f ; + ( + i r ) m ; + +( + i b ) d d + ( ) d d ( + i d ) j ; Exors ( + i z ) z ; (L ; ; d d ; m ; ; e f ; ; z ; )] Public sending raios c f = h f # (S53) w g = sw n k y h i; n b l b; (S54) g g g; = sg nk y h i; n b g r g i g; = si n k y h i; n b = s r n k yi; h (S55) (S56) (S57) m g g; = h f s m n k y h i; n b (S58) 69

73 Endogenous and exogenous variables We herefore have a dynamic sysem of 58 equaions, (S)-(S58), in 58 endogenous variables which are fc k;, c h k;, cf k; g =0, fc w;, c h w;, c f w; g =0, fc b;, c h b;, cf b; g =0, fl k;, l w;, l b; g =0, fm k;, m w;, m b g =0, fs k;, s w;, s b g =0,f k;, w;, b g =0, f k;, w;, b g n o =0, jk; h, jf k;, =0 fyh i;, k k;, x k;, m f i;, i;, w k, w w, L h i;, Lf i;, N i;g =0, f ;, j ;, z ;, m ;, L ;, f ; g =0, y g g;, kg g; =0, f,, f, ib, i d, i l g =0, w g, gg g;, gi g;, g r, m g g; f T N g =0, fd g =0, fcf g =0. This is given he ime-ahs of scal olicy insrumens, f c, y,, s w, s g, si, s r, s m g =0, he fracions of ublic deb held by rivae agens abroad and by EU insiuions, f g, eu g =0, he oulaion shares, fn k, n w, n b, n g g =0, he olicy nominal ineres raes, fiz, i r, i MRO g =0, foreign rices fh, f,, i b, i d, i l g =0, foreign quaniies, fj f k;, Lf i; g =0, he nominal exchange rae, fe g =0, which can be se a in a currency union, TARGET2 balances, f arg g =0, ne dividends from/o he ECB, fmi g =0, and he andemic shocks, fl, c g =0. Transformed variables For convenience, we re-exress some variables. We de ne f T T o be he erms of rade (an increase means an imrovemen in comeiiveness vis-à-vis he res of he world). Then, we have = (T T ), f = (T T ), e = (T T ) 2, = h T T T T and T T T T = e h e, where h h h e. Also, h e is he gross exchange rae dereciaion which is se a one all he ime. Hence, in he nal sysem, we have = h T T T T and T T T T = e and, in all oher equaions, e h h we use he ransformaions h = (T T ), f = (T T ), e = (T T ) 2. In oher words, regarding rices, insead of f,, f g =0, now he endogenous variables are T T, h,. Recall ha, in a small oen economy, =0 h h h is exogenous (we se i a all he ime), while also be reaed for simliciy as exogenous (we se i a all he ime) or, more generally, if we use = ( h ) ( f ), i can be wrien as = ( h ) h, (where we have se e e = ); in our soluions, we simly se = all he ime. A.9 The macroeconomic sysem wih ex ane defaul In his Aendix we resen he macroeconomic sysem of Aendix A.8 when we also allow for ex ane defaul. In aricular, as discussed in he main ex, we assume ha rivae agens fear ha he governmen and domesic rivae banks will arially defaul on heir obligaions. In erms of modelling, we denoe by 0 < he acual defaul rae on sovereign can =0, 70

74 ublic deb and he size of haircu/"bail-in" imlemened by rivae banks on heir resecive deosis in case of governmen defaul, so ha e + denoes he ex ane defaul rae. When we solve he model, we se he ex os defaul rae a zero, = 0, and he ex ane one a 0.2, e + = 0:2. Then, he new macroeconomic sysem is: Caial owners c k; = (ch k; ) (c f k; ) ( ) (A9.) c k; = ( k; + k; ) ( + c ) c (A9.2) 2 ( l k; s k; ) = k;( y )wk l (A9.3) 2 ( l k; s k; ) = k (s k; ) (RS g r ) k; n k k (s k; ) + n w w (s w; ) + n b b (s b; ) (A9.4) k; = k;+ ( + i d +) e + + (A9.5) k; e + f e j f k: j f e + + = k;+ ( + i d +) + + (A9.6) c h k; c f k; = ( ) f (A9.7) k; ( + c ) c k; k; = k;+ c h k; + f c f k; + (A9.8) m k; = 0 (A9.9) 7

75 Workers ( + c ) c w; = (ch w;) (c f w; ) ( ) (A9.0) c c h w; + f c c f w; + m w; ( y )ww l l w; + m w; + ( RS)g r + w (s w; ) (RS g r ) + n k k (s k; ) + n w w (s w; ) + n b b (s b; ) (A9.) c w; = ( w; + w; ) ( + c ) c (A9.2) 2 ( l w; s w; ) = w;( y )ww l (A9.3) 2 ( l w; s w; ) = w (s w; ) (RS g r ) w; n k k (s k; ) + n w w (s w; ) + n b b (s b; ) (A9.4) c h w; c f w; = ( ) f (A9.5) w; ( + c ) c w; w; = w;+ c h w; + f c f w; + (A9.6) m w; = 0 (A9.7) Public emloyees ( + c ) c b; = (ch b; ) (c f b; ) ( ) (A9.8) c c h b; + f c c f b; + m b; = = ( y )wg l l b; + m b; + ( RS)g r + b (s b; ) (RS g r ) + n k k (s k; ) + n w w (s w; ) + n b b (s b; ) (A9.9) c b; = ( b; + b; ) ( + c ) c (A9.20) 72

76 2 ( l b; s b; ) = b;( y )wg l (A9.2) 2 ( l b; s b; ) = b (s b; ) (RS g r ) b; n k k (s k; ) + n w w (s w; ) + n b b (s b; ) (A9.22) c h b; c f b; = ( ) f (A9.23) w; Price indexes ( + c ) c b; b; = b;+ c h b; + f c f b; + (A9.24) m b; = 0 (A9.25) = ( ) ( f ) (A9.26) f = e h (A9.27) Privae (inermediae goods) rms y h i; = A n g y g g; n k " (k i; ) o + ( )(m f i; )o o A k ll k; + A w nw;e (A9.28) n w l l w; n k # ( )w w + N i; w w = [( ) ( )+ + k;+ k; h + ( + )yi;+ h ( )( )A w yi; h yi; h ] (A k l l k; + A w nw;e n w l lw; ) n k (A9.29) ( )w k + N i; w k = [( ) ( )+ + k;+ k; h + ( + )yi;+ h ( )( )A k yi; h yi; h ] (A k l l k; + A w nw;e n w l lw; ) n k (A9.30) 73

77 h + k ki; = k;+ + [ + ( k i; k; +) + r+ k + k 2 2 ki;+ + k ki;+ k i; k i; ki;+ k i; ] k;+ k; k;+2 k; h + ( + )r++ k h +2 h ( +2 )r+ k (A9.3) + ( ) f = [( ) h ( )+ + k;+ k; h + ( + )yi;+ h ( )yi; h ] ( )(m f i; )o i h (k i; ) o + ( )(m f i; )o y h i; (A9.32) i; ( ) k k; = (x i; + ( ) k i; ) (A9.33) " # yi; h w w n w n k l l w; w k l f l k; m f i; [k k; ( )k k; ] k 2 kk; k k; 2 k k; 2 2 y h i;+ L h i; ( + i l ) L h i; + e L f i; ( + i l (A9.34) ) L f i; + N i; = k;+ ( + i l +) k; + (A9.35) e + N i; e = k;+ ( + i l +) e + + k; + + (A9.36) N i; L h i; + e L f i; (w w n w;e n w n k l l w; + w k l l k; ) = 0 (A9.37) where r k k; = ( )yh i;+ (k k; ) o h (k i; ) o +( )(m f i;+ )o i. 74

78 Privae banks ; j ; + z ; L ; d d e f ; m ; ( ) h (L ; ; d d ; m ; ; e f ; ; z ; ) (A9.38) j ; = ( + il + ) + L ; + ( + i b + ) e d d ( + ) d d ( + i d + ) + e + + (A9.39) +( + i + ) + e f ; + ( + i r + ) + m ; ( + i d + ) e + + ( + i z + ) + z ; + k;+ + l (L ; ) = + k; ( + i l + ) ( + i d + ) (A9.40) e + + k;+ + b ( + d d ) + = ( + ib + ) + e + + ( + k; ( + i d + ) e + + ) + (A9.4) + h + k;+ 3 + m m ; + + ( + ) d d + ( + ) + k; + k;+ + f e + + ( e + + f ; ) = + k; + + ( + i + ) e ( + i d + ) + e + (A9.42) e + k;+ + m m ; + + ( + k; ) d d = ( + i r + ) ( + i d + ) e + (A9.43) where + k;+ + z (z ; ) = + k; ( + i z + ) ( + i d + ) e + (A9.44) 75

79 n k j ; = n k j h k; + nk j f k; (A9.45) and n L ; = n k L ; = n k L h i; + n k L f i; (A9.46) (L ; ; d d ; m ; ; e f ; ; z ; ) = l 2 (L ; ) 2 + b 2 ( d d ) 2 + f 2 (e f ; ) 2 + Sae rms + m 2 (m ; + ( )b ; ) 2 + z 2 (z ; ) 2 y g g; = Ag g (k g g; )og + ( g )(m g g; )og og ( l l b; ) 2 g g g; 2 (A9.47) k g g; = ( g )k g g; + gi g; (A9.48) Consolidaed governmen budge consrain " # g r + n b w g l l b; + h g g g; + f gi g; + m g g; + + ( )( + i b ) + ( ) ( g eu )d + + ( )( + i b ) + ( ) e e g d + +( + i ) e e eu d = = d + T N + + n k m k; + n w m w; + n b m b; (n k m k; + n w m w; + n b m b; ) + +n k m ; ( + i r ) m ; + arg n k z ; ( + i z ) z ; + + i MRO P arg P + mi (A9.49) 76

80 Gross Domesic Produc (GDP) ideniy n k y h i; = n k c c h k; + nw c c h w; + n b c c h b; + nk x k; + n b (g g g; + gi g;) + c f + +n k k 2 2 kk; k k; k k; + n k 2 2 y h i;+ where c f +n k (L ; ; d d ; m ; ; e f ; ; z ; ) (A9.50) is exors o he res of he world (de ned below). Balance of aymens (economy s resource consrain) f n k c c f k; + nw c c f w; + nb c c f b; + nk m f i; + nb m g g; c f + +n k e j f k; + nk f e 2 j f 2 k; j f + n k e f ; + n k L f i; +n k ( )( + i d ) j f k; + nk ( + i l ) e L f i; + ( )( + i b ) + ( ) e e g d + +( + i ) e e eu d = = n k + i d e j f k; +nk ( + i ) e f ; +n k + i l L f i; + +n k j f k; + e nk L f i; + g d + eu d + arg + i MRO P arg P + mi (A9.5) 77

81 Tax revenues T N c [n k c ( h c h k; + f c f k; ) + nw c ( h c h w; + f c f w; )+ +n b c ( h c h b; + f c f b; )] + y [nk w k l l k; + n w w w l l w; + n b w g l l b; ]+ # + n k " y h i; w w n w n k l l w; w k l l k; f m f i; + (A9.52) + n k [( + i l ) L ; + ( + i b ) e f ; + ( + i r ) m ; + +(+i b )( ) d d + ( ) d d (+i d )( ) j ; Exors ( + i z ) z ; (L ; ; d d ; m ; ; e f ; ; z ; )] Public sending raios c f = h f # (A9.53) w g = sw n k y h i; n b l b; (A9.54) g g g; = sg nk y h i; n b g r g i g; = si n k y h i; n b = s r n k yi; h (A9.55) (A9.56) (A9.57) m g g; = h f s m n k y h i; n b (A9.58) 78

82 We again have a sysem of 58 equaions in he same 58 variables as above. Aendix B: Policy deails and daa B. Greek ublic deb and is holders In he case of Greece, over he years of he sovereign deb crisis, o cial scal rescue oeraions have been exressed by hree bailous. The rs ook lace in 200-, he second in and he hird in These were loans rovided by oher EZ counries (via he EFSF, ESM, ec) and he IMF so hey couned as ublic deb. To ge hese loans, obained a below-marke condiions, Greece signed a memorandum of undersanding o imlemen an economic adjusmen rogram ha was o cially erminaed in Augus 208. The oal amoun of loans received from hese hree o cial rescue oeraions was around 290 billion euros which is one of he larges nancial assisance ackage in hisory. Mos of his money was used for ublic deb servicing aymens (i.e. he aymen of he rincial of governmen bonds a mauriy and ineres aymen obligaions) and he nancing of rimary budge de cis (here was no rimary marke for Greek bonds beween 200 and 208). Mos of he res of he bailou money was used o nance he cos of he haircu in March 202 and he cos of rivae banks recaializaion. See e.g. Economides e al (202a) for references and deails. As a resul of hese loans, in 209, close o 70% of Greek ublic deb was owned by EU ublic insiuions (member saes of he euro area, EFSF, ESM, ec). Daa for Greek ublic deb as share of GDP, as well as he fracions of i held by EU ublic insiuions ( eu ) and foreign rivae invesors/banks ( g ) over ime are reored in Table B., while he res is in he hands of domesic rivae invesors/banks See Economides e al (202a) and Dimakooulou e al (202) for more deails. As said, he Greek NCB or he ECB urchase governmen bonds in he secondary marke only. Thus, he numbers in Table B can be hough of as urchases in he rimary marke. 79

83 Table B. Greek ublic deb o GDP and is main holders Year Toal ublic deb eu g (% of GDP) (% of oal (% of oal ublic deb) ublic deb) : : :2 9:3 46: : 9:9 24: :6 59:9 20: :4 66:3 8: :9 67:2 6: :9 68:6 6: :5 69:8 6: :2 70:9 6: :2 70:9 6: :5 70:9 6:0 Source: Public Deb Managemen Agency and Greek Minisry of Finance. Noe ha in he main aer we exlain how eu (namely, he fracion of ublic deb held by EU insiuions) has been evolving since 2020 as a resul of he loans received from he EU s Recovery Fund. B.2 The Greek NCB in he ES Here we clarify how he balance shee of a NCB ariciaing in he ES is relaed o he consolidaed balance shee of he ES and hen discuss he Greek case. The ES and is NCBs The consolidaed balance shee and he budge consrain of he ES are no di eren from hose of a sandardized cenral bank. 46 In oher words, he asse side of he balance shee of he consolidaed ES consiss mainly of foreign currency, loans o credi insiuions 47 and securiies/bonds. 48 The liabiliy side consiss mainly of banknoes in circulaion (held by he non-bank ublic), reserves which are also called curren accouns (held by rivae banks a he cenral bank) and governmen deosis. However, he consolidaed balance shee of he ES shows asses and liabiliies of he ES s NCBs and he ECB iself vis-à-vis hird aries only. I 46 See e.g. Annual consolidaed balance shee of he ES and User guide on he ES consolidaed weekly nancial saemen (available a he websie of he ECB). 47 This includes he main re nancing oeraions (MROs), longer-erm re nancing oeraions (LTROs), marginal lending faciliies, ec. I also inludes emergency liquidiy assisance (ELA) o rivae banks wih severe liquidiy roblems. 48 This includes he covered bond urchase rogram (CBPP), he securiies markes rogram (SMP), he asse urchase rogram (APP) since 205, he PEPP since 2020, ec. 80

84 does no include credis and debis among NCBs and he ECB, known as Inra-Eurosysem claims and liabiliies and recorded resecively as TAR- GET2 asses and TARGET2 liabiliies in he nancial saemens of he individual NCBs and he ECB. As exlained in he main ex, hese TAR- GET2 balances cancel each oher ou a aggregae ES level and herefore do no aear in he consolidaed balance shee of he ES; however, hey do aear in he balance shees of individual NCBs and he ECB. TARGET2 daa In he case of he ES as a whole, TARGET2 balances were very small rior o he global nancial crisis in 2008 bu have increased subsanially since hen; for insance, hey were 86 billion euros in May 2008, :24 rillion in Seember 207 and.63 rillion a a he end of 2020 (see websie of he ECB). In he case of Greece, TARGET2 liabiliies o he ES were by far he larges iem of liabiliies of he Greek NCB, and hence of is moneary base, in every year beween 2008 and 207, wih shar rises during he oliically urbulen years of 200, 20, 202 and 205. For insance, TARGET2 liabiliies were 05 billion euros in 20 which ranslaed o 5% of GDP, and 94 billion euros in 205, which ranslaed o 53% of GDP. During ha eriod and unil he imosiion of caial conrols in he summer of 205, his increase in TARGET2 liabiliies mainly nanced a igh of deosis from Greece owards core counries (see Whelan (207, secion 2.3.) for a deailed examle). Afer he sovereign deb crisis, namely afer 206, and before he eruion of he new andemic crisis in early 2020, he size of he balance shee of he Greek NCB decreased and he same haened o boh bank loans and TARGET2 liabiliies. However, since he beginning of 2020, here has been a new big rise in TARGET2 liabiliies; hese liabiliies were 26 billion euros in 209 (or 4% of GDP) and jumed o 80 billion euros in 2020 (or 47% of GDP) becoming again he larges iem of liabiliies in he balance shee of he Greek NCB. Now his means ha he Greek NCB issues money o nance he urchase of securiies (like Greek governmen bonds as ar of he PEPP ha sared in March 2020) from holders wih accouns in anoher euro counry (see Whelan (207) for a deailed examle (secion in his aer) and evidence from oher NCBs in he ES since 205 (secion 3 in his aer)). Noe ha Greek sovereign bonds were no ar of he PSPP ha sared in 205 bu are ar of he PEPP ha sared in See Dimakooulou e al (202) for furher deails. Balance shee of he Greek NCB To con rm he above narraive, Tables B.2a and B.2b dislay he evoluion of he oal balance shee as well as he bigges asses and liabiliies of he Greek NCB. 8

85 Table B.2a Bank of Greece s asses (billions of euros, end of year) Year Lending o Securiies Claims in Toal asses banks foreign currency Source: Bank of Greece. Table B.2b Bank of Greece s liabiliies (billions of euros, end of year) Year Banknoes TARGET2 Reserves Toal liabiliies Source: Bank of Greece. 82

86 Finally, in Table B.2c, we resen ro s and losses of he NCB of Greece (numbers are now in millions). Focusing on he role of he ES, he ineresing column is he hird one ( ne resul of ooling moneary income ), which reors he ne income received by he ES. 49 If osiive, i means ha he Greek NCB is a ne reciien (and vice versa if negaive) from he ES. The numbers are osiive in mos eriods, meaning ha he NCB of Greece has been a reciien member of he ECB s dividend olicy, alhough quaniaively very small. Tha is, redisribuion, if any, in erms of dividends, was very small. The las column reors he nal ro of he Greek NCB which is disbursed o he Greek governmen. Year Table B.2c Bank of Greece s ro and loss accouns (milliions of euros, end of year) Income from equiy shares Ne resul of ooling Ne ineres income and ariciaing ineress moneary income Pro of he year : : : : : : : : : Source: Bank of Greece. 49 This works as follows: he ECB collecs all ro s (he so-called moneary income) made ou of NCBs in he ES and hen redisribues hem back o each NCB so as each NCB ends u wih a share of he oal moneary income ha is roorional o is "caial key" (see e.g. Whelan (204)). However, from 205 onwards, he ECB, in an aem o reven redisribuion hrough ne income, insiued as a rule for is governmen bonds urchase rogram ha 92% of ne ro s would say a he naional cenral banks (see Reis (207)). 83

87 Dearmen of Economics Ahens Universiy of Economics and Business Lis of Recen Working Paers Incubaed Early Sage Saruers in Ahens and heir Iniiaives during he Crisis ( ), Ioannis Besis and Ioanna Safo Peelasis Alernaive Moneary Policy Rules in an Imerfecly Comeiive Dynamic Sochasic General Equilibrium Model, George Alogoskoufis and Selios Giannoulakis Quanifying Qualiaive Survey Daa: New Insighs on he (Ir)Raionaliy of Firms' Forecass, Alexandros Bosis, Chrisoh Görz and Pluarchos Sakellaris Can Counry-Secific Ineres Rae Facors Exlain he Forward Premium Anomaly?, Efhymios Argyrooulos, Nikolaos Elias, Dimiris Smyrnakis and Elias Tzavalis Signaling roduc qualiy hrough rices in an oligooly model wih cosly consumer search, Minghua Cheny, Konsaninos Serfes and Elefherios Zacharias Thinking ahead of he nex big crash: Clues from Ahens in classical imes, George C. Biros Financial crises, firm-level shocks, and large downurns: Evidence from Greece, Selios Giannoulakis and Pluarchos Sakellaris Noes on he Demand Side Secular Sagnaion, George D. Demooulos and Nicholas A. Yannacooulos Insiuions and Macroeconomic Performance: Core vs Perihery Counries in he Eurozone, Tryfonas Chrisou, Aosolis Philiooulos and Vanghelis Vassilaos 0-20 Macroeconomic Policy Lessons for Greece, George Economides, Dimiris Paageorgiou and Aosolis Philiooulos -20 Energy Transiions and he role of he EU ETS: The case of Greece, Andriana Vlachou and Georgios Panelias 2-20 Measuring he Defaul Risk of Small Business Loans: Imroved Credi Risk Predicion using Dee Learning, Yiannis Dendramis, Elias Tzavalis and Aikaerini Cheimarioi 4-20 Saving Democracy by Swiching o Cororae-like Governance, George C. Biros 5-20 The imac of he lockdown on he Greek economy and he role of he Recovery Fund, George Economides, Aosolis Philiooulos and Vanghelis Vassilaos Hisorical Cycles of he Economy of Modern Greece From 82 o he Presen, George Alogoskoufis 02-2 Greece Before and Afer he Euro: Macroeconomics, Poliics and he Ques for Reforms, George Alogoskoufis 03-2 Commodiy money and he rice level, George C. Biros Πατησίων 76, Αθήνα. Tηλ.: econ@aueb.gr / 76, Paission Sree, Ahens Greece. Tel.: (+30)

88 04-2 Desabilizing asymmeries in cenral banking: Wih some enlighenmen from money in classical Ahens, George C. Biros 05-2 Exloring he Long-Term Imac of Maximum Marku Deregulaion, Ahanasios Dimas and Chrisos Genakos 06-2 A regularizaion aroach for esimaion and variable selecion in high dimensional regression models, Y. Dendramis, L. Giraiis, G. Kaeanios 07-2 Tax Comeiion in he Presence of Environmenal Sillovers, Fabio Anoniou, Panos Hazianayoou, Michael S. Michael, Nikos Tsakiris 08-2 Firm Dynamics by Age and Size Classes and he Choice of Size Measure, Selios Giannoulakis and Pluarchos Sakellaris 09-2 Measuring he Sysemic Imorance of Banks, Georgios Morais, Pluarchos Sakellaris 0-2 Firms' Financing Dynamics Around Lumy Caaciy Adjusmens, Chrisoh Görz, Pluarchos Sakellaris, John D. Tsoukalas -2 On he rovision of excludable ublic goods General axes or user rices? George Economides and Aosolis Philiooulos 2-2 Asymmeries of Financial Oenness in an Oimal Growh Model, George Alogoskoufis 3-2 Evaluaing he imac of labour marke reforms in Greece during , Georgios Gaooulos, Alexandros Louka, Ioannis Polycarou, Nikolaos Veas 4-2 From he Ahenian silver o he bicoin sandard: Privae money in a sae-enforced free banking model, George C. Biros 5-2 Ordering Arbirage Porfolios and Finding Arbirage Ooruniies. Selios Arvaniis and Thierry Pos 6-2 Inconsisency for he Gaussian QMLE in GARCH-ye models wih infinie variance, Selios Arvaniis and Alexandros Louka 7-2 Comeiion and Pass-Through: Evidence from Isolaed Markes, Chrisos Genakos and Mario Pagliero 8-2 Exloring Okun s Law Asymmery: An Endogenous Threshold LSTR Aroach, Dimiris Chrisooulos, Peer McAdam and Elias Tzavalis 9-2 Limi Theory for Maringale Transforms wih Heavy-Tailed Mulilicaive Noise, Selios Arvaniis and Alexandros Louka 20-2 Oimal axaion wih osiional consideraions, Ourania Karakosa and Elefherios Zacharias Πατησίων 76, Αθήνα. Tηλ.: econ@aueb.gr / 76, Paission Sree, Ahens Greece. Tel.: (+30)

89 Dearmen of Economics Ahens Universiy of Economics and Business The Dearmen is he oldes Dearmen of Economics in Greece wih a ioneering role in organising osgraduae sudies in Economics since 978. Is rioriy has always been o bring ogeher highly qualified academics and o qualiy sudens. Faculy members secialize in a wide range of oics in economics, wih eaching and research exerience in world-class universiies and ublicaions in o academic journals. The Dearmen consanly srives o mainain is high level of research and eaching sandards. I covers a wide range of economic sudies in micro-and macroeconomic analysis, banking and finance, ublic and moneary economics, inernaional and rural economics, labour economics, indusrial organizaion and sraegy, economics of he environmen and naural resources, economic hisory and relevan quaniaive ools of mahemaics, saisics and economerics. Is undergraduae rogram aracs high qualiy sudens who, afer successful comleion of heir sudies, have excellen rosecs for emloymen in he rivae and ublic secor, including areas such as business, banking, finance and advisory services. Also, graduaes of he rogram have solid foundaions in economics and relaed ools and are regularly admied o o graduae rograms inernaionally. Three secializaions are offered:. Economic Theory and Policy, 2. Business Economics and Finance and 3. Inernaional and Euroean Economics. The osgraduae rograms of he Dearmen (M.Sc and Ph.D) are highly regarded and arac a large number of qualiy candidaes every year. For more informaion: hs:// Πατησίων 76, Αθήνα. Tηλ.: econ@aueb.gr / 76, Paission Sree, Ahens Greece. Tel.: (+30)