The Macroeconomic Effects of Quantitative Easing in the Euro Area: Evidence from an Estimated DSGE Model

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1 Saff Working Paper/Documen de ravail du personnel The Macroeconomic Effecs of Quaniaive Easing in he Euro Area: Evidence from an Esimaed DSGE Model by Sefan Hohberger, Romanos Prifis and Lukas Vogel Bank of Canada saff working papers provide a forum for saff o publish work-in-progress research independenly from he Bank s Governing Council. This research may suppor or challenge prevailing policy orhodoxy. Therefore, he views expressed in his paper are solely hose of he auhors and may differ from official Bank of Canada views. No responsibiliy for hem should be aribued o he Bank.

2 Bank of Canada Saff Working Paper March 2018 The Macroeconomic Effecs of Quaniaive Easing in he Euro Area: Evidence from an Esimaed DSGE Model by Sefan Hohberger, 1 Romanos Prifis 2 and Lukas Vogel 3 1 European Commission Ispra, Ialy Sefan.hohberger@ec.europa.eu 2 Canadian Economic Analysis Deparmen Bank of Canada Oawa, Onario, Canada K1A 0G9 rprifis@bankofcanada.ca 3 European Commission Brussels, Belgium Lukas.vogel@ec.europa.eu ISSN Bank of Canada

3 Acknowledgemens We hank Jean-Philippe Cayen, Julien Champagne, Fabian Eser, Sefano Gnocchi, Massimo Giovannini, Richard Harrison, Serdar Kabaca, Bearice Paaracchia, Marco Rao and Werner Roeger for very helpful suggesions and discussions, and seminar paricipans a he Bank of Canada, he 14h Annual EEFS Conference, he 47h MMF Research Group Annual Conference, he 6h IWH/INFER Workshop on (Ending) Unconvenional Moneary, he 1s CEPR Conference on Macro-Modelling and Model Comparison, he 21s Inernaional Conference on Macroeconomic Analysis and Inernaional Finance, he 2017 Annual Meeing of he German Economic Associaion, he 2017 European Winer Meeing of he Economeric Sociey, and XENOPHON 2017 for helpful commens on his and previous versions of he paper. The views expressed are hose of he auhors and should no be aribued o he Bank of Canada or he European Commission. i

4 Absrac This paper esimaes an open-economy dynamic sochasic general equilibrium model wih Bayesian echniques o analyse he macroeconomic effecs of he European Cenral Bank s (ECB s) quaniaive easing (QE) programme. Using daa on governmen deb socks and yields across mauriies, we idenify he parameer governing porfolio adjusmen in he privae secor. Shock decomposiions sugges a posiive conribuion of ECB QE o annual euro area oupu growh and inflaion in of up o 0.3 and 0.6 percenage poins (pp) in he linearised version of he model. Allowing for an occasionally binding zerobound consrain by using piecewise linear soluion echniques raises he posiive impac o up o 0.7 and 0.8 pp. Bank opics: Economic models; Ineres raes; Transmission of moneary policy JEL codes: E44, E52, E53, F41 Résumé Nous esimons, par des echniques bayésiennes, un modèle d équilibre général dynamique e sochasique en économie ouvere afin d analyser les effes macroéconomiques du programme d assouplissemen quaniaif de la Banque cenrale européenne (BCE). À parir des données poran sur l encours des ires d Éa e les aux de rendemen pour la gamme des échéances, nous évaluons le paramère qui déermine les ajusemens de porefeuilles dans le seceur privé. Les décomposiions de chocs effecuées monren qu en zone euro, les mesures d assouplissemen quaniaif de la BCE auraien enraîné, en , des effes posiifs sur la croissance annuelle de la producion e sur l inflaion à haueur de 0,3 e 0,6 poin de pourcenage dans la version linéarisée du modèle. Lorsque nous permeons que la conraine de la borne du zéro soi occasionnellemen acive au moyen de echniques de linéarisaion, l incidence favorable se chiffre respecivemen à 0,7 e 0,8 poin de pourcenage. Sujes : Modèles économiques; Taux d inérê; Transmission de la poliique monéaire Codes JEL : E44, E52, E53, F41 ii

5 Non-echnical Summary In early 2015 he European Cenral Bank (ECB) joined he group of cenral banks ha have implemened large-scale asse purchase programmes as unconvenional policy measures. The ECB's quaniaive easing (QE) programme, announced in January 2015, foresaw buying 60 billion of asses a monh from March 2015 o Sepember 2016, which in sum corresponds o circa 10% of annualised euro area (EA) gross domesic produc (GDP). I has been coninuously revised in boh size and duraion since hen. This paper analyses he macroeconomic effecs of he ECB's QE programme using a woregion dynamic sochasic general equilibrium (DSGE) model for he EA and he res of he world, esimaed wih Bayesian echniques. The esimaion of he model is underaken in an environmen where he zero lower bound may be binding and o solve such models requires exending previous algorihms. QE is inroduced ino he model by adding a cenral bank balance shee and disinguishing beween shor-erm and long-erm governmen deb. We use a formulaion of a privae-secor porfolio ha allows for non-neural effecs of cenral bank purchase programmes due o imperfec subsiuabiliy beween asses of differen mauriy. The cenral bank alers is balance shee by purchasing long-erm bonds and injecing liquidiy o he privae secor. When he cenral bank inervenes, privae invesors ha aim a re-esablishing he porfolio mix of shorerm and long-erm asses can respond by holding more corporae equiy and foreign bonds, and by reducing savings. The firs response means a porfolio reallocaion owards equiy and foreign-currency asses ha increases he price of corporae equiy (rising sock marke) and he price of foreign currency (exchange rae devaluaion). The second response implies a subsiuion away from fuure consumpion. Combining daa on governmen deb socks and yields across mauriies, he model esimaion provides a value for he parameer governing porfolio adjusmen coss in he model. The implied magniude of hese coss deermines he yield spread following QE of a given volume and ime pah, such as he one announced by he ECB in January Our resuls show ha QE as capured by he model has increased EA year-on-year oupu growh and inflaion in 2015q1-17q1 by 0.7 percenage poins (pp) and 0.8 pp on average, wih maximum impac a 1.0 pp in 2016q1 and 2017q1. Our esimaed DSGE model can also reproduce he narraive of he pre-qe growh slowdown in he EA and, in paricular, during he Grea Recession. 2

6 1. Inroducion In early 2015 he European Cenral Bank (ECB) joined he group of cenral banks ha have implemened large-scale asse purchase programmes as unconvenional policy measures. These asse purchases, also called quaniaive easing (QE), have led o a srong exension of he cenral banks' balance shees. By end-july 2015 he amoun of ourigh purchases on he balance shee had reached 24% of gross domesic produc (GDP) in he case of he US Federal Reserve, 64% of GDP in he case of he Bank of Japan, 21% of GDP in he case of he Bank of England, and 5% of GDP in he case of he ECB (Consâncio 2015). The ECB's QE programme, announced in January 2015 (Public Secor Purchase Programme), foresaw buying 60 billion of asses a monh from March 2015 o Sepember 2016, which in sum corresponds o circa 10% of annualised euro area (EA) GDP. In December 2015, he ECB exended he programme unil March 2017, and i raised he amoun of monhly purchases o 80 billion saring from April In December 2016 he programme was exended and modified again, lenghening he period of asse purchases unil (a leas) December 2017, bu a a reduced pace of 60 billion of asses a monh afer March Operaing close o he zero lower bound (ZLB), he ECB considered is convenional moneary accommodaion o be insufficien o address weak inflaion dynamics, falling inflaion expecaions and sizeable economic slack in he EA. As a resul, he balance shee inervenions were proposed o "achieve he price sabiliy objecive, given ha ineres raes have reached heir lower bound" (Draghi 2015). In pracice, he ECB purchases public secor financial asses (governmen deb) of longer mauriy and exends liquidiy (base money) o he privae secor. Research a he ECB has provided evidence for he impac of he QE programme on long-erm bond yields and spillover o oher asse prices hrough porfolio reallocaion: Alavilla e al. (2015) in an even sudy repor a basis-poin decline in 10-year governmen bond yields wih spillover ino lower corporae bond, spreads, higher equiy prices, and euro depreciaion. Andrade e al. (2016) repor a decline of EA 10-year governmen bond yields in he range of basis poins in he conex of he ECB's exended asse purchases programme wih spillover ino higher equiy prices and inflaion expecaions. The evidence in De Sanis (2016) suggess ha ECB non-sandard policy has reduced EA 10-year governmen bond yields beween Sepember 2014 and Ocober 2015 on average by 63 basis poins. This paper analyses he macroeconomic effecs of he ECB's QE programme using a woregion dynamic sochasic general equilibrium (DSGE) model for he EA and he res of he world (RoW), esimaed wih Bayesian echniques. QE is inroduced ino he model by adding a 3

7 cenral bank balance shee and disinguishing beween shor-erm and long-erm governmen deb. We use a formulaion of privae-secor porfolio preferences ha is by now esablished in he lieraure (e.g., Andrés e al. 2004, Prifis and Vogel 2016) and ha allows for non-neural effecs of cenral bank purchase programmes due o imperfec subsiuabiliy beween asses of differen mauriy. More specifically, he cenral bank alers is balance shee by purchasing longerm bonds (he laer modelled as in Woodford 2001) and injecing liquidiy ino he privae secor. Our specificaion of QE allows us o capure is effecs hrough a large number of he ransmission channels pu forward by he lieraure (see Krishnamurhy and Vissing-Jorgensen 2011) including he saving, financing cos, exchange rae, inflaion, and fiscal channels. The movemen of he exchange rae in response o QE affecs aggregae demand, oupu and inflaion and is a channel ha is absen from mos model-based sudies of QE policies (e.g., Chen e al. 2012, De Graeve and Theodoridis 2016, Gerler and Karadi 2013) which, insead, build on closed-economy frameworks. Since our framework relies on a global wo-region model, we explicily accoun for effecs ha arise from exchange rae adjusmen and he behaviour of ne expors. The conribuion of his paper is o analyse he macroeconomic impac of ECB QE using a sae-of-he-ar esimaed DSGE model. We firs show ha our model can reproduce he narraive of he pre-qe growh slowdown in he EA and, in paricular, during he Grea Recession. We hen focus on he ECB s QE programme. Combining daa on governmen deb socks and yields across mauriies, he model esimaion provides a value for he parameer governing he porfolio adjusmen coss in he model. The implied magniude of hese coss deermines he yield spread following QE of a given volume and ime pah, such as he one announced by he ECB in January Given ha ECB QE was launched only in 2015, we have few daa poins for he QE episode iself. Daa-driven idenificaion of he degree of subsiuabiliy beween shor-erm and long-erm bonds in our model herefore has o rely mainly on he pre-qe par of he sample. Lags in he ransmission of QE o he real economy furhermore imply ha he effecs of he ongoing programme have no fully maerialised ye. The analysis sars wih a sandard linearised version of he model in which he Taylor rule never his he ZLB (we refer o his as he "unconsrained model" in he ex). We hen urn o a model version wih occasionally binding consrains in which he ZLB can become binding endogenously when conracionary shocks drive he arge ("shadow") ineres rae below he lower bound (we refer o his as he "consrained model" in he ex). According o our shock decomposiions from he esimaed unconsrained model, QE as capured by he model has increased EA year-on-year oupu growh and inflaion in 2015q1-17q1 by 0.3 percenage poins (pp) and 0.5 pp on average, wih maximum impac of 0.4 pp and 0.6 pp in Including he 4

8 endogenously and occasionally binding ZLB consrain raises he 2015q1-17q1 average growh and inflaion effec of QE o 0.7 pp and 0.8 pp, respecively, wih peaks a 1.0 pp in 2016q1 and 2017q1, respecively. The sronger QE impac in he consrained model is due o he absence of a counervailing shor-erm policy rae response when he ZLB binds in in he consrained model. The remainder of he paper is srucured as follows: Secion 2 summarises he closely relaed lieraure; secion 3 oulines he general srucure of he model; secion 4 describes he model soluion and esimaion mehodology; secion 5 presens parameer esimaes; secion 6 discusses he impac of QE in he unconsrained model; secion 7 presens resuls from he model wih he occasionally binding consrain; secion 8 summarises he paper and concludes. A full model descripion is provided in he online appendix. 2. Relaed Lieraure The empirical relevance of individual channels and he aggregae macroeconomic effecs of QE are an empirical maer and likely o vary wih srucural feaures of he economy across counries and ime. So far here is lile (published) research on he effecs of he ECB QE and, paricularly, lile model-based analysis. Mos exising papers consider unconvenional moneary policy in he US and he UK and heir spillovers o he world economy. This lieraure has been summarised, e.g., in Prifis and Vogel (2016). Here, we limi ourselves o he review of model-based generalequilibrium (DSGE) analyses ha focus on he impac of QE on porfolio rebalancing and financing coss. The cenral conribuion of his paper is he incorporaion of cenral bank balance shee policy (QE) in a large-scale open-economy macroeconomic model and esimaion of his model on EA daa. The approach is similar in spiri o Chen e al. (2012), and De Graeve and Theodoridis (2016) who analyse US QE in esimaed closed-economy models of he US economy. In line wih Chen e al. (2012), De Graeve and Theodoridis (2016), and Harrison (2017), we focus on he porfolio balancing channel of QE ransmission. According o he resuls in Chen e al. (2012), he US large-scale asse purchase (LSAP II) programme, wih a volume of circa 4% of US GDP, combined wih a commimen o keep ineres raes low for an exended period of ime, has raised US real GDP growh by around 0.13% and inflaion by only 0.03 pp. According o he esimaes of De Graeve and Theodoridis (2016), "Operaion Twis", he purchase of long-erm and sale of shor-erm mauriy bonds of circa 2% of US GDP by he Federal Reserve, has increased US real GDP by 0.6% and inflaion by up o 5

9 0.3 pp. The models by Gerler and Karadi (2013) and Carlsrom e al. (2017) assume financially consrained financial inermediaries, where QE eases he consrain on financing producive invesmen in he economy. In hese models, producive capial is financed by financial inermediaries based on heir ne worh and he deposis made by households. In a calibraed version of heir model, Gerler and Karadi (2013) quanify he impac of US LSAP wih a volume of 2.5% of GDP on oupu and inflaion o 1% and 1.5 pp, respecively, if policy raes remain unchanged, and o 0.2% and 0.2 pp, respecively, if he sandard moneary policy rule is acive and parly offses expansionary QE effecs by an increase in he shor-erm rae. While he ransmission can be described in erms of he credi channel, recen empirical analyses (see, e.g., Bluwsein and Canova 2016) do no sugges ha he credi channel is a primary ransmission mechanism for QE in he EA and spillover o non-ea counries. Sahuc (2016) borrows he Gerler-Karadi model for an assessmen of ECB QE policy ha involves asse purchases of circa 9% of EA GDP. Like Gerler and Karadi (2013), he Sahuc (2016) assessmen sresses he imporance of keeping shor-run policy raes low for longer. Keeping he policy rae consan only in 2015 gives a maximum QE effec on oupu growh and inflaion of 0.2 and 0.1 pp in , whereas keeping he policy rae unchanged for anoher year raises he average oupu growh and inflaion effec in o 0.6 and 0.6 pp. 3. Model Descripion The presen analysis uses a modified wo-region (EA and RoW) framework of Kollmann e al. (2016) and exends his model o incorporae non-sandard moneary policy. The model is esimaed using quarerly daa for he period 1999q1-2017q1. The EA region assumes wo (represenaive) households, inermediae and final goods firms and a governmen. Ricardian households have access o financial markes, whereas liquidiy-consrained households consume heir disposable income in every period. Preferences of boh ypes of households exhibi habi formaion in boh consumpion and leisure. A monopolisically compeiive secor produces differeniaed goods by employing domesic labour and capial. Firms in his secor maximise he presen value of heir dividends a a discoun facor ha is sricly larger han he risk-free rae and varies over ime, subjec o invesmen and labour adjusmen coss and a varying capaciy uilisaion rae. Final goods firms combine a domesic differeniaed goods bundle wih energy inpus. Nominal differeniaed goods prices are sicky, as 6

10 are he wages paid o he workers he laer being deermined by monopolisic rade unions. The fiscal auhoriy imposes disorive axes and issues deb. The exposiion below describes he QE-relevan exensions. A deailed overview of he general model can be found in Kollmann e al. (2016) and in he online appendix. We exend he model by inroducing non-sandard moneary policy as in Prifis and Vogel (2016). Our approach is similar o he modelling of QE in Chen e al. (2012), and De Graeve and Theodoridis (2016), which focuses on he porfolio rebalancing in he ransmission of QE. However, unlike hese sudies, our wo-region model allows for an exchange rae channel of QE and rade effecs. In line wih he sandard noion, QE is inroduced as a moneary policy sraegy ha increases he size of he cenral bank's balance shee. In paricular, he cenral bank purchases longerm (governmen) bonds, wih he aim of reducing he ineres spread beween long and shor mauriies; i.e., o flaen he yield curve. The cenral bank finances he bond purchases by providing addiional liquidiy o he privae secor. QE inends o affec privae-secor porfolio and saving decisions, especially when shor-erm policy raes are already a or close o he ZLB. We inroduce shor-erm and long-erm governmen deb o incorporae invesor preferences for a mauriy mix and cenral bank balance shee operaions in he model. Following Woodford (2001), long-erm governmen deb is modelled hrough bonds for which he nominal coupon c, which is a fracion of he principal, depreciaes over ime a rae. 5 The price in peri- b od of a long-erm bond issued in ( P N ) equals he discouned value of fuure paymens P N T n b n 0 (1 i ) 1 n c, where T is he mauriy period of he bond. Analogously, he price in period of a long-erm bond issued in -1 ( P O ) equals he discouned sum of ousanding paymens, P O T 1 1 n b c. If (1 i) 1 1 n b n 0 (1 i ) and T is large, he price in of long-erm bonds issued in -1 corresponds (approximaely) o he price of newly issued long-erm bonds imes he depreciaion rae: (1) P O P b N Equaion (1) shows ha he price of he long-erm bond ha pays a declining coupon declines over ime a he rae. Toal ousanding governmen deb a face value consiss of long-erm b bonds L B, held by he privae secor ( L, B H ) and he cenral bank ( B L, C B ), and shor-erm bonds, S B : 5 The Woodford (2001) perpeual-bond formulaion is also be used by, e.g., Carlsrom e al. (2017). 7

11 (2) L, H L, C B S B B B B The shor-erm and long-erm bonds are imperfec subsiues in he model. In paricular, privae invesors have a preference for holding a mix of shor-erm and long-erm bonds, and deviaions from he arge value for he raio of long-erm over shor-erm deb induce quadraic adjusmen coss ( b ). 6 Privae households wih access o financial markes (superscrip r for Ricardian) face he following opimisaion problem: 7 r r r m a x L U ( C,1 N ) 0 0 (3) c C C N L, H S (1 ) P r P ( K (1 ) K ) P B B k 1 b 2 C 1 ( 1) L, H P P P 2 B 2 S * * * L, H N L, H B e B f e ( B B ) T R c B P B 1 b 1 0 * (1 i ) P (1 i ) P 2 P P P P 0 S * w r C B e B (1 ) W N 1 1 k k k P D ( i ( i ) ) K 1 1 k P P P P P Ricardian households receive labour income, reurns on financial asses, income k i from lending capial o firms ne of an (exogenous) risk/insurance premium given revenue uncerainy, and dividends D from firm ownership. K I (1 ) K k 1 is he capial sock as he sum of new invesmen I and he pre-period capial sock depreciaed a rae. The governmen levies ax- k es w on income from labour, k on corporae income and c on consumpion. The price in period of a shor-erm (1-period) bond of nominal value S S B is B / (1 i ), wih i being he shor-erm nominal ineres rae. Analogously, e B * * / (1 i ) is he price in domesic currency of a foreign bond B *, where e is he nominal exchange rae as he value in domesic currency of one uni of foreign currency. The maximisaion problem (3) provides he following firs-order condiions (FOC): r L P 1 N B E ( ) E ( ) ( 1) S P b L, H B P 1 i B 1 1 (4) S 6 The same formulaion has been used previously by, e.g., Andrés e al. (2004), Falagiarda (2013), Harrison (2017), and Liu e al. (2015). 7 The descripion of he budge consrain here omis adjusmen coss in he real secor of he economy (price, wage, capial sock, and labour adjusmen coss) ha do no affec he firs-order condiions for porfolio holdings and savings. These adjusmen coss (which generae, e.g., nominal price and wage sickiness) are presen in he full version of he model ha underlies he simulaions. Deails on he specificaion of he real-secor adjusmen fricions can be found in e.g., Prifis and Vogel (2016) and he online appendix. 8

12 r L N S S S P P B B B (5) b E ( ) E ( ) 1 ( 1) ( 1) L, H N L, H b L, H L, H B P c P 2 B B B b 1 (6) * * r L e P 1 e ( B B ) 1 1 E ( ) E ( ) * * f B e P 1 i P 1 r L P P 1 E ( ) E ( ) C k k k K P P (1 i ) ( i ) 1 1 (7) C 1 k k (8) r L C r U (1 ) P P C c c (9) r L N r U w (1 ) W P N Combining (4) wih (6), (7) and (8) illusraes he ransmission channels of QE o he real economy: (10) S * * 1 N B e 1 e ( B B ) P ( 1) E ( ) b L, H * f 1 i B e 1 i P 1 1 N B P 1 ( 1) E ( ) b L H C k k k 1 i B P (1 i ) ( i ) (11) P, S 1 k k S c c C 1 B (1 ) P U P ( 1) 1 i B (1 ) P U N 1 (12) b L, H c c C 1 1 C The impac on asse prices of he cenral bank's purchase of long-erm bonds derives from he privae invesors' porfolio adjusmen coss ( 0 ), i.e., imperfec subsiuabiliy beween dif- b feren financial asses. If 0, he effecs of reducing b L, B H relaive o S B in he household porfolio are similar o he impac of a reducion of he shor-erm ineres rae i in equaion (4), and unconvenional moneary policy can, hence, mimic he effec of reducions in he shor-erm ineres rae. In paricular, when he cenral bank inervenes by purchasing long-erm bonds, privae invesors ha aim a re-esablishing he porfolio mix of shor-erm and long-erm asses can respond by holding more corporae equiy and foreign bonds, and by reducing savings. The firs response means a porfolio reallocaion owards equiy and foreign-currency asses ha increases he price of corporae equiy (rising sock marke) and he price of foreign currency (exchange rae devaluaion). Equaion (10) shows ha QE leads o higher demand for foreign asses and depreciaion of he domesic currency (increase in e ) for given levels of i (resriced, e.g., a he ZLB) and i *. Equaion (11) illusraes he porfolio reallocaion from governmen bonds owards 9

13 corporae equiy. Equaion (12) shows ha QE reduces privae saving similar o a reducion in he shor-erm ineres rae. Concerning he ransmission o he real economy, i) rising sock markes reduce he financing coss of corporaions and, dampening he required reurn o capial, ranslae under decreasing reurns o capial ino sronger invesmen and capial accumulaion, ii) exchange rae depreciaion srenghens ne expors, provided ha expor and impor demand are sufficienly price elasic, and iii) reduced savings o resore he preferred porfolio mix srenghen conemporaneous consumpion demand. The sock of governmen deb, which is composed of shor-erm bonds and long-erm bonds follows: (13) S N S N L C B L ( ) 1 b 1 B B P B P c B P G E T A X P R (1 i ) P P P P P P P where P G E, T A X and CB PR are, respecively, he primary governmen expendiure (public consumpion, public invesmen, ransfers), oal ax revenue (labour, consumpion, and corporae axes), and he operaing profi of he cenral bank as an addiional source of governmen revenue. The operaing profi of he cenral bank equals he sum of base money issuance and ineres income minus he curren expendiure on buying long-erm bonds, where he laer equals he change of he value of long-erm bonds on he cenral bank's balance shee: (14) C B L, C B N L, C B N L, C B P R M c B ( P B P B ) 1 b 1 Under he cenral bank's budge consrain (14), purchases of long-erm governmen bonds can be financed eiher by increasing liquidiy (money issuance), or by reducing he cenral bank's operaing profi. 8 In line wih he sandard definiion of QE and he ECB announcemen, we consider only he case of enhanced liquidiy provision. Purchases of long-erm bonds by he cenral bank can be modelled as an endogenous response o he economic environmen (e.g., he economy's posiion in he business cycle, or he slope of he yield curve) similar o a Taylor rule, or as an exogenous pah. We use he volume of he ECB s asse purchases as observable daa and rea i as an exogenous pah ha replicaes he announced ECB programme in iming and size. 8 A hird opion, in general, is for he cenral bank o sell oher asses from is porfolio o serilise he impac of is inervenion on he cenral bank balance shee. 10

14 4. Model Soluion and Economeric Approach We compue an approximae model soluion by linearising he model around is deerminisic seady sae. Following he recen lieraure ha esimaes DSGE models, we calibrae a subse of parameers o mach long-run daa properies, and we esimae he remaining parameers using Bayesian mehods. The observables employed in he esimaion are lised in he daa appendix. The esimaion uses quarerly daa for he period 1999q1-2017q1. The model has been esimaed using he slice sampler algorihm proposed by Neal (2003). 9 We calibrae he model seady sae so ha seady-sae raios of main economic aggregaes o GDP mach average hisorical raios over he sample period. The EA seady-sae raios of privae consumpion and invesmen o GDP are se o 56% and 19%, respecively. The seadysae share of EA GDP in world GDP is 17%. The seady-sae rade share (0.5*(expors+impors)/GDP) is se a 18% in he EA (excluding inra-ea rade), and he quarerly depreciaion rae of capial is 1.4%. We se he seady-sae governmen deb/annual GDP raio a 80% of GDP in he EA. The seady-sae real GDP growh and inflaion raes are se o 0.35% and 0.4% per quarer, respecively, and he effecive rae of ime preferences o 0.25% per quarer. Regarding he model exension o non-sandard moneary policy and imperfec asse subsiuabiliy, we observe hree QE-specific series, namely (i) securiies held for moneary policy purposes as proxy for long-erm bond purchases by he cenral bank, (ii) he share of long-erm deb in oal governmen deb as an indicaor of long-erm bond supply and, afer deducing he amoun held by he cenral bank, he measure of privae-secor holding of long-erm governmen deb, and (iii) he expeced period-on-period reurn on long-erm bonds, which we calculae from curren and hree-monh-ahead swap raes on 10-year governmen bonds. The consrucion of he laer series is consisen wih our modelling assumpion ha agens are no obliged o hold longerm bonds o mauriy and can, insead, rade hese bonds in he secondary marke a each period in ime. We se he seady-sae porfolio share of long-erm o shor-erm governmen deb o in line wih he average of ousanding EA governmen deb over he sample period. The daa on swap raes of EA governmen bonds deermine he yield spread beween shor-erm and long-erm bonds. The resuls displayed in he following secions rea ECB QE as an AR(2) shock for which he esimaed parameers provide a hump-shaped pah of cenral bank holdings of long-erm gov- 9 See also Planas e al. (2015) for a deailed descripion on he heory and pracice of slice sampling. 11

15 ernmen deb. The AR(2) specificaion follows Carlsrom e al. (2017) and capures he expecaion of a furher expansion of he cenral bank balance shee in he fuure; i.e., curren bond purchases being followed by addiional purchases in he fuure, as announced by he cenral bank a he sar of he programme. As a sensiiviy check, we also esed an AR(1) process for he QE shock in line wih Chen e al. (2012) and De Graeve and Theodoridis (2016). The AR(1) specificaion implies ha bond purchases by he cenral bank are no anicipaed by he privae secor (e.g., he agens reac only o acion, even hough furher seps have already been announced by he ECB), which mues he impac of announcemen effecs wih respec o furher bond purchases. When examining he AR(1) specificaion, we esimaed very high shock persisence (almos a random walk), which implies ha agens expec no, or only a very gradual exi from, QE. In conras, he AR(2) process is closer o agens expecaions, being based on he iniial QE announcemen, which implied a coninuaion of asse purchases during several quarers and a gradual exi in he medium erm. 5. Poserior Parameer Esimaes 10 We choose priors for he non-qe relaed elemens according o he nesed model of Kollmann e al. (2016). I is crucial ha he parameer on porfolio adjusmen coss (g b ) be idenified accuraely, as i deermines he impac of QE on he spread beween shor-erm and long-erm bond yields in he model. We resor o wo approaches: one where prior informaion relaed o he performance of QE is used and anoher where we specify a uniform disribuion. The second approach is preferable if one is fully agnosic abou he prior. In he firs approach, we se he prior for g b o a mean of 15/10000 wih sandard deviaion 6/10000, which is in line wih he calibraed value in Prifis and Vogel (2016) and capures he range of changes in ineres spreads beween shor and long- erm bonds around he ime of he ECB's QE announcemen The presenaion of he resuls focuses on he role of QE and he relaed parameer esimaes, impulse responses and hisorical decomposiions. Broader discussion of resuls can be found in Kollmann e al. (2016) and he relaed online appendix, including prediced business-cycle saisics (sandard deviaions and cross-correlaions of key macro variables); hese saisics are broadly consisen wih empirical saisics. 11 The prior mean for g b is smaller, bu in line wih wo oher DSGE sudies focusing on US Fed QE: De Graeve and Theodoridis (2016) choose a prior mean of 0.05 for he elasiciy of he erm spread o bond supply; Chen e al. (2012) choose a prior mean of The model of Chen e al. (2012) includes he addiional parameer of bond marke segmenaion, however, which also impacs he effecs of QE o he real economy. Harrison (2012) is an upper bound in he lieraure and ses he prior mean of he elasiciy o 0.1, bu he does so in a sylised New- Keynesian model wihou invesigaing he impac of a paricular episode of QE policy. 12

16 Table 1: Prior and poserior disribuions of key esimaed EA model parameers. Descripion Prior Disribuion Poserior Disribuion Dis. Mean (Sd.) Mode (Sd.) Preferences Consumpion habi persisence B 0.5 (0.20) 0.90 (0.02) Risk aversion G 1.5 (0.20) 1.54 (0.17) Inverse Frisch elasiciy of labour supply G 2.5 (0.50) 2.09 (0.44) Impor price elasiciy G 2 (0.4) 2.54 (0.28) Share of Ricardian households B 0.65 (0.10) 0.82 (0.04) Nominal and real fricions Porfolio adjusmen coss G (0.0006) (0.0002) Price adjusmen cos G 60 (40) 42.6 (9.25) Employmen adjusmen cos G 60 (40) 4.58 (1.07) Nominal wage adj. cos G 5 (2) 5.55 (1.48) Moneary policy Ineres rae persisence B 0.7 (0.12) 0.80 (0.03) Response o inflaion B 2 (0.4) 1.61 (0.19) Response o GDP B 0.5 (0.2) 0.06 (0.02) Auocorrelaions of shocks QE AR(1) (purchases of long-erm bonds) N 1.8 (0.4) 1.75 (0.10) QE AR(2) (purchases of long-erm bonds) N (0.3) (0.09 ) Bond risk premium B 0.5 (0.20) 0.87 (0.05) Domesic price mark-up B 0.5 (0.20) 0.54 (0.13) Sandard deviaions (%) of innovaions Moneary policy B 1 (0.40) 0.09 (0.01) QE (purchases of long-erm bonds) G 1 (0.40) 1.12 (0.17) Invesmen risk premium G 0.1 (0.40) 0.30 (0.05) Bond risk premium G 1 (0.40) 0.17 (0.09) Domesic price mark-up G 2 (0.80) 4.46 (1.07) Noes: Col. (1) liss model parameers and shocks. Cols. (2)-(3) indicae he prior disribuion funcion (B: Bea disribuion; G: Gamma disribuion). Cols. (4)-(5) show he mode and he sandard deviaion (Sd) of he poserior disribuions of EA parameers. Wih boh prior choices, he poserior mode of he esimaion converges o he same poin, which suggess ha he daa are informaive for successfully idenifying he parameer. 12 The poserior esimaes of key model parameers for he EA are repored in Table 1. These esimaes are based on he unconsrained linearised version of he model and also used for he soluion wih an occasionally binding consrain. 12 See Figure C.1 in he online appendix. 13

17 The seady-sae consumpion share of he Ricardian household is esimaed a Esimaed habi persisence in consumpion is high (0.90), which indicaes a sluggish adjusmen of consumpion o income shocks. The risk aversion coefficien is in he range of 1.5 and he inverse of he elasiciy of labour supply is esimaed o be 2.1. The esimaed price elasiciy of aggregae impors is 2.5. The model esimaes also sugges subsanial nominal price and wage sickiness. The esimaed ineres rae rule indicaes a srong response of he EA policy rae o domesic inflaion, and a weak response o domesic oupu. Imporan in our conex, he poserior esimae of he adjusmen cos parameer aached o he mauriy srucure of he privae secor porfolio of governmen deb is The fiscal feedback rules for governmen ransfers (no shown in Table 1) exhibi very weak responses o public deb and defici levels. The esimaes also sugges ha mos exogenous variables are highly serially correlaed. The model properies discussed in wha follows are evaluaed a he poserior mode of he model parameers. 6. QE in he Unconsrained Model This secion provides resuls on he impac of QE for he unconsrained linearised version of our model. The discussion focuses on impulse responses and shock decomposiions for real GDP growh and inflaion. Using he unconsrained linearised model implies ha he sandard moneary policy (Taylor) rule is operaional a any period of ime. An operaional Taylor rule offses par of effecive QE as i reacs o rising oupu growh and inflaion by ighening shor-erm ineres raes Dynamic effecs of QE shocks Figure 1 provides impulse responses of EA endogenous variables for a posiive QE shock ha illusrae he ransmission of QE in he model. More precisely, he shock is a purchase of longerm governmen bonds by he cenral bank ha is financed by addiional liquidiy. The iniial shock is an increase in cenral bank holdings of long-erm bonds by 1% of quarerly GDP. Given he specificaion of QE as an esimaed AR(2) process, he iniial purchase (announcemen) implies a furher exension of he cenral bank s balance shee by anoher 12 quarers (3 years), unil i reverses o a slow bu gradual decline (exi) of he iniial balance shee exension. 14

18 Figure 1: Impulse responses for posiive EA QE shock Noe: Time inervals on he x-axis are quarers; unis on he y-axis are %, excep for inflaion and he rade balance (boh pp) and he shor-erm nominal ineres rae (bp). The iniial QE shock is 1pp of quarerly real GDP. The purchase of long-erm governmen deb by he cenral bank reduces he amoun of long-erm deb available o privae invesors. Given he preference of privae invesors for a mauriy mix, i.e., imperfec subsiuabiliy beween shor-erm and long-erm bonds, he price of long-erm bonds rises; heir expeced yield consequenly declines. The decline in he yield of long-erm bonds leads o porfolio rebalancing owards equiy and foreign asses. Higher demand for equiy lowers he equiy premium and causes an increase in privae invesmen, as shown in Figure 1. Higher demand for foreign asses causes depreciaion of he domesic currency (an increase in he real exchange rae in Figure 1 corresponds o real effecive depreciaion), which leads o an improvemen in he EA rade balance. The declining yield on long-erm bonds also reduces privae savings as privae invesors are less inclined o inves in shor-erm bonds away from he preferred mauriy mix in he porfolio; he decline in savings raises privae consumpion. The join increase in consumpion, invesmen and ne expors implies an increase in real GDP and (demand-driven) inflaion. Noe ha he formulaion of he cenral bank balance shee expansions as 15

19 an AR(2) process ranslaes ino a hump-shaped decline in he equiy premium and he savings rae, which is behind he hump-shaped response of invesmen and consumpion. Higher invesmen in producive capial raises he capial sock and he produciviy of workers, so ha labour demand and employmen increase and real wages rise o some exen. Noe ha he efficiency of QE in Figure 1 is dampened by an offseing response of he shor-erm policy rae. Given he posiive impac of QE on aciviy and inflaion, sandard moneary policy as capured by he Taylor rule becomes less expansionary han in he non-qe baseline. Secion 7 below will presen corresponding impulse responses wih binding ZLB consrain, i.e., wihou ighening of shorerm policy raes Decomposing EA oupu growh and inflaion To quanify he role of differen shocks as drivers of oupu and inflaion, we plo he esimaed conribuion of he differen shocks o year-on-year real GDP growh (Figure 2) and o he yearon-year growh of he GDP deflaor (Figure 3). To focus he discussion on he conribuion of QE, we group he remaining shocks coarsely in hree groups: domesic demand shocks (which include financial shocks affecing consumpion, invesmen and ne expor demand, as well as fiscal shocks); domesic supply shocks (produciviy and price and wage mark-up shocks); and rade and foreign shocks (conaining shocks o rade demand and mark-ups and o foreign demand and supply, including oil price shocks). The black solid line presens he daa, he blue surface he conribuion of he respecive group of shocks. Regarding he pre-qe era, our esimaed model mirrors he findings in Kollmann e al. (2016) (see Figure 2) for explaining he flucuaions in GDP growh and he EA double-dip recession. In paricular, a large share of he GDP growh flucuaions in is aribued o domesic demand shocks (in paricular hose driving invesmen demand), whereas he role of domesic supply shocks in he decomposiion is much smaller. Trade and foreign shocks have conribued o negaive growh during he 2009 recession (low exernal demand and decline in rade), bu have suppored GDP growh in more recen years (global recovery). Mos imporan in our conex, he decomposiion poins o a posiive impac of EA QE as capured in our model on EA growh from 2015 onwards, i.e., aking ino accoun changes in he ECB balance shee up o 2017q1. The impac of QE o GDP growh builds in early 2015 and per- 16

20 % % % % siss in Figure 2 suggess a conribuion of EA QE o annual EA real GDP growh of 0.3 pp in boh 2015 and Figure 2: Decomposiion of year-on-year growh of EA real GDP 4 2 Domesic demand shocks 4 2 Domesic supply shocks Trade and foreign shocks 4 2 Quaniaive easing Figure 3 presens a decomposiion for consumer price index (CPI) inflaion. In line wih Kollman e al. (2016), he resuls sugges a more balanced role of domesic demand and supply shocks in explaining he flucuaions in CPI inflaion. The pre-crisis demand boom has added o inflaion pressure, whereas he following conracion of domesic demand has pushed inflaion down. Domesic supply shocks, noably negaive produciviy rends and he sluggish adjusmen of wages and prices, have upheld inflaion more in recen years according o he decomposiion. The group of rade and foreign shocks has conribued negaively o inflaion hrough lower expor demand during he global recession, falling impor prices (including oil) more recenly, and nonfundamenal changes in he euro exchange rae. The esimaed conribuion of QE o annual EA CPI inflaion is 0.3 pp in 2015 and 0.6 pp in The sizeable QE conribuions o real GDP growh and inflaion in he EA occur despie 13 Noe ha he panels for QE in Figures 2 and 3 show smaller posiive growh and inflaion conribuions already before 2015, which are due o (smaller) variaions in he cenral bank holding of long-erm deb prior o 2015 ha are capured by he same shock bu are no par of he programme iniiaed in

21 % % % % he fac ha effecive QE riggers a ighening of sandard moneary policy in he unconsrained linearised normal imes model. As will be discussed in he following secion, QE effecs are sronger when accouning for he ZLB consrain. Figure 3: Decomposiion of year-on-year EA CPI inflaion 3 2 Domesic demand shocks 3 2 Domesic supply shocks Trade and foreign shocks 3 2 Quaniaive easing

22 7. QE in he Model wih an Occasionally Binding Consrain In his secion we assess he conribuion of QE when we allow he zero-bound on moneary policy o be occasionally binding. A binding ZLB implies ha he arge ( shadow ) policy rae is below he lower bound. By implicaion, an increase in oupu and inflaion hrough QE or oher facors does no lead o ighening of he shor-erm rae while he consrain is binding, i.e., while he shadow rae remains below he lower bound Implemenaion of he occasionally binding consrain We use he OccBin soluion mehod developed by Guerrieri and Iacoviello (2015) o rea he occasionally binding consrain via a piecewise linear soluion. Moreover, we use an algorihm as in Giovannini and Rao (2017) o obain smoohed esimaes of laen variables as well as he sequence of regimes along he hisorical sample. 14 We se he lower bound for quarerly shorerm ineres raes a %, in line wih he annualised rae of 0.05%, a which he ECB's main refinancing operaions paused in afer a sequence of consecuive rae reducions since The unconsrained nominal ineres rae i NC follows he usual Taylor rule wihou moneary shock: NC i = ρ i (i 1 i ) + (1 ρ i ) (η iπ (0.25 ( π r ) π c,va ) + η iy (y )) i As long as he acual policy rae is above he lower bound, he nominal ineres rae is: If i NC i LB he policy rae is consrained: 3 r=0 i = i NC inom + u i = i LB inom + u NC The variable i acs as a shadow ineres rae under a consrained regime. Under he OccBin algorihm, i allows i o be deermined endogenously when he consrain is no longer binding. 15 The algorihm used for esimaing laen variables yields iniial condiions and a sequence of c,va 14 We use he algorihm by Giovannini and Rao (2017) o obain esimaed laen variables and a corresponding sequence of hisorical regimes. The algorihm works as follows: I guesses an iniial sequence of hisorical regimes and compues he sequence of sae-space marices following he piecewise linear soluion by Guerrieri and Iacoviello (2015). Given he sae-space marices, he Kalman filer is used o esimae he smoohed variables and shocks, which endogenously deermine a new sequence of regimes. The algorihm sops when he new sequence of regimes is equal o he previous one. In our case, he algorihm converged afer hree ieraions. 15 We sill use an exogenous moneary shock under he consrained regime in order o keep observing he acual policy rae in he daa. The shock does no affec he behaviour of he piecewise linear soluion in erms of ransmission mechanisms under he ZLB consrain. 19

23 smoohed shocks ha are consisen wih he observables and ake ino accoun he occasionally binding consrain. The sequence of regimes is repored in Table 2. Table 2: Esimaion of he hisorical sequence of occasionally binding regimes in 2013q1-2017q1 Time Regime sequence 1 Saring period of regime q q q q q q q q q q q q q q q q q1 0 1 Noes: (Firs column) 0 = unconsrained, 1 = consrained. [1 0] indicaes a consrained regime. (Second column) Periods for which he regime sars: [1 5] indicaes a consrained regime for 4 periods. Based on our definiion of he ZLB as a 0.05% annual nominal ineres rae, EA moneary policy is consrained from 2014q4 onwards. While our simulaion indicaes a coninued consrained regime in 2016q4, which is expeced o las unil 2017q1, moneary policy in 2017q1 is effecively no longer consrained Dynamic effecs of QE shocks a he ZLB Based on he sequence of regimes, we perform impulse response funcions (IRFs) wih a ZLB ha are consisen wih he esimaed iming and duraion of he consrained regime. In paricular, 20

24 we perform he following exercise: We use as a saring poin he smoohed variables in 2015q1, which is a period of consrained moneary policy according o Table 2 and he official sar of QE. We shu off all QE shocks and simulae he model wih all oher shocks. Then we perform anoher simulaion adding a posiive ECB QE shock of he same size as in Figure 1, i.e., longerm bond purchases of 1% of seady-sae quarerly EA GDP. The difference beween he wo simulaions provides he IRF of he ECB QE shock under he consrained regime. The resul is shown in he comparison beween he linear (unconsrained) and piecewise linear (consrained) IRFs in Figure 4. Figure 4: IRF for posiive EA QE shock under unconsrained and consrained moneary policy Noe: Solid (blue) is he linear (unconsrained) model, dashed (red) he piecewise linear model (ZLB). The linear soluion is equivalen o he IRFs in Figure 1. Given he saring poin of our simulaions in 2015q1 and he sequence of regimes in Table 2, moneary policy in 2015q1 is expeced o be consrained for four quarers, alhough from an expos perspecive, i is consrained unil 2016q4. Figure 4 capures he expecaion of moneary policy being consrained for four quarers and going back o normal imes from 2016q1 on- 21

25 wards by a gradual increase of he consrained owards he unconsrained nominal ineres rae response afer four quarers. The change back o he normal regime is he consequence of sofening conracionary forces, i.e., he abaing of conracionary shocks and of he effeciveness of QE, i.e., i is no he resul of an exogenous regime swich. The IRFs sugges ha he impac of he QE shock on real GDP (quarerly 0.08% insead of 0.04% on impac) and CPI inflaion (0.04 pp insead of 0.02 pp on impac) doubles in he zero-bound environmen Decomposing EA oupu growh and inflaion As for he unconsrained model, we invesigae he shock conribuions o he observed daa ha are consisen wih he piecewise linear soluion, i.e., we provide an exension of he sandard hisorical shock decomposiions o he case of occasionally binding regimes. In his conex, he conribuion of individual smoohed shocks is no he mere addiive superposiion of each shock. Insead, i is a non-linear funcion of he whole se of shocks simulaneously affecing he economy. Hence, he conribuion of one shock is condiional on he sequence and combinaion of shocks simulaneously hiing he economy. 16 We use he complemen/residual conribuion o accoun for he impac of he ZLB on he conribuion of shocks o observed variables. In pracice, we compue he conribuion of QE by seing he QE shock o zero and perform simulaions using iniial condiions and he sequence of all he oher shocks. The conribuion of QE will be he complemen/residual of his simulaion o he smoohed variable. 17 Figure 5 compares he conribuion of QE o year-on-year real GDP growh and CPI inflaion in he EA under he linear (unconsrained) soluion and he piecewise linear (ZLB consrain) soluion, respecively. Accouning for he emporarily binding ZLB srenghens he posiive conribuion of QE o real GDP growh and inflaion in Compared wih he linearised normal imes soluion, he average impac of QE on annual real GDP growh rises from 0.3 pp o 0.6 pp in 2015 and from 0.3 pp o 0.7 pp in The impac on annual CPI inflaion rises from 0.3 pp o 0.4 pp in 2015 and from 0.6 pp o 0.8 pp in The more posiive conribuion of QE under he ZLB derives from he absence of a counervailing ighening of moneary policy according o he Taylor rule ha would occur in "normal" imes in he linearised model. 16 In general, we can consider wo definiions ha generalise he concep of shock conribuions in he non-linear case, which degenerae o he sandard shock decomposiion for he linear case: The condiional conribuion and he complemen conribuion. See Giovannini and Rao (2017) for a deailed descripion of boh mehods. 17 Noe ha each of hese simulaions provides a differen sequence of regimes, which in general will be differen from he hisorical one. The complemen/residual conribuion riggers key non-linear feaures associaed o he ineracion beween shock realisaion and he occasionally binding consrains. 22

26 Figure 5: QE conribuion o year-on-year EA real GDP growh and CPI inflaion in linear and piecewise linear soluion Noe: Real GDP growh and CPI inflaion are boh shown as deviaions from he seady sae, which is calibraed as he mean over he sample period from 1999q1 o 2017q1. In boh sub-plos, 0.01 on he y-axis corresponds o 1 pp. Along wih he decomposiion of GDP growh, Figure 6 displays he conribuion of QE o he growh rae of hose variables ha are he main ransmission channels of QE in our porfolio rebalancing framework, namely consumpion (reduced savings), invesmen (lower equiy premium) and he real exchange rae (currency depreciaion). The figure indicaes a paricularly pronounced impac on EA invesmen growh and a sizeable impac on consumpion growh and real effecive exchange rae (REER) depreciaion. I also indicaes a fronloading of he impac on invesmen and REER, which is he resul of forward-looking behaviour in combinaion wih anicipaion of furher asse purchases ha is embodied in he AR(2) specificaion of he QE process. The impac on consumpion growh is more gradual and delayed, due o he esimaed high degree of habi persisence in consumpion. 23