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

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1 MPRA Munich Personal RePEc Archive The Macroeconomic Effecs of Quaniaive Easing in he Euro Area: Evidence from an Esimaed DSGE Model Sefan Hohberger and Romanos Prifis and Lukas Vogel European Commission, Join Research Cenre, European Commission, DG ECFIN, European Commission, DG ECFIN 4 March 207 Online a hps://mpra.ub.uni-muenchen.de/78955/ MPRA Paper No , posed 7 May :5 UTC

2 The Macroeconomic Effecs of Quaniaive Easing in he Euro Area: Evidence from an Esimaed DSGE Model Sefan Hohberger (European Commission, Join Research Cenre) Romanos Prifis (European Commission, DG ECFIN) Lukas Vogel (European Commission, DG ECFIN) (*) 4 March 207 Absrac This paper analyses he macroeconomic effecs of he ECB's quaniaive easing programme using an open-economy DSGE model esimaed wih Bayesian echniques. 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 EA year-on-year oupu growh and inflaion of up o 0.4 and 0.5 pp in he sandard linearized version of he model. Allowing for an occasionally binding zero-bound consrain by using piecewise linear soluion echniques raises he posiive impac up o.0 and 0.7 pp, respecively. JEL classificaion: E44, E52, E53, F4 Keywords: Quaniaive easing, porfolio rebalancing, Bayesian esimaion, open-economy DSGE model, real GDP, inflaion (*) Corresponding auhor. Address: DG Economic and Financial Affairs, European Commission, CHAR 4/233, B- 049 Brussels, lukas.vogel@ec.europa.eu, Tel.: We hank Lucian Briciu, Fabian Eser, Massimo Giovannini, Marco Rao and Werner Roeger for exremely helpful suggesions and discussions and paricipans a he 4h Annual EEFS Conference (Brussels), he 47h MMF Research Group Annual Conference (Cardiff Universiy) and he 6h IWH/INFER Workshop on (Ending) Unconvenional Moneary (Halle) for helpful commens on previous versions of he paper. The views expressed in his paper are hose of he auhors and should no be aribued o he European Commission.

3 . Inroducion In early 205 he European Cenral Bank (ECB) has 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 205 he amoun of ourigh purchases on he balance shee had reached 24% of GDP in he case of he US Federal Reserve, 64% of GDP in he case of he Bank of Japan, 2% of GDP in he case of he Bank of England, and 5% of GDP in he case of he ECB (Consâncio 205). The ECB's QE programme announced in January 205 (Public Secor Purchase Programme) foresaw buying 60 billion of asses a monh from March 205 o Sepember 206, which in sum corresponds o circa 0% of annualised euro area (EA) GDP. In December 205, he ECB has exended he programme unil March 207, and i has raised he amoun of monhly purchases o 80 billion saring from April 206. In December 206 he programme has been exended and modified again, lenghening he period of asse purchases unil (a leas) December 207, bu a a reduced pace of 60 billion of asses a monh afer March 207. 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 205). In pracice, he ECB purchases public secor financial asses (governmen deb) of longer mauriy and exends liquidiy (base money) o he privae secor (Claeys e al. 205, Valiane 205). Research a he ECB has provided evidence for an impac of he QE programme on long-erm bond yields and spillover o oher asse prices hrough porfolio reallocaion: Alavilla e al. (205) in an even sudy repor a basis-poin decline in 0-year governmen bond yields wih spillover ino lower corporae bond, spreads, higher equiy prices, and euro depreciaion. Andrade e al. (206) repor a decline of EA 0-year governmen bond yields in he range 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 (206) suggess ha ECB non-sandard policy has reduced EA 0-year governmen bond yields beween Sepember 204 and Ocober 205 on average by 63 basis poins. This paper analyses he macroeconomic effecs of he ECB's QE programme using a woregion 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 cenral bank balance shee and disinguishing beween shor-erm and long-erm governmen deb. We use a formulaion of privae-secor porfolio preferences - as, e.g., Andres e al. (2004) - ha allows for non-neural effecs of cenral 2

4 bank purchase programmes due o imperfec subsiuabiliy beween asses of differen mauriy. More specifically, he cenral bank alers is balance shee by purchasing long-erm bonds (he laer modelled as in Woodford, 200) and injecing liquidiy o 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, 20) including he saving, financing cos, exchange rae, inflaion, and fiscal channels. The exchange rae channel is absen from mos model-based sudies of QE policies (e.g., Chen e al. 202, De Graeve and Theodoridis 206, Gerler and Karadi 20), which build insead on closed-economy frameworks. The conribuion of his paper is o analyse he macroeconomic impac of ECB QE using a sae-of-he-ar esimaed dynamic sochasic general equilibrium (DSGE) model. Combining daa on governmen deb socks and yields across mauriies, he model esimaion enables o exrac a value for he crucial parameer governing he porfolio adjusmen coss of households. The implied srengh of hese coss dicaes he magniude of he yield spread following QE of a given volume and ime pah, such as he one announced by he ECB in January 205. Given ha ECB QE has been launched only in 205, we have lile 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 linearized version of he model in which he Taylor rule is never hiing he ZLB (we refer o his as "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 "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 205q-6q2 by 0.3 pp and 0.3 pp on average, wih maximum impac of 0.4 and 0.5 pp in 206. Including he endogenously and occasionally binding ZLB consrain raises he 205q-6q2 average growh and inflaion effec of QE o 0.7 and 0.4 pp, respecively, wih peaks a.0 and 0.7 pp in 206q2. 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 summarizes he closely relaed lieraure; secion 3 oulines he general srucure of he model; secion 4 describes he mod- 3

5 el soluion and esimaion mehodology; secion 5 presens parameer esimaes; secion 6 discusses he impac of QE in he unconsrained model; secion 7 presen resuls from he model wih occasionally binding consrain; secion 8 summarizes he paper and concludes. 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 (206). 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 euro area daa. The approach is closes o Chen e al. (202) and De Graeve and Theodoridis (206) who analyse US QE in esimaed closed-economy models of he US economy. Boh Chen e al. (202) and De Graeve and Theodoridis (206) focus on he porfolio balancing channel of QE ransmission. According o he resuls in Chen e al. (202), he US LSAP II (large-scale asse purchase) 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 0.3% and inflaion by only 0.03 percenage poins (pp). According o he esimaes of De Graeve and Theodoridis (206), "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 0.3 pp. The models by Gerler and Karadi (203) and Carlsrom e al. (207) 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 (203) quanify he impac of US LSAP wih a volume of 2.5% of GDP on oupu and inflaion o % and.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 4

6 described in erms of he credi channel, recen empirical analyses (see, e.g., Bluwsein and Canova 206, Tillman and Ludering 206) do no sugges he credi channel o be a primary ransmission mechanism for QE in he EA and spillover o non-ea counries. Sahuc (206) 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 (203), he Sahuc (206) assessmen sresses he imporance of keeping shor-run policy raes low for longer. Keeping he policy rae consan only in 205 gives a maximum QE effec on oupu growh and inflaion of 0.2 and 0. pp in 205-6, 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. (206) and exends his model o incorporae non-sandard moneary policy. The model is esimaed using quarerly daa for he period 999q-206q2. 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 household consume heir disposable income in every period. Preferences of boh ypes of households exhibi habi formaion in boh consumpion and leisure. A monopolisicallycompeiive secor produces differeniaed goods by employing domesic labor and capial. Firms in his secor maximize 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 uilizaion rae. Final goods firms combine a domesic differeniaed goods bundle wih energy inpus. Nominal differeniaed goods prices are sicky as are he wages paid o he workers; he laer being deermined by monopolisic rade unions. The fiscal auhoriy imposes disorive axes and issue deb. The exposiion below describes he QE-relevan exensions. A deailed overview of he general model can be found in Kollmann e al. (206) and he model appendix. We exend he model by inroducing feaures of non-sandard moneary policy as in Prifis and Vogel (206), which is similar in spiri o he modelling of QE in Chen e al. (202) and De Graeve and Theodoridis (206). Similar o Chen e al. (202) and De Graeve and Theodoridis (206), our model emphasises he ransmission of QE mainly hrough porfolio rebalancing. However, unlike hese sudies, our muli-counry model allows for an exchange rae channel and poenial rade effecs from QE. 5

7 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 zero lower bound (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 (200) 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 b. The price in period of a long-erm bond issued in ( P ) equals he discouned value of fuure paymens N P N T n 0 ( i) n b n c, where T is he mauriy period of he bond. Analogously, he price in period of a long-erm bond issued in - ( P ) equals he discouned sum of ousanding paymens, P O T n b n O c. If b ( i) and T is large, he price in of long-erm bonds issued in - n0 ( i) corresponds (approximaely) o he price of newly issued long-erm bonds imes he depreciaion rae: () P P O N b Equaion () shows ha he price of he long-erm bond ha pays a declining coupon declines over ime a he rae b. Toal ousanding governmen deb a face value consiss of long-erm bonds, B, held by he privae secor ( B LH, ) and he cenral bank ( B L CB ), and shor-erm bonds, L S B : (2) B B B B L, H L, CB S 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 ). 2 The Woodford (200) perpeual-bond formulaion is also be used by, e.g., Carlsrom e al. (207). 2 The same formulaion has been used previously by, e.g., Andrés e al. (2004), Falagiarda (203), Harrison (202), and Liu e al. (205). 6

8 Privae households wih access o financial markes (superscrip r for Ricardian) face he following opimisaion problem: 3 (3) r r r 0 0 max L U ( C, N ) c C C N L, H S ( ) P r P ( K ( k ) K ) P B b B 2 C ( ) LH, P P P 2 B 2 S * * * L, H N L, H B e B f e ( B B ) TR cb bp B 0 * 0 ( i ) P ( i ) P 2 P P P P S * w r C B eb ( ) W N k k k P D ( i ( i k ) ) 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 ( k ) K invesmen I and he pre-period capial sock depreciaed a rae axes w on income from labour, is he capial sock as he sum of new k on corporae income and k. The governmen levies c on consumpion. The price in period of a shor-erm (-period) bond of nominal value S B is B / ( i ) S, wih i being he shor-erm nominal ineres rae. Analogously, e B / ( i ) is he price in domesic currency of a * * foreign bond uni of foreign currency. * B, where e is he nominal exchange rae as he value in domesic currency of one The maximisaion problem (3) provides he following firs-order condiions (FOC): r S L P N B (4) E ( ) E ( ) b P ( ) S L, H B P i B r N S S S L P P b B 2 B B (5) E ( ) ( ) ( ) ( ) L, H E N L, H b L, H L, H B bp c P 2 B B B (6) L B e P i P r * * e P e ( B B ) E ( ) ( ) * E * f r C L P P (7) E( ) E( ) C ( k ) k ( k K P P i i ) k k 3 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, e.g., in Prifis and Vogel (206) and in he appendix. 7

9 (8) r L C r U c ( ) P P c C (9) r L N r U w ( ) W P N Combining (4) wih (6), (7) and (8) illusraes he ransmission channels of QE o he real economy: (0) i B e i P S * * N B e e ( B B ) b P ( ) E ( ) LH, * f S C N B P () b P ( ) E ( ) L, H C k k k i B P ( i ) ( i ) k k S c c C N B ( ) P U (2) b P ( ) L, H c c C i B ( ) P U The impac on asse prices of he cenral bank's purchase of long-erm bonds derives from he privae invesors' porfolio adjusmen coss ( b 0 ), i.e. imperfec subsiuabiliy beween differen financial asses. If b 0, he effecs of reducing B relaive o LH, 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 (0) 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 () illusraes he porfolio reallocaion from governmen bonds owards corporae equiy. Equaion (2) 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 8

10 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: B P L B ( bp c) B PGE TAX PR (3) B ( i ) P P P P P P P where PGE, S N S N L CB TAX 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 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: (4) PR M cb ( P B P B ) CB L, CB N L, CB N L, CB b Under he cenral bank's budge consrain (4), purchases of long-erm governmen bonds can be financed eiher by increasing liquidiy (money issuance), or by reducing he cenral bank's operaing profi. 4 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 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 exogenous pah. The se-up in his paper models QE as exogenous pah ha replicaes he announced ECB programme in iming and size. 4. Model soluion and economeric approach We compue an approximae model soluion by linearizing 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 esimaion are lised in he Daa Appendix. 5 The esimaion uses quarerly daa for he period 999q-206q2. We also perform esimaion on he subsample 999q-204q4 o es he sabiliy of parameer esimaes, especially he adjusmen 4 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. 5 The observables are no demeaned or de-rended prior o esimaion. The model is esimaed on firs differences of real GDP, real demand componens and price indices, and on nominal raios of aggregae demand componens o GDP. 9

11 cos/porfolio preference parameer b, wih respec o he implemenaion of QE. The model has been esimaed using he slice sampler algorihm proposed by Neal (2003). 6 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 9%, respecively. The seady sae shares of EA GDP in world GDP is 7%. The seady sae rade share (0.5*(expors+impors)/GDP) is se a 8% in he EA (excluding inra-ea rade), and he quarerly depreciaion rae of capial is.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. Wih respec o he model exension o imperfec asse subsiuabiliy and non-sandard moneary policy, we se he seady-sae porfolio share of long-erm o shor-erm governmen deb o 0.96 in line wih he average of ousanding EA governmen deb over he sample period. We use daa on swap raes of EA governmen bonds o deermine he yield spread beween shorerm and long-erm bonds. In paricular, we use he curren and 3-monh-ahead swap raes on 0- year bonds o calculae he implied expeced period-on-period reurn on long-erm bonds. This approach is consisen wih our modelling assumpion ha agens are no obliged o hold longerm bonds o mauriy, bu raher can rade hese bonds in he secondary marke a each period in ime. The resuls displayed in he following secions rea ECB QE as an AR() shock for which he esimaed persisence is very high, as in Chen e al. (202) and De Graeve and Theodoridis (206). The specificaion as AR() 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. The high persisence innovaions have a half-life of 2 years also implies ha agens expec only very gradual exi from QE, however. Alernaively, we have esed a QE shock wih random walk assumpion. The random walk assumpion implies ha privae invesors expec he balance shee expansion o be permanen, i.e. no exi from QE in he sense of a reurn of he cenral bank balance shee o pre-qe levels. Resuls for he highly persisen AR() and he random walk shock specificaion are very similar. 7 6 See also Planas e al. (205) for a deailed descripion on he heory and pracice of slice sampling. 7 We have also esed an AR(2) specificaion of he QE shock. The AR coefficiens are boh close o 0.5 in his case and esimaion resuls very similar o he AR() case. 0

12 5. Poserior parameer esimaes 8 The poserior esimaes of key model parameers for he EA are repored in Table. These esimaes are based on he unconsrained linearized version of he model and also used for he soluion wih occasionally binding consrain. Preferences Table : Prior and poserior disribuions of key esimaed EA model parameers. Descripion Prior Disribuion Poserior Disribuion Dis. Mean (Sd.) Mode (Sd.) Consumpion habi persisence B 0.5 (0.20) 0.89 (0.02) Risk aversion G.5 (0.20).42 (0.5) Inverse Frisch elasiciy of labor supply G 2.5 (0.50) 2.29 (0.43) Impor price elasiciy G 2 ().98 (0.34) Seady sae consumpion share of Ric. HH B 0.65 (0.0) 0.85 (0.02) Nominal and real fricions Porfolio adjusmen coss G (0.0006) (0.0003) Price adjusmen cos G 60 (40) 26.6 (7.76) Nominal wage adj. cos G 5 (2) 5.86 (.37) Real wage rigidiy B 0.5 (0.20) 0.97 (0.0) Moneary Policy Ineres rae persisence B 0.7 (0.2) 0.78 (0.03) Response o inflaion B 2 (0.4).68 (0.29) Response o GDP B 0.5 (0.2) 0.06 (0.03) Response o cumulaive deflaion gap G (0.002) (0.002) Auocorrelaions of shocks QE (purchases of long-erm bonds) B 0.5 (0.2) (0.0) Bond risk premium B 0.5 (0.20) 0.77 (0.09) Domesic price mark-up B 0.5 (0.20) 0.9 (0.09) Sandard deviaions (%) of innovaions Moneary Policy B (0.40) 0.0 (0.00) QE (purchases of long-erm bonds) G (0.40) 2. (0.5) Invesmen risk premium G 0. (0.40) 0.9 (0.02) Bond risk premium G (0.40) 0.54 (0.5) Domesic price mark-up G 2 (0.80) 3.05 (0.99) Noes: Cols. () liss model parameers and shocks. Cols. (2)-(3) indicaes 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. 8 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. (206) and he relaed nofor-publicaion appendix, including prediced business cycle saisics (sandard deviaions and cross-correlaions of key macro variables); hese saisics are broadly consisen wih empirical saisics.

13 The seady sae consumpion share of he Ricardian household is esimaed a Esimaed habi persisence in consumpion is high (0.89), which indicaes a sluggish adjusmen of consumpion o income shocks. The risk aversion coefficien is in he range of.4 and he inverse of he elasiciy of labor supply elasiciy is esimaed o be 2.3. The esimaed price elasiciy of aggregae impors is 2.0. The model esimaes also sugges subsanial nominal price and wage sickiness, and srong real wage rigidiy. 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 ) 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 linearized. The discussion focuses on impulse responses and shock decomposiions for real GDP growh and inflaion. Using he unconsrained linearized 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 ineres raes. 6.. Dynamic effecs of QE shocks Figure 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 (CB) ha is financed by addiional liquidiy. The shock is a one-ime increase in CB holdings of long-erm bonds and calibraed o mach he quarerly amoun of ECB purchases of around 200 billion euro, which corresponds o circa 8% of baseline quarerly GDP. Given he specificaion of QE as highly persisen AR(), he one-ime purchase implies a long-lasing exension of he CB's balance shee by he given amoun; only half of he iniial balance shee exension will be undone afer 2 years. 9 We have esed he robusness of he parameer esimae by saring from differen (lower and higher) prior values. The esimaion has converged o he same value in boh cases. 2

14 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). Figure : Impulse responses for posiive EA QE shock (long-erm bond purchase of 8% of quarerly EA GDP) The purchase of long-erm governmen deb by he CB 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. Higher demand for foreign asses causes depreciaion of he domesic currency (an increase in he real exchange rae in Figure 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 ino 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 (demanddriven) inflaion. Noe ha he assumpion of a very persisen expansion of he CB's balance shee implies a very persisen decline in he equiy premium and he savings rae, which is behind he very persisen increase in 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 3

15 % % % % 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 zero lower bound (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. 4 2 Domesic demand shocks 4 2 Domesic supply shocks Trade and foreign shocks 4 2 Quaniaive easing Figure 2: Decomposiion of year-on-year growh of EA real GDP The decomposiion in Figure 2 mirrors he finding by Kollmann e al. (206) ha domesic demand shocks (in paricular hose driving invesmen demand) accoun for a large share of he 4

16 % % % % flucuaion in GDP growh during and, in paricular, he EA double-dip recession. The role of domesic supply shocks appears comparaively weak. Trade and foreign shocks have conribued o he 2009 recession (low exernal demand and decline in rade), bu have suppored GDP growh in more recen years (global recovery). Finally, and mos ineresingly in our conex, he decomposiion poins o a posiive impac of EA QE as capured in our model, i.e. aking ino accoun changes in he ECB balance shee up o 206Q2, o EA growh. The impac of QE is increasing gradually given he gradual pah of asse purchases and our assumpion ha fuure CB asse purchases are no anicipaed by privae invesors. Even under his limiing assumpion, Figure 2 suggess a conribuion of EA QE o EA year-on-year real GDP growh of 0.3 pp on average in 205q-6q2, wih he maximum of 0.4 pp in 206q Domesic demand shocks 3 2 Domesic supply shocks Trade and foreign shocks 3 2 Quaniaive easing Figure 3: Decomposiion of year-on-year EA CPI inflaion The decomposiion of CPI inflaion in Figure 3 suggess a more balanced role for domesic demand and supply shocks compared o Figure 2. 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 sluggish wage and price ad- 0 Noe ha he panels for QE in Figures 2 and 3 show smaller posiive growh and inflaion conribuions already before 205, which are due o (smaller) variaions in he CB holding of long-erm deb prior o 205 ha are capured by he same shock bu no par of he programme iniiaed in

17 jusmen, have upheld inflaion more recenly according o he decomposiion. Trade and foreign shocks have negaively conribued o inflaion hrough lower expor demand during he global recession and falling impor prices (including oil) more recenly. Finally, Figure 3 poins o a sizable conribuion of QE o year-on-year EA CPI inflaion, wih 0.3 pp on average in 205q- 6q2 and a peak a 0.5 pp in 206Q2. The sizable posiive conribuion of QE o real GDP growh (up o 0.4 pp) and inflaion (up o 0.5 pp) in he EA occurs despie he fac ha effecive QE riggers a ighening of sandard moneary policy in he unconsrained linearized ("normal imes") model. QE effecs are sronger when accouning for he ZLB consrain as will be discuss in he following secion. 7. QE in he model wih 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. 7.. Implemenaion of he occasionally binding consrain We use he OccBin mehod developed by Guerrieri and Iacoviello (205) o rea he occasionally binding consrain via a piecewise linear soluion. Moreover, we use an algorihm as in Giovannini and Rao (207) o obain smoohed esimaes of laen variables as well as he sequence of regimes along he hisorical sample. We se he lower bound for quarerly shor-erm ineres raes a NC The unconsrained nominal ineres rae i follows he usual Taylor rule wihou moneary shock: NC i = ρ i (i i) + ( ρ i ) (η iπ (0.25 ( π r i 3 r=0 c+g ) π c+g ) + η iy (y )+η ip (cπ c+g )) 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: i = i NC inom + u i = i LB inom + u See Giovannini and Rao (207) for a deailed descripion of he algorihm and he mehodology. 2 Previous sudies on he ZLB use a slighly higher lower bound for he ineres rae (around % annualized). In our conex, his assumpion would imply a consrained regime saring from 203q4 onwards, which would imply a sronger impac of he asse purchase shock on real aciviy paricularly in he years 203 and 204, where variaions in he CB holding of long-erm deb are unrelaed o he 205 QE programme. 6

18 NC The variable i acs as an "shadow" ineres rae under a consrained regime. Under he Occbin algorihm, i allows o be deermined endogenously when he consrain is no longer binding. 3 The algorihm used for esimaing laen variables yields iniial condiions and a sequence of 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 from 203q 206q2. Time Regime sequence Saring period of regime 2 203q 0 203q q q q 0 204q q q q q q q q q2 0 6 Noes: ( column) 0 = unconsrained, = consrained. [ 0] indicaes a consrained regime. [0 0] indicaes a regime ha anicipaes fuure consrains. (2 column) Periods for which he regime sars: [ 6] indicaes a consrained regime for 5 periods. [ 2 4] indicaes a regime ha anicipaes fuure consrains saring in period 2 unil period 4. Based on our definiion of he ZLB as zero shor-erm nominal ineres rae, EA moneary policy is consrained from 204q3 onwards, whereby agens have anicipaed he ZLB since 204q2. Our simulaion also indicaes a relaively long-lasing consrained regime. More precisely, in 206q2 i anicipaes a consrained regime for addiional 5 quarers Dynamic effecs of QE shocks Based on he sequence of regimes, we perform IRFs wih ZLB ha are consisen wih he esimaed iming and duraion of he consrained regime. In paricular, we perform he following exercise: We use as a saring poin he smoohed variables in 205q, 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, i.e. long-erm bond purchases of 8% of 3 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 behavior of he piecewise linear soluion in erms of ransmission mechanisms under he ZLB consrain. 7

19 seady-sae quarerly EA GDP. The difference beween he wo simulaions provides he IRF of he ECB QE shock under he consrained regime. Figure 4 shows he comparison of he IRFs beween he linear (unconsrained) and piecewise linear (consrained) soluion, where he former is represened by red and he laer by blue solid lines. Noe: Red is he linear (unconsrained) model, blue he piecewise linear model (ZLB). The linear soluion is equivalen o he IRFs in Figure. Figure 4: IRF for posiive EA QE shock under unconsrained and consrained moneary policy Since we use 205q as saring poin of our simulaions, moneary policy is consrained for 6 quarers unil he end of our sample in 206q2. I implies ha moneary policy is going back o normal imes from 206q3 onwards, which is refleced by an immediae jump o he unconsrained impulse response. The change back o he "normal regime" is he consequence of sofening of conracionary forces, i.e. abaing of conracionary shocks and of he effeciveness of QE iself, no he resul of an exogenous regime swich. The IRFs sugges ha he impac of he QE shock on real GDP (annualized 0.9 insead of 0.5 pp on impac) and inflaion (annualized 0.4 insead of 0.3 pp on impac for CPI inflaion) becomes significanly larger in a zero-bound environmen Decomposing EA oupu growh and inflaion Finally, we invesigae he shock conribuions o he observed daa ha are consisen wih he piecewise linear soluion, i.e. he exension of he sandard hisorical shock decomposiions o he 8

20 case of occasionally binding regimes. The conribuion of individual smoohed shocks is no he mere addiive superposiion of each shock in his case. Insead, i is a non-linear funcion of he whole se of shocks simulaneously affecing he economy. Hence, he conribuion of one shock i is condiional on he sequence and combinaion of shocks simulaneously hiing he economy. 4 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. 5 Figure 5 compares he conribuion of QE on 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 The average impac of QE on year-on-year real GDP growh in 205q-6q2 more han doubles from 0.3 o 0.7 pp, and he maximum impac increases from 0.4 o.0 pp in 206q2, which suggess ha QE is much more effecive under he consrained moneary policy regime. The impac on year-on-year CPI inflaion rises from 0.3 o 0.4 pp for he 205q-6q2 average, and he maximum impac increases from 0.5 o 0.7 pp in 206q2. The more posiive conribuion under he ZLB owes paricularly o he absence in his conex of he counervailing moneary policy ighening ha would occur in "normal" imes. 4 In general, we can consider wo definiions ha generalize 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 (207) for a deailed descripion of boh mehods. 5 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 realizaion and he occasionally binding consrains. 9

21 Noe: Real GDP growh and CPI inflaion are boh shown as deviaions from seady sae, which is calibraed as he mean over he sample period from 999q-206q2. In boh sub-plos 0.0 on he y-axis corresponds o pp. Figure 5: QE conribuion o year-on-year EA real GDP growh and CPI inflaion in linear and piecewise linear soluion The effecs of QE on EA GDP and inflaion in our esimaed model are comparable o exising lieraure for EA QE and comparable in order of magniude o resuls from similar exercises for he US QE: Sahuc (206) find effecs of ECB QE (9% of EA GDP) on EA real GDP growh (inflaion) of 0.2 (0. pp) in for shor-erm raes consan in 205, whereas keeping he policy rae unchanged for anoher year raises he average growh (inflaion) effec in o 0.6 pp (0.6 pp). For he US, Chen e al. (206) repor GDP growh (inflaion) effecs of 0. pp (0.3 pp) of US QE measures of a volume of 4 pp of GDP. De Graeve and Theodoridis (206) repor GDP growh (inflaion) effecs of 0.6 pp (0.3 pp) of he Federal Reserve's "Operaion Twis" (2%-of- GDP). Boh sudies work wih scenarios in which shor-erm policy raes do no respond (immediaely) o higher growh and inflaion. Gerler and Karadi (203) quanify he impac of US LSAP wih a volume of 2.5% of GDP on oupu growh (inflaion) o pp (.5 pp) if policy raes remain unchanged, and 0.2 pp (0.2 pp) if he sandard moneary policy rule is acive and parly offses expansionary QE effecs. 20

22 8. Conclusion We have inroduced imperfec subsiuabiliy beween bonds of differen mauriies and cenral bank balance shee operaions in a New Keynesian open-economy DSGE model. We have esimaed a wo-region (EA and res of he world) version of he model o assess he impac of he ECB s large-scale asse purchase programme (QE) on economic aciviy and inflaion in he EA. The deailed modelling of QE and porfolio adjusmen enables us o capure a large number of he ransmission channels pu forward in he lieraure, including he saving, financing cos, exchange rae, inflaion, and fiscal channels. We use daa on governmen deb socks and yields across mauriies o idenify he parameer ha governs porfolio adjusmen in he privae secor and yield, exchange rae and savings effecs of cenral bank asse purchases. The shock decomposiions for year-on-year real GDP growh and CPI inflaion in he EA sugges a posiive average conribuion of ECB QE o EA oupu growh and inflaion of 0.3 and 0.3 pp during 205q-6q2 in he sandard unconsrained ("normal imes") model and 0.7 and 0.4 pp respecively in he model ha accouns for he emporarily binding zero-bound consrain. References Adjemian, S., H. Basani, M. Juillard, F. Karamé, F. Mihoubi, G. Perendia, J. Pfeifer, M. Rao, S. Villemo (20): "Dynare: Reference Manual - Version 4," Dynare Working Papers, CEPREMAP. Alavilla, C., G. Carboni, R. Moo (205): "Asse purchase programmes and financial markes: lessons from he euro area," ECB Working Paper 864. Andrade, Ph., J. Breckenfelder, F. De Fiore, P. Karadi, O. Trisani (206): "The ECB's asse purchase programme: an early assessmen," ECB Working Paper 956. Andrés, J., D. López-Salido, E. Nelson (2004): "Tobin's imperfec asse subsiuion in opimizing general equilibrium," Journal of Money, Credi and Banking 36, Bluwsein, K., F. Canova (206): "Beggar-hy-neighbor? The Inernaional Effecs of ECB's Unconvenional Moneary Policies," Inernaional Journal of Cenral Banking, 2(3), Carlsrom, Ch., T. Fuers, M. Pausian (207): "Targeing Long Raes in a Model wih Segmened Markes," American Economic Journal: Macroeconomics, 9(), Chen, H., V. Cúrdia, A. Ferrero (202): "The Macroeconomic Effecs of Large scale Asse Purchase Programmes," Economic Journal 22(564), F289-F35. Claeys, G., A. Leandro (206): "The European Cenral Bank's Quaniaive Easing programme: Limis and risks," Bruegel Policy Conribuion, Issue 206/04, February

23 De Graeve, F., K. Theodoridis (206): "Forward guidance, quaniaive easing, or boh?" Naional Bank of Belgium Working Paper 305. De Sanis, R. (206): "Impac of he asse purchase programme on euro area governmen bond yields using marke news," ECB Working Paper 939. Falagiarda, M. (203): "Evaluaing Quaniaive Easing: a DSGE approach," MPRA Paper 49457, Universiy Library of Munich. Gerler, M, P. Karadi (203): "QE vs. 2 vs. 3.: A Framework for Analyzing Large-Scale Asse Purchases as a Moneary Policy Tool," Inernaional Journal of Cenral Banking 9(), Giovannini, M, M. Rao (207): "Laen variables and real-ime forecasing in DSGE models wih occasionally binding consrains: Can non-lineariy improve our undersanding of he Grea Recession?" mimeo. Guerrieri, L., M. Iacoviello (205): "OccBin: A oolki for solving dynamic models wih occasionally binding consrains easily," Journal of Moneary Economics 70, Harrison, R. (202): "Asse purchase policy a he effecive lower bound for ineres raes," Bank of England Working Paper 444. Kollmann, R., B. Paaracchia, R. Raciborski, M. Rao, W. Roeger, L. Vogel (206): "The poscrisis slump in he Euro Area and he US: Evidence from an esimaed hree-region DSGE model," European Economic Review 88(C), 2-4. Krishnamurhy, A., A. Vissing-Jorgensen (20): "The Effecs of Quaniaive Easing on Ineres Raes: Channels and Implicaions for Policy," Brookings Papers on Economic Aciviy 43, Liu, P., H. Mumaz, K. Theodoridis, F. Zanei (205): "Changing macroeconomic dynamics a he zero lower bound," mimeo. Neal, R. (2003): "Slice sampling," The Annals of Saisics 3, Planas, Ch., M. Rao, A. Rossi (205): "Slice sampling in Bayesian esimaion of DSGE models," European Commission Join Research Cenre, available online: hp:// Prifis, R., L. Vogel (206): "The Porfolio Balance Mechanism and QE in he Euro Area," Mancheser School 84(S), Rao, M., W. Roeger, J. in ' Veld (2009): QUEST III: An esimaed open-economy DSGE model of he euro area wih fiscal and moneary policy, Economic Modelling 26, Sahuc, J.-G. (206): "The ECB s asse purchase programme: A model-based evaluaion," Economics Leers 45(C),

24 Tillman, P., J. Luedering (206) "Moneary Policy on Twier and is Effec on Asse Prices: Evidence from Compuaional Tex Analysis," mimeo. Woodford, M. (200): "Fiscal requiremens for price sabiliy," Journal of Money, Credi and Banking 33, APPENDIX: MODEL DESCRIPTION We inroduce elemens of quaniaive easing ino a wo-region world consising of he Euro Area (EA) and he res of he world (RoW). The EA region is raher deailed, while he RoW block, which also includes US, is more sylized. 6 The EA region assumes wo (represenaive) households, a number of layers of firms and a governmen. EA households provide labor services o firms. One of he wo households (savers, or 'Ricardians') in each counry has access o financial markes, and she owns her counry s firms. The oher (liquidiy-consrained, or 'non-ricardian') household has no access o financial markes, does no own financial or physical capial, and in each period only consumes he disposable wage and ransfer income. The preferences of boh ypes of household exhibi habi formaion in boh consumpion and leisure, a feaure which allows for beer capuring persisence of he daa. There is a monopolisically-compeiive secor producing differeniaed goods, using domesic labor and capial. The firms in he secor maximize he presen value of dividends a a discoun facor ha is sricly larger han he risk-free rae and varies over ime. This is a shor-cu for capuring financial fricions facing firms; i can, e.g., be inerpreed as a principal agen fricion beween he owner and he managemen of he firm. Opimizaion is subjec o invesmen and labor adjusmen coss and a varying capaciy uilizaion rae, which les he model beer capure he dynamics of he curren accoun and oher macro variables. Toal oupu is produced by combining he domesic differeniaed goods bundle wih energy inpu. EA wages are se by monopolisic rade unions. Nominal differeniaed goods prices are sicky as are he wages paid o he workers. Fiscal auhoriies in he EA impose disorive axes and issue deb. The RoW block is simplified compared o he EA block. Specifically, he RoW consiss of a budge consrain for he represenaive household, demand funcions for domesic and impored goods (derived from CES consumpion good aggregaors), a producion echnology ha uses la- 6 The EA block builds on, bu is considerably differen han he QUEST model of he EU economy (Rao e al., 2009). 23