The Portfolio Rebalancing Channel of Quantitative Easing I

Transcription

1 The Porfolio Rebalancing Channel of Quaniaive Easing I Valenin Jouvanceau 1 Absrac This paper analyzes he porfolio rebalancing channel of Quaniaive Easing (QE hereafer) inervenions. Firs, we idenify he effecs of a QE shock using abayesianvaronusdaausingasignandzeroresricionsidenificaion scheme. We find ha QE shocks have subsanial effecs on corporae spreads wih differen raings, supporive of a porfolio rebalancing channel. Second, we build a DSGE model wih a securiizaion mechanism. We confron he resuling impulse response funcions o hose uncovered by our VAR analysis, and find a fairly good mach. Finally, we show ha he porfolio rebalancing channel crucially affecs he ransmission of QE shocks o real economy. Keywords: Quaniaive easing, securiizaion, financial inermediaion, porfolio rebalancing channel. JEL Classificaion.: E44, E52, G2. I All errors and omissions are my own. 1 Univ Lyon, Universié Lumière Lyon 2, GATE L-SE UMR 5824, F-6913, Ecully, France; jouvanceau@gae.cnrs.fr Preprin submied o Annals of Economics and Saisics Sepember 29, 217

2 1. Inroducion QE consiss in an increase in he asse side of he balance shee of a cenral bank aimed a lowering ineres raes (sovereign or corporae) a longer mauriies han achieved wih convenional policy raes (Federal funds raes). The ransmission channels of such inervenions are usually he signaling channel, he liquidiy premium channel, he credi channel, he fiscal channel and he porfolio rebalancing channel. More precisely, QE inervenions aim a reducing risk premia and reurns on long erm securiies and bonds. The porfolio rebalancing channel is hen hough o boos economic aciviy by spreading over yields on oher asses. Indeed, changes in relaive yields of purchased asses cause invesors o shif heir holdings owards close subsiues searching for higher perspecive of reurns. This ends o spread he shock along he yield curve hrough an increase in he price of long-erm asses and bonds held by financial inermediaries, which also generaes a wealh effec. In addiion, purchases of long-erm securiies or bonds affec financial condiions by reducing borrowing coss. Boh effecs are muually reinforced o provide furher simulus o he economy. This paper analyzes boh empirically and heoreically he porfolio rebalancing channel of QE inervenions. We build a Bayesian VAR model using US daa based on an exension of he algorihm of Rubio-Ramírez e al. [25] developed by Binning [1]. Idenificaion is achieved wih sign and zero resricions and our resuls suppor he presence of a porfolio rebalancing channel or a he very leas, behavioral assumpions made abou financial inermediaries on which he porfolio rebalancing channel is based. We hen design a DSGE model àla Gerler and Karadi [14] (GKb) augmened wih Special Purpose Eniies in he spiri of Meeks e al. [22]. In addiion, we consider an addiional housing marke àlaiacoviello and Neri [19], in which Governmen-Sponsored Enerprises issue Morgage Backed Securiies (MBS). Doing so provides an addiional ransmission mechanism of he QE policies. Wha is crucial in our approach is ha 1

3 we inroduce a variey of asses and bonds ha are close subsiues bu whose prices may be alered differenly by QE shocks, hereby making room for poenial porfolio reallocaions. Firs, we proceed o he empirical analysis of an idenified QE shock on US daa and find sizable effecs o he real economy. Moreover, our analysis uncovers saisically significan negaive responses of corporae spreads afer a QE shock. In paricular, he response of a spread beween privae asses ha are close subsiues (BAA and AAA raed bonds) is significan and negaive, suggesing ha invesors should rebalance heir porfolios in he wake of a QE shock. Our resuls hus poin o he presence of a porfolio rebalancing channel in he daa. Second, we build a heoreical model and calibrae i o he US pre-crisis period in line wih GKb. We hen successfully compare he impulse response funcions (IRFs) of boh models o comfor he qualiaive and quaniaive srenghs of our DSGE model. We hus consider our heoreical model as a suiable framework o idenify he key mechanisms of QE ransmission. Along he way, we compue yields o mauriy of differen asses and bonds o observe he effecs of QE policies on he erm srucure of ineres raes. Our analysis of IRFs afer a QE shock in an environmen of financial fricions allows us o dissociae he sandard credi channel from he rebalancing channel. This is done by reporing and comparing he IRFs of GKb o our dynamic. The work of GKb has only a credi channel, which means ha any difference beween our model and heirs will be relaed o he porfolio rebalancing channel. Our resuls show ha he presence of securiizaion mechanisms coupled wih a srong marke segmenaion significanly amplify he impacs of a QE shock o he economy via rebalancing effecs. The laer also parially inver he yields curve. The paper is organized as follows. Secion 2 presens a lieraure review. Secion 3describesourempiricalmehodandresuls. Secion4describeshebaseline DSGE model and discusses is calibraion. Simulaions are proposed in Secion 5. Secion 6 offers some concluding remarks. 2

4 2. Lieraure review There are few papers using empirical models o quanify he porfolio rebalancing channel of QE ransmission. A noable excepion is Joyce e al. [2], who examine porfolio reallocaions induced by he Bank of England s QE policy. They provide evidence of porfolio rebalancing bu limied o corporae bonds. D Amico e al. [7] esimae boh duraion and scarciy effecs of QE programs in he US. Their resuls sugges sizable effecs of QE1 and QE2 programs on long-erm Treasury yields. Gagnon e al. [12] esimae he overall size of he reducion in he 1-year erm premium due o QE policies. They argue ha heir effecs exend o he markes for reasuries, corporae bonds and swaps. Engen e al. [9] use survey daa o esimae changes in privae expecaions abou he policy rule and he effecs of QE programs on erm premiums. They show ha Large-Scale Asse Purchases (LSAPs) helped o sabilize he economy bu failed o provide furher moneary simulaion in he wo years following he 28 crisis in he US. They esimae ha he full effecs of QE occurred early 215. They also argue ha he Federal Open Marke Commiee is now more likely o ackle fuure crises using unconvenional moneary policies. Peersman [24] finds ha an unconvenional moneary policy in he Euro area has differen ransmission channels compared o convenional policies. He idenifies a QE shock wih he moneary base, hen wih an increase in he size of he cenral bank balance shee, and finds ha he effecs of QE shocks on oupu and inflaion are more persisen han in he US. Mos of he debae on he effecs of QE policies is concenraed on heoreical papers. Cúrdia and Woodford [5] build a New Keynesian model wih a role for he cenral bank in he deerminaion of he equilibrium. In his specific framework, hey show ha QE policies have no role o play. However, hey argue ha a cenral bank inervenion wih QE produces benefis when a financial crisis his he economy and he zero lower bound (ZLB) binds. In he same vein, Hilberg and Hollmayr [17] develop a DSGE model in which an inerbank secor 3

5 is cenral. They consider a collaeral policy rule raher han a simple Taylor rule, and consider he poenial benefis from including asse prices dynamics in he policy rule. They show ha a cenral bank should provide liquidiy when he economy experiences a bubble on asse prices. However, hey claim ha such a rule is inflaionary, and herefore should no be implemened. Differen ransmission channels are considered in he lieraure. Cúrdia e al. [4] esimae a DSGE model in which he preferred habia heory emerges. They find ha LSAPs affec he economy due o limis o arbirage and marke segmenaion beween asses/bonds of differen mauriies. In addiion, hey argue ha a commimen o a low nominal ineres rae for a period of ime leads QE programs o be a leas wice as effecive in affecing he economy. In his paper, Falagiarda [1] builds a DSGE model ha capures imperfec asse subsiuabiliy beween governmen bonds of differen mauriies. His framework exhibis a porfolio rebalancing channel of QE policies. He also finds ha he efficacy of QE policies crucially depends on he degree of subsiuabiliy among asses and exi delays. Harrison [16] focuses on opimal policy in a New-Keynesian model ha includes imperfec subsiuabiliy beween shor and long-erm bonds. He finds ha LSAPs paired wih convenional moneary policy help miigae oucomes arising from adverse shocks, especially when he ZLB is binding. Few conribuions explore he impac of a securiizaion mechanism on he ransmission of crises and QE policies. Verona e al. [26] propose a DSGE model in which bond financing depends on a shadow banking sysem. They calibrae wo spreads on bonds for normal and opimisic imes, and show ha US boombus cycles are caused by (un)expeced moneary policy shocks. They draw a lesson for moneary policy in which moneary auhoriies should imbed asse spreads in heir policy rules o avoid over-confidence and risk under-esimaion. Meeks e al. [22] develop a DSGE model wih a sylized shadow banking secor. Brokers ransform firm loans ino Asse Backed Securiies (ABS). They find ha he pass-hrough effecs depend on financial markes segmenaion and are 4

6 crucial for he dynamic of credi. The role of he housing marke is invesigaed by Iacoviello and Neri [19] among ohers, sudying he sources and dynamics of flucuaions on his specific marke. They esimae a DSGE model and show ha, over he business cycle, half of he volailiy in he housing marke is explained by housing demand and echnology shocks. In addiion, hey demonsrae ha he conribuion of moneary shocks o his volailiy has been increasing over ime and now represens around weny per cen of he oal volailiy. Finally, hey conclude ha housing marke spillovers have been growing over ime and ha hey are raher concenraed on consumpion. Dai e al. [6] provide a DSGE model wih a segmened financial inermediaion and a housing marke in he spiri of Iacoviello [18]. They consider an explici morgage marke and a corporae loan marke. They push heir economy ino financial disrupion and simulae he effecs of LSAPs of MBS and corporae bonds separaely. They emphasize ha he size of effecs are crucially dependen on wheher or no a porfolio rebalancing channel emerges. Moreover, when credi markes are fully segmened, hey show ha LSAPs have raher local effecs and fail o suppor a global recovery. Gerler and Karadi [13] (GKa) design a DSGE model wih financial inermediaries ha face endogenous consrains o heir balance shees. They simulae aypicalfinancialcrisisandevaluaeheeffecsofacenralbankcrediinermediaion. They also find ha QE policies have larger effecs when he ZLB is binding. In addiion, GKb exend heir baseline model o inroduce limis o arbirage beween long-erm governmen bonds and privae securiies, making LSAPs even more effecive. They argue ha LSAPs on bonds marke are more qualiaive han quaniaive easing, and conclude ha he main ransmission channel of QE policies goes hrough reduced credi coss, i.e. he credi channel. Despie he vas lieraure, none was found o clearly disenangle he credi and he porfolio rebalancing channels of QE ransmission. The following sec- 5

7 ions address his issue and provide empirical and heoreical evidence of he rebalancing porfolio channel of QE. 3. A Bayesian VAR model 3.1. Specificaion of he model We run a BVAR analysis on US daa wih sign and zero resricions for m = 1,...,M variables. equaions ino marices and vecors as: We allow for a resriced form of he VAR and sack all y = X + (1) where is a k 1 vecor of regression coefficiens. X is a M k marix wih k = P M j=1 k j ha includes on is diagonal x m,hek m -vecor of he h observaion of he vecor of explanaory variables, y. We allow for flexible prior disribuions of paramaers. Accordingly, we work wih priors ha ensure independance beween he VAR coefficiens and he variance-covariance marix, i.e. he independen Normal-Wishar prior. We denoe parameer priors wih underbars. Our priors have he following form: N(,V ) (2) 1 W(S 1, ) (3) On he one hand, we apply he following prior hyperparameers V = 1I KM, = M +1 and S 1 = I M.Onheoherhand,aferderending,ourseriesshow subsanial persisence. Consequenly, we se for each variable wih basic flavor of Minnesoa priors (see Doan e al. [8] and Lierman [21]). The prior mean of he regression coefficien on is firs own lag is se o be equal o is firs value of is sample parial auocorrelaion funcion, i.e..89 for he real GDP per capia,.53 for he CPI growh rae,.8 and.78 respecively for each of he corporae spreads and.82 for he governmen spread. 6

8 3.2. Daa and Idenificaion of a QE shock Our daase is aken from he Federal Reserve Economic Daa (FRED) websie 2. I feaures five US variables wih quarerly observaions saring from he firs quarer of 1962 and ending he las quarer of 27. Noice ha pos-crisis daa is excluded from our analysis o be consisen wih he mean calibraion of our heoreical model presened in he nex secion. Our BVAR analysis includes daa for real aciviy via he log of he real gross domesic produc per capia (RGDP) and he log-difference of he consumer price index (CPI). We consider wo corporae spreads: he spread beween BAA and AAA Moody s seasoned corporae bond yields (BAA-AAA) and he spread beween Moody s Seasoned BAA corporae bond yield and he 1-year Treasury consan mauriy rae (BAA-1Y). We complee he daase wih a governmen spread beween he 1-year Treasury consan mauriy rae and he effecive Federal Funds rae (1Y-FFR). All ime series are derended using a one-sided HP filer wih a smoohing parameer = Our choice of variables has been made o be consisen wih our heoreical model, which will allow for a sraighforward comparison of our empirical and heoreical IRFs. Deails abou he idenificaion of he QE shock will be given in he nex paragraph bu we argue ha anegaiveresponseofhebaa-aaaspreadosuchashockwouldbeconsidered a clear empirical evidence of he porfolio rebalancing channel of QE. Conversely, a mued or saisically non-significan response would indicae ha his channel is absen. Idenificaion is achieved using an exension of he algorihm developed by Rubio-Ramírez e al. [25] ha solves for shor and long-run resricions. However, as menioned in Canova [3], DSGE models do no offer consisen shor-run zero resricions as in a Cholesky decomposiion idenificaion scheme in which srong assumpions on he locaion and he number of zero resricions are im- 2 hps://fred.slouisfed.org/ 3 The Malab code was implemened by Meyer-Gohde [23]. 7

9 posed. To overcome hese problems, we use a mehod suggesed by Binning [1], ha allows for shor and long-run resricions along wih sign-resricions. 4 This racable mehod allows o idenify he single shock we are ineresed in, while preserving compuaional racabiliy. Table 1 summarizes he sign and zero resricions imposed in he benchmark model. The sign resricions are inspired by he heoreical model deailed in he nex secion. Table 1: Idenificaion scheme, Zero and Sign Resricions QE shock Variables Zero Sign Horizons LR Real Gross Domesic Produc per capia > 4 Consumer Index Producion BAA - AAA - < 4 BAA - 1Y spread - < 4 1Y Treasury - Federal Funds rae AsrucuralQEshockisassumedoproduceanegaiveonesandarddeviaion fall in he spread beween he 1-year Treasury rae and he Federal Funds rae. In addiion, he shock should raise real GDP for a leas 4 quarers while is longrun effecs mus be null on his laer. Furher, we wish for he shock o lower boh corporae spreads for a leas 4 quarers. The sign of he response of he inflaion rae is lef unresriced. Our esimaion uses a wo-lags specificaion of he BVAR process, and includes a consan erm. We compue 5 draws of he poserior disribuion of he BVAR coefficiens and IRFs and drop he firs 4 Compuer codes of he condiional poserior disribuion of he coefficiens and he Gibbs sampling algorihm are available upon reques. See Binning [1] for a complee and deailed descripion of he algorihm. 8

10 1 as burn-in. Our resuls are deailed in he nex paragraph Resuls and commens Figure 1 presens he dynamics of he simulaions. We repor 16%-84% confidence inervals and median IRFs. On impac, he rise in real GDP is humpshaped and slighly persisen following he imposed resricions. Is magniude reaches around wo imes he deviaion in he governmen spread, showing he sizable effecs of QE shocks on he real economy. The inflaion rae co-moves wih GDP for some periods. Hence, an accommodaing QE shock generaes lile inflaion. Our key variables of ineres, i.e. corporae spreads, show saisically significan responses ha are consisen wih our se of resricions. The BAA-1Y index of performance of corporae bonds in marke can be viewed as a proxy of credi coss o firms or he exernal finance premium. Given his assumpion, is drop confirms ha he economy is impaced via he credi channel of QE ransmission. Moreover, he fall in he BAA-AAA spread suggess ha anoher ransmission mechanism is a work. Inuiively, if we consider only he credi channel of QE policies, all else being equal, a QE shock would ulimaely pu a similar pressure on yields, shifing he yield curve bu preserving is shape. In his scenario, he BAA-AAA spread would show a non-significan or zero response o he shock which is acually no he case. We hen claim ha he decrease in BAA-AAA spread provides empirical evidence of he porfolio rebalancing channel of QE ransmission. Thus, a purchase of long-erm governmen bonds no only affecs is yields bu also hose of asses ha are close subsiues wih differen inensiies. In oher words, his suggess ha invesors lower he share of governmen bonds in heir porfolios and raise he share of high-qualiy and relaively safe corporae bonds. 9

11 Figure 1: BVAR impulse response funcions (a) Oupu (b) Inflaion Rae (c) BAA-AAA Quarers Quarers Quarers (d) BAA-1Y (e) 1Y-FFR Quarers Quarers Blue doed line: median of he impulse response funcions. 4. Model We now wan o confron he empirical IRFs uncovered in he previous secion o he predicions of a calibraed DSGE model wih financial friciions. The model is based on GKb, who propose a clear, simple, ye relaively general macroeconomic model ha capures muliple feaures of he recen financial crisis and show how LSAPs channel o he real economy. Our main objecive is o dissociae he credi channel and he porfolio rebalancing channel of QE ransmission. To do so, we inroduce securiizaion mechanisms. Firs, we model Special Purpose Eniies (SPE), ha ransform a pool of loans ino ABS along he lines of Meeks e al. [22]. In addiion, we inroduce Governmen-Sponsored Enerprises (GSE) ha ransform housing morgages ino MBS. The housing secor is modelled afer Iacoviello and Neri [19]. These differen asses and fric- 1

12 ions will allow us o differeniae he effecs of QE policies on differen spreads, and help disinguish he porfolio rebalancing channel from he sandard credi channel Commercial banks Commercial banks (c) collec households deposis and gran loans o firms and morgages o households. In addiion o hese lending aciviies, commercial banks hold a sock of long-erm governmen bonds. We consider a coninuum of idenical commercial banks and define he ypical balance shee of a commercial bank as: Q s c + q h h c + q mbs m mbs,c + q abs a abs,c + q b b c = d + n c (4) The asse side feaures corporae securiies s c,housingmorgagesh c,quaniies of MBS m mbs,c and ABS a abs,c and long-erm governmen bonds b c. The marke prices of hese asses are Q, q h, q mbs, q abs and q b respecively. The liabiliy side is made of households shor-erm deposis d and of commercial banks ne worh n c. Is evoluion is given by: n c = R s Q 1 s c 1 + R h q h 1h c 1 + R m q mbs 1 m mbs,c 1 + R a q abs + R b q b 1b c 1 R d 1 1a abs,c 1 = (R s R )Q 1 s c 1 +(R h R )q h 1h c 1 +(R m R )q mbs 1 m mbs,c 1 + (R a R )q abs 1a abs,c 1 +(R b R )q b 1b c 1 + R n c 1 (5) where R s is he sochasic reurn on corporae securiies, R h on housing morgages, R m on MBS, R a on ABS and R b on long-erm bonds. Long-erm bonds are perpeuiies ha yield a one-dollar coupon paymen per period, such ha: R b+1 = 1 P + q b +1 q b Bankers maximize he discouned sream of dividends paid o households a (6) he sochasic discoun facor,+i subjec o a survival probabiliy. The 11

13 problem is denoed as: V c = max E 1X (1 ) i 1,+i (n c +i) (7) i=1 Equaion (5) shows ha bankers can make infinie profis due o arbirage opporuniies. As in GKb, we limi his possibiliy by inroducing a moral hazard problem by which a banker can diver a fracion c of is oal asses. As in Meeks e al. [22], we inroduce a weigh < 1 according o which a commercial banker is more likely o diver corporae securiies han ABS. Parameer < 1 is also inroduced so ha a commercial banker can diver a lower fracion of governmen bonds. On he conrary, we assume ha a commercial banker has he opporuniy o diver a greaer porion of MBS and housing morgages hrough he inroducion of he weighs > 1 and verify ha V c > 1. Following GKb, we claim and is linear in he marginal values of asses (µ c s,µ c h,µc m,µ c a,µ c b )and in equiy capial, c. Overall, households are willing o deposi if he following consrain holds: V c m mbs,c = µ c sq s c + µ c hq h h c + µ c mq mbs c Q s c + q h h c + q mbs m mbs,c + µ c aq abs a abs,c + q abs a abs,c + q b c The incenive consrain always binds in equilibrium. + µ c bq b b c + c n c (8) Accordingly, he opimizaion problem yields he following firs order condiions respecively for s c,h c,m c,a c,b c, c : µ c s = µ c h = µ c m = µ c a = µ c b = c 1+ c c 1+ c c 1+ c c 1+ c c 1+ c c (9) c (1) c (11) c (12) c (13) (µ c s c )Q s c +(µ c h c )q h h c +(µ c m c )q mbs m mbs,c +(µ c a c )q abs a abs,c +(µ c b c )q b b c + c n c = (14) 12

14 Rearranging Equaion (14) gives: Q s c + q h h c + q mbs m mbs,c + q abs a abs,c + q b b c = c n c (15) where, as well as, in which c = c = c c µ c s E,+1 c +1R +1 c E,+1 c +1 (R s+1 R +1 ) (16) (17) c is he leverage raio of corporae securiies over ne worh. Afer few rearrangemens, he Bellman Equaion (7) gives he opimal condiions for each marginal value: where, µ c s = E,+1 c +1 (R s+1 R +1 ) (18) µ c h = E,+1 c +1 (R h+1 R +1 ) (19) µ c m = E,+1 c +1 (R m+1 R +1 ) (2) µ c a = E,+1 c +1 (R a+1 R +1 ) (21) µ c b = E,+1 c +1 (R b+1 R +1 ) (22) c = E,+1 c +1R +1 (23) c =(1 c (24) c = µ c c s + c (25) The problem is isomorphic o all commercial banks. Hence, summing across porfolio resricions and individual demands on each commercial bank, we obain: Q S c + q h H c + q mbs M mbs,c + q abs A abs,c + q b B c = c N c (26) Afer few rearrangemens, we find he demand for MBS: q mbs M mbs,c = (1 )qh H c +(1 )q abs A abs,c +(1 )q b B c +( c 1)N c D 1 (27) 13

15 Similarly, he demand for ABS wries: q abs A abs,c = (1 )qh H c +(1 )q mbs M mbs,c +(1 )q b B c +( c 1)N c D 1 (28) In his framework, when he consrain is binding, a cenral bank asse purchase is efficien by reducing excessive financial spreads. Given he consrained amoun of banks equiy capial, QE shocks direcly disor he relaive prices of asses. I is hen inuiive ha he efficacy of QE policies emerges from he presence of fricions o arbirage among asses. On he conrary, in a fricionless environmen, demands for asses would increase one by one wih he asses holdings of he cenral bank. In addiion, we obain he following arbirage ideniies wih equaions from (18) o (23) which underlines he role of fricions in he overall dynamic of financial markes: E,+1 c +1 (R h+1 R +1 ) = E,+1 c +1 (R s+1 R +1 ) (29) E,+1 c +1 (R m+1 R +1 ) = E,+1 c +1 (R s+1 R +1 ) (3) E,+1 c +1 (R a+1 R +1 ) = E,+1 c +1 (R s+1 R +1 ) (31) E,+1 c +1 (R b+1 R +1 ) = E,+1 c +1 (R s+1 R +1 ) (32) Given ha, he exen of financial fricions maers for he efficacy of he cenral bank unconvenional programs. Assuming his framework, he financial spreads on governmen bonds and ABS are fracions, < 1 of he spread on corporae securiies. Moreover, he financial spreads on morgage loans and MBS are weighed by, > 1. Accordingly, everyhing else being equal, governmen bonds and ABS yields will decrease less han he yield on coporae securiies following a QE argeed on his laer. On he conrary, he yields on morgage loans and MBS will be highly impaired on impac. Overall, he emergence of differences among relaive prices of asses is he linchpin of he porfolio rebalancing channel of QE policies. 14

16 4.2. Special Purpose Eniies A Special Purpose Eniy (SPE) is in charge of he securiizaion of ABS. Idenical loan brokers populae he SPE. We define a single balance shee as: Q s a = n a + q abs a abs,a (33) The asse side feaures a pool of loans s a. The liabiliy side is composed of ABS a abs,a and ne worh n a,evolvingaccordingo: n a = R s Q 1 s a 1 R a q abs 1a abs,a 1 = (R s R a )Q 1 s a 1 + R a n a 1 (34) As in he case of commercial bankers, loan brokers face he same survival probabiliy,andmaximizehediscounedsreamofdividendsheypayohouseholds a he sochasic discoun facor,+i. The problem is wrien as: V a = max E 1X (1 ) i 1,+i (n a +i) (35) i=1 Again, Equaion (34) shows ha morgage brokers can make infinie profis from he securiizaion of corporae securiies. We limi his opporuniy by allowing loan brokers o diver a fracion a of heir asses. We claim and verify ha he value funcion is linear in he marginal values of is argumens (µ a s, a a) in which µ a s = a s/q a a/q abs is he excess value of pool of loans over ABS. Overall, he securiizaion mechanism is effecive if he following consrain holds: V a = µ a sq s a + a a n a a Q s a (36) q abs The incenive consrain always binds in equilibrium. The opimizaion problem produces he following firs order condiions for s a and a : µ a s = a 1+ a a (37) (µ a s a )Q s a + a a n a = (38) q abs We rearrange Equaion (38) o find he demand for pool of loans: Q s a = a n a (39) 15

17 where, as well as, a = a = a a/q abs a µ a s E,+1 a +1R a+1 a E,+1 a +1 (R s+1 R a+1 ) (4) (41) in which a is he endogenous leverage raio of pool of loans over ne worh. Afer rearrangemens, he Bellman Equaion (35) yields he following opimal condiions for each marginal value: µ a s = E,+1 a +1 (R s+1 R a+1 ) (42) a a q abs = E,+1 a +1R a+1 (43) where, and, a =(1 a = µ a s a + a a q abs (44) (45) The problem is isomorphic o all SPEs. Hence, summing across porfolio resricions and individual demands on each SPE o obain: Q S a = a N a (46) Afer few rearrangemens we find he issuance ideniy of ABS: a q abs A abs,a 1 = a Q S a (47) 4.3. Governmen-Sponsored Enerprises AGovernmen-SponsoredEnerprise(GSE)isinchargeofhesecuriizaionof MBS. There is a coninuum of idenical GSE and morgage brokers populae GSEs. We define a single balance shee as: q h h h = n h + q mbs m mbs,h (48) 16

18 The asse side feaures a pool of morgage loans h h. The liabiliy side is composed of MBS m mbs,h and ne worh n h,haevolvesaccordingo: n h = R h q h 1h h 1 R m q mbs 1 m mbs,h 1 = (R h R m )q h 1h h 1 + R m n h 1 (49) where he sochasic reurn on MBS is R m. MBS are perpeuiies ha yields a m coupon paymen per period, such as: R m+1 = m + q mbs +1 q mbs Again, morgage brokers face he same survival probabiliy (5) and maximize he discouned sream of dividends paid o households a he sochasic discoun facor,+i. The problem wries: V h = max E 1X (1 ) i 1,+i (n h +i) (51) i=1 Equaion (49), shows ha brokers can make infinie profis from he securiizaion of morgages. We limi his opporuniy by allowing morgage brokers o diver a fracion h of heir asses. We claim and verify ha he value funcion is linear in he marginal values of is argumens (µ h h, h m) in which µ h h = h h /Q h m/q mbs is he excess value of pool of morgages over MBS. Overall, he securiizaion of morgages is effecive if he following consrain holds: V h = µ h hq h h h + h m n h h q h h h (52) q mbs The incenive consrain always binds in equilibrium. The opimizaion problem produces he following firs order condiions for h h and h : µ h h = h 1+ h h (53) (µ h h h )q h h h + h m n h = (54) q mbs We rearrange Equaion (54) and find he demand for he pool of morgages: q h h h = h n h (55) 17

19 where, as well as, in which h = h = h m/q mbs h µ h h E,+1 h +1R m+1 h E,+1 h +1 (R s+1 R m+1 ) (56) (57) h is he endogenous leverage raio of pool of morgages over ne worh. Afer rearrangemens, he Bellman Equaion (51) yields o he following opimal condiions for each marginal value: where, µ h h = E,+1 h +1 (R s+1 R m+1 ) (58) h m q mbs = E,+1 h +1R m+1 (59) h =(1 h (6) h = µ h h h + h m q mbs (61) The problem is isomorphic o all GSEs. Hence, summing across porfolio resricions and individual demands on each GSE gives: q h H h = h N h (62) Afer rearrangemens we find he issuance ideniy of MBS: h q mbs M mbs,h 1 = h q h H h (63) 4.4. Households There is a uni mass of idenical households ha swich occupaions. They are eiher workers, bankers, loan brokers or morgage brokers, and he swiching probabiliy is. A represenaive worker buys consumpion goods, chooses ahousingsockandadjussissupplyofhoursworkedomaximizelifeime welfare: U = max E 1 X i= i " ln(c +i hc +i 1 ) 18 1+' L1+' # +i + j h h1 +i 1 (64)

20 where C is he consumpion of goods, subjec o habi formaion of inensiy h, L is he number of hours worked and h is he housing sock. Le 2 [, 1] be households discoun facor, and, ', > be preference parameers. Welfare maximizaion is achieved subjec o he following ineremporal budge consrain: C + D + q h (h h 1 )+R h H 1 + Q S h apple Sh S h 2 + q b B h apple Bh B h 2 = W L + h + T + R D 1 + R s S h 1 + R b B h 1 + H (65) where W sands for he real wage, T denoes lump-sum axes and h he payous from final goods producers and he financial secor. defines Le D be he amoun of deposis o commercial banks ha pay a riskless real ineres rae R. We allow households o hold primary securiies and long-erm governmen bonds subjec o quadraic adjusmen coss 1 2 apple Sh 1 2 apple Bh S h 2 /S h and B h 2 /B h. Holding hese asses respecively pays R s and R b. In addiion, workers accumulae housing wih morgage loans H graned by commercial banks. Their borrowing capaciy is consrained by he expeced value of heir housing sock adjused by he loan-o-value raio µ. consrain is given by: The borrowing R h +1H apple µ E q h +1h (66) and saes ha he oal value of morgage paymens mus no exceed a fracion µ of he oal value of he housing sock. Le % be he marginal uiliy of consumpion and he sochasic (uiliy-adjused) discoun facor. Overall, household s firs order condiions for L,C,h and D are: L ' = W % (67) % = (C hc 1 ) 1 he (C +1 hc ) 1 (68) q h = jh h + E,+1 q+1 h +(1 E,+1 R h+1 ) H (69) % h E,+1 R +1 =1 (7) 19

21 where, E,+1 = % +1 % (71) Finally, he choices for financial securiies and long-erm governmen bonds S h and B h are: S h = S h + E,+1 (R s+1 R +1 ) apple B h = B h + E,+1 (R b+1 R +1 ) apple (72) (73) 4.5. Inermediae goods producers Inermediae goods producers use labor L and effecive capial K o produce he inermediae good Y. The oupu is sold o monopolisically compeiive reailers a he relaive price P m. The producion funcion is: Y = A K L 1 (74) where A is he oal facor produciviy. The firs-order condiions wih respec o labor and capial wrie: W = (1 ) P m Y L (75) Z = P m Y K (76) A he end of he period, inermediae goods producers carry a capial sock (1 )K. They mus buy I new unis of capial from capial producers. Accordingly, he law moion of capial is: K +1 =(1 )K + I (77) For each new uni of capial, goods producers issue a sae-coningen securiy. The value of a securiiy is he marke price Q. Because of compeiion, inermediae goods producers earn zero profis. The erminal payoff is equal o he sum of gross profis and he marke value of he ex-ane capial sock 2

22 (Z +1 +(1 )Q +1 ). Thus, he real rae of reurn o he commercial bank securiy is: Accordingly, he real reurn on ABS is: R s+1 = Z +1 +(1 )Q +1 Q (78) R a+1 = Z +1 +(1 q abs )q abs +1 (79) 4.6. Capial goods producers Capial goods producers build new capial and sell i o inermediae goods producers a he marke price Q, as saed previously. They acquire he depreciaed capial and final oupu from reailers as inpus. Moreover, hey are subjec o increasing convex adjusmen coss. Capial goods producers choose I and maximize: max E 1 X =, Q i I I apple1+f I 1 I (8) Opimizaion yields o he price of capial goods: 2 I I Q =1+f + f I I+1 E,+1 f I+1 (81) I 1 I 1 I 1 I I 4.7. Reail firms Reailers provide a final oupu o he economy. repackaging of inermediae goods. The process evolves wih: applez " 1 Y = Y " 1 " 1 " f df The laer is given from a (82) where Y f is he final oupu for each reailer f, and where " is he elasiciy of subsiuion beween reail goods. We inroduce nominal rigidiies wih price conracs àlacalvo [2]. Accordingly, a firm can adjus is price wih probabiliy 1 p. Thus, each firm chooses an opimal rese price P subjec o he abovemenioned resricions. The opimal pricing conrac maximizes: 1X apple P p,i,+i µ p P m+i Y f+1 = (83) P +i i= 21

23 The law of large numbers gives he sandard relaion of price level dynamic: P = h (1 p )(P ) 1 " + p (P 1 ) 1 "i 1 1 " (84) 4.8. Governmen policy We assume sandard moneary policy by a cenral bank ha follows a Taylor Rule wih a smoohing parameer : i =(1 )(ī + apple + apple y (logy logy )) + i 1 (85) where Y is he flexible price level of oupu. In addiion, he cenral bank is able o purchase a given amoun of corporae securiies, S g,morgageloans H g,abs,a abs,g,mbs,m mbs,g and long-erm governmen bonds, B g. The governmen finances he purchases via a riskless shor-erm obligaion held by households D g. The cenral bank s balance shee is herefore given by: D g = Q S g + q h H g + q abs A abs,g + q mbs M mbs,g + q b B g (86) The cenral bank is no balance shee consrained and ransfers back earnings o he governmen. In oher words, he cenral bank can elasically obain funds from households hrough shor-erm bond issuance. Le i be he exogenous fracions of he respecive asses he cenral bank can purchase. The amouns of purchases are: S g = s (S c + S h + S a ) (87) H g = h (H c + H h ) (88) A g = a (A abs,c M g = m (M mbs,c + A abs,a ) (89) + M mbs,h ) (9) B g = b (B c + B h ) (91) We fix governmen consumpion as an exogenous process Ḡ and impose lumpsum axes o households T. Le B be he sock of long-erm governmen 22

24 deb fixed exogenously. The consolidaed governmen budge consrain hus wries: Ḡ +(R b 1) B = T + (R s R s )Q 1 S g 1 +(R h R h )q h 1H g 1 + (R a R a )q abs 1A abs,g 1 +(R m R m )q mbs 1 M g 1 + (R b R b )q b 1B g 1 (92) where QE policies are subjec o efficiency coss i =.1 per uni of asse i purchased Marke clearing and resource consrain The aggregae resource consrain is: apple Y = C + 1+f I I 1 I + G + (93) where = s Q S g + h q h H g + a q abs A g + m q mbs M g + b q b B g. Equilibrium condiions on he markes for firm loans, ABS, morgage loans, MBS, and long-erm governmen bonds are: K +1 = S c + S a + S h + S g (94) A abs,a = A abs,c + A g (95) H = H c + H h + H g (96) M mbs,h = M mbs,c + M g (97) B = B c + B h + B g (98) Assuming a fixed and uni housing sock, he equilibrium on he housing marke is: Finally, he equilibrium on he labor marke is given by: h =1 (99) W % = L ' (1) The las marke for shor-erm deb is cleared according o he Walras law. 23

25 4.1. Yields o mauriy The major goal of QE policies is o curb long-erm ineres raes. As in GKb, we build a simple erm-srucure o model yields o mauriy of en-year equivalen securiies and bonds. Accordingly, he behavior of a en-year corporae securiy rae is given by he sequence of nominal dividends ne of depreciaion for he firs fory quarers. A principal paymen equal o he seady sae marke price level of a securiy Q occurs he nex quarer. Idenically, he yield o mauriy of a en-year ABS has an equivalen payoff srucure. Boh nominal yields o mauriy are given by: X4 P Q = E P q abs = E s=1 X4 s=1 (Z +s ) P +s (1 + i s ) s + P +4 Q (1 + i s ) 4 (11) (Z +s ) P +s (1 + i a ) s + P +4q abs (1 + i a ) 4 (12) Furher, we inroduce a en-year MBS rae ha delivers a coupon paymen m for he firs fory quarers. A he dae of mauriy, he principal paymen is he nominal seady-sae price of he MBS yield o mauriy is: P q mbs = E X4 s=1 q mbs,sohaisen-yearnominal m P +s (1 + i m ) s + P +4q mbs (1 + i m ) 4 (13) We also consider a en-year long-erm governmen deb ha pays a dollar for he firs fory quarers. A he dae of mauriy, he bond repays is face value q b. Accordingly, he nominal yield o mauriy of a en-year governmen bond is: X4 P q b 1 q = E (1 + i b ) s + b (1 + i b ) 4 (14) s=1 24

26 5. Experimens 5.1. Model calibraion We calibrae he model o he US economy. Time uni is he quarer. Our calibraion is repored in Table 2 and follows GKb for many parameers. In paricular, as in GKb, he subjecive discoun facor is =.995, he capial depreciaion rae is =.25, hecapialshareinheproducionfuncionis =.33, andheelasiciyofsubsiuionamonggoodsis" = Furher, he inverse of he Frisch labor supply elasiciy is ' =.276, herelaiveuiliy weigh on labor is =3.41 and he inverse elasiciy of invesmen is i = We se he degree of habi in consumpion o h =.815. The price rigidiy parameer is se o p =.779. On he moneary side, he Taylor rule parameers are apple =1.5, and =.8. As in GKb, we use he markup variable as a proxy of he deviaions of he oupu gap, associaed o a coefficien apple X =.125 in he Taylor rule. We also follow GKb o calibrae he parameers relaed o commercial banks. The seady sae spread beween corporae securiies reurn and he riskless rae ( R s R) is fixed a 1 basis poins and he spread beween long-erm governmen bonds reurn and he riskless rae ( R b R) is se a 5 basis poins. Households hold hree-quarers of he quaniy of long-erm governmen deb B h and half of he oal of corporae securiies, Sh.Weadjushevaluesof, c and c o hi he previous arges. The asses o equiy raio in commercial banks is fixed a c =6. We rely on Meeks e al. [22] o calibrae he parameers ha perain o SPEs. 5 5 Meeks e al. [22] design a shadow banking sysem in which shadow banks securiize corporae securiies. Securiizaion vehicles are ofen cied o be principal acors of he shadow banking sysem. Thus, we assume ha heir mean calibraion is consisen wih our he calibraion of our SPE secor. 25

27 Accordingly, he excess reurn on ABS, ( R a o equiy raio is fix he share of securiized loans R) is 25 basis poins. The asses a =7. The relaive diveribiliy of ABS is =.25 and we A abs,c S c o 3% of he oal of corporae securiies held by commercial banks. We hen adjus he values of a and a o hi he previous arges. We use he esimaes of Iacoviello and Neri [19] o calibrae he loan-o-value raio µ and he weigh on he housing sock in he uiliy funcion j h.wesehe curvaure parameer on housing o =3. Based on FRED daa from 1985 o 27, H Ȳ is calibraed o mach he mean raio of home morgages o real GDP. Using series on Agency and GSE backed morgage pools and home morgages, we fix he share of MBS. We find a quarerly mean raio of H h H =.43 over he period. The relaive raio of morgage brokers asses o equiy is rickier o calibrae. We consider a raio h = 16, which represens he mean fracion of deb securiies o equiy in GSEs in he sample. We use he primary morgage marke survey of he average spread beween he 3-year fixed morgage rae and he 1-year reasury rae provided by Freddie Mac o calibrae he excess reurn of morgages (R h R). Thislaerisseo17basispoins.Wihhis survey again, we fix our MBS spread using ime series of 5/1-year adjusable rae morgage and 1-year Treasury rae beween 25 and 27. Thus, he MBS excess reurn (R m R) is fixed o have a mean value of 115 basis poins. The ransfers o new morgage brokers h,hediverabiliyofasses h and he relaive diveribiliy of morgage loans and MBS o he previous arges. Finally, he occupaional survival probabiliy is se o and are adjused according = The raio of he sock of long-erm governmen bonds o oupu is.45 and he share of governmen spendings in GDP is ḠȲ cos is apple =1. =.2. The households porfolios ransacion 26

28 5.2. Empirical versus heoreical IRFs We can now conduc various experimens. Firs, we confron he IRFs generaed by he BVAR o hose generaed by he above DSGE. Second, we analyze he key differences in erms of IRFs beween our model and he benchmark model of GKb. We argue ha he differences characerize he porfolio rebalancing channel of QE policies while he common feaures porray he sandard credi channel. We now analyze he effecs of a QE shock in our heoreical model and compare hose o he empirical IRFs obained in our BVAR analysis. We repor he DSGE-generaed IRFs for he log deviaion of oupu Y,heinflaionrae, he corporae spread (i s1 i i1 ),andheqeshock(i i1 i). In he heoreical model, he QE shock is given by a long-erm governmen bonds purchase program where he fracion of asses purchased is adjused o mach precisely he fall in he governmen spread ha we have idenified in he daa. Accordingly, Figure 2 presens he IRFs of he experimen. Firsly, responses are fairly idenical in erms of shapes and magniude, excep for real GDP, ha does no show anegaivedeviaioninheheoreicalmodel.however,realgdpandinflaion rae display hump-shaped and sizable posiive responses in boh models. This confirms he benefis of QE policies in erms of economic aciviy. We claim ha he securizaion mechanisms inroduced in he DSGE model are he source of he replicaed porfolio rebalancing channel. As presened below, he dynamics of quaniies and relaive prices of differen asses sress he role of imperfec arbirage in he choices of invesors among asses ha are close subsiues. Accordingly, imperfec arbirage explains he observed negaive response of he heoreical and empirical corporae spreads (BAA-1Y, i s1 i i1 ), bu i is also a he hear of he porfolio rebalancing channel, illusraed by he empirical response of he BAA-AAA spread. 27

29 Figure 2: DSGE versus BVAR (a) Oupu, Y (b) Inflaion Rae, (c) BAA-AAA Quarers Quarers Quarers (d) BAA - 1Y, (i s1 i i1 ) (e) 1Y-FFR, (i i1 i) Quarers Quarers Black: DSGE model, Blue: BVAR model Quaniaive Easing policy We now compare he heoreical IRFs afer a QE shock on corporae securiies in our DSGE and in he baseline model of GKb. Boh shocks are calibraed so ha he oal of purchases represen 1% of real oupu. We model a srong marke segmenaion, i.e. he absence of equiy capial ransfers among financial inermediaries o capure he kind of disrupion of he financial inermediaion he US experienced in 28. Figures 3 and 4 presen he simulaions. Panel 1showshaallassespreadsaresignificanly(moslynegaively)reacingo he purchase of firm securiies (given by Equaion (87)). The dynamics of relaive asse prices, shown by he dynamics of spreads, generae large asse rebalancings ha are he major effecs of he program seen in Panel 2. From heses responses, we claim ha we capure boh he credi easing channel and he porfolio rebalancing channel of he purchase. 28

30 The credi easing channel works as in GKb. Firs, he cenral bank inermediaion increases he demand for bonds and asses. Wih limis o arbirage, households asses and bonds demands are quie inelasic in he shor-run. In addiion, he absence of financial fricions inermediaion process of he cenral bank shifs he preferences of households o hold shor-erm governmen debs insead of cosly deposis in commercial banks. In oher words, households arbirage away he deadweigh cos associaed wih he moral hazard problem ha bankers face. Moreover, he presence of his balance shee consrain furher amplifies he effecs of he purchase. Indeed, he issuance of firm loans mus be exacly balanced by he muliple leverage raios of equiy capial socks. All else being equal, he purchase of corporae securiies will be hen greaer han banks holdings capaciies. Given his shor-run relaive inelasiciy of oal supply of bonds and asses, he QE shock direcly pushes downward financial spreads. On one side, profis of commercial banks are parly proeced by a ne worh effec due o rises in asse prices. On he oher side, hey mus offse asse marke imbalances due o heir resricions o mee cerain leverage raios. As a resul, hey pu pressure on financial spreads, which slighly impairs heir balance shees. Thus, hey should engage in a reallocaion of asse holdings. As in GKb, Equaion (32) shows ha fricions on long-erm bonds are weaker han limis o arbirage on corporae securiies held by bankers. Thus, he yield of he former is a posiive proporion of he laer. Tha is why in GKb we observe areallocaionofbankersporfoliosfromcorporaesecuriiesowardslong-erm governmen bonds holdings (which is no he case in our framewok). This sum of effecs capure a financial acceleraor mechanism on which he credi channel of QE ransmission is based. Overall, he join effecs of limied expansion in bankers balance shees and inelasic demand for asses and bonds leads o a disinermediaion process. As a consequence, in erms of he funding of capial accumulaion, firms rely more heavily on public inermediaion and less on privae inermediaion. Up o his poin, we have negleced he housing marke and he securiizaion 29

31 mechanisms, and focused on he core dynamic of GKb. Le us now focus on he porfolio rebalancing channel and highligh he double-dip effecs of QE policies. The laer can be described as follows. From he above analysis we know ha deposis o commercial banks fall in response o a purchase of corporae securiies, which riggers a reallocaion among banks asses and bonds. Wih housing and securiizaion mechanisms, he adjusmen process is more complex. As a maer of fac, we observe a rise in he holdings of morgage loans H c in bankers porfolios. This is due o he presence of fricions in he housing marke: limis o arbirage seen in Equaion (66) sugges ha an increase in he marke value of he morgage asse q h gives he opporuniy o benefi from higher earnings hrough he deenion of furher morgage loans. Accordingly, he ne demand for morgage loans increases wih he fall in he spread (E(R h R s )), wihin he bounds of he fixed housing sock. Ineresingly, equaions (27) and (28) show ha bankers do no rebalance porfolios away from firm loans o morgage loans H c bu raher lower heir holdings of ABS, A abs,c,mbs,m mbs,c,and long-erm governmen bonds, B c. Overall, marke imbalances, he shorage of deposis and consrains on leverage raios, all lead bankers o reduce heir abiliy o pool firm loans S a and morgage loans H h. In addiion, equaions (47) and (63) show ha ABS and MBS are posiively correlaed respecively o he holdings of pool of corporae securiies and pool of morgages. Thus, he binding consrains of SPEs and GSEs rigger a reducion of securiizaion aciviies ha resuls in a fall of he supply of ABS (A abs,a )andofmbs(m mbs,h ). Again, equiy capial socks of hese inermediaries N a and N h are somehow susained by ne worh effecs due o he observed increase in asse prices. Concerning yields o mauriy, Figure 3 (Panel 1) repors he relaionship beween financial spreads and he drop in long-erm yields. As in GKb, we provide aen-year risk-free swapraei i1 based on he rae of a bond ha would pay he nominal ineres rae each quarer for en years. In he credi channel of QE ransmission, i s1 is he key variable of ineres as i drives he dynamics of invesmen expendiures. Equaions (31) and (32) indicae ha R a and R b devi- 3

32 ae in he shor-run by and imes less han R s,respecivelyinresponseoa QE shock. However, we observe ha he magniude of he respecive declines in i s1 and i b1 are differen and greaer han he porion in he long-run (a fac ha can also be seen hrough he dynamics of spreads, i s1 i i1, i b1 i i1 and i s1 i b1. Following a similar paern, he shor-erm proporion bewen i a1 and i s1 (seen in Equaion (31)) slighly increases over ime. This assessmen is also noiceable in he drops of i s1 i i1, i a1 i i1 and i s1 i a1.moreover,he weigh beween R m and R s shown in Equaion (3) is also increasing afer a QE shock on corporae securiies. Acually, i m1 drops by more han wo imes he decrease in i s1, which is also visible in he spreads i m1 i i1, i s1 i i1 and i m1 i s1. In oher words, he level of i s1 is deviaing from he level of i m1, which we ake as evidence of a porfolio rebalancing channel. This laer alers he shape of he respecive yield curves of hese differen asses. This channel complemens he credi channel ha makes all spreads fall similarly, i.e. ha shifs he yield curve downward while preserving is shape. Finally, our QE shock is ransmied o he real aciviy wih sizable differences in erms of deviaions of macroeconomic variables from heir iniial values. In paricular, capial accumulaion and oupu show larger responses. This phenomenon is mosly demand-driven and is amplified by he wo channels analyzed above. Indeed, a big par of he difference beween boh models is due o agreaerdropinhecosofcapialr s, which in urn, leads enrepreneurs o raise invesmen in physical capial. As a resul, invesmen expendiures and households consumpion rise, so ha oupu is furher simulaed wih posiive feedback effecs on aggregae demand. 31

33 Figure 3: DSGE versus GKb, purchase of firm securiies, Panel 1 (a) Q (b) q b (c) q h (d) q abs (e) q mbs (f) R (g) E(R s R) (h) E(R s R b ) (i) E(R s R a) (j) E(R h R s) (k) E(R m R s) (l) i s1 i i1 (m) i b1 i i1 (n) i s1 i b1 (o) i s1 i a (p) i a1 i i1 (q) i m1 i s1 (r) i m1 i i1 (s) i s1 () i b (u) i a1 (v) i m Black: our DSGE, Blue: model of GKb. 32

34 Figure 4: DSGE versus GKb, purchase of firm securiies, Panel 2 (a) Sg Y (b) K (c) Y (d) I (e) C Annual % of GDP Quarers (f) S h (g) B h (h) D (i) D g (j) H (k) S c (l) B c (m) H c (n) A abs,c (o) M mbs,c (p) N c (q) c (r) S a (s) A abs,a () N a (u) a (v) H h (w) M mbs,h (x) N h (y) h Black: our DSGE, Blue: model of GKb. 6. Conclusion This paper provides a dual approch using empirical and heoreical models o capure he porfolio rebalancing channel of QE. The BVAR model is able o 33