Three Essays on Unconventional Monetary Policy at the Zero Lower Bound

Transcription

1 Three Essays on Unconvenional Moneary Policy a he Zero Lower Bound A hesis submied by Yang Zhang o The Faculy of Graduae and Posdocoral Sudies In parial fulfillmen of he requiremens for he degree of Docor of Philosophy in he subjec of Economics Universiy of Oawa November 213 c Yang Zhang, Oawa, Canada, 213

2 i Absrac Chaper 1: Impac of Quaniaive Easing a he Zero Lower Bound (wih J. Dorich, R. Mendes) We inroduce imperfec asse subsiuion and segmened asse markes, along he lines of Andres e al. (24), in an oherwise sandard small open-economy model wih nominal rigidiies. We esimae he model using Canadian daa. We use he model o provide a quaniaive assessmen of he macroeconomic impac of quaniaive easing (QE) when he policy rae is a is effecive lower bound. Our resuls sugges ha a QE inervenion of 4 per cen of GDP for 4 quarers has moderae impac on ineres raes bu small impac on oupu. More specifically, when he nominal shor-erm ineres rae is consrained a he lower bound, following a decline of 1bps in he long-erm bond yield hrough QE, we find a small impac on aggregae demand (real level of GDP increases by.6%, similar o he findings of Baumeiser and Benai 21) and a much larger impac on inflaion (.1%). The iming of he moneary simulus, however, is much faser, wih peak responses on oupu and inflaion occurring afer 4 and 3 quarers, respecively. Chaper 2: Impac of Forward Guidance a he Zero Lower Bound This chaper addresses he use of condiional saemen a he zero lower bound, along wih oher forms of policy guidance. I consider alernaive moneary policy rules under commimen in a calibraed hree-equaion New Keynesian model and examine he exen o which forward guidance helps o miigae he negaive real impac of he zero lower bound (generaed by a negaive demand shock). The simulaion resuls sugges ha he condiional saemen policy prolongs he zero lower bound duraion for an addiional 4 quarers and reverses half of he decline in inflaion associaed wih he lower bound. I even generaes a period of overshooing in inflaion hree quarers afer he iniial negaive demand shock. Alernaively, he effec of price-level argeing as a forward guidance policy a he zero lower bound is slighly differen. I shorens he zero lower bound duraion by one quarer, bu generaes he highes inflaion profile among he alernaive policy rules considered. Chaper 3: Impac of Quaniaive Easing on Household Deleveraging

3 ii I exend he DSGE model in he firs chaper ha feaures imperfec asse subsiuabiliy, segmened asse marke wih some financial fricions o mach he grea raios and dynamics in he Canadian economy. I simulae he model o explore he effecs of quaniaive easing on asse prices, household balance shee. There are wo effecs of QE on aggregae oupu originaed from he model. Firs, QE leads o a decline in erm premium, which increases curren consumpion relaive o fuure consumpion. Second, i creaes a more favorable financing condiions for borrowers hrough an improvemen in he household balance shees arising from higher ne worh. This leads o a lower loan o collaeral value raio and a decline in exernal finance premium. Favorable financing condiion encourages furher accumulaion of household deb a cheaper raes, in urn, leads o an immediae higher household deb o income raio. The effec of QE beyond he iniial impac would depend on he elasiciy of loan demand o he policy. If he increase in loan is greaer han he increase in he overall collaeral value, his would lead o an ulimae deeper leverage and herefore higher defaul rae. In he consideraion of he fuure wihdrawal of any simulus provided from QE, his would pose greaer challenges as i implies much inensive household deleveraging process. I provide some sensiiviy analysis around key parameers of he model.

4 Conens 1 Inroducion Conribuion of he hesis Impac of Quaniaive Easing a he Zero Lower Bound Inroducion Relevan Lieraure on QE a he ZLB The Porfolio-Balance Effec of QE on erm premium The Domesic Effecs of QE The Open-Economy Implicaions of QE Our Approach The Model Households Firms Governmen Moneary Policy Marke Clearing The Transmission Mechanism of QE in The Model Model Esimaion Daa Calibraion and prior choice Assessing he Impac of QE Concluding Remarks Effecs of Forward Guidance a he Zero Lower Bound Inroducion The New Keynesian Model Households Firms iii

5 iv Moneary Policy Marke Clearing Condiions Mechanism of assessing forward guidance a he zero lower bound Simulaion mehodology Parameerizaion Assessing he Impac of Forward Guidance Macroeconomic impac of he zero lower bound Policy simulaions of alernaive guidance Concluding Remarks Impac of Quaniaive Easing on Household Deleveraging Inroducion The Model Households Firms Governmen Moneary Policy Marke Clearing Exogenous Shocks Calibraion Simulaion resuls Sensiiviy analysis QE wih higher housing invesmen risk QE wih higher ineres rae smoohing Concluding remarks Conclusion 99 A Appendix 13 A.1 Linearized Equilibrium Dynamics in Chaper A.2 Households opimaliy condiions in Chaper

6 Lis of Tables 3.1 Model Calibraion Benchmark Calibraion v

7 Lis of Figures 2.1 Impulse Response Funcions Marginal Impac of QE Bank of Canada s Condiional Commimen in April Effec on yield curve expecaions afer he BoC guidance Impac of zero lower bound Forward guidance wih condiional saemen Forward guidance wih price-level argeing Benchmark quaniaive easing Impac of deeper leverage on QE Impac of higher ineres rae smoohing on QE vi

8 Acknowledgemens I am indebed o my advisors Hashma Khan and Yazid Dissou for heir guidance, suggesions and coninous encouragemen. I would like o hank my hesis commiee: Serge Coulombe, Lilia Karnizova, Raul Razo-Garcia, Jean-Francois Tremblay for helpful commens and suggesions a differen sages of he hesis. I have benefied remendously from many discussion wih hem. In addiion, I would like o hank Nurlan Turdaliev for acceping o be he exernal examiner in my commiee and providing many insighful commens and suggesions. Finally, my greaes appreciaion goes o my family, who have given me all he srengh and suppor o pursue his projec. Wihou whom I could no have made i possible.

9 Chaper 1 Inroducion In normal imes, moneary policy seers he level of he key ineres raes o ensure price and oupu sabiliy over he medium erm. This convenional approach has proven o provide suffi cien moneary simulus o he economy during downurns, prevening downward inflaionary pressures and ensuring economic recovery. In he afermah of he financial and economic crisis of 27-29, cenral banks in many advanced economies cu heir policy raes very aggressively o couner rapidly deerioraing economic oulooks. During his process, many of hese cenral banks found hemselves hiing he effecive lower bound on he policy rae. In his conex, numerous unconvenional moneary ools were considered in order o provide addiional moneary simulus. 1 During abnormal imes, unconvenional moneary policy may be warraned under wo possible scenarios (Smaghi 29). Firs, he negaive economic shock is severe enough such ha he nominal ineres rae needs o be lowered down o zero (or some effecive lower bound). Second, unconvenional moneary policy may be used when moneary policy ransmission mechanism is significanly impaired, especially in an already "lowfor-long" ineres rae environmen. Since i is impossible or ineffecive o furher reduce he policy rae a he lower bound, addiional moneary simulus can be provided in hree ways: i) by guiding he long-erm ineres rae expecaions; ii) by changing he composiion of he cenral bank s balance shee, and iii) by expanding he size of he cenral bank s balance shee. I will discuss each approach in deails below. Firs, a cenral bank could reduce he spreads of longer-erm ineres rae over expeced shor-erm policy raes hrough large-scale purchases of governmen securiies. This approach is ofen referred o as quaniaive easing (QE), which aims a easing fi- 1 For example, he Bank of England has engaged in large-scale asse purchases during (Bean 29). The Federal Reserve have conduced four rounds of quaniaive easing wih some recen forward guidance which links he moneary policy acion conional on he developmen of labour marke (see FOMC release, Sepember 212). 1

10 2 nancing condiions of banks, households and firms. In pracice, as analyzed by Krugman (1998) and Svensson (24), since he cos of exernal finance is generally a premium over he shor-erm inerbank lending rae, he cenral bank could reduce he spreads beween various forms of exernal finance, hereby influencing he asse prices in he economy. When he nominal shor-erm ineres rae remains consrained a he lower bound, he real ineres rae falls as a resul of higher expeced inflaion. Since long-erm ineres raes are average of expeced shor-erm raes, he expecaion channel would end o flaen he yield curve, herefore simulae spending. The experience of he Bank of Japan during 21 and 26 provides an example of unconvenional moneary policy of his ype. 2 Recen sudies of he Fed s firs round of QE experience in 29Q1 also provide more empirical evidence. Mos of he sudies on QE use even sudy or economeric analysis o quanify he impac of addiional simulus while only a few analysis are conduced wihin a DSGE framework. 3 Alernaively, a cenral bank could reduce he economic coss of he zero lower bound by credibly signaling ha shor-erm ineres raes will remain low for a prolonged period of ime, condiional on he developmen of a paricular marke (or indicaor). This approach is ofen referred as condiional forward guidance (Evans 211). Similarly, he cenral bank s forward guidance could also offse he impac of he zero lower bound by announcing ha i will generae an overshooing of inflaion or oupu growh once he lower bound is no longer a consrain (hrough argeing a nominal anchor like he pricelevel or oupu-level). To manage expecaions effi cienly and avoid ime-inconsisency issue associaed wih policy guidance, moneary auhoriy ofen announces clear condiions under which policy raes would begin o increase. The pracice of forward guidance has undergone significan developmen since he onse of he financial crisis in he formal saemens by he Federal Open Marke Commiee (FOMC). Prior o he las guidance communicaed in Sepember 212, commimen of 2 Ugai (26) provides an evaluaion of quaniaive easing in Japan and similar o mos papers on Japanese QE experience, i shows ha alhough he unconvenional policy has generaed an accommodaive environmen for corporae financing, i did no lead o higher aggregae demand and prices. The insuffi cien funcioning of he Japanese banking secor has significanly reduced he effeciveness of injecing liquidiy ino he economy. 3 Among he mos relevan lieraure, Caglar e al. (211) examine QE in he UK using hree separae DSGE models, including financial fricions. QE can correc he effecs of a zero lower bound in DSGE models, by (i) offseing he liquidiy premium embedded in long-erm bonds and/or (ii) adoping counercyclical subsidies o bank capial and/or (iii) he creaion of cenral bank reserves ha reduce he coss of loan supply. Using a porfolio balance model, hey find limied role for QE (a fall in long-erm ineres rae of 1bp would require purchases of abou 5-75% of deb ousanding). Chen e al (211) analyze he impac of large-scale asse purchase programs in he U.S. using a DSGE model enriched wih a preferred habia framework. They esimae a moderae increase in GDP growh (by.4pp) following QE bu he impac is persisen. The impac on inflaion is also small due o he small degree of financial marke segmenaion in he model.

11 he Fed provides simulus mainly hrough expecaions of prolonged period of low nominal ineres raes. The condiional forward guidance, on he oher hand, no only works hrough expecaion of long period of low nominal ineres rae, bu also hrough expecaion of higher han expeced fuure inflaion. This furher helps o reduce marke expecaion of fuure real ineres rae and herefore effecively sabilizes he oupu gap and inflaion. 4 Condiional guidance was recenly used by he Bank of Canada in face of financial crisis in April 29, given is experience of reaching he effecive zero lower bound and he sluggish recovery of he world economy. Despie he wide use in pracice, only a few sudies have looked a he effeciveness of forward guidance policies a he zero lower bound and no sudies have examined he effecs of condiional forward guidance and guidance hrough a price-level argeing in a DSGE model framework. Boh accommodaive convenional moneary policy sance or unconvenional approaches (such as quaniaive easing or forward guidance) aim a warraning a low ineres rae environmen in response o he global financial crisis and ensure a recovery of he global economic aciviy. While keeping ineres rae low for longer would help o suppor aggregae oupu, he conduc of unconvenional policies could also furher srenghen he financial imbalances associaed wih household indebedness (hrough an increasing household deb o income raio) and inensify he misallocaions of resources (e.g., overinvesmen of residenial srucure) ha were fueled by an already low-for-long ineres rae environmen. The concerns abou he impac of house price volailiy and he resuling changes in household ne worh on amplificaion of he aggregae flucuaions have encouraged more research on household financial fricions. 5 This hesis comprise hree essays. In he firs essay "Impac of quaniaive easing a he zero lower bound" (chaper 2), we quanify he impac on aggregae demand from a cenral bank s open marke purchases of long-erm governmen bonds when he policy rae is a he zero lower bound. In he second essay "Measuring he effecs of forward guidance a he zero lower bound", I consider wo alernaive moneary policy rules under commimen in a calibraed simple hree-equaion New Keynesian model o examine he exen o which forward guidance (eiher hrough a condiional saemen or a price-level arge) helps o miigae he negaive real impac of he zero lower bound. Finally, in he hird essay, I exend he analysis of he firs essay o explore he effecs of quaniaive easing on asse prices, household balance shee as well as he implicaion of economy leverage level and moneary policy rules on raios relaed o household financial imbalances. I discuss resuls and conribuion of each essay in deails in he secion below. 4 see Woodford (1999), Eggersson and Woodford (23) and Walsh (29) for more deails. 5 See Bernanke, Gerler and Gilchris (1999), Chrisiano e al. (21) and Iacovielloa and Neri (29) for prominen examples. 3

12 4 1.1 Conribuion of he hesis This hesis falls wihin he DSGE lieraure in evaluaing he impac of unconvenional moneary policies. In he firs essay, we provide a quaniaive assessmen of he macroeconomic impac of QE when he policy rae is a is effecive lower bound. We make wo key modificaions o a sandard NK model. In paricular, we inroduce imperfec asse subsiuion (IAS) and segmened asse markes (SAMs), along he lines of Andres e al. (24), in an oherwise sandard small open economy model wih nominal rigidiies. Boh assumpions are crucial. 6 IAS allows he long-erm rae o deviae from he level implied by he sric expecaion heory of he erm srucure. In paricular, i allows he model o generae a erm premium ha can be affeced by moneary policy. SAMs allow he long-erm ineres rae o independenly affec aggregae demand over and above shor raes. IAS is inroduced by assuming ha money and long erm bonds have differen degrees of liquidiy. We capure his in he model by making uiliy depend on he raio of money o long-erm bond holdings. IAS allows he feasibiliy of implemening quaniaive easing in he sense ha he long-erm rae could deviae from he level implied by he sric expecaion heory of he erm srucure (hrough movemens in he erm premium). However, IAS alone only enables us o analyze he porfolio effecs of quaniaive easing. Only wih addiional feaure of he asse marke segmenaion, QE program could affec he real economy as consumpion is affeced by boh shor-erm and long-erm ineres raes. Given our assumpions, we have wo imporan predicions. Firs, he erm premium is a decreasing funcion of he raio of money o long-erm bond holdings. As a resul, QE has a direc impac on he erm premium as long as i affecs his raio. Second, he macroeconomic impac of QE is deermined by he sensiiviy of aggregae demand o he long-erm rae. In our framework, his sensiiviy is influenced by he fracion of households ha can only save in long-erm asses. We use his model o evaluae he effec of QE a he zero lower bound by simulaing a large and persisen conracionary consumpion demand shock. This shock is big enough ha he desired policy rae becomes negaive. As a resul, he effecive lower bound consrain becomes binding. We hen assume ha he cenral bank conducs open marke purchases of long-erm governmen bonds when he policy rae is a he lower 6 The sandard New Keynesian (NK) model, commonly used in policy discussions, assumes ha financial asses are perfec subsiues. Moreover, i predics ha aggregae demand is affeced by he evoluion of jus one ineres rae: he shor erm ineres rae (i.e. he policy rae). Therefore, in he sandard model here is no role for QE.

13 5 bound. The open marke purchases suppor aggregae demand by reducing long-erm ineres raes. The simulaion resul suggess a moderae impac of quaniaive easing. When he nominal rae is consrained a he lower bound, following a decline of 1bps in he longerm bond yield hrough quaniaive easing, we found a small impac on aggregae demand (real level of GDP increases by.6%, similar o he findings of Baumeiser and Benai 21) and a much larger impac on inflaion (.1%). The iming of he moneary simulus, however, is much faser, wih peak responses on oupu and inflaion occurring afer 4 and 3 quarers, respecively. In he second essay, I explore forward guidance as an alernaive unconvenional moneary policy ha he cenral bank uses o complemen quaniaive easing. I examine he implicaion of expecaion-formaion mechanism a he ZLB by considering alernaive moneary policy rules under commimen. Even he nominal shor-erm ineres rae remains consrained a zero, cenral banks can sill provide furher simulus by shaping privae agens expecaions abou he fuure developmen of he economy. More specifically, I compare he performance of a sae-coningen guidance (using condiional saemen) and a price-level guidance in a calibraed simple hree-equaion New Keynesian model. I examine he exen o which forward guidance helps o miigae he negaive real impac of he zero lower bound. The simulaion resuls sugges ha guidance using a condiional saemen prolongs he zero lower bound duraion for an addiional 4 quarers and reverses half of he decline in inflaion associaed wih he lower bound. In addiion, i even generaes a period of overshooing in inflaion hree quarers afer he iniial negaive demand shock. As a resul of higher more accommodaive policy and higher inflaion expecaion, GDP increases by 1.8 per cen on peak wih a shor period of producion expansion abou a year and a half afer he iniial shock. The effec of price-level argeing as a guidance policy a he zero lower bound is slighly differen. The policy shorens he zero lower bound duraion by one quarer, bu generaes he highes inflaion profile among he alernaive policy rules considered. Price level reurns o pre-shock level and he overall loss is reduced o 6.4 per cen wih he price-level argeing guidance, compared o 2.4 per cen wih he condiional guidance under inflaion argeing and 1.3 per cen wih he case of zero lower bound. In he hird essay, I exend he small open-economy DSGE model wih household financial fricions o analyze he effecs of QE on household deleveraging. The model feaures heerogenous households and a financial inermediary. The paien savers can rade in boh shor- and long-erm bonds markes and have self-imposed liquidiy re-

14 6 quiremens on heir long-erm invesmens (money and long-erm bonds are imperfec subsiues). Impaien borrowers are middle-aged households who only rade in longerm bonds marke and do no face liquidiy requiremens on heir long-erm invesmens. They are he borrowers in he economy, buying long-erm governmen bonds and borrowing from he savers in he economy. The exisence of borrowers allows for he conduc of QE policies as i guaranees long-erm ineres rae o maer over and above he shor-erm raes in he aggregae demand funcion (Andres e al. 24). Borrowers purchase housing relying on morgage loans provided by a financial inermediary. Borrowing is subjec o an exernal financing premium due o loan defaul risk, which generaes endogenous movemen in borrowers loan o value raio. I find wo effecs of QE on aggregae oupu originaed from he model. Firs, QE leads o a decline in erm premium, which increases curren consumpion relaive o fuure consumpion. On he oher hand, i creaes more favorable financing condiions for borrowers hrough an increase in collaeral value and a decline in exernal finance premium. Lower finance premium encourages furher accumulaion of deb a cheaper raes and, in urn, leads o an immediae higher household deb o income raio. Morgage defaul declines on impac following QE. The effec of QE beyond he iniial impac depends on a few imporan facors. Firs, i depends on he elasiciy of loan demand o he policy. If he increase in loan is greaer han he increase in he overall collaeral value, his would lead o an ulimae deeper leverage and herefore higher defaul rae. In he consideraion of fuure wihdrawal of any simulus provided by QE, deeper leverage would pose greaer challenges as i implies much more inensive household deleveraging process. In he baseline calibraion, wih he implemenaion of QE, here is a 1.7 per cen increase in he loan demand. This is refleced in a lower finance premium and an increase in collaeral value. Overall, as household ne worh reurns o he seady sae five years afer he iniial QE policy, defaul rae remains 5 percenage poins higher han is seady sae level. The effec of QE also depends on he seady-sae housing invesmen risk level (or he exen of borrowers leverage). When he economy is in a high-leverage sae, following QE, he increase in inflaion of consumpion goods is greaer. QE hereby largely lowers borrowers real deb, leading o greaer increases in consumpion, residenial invesmen and demand for morgage loans. Morgage defaul five years afer QE is slighly higher han he benchmark case level, suggesing higher housing invesmen risks pos-qe. The effec of QE on he economy is also subjec o he moneary policy rule he cenral bank follows while conducing QE. For a srong ineria policy rule (higher smoohing parameer on he shor-erm nominal ineres rae), shor-erm rae reacs less o he decline

15 7 of long-erm ineres rae (or remains consrained a he zero lower bound for longer) given here is more smoohing. As a resul, under higher smoohing, borrowers increase heir demand for consumpion and housing more han he case when he policy rule is less ineria. Overall, keeping shor-erm ineres rae more persisen helps o beer simulae he aggregae demand, bu has less implicaions for household deleveraging as he decline in exernal finance premium is found o be smaller wih more sable demand for housing under he lower long-erm ineres rae.

16 Chaper 2 Impac of Quaniaive Easing a he Zero Lower Bound 2.1 Inroducion In normal imes, moneary policy seers he level of he key ineres raes o ensure he price or oupu sabiliy over he medium erm. This convenional measure has proven o provide suffi cien moneary simulus o he economy during downurns, prevening deflaionary pressures and ensuring economic recovery. During abnormal imes, unconvenional moneary policy may be warraned under wo possible scenarios (Smaghi, 29). Firs, he negaive economic shock is severe enough such ha he nominal ineres rae needs o be lowered down o zero. 1 Second, unconvenional moneary policy may be used when moneary policy ransmission mechanism is significanly impaired. When economic slack emerges in he economy, he cenral bank can move down he overnigh ineres rae below zero percen (or an effecive zero lower bound). his conex, moneary policy could depar from argeing ineres raes o argeing he amoun of excess reserves held by banks. In anoher word, a cenral bank can arge he quaniy of currency in he financial sysem by purchasing financial asses (in form of long-erm governmen reasury bonds in his model) in exchange for reserves. This approach is ofen referred o as quaniaive easing (QE), which aims a easing financing condiions of banks, households and firms. In our model, QE is defined as he large purchase of governmen long-erm reasury bonds ha aims o reduce he spreads of 1 Since operaionally i is impossible o furher reduce he policy rae, addiional moneary simulus can be achieved in hree complemenary ways: i) by guiding he long-erm ineres rae expecaions; ii) by changing he composiion of cenral bank s balance shee, and iii) by expanding he size of he cenral bank s balance shee. In 8

17 9 long-erm ineres rae over expeced shor-erm overnigh ineres rae. The sandard New Keynesian model, commonly used in policy discussions, assumes ha financial asses are perfec subsiues. Moreover, i predics ha aggregae demand is affeced by he evoluion of jus one ineres rae: he shor-erm ineres rae (i.e. he policy rae). Therefore, in he sandard model here is no role for QE. In his chaper, we provide a quaniaive assessmen of he macroeconomic impac of QE when he policy rae is a is effecive lower bound. We make wo key modificaions o he sandard model. In paricular, we inroduce imperfec asse subsiuion (IAS) and segmened asse markes (SAMs), along he lines of Andres e al. (24), in an oherwise sandard small open economy model wih nominal rigidiies. Boh assumpions are crucial. IAS allows he long-erm rae o deviae from he level implied by he sric expecaion heory of he erm srucure. In paricular, i allows he model o generae a erm premium ha can be affeced by moneary policy. SAMs allow he long-erm ineres rae o independenly affec aggregae demand over and above shor-erm raes. IAS is inroduced by assuming ha money and long erm bonds have differen degrees of liquidiy. We capure his in he model by making uiliy depend on he raio of money o long-erm bonds holdings. IAS allows he feasibiliy of implemening QE in he sense ha he long-erm rae could deviae from he level implied by he sric expecaion heory of he erm srucure (hrough movemens in he erm premium). However, IAS alone only enables us o analyze he porfolio effecs of QE. Wihou addiional feaure of marke segmenaion, QE program will no affec he real economy. This makes he assumpion of SAMs also necessary. We review he relevan lieraure and presen he model srucure and obain some analyical soluion. Given our assumpions, we have wo imporan predicions. Firs, he erm premium is a decreasing funcion of he raio of money o long-erm bonds holdings. As a resul, QE has a direc impac on he erm premium as long as i affecs his raio. Second, he macroeconomic impac of QE is deermined by he sensiiviy of aggregae demand o he long-erm rae. In our framework, his sensiiviy is influenced by he fracion of households ha can only save in long-erm asses. In his chaper we use his model o evaluae he effec of QE a he lower bound by simulaing a large and persisen conracionary consumpion demand shock. This shock is big enough ha he desired policy rae becomes negaive. As a resul, he effecive lower bound consrain becomes binding. We hen assume ha he cenral bank conducs open marke purchases of long-erm governmen bonds when he policy rae is a he lower bound. The open marke purchases suppor aggregae demand by reducing long-erm ineres raes.

18 1 Our work falls wihin he DSGE lieraure in evaluaing he impac of QE hrough he porfolio balancing channel. This chaper conribues o he lieraure in wo ways. Firs, i provides an empirical assessmen of QE on key macroeconomic variables like GDP and inflaion. Moreover, i provides some open-economy implicaions of he conduc of QE. Overall, our esimaed small open economy model of Canada suggess a moderae impac of QE. When he nominal rae is consrained a he lower bound, following a decline of 1bps in he long-erm bond yield hrough QE, our resul suggess a small impac on aggregae demand (real level of GDP increases by.6%, similar o he findings of Baumeiser and Benai 21) and a much larger impac on inflaion (.1%). The iming of he moneary simulus, however, is much faser, wih peak responses on oupu and inflaion occurring afer 4 and 3 quarers, respecively. This chaper is divided as follows. We sar by discussing he relevan lieraure on QE. We hen provide a descripion of he model s key srucure, followed by presening he seady sae around which we linearize he model. We esimae some key parameers of he model using Bayesian mehods and hen assess he impac of QE when he nominal shor-erm ineres rae is a is effecive lower bound. 2.2 Relevan Lieraure on QE a he ZLB The domesic ransmission of QE operaes hrough a number of channels. Firs, QE works hrough a direc ineres rae channel by reducing long-erm yields and real ineres raes, hereby encouraging invesmen and consumpion spending. Second, QE can also change he relaive demand and prices of a argeed financial asse ha is imperfec subsiue wih oher securiies, in urn, change he households porfolio decisions. This is referred as he porfolio-balance channel as in Woodford (212). The hird channel hrough which QE influences he marke is he signalling (or expecaion) channel. By communicaing he inenion o a specific fuure ineres rae pah, he cenral bank shapes marke expecaions of he long-erm yields and helps o simulae aggregae demand. Fourh, he purchase of long-erm asse may also suppor equiy and house prices hrough he asse price channel. Finally, QE also works hrough he confidence channel as i may encourage invesors o be more risk-aking. Mos of he sudies on QE use approaches like even sudy or economeric analysis o quanify he impac of QE (Baumeiser and Benai, 21; Chung e al., 211). Few work is done wihin a DSGE framework analyzing he impac of QE (e.g., Caglar e al., 211; Chen e al., 211). Our work falls wihin he DSGE lieraure in evaluaing he impac of QE wih a focus on he porfolio-balance channel. The approach used in his chaper

19 11 can be relaed o he segmened-marke model of he erm srucure (e.g., Vayanos and Vila, 29; Andres e al., 24 for examples). This chaper conribues o he lieraure in wo ways. Firs, i provides an empirical assessmen of QE a he zero lower bound on key macroeconomic variables like GDP and inflaion. More imporanly, i provides some open-economy implicaions of he conduc of QE The Porfolio-Balance Effec of QE on erm premium Through open-marke purchases of cerain argeed securiies (long-erm governmen reasury bonds for example), a cenral bank creaes he porfolio-balance effec. Woodford (212) describes he effec ha emerges as "he cenral bank holds less of cerain asses and more of ohers, hen he privae secor responds by holding more of he former and less of he laer". A change in he relaive prices of he financial asses is required o saisfy he new equilibrium porfolio for privae agens. The porfolio-balance effec requires a segmened long-erm deb marke and imperfec subsiuabiliy across he erm srucure. The implicaions of QE hrough he porfolio-balance channel has been reviewed in Thornon (212). One way o inroduce segmened marke is by considering a marke populaed by wo ypes of invesors as in Vayanos and Vila (29): he preferred-habia invesors demand only he bonds corresponding o heir desired mauriy, and he risk-averse arbirageurs opimize he Markowix risk-reurn rade-offs. Vayanos and Vila (29) acknowledge ha even hough he assumpion of he preferred-habia invesors is exreme, i is quaniaively imporan as he effec on he yield curve depends on he raio of preferred-habia invesors o arbirageurs. Greenwood and Vayanos (21) conduc furher empirical analysis o examine he effeciveness of QE hrough he porfolio balance channel using Vayanos and Vila s (29) model. Among hree measures of he mauriy srucure of he public s holding of governmen deb (he average mauriy of he deb, he fracion of he deb wih mauriy of or above 1 years, and he duraion of he deb), hey find he sronges evidence of a porfolio balance channel for longer-horizon excess reurns. D Amico e al. (21) also sugges ha QE can affec long-erm yield and erm premium hrough a duraion channel ha has similar implicaions as he porfolio-balance channel. 2 By removing he aggregae duraion from he ousanding sock of governmen 2 In addiion o he duraion channel, here are wo oher channels discussed in D Amico e al. (211). The firs is scarciy channel hrough which he asse purchase of he Federal Reserve wih a specific mauriy leads o higher prices (and lower yields) of securiies wih similar mauriies. The oher channel is called he signaling channel since he purchases convey imporan informaion abou he fuure pah of he nominal shor-erm ineres rae.

20 12 Treasury deb, QE reduces he erm premium on securiies across mauriies. The duraion channel is found o be saisically significan and accouns for abou a hird of he esimaed oal effec of QE. Similarly, Gagnon e al. (211) also sugges ha QE reduces he yields on long-erm asse because i removes a significan amoun of financial asses wih high duraion from he marke. As a resul of lower duraion risk of asses holding, he marke demands a lower premium o hold ha risk. Using wo alernaive measures of i (he 1-year Treasury bond yield and an esimae of he 1-year Treasure erm premium), hey esimae he equaion i = α + X β 1 + Deb β 2 + ε (2.1) over January 1985 o June 28 wih a vecor of key macroeconomic variables X and a measure of he public s holding of Treasury deb. Their analysis suggess ha QE1 ($1.75 rillion asse purchase) by he Fed would have reduced he erm premium by abou 52 basis poins and he 1-year Treasury yield by abou 82 basis poins. Alernaively, Hamilon and Wu (212) invesigae he effecs of QE1 by esimaing a hree facor affi ne erm srucure model and heir esimaes of he effec on he 1-year Treasury yield and erm premium are smaller han ha repored by Gagnon e al. (211) The Domesic Effecs of QE One poenial issue as poined ou by Thornon (212) of analyzing he effec of QE hrough porfolio-balance channel is ha even if he effec of QE on long-erm rae is large, he effec on domesic economic aciviy is comparaively small. Because he effeciveness of QE depends on he exen o which he long-erm bond marke being segmened from he res of he marke, he larger he effec of QE on long-erm rae, he smaller he effec on ineres raes ha are more imporan for economic aciviy. The experience of Bank of Japan during 21 and 26 provides an example of QE ha has limied effeciveness in simulaing he aggregae demand. The unconvenional policy feaures he purchase of Japanese governmen bonds o mee he arge balance of curren accoun deposis a he bank. This follows he pracical approach of QE which radiionally focuses on buying long-erm governmen bonds from banks. Ugai (27) provides an evaluaion of QE in Japan and similar o mos papers on Japanese QE experience, he shows ha alhough he unconvenional policy has generaed an accommodaive environmen for corporae financing, i did no lead o higher aggregae demand and prices. The insuffi cien funcioning of he Japanese banking secor is be-

21 13 lieved o have significanly reduced he effec of injecing liquidiy ino he economy. Recen sudies of he purchases of long-erm U.S. Treasury bonds by he Fed (QE1 or he firs-round of large-scale asse purchase program, LSAP, in March 29; and QE2 or Operaion Twis for example) provide more posiive evidence. Baumeiser and Benai (21) sugges a 4 percenage poins posiive impac on U.S. GDP in 29Q1 and a.4 percenage poin impac on U.S. inflaion in 29Q2. For a 5 bps decline in erm premium, Chung e al. (211) find ha QE suppors he level of U.S. real GDP by abou 2% by early 212 and inflaion by.7 percenage poins by 211. Following sudies on he macroeconomic effecs of QE2 in 21Q4, Chung e al. (211) documen ha wih addiional 2 bps decline in erm premium, wihou he unconvenional measures, level of GDP would be lower by 1% and inflaion would be lower by.3 percenage poin. Similar quaniaive impac is discussed by Macroeconomic Advisers (21, 211). Wih an assumpion of 2 bps decline in 1-year bond yield, he level of real GDP increases by.4% afer 8 quarers and inflaion is.1 percenage poin higher 2 years afer he implemenaion of QE. Among he mos relevan DSGE lieraure on QE, Caglar e al. (211) examine QE in he UK using hree separae DSGE models, including one wih financial fricions. More specifically, QE can correc he effecs of a zero lower bound, by (i) offseing he liquidiy premium embedded in long-erm bonds and/or (ii) adoping counercyclical subsidies o bank capial and/or (iii) he creaion of cenral bank reserves ha reduce he coss of loan supply. Using a porfolio balance model, hey find limied role for QE (a fall in long-erm ineres rae of 1bp would require purchases of abou 5-75% of deb ousanding). Chen e al. (211) analyze he impac of large-scale asse purchase programs in he U.S. using a DSGE model enriched wih a preferred habia framework. They esimae a moderae bu persisen increase in GDP growh (by.4 percenage poin). The impac on inflaion is also small due o he low degree of financial marke segmenaion in heir model The Open-Economy Implicaions of QE For a small-open economy, unconvenional moneary policy conduced domesically has some macroeconomic spillover effecs (Chen e al. 211; IMF 213a). The ransmission o he macroeconomy of foreign counry sems primarily from convenional accommodaive moneary condiions ha suppor price and financial sabiliy, simulae aggregae demand and in some cases, resore full employmen. When he nominal policy ineres rae is consrained a he ZLB, a counry conducs QE hrough large-purchase of governmen long-erm reasury bonds wih he objecive o reduce he spreads of long-erm

22 14 ineres rae over expeced shor-erm overnigh ineres rae. This is also he assumpion we used hroughou his chaper. There are a few channels hrough which QE policy affecs a foreign economy. Firs, hrough aggregae demand channel, lower borrowing coss resuled from a decline in he erm premium encourages increases in domesic consumpion, invesmen and as a resul, domesic GDP. Wih some degree of rade openness, higher aggregae demand of QE counry implies increase in demand for impors. The increase in impors, however, is parially offse by a relaive depreciaion of he domesic currency hrough he exchange rae channel originaing from a negaive ineres rae differenial versus he foreign counry. Third, QE also affecs he foreign economy hrough porfolio-balancing channel. Large-purchase of illiquid asses (governmen long-erm reasury bonds) increases cash holdings of households who hen inves in riskier asses such as corporae bonds, equiies and commodiies, some of which are in form of capial ouflows o foreign economies. This reduces he corporae risk premium in he foreign economy, lowering firms borrowing cos and increases real invesmen in he foreign counry. As foreign firms accumulae greaer capial sock, hey demand more labor. As a resul, foreign household income increases following higher wage and hours of work, leading o higher consumpion expendiure, higher inflaion and oupu in he foreign economy. Moneary policy in he foreign counry reacs by ighening o re-anchor inflaion expecaions and consrain aggregae demand. The increase in foreign policy rae furher srenghens he appreciaion, conaining he increase in expors o QE counries. In his chaper, we have absraced from discussing he implicaions of capial flows as we don include invesmen in boh domesic and foreign economies. Adding hese feaher would be an ineresing exension of exising framework. Finally, inernaional spillover of QE could also operae hrough asse price channel. Bank lending channel can be considered as a furher exension of he porfolio-balancing channel. Asse purchases in QE counry increase cash holdings of invesors, who deposi funds ino banks, leading o more lending domesically or abroad. Lower financing coss boos asse prices in foreign economy, ogeher wih currency appreciaion, leading o lower loan-o-value raios of foreign households. This is viewed o pose some poenial challenges especially during QE exi as foreign economy has higher household leverage, and greaer financial vulnerabiliy (IMF 213b). We don specify a banking secor in his chaper and herefore limi our discussion wihin a simple macroeconomic model where only moneary policy is considered as relevan policy insrumen.

23 Our Approach In his chaper, we inroduce imperfec asse subsiuion (IAS) and segmened asse markes (SAMs), along he lines of Andres e al. (24), in an oherwise sandard small open economy model wih nominal rigidiies. Boh assumpions are crucial for invesigaing he porfolio-balance channel of QE on he erm premium. Firs, IAS is inroduced by assuming ha money and long erm bonds have differen degrees of liquidiy. We capure his in he model by making uiliy of one ype of households (who have self-imposed liquidiy requiremens on heir long-erm invesmens and regard money and long-erm bonds as imperfec subsiues) depend on he raio of money o long-erm bonds holdings. IAS allows he long-erm rae o deviae from he level implied by he sric expecaion heory of he erm srucure. In paricular, i allows he model o generae a erm premium ha can be affeced by unconvenional moneary policy. Given our assumpions, we show ha he erm premium is a decreasing funcion of he raio of money o long-erm bond holdings of his ype of households. As a resul, QE has a direc impac on he erm premium as long as i affecs his raio. However, IAS alone only enables us o analyze he porfolio-balance effecs of QE. Wihou addiional feaure of he marke segmenaion, QE program will no affec he real economy. To examine he effec of QE on he real economy, we inroduce anoher ype of households who has a specific preference for long-erm bonds, in similar fashion as he preferred-habia approach as in Vayanos and Vila (29). SAMs allow he longerm ineres rae o affec aggregae demand over and above shor-erm raes and he macroeconomic impac of QE is deermined by he sensiiviy of aggregae demand o he long-erm rae. In our framework, his sensiiviy is influenced by he fracion of households ha can only save in long-erm asses. In following secions we provide more deailed discussions of hese wo assumpions. Besides separaing he porfolio-balance effec of QE on he erm premium from he effec of he long-erm rae on he real economy, our work also provides new implicaions for conducing QE in a small open economy like Canada. 2.3 The Model The following secion develops a small open economy model wih imperfec asse subsiuion and asse marke segmenaion. This model is buil by merging wo frameworks: he small open economy model proposed by Rabanal, Rubio-Ramírez and Tuesa (211) wih he imperfec asse subsiuion feaure in a closed economy model proposed by Andres e al. (24).

24 Households We assume a coninuum of infiniely-lived households, indexed by i [, 1]. A fracion ω of households can rade in boh shor- and long-erm bonds markes. We use he erm unresriced households o refer o ha subse of households. Moreover, hese households have self-imposed liquidiy requiremens on heir long-erm invesmens (money and longerm bonds are imperfec subsiues). The remaining fracion 1 ω of households can only rade in long-erm bonds markes and do no face liquidiy requiremens on heir long-erm invesmens. We refer o hese households as resriced households. Before presening he opimizaion problem of boh ypes of households, we defend he realism of he heerogeneiy in households we are assuming and discuss he pracical implicaions of hese assumpions. The unresriced agens in our model can be hough of as represening he porion of he privae secor ha saves hrough commercial bank deposis (as commercial banks end o have self-imposed liquidiy requiremens). The resriced households are assumed o represen hose who save heavily hrough agencies such as pension funds and plan o cash hem a mauriy. They can be hough as invesor clieneles wih a specific preference for long-erm bonds. This alernaive inerpreaion is consisen wih he preferred-habia view, proposed by Culberson (1957) and Modigliani and Such (1966). 3 The exisence of resriced households allows long-erm ineres rae o maer over and above he shor-erm raes in he aggregae demand. 4 Wih only unresriced households, even if hey have access o long-erm bonds marke, hey could always "bypass" his marke alogeher, and simply enforce heir consumpion plans by rading in sequences of shor-erm bonds. Imperfec subsiuabiliy beween money and long-erm bonds allows long-erm raes o deviae from he level implied by he sric expecaion heory of he erm srucure. In paricular, given he way we model imperfec subsiuabiliy, his deviaion in he long-erm rae depends upon an exogenous erm premium and an endogenous facor relaed o he raio of money o long-erm bonds. We will demonsrae his relaionship in deails using he firs order condiions of households in following secions. 3 Greenwood and Vayanos (29) discuss differen marke episodes supporing he preferred-habia view. 4 If resriced households consider money and long-erm bonds as imperfec subsiues, he longerm ineres rae will maer over and above he shor erm rae in he IS curve as long as he degree of imperfec subsiuabiliy faced by resriced households is lower han he one faced by unresriced households. See Andres e al. (24) for a deailed explanaion of his poin.

25 17 Unresriced households A ypical household of his ype seeks o maximize he following expeced discouned uiliy, aking similar form as in Andres e al. (24) E β = a U ( C u { C u 1 } h ) + V ( ) M u ξ P 1 H(Nj)dj u G(.) F (.) J(.) (2.2) where < β < 1 is a discoun facor, a is a preference shock, C u is he household s consumpion, M u /P is he household s end-of-period real money balances, P is he consumer price index (CPI), ξ is a shock o he household s demand for real money balances and N u j is he quaniy of ype j labor supply (measured in hours of work). The period indirec uiliy is deermined by he preference shock a and he following funcions: U, V, H, G, F and J. In wha follows, we impose separabiliy among consumpion, real money balances and hours by specifying hese funcions in he following forms ( ) U (.) = 1 1 σ C u { } 1 σ C u h, V (.) = 1 ( ) M u 1 δ, H (.) = (N j) u 1+ϕ 1 1 δ ξ P 1 + ϕ, G (.) = d 2 { [ ( ) M u exp c /P 1 M 1/P u 1 F (.) = v [ ] M u 2 Φ 1, J (.) = ṽ 2 B Lu 2 [ ( M u + exp c /P [ M u 2 Φ 1]. S B Lu )] 1 M 1/P u 1 ]} 2, The uiliy funcion displays inernal habi formaion and is quaniaive imporance is denoed by he size of h [, 1]. The parameer σ > deermines he degree of risk aversion and ϕ represens he inverse of he Frisch labor supply elasiciy. The unresriced household face coss G(.) when adjusing heir financial porfolios. funcion is specified following Nelson (22) and he parameers d and c in his funcion are sricly posiive. Before explaining he meaning of funcion F (.) and J (.), we discuss wo imporan assumpions abou he feaures of long-erm securiies in he model. Firs, long-erm bonds are modeled as zero-coupon bonds: here are no paymens received by he households during he period hey hold he bonds. The firs assumpion is in line wih he reamen of long-erm bonds in macroeconomic models and ensures he opimaliy condiion for long-erm bonds holding racable. 5 5 See Svensson (2). The

26 The second assumpion is ha here is no secondary marke for long-erm bonds. This assumpion can be jusified by he fac ha a large fracion of he non-bank privae secor holds long-erm bonds wih he inenion of keeping hem o mauriy. The absence of a secondary marke for long-erm securiies inroduces a "loss" of liquidiy for households when invesing in long-erm bonds marke, relaive o he same invesmen in shorerm bonds. To miigae his loss of liquidiy, we assume ha hese households have self-imposed liquidiy requiremens on heir holdings of long-erm bonds. Formally, we specify his fricion as a uiliy cos when purchasing long-erm bonds. The liquidiy cos funcions of holding domesic and foreign long-erm bonds are given by he funcions F (.) and J (.). B Lu and B Lu denoe holdings of he domesic and foreign currency denominaed long-erm (mauring L-period) bonds in period respecively. These bonds are redeemed L periods afer hey are bough. S is he nominal exchange rae expressed in unis of domesic currency required o buy one uni of foreign currency. Boh of hem are specified in erms of relaive asse holdings 6. The parameers v and ṽ measure he degree of concern for liquidiy of he households. The parameers Φ and Φ are chosen o be he inverses of he seady-sae money o long-erm bond raios (domesic and foreign currency denominaed long-erm bonds respecively), ensuring zero liquidiy cos a he seady sae. The maximizaion of he expeced uiliy is subjec o he sequence of budge consrains of he form M u + Bu (1 + R ) + S B u (1 + R )(1 + κ ) + (1 + φ )B Lu (1 + R L ) + (1 + φ )S B Lu { L L 1 } (1 + R L ) L E (1 + κ +j ) = M ul 1 + B u 1 + S B u 1 + B Lu L + S B Lu L + 1 j= 18 W j N u jdj P C u + P T u + Π u (2.3) where B u and B u denoe holdings of he domesic and foreign currency denominaed shor-erm (mauring one-period) bonds in period respecively. These bonds are redeemed one period afer hey are bough. R and R are he domesic and foreign currency shor-erm ineres raes respecively. The erm κ is inerpreable as a deb 6 We consider an alernaive version where shor-erm bonds are also considered as liquid asses in he numeraor of he raio. In his version, he deviaion of he long-erm ineres rae from wha he expecaion heory of he erm srucure predics is a complicaed funcion of money and shor erm and long erm bonds. In order o keep racable he specificaion of he erm srucure, we decide o consider only money as liquid asse.

27 elasic ineres rae premium and is given by κ = ς [ ( ) ] S NF A exp nfa 1 + ε κ (2.4) P H, Y where ς > measures he sensiiviy of he counry-risk premium o changes in he aggregae ne foreign asse posiion NF A. The parameer nfa is he seady sae value of ne foreign asse expressed as a fracion of seady sae nominal GDP (P H, is he composie good prices and Y is real GDP). ε κ is a risk premium shock. The adoped funcional form for κ ensures saionariy of he pah of he ne foreign asse o GDP raio abou is seady sae value. The erms φ and φ represen sochasic ransacion coss in he domesic and foreign long-erm bonds markes respecively. We assume ha hese coss have zero mean and represen eiher a pure loss or a benefi o he households in aggregae 7. R L and R L are he domesic and foreign currency long-erm ineres raes respecively. W j is he nominal wage paid for one hour of ype j labor. T u 19 denoes lump-sum real ransfer (or axes if negaive) households received from he governmen. Π u are he dividends from ownership of firms. The household maximizes uiliy over consumpion, money and bonds holdings wih he following firs order condiions summarizing is choices λ u = a U,C u + βe { a+1 U +1,C u } (1 + φ ) (1 + R L ) L ( λ u ) P λ u P = β(1 + R )E λ u ( λ u βe P +1 P +1 vφ ( λ u +1 P +1 M u (B Lu ) 2 ) [ M u Φ 1 B Lu ] = β L E ( λ u +L P +L ) = a V,M u { ( )} G,M u + βe G+1,M u vφ B Lu [ M u ] Φ 1 B Lu ṽ Φ S B Lu ) [ ] M u Φ 1 S B Lu (2.5) (2.6) (2.7) (2.8) 7 The main inenion of adding hese exogenous ransacion coss is o accoun for exogenous movemens of he domesic and foreign erm premium.

28 (1 + R L = β L E ( S+L λ u +L P +L S λ u P (1 + φ )S { L 1 } ) L E (1 + κ +j ) j= ) = β(1 + R )(1 + κ )E ( λ u ) P ( S+1 λ u ) +1 P +1 ṽ Φ M u S (B Lu ) 2 [ ] M u Φ 1 S B Lu 2 (2.9) (2.1) where U,C = U C, U,C+1 = U +1 C, V,M = V M, G,M = G M and G,M+1 = G +1 M. Equaion (2.5) links he Lagrange muliplier for he budge consrain, λ u, o he marginal uiliy of wealh. Wih some degree of habi persisence, λ u is affeced by preference shocks a ime and + 1. Equaion (2.6) and (2.7) correspond o he Euler equaions for domesic long- and shor-erm bonds holding, respecively. From hese wo condiions, we can derive a erm srucure ha links he long-erm ineres rae R L o he shor-erm raes R β(1 + φ ) (1 + R ( ) λ u ) (1 + R L ) E +1 L vφ M [ ] ( u M u λ u ) P +1 (B Lu ) 2 Φ 1 = β L +L E B Lu P +L (2.11) This relaionship is subjec o wo fricions. Firs, he sochasic ransacion coss of rading domesic long-erm bonds φ accoun for exogenous movemens of he domesic erm premium, following Tobin s "exogenous ineres differenials". The more imporan fricion is capured by he presence of he second erm, which is a resul of he assumpion of absence of secondary marke for long-erm securiies in he model. To miigae he liquidiy loss unresriced households incur when invesing in he long-erm bonds marke, hey have self-imposed liquidiy requiremens. As a resul, he erm premium beween long- and shor-erm ineres raes is affeced by he relaive quaniy of asses of differen mauriies. If some unconvenional moneary policy arges o reduce he relaive supply of more illiquid asses (long-erm bonds B Lu for example), he spread beween illiquid asses and liquid asses is driven down. We can see if here exiss a secondary long-erm bonds marke and he ransacion coss is zero, his relaionship collapse o he pure erm-srucure heory of ineres raes. Combining equaion (2.8) wih equaion (2.7) we have he money demand funcion λ u ( ) R = a V,M u P 1 + R { ( )} G,M u + βe G+1,M u [ ] M u vφ B Lu Φ 1 B Lu ṽ Φ S B Lu [ ] M u Φ 1 S B Lu (2.12)

29 which links he marginal rae of subsiuion beween money and wealh wih he nominal ineres rae R. Two fricions also arise from his money demand funcion. Firs, he presence of he porfolio adjusmen coss G (.) implies ha boh curren and expecaions of real income and nominal ineres rae maer for unresriced households porfolio decision oday. Second, money demand is also affeced by he relaive supply of long-erm domesic bonds B Lu (as well as foreign long-erm bonds B Lu ). This fricion is a resul of he assumpion of unresriced households self-imposed liquidiy requiremens. When here is an increase in he relaive supply of more illiquid asses (long-erm bonds), he demand for money also increases. The imporance of his fricion is governed by wo facors: he degree of concern for liquidiy of he households owards invesing in domesic and foreign long-erm bonds (v and ṽ respecively) and he (inverse of) seady-sae money o long-erm bond raios (Φ and Φ respecively). Equaion (2.9) and (2.1) correspond o he Euler equaions for foreign long- and shor-erm bonds holding, respecively. 21 Implicily we can also derive a similar erm srucure for foreign long-erm and shor-erm ineres raes ( β L S+L λ u ) ( +L E = β(1 + φ (1 + R )(1 + κ ) S+1 λ u ) +1 ) { P L 1 }E (2.13) +L P +1 (1 + R L ) L E (1 + κ +j ) ṽ Φ M u S (B Lu ) 2 j= [ M u Φ 1 S B Lu ] (2.14) In addiion o he sochasic ransacion coss of rading foreign long-erm bonds φ and he liquidiy loss associaed wih invesing in foreign long-erm bonds (second erm), expecaions of exchange rae S +L and counry-risk premium κ +j also play roles in affecing he deviaions of foreign long-erm ineres rae R L from he pure erm-srucure heory of ineres rae. For simpliciy, in his chaper, we absrac from discussing he policy implicaions when a foreign economy also conducs some unconvenional moneary policy. Such experimen, however, is feasible exension of our specificaion. We also absrac from discussing he labor marke dynamics in his chaper by using he assumpion of union o simplify he wage seing. The labor marke srucure is specified following Schmi-Grohe and Uribe (26). Following his seing, we assume ha household does no maximize wih respec o labor and aggregae wage is fixed by monopolisicaly compeiive unions. As a resul, hours worked are deermined by labor demand. There is a separae subsecion ha describes he unions problem and he labor demand ha hese unions face.

30 22 Resriced households We have shown from he opimizaion problem of unresriced households ha here exis some deviaions of domesic long-erm ineres rae R L from he pure erm-srucure heory of ineres rae. Such deviaion is a resul of he presence of sochasic ransacion coss of rading long-erm asses and he self-imposed liquidiy requiremens by unresriced households due o imperfec subsiuion beween asses of differen mauriies. As a resul, unconvenional moneary policy like QE could affec he spread beween illiquid and liquid asses by changing he relaive quaniy of asses of differen mauriies. In anoher word, IAS of unresriced households ensures he effeciveness of QE on he erm premium hrough he porfolio-balancing channel. However, wih only unresriced households, even if hey consider shor- and longerm bonds as imperfec subsiues, hey could always "bypass" he long-erm bonds marke alogeher, and simply enforce heir consumpion plans by rading in sequences of shor-erm bonds. This suggess ha even hough IAS allows QE o affec he longerm ineres rae hrough erm premium, IAS alone does no guaranee any effec on aggregae demand from QE wihou addiional link from long-erm ineres rae o aggregae demand. Therefore, o allow for an independen role of long-erm ineres rae over and above he shor-erm raes in he aggregae demand, we need o inroduce some heerogeneiy in households. We define he second ype of households "resriced households" in ha hey have specific preference owards invesing in long-erm asses. The exisence of resriced households can be jusified following he preferred-habia view as in Vayanos and Vila (29). A represenaive resriced household seeks o maximize he following expeced discouned uiliy E β = a U ( C r { C r 1 } h ) + V ( ) M r ξ P 1 H(Nj)dj r G(.) (2.15) where C r is he household s consumpion, M r /P is he household s end-of-period real money balances and Nj r is he quaniy of ype j labor supply (measured in hours). The period indirec uiliy is deermined by he preference shock a and he funcions U, V, H, and G, which have he same funcional form of hose adoped o solve he unresriced households opimizaion problem. Noice ha hese agens do no face any liquidiy requiremens on heir long-erm invesmens (money and long-erm bonds are viewed as perfec subsiues). This explains why he funcions F and J do no appear in he

31 period uiliy funcion, as i was he case of unresriced households. If we relax his assumpion and allow for some degree of imperfec subsiuabiliy for he resriced agens, hen heir relaive holdings of money and long-erm deb socks will also maer over and above ineres raes in he aggregae demand. Given ha he convenional view is ha asse quaniies do no ener direcly he aggregae demand, we decide o keep he assumpion ha money and long-erm bonds are perfec subsiues for resriced agens. The maximizaion of he expeced uiliy is subjec o he sequence of budge consrains of he form M r + (1 + φ )B Lr (1 + R L ) = M r L 1 + B L Lr W j N r jdj P C r + P T r (2.16) where B Lr denoe holdings of he domesic currency denominaed long-erm bonds in period. For simpliciy, we assume ha resriced households do no rade in foreign long-erm bonds. T r denoes lump-sum real ransfer (or axes if negaive) received from he governmen. Noice ha we allow hese ransfers o differ from hose received by unresriced households. We consider he dividends from ownership of firms as a shor-erm asse. Therefore, by assumpion, resriced households do no have access o dividends. The firs order condiions for he resriced households can be wrien as λ r = a U,C r + βe { a+1 U +1,C r } (1 + φ ) (1 + R L ) L ( λ r ) ( λ r = β L E P +L P +L a V,M r { G,M r + βe ( G+1,M r )} = λ r P βe ) ( λ r +1 P +1 ) (2.17) (2.18) (2.19) where he funcions U,C, U,C+1, V,M, G,M and G,M+1 have he same forms as ha of unresriced households opimizaion problem. Equaion (2.17) deermines he Lagrange muliplier for he budge consrain, λ r, which is affeced by preference shocks a ime and + 1. Equaion (2.18) corresponds o he Euler equaions for domesic long-erm bonds holding. Equaion (2.19) corresponds o money demand funcion, subjecing o he porfolio adjusmen coss G (.).

32 24 Unions The labor marke srucure is specified following Schmi-Grohe and Uribe (26). The economy has a coninuum of unions, each represening a ype of labor. Each union ses he wage rae for is members. In each union, here is a fracion ω from unresriced households and a fracion 1 ω from resriced households. As a resul, a coninuum of measure one of labor services are sold o firms. All represenaive household of he same ype supply he same amoun of hours worked, i.e., N u = N r. Firms allocae labor demand uniformly across differen workers providing ype j labor, independenly of heir household ype. We absrac from discussing he labor marke dynamics in his chaper by using he assumpion of union o simplify he wage seing. Following his seing, we don have o specify wo differen labor aggregaors (for unresriced and resriced labor ypes) and wo differen wages a he equilibrium. Given his assumpion, i follows ha N ul j = N rl j = N j. Unions se wages in a saggered fashion. In each period, a union is allowed o rese he nominal wage rae W j wih a probabiliy 1 θ w. If he union is no allowed o re-opimize, i keeps he wage se in he previous period, W j, 1. Those unions ha are allowed o rese is wage choose W j o maximize he following objecive funcion E s= (βθ w ) s {ωf u s + (1 ω)f r s} (2.2) subjec o ω consrains like(2.3), 1 ω consrains like(2.16) and he following labor demand schedule F u s N j = ( Wj W ) ɛw Ñ (2.21) and F r s represen he uiliy funcions of he unresriced and resriced households respecively in period s. ɛ w > 1 and is he elasiciy of subsiuion beween differeniaed labor service, which is assumed o be consan across ypes. The demand for differen ypes of labor comes from a represenaive perfecly compeiive labor packer ha generaes homogenous labor services according o he following echnology Ñ = 1 N 1 1 ɛw j dj ɛw ɛw 1 (2.22) where N j denoes he quaniy of ype j labor employed by he labor packer in period.

33 25 The labor packer hen sells he homogenous labor H a he compeiive price W o he differeniaed good producers ha are presened in he firms secion. The opimizaion process of he represenaive perfecly compeiive labor packer implies ha: W = 1 W 1 ɛw j dj 1 1 ɛw (2.23) Given our assumpions of fixed proporions of unresriced/resriced labor ypes in each union, all unions reseing heir wage in any given period will choose he same wage rae because hey face an idenical problem. In paricular, i can be shown ha he opimal wage W is given by he following equaions: W ɛ w W 1 = E P (ɛ w 1) W (2.24) where W 1 = ( W P ) ɛw a (Ñ) 1+ϕ + βθ w (1 + π +1) ɛw W 1 +1 (2.25) W = ( W P ) ɛw {ωλ u + (1 ω)λ r } Ñ + βθ w (1 + π +1 ) ɛw W +1 (2.26) Moreover, he fac ha all unions reseing heir wage choose he same wage implies ha we can rewrie he aggregae wage index as: W = [ θ w (W 1 ) 1 ɛw + (1 θ w )(W ) 1 ɛw] 1 1 ɛw (2.27) Aggregaion Aggregae consumpion, money and domesic long-erm bonds are given by a weighed average of he corresponding variables for each consumer ype. Formally, C = ωc u + (1 ω)c r (2.28) M = ωm u + (1 ω)m r (2.29) B L = ωb Lu + (1 ω)b Lr (2.3) Similarly, aggregae shor erm bonds and foreign long erm bonds are given by: B = ωb u (2.31)

34 26 B = ωb u B L = ωb Lu (2.32) (2.33) Regarding hours worked, he following relaions hold: N j = ωn u j + (1 ω)n r j (2.34) N u = 1 N u jdj (2.35) N r = 1 N r jdj (2.36) N = 1 N j dj (2.37) N = ωn u + (1 ω)n r (2.38) Firms There are four ypes of domesic firms in he model: i) perfecly compeiive firms ha produce an homogenous final good ha is used for privae consumpion C, ii) perfecly compeiive firms ha produce he composie goods Y H, and Y F,, used as inpus o produce he final good Y C, iii) monopolisically compeiive firms producing differeniaed domesic goods, used as inpus o produce Y H, and iv) firms ha impor foreign differeniaed goods ha are used as inpus o produce Y F,. Final good producers The final good is produced by a represenaive, perfecly compeiive firm wih a consan reurns echnology of he form Y C = ((1 α) 1 η (YH, ) η 1 η ) + α 1 η (YF, ) η 1 η η 1 η (2.39) where Y H, is he quaniy of he composie of inermediae home goods, Y F, is he amoun of he composie of inermediae foreign goods, α is he share of foreign goods ha are used as inpu and η > is he elasiciy of subsiuion beween he domesic

35 and impored goods. Profi maximizaion, aking as given he final good price P and he inpu prices P H, and P F,, yields he following demand funcions 27 Y H, = (1 α) ( PH, P ) η Y C (2.4) Y F, = α ( PF, P and he following zero profi condiion: ) η Y C (2.41) P = { (1 α)(p H, ) 1 η + α (P F, ) 1 η} 1 1 η (2.42) Composie goods producers The composie goods are Y H, and Y F,. Boh are produced by wo differen represenaive, perfecly compeiive firms using he following echnologies [ 1 Y H, = Y H, (h) ε 1 ε ] ε ε 1 dh (2.43) and [ 1 Y F, = Y F, (f) ε 1 ε ] ε ε 1 df (2.44) where Y H, (h) and Y F, (f) are home and foreign inermediae goods of ype h and f respecively. The elasiciy of subsiuion beween any wo ypes of inermediae goods is denoed by ε > 1. Profi maximizaion, aking as given he composie good prices P H, and P F, and he inpu prices for all inermediae goods P H, (h) and P F, (f) for all h [, 1] and f [, 1], yields he following demand funcions: [ ] ε PH, (h) Y H, (h) = Y H, for all h [, 1] (2.45) P H, [ ] ε PF, (f) Y F, (f) = Y F, for all f [, 1] (2.46) P F,

36 28 and he following zero profi condiions: ( 1 ) 1 P H, = P H, (h) 1 ε 1 ε dh ( 1 P F, = P F, (f) 1 ε df ) 1 1 ε (2.47) (2.48) Differeniaed domesic good producers We assume here are a coninuum of monopolisically compeiive firms producing differeniaed goods. These differeniaed goods are sold o he producers of he composie good Y H, or expored. Following Jusiniano and Preson (28) and Monacelli (25), we adop a linear producion funcion in labor for a ypical differeniaed good producer. This funcion is given by: Y H, (h) + YH,(h) = Z Ñ (h) (2.49) where YH, (h) denoes he quaniy expored of good of ype h, Z denoes he labor produciviy and N (h) is he hours demanded by a firm ha produces he ype h. We assume ha labor produciviy follows a simple sochasic auo-regressive process of he form: log Z = ρ z log Z 1 + ε z where ρ z 1 and ε z is an i.i.d shock. Real marginal cos is common o all firms and is given by: MC = W P H, Z (2.5) Differeniaed domesic good producers are assumed o se nominal prices in a saggered fashion, according o he sochasic ime-dependen rule proposed by Calvo (1983). Each firms reses is price wih probabiliy 1 θ H every period. For simpliciy, we assume ha he rese price for good h is he same for boh he domesic marke and he foreign marke. Moreover, in order o have a symmeric expor demand for good h, we assume ha he law of one price holds for ype H goods 8. All firms having he opporuniy o 8 Given ha differeniaed domesic goods prices are sicky in he domesic currency, he law of one

37 rese heir price in period face he same decision problem. Therefore, all of hem se a common price P H, ha solves he following opimizaion problem: max P H, k= { ( θ k HE Q,+k YH,+k (h) + YH,+k(h) ) [ ]} P H, MC +k P H,+k subjec o he sequence of demand consrains 29 (2.51) Y H,+k (h) = and [ PH, P H,+k ] ε Y H,+k (2.52) Y H,+k(h) = [ PH, P H,+k ] ε Y H,+k (2.53) where Q,+k is he sochasic discoun facor used by unresriced households 9. The firs order condiion of his opimizaion problem is given by: k= { ( θ k HE Q,+k YH,+k (h) + YH,+k(h) ) [ P H, ε ]} P H,+k ε 1 MC +k = (2.54) The equaion describing he dynamics of he aggregae price level of differeniaed domesic goods is given by P H, = [ ] θ H P 1 ε H, 1 + (1 θ 1 ε 1 1 ε H)P H, Imporers of foreign differeniaed goods (2.55) We assume here are a coninuum of monopolisically compeiive firms imporing foreign differeniaed goods for which he law of one price holds a he docks. These differeniaed goods are sold o he producers of he composie good Y F,. In seing he domesic currency price of he differeniaed goods, hese firms solve an opimal dynamic mark-up problem. This leads o a violaion of he law of one price in he shor run. price implies ha he price expressed in foreign currency is flexible. 9 Noice ha when presening he expor demand for good h, we have used he fac ha he law of [ ] ε [ ] one price. Formally, YH, (h) = PH, ε YH, = PH, P H, where P H, is he price of he domesic good P H, expressed in unis of he foreign currency and he second equaliy has made use of he law of one price assumpion.

38 3 Real marginal cos of firm imporing he ype f good is given by: MC (f) = S P F, (f) P F, (2.56) where PF, (f) is he res-of-he-world price of ype f good. Noice ha his cos is firmspecific. In order o make his cos common o all firms, we assume ha here is no price dispersion in he res of he world (i.e., PF, (f) = P F, 1 ). These imporers are assumed o se nominal prices in a saggered fashion, like he producers of he differeniaed domesic goods. Each firm reses is price wih probabiliy 1 θ F every period. Given ha here is no price dispersion in he res of he world, all imporers having he opporuniy o rese heir price in period face he same decision problem. Therefore, all of hem se a common price P F, ha solves he following opimizaion problem: max P H, k= [ θ k PF, P F E {Q ]} F,+k,+k Y F,+k (f) S +k P F,+k P F,+k subjec o he sequence of demand consrains (2.57) Y F,+k (f) = [ PF, P F,+k ] ε Y F,+k (2.58) The firs order condiion of his opimizaion problem is given by: k= [ θ k PF, F E {Q,+k Y F,+k (f) P F,+k ε ε 1 S +k P F,+k P F,+k ]} = (2.59) The equaion describing he dynamics of he aggregae price level of differeniaed impored goods is given by: P F, = [ ] θ F P 1 ε F, 1 + (1 θ 1 ε 1 1 ε F )P F, (2.6) 1 There are wo alernaive sories o defend his assumpion. The firs one is ha prices are flexible and firms face he same echnology and demand funcions in he res of he world. The second sory is ha prices are sicky bu moneary policy eliminaes his disorion by reaching price sabiliy and implemen he flexible price allocaion.

39 Governmen The governmen budge consrain is specified as: M + B (1 + R ) + B L (1 + R L ) L (B 1 + B L 1 + M 1 ) = P T (2.61) where T = ωt u +(1 ω)t r. Given ha he focus of he chaper is no on fiscal policy, we absrac from modeling governmen expendiures and axes. 11 For simpliciy, we assume ha long-erm bonds follow a simple AR(1) process of he form: B L P = ( B L 1 P 1 ) ρb exp(ɛ BL ) (2.62) where ρ B [, 1] and ɛ B L is an i.i.d exogenous disurbance. Therefore, shor-erm deb is used as a residual means of public financing. The governmen in his model finances is ransfers by issuing shor-erm bonds in order o mainain a desired deb-o-gdp raio, ( B ) P, over he medium erm. To guaranee dynamic sabiliy and a unique equilibrium in he model, we also assume ha aggregae ransfers and ransfers o he resriced households are se according o he following rules: [ B 1 T T = κ B B ] + ɛ T (2.63) P 1 P [ T r B 1 T r = κ B B ] + ɛ Tr (2.64) P 1 P where κ B [, 1]. T,T r and B are he seady-sae values of aggregae ransfers, ransfers o resriced households and shor-erm governmen bonds respecively. ɛ T and ɛ Tr P are emporary aggregae ransfer shock and emporary ransfer shock o he resriced households, respecively Moneary Policy The insrumen of moneary policy is he shor-erm nominal ineres rae (or overnigh inerbank lending ineres rae). Under he normal circumsances, he cenral bank cus he arge for he overnigh ineres rae in order o simulae lending aciviy, hereby supporing consumpion and invesmen. This is considered as "convenional moneary 11 Convenionally, governmen is also assumed o carry funcion of purchasing goods and services for he governmen and collecing axes on labour income and consumpion. We don, however, discuss hese feaures in his model.

40 32 policy" in his model. We follow Ireland (24) and assume ha he moneary auhoriy ses he nominal ineres rae following an augmened Taylor rule. In addiion o responding o he lagged ineres rae and deviaions of oupu and inflaion relaive o heir seady-sae, he nominal ineres rae also responds o nominal money growh. The presence of changes in real money balance in he moneary policy reacion funcion could indicae he exisence of money growh variabiliy in he cenral bank s loss funcion, as suggesed in Rudebusch and Svensson (22). The policy rule is specified as: [ ] ρr {( (1 + R ) ( R = R 1 ) P 1 + R P 1 ) ρπ ( Y Y 1 ) ρy ( M M 1 ) ρm } (1 ρr ) exp ( ) ε R (2.65) where R is he seady-sae nominal ineres rae. ρ r is he ineres rae smoohing parameer, ρ π is he sensiiviy of he shor-erm risk-free ineres rae o inflaion deviaion from he arge, ρ y is he sensiiviy of he shor-erm risk-free ineres rae o oupu gap, and ρ m is he sensiiviy of he shor-erm risk-free ineres rae o money growh. Y is he aggregae oupu level and ε R is normally disribued wih sandard deviaion of σ R Marke Clearing The clearing of labor and goods markes requires ha he following condiions are saisfied for every 12 : Ñ = 1 Ñ (h)dh (2.66) Y C = C (2.67) Y = Y H, + Y H, (2.68) where Y H, is given by Y H, = ( P ) η H, Y P (2.69) 12 The marke clearing condiions for he domesic and foreign differeniaed goods have been already aken ino accoun when solving he dynamic opimizaion problem of he price seers and when characerizing he evoluion of he aggregae price levels P H, and P F,.

41 Finally, combining he flow budge consrains for boh ypes of households wih ha of he governmen, and using he definiions of dividends, we ge he following equaion describing he evoluion of he balance of paymens denominaed in domesic currency: S B (1 + R )(1 + κ ) + S B L { L 1 } (2.7) (1 + R L ) L E (1 + κ +j ) j= = S B 1 + S B L L + P H, Y H, S P F,Y F, The Transmission Mechanism of QE in The Model When economic slack emerges in he economy, he cenral bank canno move down he overnigh ineres rae below zero percen (or an effecive zero lower bound). As an alernaive, he cenral bank can arge he quaniy of currency in he financial sysem by purchasing financial asses (in form of long-erm governmen reasury bonds in his model) in exchange for reserves. In our model, QE is defined as he large-purchase of governmen long-erm reasury bonds o reduce he spreads of long-erm ineres rae over expeced shor-erm overnigh ineres rae. QE aims a easing financing condiions of banks, households and firms. Boh of he domesic erm srucure and he aggregae consumpion Euler equaion play key roles in he ransmission mechanism of QE. The log-linearized versions of hese wo equaions make i more ransparen how QE operaes in he model. 13 Term Srucure The relaion beween QE and he long-erm real ineres rae can be seen in he following domesic erm srucure derived from he model: rr L, = 1 L L 1 j= rr +j + 1 L p (2.71) where rr L, is he long-erm real ineres rae, rr +j is he shor-erm real ineres rae. The erm premium p is expressed as p φ τ ( ) m u Lu b (2.72) 13 Andres e al. (24) provides deails of he log-linear approximaion of he firs order condiions.

42 where he erms φ represen he disuiliy in a form of ransacion cos he unresriced households have o pay for purchasing one uni of long-erm bond. m u and unresriced households real balances and long-erm bonds holding (in log deviaions). The elasiciy of erm premium o he unresriced households money o long-erm bonds holding raio is governed by parameer τ, expressed as τ v ( 1 + r L) L r (1 + r) b Lu (m u ) δ (2.73) where r L and r are he seady-sae real long- and shor-erm ineres rae, b Lu and m u are he long-erm bonds holdings and real balances of unresriced households a he seady sae. Paramer v affecs he degree of concern for liquidiy of he households owards invesing in domesic long-erm bonds. subsiuion beween consumpion and real balances. b Lu 34 are δ represens he inverse elasiciy of This relaionship based on imperfec asse subsiuion breaks he perfec arbirage opporuniy beween he shor- and long-erm asses and allows he long-erm rae o deviae from he level implied by he pure expecaions heory of he erm srucure. 14 The deviaion is modelled as he erm premium and is presence implies ha long-erm raes can vary independenly of he expeced pah of shor-erm raes. Equaion (2.71) shows ha an increase in he unresriced households money holdings, m u, or a decrease Lu in heir long-erm bond holdings, b, reduces he erm premium, and consequenly longerm real ineres raes. Wih zero long-erm bonds ransacion coss (φ = ) and wih no concern of liquidiy loss when invesing in illiquid asses (v = ), equaion (2.71) collapses o he sandard erm-srucure: rr L, = 1 L L 1 j= rr +j (2.74) QE operaions in he model affec he long-erm real ineres rae hrough he erm srucure relaionship. Since he medium- o long-erm expeced real ineres rae maers he mos for invesmen and consumpion decisions, QE consequenly affecs consumpion and oupu in he model. 14 See Andres, Lopez-Salido and Nelson (24).

43 35 Euler Equaion The log-linearized aggregae consumpion Euler equaion is given by: [ ĉ E ĉ +L = ω L 1 ] (1 ω)l rr +j rr L, + κ 1 ĉ 1 (2.75) κ 2 κ 2 κ 2 j= +β κ 1 κ 2 E ĉ +1 κ 1 κ 2 ĉ +L (2.76) β κ 1 E ĉ +L+1 + (1 βhρ a)(1 ρ L a ) â (2.77) κ 2 κ 2 (1 βh) where rr and rr L, denoe he shor- and long-erm real ineres raes respecively (boh expressed in quarerly erms). κ 1 and κ 2 are non-linear funcions of he srucural parameers, which are given by: κ 1 = (σ 1)h 1 βh, κ 2 = σ + (σ 1)βh2 βh 1 βh Equaion (2.75) shows ha he long-erm rae, rr L,, maers over and above shorerm raes, rr +j. In he model, his is a consequence of he asse marke segmenaion assumpion ha he ineremporal subsiuion decisions of resriced households are driven by long-erm raes. The imporance of he asse marke segmenaion is influenced by he share of resriced households (1 ω), he discoun facor β, he degree of risk aversion σ and he habi persisence parameer h Model Esimaion Since he impac of QE largely depends on he few key parameers of he model (he degree of concern when invesing in domesic long-erm bonds, v; he share of resriced households (1 ω), he degree of risk aversion σ and he habi persisence parameer h ec), we use a combinaion of calibraion and esimaion o selec parameers such ha he model maches some hisorical empirical observaions. Because esimaion involves a few parameers which ener he likelihood non-linearly, we use a geneic evoluionary heurisic o selec parameers which maximize he Bayesian likelihood (An and Schorfheide 27). We consruc he likelihood using he Kalman filer wih a non-linear sep based on he sae space represenaion of he raional expecaion soluion of he model. 16 In he remainder of his secion, we firs describe he daa used in esimaion, 15 Esimaion of he key parameers of he Euler equaion is discussed in laer secions. 16 The Kalman filer is ran wice in he esimaion. In he firs run, he Kalman filer uses he linearized model o generae a one-sep-ahead predicions in each of is seps. In he second run, he

44 36 followed by he parameer prior and poserior disribuions Daa We use quarerly daa for Canada from 198q1 o 212q3 for calibraion and esimaion. 17 We obain Naional Accouns variables such as GDP and consumpion. The quarerly log-difference in he core consumer price index is our measure of inflaion for he policy rule. We used 9-day risk-free bank rae as our measure of nominal shor-erm rae. The long-erm risk-free rae is defined as he average 3-5 year yield on Governmen of Canada markeable bonds. We also include money supply in he esimaion. Daa are de-rended using he LRX filer (see Berg, Karam, Laxon 26 for a deailed descripion) and he esimaion is performed on he saionary series Calibraion and prior choice The value of he discoun facor β is chosen o respec he model s seady-sae sabiliy condiion β = (1 + r) 1. Condiional on he choices for he real quarerly ineres rae, r =.8, we choose a discoun facor β =.99. We calibrae he parameers in he long-erm domesic and foreign bonds ransacion coss funcions, c and d o be 1 and.15197, following Nelson (22). The parameers measuring he degree of concern for liquidiy of he households, v and ṽ, are chosen o be.3 and.5. The sensiiviy of he counry-risk premium o changes in he aggregae ne foreign asse posiion ς is calibraed o be.8. Parameers relaed o he wage seing problems are se according o An and Schorfheide (27). In each period, he probabiliy of a union no o reopimize he nominal wage rae, θ w is se o be.5, reflecing moderae wage sickiness in he Canadian daa. The elasiciy of subsiuion beween differeniaed labor service, ɛ w is se o be 6. On firm s side, he share of foreign goods ha are used as inpu, α is calibraed o be.3, according o he impor imporance of Canadian domesic goods producion, suggesing modes degree of rade openness in Canada. The elasiciy of subsiuion Kalman filer calls a simulaion in an exac non-linear mode o produce one-sep-ahead predicions. 17 Since he sample for esimaion includes a shor period of he zero lower bound, we conduc sensiiviy analysis by esimaing he model over only normal ime o examine he robusness of he parameer esimaes. We find lile change of he resul when he lower bound period is excluded.

45 37 beween he domesic and impored inpus for final goods producion, η is se o be.8. This value is also used o calibrae he elasiciy of subsiuion beween any wo ypes of inermediae goods, denoed by ε. Finally, he proporion of firm no reseing is price θ H is chosen o be.7, implying ha domesic prices are re-opimized, on average, once every hree quarers. To pin down he seady-sae, we assume ha domesic and foreign inflaion are zero, which implies ha here is no price dispersion in seady sae. We assume ha seady sae consumpion is he same across households ypes, i.e., C u = C r = C. This oucome can always be guaraneed by an appropriae choice of governmen s real ransfers T u and T r. Because he focus of he chaper is on he differen responses of he economy o differen shocks, as opposed o seady sae differences across households, we hink his assumpion is reasonable. Given ha boh ypes of households face he same aggregae shocks, our assumpion of compeiive labor markes combined wih symmery in consumpion in seady sae, imply ha hours worked are also he same across households (i.e. N u = N r = N). Our assumpion on he funcions F (.) and J.(.), combined wih our assumpion on he random ransacion coss φ and φ, imply ha erm premium is equal o zero in seady sae. This implies R = R L and R = R L. The seady-sae values for annualized shor- and long-erm nominal ineres raes is 3 per cen. This implies a 3 per cen of he real shor- and long-erm ineres rae around he zero inflaion rae. Given ha here is no disincion beween shor- and long-erm raes in seady sae and ha here are no differences in consumpion across households, money demands are also he same across households (i.e. m = m u = m r ). We assume ha boh ypes of households hold he same amoun of domesic and foreign long-erm bonds. To pin down he aggregae real quaniies of domesic shor-erm and long-erm bonds, we solve he following sysem of wo equaions wih wo unknowns: gdeb = b + Lb L (2.78) b L = T R gdeb 1+R { } (2.79) 1 (1+R) L R L (1+R) L 1+R where eq(2.78) is he definiion of real governmen deb around a zero inflaion seady sae and eq (2.79) is he governmen budge consrain around a zero inflaion seady sae. Noice ha when wriing (2.79), we have used he definiion of governmen deb. We se L = 2, corresponding o a mauriy of long-erm bonds of 5 years in he model. We se T =.9Y, which means ha he governmen runs a primary surplus of.9

46 38 percen of GDP in seady sae. We assume ha governmen deb is equal o 1 percen of quarerly oupu (i.e gdeb = Y ), which is consisen wih he acual level of Canadian governmen deb. Given all hese assumpions, we find he seady sae values for b and b L. We assume ha he erms of rade are equal o 1 in seady sae. This implies P H = P F = P. Moreover, we assume a balanced rade. The specificaion of he counry risk premium implies ha his is equal o zero in seady sae. To pin down he aggregae quaniy of foreign shor- and long-erm bonds, we solve he following sysem of wo equaions wih wo unknowns: b = nfa Lb L (2.8) b L = Y (π R κ R κ) nfa (1+R )(1+π )(1+κ) { } (2.81) {(1+π ) L (1+R ) L (1+κ) L } (π R κ R κ) L (1+R ) L (1+π ) L (1+κ) L (1+R )(1+π )(1+κ) where equaion(2.8) is he definiion of ne foreign asse posiion around a zero foreign inflaion seady and equaion (2.81) is he definiion of he balance of paymens around a zero foreign inflaion seady sae. Noice ha when wriing (2.81), we have used he definiion of ne foreign asse posiion. We se nfa =.1, which means ha he counry has a ne foreign asse posiion of 1 percen of quarerly GDP in seady sae. Given all hese assumpions, we find he seady sae values for b and b L. Given ha he real exchange rae is consan in seady sae, and domesic and foreign inflaion are equal, his means ha nominal depreciaion in he model is zero. Table 1 repors he prior and poserior disribuion for he parameers being esimaed. Prior disribuions are consisen wih he lieraure and he means of he disribuion are aken largely from Jusiniano and Preson (21). The auoregressive coeffi ciens in he shock processes have a bea disribuion wih a mean of.5 and sandard deviaion of.25. The priors on sandard deviaions of he shocks have inverse gamma disribuion wih mean.5 and an infinie variance. Moneary policy rule parameers have priors wih gamma disribuions cenered around he values used in he lieraure (see Hofmann and Bogdanova 212 for a review). The esimaed habi persisence in consumpion, h, is moderae a a value of.51, suggesing somewha delayed peak response of consumpion o movemens in real ineres raes. The ineremporal elasiciy of subsiuion σ and he inverse of he labor supply elasiciy ϕ are esimaed o be 1.45 and.58, respecively. The moneary policy parameers are esimaed o indicae moderae degree of ineres rae smoohing, wih a value of.66 for ρ r. The response o core inflaion is significan (ρ π is esimaed o be

47 39 1.4). We also esimaed a significan response o oupu gap (ρ y is esimaed o be.25). The share of unresriced households ha have access o boh shor- and long-erm asse markes, ω, is an imporan parameer for he propery of he dynamics in he model. I helps o idenify he degree of bond marke segmenaion in he model. We chose a bea disribuion wih mean.5 and sandard deviaion.25. We esimae he share of unresriced household, ω, o be.36, suggesing here is significan degree of segmenaion in he bond marke in Canada. This resul also lies wihin he range of.7 esimae from Chen, Curdia and Ferrero (211) and.29 esimaed by Andres e al. (24). Table 1: Prior and Poserior Disribuion of Esimaed Parameers Esimaes Descripion Poserior Sd. Dev Prior Dis. (mean, Sd. Dev) σ (inverse) consumpion elasiciy Gamma (1.2,.2) ϕ (Inverse) elasiciy of labor supply Bea (.5,.25) h Consumpion habi Bea (.8,.2) ω Share of unresriced households.36.9 Bea (.2,.1) ρ R Policy rule - smoohing.66.4 Normal (.5,.25) ρ π Policy rule - inflaion Normal (1.5,.25) ρ y Policy rule - oupu gap Normal (.25,.125) 2.6 Assessing he Impac of QE In order o assess he quaniaive implicaions of QE in he model, we begin by assuming ha a large and persisen negaive demand shock his he seady sae economy so ha he shor-erm nominal rae is consrained a he ZLB for a year. In paricular, we use he ineremporal preference shock, a, o simulae he effecs of he negaive demand shock. We choose o use preference shock given is imporan role in explaining aggregae flucuaions as an unobserved demand shock in he lieraure (for example, Roemberg and Woodford 1997, Galí and Rabanal 24). We choose a value of.2 for he preference shock, a size lies wihin he empirical esimaion of he sandard deviaion of he preference shock in he lieraure. In he experimen, QE is defined as he large-purchase of governmen long-erm reasury bonds o reduce he spreads of long-erm ineres rae over expeced shor-erm overnigh ineres rae. QE aims a easing financing condiions of banks, households and firms. The dashed lines in Figure 2.1 show he impac of he preference shock when no unconvenional moneary policy is implemened and policy rae is subjec o he ZLB. Noe ha all variables are expressed in percenage deviaions from seady-sae, wih

48 he excepion of he inflaion and ineres rae variables, which are expressed in (annual) percenage poin deviaions. The shock causes oupu and inflaion o fall subsanially. Moneary policy reacs by cuing he shor-erm nominal ineres rae, reaching is lower bound and remaining consrained for five quarers. The solid lines in Figure 2.1 show he impac of he same shock when he convenional moneary policy is augmened wih QE. In his case, he size of he purchase of governmen long-erm reasury bond is equal o four per cen of GDP for four quarers. Figure 2.2 shows he marginal impac of QE (he difference beween he solid and dashed lines in Figure 2.1). The change in he relaive supply of asses generaes a significan decline in he erm premium by roughly 6 bps. QE also leads o he expecaion ha shor-erm raes will rise more quickly as i generaes some growh and inflaion. These wo effecs combined lead o an immediae decline in he long-erm rae by roughly 4 bps. The movemen in he erm premium is a resul of our assumpion of IAS, which breaks he perfec arbirage opporuniy beween he shor- and long-erm asses and allows he long-erm rae o deviae from he level implied by he pure expecaions heory of he erm srucure. Such deviaion is a resul of he presence of sochasic ransacion coss of rading long-erm asses and he self-imposed liquidiy requiremens by unresriced households due o imperfec subsiuion beween asses of differen mauriies. Since here is no secondary marke for long-erm securiies in he model, o miigae he liquidiy loss unresriced households incur when invesing in he long-erm bonds marke, hey have self-imposed liquidiy requiremens. As a resul, he erm premium beween long- and shor-erm ineres raes is affeced by he relaive quaniy of asses of differen mauriies. 4 Through open-marke purchases of cerain argeed securiies (long-erm governmen reasury bonds for example), he cenral bank creaes he porfolio balance effec as he privae secor responds o such purchase by holding less of he long-erm bonds. More specifically, since he erm premium p depends on unresriced households real balances and long-erm bonds holding, any unconvenional moneary policy ha affecs he money/long-erm bonds sock raio maers for he erm Lu premium. Equaion (2.71) shows ha a decrease in heir long-erm bond holdings, b, or an increase in he unresriced households money holdings, m u, reduces he erm premium, and consequenly long-erm real ineres raes. Through porfolio balance channel, when QE arges o reduce he relaive supply of more illiquid asses, he spread beween illiquid asses and liquid asses is driven down. This finding is in line wih he "duraion channel of QE" as in Gagnon e al. (211). When long-erm bonds are purchased by he cenral bank, invesors porfolios become

49 41 safer as i removes a significan amoun of financial asses wih high duraion from he marke. As a resul of lower duraion risk (or less exposed ineres rae risk) of asses holding, he price of risk decreases. The marke in urn is willing o demand a lower premium o hold he remaining bonds. We have shown ha unconvenional moneary policy like QE could affec he spread beween illiquid and liquid asses by changing he relaive quaniy of asses of differen mauriies. In anoher word, IAS of unresriced households ensures he effeciveness of QE on he erm premium hrough he porfolio-balancing channel. However, wih only unresriced households, even if hey consider shor- and long-erm bonds as imperfec subsiues, hey could always "bypass" he long-erm bonds marke alogeher, and simply enforce heir consumpion plans by rading in sequences of shor-erm bonds. This suggess ha even hough IAS allows QE o affec he long-erm ineres rae hrough erm premium, IAS alone does no guaranee any effec on aggregae demand from QE wihou addiional link from long-erm ineres rae o aggregae demand. Therefore, o allow for an independen role of long-erm ineres rae over and above he shor-erm raes in he aggregae demand, i s necessary o have he second ype "resriced households" who have specific preference owards invesing in long-erm asses. Overall, QE generaes a significan decline in he erm premium by roughly 6 bps. This is ranslaed o an increase in consumpion by nearly.5 per cen and year over year inflaion rises o a peak of.8 per cen above is no QE level (his prevens he shor-erm real rae from rising). Oupu also rises by abou.3 per cen above is no QE level. In addiion o he domesic effec, QE policy also affecs a foreign economy hrough aggregae demand channel. Lower borrowing coss originaed from a decline in he erm premium encourages increases in domesic consumpion and as a resul, domesic GDP. Wih some degree of rade openness, higher aggregae domesic demand implies increase in demand for impors from he foreign counry. The increase in impors, however, is parially offse by a relaive depreciaion of he domesic currency hrough he exchange rae channel originaing from a negaive ineres rae differenial versus he foreign counry. The exchange rae depreciaes for over a year, supporing Canadian expors. On ne, he aggregae demand channel dominaes he exchange rae channel in he shorrun, leading o a deerioraion of he rade balance. In he near-erm, as QE leads o a faser increase in he policy rae relaive o he ZLB case, exchange rae appreciaes in year 2 and 3, conaining he increase in expors of he QE counry. In he long-run, asse purchases in QE counry increase cash holdings of invesors, who deposi funds ino banks, leading o more lending domesically or abroad. Curren accoun of QE counry

50 42 Figure 2.1: Impulse Response Funcions 2 Year ov er year inflaion Real GDP 5 Real consumpion year year year Trade balance (% of GDP) 4 ST real ineres rae 2 Real exchange rae year year year LT ineres rae 1 ST ineres rae.5 Term premium year year year QE wih ZLB Convenional MP Wih ZLB deerioraes as a resul of increase in consumpion and impors, leading o a long-run depreciaion of he exchange rae. This finding is similar o he convenional view of he exchange rae impac from an expansionary moneary policy. The dynamics of exchange rae, however, are more volaile given he richer specificaions of he ineres raes ha maer for he exchange rae deerminaion. 2.7 Concluding Remarks The sandard New Keynesian model predics ha financial asses are perfec subsiues and aggregae demand is jus affeced by he evoluion of one-single ineres rae: he shor-erm ineres rae. However, here exiss some evidence as presened by Andres e al. (24) showing ha hese wo predicions do no hold in he daa. In pracice, he explosive growh of base money in he Unied Saes since Sepember 28 has also suggesed ha he Fed s policy has sared shifing from an ineres rae policy o

51 43 Figure 2.2: Marginal Impac of QE 1 Year ov er year inflaion.3 Real GDP.6 Real consumpion year year year Trade balance (% of GDP).5 ST real ineres rae.4 Real exchange rae year year year LT ineres rae.6 ST ineres rae.2 Term premium year year year QE wih ZLB

52 44 one ofen described as "quaniaive easing". Wih he federal funds rae reaching he effecive zero lower bound since December 28, significan developmen have also been observed in he changing composiion of he asse side hrough he Fed s unconvenional balance shee operaions. The conduc of unconvenional policy largely depends on he imperfec subsiuion among various financial asses. In his chaper, we exend he analysis of Andres e al. (24). In paricular, we develop a small open economy model wih imperfec asse subsiuion and segmened asse markes. Imperfec subsiuabiliy allows long-erm raes in he model o deviae from he level implied by he sric expecaion heory of he erm srucure. Segmened asse markes allow long-erm ineres rae o maer over and above he shor-erm raes in he aggregae demand. The modified model ness he sandard version of he New Keynesian model, which does no allow for any independen movemens in long-erm raes. As in Andres e al. (24), our resuls from a small open economy model also suppor he presence of imperfec subsiuabiliy and segmened asse markes. We esimae he model wih IAS and SAMs using Canadian daa. We hen use his model o evaluae he effec of QE when he policy rae is a is effecive lower bound. Our resuls sugges ha a QE inervenion of 4 per cen of GDP for 4 quarers has moderae impac on raes bu small impac on oupu. The key conribuion of his approach is ha he srucural naure of he model allows us o isolae he impac of independen variaion in long-erm raes (unrelaed o changes in expecaions of fuure shor-erm raes) when he effeciveness of normal moneary policy has been limied by he zero lower bound. There are several direcions in which he model presened in his chaper can be improved. Firs, adding nominal wage sickiness would help he model o generae lower movemens in inflaion and nominal wages. Second, inroducing a more acive fiscal policy could be ineresing o sudy he ineracions beween fiscal policy and unconvenional moneary policy. Third, inroducing invesmen ino he model could be useful o sudy he ineracions beween credi easing and quaniaive easing. Finally, a well-specified res of he world model could also be exended in order o sudy how unconvenional policies abroad affec he small open economy model and he implicaion of policy coordinaions among counries.

53 Chaper 3 Effecs of Forward Guidance a he Zero Lower Bound 3.1 Inroducion In he afermah of he financial and economic crisis of 27-29, cenral banks in many advanced economies cu heir policy raes very aggressively o couner rapidly deerioraing economic oulooks. During his process, many of hese cenral banks found hemselves hiing he effecive lower bounds on he policy rae. In his conex, numerous unconvenional moneary ools were considered in order o provide addiional moneary simulus. 1 A he zero lower bound (ZLB), a cenral bank could reduce he spreads of longer-erm ineres rae over expeced policy raes hrough large-scale purchases of governmen securiies (ofen referred o as quaniaive easing, QE). Alernaively, a cenral bank could reduce he economic coss of he lower bound by credibly signaling ha shorerm ineres raes will remain low for a prolonged period of ime, eiher ill a fixed dae or condiional on he developmen of a paricular indicaor (uncondiional or condiional forward guidance). Finally, i could also offse he impac of ZLB by announcing ha i will generae an overshooing of inflaion or oupu growh once he lower bound is no longer a consrain (forward guidance hrough argeing a nominal anchor like price-level or oupu-level). To manage expecaions effi cienly and avoid ime-inconsisency issue associaed wih policy guidance, moneary auhoriy ofen announces clear condiions under which policy raes would begin o increase. In his chaper, I provide a quani- 1 For example, he Bank of England has engaged in large-scale asse purchases during (see Bean 29). The Federal Reserve have conduced four rounds of quaniaive easing wih some recen forward guidance which links he moneary policy acion condiional on he developmen of labour marke. (see FOMC release, Sepember 212). 45

54 46 aive assessmen of he macroeconomic impac of differen ypes of forward guidance when he policy rae is consrained a is effecive lower bound. The pracice of forward guidance has undergone significan developmen since he onse of he financial crisis in he formal saemens by he Federal Open Marke Commiee (FOMC). In December 28 i saed " he Commiee anicipaes ha weak economic condiions are likely o warran excepionally low levels of he federal funds rae for some ime." In March 29, when he firs round of large-scale asses purchase program was announced, i reemphasized ha "economic condiions are likely o warran excepionally low levels of he federal funds rae for an exended period." Given he sluggish global recovery from a deep, synchronous recession, he FOMC saed in November 211 wih an explici iming of is policy such ha "economic condiions including low raes of resource uilizaion and a subdued oulook for inflaion over he medium run are likely o warran excepionally low levels for he federal funds rae a leas hrough mid-213." In face of he recen srains in global financial markes and is associaed downside risks, he FOMC saes in Augus 212 ha i "anicipaes ha economic condiions including low raes of resource uilizaion and a subdued oulook for inflaion over he medium run are likely o warran excepionally low levels for he federal funds rae a leas hrough lae 214." Finally, along wih he fourh round of QE, he FOMC saed in Sepember 212 ha he Fed s fund rae could be expeced o remain a excepionally low levels unil mid-215 and moneary policy reacion is condiional on he fuure developmen of he U.S. labor marke. Prior o he las guidance, commimen of he Fed provides simulus mainly hrough expecaions of prolonged period of low nominal ineres raes. The condiional forward guidance, on he oher hand, no only works hrough expecaion of long period of low nominal ineres rae, bu also hrough expecaion of higher han expeced fuure inflaion. This furher helps o reduce marke expecaions of fuure real ineres rae and herefore effecively sabilizing he oupu gap and inflaion (see Woodford 1999, Eggersson and Woodford 23 and Walsh 29). Condiional guidance was recenly used by he Bank of Canada in face of financial crisis, given is experience of reaching he effecive zero lower bound and he sluggish recovery of he world economy. The Bank has employed new ools o communicae he likely naure of fuure policy sance. The mos explici communicaion was in April 29, when he Bank lowered is arge for he overnigh rae by one-quarer of a percenage poin o 1/4 per cen, which is he effecive lower bound for he policy rae. Accompanying he policy acion, he Bank saes "condiional on he oulook for inflaion, he arge overnigh rae can be expeced o remain a is curren level unil he end of he second quarer of 21 in order o achieve

55 47 Figure 3.1: Bank of Canada s Condiional Commimen in April 29 he inflaion arge." The relevan argeing horizon of such guidance is shown below in Figure 3.1. In he April 29 Moneary Policy Repor, he Bank of Canada also provided guidance hrough wo addiional channels. Firs, i published he confidence inervals for he firs ime o illusrae he uncerainy associaed wih he economic projecions of year-over-year core and oal CPI inflaion over he horizon from 29Q2 o 211Q4. This reinforces he condiionaliy of he saemen and provided a clear band of esimaes of he uncerainy associaed wih he developmen of he economy, as well as he magniude and persisence of ongoing economic shocks. Second, he Bank also presened a framework of conducing moneary policy a low ineres raes by lising hree main insrumens ha i could consider using o achieve is moneary policy objecive a he effecive lower bound: i) a condiional saemen abou he fuure pah of policy raes; ii) quaniaive easing and iii) credi easing. 2 The adoped condiional commimen by he Bank of Canada is considered successful as i has provided he desired simulus effecs hrough he shif of he yield curve (Carney 212) 3. Several sudies have examined he effecs of cenral bank communicaion more generally (see Gurkaynak e al. 25, Kohn and Sack 24, and Bernanke e al. 24). They found ha he Federal Reserve s policy saemens have significan effecs on financial marke expecaions of fuure policy acions as well as Treasury yields. Only a few sudies have looked a he effeciveness of forward guidance policies a he zero lower bound. 2 See Bank of Canada, "Framework for Conducing Moneary Policy a Low Ineres Raes," MPR, April Figure source: Bloomberg and Bank of Canada speech "Guidance".