The Effects of Treasury Debt Supply on Macroeconomic and Term Structure Dynamics

Transcription

1 The Effecs of Treasury Deb Supply on Macroeconomic and Term Srucure Dynamics Thomas Laubach and Min Wei Preliminary and Incomplee Sepember 213 Absrac JEL classificaion: E6, H6. Keywords: Affine erm srucure models. Federal Reserve Board, The views expressed in his paper are hose of he auhors and do no necessarily reflec views of he Federal Reserve Board or he Federal Reserve Sysem.

2 1 Inroducion The relaionship beween he macroeconomy and asse pricing has been a long-sanding area of research. One aspec ha has received much aenion is he ineracion beween he macroeconomy and he erm srucure of ineres raes, and how his ineracion is shaped by he conduc of moneary policy. Whereas he moneary policy rule deermines he comovemen of macroeconomic aggregaes and expecaions of fuure shor-erm ineres raes, is implicaions, and hose of oher aspecs of he macroeconomy, for he deerminaion of erm premia are less well undersood. The use of large-scale asse purchases or quaniaive easing (QE) by a number of cenral banks since he inensificaion of he financial crisis in 28 has len urgency o a beer undersanding of macroeconomic deerminans of he yield curve, as hose policy measures are hough o operae o a large exen by influencing erm premia. In his paper, we provide empirical evidence on he join response of US Treasury yields, he embedded erm premia, and macroeconomic variables o changes in he supply of Treasury securiies. To do so, we follow he approach firs developed in Ang and Piazzesi (23) of combining an affine model of he erm srucure of Treasury yields wih he assumpion ha he facors ha maer for pricing hese bonds are macroeconomic variables whose join dynamics can be described by a linear VAR model. The focus of our analysis is on idenifying exogenous variaions in Treasury supply emanaing from fiscal and moneary policy and o esimae he response of yields and erm premia across he mauriy specrum. The objecive is o provide empirical evidence on hese responses ha is based on minimal idenifying assumpions, so as o uncover sylized facs for fuure sudy in more fully specified srucural models. An imporan moivaion, as menioned before, is he recen use of QE by a number of cenral banks. The macroeconomic effecs of hese policies are widely debaed (some relevan sudies will be discussed below). In many insances, he sudy of hese effecs has proceeded in wo seps. Firs, here are a number of case sudies ha documen he response of various asse prices o QE-relaed news in narrow even windows. Whereas wih he proper choice of even window one can hope o capure he asse price responses of such news, he responses of slower-moving macroeconomic variables such as oupu and inflaion can of course no be measured in his way. Therefore, in a second sep, he asse price responses idenified from he even sudies are used in srucural macroeconomic models o 1

3 obain resuls for he effecs of QE on oupu, he unemploymen rae, and inflaion. This second sep involves he choice of a paricular srucural model which implies numerous, and ofen conenious, assumpions abou he ransmission mechanism of he financial effecs of QE. In conras o his wo-sep approach o he esimaion of QE effecs, in his sudy we model he dynamics of macro and financial variables joinly. In he spiri of he srucural VAR lieraure, we aim o reduce he imposiion of prior assumpions abou he dynamic responses of macroeconomic variables o QE evens o a minimum of idenifying assumpions. We make use of daa on boh oal supply of markeable securiies by he Treasury and Treasury holdings by he Federal Reserve and foreign official insiuions, and build on he lieraure on fiscal SVARs o disenangle exogenous innovaions o Treasury supply emanaing from fiscal policy from hose emanaing from moneary policy. Doing so is arguably imporan, as he effecs of he former reflec boh he effecs of changes in he amoun of Treasuries held in privae porfolios and he effecs of he ax and spending decisions ha bring abou he change in Treasury supply, whereas QE-syle changes in Treasury supply are no associaed wih fiscal policy changes. Aside from he sudy of he dynamic effecs of QE, here is a long-sanding lieraure examining he informaion conen in he erm srucure, and especially is slope, for fuure economic aciviy. A premise of he macro-finance lieraure is ha risk premia, including he erm premia for bearing duraion risk, are endogenous variables ha can be affeced by various macroeconomic disurbances. Hence, reduced-form regressions of measures of economic aciviy on he slope or some oher measure of erm premia are unlikely o uncover he parial effec of a change in erm premia induced by a policy inervenion such as QE. The impulse response funcions of yields and erm premia o various shocks produced by our model shed some ligh on he correlaion paerns beween erm premia and real aciviy induced by hese shocks. Our [highly preliminary] findings are ha (i) exogenous increases in Federal Reserve or foreign official holdings raise oupu significanly and by similar amouns as esimaed in previous sudies, bu ha inflaion rises subsanially, and ha hese effecs are empered by an increase in he shor-erm ineres rae; (ii) ha exogenous increases in Treasury supply of he same size induced by fiscal policy lead o significanly larger responses of oupu, inflaion, and shor-erm ineres raes; and (iii) ha long-erm Treasury yields 2

4 rise in response o boh ypes of shocks, bu ha he response o an increase in Federal Reserve or foreign official holdings is associaed wih a sizeable and significan decline in erm premia, whereas fiscal policy-induced Treasury supply changes are no. In he remainder of his inroducion we discuss a few sudies ha are closely relaed o ours. In secion 2, we discuss he specificaion of our erm srucure model, he idenificaion sraegy, and he daa we use. Secion 3 presens our empirical findings, and secion 4 offers conclusions. The appendix spells ou furher deails regarding model specificaion, daa, and idenificaion. 1.1 Relaed lieraure The sudies by Ang and Piazzesi (23) and by Ang, Piazzesi, and Wei (26) pioneered he use of macroeconomic variables as facors in affine erm srucure models, based on he inuiion ha, if he cenral bank varies shor-erm ineres raes sysemaically in response o economic variables, hese variables mus be relevan for bond pricing. However, his use of macroeconomic variables as pricing facors is no unconroversial. If macro variables were he only facors affecing bond pricing, regressions of macro variables on yields should show high R 2 s, whereas in fac hey do no (Kim, 29; see Gürkaynak and Wrigh (212) for furher discussion). Insead here seems o be informaion in macro variables ha is relevan for fuure shor-erm raes and fuure excess reurns on longer-erm bonds, bu his informaion does no affec curren bond pricing ( unspanned macro risks, see Duffee, 211, and Joslin e al., 213). We noneheless model yields as being driven by fundamenal macroeconomic disurbances o faciliae idenificaion of economically inerpreable shocks, recognizing ha our model has only limied abiliy o explain yields. Early case sudies of he responses of long-erm (Treasury and privae) yields o QErelaed announcemens by he Federal Reserve include Gagnon e al. (211) and Krishnamurhy and Vissing-Jorgensen (211). Boh sudies find significan effecs of announcemens ha raised expecaions of Federal Reserve purchases of Treasuries or Agency MBS on yields of Treasury securiies, MBS, and o a lesser exen corporaes. An imporan quesion in his regard is he precise channel hrough which expecaions of asse purchases reduce yields. They migh do so by reducing he pah of expeced fuure shor-erm raes (he signaling channel ) or by reducing erm premia ha invesors demand, for example because of he associaed reducion in duraion risk. Krishnamurhy and Vissing-Jorgensen 3

5 (211) and D Amico e al. (212) provide evidence on he relaive srengh of various channels, where D Amico e al. focus on evidence on Treasury yields a he CUSIP level. Kiley (213a, b). (To be compleed.) Chung e al. (212), Chen e al. (212) Li and Wei (213), Vayanos and Vila (29) Blanchard and Peroi (22), Dai and Philippon (26). 2 The erm srucure model wih supply facors In his secion we specify an affine model of he erm srucure of nominal US Treasury zerocoupon securiies, in which he facors are macroeconomic variables. Our choice of facors reflecs views on which fundamenal sources of economic uncerainy are likely refleced in bond prices. These include long-run risks, such as percepions of persisen changes in inflaion or he equilibrium real ineres rae, as well as variables relevan for deermining he amoun of duraion risk held by privae invesors, such as oal Treasury supply and foreign and domesic official holdings of Treasuries. 2.1 An arbirage-free erm srucure model wih supply facors The model used o esimae he macroeconomic and erm srucure effecs of Treasury supply shocks consiss of a descripion of he relaionships beween major macroeconomic and Treasury supply variables, and a specificaion of he sochasic discoun facor ha ensures ha pricing of bonds a various mauriies is arbirage-free. The model prices nominal zero-coupon bonds ha are free of defaul risk. For reasons discussed furher below, we consider inflaion π and he one-period real ineres rae r as each being composed of a ime-varying asympoe, denoed by a bar, and saionary deviaions from his asympoe or rend: π = π + π (1) r = r + r (2) The rend componen of inflaion may reflec ime-varying percepions of he cenral bank s inflaion objecive. Since we assume ha π has an uncondiional mean of zero, he infiniehorizon expecaion of inflaion a ime is given by π. Analogously, he rend componen 4

6 of he one-period real ineres rae may reflec ime-varying percepions of rend produciviy growh or changes in risk aiudes ha affec he infinie-horizon expecaion of he equilibrium real rae of reurn on shor-erm risk-free asses. 1 Wih his noaion, we define he vecor of sae variables or facors driving yields as x = [ π, r, π, q,, s, ỹ 1 ] where q,, and s are measures of real aciviy, oal markeable Treasury deb, and domesic and foreign official holdings of Treasuries, respecively, and he derended oneperiod nominal yield ỹ 1, is linked o he observed one-period yield y 1, by y 1, = ỹ 1, + π + r (3) The dynamics of he sae vecor follow a VAR X = µ + ΦX 1 + ΩV, = 1,..., T (4) Under he assumpion (discussed furher below) ha he las five elemens of x follow a VAR(2), whereas rend inflaion and he rend real shor-erm ineres rae are assumed o follow univariae random walks, he vecors and marices in (4) are of he form X x x 1 I 2, V v φ 1 φ 2, Φ = I 2 I 5 where φ 1 and φ 2 are coefficien marices of size 5 5, and I n symbolizes he ideniy marix of size n n. Trend inflaion π and he rend real ineres rae r are laen facors, which, however, will be ighly consrained in he esimaion, as discussed furher below. The las five facors are observed wihou measuremen error. In specifying he sochasic discoun facor ha prices nominal bonds a differen mauriies, we follow he large lieraure on exponenially-affine erm srucure models (e.g. Duffee, 22). Le ξ +1 = exp ( 12 λ λ λ V ) +1 (5) 1 Spencer (28) presens a erm srucure model in which yields also depend on ime-varying asympoes of infaion and he real shor rae. 5

7 denoe he Radon-Nikodym derivaive ha convers he daa-generaing o he risk-neural probabiliy measure, such ha P n = E [M +1 P n 1,+1 ] = E [e y 1, ξ +1 P n 1,+1 ] = E Q [e y 1, P n 1,+1 ] where E Q denoes expecaion under he risk-neural measure and λ are he prices associaed wih he macroeconomic risks. These risks are given by he (as ye o be idenified) fundamenal innovaions ε, which are assumed o be i.i.d. sandard normal. A key assumpion is he specificaion of he prices of risk λ as a general linear funcion of he saes: λ = λ + λ 1 X (6) This specificaion plays an imporan role in enabling he model o explain he observed failures of he expecaions hypohesis (Dai and Singleon, 22) and o forecas yields (Duffee, 22). We assume ha he sochasic discoun facor prices only curren innovaions v, and ha he prices of risk λ depend only on he curren sae x. Oher resricions on λ and λ 1 will be discussed below. Given he decomposiion (3) of he shor rae, i can be expressed as y 1 = δ + δ 1 X (7) wih δ = and δ 1 selecing he firs wo and he las elemen of x. The model hen implies ha he yield on a nominal zero-coupon bond wih n periods o mauriy is a linear funcion y n, = a n + b nx (8) where he coefficiens a n, b n are deermined recursively. 2.2 Daa and survey expecaions used in esimaion For our empirical implemenaion we specify he model a quarerly frequency. This choice reflecs ha fac ha we are ineresed in measuring he effecs of changes in Treasury supply semming from fiscal or moneary policy acions on macroeconomic variables and yields joinly, and recognizes ha a lo variaions in yields a higher daa frequencies can likely no be aribued o hese facors. 6

8 Because he decomposiion of yields ino conribuions from expeced fuure shor-erm ineres raes and erm premia depends on an accurae modeling of financial marke paricipans expecaions, we follow Kim and Orphanides (212) by making exensive use of survey expecaions in boh esimaion and model evaluaion. In paricular, Kim and Orphanides provide evidence ha, because of heir high persisence, he physical dynamics of he yields are poorly esimaed in samples of ypical lengh, bu a he same ime are crucial for model implicaions. For example, if we were o esimae a VAR using acual inflaion insead of decomposing i ino rend inflaion π and derended inflaion, he VAR would generae long-horizon inflaion expecaions, and hereby long-horizon expecaions of shor-erm nominal ineres raes, ha are no nearly volaile enough over our sample (Kozicki and Tinsley, 21). Using long-horizon survey expecaions helps o disenangle ransiory dynamics in inflaion and real shor-erm raes from he secular movemens as in (1)-(2), mos noably he decline in long-horizon inflaion expecaions during he 198s and 199s. These wo decomposiions are moivaed by he subsanial flucuaions, shown in Figure 1, in expecaions 7 o 11 years ahead of nominal 3-monh Treasury bill yields, CPI inflaion, and he expecaions for real shor-erm ineres raes implied by heir difference. In addiion o he long-horizon expecaons for inflaion and he 3-monh yield, we use expecaions a he 6- and 12-monh horizons of he 3-monh Treasury bill yield from he Blue Chip Financial Forecass in he esimaion, and impose ha he VAR-implied expecaions a he respecive horizons are equal o hese survey measures plus i.i.d. measuremen errors. This assumpion implies linear relaionships of he form where E y svy 1,+k E y svy 1,+k = ζ y,k X + ɛ y,k (9) denoes survey expecaions of he 3-monh T bill yield k periods ahead, and he coefficiens ζ y,k are funcions of he VAR parameers. A refinemen of he decomposiion (1) is moivaed by he fac ha CPI inflaion, wheher measured a monhly or quarerly frequency, is a very noisy process. Duffee (211), Kim (29), and Gürkaynak and Wrigh (212) have argued ha no all flucuaions in inflaion are priced in bond yields. We herefore consider realized inflaion π +1 as composed of π +1 = π + π + ɛ π +1 and ha only E π +1 = π + π affecs bond pricing a dae, whereas he measuremen 7

9 Figure 1: Long-Horizon Expecaions of 3-monh Yields and Inflaion, Blue Chip monh T Bill CPI Inflaion Real Shor Rae error ɛ π does no. In paricular, we use one-quarer-ahead survey forecass of CPI inflaion, denoed E svy π +1 and assume ha E svy π +1 = π + π, hereby idenifying π condiional on an esimae of π. Similarly, we use one-quarer ahead survey forecass of real GDP growh as measure for real aciviy. As will be discussed below, we seek o idenify shocks ha resemble he quaniaive easing programs underaken in recen years by several cenral banks. Usually, he main source of variaion of he amoun and duraion of Treasury deb held by privae invesors is he Treasury iself. However, variaions associaed wih fiscal policy acions affec macroeconomic variables imporanly hrough changes in governmen spending and axaion. By conras, variaions in Treasury deb held by privae invesors engineered by cenral banks are no associaed wih fiscal measures and can herefore be expeced o have differen macroeconomic effecs han variaions due o fiscal policy. To allow us o disenangle hese differen sources of variaions in Treasury deb held by privae invesors, we include wo measures. The firs,, is he oal amoun of markeable deb ousanding, whereas he second, s, is he amoun of Treasuries held by he Federal Reserve s Sysem Open Mar- 8

10 Figure 2: Saionary variables in he sae space 1 Quarer Ahead Expeced and Trend Inflaion 14 Acual 12 Trend Quarer Ahead Expeced GDP Growh T bill rae and Trend Inflaion 5 4 Treasury Supply Toal SOMA and Foreign ke Accoun (SOMA) and foreign official insiuions. 2 Boh are expressed as percen of nominal GDP. The ime series of he elemens of x are shown in Figure 2. In ligh of he clear upward rend in s, we linearly derend i before esimaion of he VAR parameers. A fuller descripion of our sae space model is provided in Appendix A, and furher deails on he daa we use in Appendix B. 2.3 Idenifying Treasury supply shocks [Very rough and incomplee] As discussed before, we would like o separaely idenify exogenous innovaions o Treasury supply originaing from fiscal policy on he one hand, and exogenous innovaions o Federal Reserve and foreign holdings of Treasury securiies on he oher. Blanchard and Peroi (22) proposed an idenificaion sraegy ha akes accoun of endogenous responses of axes and spending o oupu. Their approach o idenificaion has been subjec o a number of criicisms, one imporan of which is he fac ha agens in he economy may be aware of he exogenous fiscal shocks before he economerician observes hem. However, 2 The series of foreign official holdings is described in Belran e al. (212). 9

11 recen work by Leeper e al. (212) and by Caldara and Kamps (213) suggess ha, in VARs ha include more variables han Blanchard and Peroi s 3-equaion model, adding measures of fiscal news doesn qualiaively aler he resuls concerning dynamic responses o ax and spending shocks. Based on hese resuls, we are adaping Blanchard and Peroi s idenificaion sraegy o our seing, in which we include no axes and spending, bu insead he oal amoun of markeable Treasury deb ousanding. In paricular, we use he approximae relaionship ha = 1 /N + g τ where g denoes he raio of federal governmen expendiures o GDP, τ he raio of federal ax revenues o GDP, and N he gross growh rae of nominal GDP beween periods 1 and. This relaionship allows us o conver idneifying assumpions for ax and spending shocks separaely ino idenifying assumpions for exogenous Treasury supply shocks induced by fiscal policy. Furher deails are presened in Appendix C. The key challenge for idenifying exogenous fiscal shocks is ha here is clear evidence of conemporaneous causaliy running in boh direcions: Real revenues and spending are conemporaneously affeced by changes in oupu and inflaion because of he auomaic sabilizers and lack of indexaion of governmen wages, and oupu is conemporaneously affeced by governmen spending and arguably by ax changes. By conras, we assume ha U.S. oupu and inflaion are conemporaneously unaffeced by exogenous changes in Federal Reserve and foreign official holdings of Treasury securiies, for essenially he same reasons ha mos of he lieraure on idenifying moneary policy shocks has assumed oupu and inflaion o be conemporaneously unaffeced by exogenous ineres rae shocks. Hence, in addiion o applying he Blanchard-Peroi idenificaion sraegy o fiscal shocks, we assume ha exogenous innovaions o he wo moneary policy insrumens, Federal Reserve and foreign official holdings and he shor-erm ineres rae, do no conemporaneously affec any of he remaining variables in he VAR. How o disenangle exogenous innovaions o he wo moneary policy insrumens is a challenging quesion. For now, we assume a recursive ordering in which Federal Reserve and foreign official holdings of Treasury securiies are chosen before he ineres rae is deermined, bu we recognize ha his is somewha arbirary. In fuure work we will wan o explore alernaive idenifying assumpions in he spiri of Faus and Rogers (23). 1

12 3 Esimaion and Resuls The model is esimaed over he sample 198q3 o 28q2, using observaions for 198q1 and 198q2 as iniial lags. We sar he sample only in 198 because he sysemaic response of moneary policy o economic condiions is an imporan elemen of our facor VAR, and here is srong evidence for a break in his sysemaic componen around 198. We end he sample jus before he inensificaion of he financial crisis in Sepember 28 because shorly hereafer he nominal shor rae reached he zero lower bound, hereby inroducing a nonlineariy in shor-rae dynamics ha our affine erm srucure model does no capure. 3 However, in discussing our resuls below, we will discuss he likely implicaions of our model for he effecs of QE a he zero lower bound. 3.1 Esimaion We are esimaing he model parameers joinly by maximum likelihood, reaing he asympoes of inflaion π and he real one-period rae r as laen facors ha are being filered. 4 The oal number of parameers o be esimaed is raher large, and i is herefore imporan o use good saring values. We iniialize he VAR parameers µ, φ 1, φ 2 and Ω wih OLS esimaes using proxies for π and r. We impose in esimaion he resricion ha only curren level risk is priced, i.e. only risk relaed o π and r, bu ha he prices of hese risks (he firs wo elemens of λ ) can be affeced by all seven saes. This resricion is consisen wih he finding of Cochrane and Piazzesi (28) ha only level risk appears o be priced. Hence, he las five rows of λ and λ 1 conain only zeros, reducing he number of elemens of λ and λ 1 o be esimaed o 16. To esimae he model, we use observaions on zero-coupon Treasury yields wih mauriies 1, 2, 3, 7, 1, and 15 years from he daa se described in Gürkaynak, Sack, and Wrigh (26). Because he erm srucure model implies he exac linear relaionships (8) beween he saes and he yields, wih k yields and only wo laen facors i is necessary o 3 Li and Wei (213) also end heir sample in 27, jus before he onse of he financial crisis. 4 An alernaive approach would be o rea he long-horizon survey expecaions as observaions for he asympoes, in which case we would esimae he parameers of he VAR for he facors by OLS, and only he risk price parameers λ and λ 1 and he measuremen error sandard deviaions for he yields by maximum likelihood. For aking his wo-sep approach, we would need o impue values for he long-horizon expecaions of he T bill yield prior o 1986, he firs year when he Blue Chip long-horizon expecaions become available. 11

13 add measuremen error o a leas k 2 yields o avoid sochasic singulariy. The n-period yield is herefore assumed o equal y n, = a n + b nx + ɛ n. The model fi, as assessed by he sandard deviaions of he yield measuremen errors, is quie impressive in comparison o oher affine erm srucure models ha use only observable facors. Noe ha, alhough he aympoes of inflaion and he real shor rae are laen facors, we calibrae he measuremen error sandard deviaions on he long-horizon survey expecaions o 25 basis poins, hus forcing he laen facors o closely follow he survey expecaions. Of course, inclusion of he one-period yield among he facors implies ha he shorer mauriies are fi quie precisely, bu he measuremen error sandard deviaions ou o mauri of 7 years are all close o 1 basis poins. Only a he longes mauriies does he sandard deviaion rise, o 2 basis poins for he 1-year yield, and o 4 basis poins for he 15-year yield. Figure 3 presens he facor loadings of our esimaed model, i.e. he conemporaneous responses of yields a various mauriies o changes in he facors. These loadings lack a srucural inerpreaion, as hey do no disinguish beween differen sources for changes in he facors, and hey are by consrucion saic mulipliers. Noneheless hey provide some insigh ino how he facors drive he yields. The upper lef panel is consisen wih he fac ha he derended shor rae is by consrucion no highly persisen, and herefore is movemens affec yields of longer mauriies very lile. The upper righ shows ha, whereas increases in oal Treasury supply affecs yields very lile conemporaneously, increases in SOMA and foreign official holdings raise yields a inermediae mauriies from 1 o 5 years upon impac. Of course, his does no imply ha yields rise in response o exogenous innovaions o foreign and SOMA holdings. Finally, he lower righ panel shows ha he asympoes of inflaion and he real shor rae ac as level facors. 3.2 Treasury supply shocks and he comovemen of yields and macro variables We now urn o some of he impulse responses o exogenous innovaions o SOMA and foreign holdings, he shor rae, and o oal Treasury supply semming from fiscal policy. 12

14 Figure 3: Facor loadings 1.8 facor loadings of yields shor rae 1.8 facor loadings of yields oal supply F&S holdings facor loading facor loading Yield mauriy (year) Yield mauriy (year) 1.8 facor loadings of yields inflaion oupu 1.8 facor loadings of yields rend inflaion rend real rae facor loading facor loading Yield mauriy (year) Yield mauriy (year) We firs focus on he responses of sae variables o hese shocks, and hen on he responses of longer-erm yields and erm premia. Figure 4 presens impulse responses o an exogenous increase in SOMA and foreign Treasury holdings in he amoun of 1 percen of GDP (roughly $15 billion a curren levels). The upper lef panel shows he response of he level of real GDP (he cumulaive response of GDP growh). The level of real GDP rises gradually by close o 2 basis poins over he four quarers following his innovaion, and hen slowly reurns o is original level. The response of inflaion (expressed a annual rae) is rapid in comparison o ha in many VAR sudies of he effecs of moneary policy, bu i should be kep in mind ha his is he response of derended inflaion π, which shows less persisence han overall inflaion (by assumpion, rend inflaion π does no respond o his shock, neiher conemporaneously nor lagged). As shown in he lower lef, he shock leads o a very persisen rise in SOMA and foreign Treasury holdings, even afer derending he series of s. In erms of he relaionship beween hese holdings and he radiional shor-rae ool of moneary policy, he lower righ shows ha he shor rae declines by abou 3 basis poins upon impac, bu hen gradually 13

15 Figure 4: Impulse response funcions o F&S shock 35 IRF of oupu o F&S holdings shock 6 IRF of inflaion o F&S holdings shock Basis poin 1 15 Basis poin Quarer Quarer IRF of F&S holdings o F&S holdings shock IRF of shor rae o F&S holdings shock Basis poin 1 6 Basis poin Quarer Quarer rises in response o he increase in oupu and inflaion. Figure 5 presens impulse responses o a moneary policy innovaion of he radiional shor-rae variey. In reponse o a 1 basis poin increase (a annual rae) of he 3-monh yield ha dies ou only gradually, he level of oupu declines by abou 3 basis poins over he 1 quarers following he shock before reurning o is original level. The response of inflaion is again quie rapid, reflecing likely he less persisen dynamics of derended inflaion. Finally, he lower lef panel indicaes ha SOMA and foreign holdings ac as complemens o shor-erm ineres raes by declining by abou 1 basis poins ($15 billion a curren levels) during he firs eigh quarers. The responses o a fiscal shock are presened in Figure 6. The increase in Treasury supply by 1 percen of GDP could reflec eiher an increase in spending or a decrease in axes; since we only include oal Treasury supply, we canno disinguish beween hese wo sources. Oupu rises upon impac by abou 6 basis poins and reaches a peak of 8 basis poins wihin wo quarers. Inflaion jumps upon impac, bu he response is shor-lived. The increase in oupu and inflaion leads o an iniial rise in he 3-monh T bill yield of 14

16 Figure 5: Impulse response funcions o shor-rae shock 2 IRF of oupu o shor rae shock 2 IRF of inflaion o shor rae shock Basis poin 2 Basis poin Quarer Quarer 2 IRF of F&S holdings o shor rae shock 1 IRF of shor rae o shor rae shock Basis poin 1 1 Basis poin Quarer Quarer abou 1 basis poins ha dies ou wihin 1 quarers. Finally, in Figure 7 we show impulse responses of he 1-year Treasury yield and he associaed erm premium o he wo shocks associaed wih moneary policy. As he boom wo panels show, he 1-year yield rises in response o an exogenous shock o he 3-monh yield by abou 6 basis poins upon impac and hen gradually reurns o zero. This increase almos enirely reflecs he expecaions hypohesis effec semming from persisenly higher 3-monh yields (as shown in Figure 5), whereas he erm premium remains essenially unchanged. By conras, an increase in SOMA and foreign holdings leads o a rise in he 1-year yield ha peaks a abou 6 basis afer 4 quarers, bu in his case he expecaions hypohesis effec, which is subsanially larger han in he case of he shor-erm rae shock, is largely offse by a persisen decline in he erm premium by abou 15 basis poins. This esimae is qualiaively similar, bu somewha larger han he esimaes repored in Li and Wei (213). 15

17 Figure 6: Impulse response funcions o fiscal shock 1 IRF of oupu o oal supply shock 175 IRF of inflaion o oal supply shock Basis poin 6 2 Basis poin Quarer Quarer IRF of oal supply o oal supply shock IRF of shor rae o oal supply shock Basis poin 6 3 Basis poin Quarer Quarer Figure 7: Impulse responses of 1-year yield and erm premium IRF of 1 year yield o F&S holdings shock 2 IRF of 1 year erm premium o F&S holdings shock 15 5 Basis poin 1 Basis poin Quarer Quarer 2 IRF of 1 year yield o shor rae shock IRF of 1 year erm premium o shor rae shock Basis poin Basis poin Quarer Quarer 16

18 4 Conclusions Sill o be done: Include yield spread in VAR as in Ang-Piazzesi-Wei. Are idenified F/S, fiscal shocks in accordance wih narraive record? Idenify exogenous changes o Treasury mauriy composiion from hisorical records. Combine SVAR and narraive approaches o idenificaion in he manner of Sock and Wason (Brookings 212), Merens and Ravn (JME 213). Revisi assumpion ha SOMA and foreign holdings don respond conemporaneously o exogenous shor-rae shocks. Simulae yields over period since 8Q2, decompose ino conribuions from SOMA purchases, forward guidance, fiscal. Examine robusness of resuls o resricions on risk price parameers. One- vs. wo-sep esimaion, calculaion of sandard errors. 17

19 References [1] Ang, Andrew, and Monika Piazzesi, 23. A no-arbirage vecor auoregression of erm srucure dynamics wih macroeconomic and laen variables. Journal of Moneary Economics 5 (4), [2] Ang, Andrew, Monika Piazzesi, and Min Wei, 26. Wha does he yield curve ell us abou GDP growh? Journal of Economerics 131 (1-2), [3] Belran, Daniel, Maxwell Krechmer, Jaime Marquez, and Charles Thomas, 212. Foreign holdings of U.S. Treasuries and U.S. Treasury yields. Federal Reserve Board, Inernaional Finance Discussion Paper 141. [4] Bernanke, Ben, Vincen Reinhar, and Brian Sack, 24. Moneary policy alernaives a he zero lower bound: An empirical assessmen. Brookings Papers on Economic Aciviy 2, 1-1. [5] Blanchard, Olivier, and Robero Peroi, 22. An empirical invesigaion of he dynamic effecs of shocks o governmen spending and axes o oupu. Quarerly Journal of Economics 117, [6] Caldara, Dario, and Chrisophe Kamps, 213. The idenificaion of fiscal mulipliers and auomaic sabilizers in SVARs. Working paper, Federal Reserve Board. [7] Chen, Han, Vasco Cúrdia, and Andrea Ferrero, 212. The macroeconomic effecs of large-scale asse purchase programs. Economic Journal 122, F289-F315. [8] Chung, Hess, Jean-Philippe Lafore, David Reifschneider, and John Williams, 212. Have we underesimaed he likelihood and severiy of zero lower bound evens? Journal of Money, Credi, and Banking 44, [9] Dai, Qiang, and Thomas Philippon, 26. Fiscal policy and he erm srucure of ineres raes. Working paper, New York Universiy, November. [1] Dai, Qiang and Kenneh Singleon, 22. Expecaions puzzles, ime-varying risk premia, and affine models of he erm srucure. Journal of Financial Economics 63,

20 [11] D Amico, Sefania, William English, David López-Salido, and Edward Nelson, 212. The Federal Reserve s large-scale asse purchase programs: Raionale and effecs. Federal Reserve Board, Finance and Economics Discussion Series [12] Duffee, Gregory, 22. Term premia and ineres rae forecass in affine models. Journal of Finance 57, [13] Duffee, Gregory, 211. Informaion in (and no in) he erm srucure. Review of Financial Sudies 24, [14] Faus, Jon, and John Rogers, 23. Moneary policy s role in exchange rae behavior. Journal of Moneary Economics 5, [15] Favero, Carlo and Francesco Giavazzi, 212. Measuring ax mulipliers: The narraive mehod in fiscal VARs. American Economic Journal: Economic Policy 4, [16] Gagnon, Joseph, Mahew Raskin, Julie Remache, and Brian Sack, 211. Large-scale asse purchases by he Federal Reserve: Did hey work? Federal Reserve Bank of New York Economic Policy Review 17, [17] Gürkaynak, Refe, Brian Sack, and Eric Swanson, 25. Do acions speak louder han words? The response of asse prices o moneary policy acions and saemens. Inernaional Journal of Cenral Banking 1, [18] Gürkaynak, Refe, and Jonahan Wrigh, 212. Macroeconomics and he erm srucure. Journal of Economic Lieraure [19] Joslin, Sco, Marcel Priebsch and Kenneh Singleon, 213. Risk premiums in dynamic erm srucure models wih unspanned macro risks. Journal of Finance, forhcoming. [2] Kiley, Michael, 213a. The response of equiy prices o movemens in long-erm ineres raes associaed wih moneary policy saemens: Before and afer he zero lower bound. Federal Reserve Board, Finance and Economics Discussion Series [21] Kiley, Michael, 213b. Moneary policy saemens, Treasury yields, and privae yields: Before and afer he zero lower bound. Federal Reserve Board, Finance and Economics Discussion Series

21 [22] Kim, Don, 29. Challenges in macro-finance modeling. Federal Reserve Bank of S. Louis Review 91 (5, Par 2), [23] Kim, Don and Ahanasios Orphanides, 212. Term srucure esimaion wih survey daa on ineres rae forecass. Journal of Financial and Quaniaive Analysis 47, [24] Kozicki, Sharon, and Peer Tinsley, 21. Shifing endpoins in he erm srucure of ineres raes. Journal of Moneary Economics 47, [25] Krishnamurhy, Arvind, and Annee Vissing Jorgensen, 211. The effecs of quaniaive easing on ineres raes: Channels and implicaions for policy. Brookings Papers on Economic Aciviy 42, [26] Li, Canlin, and Min Wei (213). Term Srucure Modelling wih Supply Facors and he Federal Reserve s Large Scale Asse Purchase Programs. Inernaional Journal of Cenral Banking 9, [27] Peroi, Robero, 24. Esimaing he Effecs of Fiscal Policy in OECD Counries. Working paper, Universia Bocconi, Ocober. [28] Rudebusch, Glenn, Brian Sack, and Eric Swanson, 27. Macroeconomic implicaions of changes in he erm premium. Federal Reserve Bank of S. Louis Review July/Augus 27, [29] Spencer, Peer, 28. Sochasic volailiy in a macro-finance model of he U.S. erm srucure of ineres raes Journal of Money, Credi and Banking 4, [3] Vayanos, Dimiri, and Jean-Luc Vila, 29. A preferred-habia model of he erm srucure of ineres raes. NBER working paper No A Specificaion of he affine erm srucure model The erm srucure model is given by he law of moion for he vecor of facors, which is assumed o be a VAR(2) under he hisorical probabiliy measure, X = µ + ΦX 1 + V, = 1,..., T 2

22 where he vecors X and V and he marix Φ are defined as in (5) in he main ex, by he affine marke price of risk specificaion (6), he shor-rae specificaion (7), and he sochasic discoun facor. This is an essenially affine erm srucure model as defined in Duffee (22). Given he normaliy of V +1, he SDF M +1 = exp ( r 12 λ Ωλ λ U ) +1 is log-normal. Under hese assumpions i is possible o express he price of he n-period bond as P n = exp(a n + B nx ) (1) where he scalars A n and vecors B n evolve recursively as A n+1 = A n + B n(µ Σλ ) B nσσ B n δ (11) B n+1 = B n(φ Σλ 1 ) δ 1 (12) wih A 1 = δ, B 1 = δ 1, and Σ defined as he square roo of he covariance marix Ω of V. Expression (1) hen leads o (8) wih a n = A n /n and b n = B n /n. A.1 The sae space model wih survey informaion The model is specified a he quarerly frequency. In he esimaion of he model, we use yields of mauriies 1, 2, 3, 7, 1, and 15 years in addiion o he 3-monh T bill yield. The vecor of observables Y herefore consiss of Y = [y 1, y 4, y 8, y 12, y 28, y 4, y 6, π svy We rea he survey expecaions π svy, r svy and r svy, E svy [π +1 ], E svy [q +1 ],, s, E svy [y 1,+2 ], E svy [y 1,+4 ]] as if hey had a consan forecas horizon, i.e. as if hey represened expecaions of average inflaion over he horizon 25 o 44 quarers ahead (deails on he acual series are provided below). The model-implied expecaion of average inflaion over his horizon is hen given by ζ πx wih where ι j selecs he j-h elemen of X. ζ π =.5(ι 1 + ι 3 )Φ 25 ( Wih hese assumpions, he sae space model consiss of he ransiion equaion given by (5) and a measuremen equaion 19 i= Φ i ) Y = A + BX + e 21

23 given by y 1, y m1,. y mn, E svy [π long ] E svy [y 1,long ] E svy [π +1 ] E svy [q +1 ] s E svy [y 1,+2 ] E svy [y 1,+4 ] = A y B y ζ π ζ r ζ 2 y ζ 4 y π r π q s ỹ 1, + ɛ m 1. ɛ m N ɛ π ɛ r ɛ y,2 ɛ y,4 (13) where m 1,..., m N denoes he mauriies of Treasury securiies included in esimaion, A y and B y he vecor and marix of he sacked corresponding a n and b n from (8), E svy [π long ] and E svy [y 1,long ] denoe he Blue Chip forecass of CPI inflaion and he 3-monh T bill yield a he longes horizon (he projeced average over he horizon roughly 7 o 11 years ahead), and E svy [y 1,+2 ] and E svy [y 1,+4 ] are he Blue Chip forecass of he 3-monh T bill yield 2 and 4 quarers ahead. The corresponding measuremen errors are denoed by ɛ. B The daa [To be compleed] The series of inflaion expecaions consiss of hree differen pieces. Unil 1981:Q1, he series is an esimaed sep funcion based on he changepoin model developed in Kozicki and Tinsley (21). From 1981:Q2 unil 1988:Q4, he series is based on he Hoey survey of bond marke paricipans, which was conduced on a quarerly basis by Richard Hoey, an economis a Drexel Burnham Lamber. Paricipans in his survey were polled for heir expecaion of CPI inflaion over he second five years of a 1-year horizon. From 1989:Q4 onwards he series is based on he expecaions for he average CPI inflaion rae roughly 7 o 11 years ahead from he Blue Chip Financial Forecass. Because he Financial Forecass poll respondens only wice a year for heir long-horizon forecass, we inerpolae he daa 22

24 o quarerly frequency. For he years from 1986 on, we use he long-horizon forecass of he 3-monh T bill yield from he Financial Forecass, and likewise inerpolae o quarerly frequency. Before 1986 no such long-horizon forecass are available, and we rea hem as missing observaions in he esimaion. C Idenificaion and esimaion of he VAR Following he noaion used in (4), le v denoe he vecor of reduced-form residuals, and ε he vecor of srucural innovaions of which we seek o idenify several elemens. As saed in he main ex, we assume ha he asympoe of inflaion π and of he one-period real rae r follow univariae random walks wih innovaions ε π and ε r. We are ineresed in idenifying he srucural shocks o oal Treasury supply, including privaely-held Treasuries, and hose o Treasury holdings by he SOMA and foreign official insiuions. Following Blanchard and Peroi (22), we assume ha fiscal policy canno respond conemporaneously o macroeconomic developmens excep by he auomaic sabilizers embedded in he ax and spending policies in place. Hence, he reduced-form innovaions o oal Treasury supply are composed of a response o curren shocks o economic aciviy q and inflaion π as implied by he auomaic sabilizers, and any exogenous fiscal policy shocks ha are unrelaed o curren macroeconomic condiions. Noe in paricular ha oal Treasury supply is assumed o be conemporaneously unaffeced by moneary policy, be ha SOMA asse holdings or he one-period ineres rae (where we follow he convenion of assuming no conemporaneous response of real aciviy and inflaion o innovaions o y 1, ). Wih hese assumpions, he conemporaneous relaionship beween he reduced-form innovaions v, v q, and vπ o Treasury supply, real aciviy, and inflaion respecively, and he srucural fiscal (Treasury supply) shock ε is v = η,π v π + η,q v q + ε where he coefficiens η,x can be consruced as η,x = η τ,x η g,x from he underlying calibraed parameers in he equaions for log real axes τ and log real spending g v τ = η τ,π v π + η τ,q v q + ετ v g = η g,π v π + η g,q v q + εg 23

25 Consrucing he coefficiens η,π and η,q in he manner of Blanchard and Peroi (22) is criical because inflaion and real aciviy are assumed o be conemporaneously affeced by fiscal policy and hence by ε. By conras, SOMA (and foreign official) Treasury holdings f are also assumed o respond conemporaneously o real aciviy and inflaion, whereas hey are no assumed o affec real aciviy and inflaion, in analogy o he convenional assumpion in he lieraure ha moneary policy shocks (in he form of srucural shocks o he shor-erm ineres rae) do no affec hese variables conemporaneously. The relaionships beween he reducedform residuals v and he srucural innovaions ε can hus be wrien as v = ηε wih v π v r v π v q v v s v y = 1 1?? 1???? 1??? η,π η,q 1???? 1?????? 1 ε π ε r ε π ε q ε ε s ε y (14) The parameers η,π and η,q are calibraed based on he values for hese parameers repored in Peroi (24). The parameers denoed wih? are esimaed by insrumenal variables. Specifically, he srucural residuals ε π and ε r are simply he firs differences of he series π and r ; he unknown parameers in he hird row of he marix are esimaed by regressing v π on ε π, ε r, and v,, using ε as insrumen ec. 24