Federal Reserve Bank of Chicago

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1 Federal Reserve Bank of Chicago Escaping he Grea Recession Francesco Bianchi and Leonardo Melosi January 2014 WP

2 Escaping he Grea Recession Francesco Bianchi Cornell Universiy Duke Universiy CEPR and NBER Leonardo Melosi FRB of Chicago This draf: January 2014 Firs draf: Augus 2012 Absrac While high uncerainy is an inheren implicaion of he economy enering he zero lower bound, deflaion is no, because agens are likely o be uncerain abou he way policymakers will deal wih he large sock of deb arising from a severe recession. We draw his conclusion based on a new-keynesian model in which he moneary/fiscal policy mix can change over ime and zero-lower-bound episodes are recurren. Given ha policymakers behavior is consrained a he zero lower bound, beliefs abou he exi sraegy play a key role. Announcing a period of auseriy is derimenal in he shor run, bu i preserves macroeconomic sabiliy in he long run. A large recession can be avoided by abandoning fiscal discipline, bu his resuls in a sharp increase in macroeconomic insabiliy once he economy is ou of he recession. Conradicory announcemens by he fiscal and moneary auhoriies can lead o high inflaion and large oupu losses. The policy rade-off can be resolved by commiing o inflae away only he porion of deb resuling from an unusually large recession. We are graeful o Gadi Barlevy, Dario Caldara, Jeff Campbell, Gaui Eggersson, Mary Eichenbaum, Marin Ellison, Jesus Fernandez-Villaverde, Jonas Fisher, Alejandro Jusiniano, Chrisian Mahes, Maurice Obsfeld, Giorgio Primiceri, Ricardo Reis, David Romer, Chris Sims, Marin Uribe, Mike Woodford, as well as all seminar paricipans a he NBER Summer Insiue, SITE-Sanford Universiy, Norhwesern Universiy, NY Fed, Chicago Fed, SED Annual Meeing, Cornell Universiy, Universiy of Wisconsin-Madison, Cleveland Fed, UPF, ECB, ESSIM Tarragona, Goehe Universiy, Bonn Universiy, Bank of England, UC Irvine, and he Universiy of Briish Columbia for useful commens and suggesions. The views in his paper are solely he responsibiliy of he auhors and should no be inerpreed as reflecing he views of he Federal Reserve Bank of Chicago or any oher person associaed wih he Federal Reserve Sysem. Correspondence: Francesco Bianchi, francesco.bianchi@duke.edu, Leonardo Melosi, lmelosi@frbchi.org. 1

3 JEL Codes: E31, E52, E62, E63, D83 Keywords: Policy uncerainy, macroeconomic uncerainy, Markov-swiching models, shockspecific policy rules, zero lower bound. 2

4 1 Inroducion The recen financial crisis and he recession ha followed led o an increase in macroeconomic uncerainy (Jurado, Ludvigson, and Ng 2013) and o a subsanial change in he conduc of moneary policy, wih ineres raes suck a he zero lower bound for he pas four years. While in a new-keynesian framework he zero lower bound is associaed wih deflaion, inflaion in he daa has remained remarkably close o is arge value. Following Hall s Presidenial Address o he American Economic Associaion, some researchers have labeled his observaion he "Bob Hall s puzzle" (Hall 2011). A he same ime, he crisis has riggered a widespread policy debae abou he bes way o miigae he consequences of a deep recession once moneary policy is consrained by he zero lower bound. While his debae is animaed by a wide specrum of opinions, here seem o be wo popular polar views. The firs one advocaes a disconinuiy wih respec o he policies of he pas, calling for a robus fiscal inervenion, perhaps associaed wih a reducion on he focus on inflaion sabilizaion. The second one srongly opposes he idea of explicily abandoning policies ha have arguably led o a sable macroeconomic environmen since he Volcker disinflaion. As a resul of his debae, policy uncerainy is a hisorical maxima (Baker, Bloom, and Davis 2011). In his paper, we will show ha policy uncerainy can accoun for boh he absence of deflaion and he increase in macroeconomic uncerainy. We consruc a dynamic general equilibrium model ha capures he policy rade-off ha seems o characerize he curren economic environmen: choosing beween miigaing a large recession and preserving a repuaion for fiscal discipline. In he model, when he zero lower bound is no binding, policymakers behavior is characerized by wo very disinc policy combinaions. Under he Moneary led policy mix, he fiscal auhoriy moves primary surpluses in response o flucuaions in he raio of public deb o gross domesic produc (GDP), while he cenral bank reacs srongly o deviaions of inflaion from is arge. If agens expec his regime o prevail for a long ime, any fiscal imbalance is backed by fuure fiscal adjusmens and repuaion for fiscal discipline is srong. Under he Fiscally led policy mix, he fiscal auhoriy does no reac srongly enough o deb flucuaions and he cenral bank disregards he Taylor principle. In his second case, agens undersand ha policymakers are unlikely o implemen he fiscal adjusmens necessary o preserve deb sabiliy. 1 Periodically, a large swing in preferences induces agens o subsanially reduce consumpion. In his case, a sandard Taylor rule would imply a negaive nominal ineres rae. This forces policymakers ino a zero lower bound regime in which he federal funds rae is resriced o zero and he fiscal auhoriy disregards he level of deb in an aemp o miigae he resuling deep recession. As in Krugman (1998), Eggersson and Woodford (2003), and Chrisiano, Eichenbaum, and Rebelo (2011), he real 1 In he language of Leeper (1991) he Moneary led regime corresponds o Acive Moneary policy and Passive Fiscal policy, whereas he Fiscally led regime is associaed wih Passive Moneary policy and Acive Fiscal policy. 3

5 ineres rae is now oo high wih respec o wha would be desirable. Policymakers would hen find i beneficial o induce a jump in inflaion expecaions in order o cause a drop in real ineres raes and push he economy ou of he recession. We firs poin ou ha when he possibiliy of enering he zero lower bound is ruled ou, he Moneary led regime is preferable o he Fiscally led regime because he former leads o a more sable macroeconomic environmen. When policymakers are expeced o follow he Moneary led rule for many periods ahead, all he shocks ha hi he deb-o-gdp raio are neuralized by he fiscal auhoriy and he economy is herefore insulaed wih respec o fiscal disurbances. However, if he Fiscally led regime is expeced o be in place mos of he ime, agens realize ha inflaion, no axaion, will be used o keep deb on a sable pah. Therefore, all he fiscal imbalances ha are sysemaically neuralized under he Moneary led regime will now affec inflaion. In he presence of nominal rigidiies, inflaion volailiy ranslaes ino oupu volailiy, resuling in a more uncerain macroeconomic environmen. We hen show ha while high uncerainy is an inheren implicaion of he economy enering he zero lower bound, deflaion is no. This is because agens are likely o be uncerain abou he way policymakers will deal wih he large sock of deb arising from a severe recession. Given ha a he zero lower bound policymakers behavior is in fac consrained, agens beliefs abou policymakers behavior once he economy is ou of he zero lower bound play a key role in deermining macroeconomic oucomes a he zero lower bound. We model his idea by inroducing a series of regimes ha are characerized by he same policy rules bu ha differ in erms of he exi sraegy. If policymakers announce ha as he economy exis he zero lower bound, a prolonged period of fiscal discipline will follow, inflaion expecaions drop, leading o deflaion and a severe recession. Therefore, while he Moneary led policy mix is desirable during regular imes, i can be derimenal a he zero lower bound. If insead policymakers announce a prolonged deviaion from he Moneary led policy mix, inflaion immediaely increases because agens expec ha deb will be inflaed away. This, in urn, leads o a drop in he real ineres rae ha pushes he economy ou of he recession. However, announcing a swich o he Fiscally led policy mix also resuls in an increase in macroeconomic volailiy once he economy is ou of he zero lower bound. The wo resuls go ogeher. The announcemen is effecive if and only if i is able o convince agens ha he Fiscally led policy mix will prevail for a long ime. As explained earlier, in his siuaion he macroeconomy is no insulaed anymore wih respec o fiscal disurbances. Finally, if policymakers do no make any explici announcemens abou he way hey will deal wih an increasing sock of deb once he economy will be ou of he zero lower bound, agens are likely o form expecaions ha ake ino accoun all possible alernaive scenarios. In his case, he model is able o raionalize why, despie he ime spen a he zero lower 4

6 bound, we have no observed deflaion in he Unied Saes. Therefore, if deflaion occurs or no a he zero lower bound depends on which exi sraegy agens regard o be he mos likely. A he same ime, across all he cases described before, shor-run macroeconomic uncerainy urns ou o be high. If agens expec a reurn o he Moneary led regime, uncerainy is high because boh inflaion and real economic aciviy are far from where hey will be once ou of he recession. Given ha he iming of he end of he recession is unknown, he possibiliy of a large swing in real aciviy creaes uncerainy. If insead he Fiscally led regime is expeced o follow he recession, inflaion and oupu move closer o heir respecive seady saes, bu agens come o realize ha all shocks ha are neuralized under he Moneary led regime will now be inflaed away, again causing an increase in macroeconomic uncerainy. These resuls square well wih recen conribuions by Baker, Bloom, and Davis (2011), ha show ha policy uncerainy has increased since he beginning of he recession, Kisul and Wrigh (2013), ha poin ou ha markes seem o swing beween fear of inflaion and fear of deflaion, and Jurado, Ludvigson, and Ng (2013) and Bloom, Floeoo, Jaimovich, Sapora-Eksen, and Terry (2012) ha documen an overall increase in macroeconomic uncerainy during he recen recession. While shor-run uncerainy is high in boh cases, he wo scenarios differ in erms of he consequences for long-run uncerainy. If he Moneary led regime is expeced o prevail, long-run uncerainy remains anchored because, in he long run, agens expec o be ou of he recession and back o a sable macroeconomic environmen. If he Fiscally led regime is announced insead, agens expec he volaile macroeconomic environmen o prevail for a long ime. Finally, if no announcemen is made and agens aach similar probabiliies o he wo scenarios described before, uncerainy increases a all horizons. Policy uncerainy can also resul in perverse oucomes if i reflecs a lack of coordinaion beween he fiscal and moneary auhoriies. For example, he moneary auhoriy migh insis ha once he economy is ou he zero lower bound, inflaion sabiliy will be preserved, while he fiscal auhoriy, in an aemp o simulae privae expendiure, migh implicily announce ha no increase in axaion will follow he crisis. These wo saemens are conradicory, as he cenral bank canno sabilize inflaion wihou fiscal backing, and can lead o explosive dynamics for deb and inflaion. Therefore, if agens expec ha he crisis will be followed by a period during which he cenral bank ries o regain conrol of inflaion wihou he suppor of he fiscal auhoriy, high inflaion and low growh could arise. To undersand why, suppose ha inflaion is above arge and he cenral bank reacs more han one-o-one o he deviaion. The cenral bank is able o induce a recession ha, ogeher wih he increase in real ineres raes, leads o an increase in he deb-o-gdp raio. If agens expec ha he fiscal auhoriy will evenually prevail, his expecaion causes an increase in he amoun of deb ha will have o be inflaed away, and inflaion expecaions go up. As a resul, inflaion increases raher han decreases. The expecaion ha hese inflaionary and conracionary spirals will prevail once 5

7 he economy is ou of he zero lower bound can hen compleely jeopardize he effeciveness of any aemp made by he wo auhoriies o simulae he economy a he zero lower bound. In summary, a policy rade-off arises he momen ha a large negaive preference shock pushes moneary policy o he zero lower bound. The fac ha he Moneary led regime resuls in a more sable macroeconomic environmen in he long run provides suppor o hose who are relucan o explicily abandon he policies ha prevailed from he Volcker disinflaion o he curren crisis. Ye, he possibiliy of miigaing he recession by moving o he Fiscally led regime can explain why some policymakers and economiss have suggesed disconinuiy wih respec o he pas. Finally, failure o resolve his laen conflic beween shor-run and long-run goals by policymakers could lead o perverse oucomes. I is hen naural o ask if i is possible o go beyond hese wo polar views. In oher words, i would be ineresing o see if i is possible o escape he Grea Recession by generaing an increase in inflaion expecaions via he fiscal mechanism oulined in his paper and a he same ime preserve long-run macroeconomic sabiliy. We show ha in fac a way ou exiss: Policymakers could commi o inflae away only he porion of deb resuling from he excepionally large recession. 2 This shock specific rule provides a sor of auomaic sabilizer: The large negaive preference shock can lead o a deep recession and a corresponding large increase in he deb-o-gdp raio. The expecaion ha his exra fiscal burden is going o be inflaed away deermines a drop in he real ineres rae ha simulaes demand, reducing he size of he oupu conracion and he amoun of deb ha needs o be inflaed away. This mechanism can be srong enough o preven he economy from hiing he zero lower bound. Furhermore, given ha he recession is now largely miigaed, he resuling increase in he deb-o-gdp raio is small and so is he increase in inflaion necessary o sabilize i. A he same ime, policymakers never changed heir behavior wih respec o he pre-crisis sock of deb and in response o oher exogenous business cycle disurbances ha are unlikely o push he economy o he zero lower bound. This has wo very imporan consequences. Firs, he level of deb ha exised before he crisis is irrelevan for he amoun of inflaion ha is generaed because i is sill backed by fuure fiscal adjusmens. Second, agens expec ha all fuure fiscal imbalances will sill be aken care of by he fiscal auhoriy. Therefore, he proposed policy is successful in miigaing he recession and preserving long-run sabiliy. This paper is organized as follows. Secion 2 reviews he relaed lieraure. Secion 3 presens he model. Secion 4 illusraes ha he Moneary led regime leads o a sable macroeconomic environmen. Secion 5 shows ha policy uncerainy can accoun for he lack of deflaion and high macroeconomic uncerainy. Secion 6 proposes he shock-specific policy response. Secion 7 concludes. 2 This policy has been advocaed by Krugman (2013) and Rogoff (2008) among several ohers. 6

8 2 Relaed Lieraure Our work is relaed o he vas heoreical lieraure on he zero lower bound. Wolman (1998), Fuhrer and Madigan (1994), Krugman (1998), and Orphanides and Wieland (1998, 2000) are among he firs o sudy he zero lower bound and moneary policy in an ineremporal framework. Eggersson and Woodford (2003) show ha opimal moneary policy a he zero lower bound involves a commimen o generae fuure inflaion. Eggersson (2006) argues ha such a policy can suffer from a ime-inconsisency problem, while Eggersson (2008), using a model in which axaion is cosly, shows ha Presiden Franklin Delano Roosevel was able o make he promise of fuure inflaion credible by expanding fiscal deficis. Benhabib, Schmi-Grohe, and Uribe (2001b) show ha acive moneary policy rules can lead o a liquidiy rap, while Benhabib, Schmi-Grohe, and Uribe (2002) explain how fiscal and moneary policies can be designed in order o rule ou deflaionary spirals. Correia, Farhi, Nicolini, and Teles (2012) show how disorionary axes can be used o replicae he effecs of negaive nominal ineres raes and compleely circumven he zero bound problem. Werning (2012) works in a deerminisic environmen and shows ha he effeciveness of policies a he zero lower bound crucially depends on wha agens expec afer he consrain is no binding anymore. Fernandez-Villaverde, Guerron-Quinana, and Rubio-Ramirez (2011) show how supply-side policies may play a role in prevening an economy from hiing he zero lower bound. Schmi-Grohe and Uribe (2012) presen a model ha can accoun for a recession associaed wih a proraced liquidiy rap and a jobless recovery. Our work differs from each of hese papers in one or more of he following dimensions. Firs, we invesigae he effecs of policy uncerainy a he zero lower bound on macroeconomic uncerainy. In his respec, he paper is relaed o he lieraure on he macroeconomic effecs of uncerainy (e.g., Bloom 2009; Fernandez-Villaverde, Guerron-Quinana, Rubio-Ramirez, and Marin Uribe 2011; Fernandez-Villaverde, Kueser, Guerron-Quinana, and Rubio-Ramirez 2011; Gilchris, Sim, and Zakrajsek 2012; Williams 2012; and Basu and Bundick 2012). Second, we work in a sochasic environmen (no perfec foresigh/deerminisic) wih a sandard new-keynesian model augmened wih a fiscal block. This makes our framework suiable for a quaniaive assessmen of he differen exi sraegies. Third, zero lower bound episodes are recurren, and agens ake his ino accoun when forming expecaions. In conras, he lieraure generally considers siuaions in which he economy is currenly a he zero lower bound and i will never be here again. Moreover, our paper proposes an alernaive way for modeling recurren zero-lower-bound evens in microfounded dynamic sochasic general equilibrium (DSGE) models o hose of Gus, Lopez-Salido, and Smih (2013) and Aruoba and Schorfheide (2013), and is relaed o he growing lieraure ha allows for parameer insabiliy in DSGE models (Jusiniano and Primiceri 2008). Finally, our resuls are based on he possibiliy of 7

9 generaing an increase in inflaion expecaions hrough a change in he moneary/fiscal policy combinaion and do no require he use of disorionary axaion. Oher papers have addressed Bob Hall s puzzle (Ball and Mazumder 2011; King and Wason 2011; and Del Negro, Giannoni, and Schorfheide 2013). Unlike hose conribuions, his paper focuses on he consequences of uncerainy abou fuure policymakers behavior, showing ha policy uncerainy in an oherwise sandard New Keynesian model accouns for boh he lack of deflaion and he high uncerainy observed a he zero lower bound. Our choice of working wih regimes gives us he possibiliy of capuring he consequences of policy uncerainy and o compare differen scenarios. Oher auhors have approached he problem of he zero lower bound from a differen angle, i.e., by solving for opimal policies. While such an approach has provided he heoreical foundaions of our undersanding of he zero lower bound, i does no leave space for comparaive analysis or he possibiliy of allowing for policy uncerainy in he momen ha one opimal policy emerges. Accouning for policy uncerainy is imporan in ligh of a growing lieraure ha argues ha here were in fac changes in policymakers behavior over he pas 60 years (Clarida, Gali, and Gerler 2000; Lubik and Schorfheide 2004; Davig and Doh 2013; Fernandez-Villaverde, Guerron-Quinana and Rubio-Ramirez 2010; and Bianchi 2013). Finally, since he seminal conribuion of Sims and Zha (2006), regimes have become a popular way o hink abou changes in policymakers behavior in applied work. This paper is relaed o a research agenda ha aims o undersand he role of fiscal policy in explaining changes in he reduced form properies of he macroeconomy. Using a Markovswiching DSGE model, Bianchi and Ilu (2012) show ha he rise and fall of US inflaion can be explained in ligh of a change in he moneary/fiscal policy mix ha occurred a few years afer he appoinmen of Paul Volcker as Federal Reserve Chairman. Bianchi and Melosi (2013) inroduce he noion of dorman shocks, showing ha a fiscal imbalance can lead o an increase in inflaion many years afer i occurred. This paper differs from he wo aforemenioned conribuions across several dimensions. Firs, we here allow for he zero lower bound and sudy he consequences of policy uncerainy. Second, we ouline ha a he zero lower bound a policy rade-off beween miigaing a large recession and preserving long run macroeconomic sabiliy emerges. Finally, we show how policymakers can resolve his rade-off using a shockspecific rule. Our work is hen relaed o he sudy of he ineracion beween fiscal and moneary policies in deermining inflaion dynamics (Sargen and Wallace 1981; Leeper 1991; Sims 1994; Woodford 1994, 1995, 2001; Schmi-Grohe and Uribe 2000; Cochrane 1998, 2001; among many ohers) and o he vas lieraure on fiscal mulipliers (Blanchard and Peroi 2002; Mounford and Uhlig 2009; Uhlig 2010; Romer and Romer 2010; Merens and Ravn 2011, 2013; Leeper, Walker, and Yang 2013; Misra and Surico 2013). Merens and Ravn (2010) and Drauzburg 8

10 and Uhlig (2011) use a DSGE model o sudy he fiscal muliplier when ineres raes are suck a he zero bound. Coibion, Gorodnichenko, and Wieland (2012) sudy he opimal inflaion arge in a new-keynesian model in which he policy rae occasionally ges consrained by he zero lower bound. 3 The Model We exend he basic new-keynesian model employed by Clarida, Gali, and Gerler (2000), Woodford (2003), Gali (2008), and Lubik and Schorfheide (2004) o include a fiscal rule and he possibiliy of recurren zero lower bound episodes. 3.1 A New-Keynesian model The economy consiss of a coninuum of monopolisic firms, a represenaive household, and a moneary policy auhoriy (or cenral bank). The household derives uiliy from consumpion C and disuiliy from labor h : [ E 0 =0 β exp (d ) [log (C ) h ] ], (1) where β is he household s discoun facor and he preference shock d = d ξ d can assume wo values: high or low (d h or d l ). The variable ξ d conrols he regime in place and evolves according o he ransiion marix H d : [ ] H d = p hh 1 p ll 1 p hh p ll, where p ji = P ( ξ d +1 = j ξ d = i ). This specificaion is in he spiri of Chrisiano, Eichenbaum, and Rebelo (2011). However, in he curren seup shocks o preferences are assumed o be recurren, and agens ake ino accoun ha hese episodes can lead o unusual policymakers responses, as discussed laer on. The household budge consrain is given by: P C + B + P T = P W h + R 1 B 1 + P D, (2) where B represens bond holdings, D capures dividends paid by firms, W is he real wage, T is a ne lump sum ax, P is he price level, and R is he one-period gross ineres rae. Each of he monopolisically compeiive firms faces a downward-sloping demand curve: Y (j) = (P (j)/p ) 1/υ Y, (3) where P (j) is he price chosen by firm j and he parameer 1/υ is he elasiciy of subsiuion 9

11 beween wo differeniaed goods. The firms ake as given he general price level P and level of real aciviy Y. Whenever a firm wans o change is price, i faces quadraic adjusmen coss represened by an oupu loss: AC (j) = (ϕ/2) (P (j)/p 1 (j) Π) 2 Y (j), (4) where Π is he deerminisic seady-sae level for gross inflaion. The firm chooses he price P (j) o maximize he presen value of fuure profis: E 0 [ =0 Q (P (j)y (j)/p W h (j) AC (j))], where Q is he household s sochasic discoun facor. Labor is he only inpu in a linear producion funcion, Y (j) = A h (j), where oal facor produciviy z = ln (A /A) follows an auoregressive process: z = ρ z z 1 + σ z ɛ z,, ɛ z, N (0, 1). The cenral bank follows he rule: R ( ) ( R = R 1 1 Z ξ d R ) ρr [ (Π Π ) ψπ,ξ p ( Y Y n ) ψy ] (1 ρr ) e σ Rɛ R, + Z ξ d R where ɛ R, N (0, 1), R is he seady-sae gross nominal ineres rae, Y n is naural oupu, he level of oupu ha would prevails in absence of nominal rigidiies, Π is he arge/seady-sae level for gross inflaion, he variable ξ p capures he moneary/fiscal policy combinaion ha is in place a ime, and he dummy variable Z ξ d conrols if he economy is in or ou of he zero lower bound. When d ξ d = d h, he economy is ou of he zero lower bound and moneary and fiscal policies are no consrained (Z ξ d = 0). In his case he evoluion of he policy mix can be described by he wo-regime Markov swiching process ξ p. The properies of he ransiion marix and of he regimes will be described laer. When d ξ d = d l, he zero lower bound is binding, given ha a sandard Taylor rule would require a negaive nominal ineres. 3 In his case, policymakers abandon he policy mix ha hey were following and se he ne nominal ineres rae o zero (Z ξ d = 1). The governmen budge consrain is given by: b = b 1 (Y Π /Y 1 ) 1 R 1 s, 3 We assume ha whenever he negaive preference shock his, policymakers move o he zero-lower-bound regime described laer on and we choose he parameers values in a way ha he zero lower bound is binding wih high probabiliy when d ξ d = d l. Our approach o model he zero lower bound differs from he convenional one (e.g., see Eggersson and Woodford 2003; Benhabib, Schmi-Grohe, and Uribe 2002 ), which implies R = max (0, R ), where R is he ineres rae implied by he Taylor rule. While our approach canno rule ou ha here exis some unlikely saes of he world in which he nominal rae R assumes negaive values, i has he advanage of making he model racable and allows us o sudy he consequences of policy uncerainy. 10

12 where b = B / (P Y ) and s = S / (P Y ) are he deb-o-gdp raio and he primary-surpluso-gdp raio, respecively. We assume ha he governmen only moves lump-sum axes and provides a subsidy. In oher words, we exclude governmen purchases and we assume ha he primary surplus coincides wih ne lump-sum axes (T = S ). This will allow us o compleely isolae he effecs of fiscal shocks deriving from he lack of fiscal discipline. Inroducing governmen purchases (G ) would no modify he mechanism oulined here, bu would make he inerpreaion of he resuls less immediae. The fiscal auhoriy moves he primary surplus according he following rule (s s) = δ b,ξ p (b 1 b) + δ y (y y n ) + x, (5) x = ρ x x 1 + σ x ɛ x,, ɛ x, N (0, 1), (6) where y = ln (Y ) and y n = ln (Y n ). We will refer o ɛ x, as a fiscal shock. Noice ha he parameer conrolling he response of primary surpluses o deb, δ b,ξ p, is also indexed wih respec o ξ p. 3.2 Linearizaion The model is solved and linearized around he deerminisic seady sae. We firs compue he ergodic mean d for he preference shock and verify ha he zero lower bound does no bind in his case. We hen compue he seady sae associaed wih his value and linearize around i. From now on, all variables should be inerpreed as deviaions from seady sae. 4 The privae secor can be described by he following sysem of equaions: π = βe ( π +1 ) + κ(ỹ z ), (7) ( ) ỹ = E (ỹ +1 ) R E (ỹ +1 ) + d ( ) E d+1, (8) d = d ξ d, (9) z = ρ z z 1 + σ z ɛ z,, ɛ z, N (0, 1), (10) where d = d d and d ξ d = d ξ d d. Inflaion dynamics are described by he expecaional Phillips curve (7) wih slope κ. Equaion (8) is he linearized ineremporal Euler equaion describing he households opimal choice of consumpion and bond holdings. The linearized governmen budge consrain is given by: ( ) b = β 1 b 1 + bβ 1 R 1 π ỹ s, (11) 4 We linearize wih respec o deb and primary surpluses, given ha hese variables can change sign, while we log-linearize wih respec o all he ohers. Appendix A.1 provides addiional deails on how we handle he Markov-swiching preference shock. 11

13 where b and s represen now deb and surplus in erms of GDP in linear deviaions from he seady sae. The fiscal policy mix is given by: s = δ b,ξ p b 1 + δ y (ỹ z ) + x, (12) x = ρ x x 1 + σ x ɛ x,, ɛ x, N (0, 1), (13) while he linearized moneary policy policy mix is: R = ] [ ( ) ] [1 Z ξ ρ d R R 1 + (1 ρ R ) ψ π,ξ p π + ψ y [ỹ z ] + σ R ɛ R, Z ξ d log (R), (14) where ɛ R, N (0, 1). Therefore, ( ) R = ρ R R 1 + (1 ρ R ) ψ π,ξ p π + ψ y [ỹ z ] + σ R ɛ R,, (15) if he economy is ou of he zero lower bound (Z ξ d bound binds (Z ξ d = 1). = 0), while R = log (R) if he zero lower 3.3 Regime changes To characerize policymakers behavior ou of he zero lower bound, we will make use of he pariion of he parameer space inroduced by Leeper (1991). We can disinguish four regions (Table 1) based on he properies of he model under fixed coeffi ciens. When he values of model parameers are fixed, he wo policy rules are key in deermining he exisence and uniqueness of a soluion. There are wo deerminacy regions. The firs region, Acive Moneary/Passive Fiscal (AM/PF), is he mos familiar one: The Taylor principle is saisfied and he fiscal auhoriy moves axes in order o keep deb on a sable pah: ψ π > 1 and δ b > β 1 1. To grasp he inuiion behind his resul, subsiue he ax rule in he law of moion for governmen deb (assuming for simpliciy ρ x = 0 = δ y ) and isolae he resuling coeffi cien for lagged governmen deb: b = ( ( ) β 1 δ b ) b 1 + bβ 1 R 1 π ỹ σ s ɛ s,, Inuiively, in order o guaranee sabiliy of governmen deb, we need his coeffi cien o be smaller han one (β 1 δ b < 1), so ha deb is mean revering. This in urn requires he coeffi cien on deb in he ax rule o saisfy he condiion δ b > β 1 1. Therefore, we can hink of fiscal policy as passive o he exen ha i passively accommodaes he behavior of he moneary auhoriy ensuring deb sabiliy. We will refer o his policy combinaion as Moneary led regime. 12

14 Acive Fiscal (AF) Passive Fiscal (PF) Acive Moneary (AM) No Soluion Deerminacy Passive Moneary (PM) Deerminacy Indeerminacy Table 1: Pariion of he parameer space according o exisence and uniqueness of a soluion (Leeper 1991). The second deerminacy region, Passive Moneary/Acive Fiscal (PM/AF), is less familiar and corresponds o he case in which he fiscal auhoriy is no commied o sabilizing he process for deb: δ b < β 1 1. Now i is he moneary auhoriy ha passively accommodaes he behavior of he fiscal auhoriy, disregarding he Taylor principle and allowing inflaion o move in order o sabilize he process for deb: ψ π < 1. Under his regime, even in he absence of disorionary axaion, shocks o ne axes can have an impac on he macroeconomy as agens undersand ha hey will no be followed by fuure offseing changes in he fiscal variables. We will label his policy combinaion as Fiscally led regime. Finally, when boh auhoriies are acive (AM/AF) no saionary equilibrium exiss, whereas when boh of hem are passive (PM/PF) he economy is subjec o muliple equilibria. 5 In he benchmark model, when he preference shock is high (ξ d = h), he economy is ou of he zero lower bound (Z ξ d = 0) and he evoluion of policymakers behavior is capured by a wo-regime Markov chain ha evolves according o he ransiion marix H p : H p = [ p MM 1 p F F 1 p MM p F F where p ji = P ( ξ p +1 = j ξ p = i ). This ransiion marix is supposed o capure he sochasic oucome of a game beween he moneary and fiscal auhoriies ha is no explicily modeled in his paper. Regime M is he Moneary led regime, under which he Taylor principle is saisfied and fiscal policy accommodaes he behavior of he moneary auhoriy. ], In erms of policy parameers, his implies ha ψ π,m = ψ A π > 1 and δ b,m = δ P b > β 1 1. Regime F is he Fiscally led regime. Under such a regime, he cenral bank reacs less han one-forone o inflaion and he fiscal auhoriy does no move surpluses in response o movemens in governmen deb: ψ π,f = ψ P π < 1 and δ b,f = δ A b < β 1 1. When he low value for he preference shock occurs (ξ d = l), he zero lower bound becomes binding (Z ξ d = 1), and policymakers behavior is now consrained. In his hird policy combinaion he nominal ineres rae is se o zero and he fiscal auhoriy disregards he level of deb: δ Z = 0. Noice ha he zero-lower-bound policy mix can be considered as an exreme version of he Fiscally led policy mix. However, while ou of he zero lower bound, swiches 5 Benhabib, Schmi-Grohe, and Uribe (2001a) show ha if money is assumed o ener or no preferences and echnology maers for wheher a paricular moneary/fiscal regime is conducive o deerminacy. Our seing is sandard in his respec and Leeper s (1991) pariion applies. 13

15 Parameer Value Parameer Value Parameer Value ψ π,m 2.00 ψ y σ R 0.20 ψ π,f 0.80 ρ R σ x 0.50 δ b,m 0.03 δ y σ z 0.70 δ b,f, δ b,z 0.00 ρ z 0.90 d h 0 Z h 0 ρ x 0.90 d l.1 Z l 1 b 1.00 p hh 98% p MM 99% κ p ll 80% p F F 99% β Table 2: Parameer choices of he DSGE parameers and of he ransiion marix elemens. o he Fiscally led regime capure deliberae choices of policymakers, he adopion of he zerolower-bound regime is induced by an exogenous negaive preference shock ha promps he fiscal auhoriy o forgo fiscal adjusmens o couner he effecs of a deep recession. Once he preference shock is back o is high value (ξ d = h), policymakers behavior is no consrained anymore. I is worh emphasizing ha even if he zero lower bound imposes a consrain on policymakers behavior, agens beliefs are no consrained. Therefore, announcemens abou he exi sraegy and policy uncerainy are going o be key o undersand wha occurs a he zero lower bound. To capure his feaure, he effecive number of regimes a he zero lower bound needs o be expanded in order o reflec agens beliefs abou policymakers fuure behavior. For example, if we wan o model an economy in which from he zero lower bound policymakers can decide o move o eiher he Fiscally led regime or he Moneary led regime, we need o inroduce wo zero-lower-bound regimes ha simply differ in erms of wha he announced exi sraegy is. Therefore, for each of he zero-lower-bound regimes we will have o specify he enering probabiliy, he probabiliy of moving o anoher zero-lower-bound regime, and policymakers exi sraegy. We assume ha hese are capured by he marices H i, H z, and H o, where i, z, and o sand for in, a he zero lower bound, and ou of he zero lower bound, respecively. Laer on we will see ha differen exi sraegies can subsanially change he dynamics of he model. In summary, he evoluion of policymakers behavior can be described by a ransiion marix obained by combining he ransiion marix H d, which describes he evoluion of he preference shock; he ransiion marix H p, which describes policymakers behavior ou of he zero lower bound; he marix H i, which describes he probabiliy of enering each of he zero-lower-bound regimes; he marix H z, which describes he probabiliy of moving across he zero-lower-bound regimes; and he marix H o, which describes he exi sraegy for each of he zero-lower-bound 14

16 regimes: H = [ p hh H p (1 p ll ) H o (1 p hh ) H i p ll H z ]. For each of he models considered in his paper, Appendix A.2 repors he corresponding choice for he marix H. The oher parameer values for he model are chosen in line wih he esimaes obained by Bianchi and Ilu (2012) and are repored in Table 2. 6 In our benchmark model, moneary and fiscal policies move ogeher. Our seup can easily accommodae cases in which only one of he wo auhoriies changes behavior. We will consider some of hese cases in Secion 5. The model can be solved wih any of he soluion mehods developed for Markov swiching DSGE models. We use he soluion mehod of Farmer, Waggoner, and Zha (2009). I is worh emphasizing ha in our model, agens form expecaions while aking ino accoun he possibiliy of enering he zero lower bound. Furhermore, hey undersand ha enering he zero lower bound is an even induced by an exogenous shock ha can modify policymakers behavior even once he consrain sops binding. In oher words, our approach allows us o model recurren zero-lower-bound episodes and o capure he impac of differen exi sraegies for policymakers behavior a he zero lower bound. 4 No Zero-Lower-Bound Episodes In his secion, we show ha when he possibiliy of zero-lower-bound episodes is ruled ou, he Moneary led regime leads o a more sable macroeconomic environmen. The model parameers are as described in Table 2, wih he only excepion ha he preference shock is always assumed o be a he ergodic mean d. Laer on we will relax his assumpion in order o allow for recurren zero-lower-bound episodes. 4.1 Impulse responses and policymakers behavior In order o undersand he differences beween he Fiscally led and he Moneary led regimes, Figure 1 repors he impulse responses o a primary defici shock. Impulse responses are compued condiionally on one regime being in place over he enire horizon. Neverheless, model dynamics reflec he possibiliy of regime changes. When he Fiscally led regime is in place, agens undersand ha in he near fuure he probabiliy of a fiscal adjusmen in 6 For he sake of simpliciy, we assume ha under he zero-lower-bound policy mix and he Fiscally-led policy mix, policymakers compleely disregard movemens in he deb-o-gdp raio. This choice has he advanage of leading o sharp resuls, making he analysis ha will follow clearer. Our conclusions would be virually unchanged if we assumed ha he response o he deb-o-gdp raio is larger han zero bu sricly lower han he hreshold ( β 1 1 ). 15

17 2 Oupu GAP 7 Inflaion Moneary Led Fiscally Led FFR 30 B/GDP Figure 1: Impulse responses o a primary defici shock condiional on a regime being in place over he relevan horizon. response o he curren increase in he primary defici is fairly low. This deermines an increase in inflaion ha is made possible by he accommodaing behavior of he Moneary auhoriy. Given ha he Taylor principle does no hold, he response of he nominal ineres is less han one-o-one. The resuling decline in he real ineres deermines an increase in real aciviy. The deb-o-gdp raio is hen sabilized because of he fall in he real ineres rae and he faser growh in real economic aciviy. The macroeconomy is herefore no insulaed wih respec o fiscal imbalances even if axaion is non-disorionary. Under he Moneary led regime he primary defici shock riggers only a negligible increase in inflaion because he fiscal auhoriy is expeced o implemen he necessary fiscal adjusmens. However, he response of inflaion is no exacly zero because agens form expecaions by aking ino accoun he possibiliy of moving o he Fiscally led regime. As a resul, a high level of deb deermines some sligh inflaionary pressure even when he Moneary led regime is in place, in line wih he resuls obained by Bianchi and Ilu (2012) in an esimaed model, Davig and Leeper (2006) in a calibraed model, and Davig, Chung, and Leeper (2007) in an analyical example. Given ha he Taylor principle holds, he cenral bank reacs more han one o one o he increase in inflaion. The resul is a prolonged period of negaive oupu gaps ha las as long as he deb-o-gdp raio is no fully repaid. In summary, wo imporan lessons can be drawn from his exercise. Firs, under he Moneary led regime, he macroeconomy is largely insulaed wih respec o fiscal imbalances. Second, as long as agens are aware of regime changes, even under he Moneary led regime he macroeconomy is no compleely insulaed and fiscal imbalances have inflaionary pressure. This inflaionary pressure would disappear only if he Moneary led policy mix were he only possible one. 16

18 Sd Oupu GAP 8 6 Moneary Led Fiscally Led Inflaion Horizon Horizon Figure 2: Evoluion of uncerainy aking ino accoun he possibiliy of regime changes for differen saring regimes. 4.2 Uncerainy and policymakers behavior In his subsecion, we show ha he Moneary led regime leads o a more sable macroeconomic environmen. For each regime, Figure 2 repors he evoluion of uncerainy a differen horizons, from 1 quarer o 5 years. This measure of uncerainy is compued while aking ino accoun he possibiliy of regime changes and he occurrence of Gaussian shocks by using he mehods described in Bianchi (2013a). For a variable X and an horizon h, i corresponds o he condiional sandard deviaion sd (X +h ). When policymakers follow he Moneary led policy mix, agens anicipae ha wih high probabiliy fuure fiscal imbalances will be neuralized hrough he acions of he fiscal auhoriy. This leads o a reducion in macroeconomic uncerainy. A he same ime, he cenral bank behaves according o he Taylor principle, leading o a furher reducion in volailiy. If insead policymakers follow he Fiscally led regime, uncerainy increases a all horizons. This is because of wo reasons. Firs, he cenral bank reacs less aggressively o economic flucuaions given ha he Taylor principle is no saisfied. Second, agens anicipae ha all fiscal imbalances ha are largely neuralized when policymakers follow he Moneary led regime will now srongly affec inflaion and real economic aciviy. Inflaion, no axaion, will be mainly adjused o sabilize he pah for deb. In oher words, he macroeconomy is heavily affeced by fiscal imbalances when he policymakers adop a Fiscally led policy mix. As a resul, under his policy mix, uncerainy is higher a every horizon because agens expec all fuure fiscal imbalances o be largely inflaed away. The level of uncerainy under he Moneary led regime is higher han wha would be if he Moneary led regime were he only possible one. This is for wo reasons. Firs, as shown in he previous subsecion, he macroeconomy is no fully insulaed wih respec o fiscal imbalances because agens always discoun he possibiliy of a swich o he Fiscally led policy mix. This effec is presen a all horizons. Second, uncerainy is compued by aking ino accoun ha in he fuure he economy migh in fac swich o he Fiscally led policy mix. This effec is 17

19 increasing wih he ime horizon. In fac, as he horizon approaches o infiniy, he regime probabiliies converge o heir ergodic values and so does uncerainy. In summary, he model predics ha when zero-lower-bound episodes are ruled ou, he Moneary led regime is generally preferable because i leads o a sable macroeconomic environmen. We obain his resul because under he Moneary led regime he Taylor principle is saisfied and he macroeconomy is largely insulaed wih respec o fiscal imbalances. Furhermore, a furher reducion in macroeconomic uncerainy would occur if agens regarded he Moneary led regime as he only possible one, since he macroeconomy would be compleely insulaed wih respec o fiscal imbalances. To he exen ha macroeconomic sabiliy is desirable, counries wih a srong repuaion for fiscal discipline will benefi from a more favorable oucome during regular imes. 5 The Policy Trade-off While he Moneary led regime leads o a more sable macroeconomic environmen during regular imes, exraordinary evens can make deviaing from such a regime desirable. One of such evens is a significan drop in aggregae demand, which is induced by he discree preference shock d l. In his secion, we will firs review he sandard resul of he new-keynesian lieraure ha predics ha such a large conracion in aggregae demand should lead o deflaion as a resul of he nominal ineres rae hiing he zero lower bound. Then, we will provide a possible explanaion for why his predicion of he benchmark model does no seem o be in line wih US daa. Specifically, we will show ha if agens are uncerain abou how policymakers will deal wih he large sock of deb arising from a deep recession, deflaion is no a necessary implicaion of enering he zero lower bound, while high uncerainy is. This will also allow us o ouline he policy rade-off ha arises a he zero lower bound: miigaing he large recession or preserving long-run macroeconomic sabiliy. 5.1 A useful benchmark: The exbook new-keynesian model Consider he model described in Secion 3, assuming ha policymakers behavior is always characerized by he Moneary led regime. Suppose ha he economy is hi by he negaive preference shock (ξ d = l) a ime 10 and swiches back o he high value (ξ d = h) a ime 20. This preference shock deermines a large conracion in oupu as illusraed in Figure 3. In his siuaion he drop in he oupu gap and inflaion is so large ha he desired moneary policy ineres rae becomes negaive. This is exacly when he zero-lower-bound consrain becomes binding. The black dashed line in Figure 3 illusraes wha would happen if he cenral bank could se a negaive nominal ineres rae. Noice ha he conracion in oupu would 18

20 0 Oupu GAP 2 Inflaion FFR B/GDP Benchmark No ZLB consrain Figure 3: Benchmark new-keynesian model and he zero lower bound. This figure illusraes he behavior of an economy in which policymakers always follow he Moneary led regime. The blue solid line imposes he zero-lower-bound consrain, while he black dashed line does no. All Gaussian shocks (i.e., ɛ z,, ɛ x,, and ɛ R, ) are se o zeros a all imes in hese simulaions. The verical red doed lines indicae he period in which he economy is a he zero lower bound. be relaively small and here would be lile effec on inflaion and on he deb-o-gdp raio. Insead, he blue solid line imposes he zero-lower-bound consrain. 7 The fac ha in realiy he cenral bank canno se a negaive nominal ineres rae has pervasive consequences for he law of moion of he economy. Firs of all, he drop in he oupu gap is subsanially larger, because he implied real ineres rae is oo high. A he same ime, he economy experiences srong deflaion. Finally, a large sock of deb is accumulaed as a resul of he auomaic adjusmen of he primary surplus o economic condiions. I is worh poining ou ha agens compleely undersand he srucure of he economy. This implies ha while a he zero lower bound hey know ha here is a posiive probabiliy of exiing, bu hey do no know when his will occur. A he same ime, in our seup, agens are fully aware ha such a large negaive preference shock is a recurren even. Therefore, he model dynamics ou of he zero lower bound are also affeced. Agens realize ha in every period here is a (small) probabiliy of observing a large conracion in inflaion and real economic aciviy. This feaure deermines deflaionary pressures ou of he zero lower bound. Thus, as shown in Figure 3 inflaion is slighly lower han wha would arise if he zero-lowerbound consrain is no imposed. Given ha he Taylor principle is saisfied, he cenral bank ries o correc hese deflaionary pressures by keeping he ineres rae relaively lower. This correcive acion leads o a slighly posiive oupu gap. As a resul, he deb-o-gdp raio is 7 Technically, imposing he zero-lower-bound consrain boils down o assuming ha whenever he negaive preference shock is realized he moneary policy policy rule eners he zero-lower-bound regime (Z ξ p = 1). 19

21 slighly lower han wha is observed when he zero-lower-bound consrain is no imposed. 5.2 Uncerainy and announcemens In his subsecion, we will illusrae ha while uncerainy is an inheren implicaion of enering he zero lower bound, deflaion is no. This is because a deep recession leads o a large accumulaion of deb ha provides inflaionary pressure. Furhermore, as i will be shown here, he recession can be miigaed by inflaing away all or par of deb. As a resul, agens are going o be very uncerain abou policymakers behavior and, consequenly, fuure economic oucomes. In wha follows, we assume ha agens recognize ha he zero-lower-bound regime is riggered by an exogenous even over which policymakers have no conrol. In his siuaion, agens pay aenion o policy announcemens o ge some guidance abou policymakers fuure behavior. We will see ha policymakers can miigae he recession a he cos of raising long run macroeconomic volailiy Coordinaed announcemens In he pas hree years, he Federal Reserve has kep he federal funds rae a zero. As shown earlier, in he exbook new-keynesian model once he policy rae his he zero lower bound, deflaion occurs. A large preference shock ha induces consumers o drasically reduce demand can lead o his siuaion. Agens wan o save more, so hey reduce consumpion and demand falls; consequenly, real economic aciviy and inflaion fall. If he drop is large enough, he desired policy ineres rae becomes negaive and he bes ha he cenral bank can do is o drive he ineres rae o zero. Therefore, he real ineres rae is in fac oo high compared wih wha would be desirable, and he economy can experience a very large drop in real economic aciviy and deflaion. These basic predicions of he benchmark new-keynesian model seem a odds wih US daa ha show ha inflaion has been flucuaing around he implici Federal Reserve s inflaion arge. In his subsecion, we show ha he behavior of inflaion during his period is consisen wih he high uncerainy ha surrounds how policymakers will behave in he fuure. Uncerainy ofen characerizes excepional evens and he Grea Recession is no an excepion. Policymakers do no seem o have oulined a clear exi sraegy ye. Arguably, his creaes some uncerainy abou he way hey will deal wih he large sock of deb ha originaed from he curren crisis. As discussed earlier, he oucomes of he policy implemened a he zero lower bound criically depend on wha agens expec o happen once he economy has exied he zero lower bound. We consider an economy ha is hi by a large negaive preference shock ha pushes he economy o he zero lower bound and lass for en periods. We assume ha before he shock 20

22 Oupu GAP Inflaion Uncerainy Fiscally led Moneary led FFR B/GDP Figure 4: Macroeconomic Dynamics wih Coordinaed Announcemens: The figure repors he effecs of a large negaive preference shock ha forces he ineres rae o he zero lower bound. A he ime he preference shock his, he economy has a sock of deb above he seady sae resuling from an increase in primary deficis. Three cases are considered for he exi sraegy. In he firs case ("Moneary led"), policymakers announce a reurn o he Moneary led regime; in he second case ("Fiscally led"), a swich o he Fiscally led regime is announced; and in he hird case ("Uncerainy"), no announcemen abou he exi sraegy is made and agens aach equal probabiliies o he oher wo sraegies. The verical green doed lines indicae he period in which he economy is a he zero lower bound. Figure 5: Evoluion of Uncerainy wih Coordinaed Announcemens: The figure repors he evoluion of uncerainy for an economy wih an above-seady-sae sock of deb ha eners he zero lower bound regime under he Moneary led regime. Three cases are considered for he exi sraegy. In he firs case (he boom panels), policymakers announce a reurn o he Moneary led regime; in he second case (he middle panels), a swich o he Fiscally led regime is announced; in he hird case (he op panels), no announcemen is made abou he exi sraegy and agens aach equal probabiliies o he oher wo sraegies. The zero-lower-bound period lass from period = 11 hrough period =