Measuring the equilibrium real interest rate

Transcription

1 Measuring he equilibrium real ineres rae Alejandro Jusiniano and Giorgio E. Primiceri Inroducion and summary In conducing moneary policy policymakers find i useful o monior he performance of he economy relaive o some benchmark. For insance he policy decision wheher o raise or lower he shor-erm nominal ineres rae migh be affeced by he deviaions of curren inflaion from policymakers comfor zone of oupu from poenial oupu and of he real ineres rae (curren nominal rae minus expeced fuure inflaion) from is equilibrium value (he rae ha would be consisen wih oupu a is poenial level). Unforunaely hese benchmark conceps are no direcly observed in he daa bu can only be defined in he conex of a specific heoreical framework. Over he pas decade he new Keynesian model has become he workhorse for he analysis of moneary policy. This model depars from he neoclassical framework of he 198s by assuming imperfec compeiion in goods and labor markes and sicky (meaning rigid or inflexible) prices and wages neoclassical models assume prices and wages are flexible and adjus quickly. These ingrediens in he new Keynesian model aler he ransmission of fundamenal shocks perurbing he economy and allow moneary policy o have emporary real effecs. The equilibrium real ineres rae is a crucial concep in he new Keynesian class of models. This rae represens he real rae of reurn required o keep he economy s oupu equal o poenial oupu which in urn is he level of oupu consisen wih flexible prices and wages and consan markups in goods and labor markes (Woodford 3; and Galí 8). 1 Meanwhile he difference beween he ex ane real ineres rae he nominal ineres rae minus expeced inflaion and he equilibrium real ineres rae is defined as he real ineres rae gap. In he new Keynesian model he real ineres rae (RIR hereafer) gap is cenral o he deerminaion of oupu and inflaion. Loosely speaking if his RIR gap is posiive oupu will decline relaive o poenial. This is because people will be inclined o pospone spending decisions oday o ake advanage of higher reurns o savings. All else being equal a negaive oupu gap will hen pu downward pressures on prices and wages because of weaker aggregae demand. Conversely a negaive RIR gap will ypically be associaed wih a posiive oupu gap seing in moion inflaionary forces higher demand leads o higher prices. The main policy implicaion of his observaion is ha policymakers concerned wih mainaining oupu close o is poenial level should se shor-erm nominal ineres raes he policy insrumen of mos cenral banks in order o minimize he RIR gap. In he absence of a rade-off beween sabilizing inflaion and oupu his simple policy prescripion would also compleely sabilize inflaion. In pracice however here may well be a rade-off beween he wo objecives of oupu and inflaion sabilizaion. Noneheless he equilibrium RIR consiues a naural benchmark for he conduc of moneary policy and he RIR gap can be viewed as providing some indicaion of he sance of moneary policy (Neiss and Nelson 3). While he equilibrium RIR is heoreically appealing is use in guiding moneary policy decisions faces a leas wo major hurdles. Firs and foremos he equilibrium RIR is no direcly observable in he daa limiing is usefulness as a arge for moneary policy in pracice. 3 Moreover raher han being consan he Alejandro Jusiniano is a senior economis in he Economic Research Deparmen a he Federal Reserve Bank of Chicago. Giorgio E. Primiceri is an assisan professor in he Deparmen of Economics a Norhwesern Universiy. The auhors are graeful o Anna Paulson Richard Porer Spencer Krane and seminar paricipans a he Federal Reserve Bank of Chicago for helpful commens. 1 1Q/1 Economic Perspecives

2 equilibrium RIR flucuaes over ime in response o a variey of shocks o preferences and echnology ha perurb he economy. Second seing nominal ineres raes o rack he equilibrium RIR may no be feasible a imes because of he exisence of he zero bound; ha is nominal ineres raes canno be se lower han zero. Indeed he equilibrium RIR may fall enough o induce a posiive RIR gap even wih he nominal ineres rae a zero. Oupu would hen decline below poenial engendering deflaion. In his way he gap helps us o gauge he consrain imposed by he zero bound on moneary policy. Wih shor-erm nominal ineres raes now a hisorically low levels in he Unied Saes and a number of oher indusrialized counries his scenario is receiving a lo of aenion from boh he academic communiy and policymakers. Given he imporance ha he equilibrium RIR plays for he design of moneary policy in modern macroeconomic models our purpose in his aricle is o provide an esimae of his unobservable variable. We do so by inferring i from an empirical new Keynesian model fied o U.S. quarerly daa on a few key macroeconomic variables from 196:Q1 hrough 8:Q. Specifically our analysis accomplishes hree objecives. Firs we describe he hisorical evoluion of he equilibrium RIR. We find ha his rae has been negaive a imes paricularly in he lae 197s and mos ineresingly during he laes recession. Second we esimae he shor-erm RIR gap as he difference beween he curren (as opposed o fuure) ex ane RIR and he equilibrium RIR. This provides some indicaion of he sance of moneary policy. Consisen wih he anecdoal view he esimaed shorerm RIR gap suggess ha policy was loose during mos of he 197s. In conras policy would seem o have been igh a he end of our sample. However his mosly reflecs he zero bound problem policymakers inabiliy o lower shor-erm nominal ineres raes below zero and provides a raionale for he nonconvenional policy measures underaken by he Federal Reserve during he mos recen recession such as direc purchases of longer-erm securiies and he creaion of special faciliies and programs (for example he Term Asse-Backed Securiies Loan Faciliy or TALF) inended o increase access o credi. Finally we compare he evoluion of he shorerm and long-erm RIR gaps where he laer is defined as he sum of he curren and expeced fuure shor-erm RIR gaps or alernaively he difference beween he ex ane long-erm RIR and he equilibrium long-erm RIR. Long-erm raes reflec he pah of curren and expeced fuure shor-erm raes. Therefore long-erm gaps summarize privae expecaions abou fuure macroeconomic oucomes and moneary policy providing a more forward-looking measure of he policy sance. For insance according o his measure policy was no loose in he 6 period which preceded he recen economic downurn. This characerizaion of he policy sance conrass wih wha is suggesed by he shor-erm RIR gap and in paricular wih he view of several commenaors (see for insance Taylor 7). Several papers have ackled he esimaion of he equilibrium RIR before mos noably Laubach and Williams (3) and Kozicki and Clark (5). In conras o hese earlier sudies our esimae of he equilibrium RIR is based on a micro-founded model which builds on he opimizing behavior of households and firms seeking o maximize heir uiliy and profis. In his respec his aricle is relaed o he approach of Neiss and Nelson (3) Amisano and Trisani (8) and in paricular Edge Kiley and Lafore (8). However in conras o hese earlier sudies we sress he imporance of boh curren and expeced fuure RIR gaps for he deerminaion of macroeconomic oucomes. As wih all empirical work based on srucural models our resuls may be sensiive o some aspecs of he model specificaion. To illusrae his poin we compare our resuls across wo models ha differ in scale shocks and ransmission mechanisms of hese disurbances. The aricle is organized as follows. Firs we provide a brief descripion of our baseline model economy. Then we describe he daa and he esimaion approach. Nex we presen he main resuls ha is we presen our esimaes of he equilibrium RIR and RIR gaps. We also discuss he robusness of hese esimaes when inferred from a larger-scale model. We conclude wih a few commens and caveas o our analysis paricularly wih regard o he curren economic siuaion. More specifically we noe how he larger-scale model also suggess he presence of posiive shor-erm and long-erm RIR gaps for he fourh quarer of 8. This provides a furher raionale for he Federal Reserve s response o he curren crisis wih nonconvenional measures o ease moneary policy. We do however emphasize he need o enhance hese models abiliy o capure he inerplay beween he financial secor and he real economy paricularly in ligh of recen evens. The model In his secion we skech our baseline new Keynesian model and analyze wo of is key equilibrium relaions he aggregae demand and supply Federal Reserve Bank of Chicago 15

3 equaions. The presenaion is mosly narraive wih mos of he echnical deails relegaed o he appendix. Ineresed readers can refer o Jusiniano and Primiceri (8) for greaer deails on he model or hey can see he comprehensive reamen of new Keynesian models in Woodford (3) and Galí (8) as well as he excellen primer by Galí and Gerler (7). For simpliciy relaive o Jusiniano and Primiceri (8) he model here absracs from he roles of habi formaion indexaion and endogenous capial accumulaion. We presen he resuls based on a larger-scale model wih hese addiional feaures as a robusness check in a laer secion. There are five ypes of agens in our model economy: 1) households ) employmen agencies 3) firms producing inermediae goods ) firms producing final goods and 5) he moneary auhoriy. We now briefly describe he behavior of each of hem. Households We assume ha we have a large number of households seeking o maximize heir sream of curren and expeced fuure uiliy which depends posiively on heir consumpion of a single final good and negaively on he number of hours hey work for he producion of inermediae goods. Each household is he sole supplier of a specialized ype of labor ha i sells o he employmen agencies in exchange for wages. Raher han aking wages as given as under he neoclassical assumpion of perfec compeiion each household has some marke power and can pos is wage. This in urn deermines he amoun of heir specialized labor demanded by he employmen agencies. We inroduce sicky wages in he labor marke by assuming ha a each poin in ime only a random fracion of households can change heir posed wage. Hence when seing is wage each household akes ino consideraion no only curren bu also fuure labor demand and coss of working. For example if fuure labor demand is expeced o rise households will preempively pos higher wages since hey migh no be able o do so in he near fuure. Finally all households have access o savings hrough wo ypes of asses: one-period governmen bonds and sae-coningen securiies which pay only if a cerain fuure sae is realized. The former are used o smooh consumpion over ime. Sae-coningen securiies serve insead o insure agains he idiosyncraic risk arising from he uncerainy abou he lengh of ime before households will be able o rese heir wages. Employmen agencies Employmen agencies mediae he demand and supply of labor beween households and firms producing inermediae goods. Their role is o purchase all ypes of specialized labor supplied by households and bundle hem ino a single homogenous labor inpu sold o inermediae goods firms. Employmen agencies operae in a perfecly compeiive marke aking he wage received for he labor bundle as given and making zero profis. Inermediae goods producers A large number of inermediae goods producers combine echnology wih labor inpus purchased from employmen agencies o produce differeniaed inermediae goods which are hen sold o final goods producers. Each of he inermediae goods producers has some marke power and can herefore pos he price of is good. This in urn deermines he amoun of is oupu demanded by he final goods producers. We inroduce sicky prices in he goods marke by assuming ha a each poin in ime only a random fracion of firms can change heir posed price. Hence when seing is price each firm akes ino consideraion no only curren bu also fuure demand and marginal coss where he laer depend on wages. For example if fuure demand is expeced o rise producers will preempively increase prices since hey migh no be able o adjus hem in he near fuure. Final goods producers Final goods producers mediae beween inermediae goods producers and households. They produce he final good by bundling all inermediae goods ino a single final homogenous commodiy purchased by households. Final goods firms maximize profis as well bu in conras o he inermediae goods producers hey operae under perfec compeiion aking he price for he final good as given and making zero profis. Moneary auhoriy The cenral bank deermines moneary policy by seing he shor-erm nominal ineres rae in response o price inflaion and oupu growh. This ineres rae rule is a varian of he insrumen rule proposed by Taylor (1993) he Taylor rule which approximaes he hisorical behavior of he U.S. federal funds rae. According o his rule nominal ineres raes rise more han one-o-one wih inflaion and fall in response o oupu conracions. Demand supply and he equilibrium RIR Before presening our esimaion resuls we highligh he main insighs of he wo crucial equilibrium relaions in he model. This helps explain he roles of he equilibrium RIR and RIR gaps in he deerminaion of oupu and inflaion. 16 1Q/1 Economic Perspecives

4 Aggregae demand In he model aggregae spending is deermined by he behavior of he represenaive household which seeks o smooh consumpion over ime by invesing is savings in one-period governmen bonds. This opimizing behavior resuls in he following (loglinearized) aggregae demand equaion which is also known as he IS equaion: 1) y = E y r +1 where y and r are oupu and he RIR respecively and he ha symbol ( ) denoes deviaions from he equilibrium level. Hence y denoes he oupu gap and r sands for he shor-erm RIR gap. Inuiively according o he aggregae demand equaion flucuaions in he shor-erm RIR gap induce deviaions of he oupu gap from is expeced fuure value E y +1 where he operaor E denoes households expecaion of fuure values condiional on he informaion available oday. Equaion 1 can be ieraed forward o express he oupu gap oday only as a funcion of he curren and expeced fuure shor-erm RIR gaps. This procedure yields he expression + ) y = Er + j j= by which he oupu gap is negaively associaed wih he long-erm RIR gap. The laer corresponds o he sum of curren and expeced fuure shor-erm RIR gaps. 5 Noice herefore ha if he long-run RIR gap is negaive he oupu gap will be posiive and vice versa. Aggregae supply In erms of he supply side inermediae goods firms se prices according o he curren and expeced fuure evoluion of marginal coss and demand condiions. Profi-maximizing behavior resuls in he following (log-linearized) aggregae supply or Phillips curve equaion: 3) π = βe π +1 + κs + λ π where π and s sand for price inflaion and real marginal coss respecively and λ π is a markup shock ha represens exogenous variaion o he level of markup desired by inermediae goods producers. Finally β is a consan very close o one ha represens he emporal discoun facor and κ is a posiive consan ha is inversely relaed o he degree of price sickiness. Inuiively inflaion exceeds is expeced fuure level eiher if real marginal coss increase or if inermediae goods firms change heir desired markup of prices over marginal coss for oher reasons exogenous o he model. To highligh he imporance of he RIR gap for inflaion deerminaion we briefly analyze a special case of our model obained by assuming perfecly flexible wages. Under his assumpion real marginal coss are proporional o he oupu gap. Hence all else being equal a posiive oupu gap will cause inflaion o rise relaive o is expeced fuure level. Moreover if he oupu gap is projeced o remain posiive in he fuure expeced fuure inflaion will also increase furher fueling he rise in curren inflaion. Tha is curren and expeced fuure RIR gaps engender pressures on prices hrough heir effecs on aggregae demand. This crucial insigh also holds in our general model wih wage rigidiies alhough wih sicky wages he link beween he oupu gap and real marginal coss is more complex. RIR gaps and moneary policy Equaions 1 and 3 highligh he imporance of RIR gaps for oupu and inflaion deerminaion. Curren and fuure expeced deviaions of ex ane RIRs from heir corresponding equilibrium values affec he oupu gap which in urn influences he inflaion rae. Since he ex ane RIRs depend on he nominal ineres raes se by he moneary auhoriy he conduc of moneary policy is cenral o he behavior of he RIR gaps and hence oupu and inflaion. Consider for insance a cenral bank ha seeks o sabilize price inflaion and he oupu gap. Absen any markup shocks (λ π ) he cenral bank can achieve full sabilizaion of boh oupu and inflaion by commiing o se nominal ineres raes according o an appropriae insrumen rule ha delivers a zero RIR gap a every poin in ime. However as we menioned in he inroducion racking he equilibrium RIR may no be feasible when he zero bound on nominal ineres raes becomes binding. Pu anoher way someimes he equilibrium RIR may fall enough ha even wih he shor-erm nominal ineres rae a zero posiive RIR gaps would emerge. In his case according o he model oupu would decline relaive o poenial and inflaion would fall. Even absracing from he zero bound in pracice opimal moneary policy is more involved han he simple prescripion of racking he equilibrium RIR. This is due o he fac ha markup shocks bring abou a rade-off beween sabilizing he oupu gap and inflaion. 6 Noneheless despie hese consideraions Federal Reserve Bank of Chicago 17

5 he equilibrium RIR remains an imporan reference poin for he conduc of moneary policy assuming ha i can be accuraely esimaed and forecased. This is he ask we underake nex. Model soluion and esimaion In his secion we provide a brief overview of he approach ha we adop o esimae he model s parameers and o infer he evoluion of he laen (unobservable) variables. The discussion is somewha echnical alhough we do no aim o provide a comprehensive overview of he echniques we used. For more deails on hese echniques ineresed readers should refer o An and Schorfheide (7). Model soluion and sae-space represenaion The model we described in he preceding secion has a soluion of he form = G( ) + M ( ) ) ξ θ ξ θ 1 ε where he sae vecor x collecs all variables excep for he shocks. The elemens of x are expressed in (log) deviaions from he model s nonsochasic seady sae which corresponds o he consan values of all variables ha he economy would converge o in he absence of shocks. The shocks inducing emporary deviaions from he seady sae are sacked in he vecor ε. Meanwhile G (θ) and M (θ) are marices whose elemens are funcions of he vecor of model srucural parameers denoed by θ. Our goal is o esimae hese parameers and o uncover he hisorical behavior of he unobserved variables in he sae vecor. In fac while some elemens of he sae vecor are direcly observed in he daa (for insance inflaion and oupu) ohers are no (such as he equilibrium RIR and expeced inflaion). Therefore in order o esimae he model equaion mus be combined wih an addiional se of equaions specifying which elemens of he sae vecor are observed in he daa. The general form of his addiional se of equaions is 5) x = Z ξ + C( θ) ( ) where Z is a marix mapping he elemens of x ino x (he vecor of observable daa) and where C is a vecor of consan erms (which may depend on θ) represening he seady sae of he observable elemens of x. Equaions and 5 consiue he ransiion and measuremen equaions of a linear sae-space model. Daa We esimae he model using five series of U.S. quarerly daa: 1) real per capia gross domesic produc (GDP) ) per capia hours worked 3) real per capia wages ) quarerly inflaion and 5) he shor-erm nominal ineres rae. We consruc real GDP by dividing nominal GDP by he populaion aged 65 and he GDP deflaor. 7 For hours we use a measure of hours in all secors of he economy following Francis and Ramey (8). This is also our source for he populaion series. Real wages correspond o nominal compensaion of employees from he U.S. Bureau of Economic Analysis s naional income and produc accouns (NIPAs) divided by hours and he GDP deflaor; for he nominal ineres raes we use he effecive federal funds rae. The sample period spans 196:Q1 hrough 8:Q. 8 We do no de-mean or de-rend any series. Bayesian inference The sae-space represenaion of he model allows us o use a very powerful algorihm known as he Kalman filer o esimae he parameers θ and rerieve he mos likely pah of he unobservable elemens of x. We discuss each in urn. A naural way o esimae he model is o find he value of he parameers θ ha maximizes he likelihood funcion. The likelihood funcion summarizes all informaion abou θ conained in a sample of daa and plays a pivoal role in economerics and saisics. The likelihood funcion of our sae-space model can be evaluaed using he Kalman filer. In pracice however he likelihood funcion associaed wih mos modern macroeconomic models is ypically a complicaed nonlinear funcion of he model parameers. This makes finding a unique value ha maximizes he likelihood a raher arduous ask. For his reason mos of he recen lieraure esimaing macro models has urned o Bayesian mehods which discipline he se of plausible values for θ hrough he use of prior informaion. Bayesian inference hen seeks o characerize he disribuion of θ ha resuls from combining he likelihood funcion wih he prior informaion. This is known as he poserior disribuion from which we can compue he locaion of a parameer (mean or median) and a measure of uncerainy. For insance he uncerainy surrounding θ can be conveyed by reporing poserior probabiliy bands ha conain he range of values ha parameers are likely o ake wih say 99 percen probabiliy. Prior beliefs abou he elemens of θ may be informed by heory or simply reflec and summarize 18 1Q/1 Economic Perspecives

6 percen 8 6 figure 1 Equilibrium real ineres rae Noe: The dashed lines are he 99 percen poserior probabiliy bands. Sources: Auhors calculaions based on daa from Haver Analyics and he U.S. Bureau of Labor Saisics. informaion no conained in he esimaion sample. In pracice his prior informaion is formulaed by specifying a cerain disribuion for each elemen of he parameer vecor cenered a a paricular value (mean) and wih an associaed measure of uncerainy (sandard deviaion). Once we have esimaed he model s parameers we can employ he Kalman filer o sequenially and sysemaically updae our guess for he unobserved elemens of he sae vecor. More precisely a each poin in ime our guess for x based on daa available in he previous quarer is updaed afer we observe he daa for he curren period. This filered (or one-sided) esimae for he sae vecor forms he basis for our guess on he value of he sae vecor nex period which we also updae once we have daa for he nex quarer and so on. Having followed his procedure for all periods we can go back and revise he filered esimae of x condiional no only on informaion up o ime bu also on he whole sample of daa. We call he sae vecor emerging from his procedure he smoohed (or wo-sided) esimae. We analyze hese esimaes in he nex secion. Equilibrium RIR and RIR gaps in he esimaed model We do no repor he esimaed parameers in his aricle. They are similar o hose of Jusiniano and Primiceri (8) who use a longer sample. Here we focus on our esimaes of he equilibrium RIR and he RIR gaps. The equilibrium RIR Figure 1 plos he smoohed esimae of he equilibrium RIR (solid blue line). I is also imporan o characerize he uncerainy surrounding he esimaed equilibrium RIR paricularly since his is cied as a possible concern regarding is usefulness for moneary policy analysis. Therefore we also repor uncerainy bands (dashed black lines) which represen he values his variable is likely o have aken wih 99 percen probabiliy. We firs highligh a few properies of he smoohed esimae and laer discuss hese probabiliy bands. The firs hing o noice is ha he inferred equilibrium RIR has flucuaed subsanially over our sample wih a sandard deviaion of 1.9 percen around a mean of.6 percen (annualized). 9 A second ineresing feaure of figure 1 is ha he equilibrium RIR has urned negaive in a few insances. This occurred around 1975 and he end of 8 wo recession daes as deermined by he Naional Bureau of Economic Research and during he 3 period. These episodes were characerized by a subsanial decline in he federal funds rae in response o weak economic condiions. However he 8 episode is he only one in our sample for which he uncerainy bands are compleely below zero. Indeed he hird ineresing observaion is ha he equilibrium RIR has plummeed in he laes par of he sample. In paricular during he laes recession he equilibrium RIR seems o have recorded by far is larges decline wih an esimae for 8:Q of roughly.15 percen. The ighness of he poserior probabiliy bands deserves some commen. In paricular he precision wih which he equilibrium RIR is esimaed perhaps seems implausible especially considering ha hese bands accoun for he uncerainy surrounding boh he unobserved saes and he model parameers. I is imporan o keep in mind however ha hese probabiliy bands absrac from model uncerainy. Tha is alernaive specificaions of he model (for example a differen hisorical characerizaion of U.S. moneary policy or a model wih addiional propagaion mechanisms and/or shocks) migh deliver differen esimaes of he equilibrium RIR. We reurn o his issue in he secion explaining he larger-scale model. Federal Reserve Bank of Chicago 19

7 This being said he cross-secional dispersion a differen poins in ime is larger han perhaps suggesed visually by figure 1. For example figure plos he poserior disribuion of he equilibrium RIR for he las poin in he sample 8:Q. Values of he equilibrium RIR are on he horizonal axis wih he verical line drawn a he median of.15 percen which coincides wih he esimae repored in he previous figure. Noice ha his disribuion has a range from roughly percen o.5 percen wih hardly any weigh assigned o values close o zero. Therefore our modelbased esimaes sugges ha i is quie likely ha he equilibrium RIR became negaive in 8. To wha exen did his induce posiive RIR gaps? We address his key issue nex. The shor-erm RIR gap The ex ane RIR is given by he difference beween he nominal ineres rae and he inflaion rae expeced for nex quarer. While he former is direcly observable in our daa he laer is par of he unobservable sae vecor and mus be backed ou using he Kalman filer. Figure 3 shows he smoohed esimae of he ex ane RIR (blue line) ogeher wih he equilibrium RIR (black line). The mean of he ex ane RIR is.37 percen (annualized) wih a sandard deviaion of.5 percen. These saisics are similar o hose corresponding o he equilibrium RIR. The overall conours of hese wo series coincide alhough hey have differed a imes. In order o highligh he discrepancies beween he ex ane RIR and he equilibrium RIR figure plos heir difference ogeher wih is 99 percen probabiliy bands. We refer o his difference as he shor-erm RIR gap in order o disinguish i from he long-erm gap ha we analyze nex. Noe ha he shor-erm gap has also flucuaed considerably over ime wih an average of.33 percen and a sandard deviaion of 1.8 percen. As we noed earlier he shor-erm RIR gap is commonly aken as a measure of he moneary policy sance. And indeed figure Poserior disribuion of equilibrium real ineres rae in 8:Q equilibrium real ineres rae in percen Sources: Auhors calculaions based on daa from Haver Analyics and he U.S. Bureau of Labor Saisics. figure 3 Ex ane and equilibrium real ineres raes percen Ex ane rae Equilibrium rae Sources: Auhors calculaions based on daa from Haver Analyics and he U.S. Bureau of Labor Saisics. 1Q/1 Economic Perspecives

8 percen figure Shor-erm real ineres rae gap Noe: The dashed lines are he 99 percen poserior probabiliy bands. Sources: Auhors calculaions based on daa from Haver Analyics and he U.S. Bureau of Labor Saisics. a leas for some episodes he evoluion of he RIR gap aligns well wih he anecdoal characerizaion of moneary policy ha we see in he lieraure. For insance according o our esimaes he equilibrium RIR exceeded he ex ane real ineres rae during mos of he 197s exacly when U.S. inflaion was a hisorically high levels. This is consisen wih he view ha moneary policy during his period was characerized by an insufficien response o he rise in inflaion (Clarida Galí and Gerler ). Similarly he significan increase in he shor-erm RIR gap in he early 198s accords well wih he convenional view ha he disinflaion in he U.S. economy was engineered by a subsanial policy ighening under hen-federal Reserve Chairman Paul Volcker. The long-erm RIR gap While he behavior of he shor-erm RIR gap presened in figure squares quie well wih he convenional view here are a few caveas ha call for cauion in inerpreing his gap as a good proxy for he sance of moneary policy. In paricular as we explained earlier i is imporan o recognize ha he whole pah of expeced fuure shor-erm RIR gaps raher han jus is conemporaneous value maers for he deerminaion of oupu and inflaion in he new Keynesian model (see equaion p. 17). From his perspecive we migh judge he moneary policy sance beer by looking a he longerm RIR gap which summarizes he informaion conained in he curren and expeced fuure values of he federal funds rae inflaion and he equilibrium RIR. To his end figure 5 compares he shor-erm RIR gap (blue line) wih he evoluion of he long-erm one (black line). Alhough he wo series ofen move ogeher he correlaion coefficien is equal o.56 he message abou he sance of moneary policy implied by he wo lines differs during some hisorical episodes. The 6 period provides an ineresing example. In :Q3 he federal funds rae sood a 1.75 percen bu i had declined o 1 percen by 3:Q3 and remained here for he nex hree quarers. The federal funds rae hen rose gradually reaching 5.5 percen in 6:Q3. Some have argued ha moneary policy was oo accommodaive during his period (for example Taylor 7). Alhough he negaive value of he shor-erm RIR gap seems o accord wih his claim (blue line) he posiive value of he long-erm RIR gap (black line) does no suppor he view ha policy was oo expansionary. In paricular i suggess ha he privae secor expeced a decline of he equilibrium RIR or a moneary ighening. The difference beween shor-erm and long-erm gaps oward he end of he sample is also informaive. For insance our esimae of he shor-erm RIR gap in 8:Q is roughly 1.5 percen. This suggess ha according o he model he federal funds rae of.5 percen was probably above he equilibrium RIR. Furhermore i suggess ha he zero bound on nominal ineres raes would have been binding before addiional ineres rae cus could have closed he shorerm RIR gap. In addiion he esimaed long-erm RIR gap exceeds 3 percen. Taken a face value his would sugges ha a he end of 8 posiive shorerm gaps were expeced o persis and he zero bound was expeced o bind beyond a single quarer. Before we inerpre his resul as indicaive of conracionary moneary policy we mus acknowledge ha hese gaps can only reflec he sance of convenional moneary policy. By his we mean he Federal Reserve s managemen of he shor-erm nominal ineres rae. During he curren economic crisis he Federal Reserve has also employed a variey of nonconvenional policy measures; and hese measures have been refleced in he changing size and composiion of he Federal Reserve s balance shee. Our simple analysis suggess ha hese measures have been appropriae insofar as boh he shor-erm RIR and long-erm RIR exceeded he equilibrium Federal Reserve Bank of Chicago 1

9 RIR. However hese exraordinary measures are no refleced in our analysis of he shor-erm and long-erm RIR gaps. A larger-scale model figure 5 Shor-erm and long-erm real ineres rae gaps percen The baseline model can be summarized in a few simple equaions ha as 3 discussed clearly highligh he role of he equilibrium RIR for he dynamics 1 of oupu and inflaion. This simpliciy however comes a he expense of absracing from oher feaures ha impar 1 more realism o he model. In paricular addiional shocks can be included and oher mechanisms added (such as 3 endogenous capial accumulaion) hrough which disurbances influence he evoluion of he economy. For his reason we es he robusness of our main conclusions by using a larger-scale model esimaed on a richer daa se. This exended model is discussed in Jusiniano and Primiceri (8) and is based on he well-known sudies of Chrisiano Eichenbaum and Evans (5) and Smes and Wouers (7). Relaive o our baseline model he larger-scale model includes he addiional propagaion mechanisms provided by endogenous capial accumulaion invesmen adjusmen coss a choice of capial uilizaion habi formaion in consumpion and indexaion in boh prices and wages. These feaures are essenially mean o increase he lengh of ime for which a given shock will affec he evoluion of he economy. There are hree addiional disurbances perurbing he model economy specifically shocks o he marginal efficiency of invesmen o he disuiliy of labor and o governmen spending. Finally we esimae he model over he same sample 196:Q1 hrough 8:Q bu we incorporae addiional daa on consumpion and invesmen. Figure 6 repors he smoohed esimaes of he equilibrium RIR and he ex ane RIR as well as he shor-erm and long-erm RIR gaps. In each panel he black line reproduces he esimaes from he baseline model and he blue line corresponds o esimaes from he exended model. Panel A highlighs he fac ha he cyclical paern of he equilibrium RIR is very similar across models alhough he equilibrium RIR is subsanially more volaile in he larger-scale model. 1 One implicaion of his finding is ha according o he exended model he equilibrium RIR has declined below zero more Shor-erm rae gap Long-erm rae gap Sources: Auhors calculaions based on daa from Haver Analyics and he U.S. Bureau of Labor Saisics. frequenly han wha is prediced by our baseline framework. Furhermore he decline in he curren downurn while subsanial is no as dramaic by hisorical sandards as suggesed by he baseline model. Since he inferred ex ane RIR (panel B) is almos idenical across models i is no surprising ha he shor-erm RIR gap (panel C) and long-erm RIR gap (panel D) are more volaile in he larger-scale model as well. Noice also ha he esimaes from our baseline model and larger-scale model co-move more closely in he case of he long-erm gap for which he wo lines essenially overlap during he laes par of he sample. Regarding he 6 period he discrepancy beween he shor-erm and long-erm RIR gaps is far less eviden in he larger-scale model han in our baseline model. However boh measures in he largerscale model remain posiive or very close o zero. This confirms our earlier observaion ha policy may no have been as accommodaive during his period as has been suggesed (for example Taylor 7). Consisen wih he baseline model he larger-scale framework also predics large posiive shor-erm and long-erm RIR gaps for he fourh quarer of 8. However he same caveas we raised earlier abou inerpreing hese endpoin esimaes as reflecing he policy sance apply o he larger-scale model as well. 1Q/1 Economic Perspecives

10 figure 6 Real ineres rae levels and gaps in he baseline model and larger-scale model A. Equilibrium real ineres rae percen B. Ex ane real ineres rae percen C. Shor-erm real ineres rae gap percen 8 6 D. Long-erm real ineres rae gap percen Baseline model Larger-scale model Sources: Auhors calculaions based on daa from Haver Analyics and he U.S. Bureau of Labor Saisics. Overall despie some obvious discrepancies we view hese resuls as an imporan assessmen of robusness of our main findings. Furhermore hey sugges in line wih our earlier hypohesis ha model uncerainy is likely o be a crucial facor surrounding he measuremen of he unobservable equilibrium RIR and relaed componens. This source of uncerainy is someimes ignored in sudies presening model-based esimaes of he RIR alhough our findings sugges ha his should be a major issue for furher empirical work in his area. Conclusion In his aricle we sudy he evoluion of he equilibrium RIR and RIR gaps using boh a prooypical new Keynesian model and a larger-scale model similar o hose in Chrisiano Eichenbaum and Evans (5) and Smes and Wouers (7). Our esimaes poin o a subsanial degree of ime variaion in he equilibrium RIR. Moreover we find ha his rae has someimes become negaive in he pos-war period. In paricular our analysis suggess ha he equilibrium RIR fell sharply below zero oward he end of 8 (alhough Federal Reserve Bank of Chicago 3

11 he magniude of his decline relaive o hisorical sandards is model dependen) resuling in posiive shor-erm and long-erm expeced RIR gaps. This provides some suppor for he Federal Reserve s response o he curren crisis wih nonconvenional measures o ease moneary policy. We conclude by noing ha he models we use here even he larger-scale one are o some exen very sylized and have some shorcomings. One of hese shorcomings is he absence of an explici heoreical framework of he financial secor and financial fricions. I would be useful o analyze how he inroducion of hese addiional feaures would affec our resuls (as for insance in Chrisiano Moo and Rosagno 7). These feaures seem paricularly relevan for he analysis of curren economic evens. NOTES 1 Hence we could alernaively refer o he equilibrium real ineres rae as he real ineres rae a poenial. We prefer he former erminology because i is more popular in he lieraure and policy discussions as exemplified by he discussion in Ferguson (). Meanwhile poenial oupu is proporional bu lower han he efficien level of oupu. The efficien level of oupu is he level of oupu under perfec compeiion and herefore wih zero markups. In he goods marke he markup is defined as he amoun by which prices exceed he marginal cos of producion. In he labor marke he markup is defined as he excess of wages over he marginal cos of supplying labor. Exogenous variaions in desired markups usually referred o as markup shocks inroduce such a rade-off (see for example Clarida Galí and Gerler 1999). 3 Poenial oupu is no direcly observable eiher and he policy implicaions of is measuremen have received subsanial aenion following he work of Orphanides (1). See also Jusiniano and Primiceri (8). We also esimae he model s unknown parameers and subsequenly exrac all unobserved model-based variables such as expeced inflaion nex period. 5 While seemingly dauning o compue he long-run raes can be backed ou from he Lagrange muliplier of he household s budge consrain. 6 If wages are rigid opimal moneary policy mus aribue some weigh o wage inflaion sabilizaion as well. 7 All daa excep for hours are from Haver Analyics. We are very graeful o Shawn Sprague of he U.S. Bureau of Labor Saisics for providing us he series of hours in all secors of he economy. 8 We use he eigh years prior o he sample period o iniialize he Kalman filer. 9 This resul is consisen wih he large degree of ime variaion repored by Laubach and Williams (3) and Edge Kiley and Lafore (8) bu sands in conras o he analysis of Neiss and Nelson (3) who argue ha he equilibrium real ineres rae exhibis very lile volailiy. 1 The main reason he equilibrium RIR in he larger-scale model is more volaile is ha his model includes habi formaion. 1Q/1 Economic Perspecives

12 Appendix: Model EQUATIONS We presen he main equaions of he model for each of he five classes of agens described in he main ex. Households The expeced discouned sream of uiliy ha each household j maximizes is given by A1) E s log C L ϕ s +s β b+s +s = 1 1 ( j) + ν + ν where C denoes consumpion and he second argumen of he uiliy funcion represens he marginal disuiliy of each household s specific labor L(j) ha depends on he parameer v known as he inverse Frisch elasiciy of labor supply. Fuure uiliy is discouned a he rae β and b is a discoun facor shock affecing boh he marginal uiliy of consumpion and he marginal disuiliy of labor. The logarihm of b is modeled as a Gaussian auoregressive process of order 1 denoed as AR(1) for shor. A every poin in ime each household s sources and uses of income mus be equal as summarized by he budge consrain P C + T + B R 1 B 1 + Q 1 (j) + + W (j)l (j) where T is lump-sum axes and ransfers B denoes holdings of governmen bonds R is he gross nominal ineres rae Q (j) is he ne cash flow from paricipaing in sae-coningen securiies ha insure agains idiosyncraic risk and is he per capia profi ha households ge from owning he inermediae goods firms. Following Erceg Henderson and Levin () we permi in every period only a fracion 1 ξ w of households o rese heir wages o minimize he expeced discouned sream of labor disuiliy for he periods in which he posed wage is anicipaed o remain in place E s s ξ β b s= w + s L + s( j) ϕ 1+ ν 1+ ν. This is subjec o he labor demand funcion of employmen agencies specified nex. Wages for he remaining ξ w fracion of households are indexed o seady-sae inflaion and produciviy. Employmen agencies Compeiive employmen agencies operae in compeiive markes and bundle each household s specialized labor L (j) ino a homogenous labor inpu according o w L = j dj 1+ Λ L ( ) Λw Homogeneous labor is sold o inermediae goods firms. Profi maximizaion and he zero profi condiion imply a specialized labor demand funcion W ( j) w L ( j) = L Λ W 1 w + Λ where W ( j) is he wage paid by he employmen agencies o he household supplying labor of ype j and W is he hourly wage paid by inermediae goods firms for heir homogenous labor inpu. The demand schedule for labor j is decreasing in he relaive wage and depends on he elasiciy of subsiuion among varieies of labor given by Λ w. Noice ha his elasiciy is ime varying and we assume ha log (1+ Λ w ) is a Gaussian independen and idenically disribued (i.i.d.) process. In he lieraure his is referred o as he wage markup shock and i is analyzed in deail in Jusiniano and Primiceri (8). Inermediae goods producers A monopolisically compeiive firm produces he inermediae good Y (i) wih he producion funcion Y (i) = A L (i) a where L (i) denoes he bundled labor inpu purchased from employmen agencies for he producion of good i and A represens a produciviy shock. We model A as nonsaionary wih is growh rae following a Gaussian AR(1) process. As in Calvo (1983) a each poin in ime a fracion ξ p of firms canno reopimize heir prices and index hem o seady-sae inflaion. The remaining fracion 1 ξ p of firms pos a new price P ( i) o maximize he expeced discouned sream of profis for he periods in which he new price is anicipaed o remain in place. Federal Reserve Bank of Chicago 5

13 s s s E ξ pβ Λ s P i π + { ( ) Y + s ( i) W + sl + s ( i) } s= where Λ +s is he marginal uiliy of consumpion used o value fuure income subjec o he goods demand funcion specified in he nex secion. Final goods producers Perfecly compeiive firms produce he final good Y by bundling all inermediae goods according o Y = Y i p i Λ ( ) d 1+ Λp Profi maximizaion and zero profi condiion for he final goods producers imply he following demand funcion for he inermediae good i: P ( i) Y ( i) = P 1 p + Λ Λp Y where P corresponds o he aggregae price level. The demand schedule for inermediae good i is decreasing in is relaive price and depends on he elasiciy of. subsiuion Λ p among varieies of inermediae goods. This elasiciy is ime varying and we assume ha log (1+ Λ p ) is a Gaussian i.i.d. process. This disurbance is known as he price markup shock. Moneary auhoriy The Taylor ype rule for he shor-erm nominal ineres rae R is given by R R = R 1 R ρr 3 Π π s= π 1/ φ π s ( Y / Y ) e 1/ φy γ 1 ρ R ε e R wih R being he seady sae for he gross nominal ineres rae and ε R being a Gaussian i.i.d. moneary policy shock. The parameers φ π and φ Y capure how aggressively he moneary auhoriy responds o variaions in inflaion and oupu growh over he curren and previous hree quarers. There is a ime-varying inflaion arge π which evolves exogenously according o a Gaussian AR(1) process. Finally noice ha shorerm nominal ineres raes are adjused gradually as given by ρ R referred o as he smoohing coefficien. 6 1Q/1 Economic Perspecives

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