Research Division Federal Reserve Bank of St. Louis Working Paper Series

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1 Research Dvson Federal Reserve Bank of S. Lous Workng Paper Seres Moneary Polcy and Naural Dsasers n a DSGE Model: How Should he Fed Have Responded o Hurrcane Karna? Benjamn D. Keen And Mchael R. Pakko Workng Paper B hp://research.slousfed.org/wp/2007/ pdf January 2008 FEDERAL RESERVE BANK OF ST. LOUIS Research Dvson P.O. Box 442 S. Lous, MO 6366 The vews expressed are hose of he ndvdual auhors and do no necessarly reflec offcal posons of he Federal Reserve Bank of S. Lous, he Federal Reserve Sysem, or he Board of Governors. Federal Reserve Bank of S. Lous Workng Papers are prelmnary maerals crculaed o smulae dscusson and crcal commen. References n publcaons o Federal Reserve Bank of S. Lous Workng Papers (oher han an acknowledgmen ha he wrer has had access o unpublshed maeral should be cleared wh he auhor or auhors.

2 Moneary Polcy and Naural Dsasers n a DSGE Model: How Should he Fed Have Responded o Hurrcane Karna? Benjamn D. Keen Asssan Professor Deparmen of Economcs Unversy of Oklahoma 329 Heser Hall, 729 Elm Ave. Norman, OK 7307 ( ben.keen@ou.edu Mchael R. Pakko Research Offcer Research Deparmen Federal Reserve Bank of S. Lous P.O. Box 442 S. Lous, MO 6366 ( pakko@sls.frb.org June 20, 2007 Revsed: January 25, 2008 Keywords: Opmal Moneary Polcy, Nomnal Rgdes, Naural Dsasers, Hurrcane Karna JEL Classfcaon: E3, E32, E42 ABSTRACT In he mmedae afermah of Hurrcane Karna, speculaon arose ha he Federal Reserve mgh respond by easng moneary polcy. Ths paper uses a dynamc sochasc general equlbrum (DSGE model o nvesgae he approprae moneary polcy response o a naural dsaser. We show ha he sandard Taylor (993 rule response n models wh and whou nomnal rgdes s o ncrease he nomnal neres rae. Tha fndng s unchanged when we consder he opmal polcy response o a dsaser. A nomnal neres rae ncrease followng a dsaser mgaes boh emporary nflaon effecs and oupu dsorons ha are arbuable o nomnal rgdes. The vews expressed n hs paper are hose of he auhors and do no necessarly reflec offcal posons of he Federal Reserve Bank of S. Lous, he Federal Reserve Sysem, or s Board of Governors.

3 I. Inroducon In lae Augus 2005, Hurrcane Karna h he U.S. Gulf coas wh a caasrophc fury ha caused unprecedened damage o he regon. Buron and Hcks (2005 calculae ha he oal damage o homes, busnesses, and nfrasrucure was more han $50 bllon, makng Karna he cosles hurrcane ever. Tha esmae, n economc erms, represens abou percen of he Bureau of Economc Analyss s fgure for oal fxed capal and consumer durables a he end of Economc acvy n he Gulf coas regon also was dsruped durng and mmedaely afer he hurrcane. As a resul, quarerly U.S. GDP growh s esmaed o have declned by around percen n he hrd quarer of The magnude of he dsaser fueled speculaon by fnancal marke parcpans ha he Federal Open Marke Commee (FOMC mgh ease polcy a s meeng of Sepember 20 by posponng a wdely expeced 25 bass pon ncrease n he federal funds rae. The change n expecaons was wdely repored by he fnancal press. For example, an arcle n he Cncnna Pos on Sepember 7 saed ha, Before he hurrcane economss consdered a foregone concluson ha Fed polcy makers would boos shor-erm neres raes by anoher quarer percenage pon Now, a growng number of economss say he odds are rsng ha he Fed mgh ake a pass Esmaes on he economc losses from Hurrcane Karna vary. Rsk Managemen Soluons, for example, on Sepember 9, 2005, esmaed ha nsured losses were beween $40 and $60 bllon, whle oal economc losses exceeded $00 bllon. 2 A quarerly declne of % n U.S. hrd quarer GDP s based on esmaes by he forecasng frms Macroeconomc Advsors and Global Insgh. Accordng o Cashell and Labone (2005, Macroeconomc Advsors lowered her hrd quarer GDP annual growh forecas from 4.6% o 3.2% and her fourh quarer forecas from 3.6% o 3.3%. Insgh lowered s forecas for annual GDP growh n he second half of 2005 by 0.7%. Evaluang hese magnudes for a sngle quarer, a a non-annualzed rae, suggess an mpac on oupu of approxmaely %.

4 Daa from federal funds fuures markes also confrm hs shf n expecaons. Fgure shows ha he expeced average funds rae for Sepember and Ocober began fallng on he day afer Karna s landfall. From Augus 29 o Sepember 6, he expeced rae derved from he Sepember conrac fell 5 bass pons, whle he expeced funds rae for Ocober fell by bass pons. A he Sepember 20 meeng, he FOMC rased he federal funds rae by 25 bass pons, as was wdely expeced before Karna. The press release followng he meeng saed ha Whle hese unforunae developmens have ncreased uncerany abou near-erm economc performance, s he Commee s vew ha hey do no pose a more perssen hrea [FOMC (2005]. 3 Gven he FOMC was expeced o rase s funds rae arge pror o Karna, he Commee s subsequen decson o follow ha course of acon ndcae ha moneary polcy dd no respond o he dsaser. 4 Ths paper uses a dynamc sochasc general equlbrum (DSGE model o nvesgae how moneary polcy should respond o caasrophc evens such as Hurrcane Karna. We model nfrequen caasrophc evens usng a wo-sae Markov swchng process. Mos of he me, he economy s n he non-dsaser (or normal sae. In each perod, however, a small probably exss ha he economy wll experence a dsaser. A dsaser s characerzed by he desrucon of a poron of he capal sock and a emporary negave echnology shock ha reduces oupu. We hen analyze he mpac of a dsaser shock n model specfcaons wh and whou nomnal prce and wage rgdes. 3 In hs lone dssen, Governor Olsen recommended no change n he federal funds rae pendng he recep of addonal nformaon on he economc effecs resulng from he severe shock of Hurrcane Karna. 4 Alhough he FOMC dd no respond drecly o Hurrcane Karna, he Commee dd ake explc acon n he wake of a prevous caasrophc even: he 9/ aack. The 9/ even dffered from oher dsasers n ha hreaened o dsrup he effcen funconng of he fnancal sysem [Neely (2004]. 2

5 Our resuls ndcae ha he moneary auhory should rase s nomnal neres rae arge followng a dsaser. Ths prescrbed ncrease n he federal funds rae clearly runs conrary o he convenonal wsdom followng Hurrcane Karna. The press and fnancal markes based her belefs on an assumpon ha he Federal Reserve s movaed o dampen he fall n oupu caused by a dsaser. When conducng moneary polcy whn a Taylor (993 rule framework, however, he nomnal neres rae responds prmarly o hgher nflaon raher han o lower oupu. Ths fndng also holds when an explc dsaser varable eners he polcy rule. Usng opmal-conrol heory, as appled by Woodford (2002 and ohers, he moneary auhory should srve o replcae he dynamcs of a flexble prce and wage equlbrum. Generang hese dynamcs requres an ncrease n he nomnal neres rae n response o hgher nflaon and also o he hgher real neres rae assocaed wh depleon of he capal sock. Such a polcy mnmzes real dsorons due o nomnal prce and wage rgdes. The paper proceeds as follows. Secon II oulnes he model. Secon III presens he specfcaon of our dsaser shock and s effecs on he capal sock and oupu. Secon IV examnes he mpac of a dsaser when he Federal Reserve follows a sandard Taylor rule. We also consder he effecs of a dscreonary polcy approach ha leaves he nomnal neres rae nally unchanged. Secon V analyzes he opmal moneary polcy response o a dsaser. Secon VI concludes. II. Model Framework We examne a fully arculaed DSGE model where frms are monopolscally compeve producers of goods and households are monopolscally compeve supplers of labor. Imperfec compeon n he goods and labor markes enables us o consder models wh prce and nomnal wage rgdes. Specfcally, we consder hree dfferen specfcaons of our benchmark DSGE 3

6 model: flexble prces and wages ( flexble model, scky prces and flexble wages ( scky prce model, and scky prces and scky wages ( scky prce and wage model. 5 Households are nfnely lved agens who maxmze expeced dscouned uly over consumpon, lesure, and real money balances. They hold money for lqudy purposes, rade bonds beween hemselves, nves n physcal capal subjec o Hayash (982 syle adjusmen coss, and parcpae n sae-conngen secures markes. Each perod, households supply dfferenaed labor servces o frms n a monopolscally compeve marke. Toal labor supply hen s calculaed as a Dx and Sglz (977 connuum of labor servces provded by he households. Wage adjusmen opporunes follow a Calvo (983 specfcaon. Tha s, he probably ha a household can opmally adjus s nomnal wage s η w, whle he probably ha he nomnal wage rses by only he seady-sae nflaon rae s ( η w. 6 Frms ren capal and labor servces from he household secor o produce dfferenaed goods n a monopolscally compeve marke accordng o a Cobb-Douglas producon funcon. Aggregae oupu comprses a Dx and Sglz connuum of dfferenaed producs and prce adjusmen follows a Calvo process. In each perod, a random fracon, η p, of frms can opmally adjus her prce, whle he remanng frms, ( η p, can adjus only by he seadysae nflaon rae. Moneary polcy s mplemened by argeng he nomnal neres rae, R. Specfcally, he moneary auhory uses a generalzed Taylor rule: Rˆ = θ π ˆπ θ ŷ θ ΔŴ θ Dˆ ε, ( y W D where ^ denoes a varable s log devaon from s seady sae, y s oupu, π s he gross prce 5 Our model s a varan of he model analyzed n Gavn, Keen, and Pakko ( Erceg, Henderson, and Levn (2000 also use hs specfcaon. 4

7 nflaon rae, ΔW s he gross wage nflaon rae, D s a dsaser shock, and ε s a dscreonary polcy shock wh a zero mean and varance of σ ε 2. The Appendx provdes a more dealed descrpon of he model. III. The Dsaser Shock We consder wo crucal characerscs of a naural dsaser lke Hurrcane Karna. Frs, a dsaser desroys an economcally relevan share of he economy s producve capal sock. Second, a dsaser emporarly dsrups producon, whch we model as a ransory negave echnology shock. Snce a dsaser s an nfrequen even, he dsaser shock s modeled as a wosae Markov swchng process. The negave shocks o he capal sock and o echnology are specfed hen as funcons of he wo-sae dsaser varable. A. A Markov-Swchng Represenaon The dsaser shock varable, D, can ake on one of wo saes. Sae s he normal or non-dsaser sae, whle sae 2 s defned as a dsaser. The wo saes evolve accordng o a ranson marx wh he followng calbraed probables: p p p p = , 2 j where p = prob D = D D = D. For he gven probably values, here s a 2% j ( probably a dsaser wll occur, regardless of he dsaser varable s sae n he prevous perod. The dsaser shock affecs boh he level of echnology and he capal sock. Frs, echnology s an economy-wde facor ha eners each frm s Cobb-Douglas producon funcon mulplcavely. The overall echnology shock, Z, comprses he ypcal echnology shock, z, ha follows a frs-order auoregressve process and an addonal componen relaed o he 5

8 dsaser varable s sae: Zˆ = zˆ ζ( Dˆ. (4 Second, he dsaser shock drecly nfluences he accumulaed capal sock. The mng of he dsaser shock s mporan. In perod, he nondeprecaed capal, ( δk -, and new nvesmen,, are combned o ge he amoun of capal, k, carred no perod : k = ( δ k AC, (5 where AC represens a capal adjusmen cos. 7 A dsaser, f occurs, hen wll be realzed a he begnnng of perod, desroyng a poron of he prevously accumulaed capal. The remanng capal avalable for producon n perod s kˆ = kˆ κ( Dˆ. (6 B. Log-Lnear Approxmaon of he Dsaser Shock In order o map he regme-shfng framework ono he canoncal dfference-equaon srucure of he model, a log-lnearzed verson of he Markov-swchng process s expressed n he followng form 8 : Dˆ ρ ˆ ε. (7 = D D D I s convenen o defne he baselne seady sae as he uncondonal expeced value of he dsaser shock: p22 p 2 ln( D = ln( D ln( D. (8 2 p p 2 p p 22 The compose expressons weghng he wo values of D n (8 are he ergodc probables of 22 7 The specfc funconal form of he capal adjusmen coss s oulned n he appendx. 8 See Hamlon (994, p. 684 for a dealed descrpon of he AR( represenaon of he wo-sae Markov process. Ths procedure of lnearzng a wo-sae Markov process also s used n Pakko (

9 beng n each of he wo saes. When D s n sae, s logarhmc devaon from he baselne seady sae s p ln( D ln( D = [ln( D ln( D ]; (9 2 p p ˆ 2 D and when D s n sae 2, s 22 2 p22 2 ln( D ln( D = [ln( D ln( D ]. (0 2 p p ˆ 2 D A useful propery of a wo-sae Markov-swchng process s ha he condonal probables mplc n he expecaon erm n (7 can be represened as a frs-order auoregressve process. Usng (9 and (0 and he probably ranson marx, s sraghforward o show ha he 22 auoregressve coeffcen defned as E ˆ ˆ ˆ ( D D / D s ndependen of he presen sae and s equal o p p For he lnearly approxmaed smulaons, hs expresson defnes he value for ρ D. 0 The sequence of dsurbances placed no he model s calculaed as ε Dˆ E ( Dˆ = Dˆ ( p p Dˆ. ( D = 22 IV. Smulaon Expermens A. Calbraon The dsaser shock varable s calbraed o reflec he magnude of Hurrcane Karna s economc mpac. Frs, he rao D 2 /D s se o.004, provdng a baselne magnude for he shock s mpac. The effec of Dˆ on capal and echnology are calbraed o generae specfc mpulse responses conssen wh he mpac of Hurrcane Karna. In parcular, he dsaser 9 The expresson p p 22 defnes he sable egenvalue of he probably ranson marx, P. 0 Gven our assumed values for he elemens of he probably ranson marx, he mpled auocorrelaon coeffcen equals zero n hs applcaon. 7

10 varable s effec on he capal sock and echnology are calbraed such ha boh he capal sock and oupu declne by % n he flexble prce and wage equlbrum when he economy s n he dsaser sae. In erms of equaons (4 and (6, hs requres ha we se ( Dˆ = ˆ κ ( Dˆ = Dˆ. ζ D and The exsence or absence of nomnal prce and wage rgdes depends on he calbraon of he probably of prce adjusmen, η p, and he probably of wage adjusmen, η W. The probably of prce adjusmen equals when prces are flexble and 5 when prces are scky. Our calbraon for he scky prce specfcaon ndcaes ha frms rese her prce, on average, once per year, whch s conssen wh fndngs n Roemberg and Woodford (992. The probably of wage adjusmen s se o f wages are flexble and 5 f wages are scky. The scky wage calbraon, whch s conssen wh Erceg, Henderson, and Levn (2000, suggess ha nomnal wage readjusmen occurs, on average, once every year. The Appendx deals he calbraon of he model s oher parameers, excep he parameers n he polcy rules (whch are dscussed below. Table summarzes he model s calbraed parameers. A. Taylor Rule Responses Fgure 2 llusraes he mpac of a dsaser on he flexble model, scky prce model, and he scky prce and wage model when he cenral bank follows a Taylor rule wh θ π =. 5 and θ y = 5. We calbrae he shock o delver a % fall n oupu for he flexble model. The negave shock o he capal sock and producvy facor promps frms o lower her oupu and rase prces. Tha declne n oupu and rse n nflaon s moderaed when prces are scky Ths calbraon of he response o oupu s he equvalen of a coeffcen of 0.5 on annualzed percen changes. In addon, he coeffcens on he gross wage nflaon rae and he dsaser shock are se o zero. 8

11 because some frms canno opmally rese her prce. To compensae for los producvy and a lower capal sock, he non prce-adjusng frms mus ncrease her labor o manan her producon levels. Conversely, prce adjusng frms reduce her labor demand as oupu falls. As a resul, employmen ncreases n he scky prce model and scky prce and wage model, bu decreases n he flexble model. The larger oupu declne n he flexble model lowers household ncome gvng hem fewer resources o nves n capal han n he prce sckness models. In he perod afer he dsaser, he reurn of producvy o s pre-dsaser level perms frms o ncrease oupu, whch lfs households ncome and enables hem o ncrease her nvesmen n physcal capal. Tha process connues for a number of perods as he capal sock s slowly reconsruced. In he longer erm, he proraced rebuldng of he capal sock s assocaed wh below-rend oupu and perssen, above-rend pahs for employmen, nvesmen, and nflaon. 2 The endogenous response of moneary polcy o nflaon and oupu, va he Taylor rule, drves he movemens n he nomnal neres rae. The polcy reacon o hgher nflaon afer a dsaser pus upward pressure on he nomnal neres rae, whle he declne n oupu generaes downward pressure. In he sandard Taylor rule calbraon, he nflaon rae effec domnaes, so ha an ncrease n he nomnal neres rae s he prescrbed moneary polcy response. The nal ncrease n he nomnal neres rae s over 80 bass pons n he flexble model, whle rses only by abou 30 bass pons n he scky prce model and he scky prce and wage model. Desrucon of he capal sock also ncreases fuure capal renal raes, whch causes he equlbrum real neres rae o rse. The real neres rae rses nally by around 50 bass pons 2 These longer-erm effecs dsngush our dsaser shock from a smple, ransory echnology shock. The perssen ncrease n nflaon s one propery of he Taylor rule polcy ha ndcaes s subopmaly. 9

12 n he flexble model, bu only by abou 20 bass pons n he models wh nomnal rgdes. Fnally, he gradual reconsrucon of he capal sock keeps nflaon and nflaon expecaons above her seady saes for an exended perod of me n all of he models. Boh componens of he dsaser shock he desrucon of he capal sock and he emporary declne n echnology affec key economc varables afer such a shock. Table 2 decomposes he conemporaneous mpac of a dsaser shock on oupu, nflaon, and he nomnal neres rae no he wo separae componens on he models n Fgure 2. Immedaely followng he dsaser shock, he emporary reducon n echnology amplfes he declne n oupu and he rse n nflaon and he nomnal neres rae caused by he desrucon o he capal shock. In subsequen perods, he perssen responses of he varables shown n Fgure 2 are enrely arbuable o he gradual rebuldng of he capal sock. To evaluae he opmaly of polcy rules, we make use of Woodford s (2002 fndng ha an opmal moneary polcy replcaes he effcen level of oupu. 3 The nroducon of monopolsc compeon n our model creaes an neffcency wedge beween he effcen level of oupu and he flexble prce and wage level of oupu. 4 Those markup dsorons, however, are nonsochasc, so ha wedge remans consan. In parcular, our dsaser shock whch produces a emporary declne n echnology and a loss of capal has no effec on he wedge. Accordngly, he opmal moneary polcy response o a dsaser shock s closely approxmaed by he oupu dynamcs of he flexble model. 5 Usng hs creron, he dynamcs llusraed n Fgure 2 show ha hs calbraon of he Taylor rule s subopmal n he presence of nomnal 3 Km and Henderson (2005 also analycally derve hs resul n a model wh one-perod prce and wage conracs. 4 The effcen level of oupu occurs when he economy has no nomnal rgdes and no dsorons due o marke power or axes. 5 Smes and Wouers (2003 also use hs creron for evaluang opmal moneary polcy. 0

13 dsorons. An opmal moneary polcy should enable oupu o reach s flexble prce and wage equlbrum. B. A Dscreonary Polcy Response: Nomnal Ineres Rae Remans Unchanged The Taylor rule suggess ha he moneary auhory should rase he nomnal neres rae n response o a dsaser shock. Snce a moneary ghenng was no wdely ancpaed a he me of Hurrcane Karna, we consder he mplcaons of holdng he nomnal neres rae consan durng he dsaser perod. For each model, an ndependenly and dencally dsrbued shock o he Taylor rule [ε n equaon (] s calbraed o overrde he nomnal neres rae ncrease dsplayed n Fgure 2. Specfc values of he shock for he hree models dffer, bu n each case he shock causes he nomnal neres rae o reman he same durng he perod of he dsaser shock. Fgure 3 demonsraes he dynamc effecs of holdng he nomnal neres rae consan durng he dsaser perod. The mpulse responses for he flexble model are subsanally dfferen from he responses for he models wh nomnal rgdes. The dfference sems from he fac ha he mmedae adjusmen of prces and wages prevens moneary polcy from affecng real varables, whereas he presence of nomnal rgdes enables moneary polcy o have real effecs on he economy. The mpac of mananng a consan nomnal neres rae durng he dsaser shock perod can be undersood by decomposng he nomnal neres rae no real and expecednflaon componens, accordng o he Fsher equaon. In he flexble model, for example, he response of he real varables s unaffeced by a polcy desgned o keep he nomnal neres rae consan. Snce he real neres rae rses afer a dsaser shock, he only way o preven he nomnal neres rae from rsng s o have an equal reducon n nflaon expecaons. The

14 moneary auhory acheves hs resul by engneerng a declne n boh curren nflaon and expeced fuure nflaon. Nomnal rgdes preven prces and/or wages from compleely adjusng o moneary polcy changes and enable moneary polcy o have real effecs on he economy. In conras o he flexble model, a dscreonary polcy desgned o keep he nomnal neres rae consan acually smulaes oupu, employmen, and nvesmen n he models wh nomnal rgdes. The hgher oupu ncreases savngs, whch pus downward pressure on he real neres rae. Tha effec domnaes he upward pressure on he real neres rae due o he desrucon of he capal sock, so ha he real neres rae falls. The declne n he real neres rae, however, s offse by an equal rse n nflaon expecaons, whch keeps he nomnal neres rae consan n he dsaser perod. 6 Our resuls sugges ha a dscreonary polcy of holdng he nomnal neres rae consan durng he dsaser perod s no preferable o a Taylor-rule response. A comparson of oupu s responses n Fgures 2 and 3 ndcaes ha he dscreonary polcy response pushes he scky prce model and scky prce and wage model even furher from he effcen flexble prce and wage equlbrum. In oher words, he dscreonary polcy nduces a movemen furher away from he opmal moneary polcy n models wh nomnal rgdes. The dscreonary polcy also produces a larger rse n nflaon afer a dsaser shock. Alhough such a feaure s no explcly presen n our models, polcymakers mgh be concerned ha he economy could experence an expecaons rap [Char, Chrsano, and Echenbaum (998], where hgher 6 Ths fndng s based on he assumpon ha he model ncludes a modes degree of capal adjusmen coss. Our calbraon of he model assumes here are no average or margnal capal adjusmen coss and he elascy of he nvesmen-o-capal rao equals. When capal adjusmen coss are small or nonexsen, dscreonary moneary polcy s unable o generae a fall n he real neres rae. In ha case, he moneary auhory mus ghen moneary polcy, so ha nflaon expecaons fall n order o keep he nomnal neres rae unchanged. As a resul, oupu, nvesmen, and employmen declne. 2

15 nflaon becomes embedded n nflaon expecaons. If ha escalaon occurs, polcymakers are confroned wh he undesrable opon of eher accepng hgher nflaon expecaons or reducng he elevaed nflaon expecaons by ghenng moneary polcy. V. Opmal Moneary Polcy The specfcaons of he Taylor rule consdered n he prevous secon fal o generae he opmal moneary polcy response o a dsaser shock, and a dscreonary deparure from he Taylor rule can worsen he oucome from a welfare perspecve. In hs secon, we consder sysemac opmal moneary polcy rules as derved n he leraure and evaluae her mplcaons for our dsaser-shock model. Because such polcy rules may no be feasble n pracce, we also consder a consraned-opmal moneary polcy n whch he moneary auhory responds drecly o he dsaser shock. A. An Example of Opmal Moneary Polcy The opmal moneary polcy rule depends on he source of nomnal rgdes n he economy. Woodford (2002 argues ha sablzng he prce level s he opmal moneary polcy when prces are scky. In a Taylor rule seng, ha fndng ndcaes ha he parameer on nflaon, θ π, should be se o an exremely hgh value. Erceg, Henderson, and Levn (2000 fnd ha s opmal for he moneary auhory o arge he wage nflaon rae when wages are scky. Tha s, he moneary auhory should place a large wegh on he wage nflaon parameer, θ W, n he Taylor rule. In a scky prce and wage model, however, neher exreme moneary polcy rule wll suffce. A moneary polcy rule vgorously argeng prce nflaon elmnaes he effecs of he prce dsoron bu he wage rgdy remans. When wage nflaon s he arge of moneary polcy, he effecs of he wage dsoron are removed from he model, 3

16 bu he mpac of prce sckness remans. The mpac of a dsaser shock when he moneary auhory follows an exreme prcenflaon conrol polcy ( θ π = 0, 000 s llusraed n Panel A of Fgure 4. When he moneary auhory aggressvely responds o prce nflaon, moneary polcy effecvely prevens prce nflaon from changng, whch elmnaes dsorons due o he prce rgdy. Tha polcy s opmal for he scky prce model because enables he model o generae precsely he same oupu response as he flexble model. Elmnaon of he prce dsoron also causes he scky prce and wage model o resemble a model wh nomnal wage rgdes. The reducon n oupu pushes down labor demand, whch produces a declne n he real wage. Snce prce nflaon s unchanged, he nomnal wage nflaon rae falls afer a dsaser shock n all of he models. Panel B of Fgure 4 shows he effec of a dsaser shock when he moneary auhory pursues an exreme wage-nflaon arge ( θ W = 0,000. By aggressvely argeng he wage nflaon rae, he moneary auhory elmnaes dsorons caused by he nomnal wage rgdy. Therefore, wage nflaon s unchanged afer a dsaser shock n all hree models. Tha polcy causes he scky prce and wage model o resemble he scky prce model. Targeng wage nflaon, however, s no opmal for eher of he models wh nomnal rgdes because real oupu devaes from he flexble prce and wage equlbrum. The lower real wage rae caused by lower labor demand combned wh a moneary polcy objecve of mananng a consan nomnal wage rae forces prce nflaon o rse n all hree models. A moneary polcy ha aggressvely arges boh prce nflaon and wage nflaon fals o elmnae he effecs of eher prce or wage dsorons. Panel C of Fgure 4 shows he mpac of a dsaser shock for a polcy ha arges boh prce and wage nflaon. In all of he models, prce nflaon rses bu wage nflaon declnes. The wage nflaon declne s caused by a fallng real 4

17 wage rae ha domnaes he prce nflaon ncrease. In he Taylor rule, he downward pressure from wage nflaon cancels ou he upward pressure on he nomnal neres rae from he rsng prce nflaon rae. Snce he effecs of boh nomnal rgdes are sll presen, he oupu response s subopmal n boh he scky prce model and he scky prce and wage model. B. Consraned-Opmal Polcy Responses A moneary polcy rule ha vgorously responds o prce or wage nflaon flucuaons may be opmal n heory, bu may no be feasble n pracce. The mpulse responses llusraed n Fgure 4 requre ha he marke parcpans beleve he moneary auhory wll respond wh excessve force o any prce or wage devaons, so ha prces or wages wll never change. Assumng ha such a polcy s no feasble n pracce, we consder an alernave sraegy n whch he moneary auhory sysemacally and drecly responds o a dsaser shock n an oherwse sandard Taylor rule. We begn by searchng for he opmal moneary polcy response o he dsaser shock, θ n a sandard calbraon of he Taylor rule ( θ π =.5, θ y = 5, and = Followng D, θ W Woodford (2002, he opmal polcy response o a dsaser shock n a model wh nomnal rgdes s he value of θ D ha mnmzes varaon of oupu from s flexble prce and wage equlbrum. Fgure 5 dsplays a grd-search across a range of values for θ D, where a posve value for θ D mples an ncrease n he nomnal neres rae arge. 7 In boh models wh nomnal rgdes, he opmal value for θ D s posve, whch suggess ha he opmal condonal response o a dsaser shock s a polcy ghenng. A comparson of he oupu 7 For each se of parameer values, he model s smulaed,000 mes over a sample perod of 60 quarers. 5

18 responses n Fgure 6 ndcaes ha when θ D s se equal o s opmal value, he neres rae rses more han ndcaed by he Taylor rule alone, and he reducon n oupu more closely mrrors he flexble prce and wage equlbrum. The opmal coeffcen on he response of he nomnal neres rae arge o a dsaser shock can be negave n some crcumsances. Fgure 4 shows ha when he opmal polcy rule for scky prces s appled o he scky prce and wage model, oupu declnes more n ha model han n he flexble model. Such a response suggess ha he opmal coeffcen on he dsaser shock parameer n he Taylor rule can be negave. Fgure 7 llusraes an example of a plausble polcy rule calbraon ( θ π = 5.0, =, and θ W = 0. 0 where he opmal value of θ D s found o be negave for he scky prce and wage model. In hs case, he sysemac response o prce nflaon n he polcy rule now elmnaes much of he dsoron from he prce sckness. Ineffcences from he nomnal wage rgdy, however, reman n he scky prce and wage model. Elmnang ha wage dsoron requres an easng of moneary polcy n drec response o a dsaser shock (.e., θ D s negave. Fgure 8 demonsraes ha he oupu response o a dsaser shock s much closer o he opmal oupu response from he flexble model when polcy drecly responds o he dsaser shock. On he oher hand, also shows ha he aggressve response of moneary polcy o rsng nflaon sll makes opmal o rase he nomnal neres rae arge n response o a dsaser shock. The drec response o he dsaser ( θ D <0 only parly mgaes he ncrease n he nomnal neres rae. θ y VI. Concluson Once he damage from Hurrcane Karna became apparen, he meda and fnancal markes speculaed ha he Federal Reserve mgh ease polcy by delayng an expeced 25-bass- 6

19 pon ncrease n he federal funds rae. Three weeks laer a s nex meeng, however, he Federal Reserve decded o manan s pre-karna polcy sance and rase he federal funds rae by 25 bass pons. Ths paper examnes he approprae moneary polcy response o a naural dsaser such as Hurrcane Karna. Our fndngs sugges ha, n mos crcumsances, he moneary auhory should ncrease s nomnal neres rae arge afer a naural dsaser ha emporarly reduces producvy and desroys some capal sock. When moneary polcy s conduced usng a Taylor syle rule, he hgher nflaon effec domnaes he lower oupu effec such ha he endogenous polcy response o a dsaser s a rse n he nomnal neres rae. We hen apply Woodford s (2002 fndngs on opmal moneary polcy o show ha he opmal response o a dsaser depends on he sources of nomnal rgdes. Any drec easng afer a dsaser, noneheless, s domnaed by he need o ghen polcy n response o hgher nflaon and o accommodae he ncrease n he real neres rae. Thus, he opmal moneary polcy response o a naural dsaser enals an ncrease n he nomnal neres rae. The reacon of moneary polcy o any recurrng shock should be evaluaed n erms of sysemac responses o nfrequen evens, no as dscreonary responses o random shocks. Indvduals observe polcy acons and form expecaons abou smlar fuure evens. These expecaons mus be endogenzed whn economc models n order o provde robus polcy analyss. The fndngs from our dsaser-scenaro framework show ha a rgorous model-based approach o polcy analyss somemes generaes counernuve resuls. 7

20 References Buron, Mark L. and Mchael J. Hcks. Hurrcane Karna: Prelmnary Esmaes of Commercal and Publc Secor Damages, Workng Paper, Cener for Busness and Economc Research, Marshall Unversy, Sepember Calvo, Gullermo A. Saggered Prces n a Uly-Maxmzng Framework, Journal of Moneary Economcs 2 (983, Cashell, Bran W. and Mark Labone. The Macroeconomc Effecs of Hurrcane Karna, Congressonal Research Servce, Repor RS22260, Sepember 3, Char, V. V., Lawrence J. Chrsano, and Marn Echenbaum. Expecaon Traps and Dscreon, Journal of Economc Theory 8 (998, Cncnna Pos, Fed May Wa on Rae Hke, Sepember 7, Dx, Avnash and Joseph Sglz. Monopolsc Compeon and Opmum Produc Dversy, Amercan Economc Revew 67 (977, Erceg, Chrsopher J., Dale W. Henderson, and Andrew T. Levn. Opmal Moneary Polcy wh Saggered Wage and Prce Conracs, Journal of Moneary Economcs 46 (2000, Federal Open Marke Commee, Press Release, Sepember 20, Gavn, Wllam T., Benjamn D. Keen, and Mchael R. Pakko. Inflaon Rsk and Opmal Moneary Polcy, Workng Paper , Federal Reserve Bank of S. Lous, May Hamlon, James D. Tme Seres Analyss, Prnceon: Prnceon Unversy Press, (994. Hayash, Fumo. Tobn s Margnal and Average q: A Neoclasscal Inerpreaon, Economerca 50 (982, Km, Jnll and Dale W. Henderson. Inflaon Targeng and Nomnal Income Growh Targeng: When and Why are hey Subopmal? Journal of Moneary Economcs 52 (2005, Kng, Rober G. and Mark W. Wason. The Soluon of Sngular Lnear Dfference Sysems Under Raonal Expecaons, Inernaonal Economc Revew 39 (998, Kng, Rober G. and Mark W. Wason. Sysem Reducon and Soluon Algorhms for Sngular Lnear Dfference Sysems Under Raonal Expecaons, Compuaonal Economcs 20 (2002,

21 Neely, Chrsopher J. The Federal Reserve Responds o Crses: Sepember h Was No he Frs, Federal Reserve Bank of S. Lous Revew 86, (2004, Pakko, Mchael R. Changng Technology Trends, Transon Dynamcs, and Growh Accounng, Conrbuons o Macroeconomcs 5( (2005, Arcle 2. Rsk Managemen Soluons, Press Release, Sepember 9, 2005, hp:// Roemberg, Julo and Mchael Woodford. Olgopolsc Prcng and he Effecs of Aggregae Demand on Economc Acvy, Journal of Polcal Economy 37 (992, Smes, Frank and Raf Wouers. An Esmaed Dynamc Sochasc General Equlbrum Model of he Euro Area, Journal of he European Economcs Assocaon (2003, Taylor, John B. Dscreon versus Polcy Rules n Pracce, Carnege-Rocheser Conference Seres on Publc Polcy 39 (993, Woodford, Mchael. Inflaon Sablzaon and Welfare, Conrbuons o Macroeconomcs 2( (2002, -5. 9

22 APPENDIX The appendx oulnes he dealed equaons of our dynamc sochasc general equlbrum (DSGE model wh boh scky prces and scky wages. Our model s smlar n srucure o ha n Gavn, Keen, and Pakko [2006], excep ha ncludes a dsaser shock. The calbraons needed o conver he prce and wage sckness no flexble specfcaons and he parameerzaon of he moneary polcy rule are dscussed n he ex of he paper. Calbraed values for he remanng parameers are presened n Table of he appendx. Once he sysem of equaons s calbraed, he model s solved for s seady sae parameer values; he model s lnearzed around ha seady sae; and he raonal expecaons soluon s calculaed usng he mehodology of Kng and Wason (998, Households: Households supply dfferenaed labor servces o he frms n a monopolscally compeve labor marke. Toal aggregae labor hours, n, s calculaed as a Dx and Sglz (977 connuum of labor hours, n,h, suppled by each household, h [0,] : n = ( n 0 h, ε w /( ε w dh ( ε w / ε w, where ε w s he wage prce elascy of demand for household h s labor servces. Frms demand for household h s labor servces are calculaed by mnmzng labor coss subjec o he equaon of aggregae labor hours: n ε W w h, h, = W where W h, s he nomnal wage rae of household h, and W s nerpreed as he aggregae nomnal wage rae: W ( W = 0 h, 20 (ε w n, dh /(ε w.

23 Households are nfnely lved agens who parcpae n sae conngen secures markes. Tha assumpon enables households o be homogenous wh respec o consumpon, nvesmen, capal, money, and bonds. Household h values consumpon, c, and real money balances, (M /P, bu dslkes labor. Those preferences are summarzed by he followng expeced uly funcon: where E σ n *, ln(, h β c χ σ = 0 c * = M P ( σ 2 / σ 2 σ 2 /( σ 2 ( σ 2 / 2 ( σ c b, E s he condonal expecaon a me and β s he dscoun facor. Households own he capal sock, k, and ren o he frms. In each perod, household h selecs a level of nvesmen,, such ha: k = φ( / k k 2 ( δ k, where k s amoun capal carred no perod, φ( represens a Hayash [982] form of capal adjusmen coss and δ s he deprecaon rae. The capal adjusmen coss are he resources los n he converson of nvesmen o capal, φ / k k, and are an ncreasng ( and convex funcon of he seady sae nvesmen-o-capal rao such ha φ ( > 0 and φ ( < 0. A dsaser, f srkes, occurs a he begnnng of perod before producon begns. The non-desroyed capal, k, ha s avalable for use n producon s k k κ Dˆ = ( Household h begns a perod wh an nal sock of nomnal money balances, M -, and receves a paymen, R - B -, from s nomnal bond holdngs, B -, where R s he gross nomnal.

24 22 neres rae. Durng he perod, household h receves labor ncome, W h, n h,, renal ncome from capal, P q k, dvdends from he frms, D, a lump-sum ransfer from he moneary auhory, T, and a paymen from he sae conngen secures markes, A h,, where q s he real renal rae of capal. Those funds hen are used o fnance consumpon and nvesmen purchases and end-ofhe-perod bond, B, and money, M, holdngs. The budge consran for household h s represened as follows:. (,,, h h h A M T B R D k P q n W M c P B = Fnally, household h chooses a level of c,, k, B, and M ha maxmzes s expeced uly subjec o s capal accumulaon and budge consran equaons. Household h negoaes a wage conrac ha can reman n place for an unknown number of perods. The opporuny o renegoae a wage conrac follows a Calvo [983] model of random adjusmen. Tha s, η w s he probably ha household h can se a new nomnal wage, W *, and ( η w s he probably ha s nomnal wage can only ncrease by he seady sae nflaon rae, π. When a wage adjusmen opporuny occurs, household h selecs a nomnal wage, W *, whch maxmzes s uly gven he frms demand for s labor: ( ( ( ( ( ( ( (, / / ( * 0 ( 0 * = = = σ ε σ σ σ ε σ σ ε π π η β π η β ε χε w w w w w w w c c n W P E n W E W where ( η w s he probably ha anoher wage adjusmen opporuny wll no ake place n he nex perods. Fnally, a value η w equal o mples ha he nomnal wage s perfecly flexble. Frms: Frms, whch are owned by he households, produce dfferenaed goods n a monopolscally compeve marke. Frm f hres labor, n f,, and rens capal, k f,, from he

25 households o produce s oupu, y f,, accordng o a Cobb-Douglas producon funcon: y f, = ( k f, ( n f, α (α, where 0 α. Frm f hen chooses he combnaon of labor and capal ha mnmzes s producon coss, w n q k, gven s producon funcon. Solvng frm f s cos f, f, mnmzaon problem yelds he followng facor demand equaons: q = ψ α( n f / k f,, (α, W / P = ψ ( α( k f, / n f, where ψ s he Lagrange mulpler on he cos mnmzaon problem and s nerpreed as he real margnal cos of producng an addonal un of oupu. The margnal cos, ψ, s dencal for all frms because every frm pays he same renal raes for capal and labor. Aggregae oupu, y, s a Dx and Sglz (977 connuum of dfferenaed producs: α, y = ( y 0 f, ε /( ε p p df ( ε / ε p p, where ε p s he prce elascy of demand for good f. Cos mnmzaon by households yelds he demand equaon for frm f s good: y ε P p f, f, = P where P f, s he prce charged by frm f and P s a nonlnear prce ndex: y, P = ( Pf 0, (ε p df /(ε p. Each perod, frm f also may have an opporuny o selec a new prce, P f,, for s produc, y f,. Frm prce adjusmen opporunes follow a Calvo [983] model of random adjusmen. Tha s, he probably a new prce, P *, can be se s η p, and he probably he prce 23

26 24 only can adjus by he seady sae nflaon rae, π, s ( η p. A prce adjusng frm selecs a prce, P *, ha maxmzes he dscoun value of s expeced curren and fuure profs subjec o s facor demand and produc demand equaons: ( ( ( (, 0 0 * = = = p p p p y P E y P E P p p ε ε π η π λ β ψ π η π λ β ε ε where β λ π s he households real value n perod of an addonal un of profs n perod, and ( η p s he probably ha he frm wll no have anoher prce adjusng opporuny n he nex perods. Fnally, prces are compleely flexble n hs specfcaon when η p equals. The Moneary Auhory: The moneary auhory ulzes a generalzed Taylor (993 rule:, / ln( / ln( / ln( / ln( / ln(, R D y W D D y y W W R R ε θ θ θ π π θ π Δ Δ = where R s he nomnal neres rae, π s he acual gross nflaon rae, W Δ s he gross nomnal wage growh rae, D s he dsaser shock varable, and R, ε s a ransory moneary polcy shock. Fnally, W Δ equals π n he seady sae because he model do no nclude any endogenous growh.

27 Table : Parameer Calbraons Parameer Symbol Value Deprecaon rae δ 25 Dscoun facor β 0.99 Lesure uly parameer σ 0.33 Consumpon uly parameer σ Capal s share of oupu α 0.33 Seady sae gross quarerly nflaon rae π.005 Seady sae labor supply n 0.3 Seady sae nomnal money supply M.0 Prce elascy of demand ε p 6.0 Wage elascy of demand ε w 6.0 Average capal adjusmen coss parameer φ ( /k Margnal capal adjusmen coss parameer φ (.0 Elascy of he /k-rao wh respec o Tobn s q χ = [( / k φ ( / φ ( ] Table 2: The Conemporaneous Impac of a Dsaser Shock (Percen Flexble Model y π (a.r. R (a.r Full Dsaser Shock Capal Only (ζ = Technology Only (κ = Scky Prce Model y π (a.r. R (a.r Full Dsaser Shock Capal Only (ζ = Technology Only (κ = Scky Prce and Wage Model y π (a.r. R (a.r Full Dsaser Shock Capal Only (ζ = Technology Only (κ =

28 Fgure : Reacon of Fed Funds Fuures Impled Fed Funds Rae 30-Day Fed Funds Fuures, Sepember 2005 Conrac Percen Hurrcane Karna Makes Landfall //2005 8/8/2005 8/5/2005 8/22/2005 8/29/2005 9/5/2005 9/2/2005 9/9/2005 9/26/2005 Impled Fed Funds Rae 30-Day Fed Funds Fuures, Ocober 2005 Conrac Percen Hurrcane Karna Makes Landfall //2005 8/8/2005 8/5/2005 8/22/2005 8/29/2005 9/5/2005 9/2/2005 9/9/2005 9/26/

29 Fgure 2: Taylor Rule Response Oupu Employmen Percen Percen Capal Sock Invesmen Percen Percen Inflaon Nomnal Ineres Rae Percen, a.r. Percen, a.r. 0.6 Real Ineres Rae Flexble Model Percen, a.r. Scky Prce Model Scky Prce and Wage Model 27

30 Fgure 3: Polcy Response wh Dscreon Oupu Employmen Percen Percen Capal Sock Invesmen Percen Percen Inflaon Nomnal Ineres Rae Percen, a.r. Percen, a.r. 0.6 Real Ineres Rae Flexble Model Percen, a.r. Scky Prce Model Scky Prce and Wage Model 28

31 Fgure 4: Fully Credble Prce and Wage Inflaon Conrol Panel A: Opmal Conrol for Scky Prces Panel B: Opmal Conrol for Scky Wages Panel C: Combnaon Polcy Oupu Oupu Oupu Percen Percen Percen Prce Inflaon Prce Inflaon Prce Inflaon Percen, a.r. Percen, a.r. 0.5 Percen, a.r Wage Inflaon Wage Inflaon Wage Inflaon (ar Percen, a.r Percen, a.r Percen, a.r Flexble Model Scky Prce Model Scky Prce and Wage Model 29

32 Fgure 5: Drec Responses o Dsaser Shocks (n a Taylor Rule Seng 0.6 Oupu Gap Sd. Dev Dsaser Response Parameer Scky Prce Model Scky Prce and Wage Model * Parameer values: θ π =.5, θ y = 5 30

33 Fgure 6: Taylor Rule wh Drec Responses o Dsaser Shock Scky Prces Scky Prces and Wages Oupu Oupu Percen -0. Flexble Model Percen -0. Flexble Model Nomnal Ineres Rae (ar Nomnal Ineres Rae (ar Percen, a.r. 0.3 Percen, a.r Polcy rule whou drec response Wh drec response o dsaser shock * Parameer values: θ π =.5, θ y = 5 3

34 Fgure 7: Drec Responses o Dsaser Shocks (Wh enhanced reacon o nflaon 0.0 Oupu Gap Sd. Dev Dsaser Response Parameer Scky Prce Model Scky Prce and Wage Model * Parameer values: θ π = 5.0, θ y = 0 32

35 Fgure 8: Enhanced Response o Inflaon wh Drec Responses o Dsaser Shock Scky Prce Model Scky Prces and Wage Model Oupu Oupu Percen -0. Flexble Model Percen -0. Flexble Model Nomnal Ineres Rae (ar Nomnal Ineres Rae (ar Percen, a.r. 0.3 Percen, a.r Polcy rule whou drec response Wh drec response o dsaser shock * Parameer values: θ π = 5.0, θ y = 0 33