speeches · October 16, 2008

Regional President Speech

James Bullard · President

INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY PANEL DISCUSSION: THE ROLE OF POTENTIAL OUTPUT IN POLICYMAKING JamesBullard* FederalReserveBankofSt. Louis 33rdAnnualEconomicPolicyConference St. Louis,MO October17,2008 ViewsexpressedarethoseoftheauthoranddonotnecessarilyreflectofficialpositionsoftheFOMCortheFederalReserveSystem. INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY MY DISCUSSION Describeideasabout“proper”detrending. Coreidearequiresexplicittheoryofbothgrowthand fluctuations. Ambition: Thedatashouldthenbedetrendedbythetheoretical growthpath. Question:Howtogetthegrowthpathtolooklikethedata? Answer:Simplegrowthmodelwithoccasionaltrendbreaksand learning. ApplicationsinRBCandNKmodels. J.BullardandJ.Duffy.“LearningandStructuralChangein MacroeconomicData.” J.BullardandS.Eusepi.“DidtheGreatInflationOccurDespite PolicymakerCommitmenttoaTaylorRule?” Policy: HowTaylorrulescanleadyouastray. INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY MAIN IDEAS Equilibriumbusinesscycleresearch:Awideclassofmodels includingRBC,NK. Allbasedontheconceptofabalancedgrowthpath. DataassummarizedbyPerron(1989)andHansen(2001)suggest breaksintrends. Nonstationaryaspectsofthedataaredifficulttoreconcilewith availablemodels. INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY CURRENT PRACTICE Trend-cycledecompositiondonemostlywithatheoretic, statisticalfilters. SeeKingandRebelo(1999). Thedisciplineimpliedbythebalancedgrowthassumptionis dropped. Thisisamistake,butonethatdominatestheliterature. INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY SOME WELL-KNOWN CRITICISMS Filtersdonotremovethesametrendthatthebalancedgrowth pathrequires. Currentpracticedoesnotrespectthecointegrationofthe variables,themultivariatetrend,thatthemodelimplies. Filteredtrendsimplychangesingrowthrates,andagentswould wanttoreacttothesechanges. The"businesscyclefacts"arenotindependentofthestatistical filteremployed. Estimation,e.g.,Smets-Woutersdoesnotaddressthisissue. INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY HOW TO IMPROVE ON THIS? Thecriticismsarecorrectinprinciple. Theyarequantitativelyimportant. Theseissuescannotberesolvedbyalternativestatisticalfilters, becausethosefiltersareatheoretic. Instead,usetheorytotelluswhatthegrowthpathshouldlook like. INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY CORE IDEAS "Model-consistentdetrending." Thetrendsremovedfromthedataareexactlythesameasthe onesimpliedbythemodel. Allowagentstoreactto(rare)changesintrendgrowthrates. Respectthecointegrationofthevariablesthatthebalanced growthpathimplies. Themethodologyhaswideapplicability. INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY FEATURES OF THE ENVIRONMENT Simpleequilibriumbusinesscyclemodelwithexogenous, stochasticgrowth. ReplacerationalexpectationswithlearningviaEvansand Honkapohja(2001). Verifyexpectationalstability. Calibrate,allowingoccasionaltrendbreaks,inspiredbyPerron (1989). INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY MAIN FINDINGS Amoresatisfactorymethodofdetrending. Alargefractionoftheobservedvarianceofoutputrelativeto trendcanbeattributedtostructuralchange. IntheNKworld,learningaboutaproductivityslowdowncan sendinflationupby300b.p. INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY PREFERENCES AsinCooleyandPrescott(1994),arepresentativehousehold maximizes ∞ E ∑ βtηt lnC +θln 1 `ˆ (1) t t t (cid:0) t=0 h (cid:16) (cid:17)i subjectto C +I Y , (2) t t t (cid:20) I t =K t+1 (1 δ)K t , (3) (cid:0) (cid:0) and... INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY TECHNOLOGY Theproductiontechnologyis 1 α Y =sˆ Kα X N `ˆ (cid:0) , (4) t t t t t t (cid:16) (cid:17) X = γX , X =1, γ >0. (5) t t 1 0 (cid:0) N = ηN , N =1, η >0. (6) t t 1 0 (cid:0) sˆ =sˆ ρ e , sˆ =1, (7) t t 1 t 0 (cid:0) INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY BALANCED GROWTH Aggregateoutput,consumption,investment,andcapitalwill growatgrossrateγηalongthebalancedgrowthpath. Definekˆ = Kt ,yˆ = Yt ,cˆ = Ct ,andrewritethefirstorder t XtNt t XtNt t XtNt conditionsandconstraintsoftheproblem. Thenew,stationarysystemhasasteadystate cˆ ,yˆ ,kˆ ,`ˆ = c¯,y¯,k¯,`¯ t. t t t t 8 T(cid:16)hesteady(cid:17)state(cid:0)values(cid:1)dependuponthegrossgrowthratesγ andη. INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY KEY RATIOS Capital-outputratioalongabalancedgrowthpath k¯ αβ = , (8) y¯ γ β(1 δ) (cid:0) (cid:0) Consumption-outputratioalongabalancedgrowthpath c¯ γ β(1 δ) αβ(γη 1+δ) = (cid:0) (cid:0) (cid:0) (cid:0) . (9) y¯ γ β(1 δ) (cid:0) (cid:0) INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY LINEAR APPROXIMATION NeedalinearsystemtoapplyEvansandHonkapohja(2001). Uselogarithmicdeviationsfromsteadystate. Define cˆ kˆ `ˆ c˜ =ln t , k˜ =ln t , `˜ =ln t , (10) t (cid:18) c¯ (cid:19) t k¯ ! t `¯ ! yˆ sˆ y˜ =ln t , ands˜ =ln t . (11) t t y¯ s¯ (cid:18) (cid:19) (cid:18) (cid:19) Rewritesystemintermsoftildevariables. INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY MORE ON LINEAR APPROXIMATION Thelinearizedsystemisstillnotsatisfactory,becausethelog deviationsinvolve c¯,y¯,k¯,`¯ . Wanttheagentstolearnthevector c¯,y¯,k¯,`¯ whenachangein (cid:0) (cid:1) growthoccurs. (cid:0) (cid:1) Definec =lncˆ ,k =lnkˆ ,y =lnyˆ ,` =ln`ˆ ,ands =lnsˆ . t t t t t t t t t t Alsodefinec=lnc¯,k=lnk¯,y=lny¯,` =ln`¯,ands=lns¯ =0. Rewritethesystemintermsoftheseredefinedvariables;reduce systemtothreeequations. INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY THE SYSTEM UNDER RATIONAL EXPECTATIONS Thesystem: c t = 10 + 11 E t c t+1 + 12 E t k t+1 + 13 E t s t+1 (12) B B B B k = + c + k + s (13) t 20 21 t 1 22 t 1 23 t 1 D D (cid:0) D (cid:0) D (cid:0) s = ρs +ϑ (14) t t 1 t (cid:0) The and arecompositesoffundamentalparameters. Also, ij ij B D ϑ =lne . t t INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY RECURSIVE LEARNING Studythissystemunderarecursivelearningassumption. Assumeagentshavenospecificknowledgeoftheeconomy. Endowthemwithaperceivedlawofmotionwhichlooksalot likeaVAR. INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY MORE ON RECURSIVE LEARNING Thesystem: c t = B 10 + B 11 E t ?c t+1 + B 12 E t ?k t+1 + B 13 E t ?s t+1 +∆ t (15) k = + c + k + s (16) t 20 21 t 1 22 t 1 23 t 1 D D (cid:0) D (cid:0) D (cid:0) s = ρs +ϑ (17) t t 1 t (cid:0) Theshock∆ preventsperfectmulticollinearity. Ithasstandard t deviation1/1000thofe . t INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY THE PERCEIVED LAW OF MOTION Theagentsuse c = a +a c +a k +a s , (18) t 10 11 t 1 12 t 1 13 t 1 (cid:0) (cid:0) (cid:0) k = a +a c +a k +a s . (19) t 20 21 t 1 22 t 1 23 t 1 (cid:0) (cid:0) (cid:0) Thiscorrespondsinformtotheequilibriumlawofmotionfor theeconomy. Theagentsaregivenequation(17). Theycouldestimateρas wellwithoutmateriallychangingtheresults. Thepresenceofconstanttermsallowstheagentstolearnsteady statevaluesofvariables. INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY THE MAPPING FROM PLM TO ALM Assumet 1datingofexpectations. (cid:0) TakeexpectationsbasedonthePLM. Substitutetoobtaintheactuallawofmotion(ALM) INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY MORE ON THE MAPPING FROM PLM TO ALM Thisimplies c =T +T c +T k +T s +∆ (20) t 10 11 t 1 12 t 1 13 t 1 t (cid:0) (cid:0) (cid:0) where T = + [a +a a +a a ]+ 10 10 11 10 11 10 12 20 B B [a +a a +a a ], (21) 12 20 21 10 22 20 B T = a2 +a a + [a a +a a ], (22) 11 B 11 11 12 21 B 12 21 11 22 21 h i T = [a a +a a ]+ a a +a2 , (23) 12 B 11 11 12 12 22 B 12 21 12 22 h i T = [a a +a a +a ρ]+ 13 11 11 13 12 23 13 B [a a +a a +a ρ]+ ρ2 . (24) 12 21 13 22 23 23 13 B B h i INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY THE SYSTEM UNDER LEARNING Write c T T T T c t 10 11 12 13 t 1 k = + k (cid:0) t 20 21 22 23 t 1 2 3 2D 3 2D D D 32 (cid:0) 3 s 0 0 0 ρ s t t 1 (cid:0) 4 5 4 5 4 54 1 5 0 0 ∆ t + 0 0 0 0 . (25) 2 32 3 0 0 1 ϑ t 4 54 5 INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY RATIONAL EXPECTATIONS AstationaryMSVsolutionsolves T =a , (26) 1i 1i fori=0,1,2,3,withalleigenvaluesofthematrix T T T 11 12 13 (27) 21 22 23 2D D D 3 0 0 ρ 4 5 insidetheunitcircle. Thereisonlyonesuchsolutionforthismodel. INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY EXPECTATIONAL STABILITY Expectationalstabilityisdeterminedbythefollowingmatrix differentialequation d (a) =T(a) a, (28) dτ (cid:0) whereT = (T ,T ,T ,T )anda=a withi=1,2and 10 11 12 13 i,j j=1,2,3,4. AparticularMSVsolutionisE-stableiftheMSVfixedpointof thedifferentialequation(28)islocallyasymptoticallystableat thatpoint. CalculatedE-stabilityforthismodelandfoundthatitholdsat baselineparametervalues(includingthevariousvaluesofγand ηused). Arealtimelearningversioncanbeimplemented. INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY STABILITY UNDER CONSTANT GAIN LEARNING Thesystemshouldbelocallystableintherealtimelearning dynamicswithgainoft 1. (cid:0) Withaconstantgain,thesystemmaydepartthedomainof attraction. Buttheconstantgainalsoallowstheagentstotrackthebalanced growthpath,shouldanunderlyingparameterchange unexpectedly. Theagentsadmittheirmodelmaybemisspecified. Howwouldthesystemrespondtoanysmallenoughparameter change? INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY AN APPLICATION TO US DATA Modelistoosimpletomatchdirectlywithdata. Butitisalsoawell-knownbenchmarkmodel. Soitispossibletoassesshowimportantthedetrendingissueis fordeterminingthenatureofthebusinesscycleaswellasforthe performanceofthemodelrelativetothedata. INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY DATA QuarterlyU.S.data1948Q1to2002Q1. Concernthattheaggregatesaddup. Subtractrealgovernmentpurchasesandfarmbusinessproduct fromrealGDPtogetnonfarmprivatesectoroutput. Usingnonfarmprivatesectorhoursfromtheestablishment survey. INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY MORE ON THE DATA Nonfarmprivatesectorproductivitycreatedfromthese. Consumptiondefinedaspersonalconsumptionexpendituresfor nondurablegoodsandservices,plusnetexportsofservices,less farmbusinessproduct. Investmentdefinedasgrossprivatedomesticinvestmentplus personalconsumptionexpendituresonconsumerdurables,plus netexportsofgoods. Seriesessentiallyaddupdespitechain-weighting. Allocated discrepenciesusingtheconsumption-outputratioforthatyear. INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY A STANDARD CALIBRATION CooleyandPrescott(1994). β =.987,θ =1.78,α =.4,ρ =.95,σ =.007. e Growthratesofproductivityandlaborinput: allowthoseto change. Gainchoseninformallyatg=.00025;doesnotseemtoimpact resultsimportantly. INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY BREAKS ALONG THE BALANCED GROWTH PATH Productivityslowdown: Hansen(2001),Perron(1989),Bai, Lumsdaine,andStock(1998). Onlyallowtrendbreakswherecleareconometricevidenceis available? INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY HOW TO CHOOSE BREAK DATES Oneapproach: conformitybetweenmeasuredproductivityand laborinput,inthemodelandinthedata. 1 Choosebreakdatesandgrowthrates. 2 Compareimpliedtrendsinmeasuredproductivityandlaborinput todata. 3 Ifdiscrepenciesexist,returnto1,otherwiseterminateatafixed point. Useasearchprocess(geneticalgorithm)toimplementthis process. INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY OPTIMALTRENDBREAKS N(t) X(t) Initialannualgrowthrate,percent 1.20 2.47 Breakdate 1961,Q2 1973,Q3 Mid-sampleannualgrowthrate,percent 1.91 1.21 Breakdate 1993,Q3 (cid:0) Endingannualgrowthrate,percent 1.91 1.86 TABLE: Optimalbreakdatesandgrowthratesforfundamentalfactors drivinggrowthinthemodel,basedonasearchofpossibledatesand growthrates.Thesechoicesproducemeasuredproductivityandhours seriesthatconformbesttotheUSdata. INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY DEFINING A TREND Atrendistheeconomy’spathifonlylowfrequencyshocks occur. Turnthenoiseonthebusinesscycleshockdown,multiplyingσ e by1/1000. Whathappensintheeconomywheretheonlymeaningful shocksarethosetoproductivitygrowthandhoursgrowth? Normalization: initiallyonabalancedgrowthpath. INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY ARTIFICIAL ECONOMIES ConfirmthatestimatedcoefficientsareinitiallyclosetoRE values. Collectanadditional217quartersofdata,withtrendsbreaking asdescribedabove. Detrendthedatausingthesame(multivariate)trendthatisused fortheactualdata. Collectstatisticsoveralargenumberofsimulations. INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY BUSINESS CYCLE STATISTICS TABLE3. BUSINESSCYCLESTATISTICS Relative Contemporaneous Volatility Volatility Correlations Data Model Data Model Data Model Output 3.25 3.50 1.00 1.00 1.00 1.00 Consumption 3.40 2.16 1.05 0.62 0.60 0.75 Investment 14.80 8.86 4.57 2.53 0.65 0.92 Hours 2.62 1.54 0.81 0.44 0.65 0.80 Productivity 2.52 2.44 0.77 0.70 0.61 0.92 TABLE: Businesscyclestatistics,model-consistentdetrending. INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY NK APPLICATION INTRODUCTION COREIDEAS ENVIRONMENT RECURSIVELEARNING ANAPPLICATIONTOUSDATA SUMMARY SUMMARY Providessomemicrofoundationsforcurrent,atheoretical practices. Structuralchangeaccountsforalargefractionofobserved variabilityofoutput. Learningprovidesthe“glue”thatholdsthevariousbalanced growthpathstogether. Adjustmentfollowingatrendchangeisrelativelyrapid. Learningaboutstructuralchangecouldhavelargeeffectson policy.

Cite this document

APA

James Bullard (2008, October 16). Regional President Speech. Speeches, Federal Reserve. https://whenthefedspeaks.com/doc/regional_speeche_20081017_james_bullard

BibTeX

@misc{wtfs_regional_speeche_20081017_james_bullard,
  author = {James Bullard},
  title = {Regional President Speech},
  year = {2008},
  month = {Oct},
  howpublished = {Speeches, Federal Reserve},
  url = {https://whenthefedspeaks.com/doc/regional_speeche_20081017_james_bullard},
  note = {Retrieved via When the Fed Speaks corpus}
}