P aper No. 907 Banks, shadow banks, and business c



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DEstimation

Thissectioncontainsdetailsaboutthemodel’sestimation.Wediscusstheparameteri- zationandpresenttwomeasuresofmodelfit.



D.1CalibratedParameters

Anumberofmodelparametershaveaclearcounterpartinthedata,sowecalibratethem tomatchthemeaninoursample.Theseincludetheannualgrowthrateoftheeconomy µz=1.01%;theannualinflationrateπ=1.50%;theannualrateofinvestment-specific technologicalchangeΥ=0.78%;theshareofgovernmentspendinginGDPηg=0.24; thecapitalshareinproductionα=0.37;andthetaxratesonconsumptionτc=0.19, laborincomeτl=0.12,andcapitalincomeτk=0.33.

Wefixafewotherparametersasfollows.Thediscountfactorofpatienthouseholds βpequals0.9998,whichpinsdowntheannualizednominalinterestrateRto1.87%.

Thediscountfactorofimpatienthouseholdsβimustbelowerthanβpandissetto 0.97.CapitaldepreciationδandlaborsupplyelasticityσLarefixedat0.025and1, respectively.Wesetthesteady-statepriceandwagemarkupsλpandλwto1.20and 1.05,followingtheliterature.AllcalibratedparametersappearatthetopofTable4.



D.2EstimatedParameters

Weestimatetheremaining41parameterswithBayesiantechniques.Thebottompanel ofTable4reportstheirpriorandposteriordensities.Mostofthestructuralparameters arecommonintheliteratureandareassignedstandardpriors.13Ourresultsfallinline withpreviousstudies.Forinstance,thepolicyresponsetoinflationαπis2.19while theinterestratesmoothingcoefficientρpis0.66,consistentwithexistingestimates. PosteriorvaluesfortheCalvopriceξpandwageξwstickiness,of0.83and0.77respec- tively,aresensiblecomparedto0.91and0.74foundbySmetsandWouters(2003). Consumptionhabitofpatientbcpandimpatienthouseholdsbic,at0.82and0.75,look reasonable.Oneexceptionisthepriceindexationparameterιp.Overtheperiodfrom 1999Q1to2019Q4coveredbyoursample,inflationintheeurozonewasremarkably lowandstable.Theestimationprocedureaccommodatesthisbyascribingahighvalue of0.93tothiscoefficient.

Wenowdiscussthelesshabitualparameters.ThecostofadjustinghousingShis

essentialtosmooththedynamicsofimpatienthouseholdhousing,andhencehousehold debt,avariableweobserve.Becauseitiscostlytodisposeofhousingimmediately, impatienthouseholdsreactgraduallytoshocks.TheposteriormodeofSh,at52,is

13ThemainreferencesareSmetsandWouters(2003,2007),Justiniano,Primiceri,andTambalotti (2010),andChristiano,Motto,andRostagno(2014).

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whatittakestodisciplinethedynamicsofhouseholddebt.Anotherimportantparameter istheshareκofpatienthouseholdsintheeconomy.Wesetitspriorto0.5basedon theobservationthatatleasthalfofhouseholdsinEuropeholdsomeformofdebt. Ourposteriorestimateis0.74,suggestingfinancially-constrainedconsumersrepresent roughlyaquarterofthepopulation,inaccordwithmicroevidenceinKaplan,Violante, andWeidner(2014).Next,wesetthepriormeanofthesteady-statedefaultprobability ofhouseholdsFi(ω¯i)andentrepreneursFe(ω¯e)toanannualpercentagerateof3.We findahigherestimateforFi(ω¯i),consistentwiththefactthathouseholdsdefaultmore thanfirms.14Finally,twoparametersµhandµkarespecifictothefinancialsector.

Theygovernthemarkupofshadowbanksinthesecuritizedmortgageandbusinessloan markets,respectively.Wecentertheirprioraroundameanof40percent,intheupper rangeofdataonpre-taxreturnonequity.Posteriorestimatesarelower,at0.19forµh and0.22forµk,indicatingthemodeldoesnotneedahighdegreeoffinancialfrictions

toperformwellquantitatively.
Weturntotheexogenousprocesses.EachrowinthelowerpartofTable4corre-

spondstoashockandreportsapair(ρ,σ).Theonlyexceptionisthemonetarypolicy shockwhoseautocorrelationwesettozero,giventhatthereisalreadyasmoothing parameterintheTaylorrule.Themarketsentimentshockstandsout,withthehighest standarddeviationofallshocks,0.07,andapersistenceof0.939.Thisautocorrelation islowerthanwhattheliteratureusuallyfindsforfinancialanduncertaintyshocks,typi- cally0.95–0.98,andisonereasonwhytheresponsesofourmodeltoamarketsentiment shockareclosetothoseofalessstructuralVAR.




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