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

D.3ModelFit

Welookatthesteady-statepropertiesofourstylizedeconomyasafirstmeasureof modelperformance.ThetoppanelofTable5reportsselectedratiosandvariableswhen parametersaresettotheirposteriormode,alongwiththeanalogobjectsinthedata.The modelanddatamatchwell.Thisisthecasebyconstructionfortheratioofgovernment spendingtoGDPandinflation.Thegoodfitisnottrivialbecauseourobservablesare demeanedandexpressedmostlyingrowthrateandthereforetheestimationprocedure doesnotuseinformationinthedataaboutthesortofratiosshowninTable5.An exceptiontothegoodmatchisthenominalinterestrate,toohighinthemodel.Given thatinsteadystateR=πµ_z^∗/β^pandπ>0andµ_z^∗>0,wereachalowerboundforR asweincreaseβ^pclosertoone.

Oursecondmeasureofmodelfitrelatestothedynamicpropertiesofoureconomy.

14Wetreatsteady-stateentrepreneurialleverageL^easaparameterandestimateit,settingitspriormean totheaverageof2.1inoursample.Wethencalibratetheentrepreneurialdividendparameterδ^eto0.018

soastobeconsistentwithL^e’sposteriormodeof1.57.

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Table5:StaticandDynamicProperties,ModelVersusData

Steady-StateVariables ModelData ConsumptiontoGDP c/y 0.55 0.49 InvestmenttoGDP i/y 0.22 0.27 GovernmentspendingtoGDP g/y 0.24 0.24 DebttoGDP b/(4y) 1.38 1.45 Householddebttototaldebt bⁱ/b 0.48 0.40 Inflation,annualrate π 1.51 1.51 Nominalinterestrate,annual R 2.61 1.85 Businesssectorleverage L^e 1.57 2.10

DynamicVariables Correlation StandardDeviationAutocorrelation

ModelDataModelDataModelData

GDP 1.00 1.00 1.00 1.00 0.94 0.92

Consumption 0.98 0.92 0.67 0.76 0.94 0.92
Investment 0.99 0.97 2.97 2.92 0.95 0.91
Hours 0.99 0.91 1.27 0.59 0.94 0.92
Inflation 0.70 0.77 0.12 0.08 0.91 0.91
Nominalrate 0.86 0.81 0.25 0.58 0.93 0.92
Householdcredit 0.55 0.65 0.92 0.51 0.96 0.96
Businesscredit 0.46 0.13 1.09 0.79 0.97 0.92
Householdspread −0.69−0.91 0.10 0.46 0.90 0.91
Businessspread −0.53−0.96 0.07 0.27 0.90 0.90

Notes:Modelvaluesarecomputedattheposteriormode.Inthebottompanelmodelanddatavariables aredetrendedwithabandpassfilter(6,32).StandarddeviationsarenormalizedtothatofGDP.

Wesimulatethemodelbyshuttingdownallshocksexceptthemarketsentimentshock. ThebottompanelofTable5reportsmomentsofselectedvariables,whereboththe artificialandactualdataarefilteredwithabandpassfilter(6,32).Byandlarge,the modelhitbyauniquedisturbancedoesagoodjobatreplicatingthesalientfeatures ofthedata.Themainshortcomingsarethemodel’svolatilityofhours,toohigh,and interestrates,toolow.WebelievethereareinstitutionalarrangementsintheEuropean labormarketthatlimitfluctuationsinemployment.Still,itisremarkablethatthemodel matchesthedataatbusiness-cyclefrequencysoclosely,giventhatitwasnotestimated inthefrequencydomain.

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