英國的財政通脹.pdf

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1、Fiscal Inflation in the UKFrancesco BianchiJohns Hopkins UniversityNBER&CEPRQingyuan FangJohns Hopkins UniversityLeonardo MelosiUniversity of Warwick and CEPRIntroductionFiscal policy and real interest ratesWe study inflation and output dynamics in the United KingdomWe employ a model with partially

2、unfunded government debt(Bianchi,Faccini,and Melosi,QJE 2023)1At any given point in time,part of the outstanding government debt is unfunded2Unfunded debt is not backed by future fiscal adjustmentsInflationary pressureaccommodated by the central bankDebt stability achieved with a mix of fiscal adjus

3、tments and inflationWith nominal rigidities,unfunded fiscal shocks cause persistent movements ininflation and in real interest ratesA fiscal theory of persistent inflationWith respect to other shocks,policymakers follow a typical Monetary-led policyother shocks propagate as in standard business cycl

4、e modelsBianchi Fang MelosiFiscal Inflation in the UK1/23IntroductionEmpirical analysisWe augment a TANK model with partially unfunded debtDistinct implications of funded and unfunded shocks1Funded fiscal shocks:small increase in real interest rates2Unfunded fiscal shocks:large decline in real inter

5、est ratesMain results:Low-frequency movements in inflation driven by unfunded fiscal shocksPandemic:Large fiscal stimulus and accommodative monetary policy1Quick rebound in real activity counteracting adverse supply-side shocks2Rapid increase in fiscal inflation3While actual inflation has declined,f

6、iscal inflation remains elevated as of 2024Bianchi Fang MelosiFiscal Inflation in the UK2/23Endowment economiesEndowment economiesBianchi Fang MelosiFiscal Inflation in the UK2/23Endowment economiesFisherian modelConsider a linearized endowment economy:rn,t=Et t+1,(1)sb,t=1 sb,t1+rn,t1 t(1)t,(2)rn,t

7、=t,(3)t=sb,t1+t.(4)Plugging the monetary rule into the Fisher equation leads to the monetary block:Et t+1=t.(5)Combining the law of motion for debt with the fiscal rule yields the fiscal block:sb,t=11(1)sb,t1+1 rn,t1 t(1)t.(6)Bianchi Fang MelosiFiscal Inflation in the UK3/23Endowment economiesEquili

8、brium determinacy(Leeper 1991)Two regions of the parameter space deliver a unique stationary solution(Leeper,1991)Monetary-led policy mix:The fiscal authority is committed to implementing thenecessary fiscal adjustments.Fiscal policy is passive(1)because it passivelyaccommodates the behavior of the

9、active monetary authority(1).Inflation is insulated from the fiscal block.Fiscally-led policy mix:The fiscal authority is not committed to implementing thenecessary fiscal adjustments.Monetary policy is passive(1)because itpassively accommodates the behavior of the active fiscal authority(1).Inflati

10、on is not insulated from the fiscal block.Bianchi Fang MelosiFiscal Inflation in the UK4/23Endowment economiesInflation response to fiscal shocks24681000.20.40.60.81InflationAlways Monetary-led24681000.20.40.60.81Always Fiscally-led24681000.20.40.60.81Partially Unfunded DebtFunded fiscal shockUnfund

11、ed fiscal shockImpulse responses:1Inflation does not respond under the Monetary-led policy mix(=2.0;=0.2)2Inflation responds under the Fiscally-led policy mix(=0;=0)Bianchi Fang MelosiFiscal Inflation in the UK5/23Endowment economiesInflation response to fiscal shocks24681000.20.40.60.81InflationAlw

12、ays Monetary-led24681000.20.40.60.81Always Fiscally-led24681000.20.40.60.81Partially Unfunded DebtFunded fiscal shockUnfunded fiscal shockImpulse responses:1Inflation does not respond under the Monetary-led policy mix(=2.0;=0.2)2Inflation responds under the Fiscally-led policy mix(=0;=0)Bianchi Fang

13、 MelosiFiscal Inflation in the UK5/23Endowment economiesFisherian model with partially unfunded debtWe now introduce the notion of partially unfunded debt:We consider the following fiscal rule:t=M?sb,t1 sFb,t1?+F sFb,t1+Mt+Ft.(7)where Mtand Ftdenote funded and unfunded fiscal shocks,respectively,and

14、F1.The new monetary rule is:rn,t=M?t Ft?+F Ft.(8)where Ftdenotes fiscal inflation,i.e.,the amount of inflation that is tolerated by thecentral bank to stabilize the share of unfunded debt sFb,t1,M1 and F1.Bianchi Fang MelosiFiscal Inflation in the UK6/23Endowment economiesLinearized modelThe monetar

15、y block:Et t+1=M?t Ft?+F Ft.The fiscal block(F=0)sb,t=11(1)M sb,t1+1(1)sFb,t1+rn,t1 t(1)(Mt+Ft)(9)To close the model,we need to characterize the dynamics of fiscal inflation,Ft,andof the associated amount of unfunded debt,bFt.We construct a shadow economy in which the Fiscally-led policy mix is alwa

16、ys inplace and only shocks to unfunded spending Ftoccur.SubeconomiesBianchi Fang MelosiFiscal Inflation in the UK7/23Endowment economiesInflation response to funded and unfunded fiscal shocks24681000.20.40.60.81InflationAlways Monetary-led24681000.20.40.60.81Always Fiscally-led24681000.20.40.60.81Pa

17、rtially Unfunded DebtFunded fiscal shockUnfunded fiscal shockImpulse responses?M=2.0;M=0.2?;?F=0;F=0?:1Inflation does not respond to a funded fiscal shock(=2.0;=0.2)2Inflation responds to an unfunded fiscal shock(=0;=0)Bianchi Fang MelosiFiscal Inflation in the UK8/23Endowment economiesInflation res

18、ponse to funded and unfunded fiscal shocks24681000.20.40.60.81InflationAlways Monetary-led24681000.20.40.60.81Always Fiscally-led24681000.20.40.60.81Partially Unfunded DebtFunded fiscal shockUnfunded fiscal shockImpulse responses?M=2.0;M=0.2?;?F=0;F=0?:1Inflation does not respond to a funded fiscal

19、shock(=2.0;=0.2)2Inflation responds to an unfunded fiscal shock(=0;=0)Bianchi Fang MelosiFiscal Inflation in the UK8/23Fiscal inflation in production economiesProduction economiesBianchi Fang MelosiFiscal Inflation in the UK8/23Fiscal inflation in production economiesProduction economiesWe now exten

20、d the analysis to a production economy.Simple environment with no capital,but endogenous labor supply and productionTwo alternatives:1Flexible pricesequations2Nominal rigiditiesequationsNominal rigidities and unfunded shocks deliver a fiscal theory of persistent inflation:1Persistent movements in in

21、flation2Persistent movements in real interest rates3Persistent movements in output(real effects)Bianchi Fang MelosiFiscal Inflation in the UK9/23Fiscal inflation in production economiesPersistent Fiscal Inflation24681000.51Flexible pricesInflationFundedUnfunded246810-101Output246810-101Debt to GDP24

22、6810-0.200.2Ex-ante real rate24681000.51Flexible prices+F=0.8FundedUnfundedUnfunded+maturity246810-101246810-101246810-0.200.224681000.51Nominal Rigidities246810-101246810-101246810-0.200.21Absent nominal rigidities,macro-fiscal dichotomy holds for funded shocks2Absent nominal rigidities,price level

23、 increases after unfunded shocksas in the Fisherian model3Absent nominal rigidities,real economy unaffected by unfunded shocks4With flexible prices and F0,persistent inflation but no real effects in responseto unfunded shocks5Nominal rigidities:No macro effects of funded shocks as in flex pricesmacr

24、o-fiscal dichotomy6Nominal rigidities:persistent and moderate inflation response to unfunded shocks7Nominal rigidities:persistent decline in the real interest rate andreal effects of unfunded shocksBianchi Fang MelosiFiscal Inflation in the UK10/23Fiscal inflation in production economiesPersistent F

25、iscal Inflation24681000.51Flexible pricesInflationFundedUnfunded246810-101Output246810-101Debt to GDP246810-0.200.2Ex-ante real rate24681000.51Flexible prices+F=0.8FundedUnfundedUnfunded+maturity246810-101246810-101246810-0.200.224681000.51Nominal Rigidities246810-101246810-101246810-0.200.21Absent

26、nominal rigidities,macro-fiscal dichotomy holds for funded shocks2Absent nominal rigidities,price level increases after unfunded shocksas in the Fisherian model3Absent nominal rigidities,real economy unaffected by unfunded shocks4With flexible prices and F0,persistent inflation but no real effects i

27、n responseto unfunded shocks5Nominal rigidities:No macro effects of funded shocks as in flex pricesmacro-fiscal dichotomy6Nominal rigidities:persistent and moderate inflation response to unfunded shocks7Nominal rigidities:persistent decline in the real interest rate andreal effects of unfunded shock

28、sBianchi Fang MelosiFiscal Inflation in the UK10/23Fiscal inflation in production economiesPersistent Fiscal Inflation24681000.51Flexible pricesInflationFundedUnfunded246810-101Output246810-101Debt to GDP246810-0.200.2Ex-ante real rate24681000.51Flexible prices+F=0.8FundedUnfundedUnfunded+maturity24

29、6810-101246810-101246810-0.200.224681000.51Nominal Rigidities246810-101246810-101246810-0.200.21Absent nominal rigidities,macro-fiscal dichotomy holds for funded shocks2Absent nominal rigidities,price level increases after unfunded shocksas in the Fisherian model3Absent nominal rigidities,real econo

30、my unaffected by unfunded shocks4With flexible prices and F0,persistent inflation but no real effects in responseto unfunded shocks5Nominal rigidities:No macro effects of funded shocks as in flex pricesmacro-fiscal dichotomy6Nominal rigidities:persistent and moderate inflation response to unfunded s

31、hocks7Nominal rigidities:persistent decline in the real interest rate andreal effects of unfunded shocksBianchi Fang MelosiFiscal Inflation in the UK10/23Fiscal inflation in production economiesPersistent Fiscal Inflation24681000.51Flexible pricesInflationFundedUnfunded246810-101Output246810-101Debt

32、 to GDP246810-0.200.2Ex-ante real rate24681000.51Flexible prices+F=0.8FundedUnfundedUnfunded+maturity246810-101246810-101246810-0.200.224681000.51Nominal Rigidities246810-101246810-101246810-0.200.21Absent nominal rigidities,macro-fiscal dichotomy holds for funded shocks2Absent nominal rigidities,pr

33、ice level increases after unfunded shocksas in the Fisherian model3Absent nominal rigidities,real economy unaffected by unfunded shocks4With flexible prices and F0,persistent inflation but no real effects in responseto unfunded shocks5Nominal rigidities:No macro effects of funded shocks as in flex p

34、ricesmacro-fiscal dichotomy6Nominal rigidities:persistent and moderate inflation response to unfunded shocks7Nominal rigidities:persistent decline in the real interest rate andreal effects of unfunded shocksBianchi Fang MelosiFiscal Inflation in the UK10/23Fiscal inflation in production economiesPer

35、sistent Fiscal Inflation24681000.51Flexible pricesInflationFundedUnfunded246810-101Output246810-101Debt to GDP246810-0.200.2Ex-ante real rate24681000.51Flexible prices+F=0.8FundedUnfundedUnfunded+maturity246810-101246810-101246810-0.200.224681000.51Nominal Rigidities246810-101246810-101246810-0.200.

36、21Absent nominal rigidities,macro-fiscal dichotomy holds for funded shocks2Absent nominal rigidities,price level increases after unfunded shocksas in the Fisherian model3Absent nominal rigidities,real economy unaffected by unfunded shocks4With flexible prices and F0,persistent inflation but no real

37、effects in responseto unfunded shocks5Nominal rigidities:No macro effects of funded shocks as in flex pricesmacro-fiscal dichotomy6Nominal rigidities:persistent and moderate inflation response to unfunded shocks7Nominal rigidities:persistent decline in the real interest rate andreal effects of unfun

38、ded shocksBianchi Fang MelosiFiscal Inflation in the UK10/23Fiscal inflation in production economiesPersistent Fiscal Inflation24681000.51Flexible pricesInflationFundedUnfunded246810-101Output246810-101Debt to GDP246810-0.200.2Ex-ante real rate24681000.51Flexible prices+F=0.8FundedUnfundedUnfunded+m

39、aturity246810-101246810-101246810-0.200.224681000.51Nominal Rigidities246810-101246810-101246810-0.200.21Absent nominal rigidities,macro-fiscal dichotomy holds for funded shocks2Absent nominal rigidities,price level increases after unfunded shocksas in the Fisherian model3Absent nominal rigidities,r

40、eal economy unaffected by unfunded shocks4With flexible prices and F0,persistent inflation but no real effects in responseto unfunded shocks5Nominal rigidities:No macro effects of funded shocks as in flex pricesmacro-fiscal dichotomy6Nominal rigidities:persistent and moderate inflation response to u

41、nfunded shocks7Nominal rigidities:persistent decline in the real interest rate andreal effects of unfunded shocksBianchi Fang MelosiFiscal Inflation in the UK10/23Fiscal inflation in production economiesPersistent Fiscal Inflation24681000.51Flexible pricesInflationFundedUnfunded246810-101Output24681

42、0-101Debt to GDP246810-0.200.2Ex-ante real rate24681000.51Flexible prices+F=0.8FundedUnfundedUnfunded+maturity246810-101246810-101246810-0.200.224681000.51Nominal Rigidities246810-101246810-101246810-0.200.21Absent nominal rigidities,macro-fiscal dichotomy holds for funded shocks2Absent nominal rigi

43、dities,price level increases after unfunded shocksas in the Fisherian model3Absent nominal rigidities,real economy unaffected by unfunded shocks4With flexible prices and F0,persistent inflation but no real effects in responseto unfunded shocks5Nominal rigidities:No macro effects of funded shocks as

44、in flex pricesmacro-fiscal dichotomy6Nominal rigidities:persistent and moderate inflation response to unfunded shocks7Nominal rigidities:persistent decline in the real interest rate andreal effects of unfunded shocksBianchi Fang MelosiFiscal Inflation in the UK10/23Quantitative ModelA Quantitative G

45、eneral Equilibrium ModelBianchi Fang MelosiFiscal Inflation in the UK10/23Quantitative ModelThe ModelState-of-the-art TANK modelDistortionary taxation on labor and capital incomePrice and wage rigiditiesHand-to-mouth householdsLong-term government bondsTypical set of business cycle shocks plus fisca

46、l shocks and a shifter of thePhillips curve capturing market and non policy forces such as globalizationEquationsBianchi Fang MelosiFiscal Inflation in the UK11/23Quantitative ModelUnfunded debt and monetary and fiscal coordinationChanges in transfers(Mz,t,Fz,t)and purchases(Mg,t,Fg,t)determine the

47、share offunded and unfunded debtFunded debtbMtis stabilized by fiscal instrumentsUnfunded debtbFtis stabilized by fiscal inflation Ft,which the monetary authorityaccommodatesNo fiscal response to unfunded debt(F=0)No monetary response to fiscal inflation(F=0)endogenous inflation targetBianchi Fang M

48、elosiFiscal Inflation in the UK12/23Empirical AnalysisEmpirical AnalysisBianchi Fang MelosiFiscal Inflation in the UK12/23Empirical AnalysisEstimationThe model is estimated using a data set of 20 macro and fiscal variables1.Real GDP growth2.Real consumption growth3.Real investment growth4.Hours work

49、ed5.Inflation(Household consumption deflator)6.Growth rate of real average weekly earnings7.Real transfers payments growth rate8.Real government consumption and investment growth rate9.Debt to GDP ratio10.Bank Rate11-20.1Q-10Q ahead expected market path of the Bank Rate(OIS data)Sample periods:1960q

50、1-2007q4 and 2008q1-2024q1Estimated parametersSecond sample includes all the 20 observables;re-estimation of standard deviationsof fiscal shocks and the factor model governing the forward guidance shocks(Campbell et al.2012)Bianchi Fang MelosiFiscal Inflation in the UK13/23Empirical AnalysisA look a

51、t the dataInflation1960198020002020-100102030Real Interest Rate(Ex-Post)1960198020002020-20-10010Bank Rate196019802000202005101520Transfers-to-GDP Ratio196019802000202051015202530G-to-GDP Ratio196019802000202010121416182022Debt-to-GDP Ratio1960198020002020050100150Bianchi Fang MelosiFiscal Inflation

52、 in the UK14/23Empirical AnalysisFunded and unfunded transfer shocks1020304000.511.522.5InflationFunded Transfers shockUnfunded Transfers shockPersistent cost-push shock10203040-2.5-2-1.5-1-0.50Real Interest Rate10203040-4-20246Debt-to-GDP Ratio102030400246810GDP1020304000.511.522.5HoursFunded trans

53、fers:Modest impact on the macroeconomy,debt increasesUnfunded transfers:Persistent inflation increase,real rate and debt declineBianchi Fang MelosiFiscal Inflation in the UK15/23Empirical AnalysisFunded and unfunded G shocks1020304000.511.522.5InflationFunded G ShockUnfunded G ShockUnfunded Transfer

54、s Shock10203040-2.5-2-1.5-1-0.50Real Interest Rate10203040-4-3-2-101Debt-to-GDP Ratio102030400246810GDP1020304000.511.522.5HoursFunded G:Modest impact on the macroeconomy,debt increasesUnfunded G:Modest impact on inflation and real interest rateBianchi Fang MelosiFiscal Inflation in the UK16/23Empir

55、ical AnalysisGovernment transfers,purchases,and real interest rateGovernment Transfers and Purchases1960197019801990200020102020-40-30-20-100102030405060Percentage deviationsfrom balanced growthTransfers:DataPurchases:DataTransfers:TrendPurchases:TrendUnfunded Transfers,Unfunded Purchases,and Real I

56、nterest RateCorrelation(Z,rLog)=-0.61Correlation(G,rLog)=-0.671960197019801990200020102020-10-5051015Percentage points-0.4-0.200.20.40.6Changes in Unfunded Transfers(right axis)Changes in Unfunded Purchases(right axis)Real Interest Rate(left axis)Figure VIII-Government Transfers,Purchases,and Real I

57、nterest Rate.Bianchi Fang MelosiFiscal Inflation in the UK17/23Empirical AnalysisDecomposition of total government transfersPanel(A):Unfunded Transfers19601970198019902000201020200510152025Percentage deviationsfrom balanced growthPanel(B):Total Transfers1960196519701975010203040UnfundedFundedPanel(C

58、):Total Transfers1975198019851990010203040Panel(D):Total Transfers199020002010010203040Panel(E):Total Transfers202020222024010203040502020202220244681012Figure IX.1 Estimated Decomposition of Total GovernmentTransfers into their Funded and Unfunded Components.Bianchi Fang MelosiFiscal Inflation in t

59、he UK18/23Empirical AnalysisDecomposition of total government purchasesPanel(F):Unfunded Purchases1960197019801990200020102020-50510Percentage deviationsfrom balanced growth202020222024-4.8-4.6Panel(G):Total Purchases1960196519701975-30-20-100Panel(H):Total Purchases1975198019851990-25-20-15-10-505P

60、anel(I):Total Purchases199020002010-30-25-20-15-10-50Panel(J):Total Purchases2020202220240510152025Figure IX.2 Estimated Decomposition of Total GovernmentPurchases into their Funded and Unfunded Components.Bianchi Fang MelosiFiscal Inflation in the UK19/23Empirical AnalysisDrivers of inflationInflat

61、ion1960197019801990200020102020-10-505101520253035Steady stateActual inflationSimulation with unfunded transfer and unfunded G shocksSimulation with unfunded transfer,unfunded G,and short-term markup shocksFigure X.1 Drivers of InflationFiscal inflation(solid blue line)explains low-frequency movemen

62、ts in InflationBianchi Fang MelosiFiscal Inflation in the UK20/23Empirical AnalysisDrivers of hours gapHours Gap1960197019801990200020102020-20-15-10-5051015Steady stateActual hours gapSimulation with unfunded transfer and unfunded G shocksSimulation with TFP,demand,risk premium,and investment effic

63、iency shocksFigure X.2 Drivers of Hours GapUnfunded fiscal shocks(solid blue line)counteract productivity slowdown in the 1960sand 1970s+trigger a quick rebound from the pandemicBianchi Fang MelosiFiscal Inflation in the UK21/23Empirical AnalysisUnfunded fiscal shocks and post-pandemic inflationHour

64、s201920202021202220232024-20-15-10-505Inflation201920202021202220232024-20-15-10-5051015Real Interest Rate201920202021202220232024-50510151First counterfactual simulation,all fiscal shocks starting from post-pandemicexpansion(2020:Q3)are assumed to be funded(red dash-dotted line).2Second counterfact

65、ual simulation,fiscal shocks starting from Premier Trusss Minibudget(2022:Q3)are assumed to be funded(blue dashed line)Bianchi Fang MelosiFiscal Inflation in the UK22/23Empirical AnalysisConclusionsLow frequency movements in inflation related to fiscal policy:1Unfunded spending critically affects in

66、flation dynamics and real interest rates2Funded spending has a small impact on real interest rates3UK fiscal inflation in 1960s-1980s+pandemic similar to US,different in 1990s-2000sPandemic:A large fiscal stimulus and accommodative monetary policyLargeincrease in fiscal inflation1Quick rebound in re

67、al activity2Debt to GDP below pre-pandemic levelPost pandemic:Fiscal inflation remains elevated despite the decline in actualinflationsoft landing,but also inflationary pressureBianchi Fang MelosiFiscal Inflation in the UK23/23AppendixAppendixBianchi Fang MelosiFiscal Inflation in the UK23/23Appendi

68、xSubeconomiesThe linearized model economy can decomposed into two additive sub-economies1A sub-economy in which policymakers always follow the monetary-led policy mix andunfunded fiscal shocks are shut down MtandbMt2A sub-economy in which policymakers always follow the fiscally-led policy mix andall

69、 shocks except the unfunded fiscal shocks are shut down FtandbFtIt can be shown that t=Mt+Ftbt=bMt+bFtBackBianchi Fang MelosiFiscal Inflation in the UK24/23AppendixFlexible Price EconomyEuler equationEt yt+1=yt+?RtEt t+1?(10)Labor supplyn1n nt=yt+b wrt(11)Labor demand wrt=nt(12)Production function y

70、t=(1)nt(13)Real rate rt=RtEt t+1(14)Bianchi Fang MelosiFiscal Inflation in the UK25/23AppendixFlexible Price Economy(contd)Taylor ruleRt=M?t Ft?+F Ft(15)Evolution of debtbbt=t+1b?yt1 yt+Rt1 t+bt1?(16)Fiscal rule t=M?bt1bFt1?+FbFt1b+Ft+Ut(17)BackBianchi Fang MelosiFiscal Inflation in the UK26/23Appen

71、dixNew Keynesian modelEuler equationEt yt+1=yt+?RtEt t+1?(18)Labor supplyn1n nt=yt+b wrt(19)New Keynesian Phillips Curve t=wrt+Et t+1(20)Production function yt=(1)nt(21)Real rate definition rt=RtEt t+1(22)Bianchi Fang MelosiFiscal Inflation in the UK27/23AppendixNew Keynesian model(contd)Taylor rule

72、Rt=M?t Ft?+F Ft(23)Evolution of debtbbt=t+1b?yt1 yt+Rt1 t+bt1?(24)Fiscal rule t=M?bt1bFt1?+FbFt1b+Ft+Ut(25)BackBianchi Fang MelosiFiscal Inflation in the UK28/23AppendixProduction Economy510152000.51Always Monetary LedInflation510152000.51Always Fiscally Led510152000.51Partially Unfunded DebtFunded

73、fiscal shockUnfunded fiscal shock510152000.20.40.6Public Debt00.20.40.60.8100.20.40.65101520-0.500.5510152000.10.20.30.4Nominal Interest Rate510152000.10.20.30.4510152000.10.20.30.45101520-40-200Primary Surplus5101520-40-2005101520-40-200BackBianchi Fang MelosiFiscal Inflation in the UK29/23Appendix

74、Maturity structure of UK government debt19601965197019751980198519901995200020052010201520200102030405060Years Until Maturity2510204080Unique IDAverage by Treasury IDValue Weighted AverageBianchi Fang MelosiFiscal Inflation in the UK30/23AppendixCalibrated ParametersParameters Fixed in EstimationPar

75、ametersValuesDiscount factor0.9900Average duration of debt56.000Capital depreciation rate0.0250Elasticity of output to capital0.3000Wage markupw0.1200Price markupp0.1200Government expenditures to GDP ratiosgc0.1200Steady state tax rate on labor incomeL0.2900Steady state tax rate on capital incomeK0.

76、2900Steady state tax rate on consumptionC0.2000BackBianchi Fang MelosiFiscal Inflation in the UK31/23AppendixFirst Sample EstimatesPrior and Posterior Distributions for the Structural ParametersPosterior DistributionPrior DistributionParamDescriptionModeMedian5%95%TypeMeanStdsbDebt to GDP annualized

77、1.34251.34461.27481.4168N1.210.05100Steady state growth rate0.38750.36570.29350.4375N0.500.05100lnSteady state inflation0.48920.49880.41430.5481N0.500.05Inverse Frisch elasticity1.94191.88701.83661.9319G2.000.25Share of hand-to-mouth0.01470.01110.00520.0203B0.10.05wWage Calvo param0.68450.67650.6424

78、0.7131B0.500.10pPrice Calvo param0.80890.82330.79240.8508B0.500.10Capital utilization cost0.43000.36760.32760.4413B0.500.10sInvestment adjust.cost4.73734.68154.59734.7368N4.001.50wWage infl.indexation0.25920.26280.22960.2965B0.300.15pPrice infl.indexation0.20670.14420.10480.1855B0.300.15Habits in co

79、nsumption0.84390.84210.82780.8554B0.700.10GSubs.private/gov.cons.0.00890.02290.07020.0822N0.000.10BackBianchi Fang MelosiFiscal Inflation in the UK32/23AppendixFirst Sample EstimatesPrior and Posterior Distributions for the Structural ParametersPosterior DistributionPrior DistributionParamDescriptio

80、nModeMedian5%95%TypeMeanStdyInterest response to GDP0.26740.25430.22230.2872N0.110.05Interest response to infl.1.78741.69191.61241.7789N1.870.10zyTransfers response to GDP0.00210.00270.00030.0095G0.500.50gyG response to GDP0.00160.00200.00020.0084G0.500.50ZTransfers response to debt0.23160.24690.222

81、00.2995N0.200.10GG response to debt0.00080.00140.00020.0051N0.200.10KCapital tax response to debt0.00070.00150.00020.0052N0.200.10LLabor tax response to debt0.11000.11370.10400.1258N0.200.10CCons.tax response to debt0.02430.02190.10180.0364N0.200.10rAR coeff.monetary rule0.90920.90130.88500.9166B0.5

82、00.10GAR coeff.gov.cons.rule0.38980.42880.38640.5090B0.500.10ZAR coeff.transfers rule0.50170.52690.48400.5840B0.500.10BackBianchi Fang MelosiFiscal Inflation in the UK33/23AppendixFirst Sample EstimatesPrior and Posterior Distributions for the Exogenous ProcessesPosterior DistributionPrior Distribut

83、ionParamDescriptionModeMedian5%95%TypeMeanStdMeGAR coeff.funded G0.99510.99490.99320.9964B0.9950.001FeGAR coeff.unfunded G0.99530.99510.99330.9965B0.9950.001gAR coeff.short-term G0.48990.50680.41950.6079B0.5000.100MeZAR coeff.funded trans.0.99500.99480.99290.9964B0.9950.001FeZAR coeff.unfunded trans

84、.0.99490.99460.99300.9960B0.9950.001zAR coeff.short-term trans.0.49580.50600.46630.5663B0.5000.100aAR coeff.technology0.65370.64870.60340.7098B0.5000.100bAR coeff.preference0.31630.34080.28680.4174B0.5000.100mAR coeff.mon.policy0.36150.34420.28270.4141B0.5000.100iAR coeff.investment0.29230.33060.267

85、50.4477B0.5000.100rpAR coeff.risk premium0.89860.90100.87510.9272B0.5000.100NKPCAR coeff.pers.cost push0.99550.99540.99360.9967B0.9950.001BackBianchi Fang MelosiFiscal Inflation in the UK34/23AppendixFirst Sample EstimatesPrior and Posterior Distributions for the Exogenous ProcessesPosterior Distrib

86、utionPrior DistributionParamDescriptionModeMedian5%95%TypeMeanStdMGSt.dev.funded G2.05092.16761.98662.3428IG0.5000.200FGSt.dev.unfunded G0.49190.47450.44990.5029IG0.5000.200gSt.dev.short-term G0.37930.39680.36500.4348IG0.5000.200MZSt.dev.funded transfers3.69813.71223.59273.8053IG0.5000.200FZSt.dev.u

87、nfunded transfers0.45360.46180.42390.5172IG0.5000.200zSt.dev.short-term trans.0.39200.45270.38860.5231IG0.5000.200aSt.dev.technology1.90501.96711.80862.0547IG0.5000.200bSt.dev.preference4.98454.98414.96264.9976IG0.5000.200mSt.dev.mon.policy0.25720.25880.23590.2843IG0.5000.200iSt.dev.investment1.4014

88、1.32061.18781.4281IG0.5000.200wSt.dev.wage markup0.64160.64690.58420.7192IG0.5000.200pSt.dev.price markup0.59580.62710.57940.6875IG0.5000.200rpSt.dev.risk premium0.44260.41650.35010.4722IG0.5000.200NKPCSt.dev.persistent cost push0.41640.44440.40100.4863IG0.5000.200mGDPMeasur.error GDP0.94470.94920.8

89、8721.0197IG0.5000.200mbyMeasur.error Debt/GDP0.37770.26440.23780.3607IG0.5000.200BackBianchi Fang MelosiFiscal Inflation in the UK35/23AppendixSecond Sample EstimatesPrior and Posterior Distributions for the Exogenous ProcessesPosterior DistributionPrior DistributionParamDescriptionModeMedian5%95%Ty

90、peMeanStdMGSt.dev.funded G4.23834.24394.23774.2493IG2.05090.500FGSt.dev.unfunded G0.29780.29910.29710.3009IG0.49190.500gSt.dev.short-term G0.20040.19970.19870.2007IG0.37930.500MZSt.dev.funded transfers7.54997.55567.55017.5604IG3.69810.500FZSt.dev.unfunded transfers1.56531.56491.56321.5667IG0.45360.5

91、00zSt.dev.short-term trans.0.20980.20970.20890.2112IG0.39200.500mGDPMeasur.error GDP0.75310.75380.75200.7561IG0.94470.200mbyMeasur.error Debt/GDP0.27020.26970.26840.2706IG0.37770.200BackBianchi Fang MelosiFiscal Inflation in the UK36/23AppendixProduction function:yt=y+yhkt+(1)Lti.(26)Capital-labor r

92、atio:rKt wt=Ltkt.(27)Marginal cost:dmct=rkt+(1)wt.(28)Phillips curve:t=1+pEt t+1+p1+p t1+pdmct+p pt,(29)where p=(1p)(1p)/p(1+p).BackBianchi Fang MelosiFiscal Inflation in the UK37/23AppendixSaver households FOC for consumption:St=FbteFateecSt+ecSt1C1+C Ct,(30)whereFat=uat.Public/private consumption

93、in utility:ct=cScS+Gg cSt+GgcS+Gg gt.(31)Euler equation:St=Rt+EtSt+1Et t+1EtFat+1.(32)BackBianchi Fang MelosiFiscal Inflation in the UK38/23AppendixMaturity structure of debt:Rt+PBt=REtPBt+1.(33)Saver households FOC for capacity utilization:rktK1K Kt=1 t.(34)Saver households FOC for capital:qt=Et t+

94、1Rt+e?1K?rkEt rkt+1eKrkEt Kt+1+e(1)Et qt+1.(35)Saver households FOC for investment:t+11+Fat1(1+)se2 qtFit1+Et t+11+EtFat+1=11+t1.(36)BackBianchi Fang MelosiFiscal Inflation in the UK39/23AppendixEffective capital:kt=t+bkt1Fat.(37)Law of motion for capital:bkt=(1)e?bkt1Fat?+?1(1)e?h(1+)se2+ti.(38)Han

95、d-to-mouth households budget constraint:CcN Ct+?1+C?cN cNt=?1L?wL?wt+Lt?LwL Lt+z zt.(39)Aggregate households consumptionc ct=cS(1)cSt+cN cNt.(40)BackBianchi Fang MelosiFiscal Inflation in the UK40/23AppendixWage equation:wt=11+wt1+1+Et wt+1w?wtLt+StL1L Lt?+w1+t11+w1+t+1+Et t+1+1+Fat11+a1+Fat+w wt,(4

96、1)where w(1w)(1w)/hw(1+)?1+(1+w)w?i.Aggregate resource constraint:y yt=c ct+i t+g gt+(1)k t.(42)Government budget constraint:bybt+Krkkyh Kt+rkt+kti+LwLyh Lt+wt+Lti+Ccy?Ct+ct?=1byhbt1 tPBt1Fati+byePBt+gy gt+zy zt.(43)BackBianchi Fang MelosiFiscal Inflation in the UK41/23AppendixFiscal Rules J,t=J J,t

97、1+(1J)Jbt1,J K,L,C(44)zbt=Z zbt1(1Z)?Zbt1+zy yt?+z,t(45)zt=zbt+Mz,t+Fz,t(46)gbt=G gbt1(1G)?Gbt1+gy yt?+g,t(47)gt=gbt+Mg,t+Fg,t(48)Monetary Rule:Rt=max?lnR,rRt1+(1r)t+y yt?+R,t(49)The variables with thesuperscript in equations(44)to(49)above belong to the shadoweconomy.BackBackBianchi Fang MelosiFisc

98、al Inflation in the UK42/23AppendixThe block of equations that characterize the shadow economy consists in an additionalset of equations(26)to(43),where any variable that refers to the actual economy xtisreplaced by the same variable in the shadow economy xt,plus the rule for the monetaryauthorityRt=max?lnR,rRt1+(1r)t+y yt?+R,t(50)and the rules for the fiscal authority,J,t=J J,t1+(1J)Jbt1,J K,L,C(51)zbt=Z zbt1(1Z)?Zbt1+zy yt?+z,t(52)zt=zbt+Mz,t(53)gbt=G gbt1(1G)?Gbt1+gy yt?+g,t(54)gt=gbt+Mg,t(55)BackBianchi Fang MelosiFiscal Inflation in the UK43/23