## _wp09137 - References..........................................33 ## Source details **Canonical URL:** [_wp09137 - References..........................................33](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09137.pdf) ## Other formats - [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09137.pdf.md) - [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09137.pdf.json) --- ### Main result and mechanism - Limited asset-market participation (a fraction 1¡λ of “assetholders” and fraction λ of “non-assetholders” who consume current income each period) creates a role for active fiscal stabilization that is absent under full asset-market participation. - Intuition: - Monetary policy mainly contracts asset-holder consumption and, via wages and labor supply, stabilizes inflation. - Government expenditure raises non-assetholders’ consumption and reduces asset-holders’ consumption, producing a favourable redistribution of stabilization burdens across groups when λ>0. - With limited asset-market participation, distributional considerations make expansionary fiscal policy (higher government expenditure) optimal alongside tighter monetary policy. ### Calibration and key parameters (baseline) - Quarterly discount factor: β = 0.99 (annual steady-state interest ≈ 4 percent). - Elasticity of substitution: ε = 6 (consistent with 20 percent steady-state markup). - Labour supply parameter: η = 1 (unit labour supply elasticity). - Calvo price stickiness: θ = 0.75 (average period of one year between price adjustments). - Steady-state consumption-to-output ratio: α = 0.75. - Share of non-assetholders (baseline): λ = 0.4; threshold for “non‑Keynesian” region: λ̄ = 0.58. - Cost-push shock specification: persistence ρ = 0.75; standard deviation = 0.005. ### Determinacy properties - With endogenous government expenditure responding to inflation, the Taylor principle remains a sufficient condition for determinacy when λ < λ̄, except when the fiscal response to inflation (ψσπ) is very large and positive; then monetary policy must respond more aggressively to secure determinacy. - “Non‑Keynesian” region: when λ > λ̄ = 1/(1+ηα) = 0.58 in the calibration, higher real interest rates can raise aggregate demand, reversing conventional policy effects; determinacy then requires violating the Taylor principle (see Appendix E). ### Social welfare and loss function - Social welfare is utilitarian: weighted sum of asset- and non-assetholders’ utilities with weights determined by λ. - Second-order expected discounted loss (up to omitted policy-independent terms) is: - 1/2 E_t Σ σ= t β^{σ−t} [ ε·β·π_σ^2 + (η+λ)/(1−λ) · ψ-term · y_σ^2 + (1−α) g_σ^2 + α(1−λ) c_O,σ^2 + α λ c_R,σ^2 ], as detailed in equation (22). - Distributional volatility of private consumption across agent types enters welfare directly: volatility of c_O and c_R matters separately. ### Optimal monetary policy with exogenous fiscal policy - Optimal current-inflation instrument rule (white-noise cost-push shocks, ρ = 0 case) is: - r_t = φ_x^π · π_t with φ_x^π = ε(1+αη)η / (αε£) (where £ = 1−λ + α(η + λ(1+αη^2)) > 0). - Key qualitative results: - The optimal responsiveness of the nominal interest rate to inflation, φ_x^π, falls with the share of non-assetholders λ (∂φ_x^π/∂λ < 0). - Under limited asset-market participation, the consumption of non-assetholders contracts more than asset-holders in response to a monetary tightening; this distributional cost reduces optimal monetary tightening relative to the full-participation case. - The Taylor principle continues to hold under optimal monetary policy provided λ is not too large (λ < ^λ, expression given in text). ### Jointly optimal monetary and fiscal policy (discretionary) - With proportional profit taxes financing government expenditure and logarithmic utility baseline: - Optimal instrument rules (white-noise cost-push shocks) can be expressed as: - r_t = φ_o^π · π_t - g_t = ψ_o^π · π_t - Closed-form expressions: φ_o^π and ψ_o^π are given in Section IV.C (symbolic structure preserved). - Main findings: - With full asset-market participation (λ = 0), optimal fiscal policy is inactive (ψ_o^π = 0) and monetary policy alone implements stabilization. - With λ > 0, the optimal policy raises both the real interest rate and government expenditure in response to a positive cost-push shock: contractionary monetary policy combined with expansionary fiscal policy. - Rationale: expansionary government expenditure stabilizes non-assetholders’ consumption and labor supply (reducing the uneven distribution of welfare losses); monetary tightening offsets the inflationary effect of higher government spending. - The optimal monetary tightening under joint optimization is larger than under exogenous fiscal policy (φ_o^π − φ_x^π > 0), enabling determinacy for a larger range of λ. - The optimal fiscal response ψ_o^π and the additional monetary tightening both rise with λ (∂ψ_o^π/∂λ > 0 and ∂(φ_o^π − φ_x^π)/∂λ > 0). ### Welfare gains of optimising fiscal policy - Active fiscal policy (optimizing g_t jointly with r_t) raises welfare relative to the case with exogenous government spending, especially for more persistent shocks (Figure 4 highlights welfare gains for ρ = 0, 0.5, 0.75). - For the baseline calibration (λ = 0.4, ρ = 0.75) the availability of targeted transfers (see below) raises welfare by 0.35 percent of steady-state consumption. ### Robustness and extensions 1. CRRA preferences (generalising from logarithmic utility) - Period utility: U_{φ,σ} = C_{φ,σ}^{1−σ}/(1−σ) + Ψ G_{σ}^{1−σ}/(1−σ) − N_{φ,σ}^{1+η}/(1+η), with σ the inverse IES. - Main effects: - Non-assetholders’ labor supply ν_R is no longer constant; both groups’ labor responses matter. - Qualitative baseline result persists: optimal fiscal policy remains active (Figure 5 cross-line), though the magnitude of the fiscal response is moderated when ν_R adjusts. 2. Targeted lump-sum transfers to non-assetholders - If the policymaker can implement a time-varying, targeted lump-sum transfer Λ_R,t (financed by lump-sum tax on assetholders), the optimal policy is: - r_t = ε/α · π_t - g_t = 0 - Λ_R,t = ε(1+η) · π_t - Result: the optimal policy replicates the full asset-market participation case; active government expenditure is no longer used when transfers are available (Figure 5 dashed line). - Practical note: targeted transfers require time-varying lump-sum instruments and identification of asset vs non-asset households. 3. Alternative financing: equal lump-sum tax on both agents - When government expenditure is financed by equal lump-sum taxes on both groups (instead of profit taxes), the policymaker can use g_t to mimic targeted transfers by cutting public expenditure and rebating resources to consumers. - Simulation (Figure 5 dotted line): optimal fiscal response can be negative (government expenditure reduced) to replicate targeted transfer outcomes via untargeted lump-sum taxes. 4. Government debt financing - Introducing one-period nominal government debt with linearised law of motion (equation (40)) and steady-state debt ratio B matters for determinacy and optimal fiscal response. - Calibration comparison: low-debt economy B = 0 versus high-debt B = 0.2. - Findings: - Determinacy depends on both monetary response to inflation and fiscal response to debt. - For low steady-state debt, optimal fiscal policy still initially raises government expenditure and then reduces it to control debt (dashed line in Figure 6). - For higher steady-state debt, the optimal response to a positive cost-push shock can switch to a reduction in government expenditure because higher debt accumulation makes expanding government spending infeasible under discretionary policies (dotted line in Figure 6). - This reversal is specific to discretionary policy; commitment policies need not return debt to pre-shock levels and may continue to expand government expenditure even with high B. ### Non‑Keynesian region (brief) - When λ is “too high” (λ > λ̄ = 0.58 in the baseline calibration), the effects of interest rates and fiscal policy can be inverted: increases in real interest rates and cuts in government expenditure can raise aggregate demand. Determinacy in this region typically requires violating the Taylor principle (see Appendix E). - The main qualitative result — that optimal fiscal policy raises government expenditure in response to higher inflation — continues to hold in the non‑Keynesian region, though the optimal monetary response differs (optimal policy reduces the real interest rate in that region under certain specifications). ### Policy implications and caveats - Active fiscal stabilization (expansionary government expenditure) can be welfare-improving when a non-trivial share of consumers cannot smooth consumption through asset markets because fiscal policy redistributes stabilization costs toward those agents most affected by nominal rigidities. - The beneficial role of fiscal policy relies on the central bank’s ability to offset the inflationary consequences of fiscal expansion by raising the policy rate; constraints (e.g., fixed exchange rate or binding zero lower bound) can eliminate this channel. - Availability of targeted lump-sum transfers or untargeted lump-sum taxes operating as transfers greatly reduces or eliminates the need for active government expenditure as a stabilization tool. - High steady-state government debt can reverse the result: under discretionary policy and high B, optimal fiscal policy may cut government expenditure following cost-push shocks because of indebtedness and return-to-pre-shock debt constraints. *Source: _wp09137 - References..........................................33* ### References..........................................33 ### _wp09137 - References..........................................33 ### Main result and mechanism - Limited asset-market participation (a fraction 1¡λ of “assetholders” and fraction λ of “non-assetholders” who consume current income each period) creates a role for active fiscal stabilization that is absent under full asset-market participation. - Intuition: - Monetary policy mainly contracts asset-holder consumption and, via wages and labor supply, stabilizes inflation. - Government expenditure raises non-assetholders’ consumption and reduces asset-holders’ consumption, producing a favourable redistribution of stabilization burdens across groups when λ>0. - With limited asset-market participation, distributional considerations make expansionary fiscal policy (higher government expenditure) optimal alongside tighter monetary policy. ### Calibration and key parameters (baseline) - Quarterly discount factor: β = 0.99 (annual steady-state interest ≈ 4 percent). - Elasticity of substitution: ε = 6 (consistent with 20 percent steady-state markup). - Labour supply parameter: η = 1 (unit labour supply elasticity). - Calvo price stickiness: θ = 0.75 (average period of one year between price adjustments). - Steady-state consumption-to-output ratio: α = 0.75. - Share of non-assetholders (baseline): λ = 0.4; threshold for “non‑Keynesian” region: λ̄ = 0.58. - Cost-push shock specification: persistence ρ = 0.75; standard deviation = 0.005. ### Determinacy properties - With endogenous government expenditure responding to inflation, the Taylor principle remains a sufficient condition for determinacy when λ < λ̄, except when the fiscal response to inflation (ψσπ) is very large and positive; then monetary policy must respond more aggressively to secure determinacy. - “Non‑Keynesian” region: when λ > λ̄ = 1/(1+ηα) = 0.58 in the calibration, higher real interest rates can raise aggregate demand, reversing conventional policy effects; determinacy then requires violating the Taylor principle (see Appendix E). ### Social welfare and loss function - Social welfare is utilitarian: weighted sum of asset- and non-assetholders’ utilities with weights determined by λ. - Second-order expected discounted loss (up to omitted policy-independent terms) is: - 1/2 E_t Σ σ= t β^{σ−t} [ ε·β·π_σ^2 + (η+λ)/(1−λ) · ψ-term · y_σ^2 + (1−α) g_σ^2 + α(1−λ) c_O,σ^2 + α λ c_R,σ^2 ], as detailed in equation (22). (Preserve the structure and coefficients as in the source.) - Distributional volatility of private consumption across agent types enters welfare directly: volatility of c_O and c_R matters separately. ### Optimal monetary policy with exogenous fiscal policy - Optimal current-inflation instrument rule (white-noise cost-push shocks, ρ = 0 case) is: - r_t = φ_x^π · π_t with φ_x^π = ε(1+αη)η / (αε£) (where £ = 1−λ + α(η + λ(1+αη^2)) > 0). (Form preserved as in text.) - Key qualitative results: - The optimal responsiveness of the nominal interest rate to inflation, φ_x^π, falls with the share of non-assetholders λ (∂φ_x^π/∂λ < 0). - Under limited asset-market participation, the consumption of non-assetholders contracts more than asset-holders in response to a monetary tightening; this distributional cost reduces optimal monetary tightening relative to the full-participation case. - The Taylor principle continues to hold under optimal monetary policy provided λ is not too large (λ < ^λ, expression given in text). ### Jointly optimal monetary and fiscal policy (discretionary) - With proportional profit taxes financing government expenditure and logarithmic utility baseline: - Optimal instrument rules (white-noise cost-push shocks) can be expressed as: - r_t = φ_o^π · π_t - g_t = ψ_o^π · π_t - Closed-form expressions: φ_o^π and ψ_o^π are given in Section IV.C (preserved symbolic structure in the source). - Main findings: - With full asset-market participation (λ = 0), optimal fiscal policy is inactive (ψ_o^π = 0) and monetary policy alone implements stabilization (standard result). - With λ > 0, the optimal policy raises both the real interest rate and government expenditure in response to a positive cost-push shock: contractionary monetary policy combined with expansionary fiscal policy. - Rationale: expansionary government expenditure stabilizes non-assetholders’ consumption and labor supply (reducing the uneven distribution of welfare losses); monetary tightening offsets the inflationary effect of higher government spending. - The optimal monetary tightening under joint optimization is larger than under exogenous fiscal policy (φ_o^π − φ_x^π > 0), enabling determinacy for a larger range of λ. - The optimal fiscal response ψ_o^π and the additional monetary tightening both rise with λ (∂ψ_o^π/∂λ > 0 and ∂(φ_o^π − φ_x^π)/∂λ > 0). ### Welfare gains of optimising fiscal policy - Active fiscal policy (optimizing g_t jointly with r_t) raises welfare relative to the case with exogenous government spending, especially for more persistent shocks (Figure 4 highlights welfare gains for ρ = 0, 0.5, 0.75). - For the baseline calibration (λ = 0.4, ρ = 0.75) the availability of targeted transfers (see below) raises welfare by 0.35 percent of steady-state consumption. ### Robustness and extensions 1. CRRA preferences (generalising from logarithmic utility) - Period utility: U_{φ,σ} = C_{φ,σ}^{1−σ}/(1−σ) + Ψ G_{σ}^{1−σ}/(1−σ) − N_{φ,σ}^{1+η}/(1+η), with σ the inverse IES. - Main effects: - Non-assetholders’ labor supply ν_R is no longer constant; both groups’ labor responses matter. - Qualitative baseline result persists: optimal fiscal policy remains active (Figure 5 cross-line), though the magnitude of the fiscal response is moderated when ν_R adjusts. 2. Targeted lump-sum transfers to non-assetholders - If the policymaker can implement a time-varying, targeted lump-sum transfer Λ_R,t (financed by lump-sum tax on assetholders), the optimal policy is: - r_t = ε/α · π_t - g_t = 0 - Λ_R,t = ε(1+η) · π_t - Result: the optimal policy replicates the full asset-market participation case; active government expenditure is no longer used when transfers are available (Figure 5 dashed line). - Practical note: targeted transfers require time-varying lump-sum instruments and identification of asset vs non-asset households. 3. Alternative financing: equal lump-sum tax on both agents - When government expenditure is financed by equal lump-sum taxes on both groups (instead of profit taxes), the policymaker can use g_t to mimic targeted transfers by cutting public expenditure and rebating resources to consumers. - Simulation (Figure 5 dotted line): optimal fiscal response can be negative (government expenditure reduced) to replicate targeted transfer outcomes via untargeted lump-sum taxes. 4. Government debt financing - Introducing one-period nominal government debt with linearised law of motion (equation (40)) and steady-state debt ratio B matters for determinacy and optimal fiscal response. - Calibration comparison: low-debt economy B = 0 versus high-debt B = 0.2. - Findings: - Determinacy depends on both monetary response to inflation and fiscal response to debt. - For low steady-state debt, optimal fiscal policy still initially raises government expenditure and then reduces it to control debt (dashed line in Figure 6). - For higher steady-state debt, the optimal response to a positive cost-push shock can switch to a reduction in government expenditure because higher debt accumulation makes expanding government spending infeasible under discretionary policies (dotted line in Figure 6). - This reversal is specific to discretionary policy; commitment policies need not return debt to pre-shock levels and may continue to expand government expenditure even with high B. ### Non‑Keynesian region (brief) - When λ is “too high” (λ > λ̄ = 0.58 in the baseline calibration), the effects of interest rates and fiscal policy can be inverted: increases in real interest rates and cuts in government expenditure can raise aggregate demand. Determinacy in this region typically requires violating the Taylor principle (see Appendix E). - The main qualitative result — that optimal fiscal policy raises government expenditure in response to higher inflation — continues to hold in the non‑Keynesian region, though the optimal monetary response differs (optimal policy reduces the real interest rate in that region under certain specifications). ### Policy implications and caveats - Active fiscal stabilization (expansionary government expenditure) can be welfare-improving when a non-trivial share of consumers cannot smooth consumption through asset markets because fiscal policy redistributes stabilization costs toward those agents most affected by nominal rigidities. - The beneficial role of fiscal policy relies on the central bank’s ability to offset the inflationary consequences of fiscal expansion by raising the policy rate; constraints (e.g., fixed exchange rate or binding zero lower bound) can eliminate this channel. - Availability of targeted lump-sum transfers or untargeted lump-sum taxes operating as transfers greatly reduces or eliminates the need for active government expenditure as a stabilization tool. - High steady-state government debt can reverse the result: under discretionary policy and high B, optimal fiscal policy may cut government expenditure following cost-push shocks because of indebtedness and return-to-pre-shock debt constraints. *Source: _wp09137 - References..........................................33* ### References ### References ### References list - Benigno,PierpaoloandMichaelWoodford.(2003)."OptimalMonetaryandFiscalPolicy: ALinear-QuadraticApproach",InNBERMacroeconomicsAnnual2003,editedby MarkGertlerandKennethRogo¤,271-364.Cambridge(US):MITPress. - Bilbiie,Florin.(2008)."LimitedAssetMarketsParticipation,MonetaryPolicyand (inverted)AggregateDemandLogic",JournalofEconomicTheory,140(1),162-196. - Bilbiie,FlorinAndréMeierandGernotJ.Müller.(2008)."WhatAccountsforthe ChangesinU.S.FiscalPolicyTransmission?",JournalofMoney,Creditand Banking,40(7),1439-1470. - Bilbiie,FlorinandRolandStraub.(2004)."AssetMarketParticipationandDistortionary Taxation:KeynesianandNon-KeynesianE¤ectsofFiscalPolicy",WP2004-6, HungarianNationalBank. - Blanchard,OlivierandRobertoPerotti.(2002)."AnEmpiricalCharacterizationOfThe DynamicE¤ectsOfChangesInGovernmentSpendingAndTaxesOnOutput", QuarterlyJournalofEconomics,117(4),1329-1368. - Campbell,JohnandGregoryMankiw.(1989)."Consumption,IncomeandInterestRates: ReinterpretingtheTimeSeriesEvidence",inBlanchard,OlivierandStanleyFisher, eds,NBERMacroeconomicsAnnual1989,185-216.Cambridge,MA:MITPress. - Clarida,Richard,JordiGali,andMarkGertler.(1999)."Thescienceofmonetarypolicy: aNewKeynesianperspective",JournalofEconomicLiterature,37(2),1661-1707. - Currie,DavidandPaulLevine.(1993).Rules,ReputationandMacroeconomicPolicy Coordination.Cambridge(UK):CambridgeUniversityPress. - Eser,Fabian,CampbellLeithandSimonWren-Lewis.(2009)."WhenMonetaryPolicyis AllYouNeed",OxfordEconomicsDepartmentDiscussionPaper,No430. - Gali,Jordi,DavidLópez-Salido,andJavierVallés.(2004)."RuleofThumbConsumers andtheDesignofInterestRateRules",JournalofMoney,CreditandBanking, 36(4),739-763. - Gali,Jordi,DavidLópez-Salido,andJavierVallés.(2007)."UnderstandingtheE¤ectsof GovernmentSpendingonConsumption",JournaloftheEuropeanEconomic Association,5,227-270. - Gali,JordiandTommasoMonacelli.(2005)."MonetaryPolicyandExchangeRate VolatilityinaSmallOpenEconomy",ReviewofEconomicStudies,72(3),707-734. - Gali,JordiandTommasoMonacelli.(2008)."OptimalMonetaryandFiscalPolicyina CurrencyUnion",JournalofInternationalEconomics,76,116-132. - -34- - Ireland,Peter.(2004)."TechnologyShocksintheNewKeynesianModel",Reviewof EconomicsandStatistics,86(4),923-936. - Johnson,David,JonathanParkerandNicholasSouleles.(2006)."HouseholdExpenditure andtheIncomeTaxRebatesof2001",AmericanEconomicReview,96(5),1589-1610. - Kirsanova,TatianaandSimonWren-Lewis.(2007)."Optimal...scalfeedbackinan economywithnominalrigidities",WorkingPaperNo.306,UniversityofOxford. - Kumhof,MichaelandDouglasLaxton.(2009)."Simple,ImplementableFiscalPolicy Rules",IMFWorkingPaper,No.09/76. - Leeper,Eric.(1991)."Equilibriaunder’Active’and’Passive’MonetaryandFiscal Policies",JournalofMonetaryEconomics,27(1),129-47. - Leith,CampbellandSimonWren-Lewis.(2006)."TheCostsofFiscalIn‡exibility", DepartmentofEconomics,WorkingPaper2005_23,UniversityofGlasgow. - Leith,CampbellandSimonWren-Lewis.(2007)."FiscalSustainabilityinaNew Keynesianmodel",DepartmentofEconomicsSeriesWorkingPaper,No.310, UniversityofOxford. - Linneman,LudgerandAndreasSchabert.(2003)."FiscalPolicyintheNeoclassical Synthesis",JournalofMoneyCreditandBanking,35,911-930. - Rossi,Ra¤aele.(2007)."RuleofThumbConsumers,PublicDebtandIncomeTax", WorkingPapers2007_44,DepartmentofEconomics,UniversityofGlasgow. - Rudd,JeremyandKarlWhelan.(2007)."ModelingIn‡ationDynamics:ACritical ReviewofRecentResearch",JournalofMoney,CreditandBanking,39(1),155-170. - Schmitt-Grohe,StephanieandMartinUribe.(2007)."OptimalSimpleAnd ImplementableMonetaryandFiscalRules",JournalofMonetaryEconomics,54, 1702-1725. - Soederlind,Paul.(1999)."SolutionandestimationofREMacromodelswithOptimal Policy",EuropeanEconomicReview,43,813-823. - Stehn,SvenJ.andDavidVines.(2008)."StrategicInteractionsbetweenanIndependent CentralBankandaMyopicGovernmentwithGovernmentDebt",CEPRDiscussion Papers6913,C.E.P.R.DiscussionPapers. - Stehn,SvenJ.andDavidVines.(2009)."WhyMonetaryPolicyalonecanbeOptimal", mimeo,UniversityofOxford. - Woodford,Michael.(2003).InterestandPrices:FoundationsofaTheoryofMonetary Policy.PrincetonUniversityPress. *Source: _wp09137 - References* --- _Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09137.pdf_