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On the International Dimension of Fiscal Policy Gianluca Benigno and Bianca De Paoli London School of Economics and Bank of England February 2010 Benigno & De Paoli (LSE&BoE) International Dimension of Fiscal Policy February 2010 1 / 24 Motivation How should …scal policy be conducted in an open economy? - Is the prescription di¤erent than the case of closed economies? Benigno & De Paoli (LSE&BoE) International Dimension of Fiscal Policy February 2010 2 / 24 Motivation How should …scal policy be conducted in an open economy? - Is the prescription di¤erent than the case of closed economies? What is the optimal level of tax smoothing? - Does the answer depend on the optimal level of exchange rate volatility? Benigno & De Paoli (LSE&BoE) International Dimension of Fiscal Policy February 2010 2 / 24 Motivation How should …scal policy be conducted in an open economy? - Is the prescription di¤erent than the case of closed economies? What is the optimal level of tax smoothing? - Does the answer depend on the optimal level of exchange rate volatility? From a positive perspective, transmission mechanism of …scal shocks might depend on exchange rate ‡uctuations. Benigno & De Paoli (LSE&BoE) International Dimension of Fiscal Policy February 2010 2 / 24 Motivation (2): Complementing the literature Neoclassical literature on optimal …scal policy has focused mainly on closed economy models - when taxes are distortionary, taxes should be smoothed over time and across states of nature - If possible, taxes would be essentially invariant (see Lucas and Stokey, 1983 and Chari, Christiano and Kehoe, 1991) or would follow a random walk (see Barro, 1979, Aiyagari et al. 2002). Benigno & De Paoli (LSE&BoE) International Dimension of Fiscal Policy February 2010 3 / 24 Motivation (2): Complementing the literature Neoclassical literature on optimal …scal policy has focused mainly on closed economy models - when taxes are distortionary, taxes should be smoothed over time and across states of nature - If possible, taxes would be essentially invariant (see Lucas and Stokey, 1983 and Chari, Christiano and Kehoe, 1991) or would follow a random walk (see Barro, 1979, Aiyagari et al. 2002). Open economy models have concentrated in the analysis of monetary policy - Obstfeld and Rogo¤ (2002), Gali and Monacelli (2005) isomorphism result between optimal policy in open and closed economy - Corsetti&Pesenti (2001)/Benigno&Benigno (2003)/De Paoli (2008)presence of terms of trade externality eliminates the result Benigno & De Paoli (LSE&BoE) International Dimension of Fiscal Policy February 2010 3 / 24 Motivation (2): Complementing the literature Neoclassical literature on optimal …scal policy has focused mainly on closed economy models - when taxes are distortionary, taxes should be smoothed over time and across states of nature - If possible, taxes would be essentially invariant (see Lucas and Stokey, 1983 and Chari, Christiano and Kehoe, 1991) or would follow a random walk (see Barro, 1979, Aiyagari et al. 2002). Open economy models have concentrated in the analysis of monetary policy - Obstfeld and Rogo¤ (2002), Gali and Monacelli (2005) isomorphism result between optimal policy in open and closed economy - Corsetti&Pesenti (2001)/Benigno&Benigno (2003)/De Paoli (2008)presence of terms of trade externality eliminates the result Bridging the gap... Benigno & De Paoli (LSE&BoE) International Dimension of Fiscal Policy February 2010 3 / 24 Approach Theoretical, normative analysis of …scal policy Formalize a small open economy with endogenous …scal policy Characterize a utility based loss function each speci…cation Derive the optimal …scal policy (also look at the planner’s problem) Analyse the implication for tax and exchange rate volatility Benigno & De Paoli (LSE&BoE) International Dimension of Fiscal Policy February 2010 4 / 24 Anticipating the results .. Our analysis shows that in a small open economy optimal policy departs from tax smoothing. As emphasised in the optimal monetary policy literature policymakers in open economies are in‡uenced by a “terms of trade externality”. - E.g. In an open economy that is a monopolist producer of its own goods, a real exchange rate appreciation can lead to higher welfare by allowing domestic agents to consume more for lower levels of domestic production. - Thus, policymakers have an incentive to use …scal policy to exploit this externality. - As a result, distortionary taxes vary over time and across states of nature. When we consider the joint …scal and monetary policy problem, there is a trade-o¤ between price stability and tax-smoothing that arises from the terms of trade externality. Quantitatively cost of in‡ation are high and optimal in‡ation volatility is low. Benigno & De Paoli (LSE&BoE) International Dimension of Fiscal Policy February 2010 5 / 24 The Model: overview 2-country DSGE model ) small open economy Home bias ) deviations from PPP Monopolistic competition and nominal rigidities a la Calvo ) Role for monetary policy Preferences ) allow for trade imbalances Fiscal authority issues nominal debt and set income taxes (extension includes the case of indexed linked debt) Stochastic environment: domestic and foreign productivity shocks, markup and …scal shocks Benigno & De Paoli (LSE&BoE) International Dimension of Fiscal Policy February 2010 6 / 24 The model: Preferences Utility (country H – measure n) ∞ U t = Et ∑ βs s =t ∞ U t = Et ∑ βs t s =t t " [U (Cs ) log Cs V (y (h)s , εY ,s )] 1 n Z n ε η y h 1 +η Y ,s ( )s 1+η 0 # Home bias (Sutherland 2001) 1 θ θ 1 θ C = v CH (1 v ) = (1 + (1 1 θ θ 1 θ θ θ 1 v ) CF n)λ and v = nλ " # σσ 1 1 Z σ 1 1 σ n CH = c (z ) σ dz n 0 Benigno & De Paoli (LSE&BoE) International Dimension of Fiscal Policy February 2010 7 / 24 The model: Relative prices and demand Law of one price: p (z ) = S p (z ). Home bias ) PPP does not hold: Qt SOE demand yt (h) = pt (h) PH ,t σ PH ,t Pt St Pt /Pt θ RoW demand yt ( f ) = Benigno & De Paoli (LSE&BoE) λ) Ct + λ (1 pt (f ) Pt 1 Qt Ct σ Ct International Dimension of Fiscal Policy February 2010 8 / 24 The model: Asset markets Complete markets UC Ct +1 U (Ct +1 ) Qt +1 = C UC (Ct ) UC (Ct ) Qt Benigno & De Paoli (LSE&BoE) International Dimension of Fiscal Policy February 2010 9 / 24 The model: Fiscal Policy Government issues one period nominal risk free bonds expressed in local currency units, collects taxes and faces exogenous expenditure streams. Government debt Dtn , expressed in nominal terms, follows the law of motion: Dtn = Dtn 1 (1 + it 1 ) PH ,t st where st is the real primary budget surplus: st τ t Yt Gt Trt The case real bonds: Dtr = Dtr Benigno & De Paoli (LSE&BoE) r 1 (1 + it 1 ) + PH ,t st Pt International Dimension of Fiscal Policy (1) February 2010 10 / 24 The model: Monopolistic competitive …rms Firms’behavior (‡exible prices) Set prices as a markup over marginal costs pH ,t = Benigno & De Paoli (LSE&BoE) (1 σmut τ t )(σ Vy (Yt , εY ,t ) 1) Uc (CT ) International Dimension of Fiscal Policy February 2010 11 / 24 Social planner vs. competitive allocation Understanding the policy incentive: Planner problem (maximizes agents’utility subject to resourse constraint and complete markets assumption): pH ,t Uc (Ct ) = Q (RSt )Vy (Yt , εY ,t ) Competitive equilibrium: (1 σmut τ t )(σ σmut τ t )(σ 1) pH ,t Uc (Ct ) = 1) Vy (Yt , εY ,t ) E¢ ciency condition (1 Q (RSt ) = 1 ) Movements in the tax rate, in the real exchange rate, and markup shocks generate ine¢ ciencies (i.e. competitive equilibrium departs from planner’s problem) Benigno & De Paoli (LSE&BoE) International Dimension of Fiscal Policy February 2010 12 / 24 Social planner vs. competitive allocation (2) E¢ ciency condition (1 σmut τ t )(σ 1) Q (RSt ) = 1 Closed economy σmut =1 (1 τ t )(σ 1) Tax smoothing is optimal when there are no markup shocks Steady state tax subsidy eliminates steady-state distortion 1 τ̄ = σ 1 (assuming mu = 1) Open economy tax smoothing no longer optimal Steady state optimal tax depends on degree of openness and substitutability between goods Q̄ (λ, ρ, θ ) Benigno & De Paoli (LSE&BoE) International Dimension of Fiscal Policy February 2010 13 / 24 Understanding the ToT externality θρ > 1 : real exchange rate appreciation (or ToT improvement) increases welfare/ reduces loss Substitute goods: appreciation decreases CH but increases CF reduction in U (C ) smaller than in V (Y ) Complement goods: appreciation cannot divert consumption towards foreign goods (decrease in CH accompanied by decrease in CF ) θρ < 1: depreciation improve welfare ) leads to higher CH that increases marginal utility of CF : U (C ) "> V (Y ) " Externality only eliminated only when the economy is closed (λ = 0) or when θρ = 1 - in this case marginal utility of CH independent of CF , and vice-versa Benigno & De Paoli (LSE&BoE) International Dimension of Fiscal Policy February 2010 14 / 24 Linear Quadratic Approach: Motivation E¢ ciency condition can pin down the optimal level of taxes in the case of nominal bonds ) Set taxes to eliminate di¤erence between social planner and competitive equilibrium ) Government solvency condition satis…ed given in‡ation can replicate state contingent debt But in the case of real bonds this is not the case Have to solve system of non-linear equations Linear quadratic loss function can also help policy implementation Benigno & De Paoli (LSE&BoE) International Dimension of Fiscal Policy February 2010 15 / 24 Linear Quadratic Approach: Loss function Agent´ s Utility ) Welfare metric Method of Benigno&Woodford (2003), Sutherland (2002) min Uc C̄ Et0 ∑ βt Closed economy 1 Φτ (b τt 2 min Uc C̄ Et0 ∑ βt 1 b τ Tt )2 + ΦRS rs b 2t + t.i.p + O (jjξ jj3 ), 2 1 Φτ (b τt 2 b τ Tt )2 + t.i.p + O (jjξ jj3 ), Open economy: ΦRS rs b 2t arises given the terms of trade externality Corsetti and Pesenti (2001): improvements in ToT ) allow larger consumption for a given level of labour e¤ort (or domestic production) Benigno & De Paoli (LSE&BoE) International Dimension of Fiscal Policy February 2010 16 / 24 Optimal Policy: The case of nominal debt Optimal targeting rule ΦRS rs bt + Closed economy: (1 + l ) Φτ (b τt ρ (1 λ ) b τt 0 0 0 b τ Tt ) = 0. b τ Tt = 0. Taxes are constant when b τ Tt = 0 ) when there are no markup shocks and the steady state is e¢ cient Benigno & De Paoli (LSE&BoE) International Dimension of Fiscal Policy February 2010 17 / 24 Optimal Policy: Closed economy with nominal debt Sdv tax rate relative to output 0.5 0.4 0.3 0.2 0.1 0 0.5 1 1.5 Steady state markup 2 2.5 1 1.5 Steady state markup 2 2.5 With Markup Shocks 1.2 1 0.8 0.6 0.4 0.2 0 0.5 Benigno & De Paoli (LSE&BoE) International Dimension of Fiscal Policy February 2010 18 / 24 Optimal Policy: Open economy with nominal debt -3 x 10 Sdv Planner/Comp. Wedge Sdv tax rate relative to output 2 1 1.5 1 0.5 0.5 0 1 1.5 2 2.5 Steady state markup 3 0 1 1.5 2 2.5 Steady state markup 3 -3 x 10 With Markup Shocks 2 5 1.5 4 3 1 2 0.5 0 1 0 1.5 2 2.5 3 1 1.5 2 2.5 3 Steady state markup Steady state markup Benigno & De Paoli (LSE&BoE) International Dimension of Fiscal Policy February 2010 1 19 / 24 Optimal Policy: Open economy with nominal debt (e¢ cient steady state and no markup shocks) Sdv tax rate relative to output Sdv Planner/Comp. Wedge 0.05 1 0.8 0.6 0.4 0.2 0 0 0.1 0.2 0.3 -0.05 0.4 λ 0 0.1 0.2 0.4 2 2.5 λ 0.05 1 0.8 0.6 0.4 0.2 0.3 0 1 1.5 2 2.5 3 -0.05 θ Benigno & De Paoli (LSE&BoE) 1 1.5 3 θ International Dimension of Fiscal Policy February 2010 20 / 24 Optimal Policy: Open economy with real debt (e¢ cient steady state and no markup shocks) Stv of taxes relative to output Sdv Planner/Comp. wedge 1.5 0.05 1 0 0.5 0 0 0.1 0.2 0.3 0.4 0.5 -0.05 0 0.1 0.2 λ 0.3 0.4 0.5 λ Stv of taxes relative to output Sdv Planner/Comp. wedge 1.5 0.05 1 0 0.5 0 0.5 1 1.5 Benigno & De Paoli (LSE&BoE) 2 θ 2.5 3 -0.05 0.5 International Dimension of Fiscal Policy 1 1.5 2 θ 2.5 February 2010 3 21 / 24 Optimal Policy: Sticky prices targeting rules Firms set prices following partial adjustment rule a la Calvo Loss function now depends also on domestic producer in‡ation General forms of targeting rules (1 + l ) Φy ∆b yt + ΦRS ∆rs bt + (1 λ ) ρ (1 kΦπ bH (γb πH t + dss (a + 1) π t 1) = 0 τ ) + bdss k bH Et π t +1 = 0, Benigno & De Paoli (LSE&BoE) International Dimension of Fiscal Policy February 2010 22 / 24 Optimal Policy: Sticky prices targeting rules Figure: Figure 5 Benigno & De Paoli (LSE&BoE) International Dimension of Fiscal Policy February 2010 23 / 24 Concluding remarks Simple framework for …scal policy in open economy Normative analysis: Fiscal policy problem in an open economy 6= closed economy Optimal tax variability in an open economy 6= closed economy Optimal steady state tax in an open economy 6= closed economy Reason: incentive to use taxes to a¤ect the terms of trade Fiscal policy e¢ ciency depends on the type of debt. Benigno & De Paoli (LSE&BoE) International Dimension of Fiscal Policy February 2010 24 / 24