Fiscal Devaluations. Emmanuel Farhi Gita Gopinath Oleg Itskhoki Harvard Harvard Princeton. Cambridge University April / 23

Transcription

1 Fiscal Devaluations Emmanuel Farhi Gita Gopinath Oleg Itskhoki Harvard Harvard Princeton Cambridge University April / 23

2 Motivation Currency devaluation: response to loss of competitiveness New relevance: crisis in the Euro Area Quotes Fiscal devaluation: set of fiscal policies that lead to the same real outcomes but keeping exchange rate fixed Old idea (Keynes, 1931): Uniform tariff cum export subsidy More recently: VAT payroll tax swap Cavallo and Cottani (2010), IMF Fiscal Monitor (2011) No longer a theoretic curiosity: Germany 2007, France 2012, discussed in Portugal, Spain 1 / 23

3 Formal analysis of fiscal devaluations New Keynesian open economy model (DSGE) conventional fiscal instruments What we do wage and price stickiness (in local or producer currency) alternative asset market structures Numerical example: approximate fiscal devaluations 2 / 23

4 Formal analysis of fiscal devaluations New Keynesian open economy model (DSGE) conventional fiscal instruments What we do wage and price stickiness (in local or producer currency) alternative asset market structures Numerical example: approximate fiscal devaluations Relate literature 1 Partial equilibrium: Staiger and Sykes (2010), Berglas (1974) 2 Fiscal implementation: Adao, Correia and Teles (2009) cf 3 Quantitative studies of the VAT effects 4 Taxes under sticky prices: Poterba, Rotemberg, Summers (1986) 2 / 23

5 Main Findings 1 Robust Policies Small set of conventional fiscal instruments suffices for exact equivalence across a variety of economic environments 2 Simple Sufficient Statistic Size of tax adjustments depends only on the size of desired devaluation and is independent of details of environment 3 Government Revenue Neutrality Exact if all tax instruments are used Long-run; proportional to trade deficit in the short run 3 / 23

6 Main Findings 1 Two Fiscal Devaluation policies: (FD ) Uniform increase in import tariff and export subsidy OR (FD ) Uniform increase in value-added tax (with border adjustment) and reduction in payroll tax 2 In general, (FD ) and (FD ) need to be complemented with a reduction in consumption tax and increase in income tax may be dispensed with if devaluation is unanticipated 3 If debt denominated in home currency, equivalence requires partial default (forgiveness) 4 / 23

7 Outline 1 Static (one-period) model 2 Full dynamic model 3 Numerical example 4 Implementation issues non-zero initial taxes differential short-run tax pass-through non-uniform VAT and multiple variable inputs labor mobility quantitative assessment the case of monetary union 5 / 23

8 Two countries: nominal or fiscal devaluation at Home passive policy in Foreign Static Model Setup I Households: Preferences: U(C, N), C = C γ H C 1 γ F, γ 1/2 Budget constraint PC 1 + ς c + M + T WN 1 + τ n + Π 1 + τ d + B Cash in advance: PC 1 + ς c M 6 / 23

9 Setup II Firms: Y = AN Π = (1 τ v )P H C H + (1 + ς x )EP H C H (1 ςp )WN Government: balanced budget M + T + TR = 0, ( τ n TR = 1 + τ n WN + τ d ) 1 + τ d Π ςc 1 + ς c PC ( τ + (τ v P H C H ς p v + τ m ) WN) τ m P F C F ς x EPH C H 7 / 23

10 Equilibrium relationships I PCP case 1 International relative prices: PH 1 1 τ v = P H E 1 + ς x P F = PF E 1 + τ m 1 τ v S = P F PH 2 Wage and Price setting: [ W = W 1 + τ n ] 1 θw θw µ w 1 + ς c PC σ N ϕ, P H = P θp H 3 Demand cash in advance: 1 ς [µ p W p 1 τ v A ] 1 θp PC M(1 + ς c ) = P F P H E 1 + ςx 1 τ v 8 / 23

11 Equilibrium relationships II 4 Goods market clearing: Y = C H + C H 5 Exchange rate determination: Budget constraint (allowing for partial default) P C = PF Y 1 τ h B h B f E = E 1 τ v M(1 + ς c ) 1 τ h 1+τ m 1 γ Bh M γ Bf Perfect risk-sharing: ( ) σ C P E C = P/(1 + ς c ) Q E = M M Q σ 1 σ 9 / 23

12 Results I Proposition The following policies constitute a fiscal δ-devaluation 1 under balanced trade or foreign-currency debt: (FD ) τ m = ς x = δ (FD ) τ v = ς p = δ 1+δ ] and ς c = τ n = ɛ, M M = δ ɛ 1 + ɛ ɛ 2 under home-currency debt supplement with partial default: τ h = δ/(1 + δ) 3 under complete international risk-sharing need to set: ɛ = δ and M M = σ 1 σ Q Q 10 / 23

13 Results II 4 Local currency pricing Result: Same as under PCP. Law of one price does not hold details P H = P θp H 1 ς [µ p ] 1 θp 1 W p 1 + ς x E A Real effects differ under PCP and LCP 11 / 23

14 Results III 5 Revenue neutrality Result: (FD ) and (FD ) are fiscal revenue-neutral. When ς c = τ n = ɛ, revenue neutrality holds in the long run TR = [ δ 1 + δ ɛ ] ( ) PC WN 1 + ɛ }{{} = NX +Π Fiscal surplus in periods of trade deficit Revenue neutrality is relative to the fiscal effect of a nominal devaluation 12 / 23

15 Dynamic model Dynamic Calvo price and wage setting show Endogenous savings and portfolio decisions Dynamic (interest-elastic) money demand More general preferences 13 / 23

16 Dynamic model Dynamic Calvo price and wage setting show Endogenous savings and portfolio decisions Dynamic (interest-elastic) money demand More general preferences Definition: Consider an equilibrium path of the economy with E t = E 0 (1 + δ t ), given {M t }. Fiscal {δ t }-devaluation is a sequence {M t, τt m, ςt x, τt v, ςt p, ςt c, τt n, τt d } that leads to the same real allocation, but with E t E 0. Anticipated and unanticipated devaluations 13 / 23

17 Flow budget constraint of a country: j Qt P j Ω t t Two Key Dynamic Equations B j t+1 j Qt j Ω t 1 + D j t P t ] Bt j = P Ht [C Pt Ht C Ft S t, International risk sharing condition: E t { Q j t+1 + Dj t+1 Q j t P t P t+1 [ (Ct+1 C t ) σ ( Q t+1 C ) ]} σ t+1 = 0 j Ω t Q t C t Terms of Trade and Real Exchange Rate: S t = P Ft 1 1 τt v PHt E t 1 + τt m and Q t = P t E t P t /(1 + ς c t ) 14 / 23

18 Result I Complete markets Proposition A fiscal {δ t }-devaluation in a dynamic PCP or LCP economy with complete markets: (FDD ) τt m = ςt x = τt d ] = δ t (FDD ) τ v t = ς p t = δt 1+δ t, τ d t = 0 and a suitable choice of {M t}. and ς c t = τ n t = δ t, analogous to static economy: terms of trade, RER interest-elastic money demand: no additional tax instruments ( Mt (1 + ςt c ) ν ) = i t+1 χc σ t P t 1 + i t+1 15 / 23

19 1 Foreign-currency risk-free bond: Results II Incomplete markets Home country budget constraint: [ Qt Bt+1 f Bt f = PHtC Ht 1 1 τ v ] t P Ft C Ft E t 1 + τt m The optimal risk sharing condition { ( ) } C Qt σ = βe t+1 Pt t Ct P t+1 = βe t { ( Ct+1 C t ) σ P t P t+1 (1 + ς c t+1)e t+1 (1 + ς c t )E t } 16 / 23

20 1 Foreign-currency risk-free bond: Results II Incomplete markets Home country budget constraint: [ Qt Bt+1 f Bt f = PHtC Ht 1 1 τ v ] t P Ft C Ft E t 1 + τt m The optimal risk sharing condition { ( ) } C Qt σ = βe t+1 Pt t Ct P t+1 = βe t { ( Ct+1 C t Same proposition applies: (FDD ) and (FDD ) dynamic savings decision 2 Same for international trade in equities show ) σ P t P t+1 (1 + ς c t+1)e t+1 (1 + ς c t )E t 3 Home-currency bond: additionally requires partial default 1 d t = (1 + δ t 1 )/(1 + δ t ) } 16 / 23

21 Results III Unanticipated devaluation Proposition A one-time unanticipated fiscal δ-devaluation in an incomplete markets economy: (FDR ) τt m = ςt x = τt d ] = δ (FDR ) τ v t = ς p t = δ 1+δ, τ d t = 0 and M t M t, together with a one-time partial default (haircut) τ h = δ/(1 + δ) on home-currency debt. No consumption subsidy needed Applies to risk-free-bond and international-equity economies Generalization of revenue neutrality: TR t = δt 1+δ t NX t + δt Π 1+τt d t 17 / 23

22 1 Non-uniform VAT (e.g., non-tradables) match payroll subsidy 2 Multiple variable inputs (e.g., capital) uniform subsidy Model w/capital Implementation 3 Tax pass-through assumptions: equivalence of VAT and exchange rate pass-through into foreign prices VAT and payroll tax pass-through into domestic prices Generalization 4 Non-zero initial tax: τ v t = τ v 0 + δ t 1 + δ t 5 Quantitative investigation show 18 / 23

23 Implementation in a Monetary Union Coordination with union central bank: Union-wide money supply: M t = M t + M t M t/m t is endogenous Division of seigniorage between members: M t = Ω t + Ω t Special cases: unilateral fiscal adjustment suffices seigniorage is small ( M t 0) devaluing country is small ( M t / M t 0) 19 / 23

24 Numerical example Setup Small open economy calibrated to Spain With nominal friction: wage stickiness With capital and adjustment cost Initial distortionary taxes (as in Spain) Money-in-the-utility to match M1 or M2-to-GDP ratio Initial debt-to-gdp of 87% Shock to country risk premium to generate the 2008 recession: i t+1 = i + ψ ( e B B t+1 1 ) + ε t, ε t AR(1) Scenarios: Flexible wages Sticky wages, no policy intervention 10% fiscal devaluation (one-time unanticipated) Various incomplete fiscal devaluations 20 / 23

25 GDP 0.04 F S 0.02 FD Consumption F S FD Investment F S FD Trade Balance to GDP F 0.01 S FD Labor F S FD Terms of Trade F S FD Ratio of employment to capital, N/K Nominal Wages Price of Home good F S FD F S FD 0.05 F 0.1 S FD Consumer Price level F S FD Real wage F S FD Ratio of Wage to rental rate of capital F S FD / 23

26 Incomplete fiscal devaluations Loss relative to no shock Permanent 10 quarters Sticky wages, no intervention 0.64% 3.65% Flexible wages 0.47% 2.66% 10% one-time devaluation 0.45% 2.55% Of this gap 10% fiscal devaluation 100% 5% fiscal devaluation 53% Fiscal devaluation w/out capital subsidy 68% Anticipated fiscal devaluation 79% No seigniorage transfer 83% 22 / 23

27 Summary Two robust FD policies: uniform import tariff and export subsidy, OR uniform increase in VAT and reduction in payroll tax Unanticipated devaluation: no additional instruments. Overall, small set of conventional fiscal instruments Require minimal information: size of desired devaluation δ Robust in particular to: price and wage setting asset market structure Revenue-neutrality Sidesteps the trilemma in international macro 23 / 23

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29 Quotes Popular arguments for abandoning Euro and devaluation: Feldstein (FT 02/2010): If Greece still had its own currency, it could, in parallel, devalue the drachma to reduce imports and raise exports... The rest of the eurozone could allow Greece to take a temporary leave of absence with the right and the obligation to return at a more competitive exchange rate. Krugman (NYT): Why devalue? The Euro Trap, Pain in Spain Now, if Greece had its own currency, it could try to offset this contraction with an expansionary monetary policy including a devaluation to gain export competitiveness. As long as its in the euro, however, Greece can do nothing to limit the macroeconomic costs of fiscal contraction. Roubini (FT 06/2011): The Eurozone Heads for Break Up... there is really only one other way to restore competitiveness and growth on the periphery: leave the euro, go back to national currencies and achieve a massive nominal and real depreciation. Keynes (1931) in the context of Gold standard Precisely the same effects as those produced by a devaluation of sterling by a given percentage could be brought about by a tariff of the same percentage on all imports together with an equal subsidy on all exports, except that this measure would leave sterling international obligations unchanged in terms of gold. back to slides 25 / 23

30 Related Literature Comparison to ACT (Adao, Correia and Teles, JET, 2009) ACT (2009) FGI (2011) Allocation Flexible-price (first best) Nominal devaluation one-time unexpected Implementation General non-constructive fiscal implementation principle Specific implementation: simplicity, robustness, feasibility Environment Nominal frictions Sticky prices (PCP or LCP) Sticky prices (PCP and LCP) and sticky wages Arbitrary markets incomplete Instruments Implementability Analytical characterization of taxes Int l coordination of taxes Tax dependence on microenvironment Int l asset markets Risk-free nominal bonds Arbitrary degree of completeness Separate consumption taxes by origin of the good and income taxes in both countries; additional instruments in other cases No Yes In general, yes Tax dynamics In general, complex dynamic path VAT, payroll, consumption and income tax in one country VAT and payroll tax only in one country Yes, simple characterization and expressions No, unilateral policy No, robust to any changes in environment Path of taxes follows the path of devaluation Only one-time tax change back to slides 26 / 23

31 Law of one price does not hold Price setting in consumer currency PH = 1 ς P θp H [µ p p P F = P θp F Terms of trade appreciates Local currency pricing 1 + ς x 1 E 1 + τ [µ m p 1 τ v E W A S = P F 1 1 τ v PH E 1 + τ m Foreign firm profit margins decline ] W 1 θp, A ] 1 θp Π = PF C F + P 1 1 τ v F C F E 1 + τ m W N back to slides 27 / 23

32 Price setting P Ht (i) = E t s t (βθ p) s t Cs σ E t P 1 s P ρ Hs Y s s t (βθ p) s t Cs σ ρ (1+ςs c )(1 ςs p ) ρ 1 1+τs d Ps 1 (1+ςs c)(1 τ s v ) 1+τs d W s /A s (i), Under (FDD ), (1 + ς c s )(1 τ v s ) = (1 + ς c s )(1 ς p s ) = 1, therefore the reset price P Ht stays the same, and hence so does P Ht (FDD ) additionally requires compensating with τ d s = δ t, unless devaluation is unanticipated back to slides 28 / 23

33 Budget constraint International trade in equities P tc t 1 + ς c t + M t + (ω t+1 ω t) E t {Θ t+1v t+1} (ω t+1 ω t ) E t {Θ t+1e t+1v t+1} WtNt 1 + τ n t + ω t Π t 1 + τ d t + (1 ω t )E tπ t + M t 1 T t, Value of the firm: V t = E t V t = E t Θ t,s s=t s=t Θ t,sπ s Π s 1 + τ d s, Θ t,s = s l=t+1 Θ l, Θ l = β ( Ct+1 C t ) σ P t 1 + ςt+1 c, P t ςt c Risk-sharing conditions ( ) E t Θ t,s Θ E t Πs t,s E s 1 + τs d s=t back to slides = 0 and E t s=t ( ) E s Θ t,s Θ t,s Π s = 0. E t 29 / 23

34 Home-currency Bond Partial defaults on home-currency bonds: contingent sequence {d t } The international risk sharing condition becomes { (C ) } σ Q t = βe t+1 Pt E t t Ct Pt+1 E (1 d t+1 ) t+1 { (Ct+1 ) } σ P t 1 + ςt+1 c = βe t C t P t ςt c (1 d t+1 ), Country budget constraint can now be written as Q t 1 E t B h t+1 (1 d t ) E t 1 E t 1 E t 1 B h t [ = (1 γ) Pt Ct 1 1 τt v P t C t E t 1 + τt m ] back to slides 30 / 23

35 Choice of capital input by firms: N t = α (1 ςt R ) R t K t 1 α (1 ς p t ) W t Model with capital Choice of capital investment by households: [ ] (1 + ςt c R U c,t ( ) t+1 (1 + ς c = βe 1 + ς I tu c,t+1 ( t+1) ) + (1 δ) ( (1 + ςc t+1) ) t P t τ K t ς I t+1 Results: 1 When consumption subsidy ςt c is not used, only capital expenditure subsidy to firms ςt R is required (parallel to payroll subsidy). All variable inputs should be subsidized uniformly 2 Otherwise, investment subsidy and capital income tax need to be used in addition: ς I t = τ K t = ς c t = δ t back to slides 31 / 23

36 Pass-through of VAT and payroll tax Static model with differential pass-through ξ p > ξ τ : [ ] P H = P H (1 θp [ ] ςp ) ξp 1 ς p 1 θp W µ p (1 τ v ) ξτ 1 τ v A Proposition Fiscal devaluation is as characterized in Results I-III, but with payroll subsidy given by ( 1 ς p = δ ) ξv θp +1 θp ξp θp +1 θp. still τ v = δ/(1 + δ), to mimic international relative prices ξ v > ξ p implies ς p > τ v = δ/(1 + δ) as θ p decreases towards 0, ς p decreases towards δ/(1 + δ) back to slides 32 / 23

37 Quantitative investigation Source: Gopinath and Wang (2011) Germany Spain Portugal Italy Greece Taxes VAT 13% 7% 11% 9% 8% payroll contributions 14% 18% 9% 24% 12% including employee s SSC 27% 22% 16% 29% 22% % change, wages 25% 61% 64% 39% 127% productivity 17% 19% 28% 3% 42% Required devaluation 34% 28% 28% 77% Maximal fiscal devaluation 23% 11% 32% 14% with German fiscal revaluation 38% 26% 47% 29% additionally reducing employee s SSC 43% 34% 56% 43% Required devaluation brings unit labor cost (W t /A t ) relative to Germany to its 1995 ratio Maximal fiscal devaluation is constrained by zero lower bound on payroll contributions and 45% maximal VAT rate (which is never binding). A reduction of x in payroll tax and similar increase in VAT is equivalent to a x/(1 x) devaluation Maximal German revaluation is an additional decrease in German VAT of 13% and a similar increase in German payroll tax, equivalent to an additional 15% devaluation against Germany back to slides 33 / 23