Trade policies and fiscal devaluations

Board of Governors of the Federal Reserve System International Finance Discussion Papers ISSN 1073-2500 (Print) ISSN 2767-4509 (Online) Number 1347 June 2022 Trade policies and fiscal devaluations Christopher Erceg, Andrea Prestipino, and Andrea Raffo Please cite this paper as: Erceg, Christopher, Andrea Prestipino, and Andrea Raffo (2022). “Trade policies and fiscal devaluations,” International Finance Discussion Papers 1347. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/IFDP.2022.1347. NOTE: International Finance Discussion Papers (IFDPs) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the International Finance Discussion Papers Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Network electronic library at www.ssrn.com.

∗ Trade Policies and Fiscal Devaluations Christopher Erceg, Andrea Prestipino, and Andrea Raffo June 20, 2022 Abstract Fiscal devaluations—an increase in import tariffs and export subsidies (IX) or an increase in value-added taxes and payroll subsidies (VP)—have been shown to provide as muchstimulusunderfixedexchangeratesasacurrencydevaluation. Wefindthatifagents expect policies to be reversed and the tax pass-through is large, VP is contractionary and IXprovidesamodestboost. Inourmedium-scaleDSGEmodel,bothfeaturesarecrucialin accounting for Germany’s weak output response to VP in 2007. These findings cast doubt on fiscal devaluations as a cyclical stabilization tool when monetary policy is constrained. JEL classification: E32, F30, H22 Keywords: Trade Policy, Fiscal Policy, Exchange Rates, Fiscal Devaluation 1 Introduction There is a long-standing debate about how trade and fiscal policies can provide macroeconomic stimulusbyboostinginternationalcompetitiveness. Inconsideringdifferentwaysofalleviatinga ∗Erceg: International Monetary Fund (email: CErceg@imf.org); Prestipino: Federal Reserve Board (email: andrea.prestipino@frb.gov); Raffo: Federal Reserve Board (email: andrea.raffo@frb.gov). A previous version of this paper circulated under the title “The Macroeconomic Effects of Trade Policies.” For insightful comments, we thank our discussants R. Ossa, M. Cacciatore, N. Traum, F. Di Pace, and E. Farhi, seminar participants at the Federal Reserve Banks of Boston and Philadelphia, Macroeconomic Meetings of the Federal Reserve System, XXIX Villa Mondragone Economic Seminar, NBER Summer Institute, ITAM-PENN Macroeconomic Meetings, Melbourne Institute Macroeconomic Policy Meetings, CEBRA-BOE IFM Annual Meeting, NBER IFM Fall Meetings, European Central Bank, XX Inflation Targeting Conference of the Central Bank of Brazil, and SED Meetings, as well as anonymous referees and the editor. The views expressed in this paper are those of the authors and do not necessarily represent the views of the International Monetary Fund, its Executive Board, or IMF Management; or the views of the Board of Governors of the Federal Reserve System, or any other person associated with the Federal Reserve System. 1

deepeconomicrecessionwithintheconfinesofthegoldstandard, KeynesarguedthattheUnited Kingdom could derive a similar degree of stimulus from raising import tariffs and providing export subsidies as through devaluing the pound against gold.1 However, even if these policies can provide stimulus under fixed exchange rates, it is unclear to what extent they would do so under flexible exchange rates. Mundell (1961) questioned whether the mercantilist prescription of higher import tariffs and export subsidies would stimulate demand in economies with floating exchange rates, as “equilibrium in the balance of payments is automatically maintained by variations in the price of foreign exchange.” More recently, there has been renewed interest in the question of how countries constrained by membership in a currency union can implement changes in tax instruments with economic effects akin to a currency depreciation. The approach of financing competitiveness-enhancing payrolltaxcutswithVATincreases, inparticular, hasastrongintuitiveappealandhasreceived attention by both academics and policymakers.2 In a seminal contribution, Farhi et al. (2014) (FGI henceforth) provide conditions so that, under fixed exchange rates, fiscal devaluations implemented via either uniform import tariffs and export subsidies (IX policy) or a reduction in employer payroll taxes financed by an increase in VAT rates (VP policy) reproduce the same allocation as an exchange rate devaluation. Although these policies may need to be supplemented by additional tax instruments, these authors show in a quantitative application that a simple VP policy in Spain would have boosted economic activity significantly during the Great Recession. Some euro-area governments have attempted to provide macroeconomic stimulus by implementing “fiscal devaluations,”including the government of Germany in 2007. Inthispaper, wemakethreecontributionstotheunderstandingoftheseimportantacademic and policy issues by studying IX and VP policies in a New Keynesian open-economy framework that builds on contributions by Gali and Monacelli (2005a) and Corsetti et al. (2010). First, we show that the transmission of IX and VP policies hinges critically on the degree of passthroughoftaxes. Indeed, inaspecialcaseoftenconsideredintheliterature, underourpreferred assumption of full pass-through of taxes, IX implements a currency devaluation in a fixed exchange rate regime, whereas VP turns out to have no allocative effects. Second, we study how 1See Macmilan et al. (1931). Eichengreen (1981) provides a detailed account of the contentious political debate that preceded the United Kingdom’s shift toward protectionist trade policies in the early 1930s. 2See Calmfors (1998) for an early argument. Correia et al. (2013) also study the role of VAT changes when monetary policy is constrained by the ZLB. 2

the effects of these policies depend on agents expectations about their persistence. Temporary IX policies tend to boost output even under flexible exchange rates. The macroeconomic effects of temporary VP, instead, depend critically on the relative strength of two offsetting channels. On the one hand, intertemporal substitution effects make VP contractionary; on the other hand, sluggish wage adjustments allow payroll subsidies to boost aggregate supply and output. We find that the first channel can easily dominate and that the contractionary effects of VP are larger when monetary policy is constrained (e.g., under an exchange rate peg or in a currency union). Third, we assess the empirical relevance of our novel theoretical predictions by studying the effects of the German fiscal reform in 2007 during which payroll taxes where lowered and VAT taxes increased by similar amounts. We find that a quantitative version of our model can account for the weak GDP response of the German economy to this VP policy. In a counterfactual experiment, we also show that a temporary IX policy would have caused a much smaller output boost than an exchange rate devaluation. Hence, with VP likely to be contractionary and IX providing only a modest boost, our quantitative results suggest that neither policy can be considered as a counter-cyclical policy substitute for flexible exchange rates. To highlight our theoretical contribution, we begin by illustrating the different transmission mechanisms of IX and VP policies in the special case of unexpected and permanent policy changes and flexible wages.3 Under flexible exchange rates, IX and VP policies are equivalent and have no allocative effects, as they both are offset by a permanent real exchange rate appreciation of an amount equal to the size of the policy. Nonetheless, the two policies are only beguilingly equivalent, as they achieve neutrality through different adjustments. In the case of IX, an immediate jump in the nominal exchange rate offsets the effect of the policy on import and export prices.4 In the case of VP, the nominal exchange rate does not need to move at all. A jump in the nominal wage–proportional to the VAT hike–offsets the reduction in marginal costs caused by the payroll subsidy, thus inducing firms to keep labor demand unchanged. The nominal wage hike also makes households willing to keep their labor supply 3Theexactconditionsthatcharacterizethisspecialcasealsoincludethatforeign-currencydenominatedbonds representtheonlyinternationallytradedassetandthatexportersletpricesvaryoneforonewithexchangerates (producer currency pricing). 4This finding can be interpreted as an application of Lerner (1936) to dynamic economies. See also Costinot and Werning (2017). 3

unchanged by offsetting the reduction in real wages caused by higher consumer prices. Notably, as VAT changes apply to both imported and domestic goods, the relative price of traded goods is unaffected, and consumer prices drive the appreciation of the real exchange rate. These considerations also underscore the different transmission channels of IX and VP policies, with the former affecting domestic firms’ competitiveness in international markets, and the latter equilibrium in the domestic labor market. The different general equilibrium adjustments that deliver neutrality of IX and VP provide theintuitionforourfirsttheoreticalcontributiontothefiscaldevaluationliterature: Underfixed exchange rates, IX policies implement the same allocation as an exchange rate devaluation, but VPpoliciesremainneutral. GiventhatIXpoliciesrequireanominalappreciationforneutrality, absent an exchange rate response, IX turns out to elicit economic effects identical to a currency depreciation. Instead, because the neutrality of VP does not require any adjustment in the nominalexchangerate, thefixedexchangerateregimedoesnotposeanyconstrainttoachieving the same neutrality outcome as under flexible exchange rates. This result is in contrast to FGI and reflects a key difference between our frameworks. In particular, while we assume that pre-tax prices are sticky and VAT changes are fully passed through to consumer prices, FGI assume that prices are sticky inclusive of VATs and firms reduce margins in response to VAT increases. We next provide a broader characterization of the macroeconomic effects of the two policies once we depart from the restrictive conditions of the special case described earlier. First, we abandon the assumption that agents believe that policy changes will remain in place forever. We use a Markov-switching framework to capture the possibility that policy actions may be reversed because of political shifts or that they may induce retaliation by other countries. Second, we consider the role of wage rigidity for the transmission of these policies. The appeal of competitiveness-enhancing payroll tax cuts financed with VAT hikes appears greater when nominal rigidities prevent a strong offsetting wage response.5 We find that, when IX is expected to be reversed or to trigger retaliation, it tends to boost output and inflation even under flexible exchange rates. In this case, the exchange rate must 5For an early argument in favor of variations in payroll taxes in the presence of wage rigidities, see Calmfors (1998). For a recent discussion on the effects of wage rigidity in a small open economy belonging to a currency union, see also Gal´ı and Monacelli (2016). 4

eventually return to its pre-shock level, and, as a consequence, the immediate appreciation of the currency falls short of completely offsetting the expenditure-switching effects of the policy on imports and exports. We find that the resulting boost to net exports and output is robust to a wide range of environments, including departures from flexible wages and different monetary policy regimes. The macroeconomic effects of VP are much more sensitive to the details of the environment. We first show that a VP policy that is not perceived as permanent, perhaps because it may be reversed by future governments, has contractionary effects due to an intertemporal substitution channel. As the expected decline in future VAT rates raises the price of current consumption relative to future consumption, households increase savings and aggregate demand declines. Thus, a temporary VP exerts a strong contractionary impetus unless monetary policy cuts interest rates sufficiently and is even more likely to reduce output under fixed exchange rates or in a currency union. That said, we then show that VP policies can provide macroeconomic stimulus if wages are sufficiently sticky and the policy shift is expected to be permanent or nearly so, as the reduction in firms’ marginal costs induced by payroll subsidies is not fully offset by higher wages. In sum, our novel theoretical predictions underscore the importance of assumptions about tax pass-through and expectations about the evolution of policies. Direct empirical evidence on these features is limited. Several studies find large and immediate pass-through of VAT increases to consumer prices.6 However, existing evidence does not study pass-through during fiscal devaluations and it is possible that firms’ pricing response to VAT changes is different when payroll subsidies are also introduced.7 Similarly, it is difficult to construct direct measures of agents’ expectations about policy reversal. For these reasons, we employ an indirect inference approach to provide some evidence about these two key features of our analysis. We consider the 2007 fiscal policy reform in Germany as a laboratory to study the extent to which VP and IX policies can, quantitatively, provide as much stimulus as a currency devaluation. In January 2007, the German government simultaneously increased VAT rates and reduced payroll taxes by similar magnitudes. We document that, in the data, this VP policy 6See, for instance, Carbonnier (2007), Cashin and Unayama (2016) and Karadi and Reiff (2019). The range of estimates for the pass-through of a VAT increase in these studies is always above 60 percent. 7We thank Emmanuel Farhi for this comment. 5

was associated with a large pass-through of the VAT increase to consumer prices and a contraction in domestic demand and output, notwithstanding a small boost to net exports. We then use a medium-scale version of our model–extended to allow for heterogeneity in the price response to VAT changes–to study whether this fiscal reform can account for the economic underperformance of Germany in 2007. We estimate the values of the parameters controlling the share of firms that fully pass through VAT changes and the perceived persistence of the policy change so that they minimize the distance between the German data on output and inflation and the corresponding model simulated series. We find that the estimated model response to the VP policy can account well for the dynamics of key German macroeconomic variables over 2007. Our estimates suggest that a sizeable fraction of firms passed through the VAT increase quickly, and that agents attached a significant probability to an eventual policy reversal.8 As a result, intertemporal substitution effects dominate, and contribute to a drag on output, consumption, and investment. The limiting assumption of permanent policy changes and gradual pass-throughofvalue-addedtaxes, typicallyadoptedinthefiscaldevaluationliterature, appears strongly rejected by the data. We then compare the effects of the German VP to those that our model would imply if Germany could implement an IX policy or a currency devaluation. While Germany’s euro-area membership would preclude it from pursuing the latter policies, it is interesting to consider whether they would be more potent in delivering stimulus than VP if feasible to deploy. In line with our theoretical predictions, we find that IX would have delivered an output boost through its effects on external competitiveness. That said, an IX policy that is expected to be reversed has only a muted effect on aggregate demand and hence provides a much smaller boost to output than a currency devaluation. The paper is organized as follows. Section 2 describes the model. Section 3 develops some intuition about the effects of IX and VP starting from conditions for equivalence and neutrality. Section 4 discusses the transmission mechanisms of IX and VP policies once we depart from the conditions for equivalence and neutrality, with a focus on policy reversals and on sticky 8While obtained purely from aggregate data, our estimate of high tax pass-through is in line with the heterogeneous pricing response across firms documented in Bundesbank (2007). Similarly, the positive probability of policy reversal is consistent with reasonable assumptions about the likelihood of political turnover and its implications for the evolution of fiscal policy, as discussed in D’Acunto et al. (2016). 6

wages. Section 5 presents our quantitative analysis about the implementation of a VP policy in Germany in 2007. Section 6 concludes. 2 Model The economy consists of a home (H) country and a foreign (F) country that are isomorphic in structure. Foreign variables are denoted with an asterisk. Agents in each economy include households, retailers, producers of intermediate goods, and the government. For ease of exposition, the next sections describe the optimization problems solved by each type of agent under the assumptions of producer currency pricing (PCP), fully flexible wages, and a simple financial market structure in which only a foreign currency bond is traded internationally. Appendix A presents a more general model that allows for alternative assumptions about price and wage setting and financial market structure, as well as for differences in country size; all of the theoretical results are derived within the context of this general framework. 2.1 Households Households in the home country derive utility from a final good consumption (C ) and disutility t from labor (N ). They maximize expected lifetime utility t E Σ∞ βtU (C ,N ) (1) 0 t=0 t t subject to the budget constraint (cid:104) χ (cid:105) P C +B +ε B + (cid:0) B −B ¯ (cid:1)2 = R B +ε R∗ B +W N +Π(cid:101) +T (2) t t Ht t Ft 2 Ft F t−1 Ht−1 t t−1 Ft−1 t t t t where P is the consumer price index, B are noncontingent nominal bond holdings denomt Ht inated in domestic currency, B are noncontingent nominal bond holdings denominated in Ft foreign currency, R∗ is the foreign nominal interest rate, ε is the nominal exchange rate (det−1 t fined as the price of one unit of foreign currency in terms of units of the home currency), W is t the wage rate, Π(cid:101) is the aggregate profit of the home firms assumed to be owned by the home t consumers, and T is a lump-sum transfer from the government. The parameter χ ≥ 0 allows for t the possibility that home households face quadratic costs of adjusting their holdings of foreign 7

bonds.9 10 We assume that the period utility function takes the form 1 1 U(C,N) = C1−σ − N1+η (3) 1−σ t η +1 t Optimality requires W NηCσ = t (4) t t P t (cid:20) (cid:21) P 1 = E Λ t R (5) t t,t+1 t P t+1 (cid:20) (cid:21) P ε 1 = E Λ t t+1 R∗ (6) t t,t+1 P ε t t+1 t (cid:16) (cid:17)σ where Λ = βs−t Ct is the real stochastic discount factor of the home household. The t,s Cs corresponding optimality condition for foreign household holdings of the foreign bond is (cid:20) P∗ (cid:21) 1 = E Λ∗ t R∗ (7) t t,t+1P∗ t t+1 Combining the optimality conditions for bond holdings (6) and (7), one obtains the risk-sharing condition (cid:26)(cid:20) Q (cid:21) P∗ (cid:27) E Λ t+1 −Λ∗ t = 0 (8) t t,t+1 Q t+1 P∗ t t+1 where Q is the real exchange rate expressed as the price of the foreign consumption bundle in t home currency relative to the price of the domestic consumption bundle, that is, P∗ Q = ε t (9) t t P t 9All of our theoretical results go through irrespective of the value of χ provided that χ ≧ 0. For simplicity, the first-order conditions we report in the text assume χ=0. In our simulations, we introduce very small costs of adjustment to ensure stability of a first-order approximation. See Schmitt-Groh´e and Uribe (2003). 10Inourbaselinecalibrationwefocusonthecase,oftenconsideredintheliterature,inwhichforeignhouseholds cannot invest in the domestic bond so that only the foreign bond is traded internationally. That is, the budget constraint for foreign households is given by P t ∗C t ∗+B F ∗ t + ε 1 t (cid:104) B H ∗ t + χ 2 ∗ (cid:0) B H ∗ t −B¯ H (cid:1)2 (cid:105) =R t ∗ −1 B F ∗ t−1 + ε 1 t R t−1 B H ∗ t−1 +W t ∗N t ∗+Π(cid:101)∗ t +T t ∗ In our baseline analysis, we set χ∗ = ∞ so that only foreign currency bonds are traded internationally. We consider relaxing this assumption in Section 4.4. 8

2.2 Retailers Competitive home retailers combine home and foreign intermediate goods to produce the final consumption good according to the constant-elasticity-of-substitution (CES) aggregator (cid:104) 1 θ−1 1 θ−1(cid:105) θ− θ 1 C t = ω H θY Ht θ +(1−ω H )θ Y Ft θ (10) where θ ≥ 0 determines the elasticity of substitution between home and foreign intermediate goods and ω ∈ [0.5,1] governs home bias. The home good (Y ) and the foreign good (Y ) H Ht Ft consist of CES aggregators over home and foreign varieties (cid:20)(cid:90) 1 γ−1 (cid:21) γ− γ 1 Y Ht = Y Ht (i) γ di (11) 0 (cid:20)(cid:90) 1 γ−1 (cid:21) γ− γ 1 Y Ft = Y Ft (i) γ di (12) 0 where γ ≥ 0 determines the elasticity of substitution across varieties. Profits for the home retailers are ΠR = (1−τv)[P C −P Y −P Y ] (13) t t t t Ht Ht Ft Ft where P and P are the price indexes of the home and foreign goods and τv is the VAT Ht Ft t rate. Prices are inclusive of VATs and, in the case of imported goods, are also inclusive of home tariffs (τm). t Given the CES structure of these aggregators, the home and foreign good demand functions are characterized by (cid:20) P (cid:21)−θ Ht Y = ω C (14) Ht t P t (cid:20) P (cid:21)−θ Ft Y = (1−ω) C (15) Ft t P t (cid:20) P (i) (cid:21)−γ Ht Y (i) = Y (16) Ht Ht P Ht (cid:20) P (i) (cid:21)−γ Ft Y (i) = Y (17) Ft Ft P Ft 9

The zero profit conditions for home retailers imply that price indexes satisfy (cid:2) (cid:3) 1 P = ωP1−θ +(1−ω)P1−θ 1−θ (18) t Ht Ft (cid:20)(cid:90) 1 (cid:21) 1− 1 γ P = P (i)1−γdi (19) Ht Ht 0 (cid:20)(cid:90) 1 (cid:21) 1− 1 γ P = P (i)1−γdi (20) Ft Ft 0 2.3 Producers Each country features a continuum i ∈ [0,1] of monopolistically competitive firms that produce different varieties of intermediate goods. Producers use the technology Y (i)+Y∗ (i) = A Nα(i) (21) Ht Ht t t where Y (i) and Y∗ (i) are firm i′s sales in the domestic and foreign market, respectively; A Ht Ht t is the aggregate level of technology; and α ∈ (0,1) controls the curvature of the production function. Inourbenchmarkspecification, weassumePCP,thatis, producerssetpricesinthedomestic currency while letting prices in the foreign market adjust to ensure that unit revenues are equalized across markets. We can then write firm i′s profits as ΠP(i) = P (i)[Y (i)+Y∗ (i)]−(1−ςp)W N (i) (22) t Pt Ht Ht t t t where P (i) denotes the unit revenue from domestic sales of the home variety and ςp is a Pt t payroll subsidy to employers. The presence of VATs introduces a wedge between unit revenues P (i) and the price paid Pt by domestic retailers for P (i) : Ht P (i) = (1−τv)P (i) (23) Pt t Ht Similarly, import tariffs (τm) and export subsidies (ςx) create a wedge between the foreign t t 10

currency price paid by foreign retailers, P∗ (i), and firm i′s foreign currency unit revenue from Ht exports, PPt(i): εt (1+τm∗) P (i) P∗ (i) = t Pt (24) Ht (1+ςx)(1−τv∗) ε t t t Producers set prices in staggered contracts by following a Calvo-style timing assumption and with full pass-through of VATs. That is, a domestic firm that adjusts its price at time t sets the unit revenues P (i), and, absent any price adjustment until time s > t, changes in Pt VATs are fully reflected in retailers’ costs of purchasing the home variety P (i) Pt P (i) = . (25) Hs (1−τv) s ¯ Each firm that reoptimizes at time t will then choose P to solve Pt, (cid:88) (cid:26) P ¯ (i)[Y (i)+Y∗ (i)]−(1−ςp)W N (i) (cid:27) maxE ζs−tΛ Pt Hs Hs s s s (26) t P t,s P s s≥t where ζ is the probability that the firm will not be able to adjust its price in any given P period, labor demand satisfies (21), and domestic and foreign sales are determined by retailers’ demand schedules in both the home and foreign market (i.e., equation (16) and its foreign analogue, respectively). The reset price P (i) is a fixed markup over a weighted average of Pt future marginal costs: (cid:88) (1−ςp) γ W P ¯ (i) = (1−ςp)E Λ ˜ (i) s s (27) Pt t t t,s (1−ςp)γ −1αA Nα−1(i) s≥t t s s where the weights ζs−tΛ Pt [Y (i)+Y∗ (i)] Λ ˜ (i) = P t,sPs Hs Hs (28) t,s E (cid:80) ζu−tΛ Pt [Y (i)+Y∗ (i)] t u≥t P t,uPu Hu Hu take into account the probability that the contract price will remain in effect, ζs−t; households’ P relative value of money over time, Λ Pt; and firms’ future sales volumes [Y (i)+Y∗ (i)]. t,sPs Hs Hs We let the domestic producer price index P be defined in a way that mimics the consumer Pt price index in (19) (cid:20)(cid:90) (cid:21) 1 1−γ P = P (i)1−γdi , (29) Pt Pt and our Calvo-style pricing assumption then implies that domestic producer price inflation is 11

given by (cid:34) (cid:35) 1 (cid:18) P ¯ (cid:19)1−γ 1−γ P,t π = ζ +(1−ζ ) (30) P,t P P P P,t−1 Expression (30) indicates that domestic producer price inflation depends on future marginal ¯ costs through the optimal reset price P , which is identical across all firms that reset at time P,t t. Combining equations (27) and (30), one obtains the familiar New Keynesian Phillips curve linking domestic producer price inflation to current and future marginal costs. Similarly, foreign firm j sells its good in the foreign country at a price of P∗ (j) and in the Ft home country according to the PCP condition (1+τm) P (j) = t ε P∗ (j) (31) Ft (1+ςx∗)(1−τv) t Pt t t ∗ Foreign firms that are allowed to reset their price choose their contract price P (j) so that Pt (cid:88) (1−ςp∗) γ W∗ P ¯∗ (i) = (1−ςp∗)E Λ ˜∗ (i) s s (32) Pt t t t,s (1−ςp∗)γ −1αA∗N∗α−1(i) s≥t t s s 2.4 Government Policy Fiscal policy in the home country and in the foreign country is characterized by a vector of fiscal instruments s = (τm,ςx,τv,ςp,τm∗,ςx∗,τv∗,ςp∗) (33) t t t t t t t t t Weassumethatpolicyactionss ∈ S followafinite-stateMarkovchain. WeconsiderIXand t VP policies in isolation. Specifically, when considering IX, the policy regime is in one of three (cid:8) (cid:9) (cid:0) (cid:1) different states s ∈ SIX = sNT,sIX,sIX,IX . In the first state sNT , no country levies any t (cid:0) (cid:1) import tariffs or provides any export subsidy (“No Tax” state). In the second state sIX , the home country unilaterally adopts an IX policy that raises import tariffs and export subsidies (cid:0) (cid:1) by the same amount δ (i.e. τm = ςx = δ). In the third state sIX,IX , the foreign country t t retaliates in a symmetric way by raising its own tariffs and subsidies by the same amount as the home country, i.e., τm = ςx = τm∗ = ςx∗ = δ.11 Similarly, when considering VP policies, we t t t t 11Although we restrict our analysis to symmetric retaliatory actions by the foreign government, we also experimented with departures from this assumption (e.g., the foreign government retaliates by imposing only a 12

(cid:8) (cid:9) assume that s ∈ SVP = sNT,sVP,sVP,VP . t The transition probability matrix Ω can be expressed as:   1−a a 0   Ωz =  (1−π)(1−ρ) ρ π(1−ρ)  (34)     (1−φ) 0 φ where z ∈ {IX,VP} and element Ω indicates the probability of moving from state i to state i,j j. For instance, the first row of matrix ΩIX implies that the transition from the no-tax state sNT to the sIX state−where the home country implements the IX policy unilaterally−is anticipated with probability a. The second row indicates that, given an implementation of IX, the economy remains in the state sIX with probability ρ, returns to the no-tax state with probability (1−π)(1−ρ), and transitions to the retaliation state sIX,IX with probability π(1−ρ). Once the foreign country retaliates, the economy returns to a no-tax state with probability 1−φ, while, with probability φ, it remains in the trade war regime. In this specification, the foreign country does not abandon its retaliatory policies unilaterally, so a trade war can end only through a coordinated policy reversal by both countries.12 This general specification for the policy regime is helpful for considering a wide range of policy configurations and dynamics as special cases. These include unilateral changes in policies that are either permanent or expected to eventually be reversed, and also foreign retaliation. Moreover, the Markov structure can be used to study how expectations of future changes in policies affect current macroeconomic outcomes. The home government balances its budget in every period through lump-sum transfers T : t (cid:20) τm +τv(cid:21) ςx T = t t P Y +τvP Y − t P Y∗ −ςpW N . (35) t 1+τm Ft Ft t Ht Ht (1+ςx) Pt Ht t t t t t Monetary policy follows a Taylor-style interest rate rule: 1 R = (π )φπ (y˜)φy (ε )φε (36) t Pt t (cid:101)t β where φ is the weight on producer price inflation (π ), φ is the weight on the output gap π Pt y tariff). Results are available upon request. 12In our calibration the exact value of φ does not have material effects on outcomes (see the discussion in Appendix A.5). Thus, in our experiments, we set φ equal to ρ. 13

(y˜), and φ determines how policy rates respond to deviations of the nominal exchange rate t ε (cid:0) (cid:1) from an exchange rate target i.e., ε = εt .13 When φ = 0, the home interest rate responds (cid:101)t ε¯ ε exclusively to fluctuations in the output gap and domestic inflation. This specification implies that the central bank looks through changes in inflation due to the direct effects of tariffs and VATs. When φ = M, with M large, the interest rate is set so that the country pegs its ε exchange rate to a predetermined target (ε¯). 2.5 Market Clearing and Equilibrium Labor market clearing equates households’ supply of labor with aggregate firms’ demand (cid:90) N = N (i)di. (37) t t Bond market clearing requires B +B∗ = 0 (38) Ft Ft B +B∗ = 0 (39) Ht Ht Combining home and foreign households’ budget constraints and using the bond market clearing conditions, we get a balance of payments equilibrium equation, ε B −B∗ = ε B R∗ −B∗ R +NX (40) t Ft Ht t Ft−1 t−1 Ht−1 t−1 t which requires that home households increase their holdings of foreign bonds to meet the total amount of new borrowing demand from abroad, given by home net exports: P NX = Pt (Y∗ −S Y ) (41) t (1+ςx) Ht t Ft t where S denotes the terms of trade, the equation for which is t (1+ςx) P∗ S = ε t Pt. (42) t t (1+ςx∗)P t Pt Let the initial condition for home holdings of bonds and individual producer prices in the 13Since Gali and Monacelli (2005b), the targeting of domestic producer price inflation in open-economy New Keynesian models has become standard practice. See also Gal´ı and Monacelli (2016). The output gap in the Taylor rule is constructed as output relative to the level of output that would prevail in the absence of price rigidity. For a discussion of interest rate rules that maintain a fixed exchange rate, see Benigno et al. (2007). 14

home and foreign market be (cid:2) (cid:3) x = B R∗ ,B∗ R ,P (i),P∗ (i) 0 F−1 −1 H−1 −1 H−1 F−1 Definition. Given an initial state x and a stochastic process for fiscal policy {s }, an equi- 0 t librium consists of (i) an allocation at home, Ξ = {C ,B ,N ,Y ,Y ,Y (i),Y (i)} , and t F t Ht Ft Ht Ft t≥0 abroad Ξ∗;(ii)firm-level prices and production decisions at home, Φ = (cid:8) P ¯ (i),N (i),P (i), Pt t Ht (cid:8) (cid:9) P∗ (i)} ,and abroad Φ∗; (iii)aggregate prices at home, Γ = P ,P ,P ,P ,πP,W ,R Ht t≥0 t Ht Ft Pt t t t t≥0 and abroad Γ∗; and (iv) (domestic) bond holdings, net exports, currency exchange rates and terms of trade {B ,B∗ ,NX ,ε ,S } such that Ht Ft t t t 1. The allocation Ξ satisfies households’ and retail firms’ optimality conditions (4) − (6) and (14)−(17) as well as the analogous conditions in the foreign country; 2. Individual producer prices and production decisions Φ maximize firm profits, i.e., they satisfy conditions (21),(23),(24), and (27) as well as the analogous conditions in the foreign country; (cid:8) (cid:9) 3. Prices Γ clear all markets. That is, price indexes, P ,P ,P ,P ,πP , satisfy t Ht Ft Pt t t≥0 (18)−(20), (29)−(30); wages clear the labor market, i.e., (37) is satisfied; and nominal interest rates are determined according to (36). Analogous conditions pin down Γ∗. 4. The bond market clears, i.e., equations (38)−(42) are satisfied. 3 Trade and Fiscal Policies: A Theoretical Analysis Inthis section, wediscuss thekeydifferencesin transmissionofIX andVPpolicies. Tothisend, wefirstsummarizeconditionsunderwhichbothIXandVPareequivalentandhavenoallocative effects under flexible exchange rates, and we highlight the key role of the real exchange rate as an adjustment mechanism. We show that under such extreme conditions, these two policies look only beguilingly similar, as the forces driving the adjustment in the real exchange rate are fundamentally different. We then present the main result of this section: Under fixed exchange rates, IX policies implement a currency devaluation and provide macroeconomic stimulus, whereas VP policies 15

remain neutral. As these findings appear in contrast with conventional wisdom (such as, for instance, FGI), we conclude this section with a discussion of the key assumption about tax pass-through. 3.1 Neutrality Under Flexible Exchange Rates Proposition 1. In an economy with flexible exchange rates (φ = 0), both a unilateral IX ε policy of size δ and a unilateral VP policy of size δ cause a δ−percent appreciation of the 1+δ real exchange rate and have no allocative effect if 1. The policy is permanent and unanticipated, and there is no probability of retaliation (a = π = 0, and ρ = 1); 2. Foreign holdings of home-currency-denominated bonds are always zero (χ∗ = ∞); 3. Export prices are set in the producer’s currency (PCP), or prices are flexible. The result of IX neutrality contained in Proposition 1 extends Lerner’s Symmetry Theorem (Lerner (1936)) to our dynamic monetary framework.14 Similarly, neutrality of VP has been discussed in the literature within static models of international trade.15 The greater relevance of this result for our purposes is that it provides a theoretical benchmark to illustrate the different general equilibrium adjustments that deliver equivalence and neutrality in response to the two policies. This discussion will provide most of the intuition of how the relaxation of conditions 1−3 of Proposition 1 affects transmission of IX and VP. We include the formal proof of proposition 1 in Appendix B.16 As stated in the proposition, in response to both unilateral IX and VP, the real exchange rate appreciates permanently by an amount equal to the size of the policy. That is, the relative 14ForotherworkonLerner’ssymmetryresult,see,forinstance,McKinnon(1966)and,morerecently,Costinot and Werning (2017). Eichengreen (1981) provides an intuitive discussion of the conditions needed to achieve neutralityinaframeworksimilartoours. Lerner’sSymmetryTheoremisalsoarelevantresultfortheneutrality of border tax adjustments, as in Meade (1974), Grossman (1980), Auerbach et al. (2017),Erceg et al. (2018), Lind´e and Pescatori (2019), and Barbiero et al. (2019). 15See, for instance, Auerbach et al. (2017). 16While we do not prove that these conditions are necessary, we illustrate in Section 4 and in the Appendix that they are tight in the sense that relaxing any one of them breaks the neutrality of IX. 16

price of the foreign consumption bundle in terms of the domestic consumption bundle P∗ P∗ Q = ε t = ε (1−τv) pt (43) t t P t t P t pt declines permanently by δ, where δ is the size of the policy.17 In the case of IX, this real exchange rate adjustment happens through a jump in the nominal exchange rate (ε ). In the t case of VP, however, the adjustment is mechanically induced by the VAT increase which raises home consumer prices. Hence, VP does not require any change in the value of the currency. To illustrate why this is the case, it is useful to collect the key equilibrium conditions into two blocks. The first block collects the conditions that regulate trade among countries and its intermediation through foreign bonds: Y (cid:20) P∗ (cid:21)−θ Ft = (1+τm)ε Pt (44) Y t t P Ht Pt Y∗ (cid:20) 1 P (cid:21)−θ Ht = Pt (45) Y∗ (1+ςx)ε P∗ Ft t t Pt B∗ B∗ P (cid:20) P∗ (cid:21) B − Ht = B R∗ − Ht−1R + Pt Y∗ −(1+ςx)ε PtY (46) Ft ε Ft−1 t−1 ε t−1 (1+ςx)ε Ht t t P Ft t t t t Pt ε = R∗E     Λ ε P Pt 1−τ t v +1   ω +(1−ω) (cid:104) (1+τ t m)ε tP P P P ∗ t t (cid:105)1−θ   1− 1 θ     (47) t t t   t,t+1 t+1 P Pt+1 1−τ t v  ω +(1−ω) (cid:104) (cid:0) 1+τm (cid:1) ε P P ∗ t+1 (cid:105)1−θ    t+1 t+1PPt+1  Equations (44) and (45) determine the relative demand for domestic and foreign varieties in the home and foreign country.18 Equations (46) and (47) determine equilibrium in the foreigncurrency-denominated bond market. Equation (46) equates home demand for new foreigncurrency bonds with foreign supply as determined by the level of foreign trade deficits. Demand for foreign-currency bonds in the home country is determined by equation (47). Equations (44) and (45) show that, for a given level of the exchange rate, import tariffs and export subsidies shift demand away from foreign goods and toward domestically produced goods, both in the home country and in the foreign country. However, the relative prices of 17All equations reported in this section abstract from foreign instruments for ease of exposition, given that undercondition1inProposition1and2(below)foreigngovernmentsdonotretaliatetothepoliciesconsidered. 18Equation (44) can be derived from the demand schedules in (14) and (15), and the PCP conditions (25) and (31). Analogous derivations for the foreign economy yield 45. 17

importedtodomesticgoodsintheright-handsidesofequations(44)and(45)remainunchanged if a δ-percent increase in both import tariffs and export subsidies causes an exchange rate appreciation of the same exact size. In other words, under PCP, the exchange rate appreciation lowers the cost of imports in the home country just enough to offset the increase in tariffs and lowers the revenues from sales of domestic varieties in the foreign country by as much as the higher export subsidy. Equation (44) also shows why the assumption of PCP is important in delivering the result as it ensures that foreign exporters’ prices, ε P∗ , immediately reflect t Pt exchange rate fluctuations. If foreign exporters were unable to do so−such as under local currency pricing−this neutrality result would immediately break.19 Moreover, as shown in equation (46), the currency appreciation offsets the effect of export subsidies on net exports and leaves the balance of payments unaffected, as, under condition 2 of Proposition 1, all trade is intermediated in foreign-currency-denominated bonds (i.e., B∗ = 0 for all s).20 Finally, Hs equation (47) shows that as long as the IX policy change is permanent, demand for foreign currency bonds is unaffected. Section 4 discusses in detail how departures from condition 1 of Proposition 1 affect the transmission of IX by implying that the exchange rate offset to the policy change is only partial. Regarding VP, equations (44) - (46) make clear that this policy has no direct effect on relative demand for home and foreign varieties and, hence, on net exports. This observation is a consequence of the fact that VAT changes affect equally the price of imported and domesticallyproduced goods.21 In addition, as long as it is permanent, VP does not affect home savings demand and, thus, also leaves (47) unaffected. Consequently, under VP, no general equilibrium adjustment of the nominal exchange rate is required to insulate international relative prices from the effects of the policy. The second block of equations collects the conditions determining equilibrium in the domestic labor market and aggregate demand: (cid:40) (cid:41) 1 (cid:20) P∗ (cid:21)1−θ 1−θ W (1−τv) = ω +(1−ω) (1+τm)ε Pt P CσNη (48) t t t t P Pt t t Pt 19We discuss alternative pricing assumptions in more detail in the Appendix. 20Section A.80 in the Appendix discusses the case in which foreign households can hold home currency denominated bonds. 21See Feldstein and Krugman (1990) for a similar argument. 18

(cid:88) (1−ςp) γ W P ¯ (i) = (1−ςp)E Λ ˜ (i) s s (49) Pt t t t,s (1−ςp)γ −1αA Nα−1(i) s≥t t s s βE     C t σ R t 1−τ t v +1   ω +(1−ω) (cid:104) (1+τ t m)ε tP P P P ∗ t t (cid:105)1−θ   1− 1 θ     = 1 (50) t   C t σ +1 π pt+1 1−τ t v  ω +(1−ω) (cid:104) (cid:0) 1+τm (cid:1) ε P P ∗ t+1 (cid:105)1−θ    t+1 t+1PPt+1  IX enters (48) and (50) only through its effect on import prices, which, as explained earlier, is perfectly offset by the currency appreciation. The transmission of VP, instead, works through its direct effects on the equilibrium in the labor market. Equations (48) and (49) show that the increase in the payroll subsidy and the VAT hike have offsetting effects on labor demand and labor supply. Under our assumption of full pass-through of taxes, at fixed producer prices, a VAT hike induces consumer prices (P ) to jump by δ percent (see equation (23)). In order for the households’ labor supply to t remain unchanged, equation (48) requires an adjustment in the nominal wage of the same exact percentage of the VAT hike. In addition, as evident from the optimal pricing decision of producers(49),thecommensurateincreaseinpayrollsubsidies(ςp)ensuresthatfirmsarewilling t topaythishigherwage, sothatlabordemandisalsounaffected. Equation(49)alsoimpliesthat a VP policy that is expected to be eventually reversed would have direct effects on aggregate supply, breaking the neutrality result. The importance of assumption 1 in Proposition 1 for the neutrality of VP can also be seen by inspection of the intertemporal optimality conditions for households consumption. In particular, the intertemporal substitution effects induced by expectations about the future declines in the VAT, as implied by equation 50, turn out to have large quantitative effects on the economic response to VP. We will discuss this channel in detail in section 4.1 and assess its quantitative relevance in our empirical experiment of Section 5.4. 3.2 Fiscal Devaluations Revisited We now turn to study the effects of IX and VP policies under the assumption that exchange rates are fixed by the monetary policy of the home economy. Proposition 2. In a fixed exchange rate regime (φ = ∞), under assumptions 1.- 3. of ε Proposition 1, an IX policy of size δ has the same allocative effects as a once-and-for-all unexpected currency devaluation of size δ. A VP policy of the same size δ has no effect on 1+δ 19

the allocation but causes the real exchange rate to appreciate by δ.22 After our earlier discussion about how neutrality is achieved by IX and VP, this result should come as no surprise. Given that when the currency exchange rate is free to move the effects of an IX policy are perfectly offset by a nominal appreciation, it follows that, absent an exchange rate response, IX elicits economic effects identical to a currency depreciation. In contrast, as VP neutrality does not require any adjustment in the currency exchange rate, the fixed exchange rate regime does not pose any constraint to achieving the same outcome as under flexible exchange rates. VP remains neutral under fixed exchange rates. The neutrality of VP under fixed exchange rates is in contrast with recent results in the fiscal devaluation literature, such as FGI. The key difference between the two frameworks is the assumption about how VAT changes are passed through to consumer prices in the presence of nominalrigidities. Ouranalysisassumesthatpre-taxpricesarestickyandtaxesarefullypassed through. Specifically, we assume that absent a price adjustment by the firm, producer prices P remain unchanged and consumer prices P = PPt jump in response to a VAT increase. Pt Ht (1−τv) t In the fiscal devaluation literature, instead, prices are typically assumed to be sticky inclusive of taxes (and hence pre-tax prices are free to adjust). That is, firms control directly consumer prices P and, absent price adjustment by the firm, VAT increases are absorbed through a H,t reduction in firms’ margins, i.e., producer prices decline P = P (1 − τv). To understand pt Ht t how this assumption would affect transmission of VP through the margin determining relative demand for domestic and foreign varieties, we rewrite (44) and (45) using consumer prices rather than producer prices: Y (cid:20) (1+τm)ε P∗ (cid:21)−θ Ft = t t Pt (51) Y (1−τv) P Ht t Ht Y∗ (cid:20) (1−τv) P (cid:21)−θ Ht = t Ht (52) Y∗ (1+ςx)ε P∗ Ft t t Pt Notice that, by virtue of (23), equations (51) and (52) are equivalent to (44) and (45). Equations (51) and (52), however, make clear that if the adjustment in consumer prices, P , Ht is sluggish in response to a VAT increase, then the VAT policy itself gives domestic firms a competitive boost and acts exactly as the IX policy. Under our assumption that firms’ prices 22Condition 3 of Proposition 1 also includes the possibility that prices are flexible. In this case all three policies are equivalent and neutral. We thank an anonymous referee for pointing this out. 20

P are slow to adjust, in contrast, this competitiveness-enhancing effect of VATs disappears, Pt as evident from (44) and (45). 4 Macroeconomic Effects of IX and VP Policies In this section, we provide a broader characterization of the macroeconomic effects of IX and VP policies and their different transmission mechanisms. To this end, we focus on two departures from the limiting case considered in Section 3 that appear to be the most relevant both qualitatively and quantitatively.23 Specifically, we first study the role of agents’ beliefs about the persistence of tax changes and the risk of retaliation by the foreign economy. We show that, when IX policies are expected to be reversed (or trigger symmetric retaliatory policies abroad), they exert sizable expansionary effects even under flexible exchange rates. In contrast, when VP policies are expected to be eventually reversed, intertemporal substitution effects tend to make them contractionary, especially if monetary policy is constrained as in a currency union. We then turn to the role of wage rigidity in affecting transmission of the two policies. While transmission of IX is affected only quantitatively by the presence of wage rigidities, VP policies haveabetterchanceprovidingmacroeconomicstimuluswhenwagesadjustsluggishlyaspayroll subsidies boost aggregate supply. In our discussion, we calibrate the model with fairly standard values used in the literature, which are reported in the top panel of Table 1.24 4.1 IX and VP Policies: The Role of Reversal The neutrality of IX policies in our dynamic framework requires that the real exchange rate jumps to a new long-run value, reflecting the public’s belief that trade actions will remain in place forever. However, historical experience suggests that trade policy actions are often reversed or spur retaliation. These reversals may occur because the trade policies are implemented as cyclical measures to boost the economy or as a negotiating tool in foreign policy.25 23The Appendix contains a full treatment of deviations from the remaining conditions. 24See, for instance, Gali and Monacelli (2005a) 25 In this vein, Irwin (2017) discusses how President Nixon favored the imposition of a 10 percent across-theboard tariff in 1971 partly to enhance his prospects in the 1972 election, as well as to put pressure on foreign trading partners to revalue their exchange rates. As it turned out, the tariffs were lifted fairly quickly when the foreign policy objectives were viewed as largely achieved, as well as from pressure coming even from some 21

Table 1: Baseline Model Calibration Parameter Value Discount factor β 0.99 Risk aversion σ 1.00 Frisch elasticity of labor supply η−1 1.00 Labor share α 0.64 Good variety elasticity γ 11.0 Price stickiness ζ 0.85 P Trade elasticity θ 1.25 Import share 1−ω 0.15 H Output gap weight in the Taylor rule φ 0.125 y Inflation weight in the Taylor rule φ 1.50 π Alternatively, they may result from an electoral shift toward a political party more supportive of free trade.26 Moreover, although some trade policy legislation has been enacted with the expectation that it would remain in effect for a long time, the tariff wars that ensued during the 1930s or, more recently, between the United States and China, serve to underscore the high likelihood of foreign retaliation under such circumstances. Given these considerations, we next apply our benchmark model to study the effects of IX policies that have no long-run effect on the real exchange rate. Through the lens of our Markov structure, the effects on the exchange rate may prove temporary because the policy action is reversed or, alternatively, because the home country’s implementation of IX policies prompts the foreign government to retaliate by adopting similar policies. As the implications of either type of policy turn out to be nearly identical, for expositional simplicity, we focus here on the case in which a unilateral IX policy is expected to be reversed (1−ρ > 0, π = 0). In our benchmark framework, a unilateral IX policy of size δ that is expected to be reversed withprobability1−ρ > 0exertsallocativeeffectsbyboostingrealnetexports, astheassociated members of the Administration. 26For example, in the U.S. experience, President Wilson, a free-trade Democrat, strongly supported the passage of the Underwood Tariff Act of 1913 which scaled back the high tariffs that had prevailed under previous Republican Administrations (see Irwin (2017)). 22

exchange rate appreciation only partially insulates international relative prices. To understand this result, it is helpful to recognize that for the allocation to remain unchanged, the exchange rate would have to appreciate by δ for as long as the policy remained in effect (by equations (44) and (45) ). This exchange rate movement would completely offset the effects of IX on relative prices and leave the relative demand for imported and domestic varieties unaffected. However, the expectation that the IX policy will eventually be reversed implies that the home exchange rate depreciates in the future which in effect increases the return to holding foreign bonds (that is, ε R rises), as seen from equation t+1 t (cid:26) Cσ P (cid:27) ε = βE t t ε R∗. (53) t t Cσ P t+1 t t+1 t+1 This increase in the return to holding foreign bonds dampens the initial appreciation of the home exchange rate – so that it is less than δ – and hence the IX policy leads to some expansion of net exports.27,28 The solid lines in Figure 1 show the expected paths of key variables after the home country adopts a unilateral IX policy in our benchmark model with sticky prices. The IX policy consists of a 10 percentage point increase in import tariffs and export subsidies that is expected to be reversed with probability (1−ρ) = 0.05 by the following quarter. The policy causes a small appreciation of the exchange rate that does not fully insulate relative prices, and, as a consequence, imports fall and exports rise. Monetary policy reacts to the stronger external demand by raising interest rates, which reduces home consumption and contributes to the appreciation of the real exchange rate, thus dampening some of the stimulus to net exports. Because the stimulus to domestic output occurs through expenditure-switching channels, it has negative spillovers to the foreign economy so that both foreign output and inflation decline (not shown). IX policies operate not only through trade channels, but also through intertemporal channels. As seen in equation (50), an increase in import tariffs that is expected to be reversed raises the relative price of current consumption, as imported goods are expected to be cheaper 27Theuseofappropriatelytargetedcapitalcontrols,i.e. designedsothatequation(53)holdswithoutrequiring an adjustment in the interest rate, would restore neutrality. We thank our discussant Emmanuel Farhi for this insight. 28Notably, this argument does not rely on nominal rigidities. In fact, transitory IX policies are non-neutral both under flexible prices and under sticky prices, although specific assumptions about the form of nominal rigidities and the monetary policy rule affect the transmission of the boost to net exports to the rest of the economy. 23

Figure 1: Macroeconomic Effects of IX with Expected Reversal Real Exchange Rate Nominal Exchange Rate Net Exports Nominal Wage 10 10 4 10 S 8 8 S3 8 S S m 6 S S m 6 m o rf 2 S S m 6 o rf 4 o rf 4 P D o rf 4 % 2 % 2 G fo tc p0 1 % 2 0 0 0 -1 0 10 20 0 10 20 0 10 20 0 10 20 Home Inflation Home Policy Rate Home Consumption Home Output 3 1 1 4 2.5 0.5 )q 4 ( S S m o tc r p f 0 1 . . 0 1 2 5 5 .r.a S S m o tc r p f - 0 0 . . 0 5 5 S S m o % rf -0 - . 0 1 5 S S m o % rf 0 1 2 3 -1.5 -0.5 -1 -1 -2 -1 0 10 20 0 10 20 0 10 20 0 10 20 IX Tariff Only In both experiments we assume that prices are sticky, wages are flexible, and the exchange rate is flexible. The figure shows the expected path of each variable after the policy is implemented and given that it is expected to be permanently abandoned with probability 0.05 as long as it is in place. in the future. These dynamic effects of tariffs not only differ markedly from the effects of export subsidies−which affect the real interest rate only through the strength of the monetary policy response−but also are quantitatively important in pushing down consumption. Figure 1 also shows the effects of imprt tariffs alone (the dashed lines). An increase in import tariffs has essentially no effect on output under our baseline calibration (σ = 1;θ = 1.25), so that all of the output stimulus from IX policies comes from the increase in export subsidies (i.e., the distance between the solid and dashed lines). The quasi-invariance of output to the tariff increase reflects that the expenditure-switching effect, which pushes up the desired share of consumption spent on home goods, is offset by the intertemporal-substitution effect, which pushes down overall consumption. Stepping beyond our specific calibration, we find that the 24

Real Exchange Rate Nominal Exchange Rate Net Exports Nominal Wage 10 10 4 10 S 8 8 S3 8 S S m 6 S S m 6 m o rf 2 S S m 6 o rf 4 o rf 4 P D o rf 4 % 2 % 2 G fo tc p0 1 % 2 0 0 0 -1 0 10 20 0 10 20 0 10 20 0 10 20 Home Inflation Home Policy Rate Home Consumption Home Output 3 1 1 4 2.5 0.5 )q 4 ( S S m o tc r p f 0 1 . . 0 1 2 5 5 .r.a S S m o tc r p f - 0 0 . . 0 5 5 S S m o % rf -0 - . 0 1 5 S S m o % rf 0 1 2 3 -1.5 -0.5 -1 -1 -2 -1 0 10 20 0 10 20 0 10 20 0 10 20 Temporary IX Fixed Temporary IX Flex Figure 2: Macroeconomic Effects of IX with Expected Reversal Fixed vs. Flex Exchange Rate Regime In both experiments we assume that prices are sticky and wages are flexible. The solid line shows the case in which the home country pegs to the foreign country which follows a standard Taylor rule. The dashed line is the case in which the exchange rate is flexible. The figure shows the expected path of each variable after the policy is implemented and given that it is expected to be permanently abandoned with probability 0.05 as long as it is in place. output effects of higher import tariffs depend on the relative strength of these two effects. If the intertemporal elasticity of substitution is low relative to the trade price elasticity, higher tariffs would tend to boost output (as the expenditure-switching effect dominates), whereas higher tariffs would reduce output if the intertemporal elasticity is high relative to the trade elasticity. Even so, under standard calibrations for these parameters, a combination of import tariffs and export subsidies that is expected to be reversed increases output in the near term. The magnitude of the stimulus from temporary IX policies depends on the response of monetary policy as well. For instance, a larger interest rate response to producer price inflation (higher φ in the policy rule) and, consequently, to the external demand stimulus would imply π 25

smaller output effects. By contrast, when monetary policy gives high weight to stabilization of the exchange rate (high φ in the policy rule), the output stimulus is larger, with a fixed ε exchange rate regime an interesting limiting case. In this spirit, Figure 2 shows how the IX policies play out in our baseline model, in which the home exchange rate is fixed to that of the foreign economy (solid lines). Home output rises significantly more in this case than under flexible exchange rates. This larger output expansion largely reflects that consumption expands robustly−rather than contracts−as the home policy rate declines in lockstep with the foreign policy rate. The rise in output is also reinforced by a larger increase in exports. We next turn to the effects of VP policies that are expected to be reversed. As evident from equation (50), temporary VP policies have strong intertemporal substitution effects on consumption, muchmoresothantemporaryIXpolicies. WhileIXpoliciesgeneratedeflationary pressure only through higher prices of imported goods, VP policies induce direct deflationary pressure on the entire consumption bundle. Thecontractionaryeffectofthisintertemporalsubstitutionchannelturnsouttobethemost relevant quantitative force driving the macroeconomic effects of temporary VP policies. Figure 3 shows the effects of VP policies of size δ = 10 percent that are reversed with probability (1−ρ) = 0.05 by the following quarter. The red solid line shows the case in which exchange rates are flexible, while the red dashed line shows the case in which exchange rates are fixed. In bothcasestheimmediateincreaseinconsumerpricescausestherealexchangeratetoappreciate substantially. The higher real interest rate under VP depresses aggregate demand markedly, causingacontractioninoutput. Whenexchangeratesareflexible,thecentralbanklowerspolicy rates in response to depressed economic activity, which limits the decline in consumption and causes the nominal exchange rate to depreciate, boosting net exports. The output decline is noticeably larger under fixed exchange rates given that the central bank can’t lower interest rates to provide needed stimulus. While the contractionary effects of a temporary VP contrast sharply with the expansion of output under a temporary IX, the two policies have similar effects on trade quantities. This outcome, however, reflects very different channels. The IX policy has direct ”competitiveness- enhancing” effects on relative trade prices that raise exports and cause imports to contract. This stimulus is only partially counterbalanced by a tightening of policy rates and an appreciation of the home currency. In contrast, the stimulus to net exports from the VP policy is mainly due to a decline in import demand amidst a contraction of domestic 26

Real Exchange Rate Nominal Exchange Rate Net Exports Nominal Wage 10 10 4 10 8 S S 2 S S m 6 S S m 5 m o rf 0 S S m 5 o rf 4 o rf 0 P D -2 o rf 0 % 2 % -5 G fo tc -4 % -5 p -6 0 -10 -8 -10 0 10 20 0 10 20 0 10 20 0 10 20 Home Inflation Home Policy Rate Home Consumption Home Output 1 2 4 14 0.5 12 0 2 )q 4 ( S S m o tc r p f 10 0 2 4 6 8 .r.a S S m o tc r p f - - 1 0 - - . . 0 2 1 5 5 S S m o % rf - - - 6 4 2 S S m o % rf - - 0 4 2 -8 -6 -2 -2.5 -4 -3 -10 -8 0 10 20 0 10 20 0 10 20 0 10 20 Temporary VP Fixed Temporary VP Flex Figure 3: Macroeconomic Effects of VP with Expected Reversal Fixed vs. Flex Exchange Rate Regime In both experiments we assume that prices are sticky and wages are flexible. The solid line shows the case in which the home country pegs to the foreign country which follows a standard Taylor rule. The dashed line is the case in which the exchange rate is flexible. The figure shows the expected path of each variable after the policy is implemented and given that it is expected to be permanently abandoned with probability 0.05 as long as it is in place. consumption (amplified by exchange rate depreciation in the case of flexible exchange rates). Taken together, our results underscore how the different transmissions of VP and IX imply that, once the restrictive conditions in Proposition 1 are relaxed, these policies will, in general, have very different macroeconomic effects. In particular, given the importance of intertemporal substitution channels in shaping the macroeconomic effects of a temporary VP, such a policy runs the risk of providing a contractionary impetus to output, especially if the policy interest rate and exchange rates cannot adjust much. One important caveat to this claim is that VP can in principle boost output if wages are sticky – a case to which we next turn. 27

Real Exchange Rate Nominal Exchange Rate Net Exports Nominal Wage 10 10 25 14 8 12 S S 8 20 S S m 6 S S m 10 8 m o rf 6 S S m 15 o % rf 2 4 o % rf 2 4 6 P D G fo tc 2 4 o % rf 10 5 p 0 0 0 0 -2 0 10 20 0 10 20 0 10 20 0 10 20 Home Inflation Home Policy Rate Home Consumption Home Output 10 1 10 10 )q 4 ( S S m o tc r p f 0 2 4 6 8 .r.a S S m o tc r p f - 0 0 . . 0 5 5 S S m o % rf 2 4 6 8 S S m o % rf 2 4 6 8 -2 0 0 -4 -1 -2 0 10 20 0 10 20 0 10 20 0 10 20 VP IX Figure 4: Permanent IX and VP with Sticky Wages and Fixed Exchange Rates In both experiments we assume that prices and wages are sticky, and the exchange rate is flexible. The solid line shows the response to VP and the dashed line the response to IX. In both cases the policies are (expected to be) permanent. 4.2 IX and VP Policies: The Role of Wage Rigidity A large macroeconomic literature assumes that households set nominal wages in Calvo-style staggered contracts that are similar in form to the price contracts outlined in Section 2.29 In addition, the appeal of competitiveness-enhancing payroll tax cuts financed with VAT increases appears greater when rigid wages prevent strong offsetting general equilibrium responses.30 Figure 4 shows the response of the economy to unexpected and permanent VP (solid red lines) andIX(dashedbluelines)policiesunderfixedexchangeratesandstickywages.31 TheIXpolicy 29See, for instance, Erceg et al. (2000). 30For instance, the quantitative analysis in FGI suggests that an appropriately calibrated VP policy would have allowed the Spanish economy to suffer almost no employment and output losses in 2008-09, largely by correcting the macroeconomic instability introduced by rigid wages. 31We choose the parameter controlling the degree of wage stickiness to imply that wages are adjusted with the same frequency as prices. 28

implementsthesameallocationasaonceandforall10-percentcurrencydevaluation. Thedirect stimulative effects of net exports are greatly amplified by an accomodative monetary policy response, which, under a peg, mimics the declines in interest rate implemented by the foreign economy. The resulting increase in domestic demand causes output to increase substantially. The permanent VP policy provides modest stimulus through the competitive enhancing effects of payroll subsidies. With sticky wage adjustment, the employer payroll subsidy persistently reduces producers’ marginal costs. As supply slowly expands in response to the enhanced competitiveness, output and consumption rise, and exports expand. However, the rise in domestic demand is only modest and the boost to net exports is muted by a large real exchange rate appreciation. And, critically, the stimulus from VP hinges on the policy change being perceived as permanent or at least very highly persistent. Intertemporal substitution effects dominate if agents see a material chance of reversal, and VP causes output to contract. 5 A Quantitative Assessment of Fiscal Devaluations Inthissection, weconsiderthe2007fiscalpolicyreforminGermanyasalaboratorytostudythe extent to which VP and IX policies can, quantitatively, provide as much stimulus as a currency devaluation. We use a medium-scale version of our baseline model to study whether this fiscal reform can account for the economic underperformance of Germany in 2007. We estimate the degree of pass through of VAT changes and the perceived persistence of the policy change so that they minimize the distance between the German data on output and inflation and the corresponding model simulated series. We then perform a counterfactual experiment under the estimated parameters to determine whether IX could have been a more effective substitute for a currency devaluation. 5.1 Data In 2006, the German government announced its intentions to increase fiscal revenues through a VAT hike and boost competitiveness by cutting payroll taxes. The details of these tax shifts were finalized over the course of 2006 and went into effect starting January 2007. Figure 5 presents the evolution of key macroeconomic variables in Germany and other euro- 29

areaeconomiesintheyears2006and2007. InJanuary2007, thestandardVATrateinGermany increased from 16 percent to 19 percent.32 The increase in the VAT rate affected about half of the bundle of goods included in the consumer price index, resulting in an average VAT increase ofabout1.4percent.33 Atthesametime, payrolltaxesdeclinedmorethan1percent(blacklines inthefirstandsecondpanels). Notably,VATandpayrolltaxesremainedstableintherestofthe euro area (dashed red lines). Hence, the 2007 VP reform in Germany can be viewed as broadly akin to a fiscal devaluation by a currency union member. In what follows we use the time series evidence in Figure 5 as a direct measure of the effects of VAT and payroll tax changes on the German economy. That is, we attribute the difference between the performance of the German economy and other euro-area economies over the 2006Q1-2007Q4 period to the implementation of this fiscal reform. Two considerations support this assumption. First, the historical narrative indicates that these tax changes were the most important economic development in Germany during this period.34 Second, the stable performance of the remaining euro-area economies over this period seems to be inconsistent with the hypothesis that a common macroeconomic shock had disproportionately larger effects in Germany than in other countries.35 The German VP failed to elicit the boost in economic activity typically associated with a currency devaluation. As shown in Figure 5, the implementation of this VP policy produced two main effects on the German economy. First, consumer prices increased markedly in the first quarter of 2007, when the VAT rate increase went into effect. Second, barring some 32ThereducedVATrateremainedunchangedat7percent. Anumberofservices,includingthosefornon-profit organizations and services provided directly by the government, are exempt from the VAT. 33We are implicitly assuming that the goods affected by and those excluded from the tax increases feature very limited substitutability, at least in the short run, and similar aggregate demand and supply schedules. A richer multisector model with empirically realistic assumptions on the industry level elasticities of substitution, demand, and supply, would be needed to gauge the quantitative plausibility of this assumption. That said, the sizeable observed effects of the policy on economic activity suggest that substitutability between affected and excluded categories was indeed limited. 34See, for instance, Bundesbank (2007) and D’Acunto et al. (2016). During 2007 government expenditure in Germany grew less than in the rest of Europe. However the difference was small and cannot plausibly account for the observed behavior of German aggregate demand. We discuss this in the Appendix. 35Our focus on a narrow time window around the implementation of the VP policy minimizes the possible confounding effects of reforms that had happened in Germany in early 2000s. Notably, between 2003 and 2005, the German government implemented a series of labor market reforms, the Hartz reforms, which addressed structural weaknesses in the German labor market. Existing studies suggest that most of the effects of the Hartz reforms materialized before the end of 2006. See for instance Krause and Uhlig (2012). Moreover, these typesofreformstendtohavestimulativeeffectsoneconomicactivity,sotheywouldnotgointhesamedirection oftheeffectofVPimpliedbyourapproachandpredictedbyourmodel. SeeagainKrauseandUhlig(2012)for a model based argument and, for instance, Chodorow-Reich et al. (2019) and references therein for empirical studies that find stimulative effects associated with reductions in unemployment benefits. 30

Germany EA ex-Germany VAT Standard Tax Rates Payroll Taxes HICP Inflation 20 50 2.5 19 48 2 18 46 1.5 17 44 1 16 42 0.5 15 40 0 GDP Consumption Investment 4 4 5 2 2 0 0 0 -5 -2 -2 -10 Hours Net Exports to EA Labor Cost Inflation 4 5.5 4 2 5 3 2 4.5 0 1 4 -2 0 3.5 Q1Q2Q3Q4Q1Q2Q3Q4 Q1Q2Q3Q4Q1Q2Q3Q4 Q1Q2Q3Q4Q1Q2Q3Q4 2006 2006 2006 2006 2007 2007 2007 2007 2006 2006 2006 2006 2007 2007 2007 2007 2006 2006 2006 2006 2007 2007 2007 2007 Figure 5: 2007 German VP: Data Macroeconomic data for Germany and the euro area (EA) are from Haver (EU Database). See Appendix for details. Consumption, investment and GDP are normalized to equal one in 2006Q3. To be consistent with our model we show net exports from Germany to the other EA countries. Accordingly, GDP excludes trade with the rest of the world both for Germany and for EA ex-Germany. pulling forward of aggregate demand in anticipation of the VAT hike, economic activity in Germany underperformed relative to its euro-area counterparts. In 2007, consumption growth in Germany was negative, investment was weak, and, despite a boost to net exports, GDP growth remained significantly below that in the euro area.36,37 36The Eurostat measure of consumption for European economies includes non-durable goods, durable goods, and services. Much of the initial increase and subsequent decline in German consumption is due to changes in durable goods, such as motor vehicle purchases, for which there is evidence of nearly full pass-through of the VAT increase. See Erceg et al. (2018) and D’Acunto et al. (2016) for further discussion. 37See the Appendix for a detailed description of how the data is constructed. 31

5.2 The Extended Model We next extend our baseline model along several dimensions to study the observed economic effects of the 2007 German VP policy within the euro area. First, we model the monetary policy framework of the European Central Bank (ECB) via an inertial Taylor rule that responds to an average measure of consumer price inflation and the output gap within the currency union, with the home country representing Germany (H) and the foreign country representing an aggregate of all other euro-area economies (F). Monetary policy is described by the rule (cid:18) REA(cid:19) (cid:18) REA(cid:19)ρR t = t−1 (cid:0) πsπ∗1−s (cid:1)φπ (cid:0) y˜s,y˜∗1−s (cid:1)φy (54) R ¯ R ¯ t t t t where (REA) is the euro-area policy rate, ρ is the interest-smoothing parameter, and s denotes t R the normalized size of the home country (Germany).38 Second, we introduce capital as an additional input in the production function and allow households to optimally adjust its utilization Y = u KαL1−α (55) t t t t where u is capital utilization, K is the physical capital stock, and L is the aggregate labor t t t input consisting of differentiated labor services supplied by households. There are convex costs of varying capital utilization from its steady state level of unity which are given by rk (exp(σ (u −1))−1), (56) u t σ u where rk is the steady state rental rate of capital, and σ measures the inverse elasticity of u utilization to variation in the rental rate of capital.39 We also assume that capital accumulation is subject to adjustment costs. The law of motion of capital is: κ (cid:20) K −(1−δ )K (cid:21)2 t+1 K t I = K −(1−δ )K + −1 K (57) t t+1 K t t 2 δ K K t where I is investment in final goods, δ is the depreciation rate, and κ is the parameter t K 38Notethatinequation(54),thepolicyraterespondstoconsumerpriceinflationintheeuroarea,ratherthan domestic goods inflation π , and hence reacts to VAT changes. Even so, our quantitative results are robust to P,t choosing an alternative specification for monetary policy which sees through VAT changes as in equation (36). 39This specification follows Christiano et al. (2005). See the Appendix for details. 32

governing the curvature of the cost of adjusting capital. Third, given the large body of evidence in support of wage rigidity and its importance for the macroeconomic effects of VP policies, we depart from the baseline assumption of flexible wages and consider sticky wages. As in Erceg et al. (2000), we assume that monopolistically competitive households supply labor services that are considered imperfect substitutes by the production sector. Taking labor demand as given, households set nominal wages in staggered contracts that are analogous to the price contracts described for producers. These assumptions yield the conditions (cid:88) γ n (i)η W ¯ = E Λ ˜W (i) W s (58) t t t,s γ −1 C−σ s≥t W s (cid:34) (cid:35) 1 W (cid:18) W ¯ (cid:19)1−γW 1−γW t t = ζ +(1−ζ ) (59) W W W W t−1 t−1 ¯ determining the optimal reset wage W and the evolution of wages, which jointly imply a t standard wage Phillips curve. The parameter ζ is the probability that the household will not W be able to adjust its wage in a given period and γ governs the elasticity of substitution across W labor services.40 Finally, we introduce heterogeneity in the price response to VAT changes. We assume that firms in the set F of measure µ fully pass through VAT changes as in our baseline model (described above). For the remaining proportion 1 − µ of firms in the set I, we assume that prices are sticky inclusive of taxes and thus the pass-through is incomplete, as in FGI. Hence, the price indexes for the two sets of firms are (cid:104) (cid:105) 1 PF = ζ (cid:0) PF (cid:1)1−γ +(1−ζ ) (cid:0) P ¯F (cid:1)1−γ 1−γ (60) P,t P P,t−1 P P,t   1 (cid:32) (cid:33)1−γ 1−γ PI P P I ,t = (1−τ t v)ζ P 1− P, τ t− v 1 +(1−ζ P ) (cid:0) P ¯ H I ,t (cid:1)1−γ  (61) t−1 Equation (61) shows that, for firms in the set I that do not adjust their price, an increase in the VAT causes producer prices, and hence margins, to drop mechanically. The overall response of average prices for firms in I will then depend on the endogenous response of optimizing firms that reset consumer prices P ¯I . H,t 40See the Appendix for details. 33

Domesticproducerpriceinflationinthehomecountryisapproximatelygivenbytheweighted average of the inflation rates of the two sets of firms π ≈ µπF +(1−µ)πI (62) P,t P,t P,t 5.3 Parameter Values Table 2 presents the parameter values used in our quantitative analysis. We partition the model parameters in two sets. The first includes conventional parameters that are either fixed to standard values commonly used in the literature or calibrated using German data. We set the discount factor β to 0.99; the coefficient of relative risk aversion σ to unity; the elasticities of substitution among good varieties γ and among labor varieties γ to 11 and 6, respectively; W the labor share α to 0.64, and the capital depreciation rate δ to 0.025. In addition, we set the K coefficient controlling inertia in the monetary policy response ρ to 0.85, and the coefficients R controlling the response to inflation and the output gap, φ and φ , to 1.5 and 0.25, respectively. y These values are all fairly conventional. We then calibrate the size of the home country and the import share to match the share of German GDP in the euro area and the average value of goods and services imported from other euro-area countries relative to German GDP between 2000 and 2006. The resulting parameter values are s = 0.25 and 1−ω = 0.15. H For the Frisch elasticity of labor supply, η−1, we choose a value of 1, which is in the middle of the range of estimates. For the value of the elasticity of substitution between domestic and foreign goods, θ, we choose a value of 1.25 based on the evidence discussed in FGI and Imbs et al. (2010). The Calvo parameters controlling price and wage stickiness, ζ and ζ , are both P W set to 0.85, consistent with the evidence for euro-area countries discussed in Gal´ı and Monacelli (2016). We calibrate the curvature of the capital adjustment cost function to 10, in the middle of the range of estimates that go from more than 20 (Hayashi (1982)) to as low as 2 (Cao et al. (2019)). Finally we set the inverse elasticity of capital utilization, σ , to 0.01, as in Christiano u et al. (2005). The finite-state Markov chain that controls the evolution of tax instruments is calibrated to the German fiscal devaluation. In particular, VATs and payroll subsidies are a function of the Markov state s , τν = ψ (s) and ςp = ψ (s), where s ∈ S = {s¯ ,s¯ ,s¯ }. The transition t t τ t σ t 1 1 3 34

Table 2: Parameter Values for the Extended Model Parameter Value Calibrated Parameters Discount factor β 0.99 Risk aversion σ 1.00 Frisch elasticity of labor supply η−1 1.00 Good variety elasticity γ 11.0 Labor variety elasticity γ 6.0 W Price stickiness ζ 0.85 P Wage stickiness ζ 0.85 W Trade elasticity θ 1.25 Import share 1−ω 0.15 H Labor share α 0.64 Capital depreciation rate δ 0.025 K Capital adjustment cost κ 10 Inverse Elasticity of Utilization σ 0.01 u Country size s 0.25 Inertia in the Taylor rule ρ 0.85 R Output gap weight in the Taylor rule φ 0.125 y Inflation weight in the Taylor rule φ 1.50 π Estimated Parameters Complete pass-through µ 0.60 Persistence ρ 0.97 probability matrix is given by   1 0 0   T =  0 0 1  (63)     (1−ρ) 0 ρ where the element in the ith row of the jth column of T measures the probability of moving from state i to state j. The first state is the steady state with no taxes ψ (s¯ ) = ψ (s¯ ) = 0. In τ 1 σ 1 the second state, taxes are still not implemented, ψ (s¯ ) = ψ (s¯ ) = 0, but they are announced τ 1 σ 1 for the following quarter, Pr{s = s¯ |s = s¯ } = 1. In the third state, the VP policy is t+1 3 t 1 implemented, ψ (s¯ ) = τV and ψ (s¯ ) = ςP. The third row of matrix T indicates that 1 − ρ τ 1 ς 1 35

measures the probability that the policy is reversed and fiscal policy returns to the steady state. We set τV = 1.45 percent and ςP = 1.25 percent, consistent with the fiscal measures implemented by the German government in 2007. The second set of parameters, which includes the fraction of firms that fully pass VAT changes through to consumer prices (µ) and the parameters that control the evolution of VATs and payroll subsidies (ρ), is estimated. Given the importance of these parameters for the macroeconomiceffectsofVPpolicies,wesetΘ=[µ; ρ]sothatitminimizesthedistancebetween the German data on output and inflation presented in Figure 5 and the corresponding modelimplied series. In particular, we denote by M = {{π˜D}T ,{y˜D}T }, with t = 2006 : Q4 D t t=t0 t t=t0 0 and T = 2007 : Q4, the vector containing data on German output and consumer price inflation in deviation from the euro-area data on output and inflation between 2006:Q4 and 2007:Q4. Similarly, we let M (Θ) = {{π˜M}T ,{y˜M}T } denote the corresponding vector of model- M t t=t0 t t=t0 simulated series obtained under a specific vector of parameter Θ, conditional on the calibrated valuesofallotherparametersdiscussedearlier,includingthesizeofthepolicyinnovations.41 We assume that in 2006:Q3, the model economy is in the steady state, s = s¯ for t = 2006 : Q3. t 1 The policy is then announced in 2006:Q4, and agents expect it to be implemented in the following quarter, s = s¯ for t = 2006 : Q4. The policy is implemented in 2007:Q1 and remains t 2 in effect throughout 2007, although agents give positive probability, 1−ρ, to a reversal. That is, for t ∈ {2007 : Q1,2007 : Q2,2007 : Q3,2007 : Q4}, s = s¯ so that in 2007:Q1 τV increases t 2 t 1.45 percent and ςP increases 1.25 percent, and they remain at the higher level throughout 2007 t as in the data. We then choose Θ to solve Θ∗ = argmaxO(Θ) = argmax−[M −M (Θ)]′[M −M (Θ)] (64) D M D M Figure 6 presents how the objective function O behaves as we vary Θ. Two key results emerge. First, the objective function is maximized at the point Θ∗ = [0.6; 0.93]. These values suggest that, in order to account for the price increase and output decline observed in the data, the model requires a significant fraction of firms passing VAT changes through to 41GiventhesmallGDPshareofthehomecountry,spilloverstotheforeigncountryarequantitativelynegligible in the model, as in the data. Hence, we include in M (Θ) the model response of the German economy in M deviationfromthesteadystate, whichwillfacilitatetheeconomicinterpretationofoursimulations. Theeffects on the other euro-area economies are shown in the Appendix. 36

Figure 6: Policy Reversal, Pass-Through, and Distance between German Data and Model The figure plots the objective function in (64), that is the negative of the squared distance between the model implied time series on inflation and output and the observed realizations. The blue diamonds show the optimal point on the surface and its projection in the (x,y) plane which reports an optimal value of µ∗ = 0.6 and 1−ρ∗ = 0.07. 37

consumer prices (µ = 0.6) and a positive probability of policy reversal (1−ρ = 0.07). While the large estimated share of firms passing through VAT changes to prices is obtained purely from aggregate data, it is also in line with the heterogenous pricing response across sectors documented in Bundesbank (2007). For instance, the pass-through during the first quarter of 2007 was full in the automotive sector but muted in the retail sector. Similarly, an expected duration of the policy of about eight years, as implied by our estimated value of ρ, is consistent with reasonable assumptions about the likelihood of political turnover and its implications for the evolution of fiscal policy.42 Second, the limiting assumption of permanent policy changes (1 − ρ = 0) and all prices sticky inclusive of VATs (µ = 0), typically adopted in the fiscal devaluation literature, appears to be strongly rejected by the data. As shown in Figure 6, the fit of the model declines sharply as Θ takes these limiting values, with the objective function O reaching its lowest value of negative 12, compared with a value of negative 2 at the optimum. In addition, the objective function features a strongly nonlinear behavior. There is a large flat region around the optimum suggesting that several values of (µ,ρ) close to Θ∗ deliver similar responses for output and inflation. The fit of the model then deteriorates very quickly when approaching extremely low values in either dimension. Both low levels for the proportion of firms that fully pass-through VAT changes (i.e. around µ = .2 or lower) and very low levels for the probability of reversal (i.e. around ρ = .02 or lower) seem to be at odds with the time-series data for German GDP and inflation. 5.4 Model vs. Data Figure 7 compares the response of the German economy with an announced VP policy in our model and in the data. For each variable except net exports, the data lines present German variables relative to their euro-area counterparts. The model lines show the response in the home country in deviation from the steady state. In particular, the solid blue line shows our “Baseline”experiment constructed using our estimated values (µ∗,ρ∗) = (0.6,0.93). The dashed red line shows the response of the economy in the case of a “quasi” fiscal devaluation as in FGI, 42AsnotedinD’Acuntoetal.(2016),atthetimetherewasseveredisagreementbetweenthetwomainparties on the benefit of the VP policy and, thus, uncertainty about the duration of the policy in case of a change in government. 38

which we capture by assuming that there is no pass-through of VAT changes (µ = 0) and that the policy is known to be permanent (1−ρ = 0).43 As the first two panels show, in our baseline experiment, even though agents give positive probability to a reversal, the policy remains in effect throughout 2007. Our baseline experiment reproduces, both qualitatively and quantitatively, the evolution of German macroeconomic data. First, the model reproduces well the behavior of output and inflation. While these series were targeted in the estimation of (µ∗,ρ∗), this estimation was conditional on the calibrated values of all other parameters, including the size of the policy changes, and the assumption that VP was the only shock hitting the German economy. Second, itisquiteremarkablehowwellthemodelcapturesthebehaviorofothermacroeconomic data not targeted in the estimation, including the components of GDP. Both consumption and investment increase upon announcement of the tax changes, as agents substitute away from future expenditures in anticipation of higher prices. When the policy is implemented, consumption and investment drop as the transitory increase in intertemporal prices due to the dynamics of the VAT changes more than offsets the stimulative effects of the payroll subsidy.44 One key channel that allows the model to replicate the behavior of investment is variable capital utilization, which dampens fluctuations in the rental rate of capital and thus implies that investment is largely determined by the real interest rate. Variable capital utilization also helps the model match the behavior of labor input as variation in utilization accounts for most of the variation in output in response to these tax changes. Consequently, labor input is only slightly affected, in line with the data. Similarly, the model reproduces very well the increase in net exports, and the overall evolution of wages. In contrast, the VP policy under the FGI assumptions generates a boom in aggregate demand and output that appears at odds with the data. Given that the policy is expected to be permanent, VAT changes do not directly distort intertemporal prices in this case. In addition, as all prices are assumed to be sticky inclusive of VATs, there is no pass-through of 43As explained in FGI, this VP policy would only approximate a currency devaluation for three reasons: First, a devaluation would require a capital subsidy. Second, monetary policy for the currency union responds to developments in the home country. Third, in our calibrated experiment, the change in the VAT is slightly different from the change in the payroll subsidy. That said, their quantitative analysis suggests that this policy would still provide significant macroeconomic stimulus, as confirmed by our experiment. 44As argued by Gal´ı and Monacelli (2016) temporary payroll tax reductions are much less effective in stimulating economic activity under a fixed exchange rate regime. 39

DATA Baseline FGI (2014) VAT taxes Payroll subsidies HICP Inflation 1.5 1.5 2 1 1 1 0.5 0.5 0 0 0 -1 GDP Consumption Investment 2 2 5 1 1 0 0 0 -1 -1 -2 -2 -3 -3 -5 Hours Net Exports to EA Labor Cost Inflation ( with payroll taxes: W * (1- x) ) 2 5.5 0.5 1 5 0 -0.5 0 4.5 -1 -1 -1.5 -2 4 -2 -3 3.5 -2.5 Q3 Q4 Q1 Q2 Q3 Q4 Q3 Q4 Q1 Q2 Q3 Q4 Q3 Q4 Q1 Q2 Q3 Q4 2006 2006 2007 2007 2007 2007 2006 2006 2007 2007 2007 2007 2006 2006 2007 2007 2007 2007 Figure 7: 2007 German VP, Model vs Data For all variables except net exports the data line (black crossed) shows difference between the variable in Germany and in the EA ex-Germany, i.e. the difference between the black solid line and the red dotted line in Figure 5. The model lines show the response in the home country in deviation from steady state to a perfectly anticipated VP policy announced in 2006Q4 and implemented in 2007Q1. HICP and wage inflation are four-quarter percent changes. Net exports are in percent of GDP. The other variables are percent deviations from steady state. The blue solid line assumes that pass-through of VAT taxes is complete for a share µ∗ = 0.6 of firms and that, while VP remains in place throughout 2007, it is expected to be abandoned with a 0.07 probability in the following quarter. The dashed red line assumes that the tax pass-through of VAT changes is incomplete and the policy is (expected to be) permanent. VAT changes to consumer prices in the short run and aggregate demand increases on impact. The increase in VAT mechanically induces a reduction in producer prices for firms that cannot adjust, thus boosting external competitiveness. These forces produce a counterfactually large and persistent boom in output and its components as well as labor input. Of note, the increase in prices in 2007:Q1 is largely driven by the mechanical increase in import prices induced by the VAT increase.45 45Irrespective of the value of µ, the pass-through of VAT changes into import prices is full and complete. 40

DATA Baseline =1 =.9 VAT taxes Payroll subsidies HICP Inflation 1.5 1.5 2 1 1 1 0.5 0.5 0 0 0 -1 GDP Consumption Investment 2 2 5 1 1 0 0 0 -1 -1 -2 -2 -3 -3 -5 Hours Net Exports to EA Labor Cost Inflation ( with payroll taxes: W * (1- x) ) 2 5.5 0.5 1 5 0 -0.5 0 4.5 -1 -1 -1.5 -2 4 -2 -3 3.5 -2.5 Q3 Q4 Q1 Q2 Q3 Q4 Q3 Q4 Q1 Q2 Q3 Q4 Q3 Q4 Q1 Q2 Q3 Q4 2006 2006 2007 2007 2007 2007 2006 2006 2007 2007 2007 2007 2006 2006 2007 2007 2007 2007 Figure 8: The role of expectations about policy reversal The data line (black crossed) and the baseline (blue solid) are as in figure 7. The dashed red line assumes permanent VP. The dotted green line assumes that while VP remains in place throughout 2007, it is expected to be abandoned with a 0.1 probability in the following quarter. All experiments assume µ = µ∗. Figures 8 and 9 describe how the parameters controlling VAT pass-through and expected policy reversal each help the baseline experiment account for the German data. The red dashed lines in figure 8 show that even under our estimated value of VAT pass-through (µ∗), a permanent VP policy provides a large boost to investment and employment, as the intertemporal substitution effect is absent when the policy is expected to remain in place forever. As noted earlier, the relationship between the economic effects of VP and variations in ρ appears highly nonlinear: When the persistence of the policy is decreased to 0.9, the dotted light-green lines, the macroeconomic effects of the policy are essentially identical to those under the baseline estimated value of ρ∗ = 0.93. Similarly, the dashed red lines in Figure 9 show that, when prices are sticky inclusive of taxes for all firms (µ = 0), the intertemporal substitution effects are muted even under policy reversal, as VATs are slow to show through in consumer prices. As a result, 41

DATA Baseline =0 =1 VAT taxes Payroll subsidies CPI Inflation (4 quarter changes) 1.5 1.5 2 1 1 1 0.5 0.5 0 0 0 -1 GDP Consumption Investment 2 2 2 1 1 0 0 0 -1 -1 -2 -2 -2 -3 -3 -4 Employment Net Exports to EA Labor Cost Inflation ( with payroll taxes: W * (1- x) ) 2 5.5 0.5 1 5 0 -0.5 0 4.5 -1 -1 -1.5 -2 4 -2 -3 3.5 -2.5 Q3 Q4 Q1 Q2 Q3 Q4 Q3 Q4 Q1 Q2 Q3 Q4 Q3 Q4 Q1 Q2 Q3 Q4 2006 2006 2007 2007 2007 2007 2006 2006 2007 2007 2007 2007 2006 2006 2007 2007 2007 2007 Figure 9: The role of the tax pass-through The data line (black crossed) and the baseline (blue solid) are as in figure 7. The dashed red line assumes incomplete pass-through for all firms. The dotted green line assumes complete pass-through for all firms. All experiments assume ρ = ρ∗. consumption is flat and investment drops less. Moreover, the boost to international competitiveness induced by higher VATs under incomplete pass-through leads to a larger increase in net exports, leaving output little changed. In contrast, when all firms fully pass through VAT increases, the dotted light-green lines show that the macroeconomic effects of VP are broadly similar to our baseline effects, apart from the larger immediate increase in consumer prices that is offset by subsequent declines. All told, both a substantial share of firms that fully passes through VAT increases and a non-negligible probability of future policy reversal appear to be necessary in order for the model to match the observed performance of the German economy. 42

5.5 IX, VP, and Currency Devaluations We now reinterpret the effects of the 2007 fiscal reform in Germany through the lens of our theoretical analysis of fiscal devaluations in sections 3 and 4. In particular, we use our extended modeltoasktwoquestions. First,whatwouldhavebeentheeffectsontheGermaneconomyofa currency devaluation against other euro-area countries? Second, could the German government have achieved outcomes similar to a devaluation even within a currency union by implementing an IX policy rather than a VP policy? While Germany’s euro-area membership would preclude it from pursuing such policies, it is interesting to assess whether they would be more effective than VP if they were in fact viable policy options. The experiments depicted in figure 10 address these two questions by studying the effects of a currency devaluation (blue solid line) and an IX policy (red-dashed line). In the currency devaluation experiments we assume that the German economy pegs its interest rate to the ECB policy rate, which is set according to a standard Taylor that responds to CPI inflation and the output gap in the EA ex-Germany bloc. The panels in the first row depict the response of the economy when the policies are expected to be permanent, while those in the second row assume that all policies are expected to be reversed. As in the VP experiment above, the probability of reversal in the following quarter is 0.07 and the size of the tax changes is 1.23 percent. For simplicity, and differently from before, we assume that the policies are unanticipated. Figure 10 shows that a currency devaluation provides substantial stimulus to the economy irrespective of whether or not it is expected to be reversed. In both cases, the direct boost to exports is amplified by an expansion in domestic demand caused by a persistent decline in real interest rates. When the devaluation is expected to be permanent, the expected inflationary effects of the policy cause a decline in real rates with the policy rate almost unchanged. When devaluation is expected to be reversed, the inflationary effects are dampened, given that a reversal eventually causes inflation to decline. That said, given that agents expect the currency to eventually appreciate back to steady state, the policy rate has to fall below the foreign policy rateinordertoimplementthesamesizedevaluation. Asaresult, theboosttodomesticdemand and output is somewhat larger when the currency devaluation is expected to be temporary.46 The figure also shows that an IX policy within a currency union could deliver stimulus akin 46Notice that we plot short-term real interest rate, while aggregate demand depends on the expected sum of all future interest rates which is smaller in the case of the transitory experiment. 43

DATA Currency Deval IX VP Domestic Demand Real Rate Net Exports to EA GDP C+I 400*( R - E( t+1 )) 2 0.2 5.5 2 1 0 1 )1 5 = ( tn e 0 -0.2 4.5 0 n a -1 -0.4 -1 m re P 4 -2 -0.6 -2 -3 -0.8 3.5 -3 2 0.5 5.5 2 )4 1 5 1 9 .0 = 0 0 ( y 0 4.5 ro tis -1 -1 n a rT -2 4 -2 -3 -0.5 3.5 -3 Q3Q4Q1Q2Q3Q4 Q3Q4Q1Q2Q3Q4 Q3Q4Q1Q2Q3Q4 Q3Q4Q1Q2Q3Q4 2006 2006 2007 2007 2007 2007 2006 2006 2007 2007 2007 2007 2006 2006 2007 2007 2007 2007 2006 2006 2007 2007 2007 2007 Figure 10: VP, IX, and Currency Devaluations The data lines (black crossed) are as in figure 7. The dashed red lines refer to permanent (top row) and transitory (bottom row) IX policies. The dotted blue lines refer to permanent (top row) and transitory (bottom row) VP. The solid green lines refer to permanent (top row) and transitory (bottom row) currency devaluations. All experiments assume assume µ = µ∗ and the transitory experiments assume ρ = ρ∗. to a currency devaluation, provided that it is permanent. While IX is not exactly identical to a currency devaluation, as we assume that the ECB gives positive weights to inflation and output dynamics in Germany, the responses shown in the first row are quantitatively very close.47 In contrast, when IX is expected to be reversed, its stimulative effects on domestic demand vanish. In this case, the ECB policy rate remains unchanged in response to the German IX policy, which has offsetting effects in the two blocs. As a result, the eventual reversal of IX is sufficienttoneutralizetheintertemporalsubstitutioneffectscausedbyhigherexpectedinflation in the short run. All told, these results confirm our theoretical prediction that IX could be an useful cycli- 47This argument is developed in Farhi et al. (2014). 44

cal tool for boosting economic activity by inducing an expansion in net exports. Its effects on domestic demand, however, are much more sensitive to expectations about future policy reversal than a currency devaluation, as a currency devaluation would be accompanied by an accommodative monetary policy response. 6 Concluding Remarks Existing literature suggests that a uniform increase in import tariffs and export subsidies (IX) and an increase in value-added taxes accompanied by a payroll tax deduction (VP) are equivalent, are neutral under flexible exchange rates, and can provide as much stimulus as a currency devaluationunderfixedexchangerates. Theseresultsareparticularlyrelevantforcountriesconstrained by membership in a currency union. In 2007, the German government implemented a fiscal reform along these lines, as “shifting the tax burden from direct taxation and fiscal charges to indirect taxation...are elements of a revenue structure that is both more conducive to growth and more competitive.”48 Inthispaper, wequestionthisconventionalwisdom. First, wearguethatthetransmissionof IXandVPpoliciesisfundamentallydifferentundertheassumptionoffullpass-throughoftaxes. Indeed, in a special case often considered in the literature, we show that under fixed exchange rates IX implements a currency devaluation, whereas VP turns out to have no allocative effects. Second, we find that IX policies that are expected to be reversed or trigger retaliation tend to boost output even under flexible exchange rates. The macroeconomic effects of VP, instead, are ambiguous and depend critically on the relative strength of two offsetting channels. On the one hand, intertemporalsubstitutioneffectsmakeVPcontractionary, especiallyinacurrencyunion. On the other hand, sluggish wage adjustments allow payroll subsidies to boost aggregate supply and output. Third, we assess the empirical relevance of our novel theoretical predictions about these policies by studying the effects of the 2007 German fiscal reform. We find that a canonical DSGEmodelofacurrencyunioncanaccountfortheunder-performanceoftheGermaneconomy in the aftermath of this attempted fiscal devaluation. In order for the model to fit the data, it is essential that a large share of firms fully passes VAT increases through to consumer prices and that the policy is expected to be eventually reversed with positive probability. In contrast, 48See Germany SPG (2007). 45

the limiting assumption of limited tax pass-through and permanent policy changes, typically adopted in the fiscal devaluation literature, appears strongly rejected by the data. An IX policy would have delivered an output boost through its effects on external competitiveness. That said, when expected to be reversed, IX has only a muted effect on aggregate demand and hence provides a much smaller boost to output than a currency devaluation. All told, our analysis provides some caveats on the practical viability of fiscal devaluations as a tool to supply macroeconomic stimulus in a currency union. 46

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Appendix A Appendix A.1 Model Equations A.1.1 Households Household i ∈ H = [0,1] chooses {w¯ (i),w (i),n (i),c (i),a (i),B (i),B (i)} to maxt t t t t,t+1 Ht Ft imize (cid:34) (cid:35) [c (i)]1−σ [n (i)]1+η maxE Σ∞ βt t − t (A.1) 0 t=0 1−σ 1+η s.t (cid:104) (cid:105) P c (i)+Σ q a (i)+B (i)+ε B (i)+ χ (cid:0) B (i)−B ¯ (cid:1)2 = t t t+1 t,t+1 t,t+1 Ht t Ft 2 Ft F (A.2) R B (i)+ε R∗ B (i)+P a (i)+w (i)n (i)+Π(cid:101) +T t−1 Ht−1 t t−1 Ft−1 t t−1,t t t t t (cid:26) w (i) w.p. ζ w (i) = t−1 W (A.3) t w¯ (i) w.p. 1−ζ t W (cid:20) w (i) (cid:21)−γn t n (i) = N (A.4) t t W t where W is a wage index (described below) and q is the price of a state contingent t t,t+1 Arrow security paying one unit of consumption in a specific state at time t+1. We assume that a complete set of Arrow securities is traded domestically so that perfect risk sharing within each country allows for simple aggregation. Equation (A.3) states that households can only adjust their wage with probability ζ . Equation (A.4) is the firms’ demand schedule for labor W variety i, derived below. Optimality conditions are (cid:20) C−σ P (cid:21) 1 = βE t+1 t R (A.5) t C−σ P t t t+1 (cid:20) C−σ P ε (cid:21) 1+χ (cid:0) B (i)−B ¯ (cid:1) = βE t+1 t t+1 R∗ (A.6) Ft F t C−σ P ε t t t+1 t (cid:88) (cid:26) [n (i)]η γ W ¯ (cid:27) E ζs−t C−σ s n − t n (i) = 0 (A.7) t W s C−σ (γ −1) P s s n s A.1.2 Retailers The problem of retailers is as described in the main text. A.1.3 Producers PCP pricing A.1

Producer i ∈ F = [0,1] chooses an optimal reset price P (i), export prices {P∗ (i)} Pt Hs s≥t (cid:110) (cid:111) quantities {Y (i),Y∗ (i)} and employment N (i),{n (j;i)} to maximize Hs Hs s≥t s s j s≥t maxE (cid:88) ζs−tΛ (1−τπ) (cid:40) P ¯ Pt (i) (cid:2) Y Hs (i)+ s s ∗Y H ∗ s (i) (cid:3) −(1−ς s p) (cid:82) w s (j)n s (j;i)dj (cid:41) (A.8) t P t,s s P s s≥t s.t. s∗ Y (i)+ Y∗ (i) = A Nα(i) (A.9) Hs s Hs s s (cid:26)(cid:90) (cid:27) γn γn−1 γn−1 N s (i) = [n s (j;i)] γn dj (A.10) (cid:20) ¯ (cid:21)−γ P (i) Pt Y (i) = Y (A.11) Hs Hs P Ps (cid:20) P∗ (i) (cid:21)−γ Y∗ (i) = Hs Y∗ (A.12) Ht P∗ Ht Hs (1+τm∗)P ¯ (i) P∗ (i) = s Pt (A.13) Hs (1+ςx) ε t s where s∗ and s are the size of the foreign and home country respectively. The optimality conditions for this problem are constraints (A.9) − (A.13) as well as an optimal pricing condition as in the text: (cid:20) s∗ (cid:21) 1 (cid:20) γ (1−ςp)W (cid:21) E Σ∞ ζs−tΛ Y (i)+ Y∗ (i) (1−τπ) P (i)− s s = 0 (A.14) t s=t P t,s Hs s Hs s P Pt γ −1αA N (i)α−1 s s s where W is the wage index s (cid:20)(cid:90) (cid:21) 1 W = [w (j)]1−γndj 1−γn (A.15) s s LCP pricing Producer i chooses optimal reset prices P ¯ (i) and P ¯∗ (i), where P ¯∗ (i) is the foreign cur- Pt Xt Xt rencypriceofdomesticexportnetoftariffs,exportprices{P∗ (i)} ,quantities{Y (i),Y∗ (i)} Hs s≥t Hs Hs s≥t (cid:110) (cid:111) and employment N (i),{n (j;i)} to maximize s s j s≥t maxE (cid:88) ζs−tΛ (cid:40) P ¯ Pt (i)Y Hs (i)+ε s P X ∗ t (i)(1+ς s x) s s ∗Y H ∗ s (i)−(1−ς s p) (cid:82) w s (j)n s (j;i)dj (cid:41) t P t,s P s s≥t (A.16) s.t. s∗ Y (i)+ Y∗ (i) = A Nα(i) (A.17) Hs s Hs s s A.2

(cid:26)(cid:90) (cid:27) γn γn−1 γn−1 N s (i) = [n s (j;i)] γn dj (A.18) (cid:20) ¯ (cid:21)−γ P (i) Pt Y (i) = Y (A.19) Hs Hs P Ps (cid:20) P∗ (i) (cid:21)−γ Y∗ (i) = Hs Y∗ (A.20) Ht P∗ Ht Hs P∗ (i) = (1+τm∗)P∗ (i) (A.21) Hs s Xt The optimality conditions for this problem are constraints (A.17) − (A.21) and optimal pricing conditions for domestic and foreign markets: Y (i) (cid:20) γ (1−ςp)W (cid:21) E Σ∞ ζs−tΛ (1−τπ) Hs P ¯ (i)− s s = 0 (A.22) t s=t P t,s s P Pt γ −1αA N (i)α−1 s s s Y∗ (i) (cid:20) γ (1−ςp)W (cid:21) E Σ∞ ζs−tΛ (1−τπ) Hs ε (1+ςx)P∗ (i)− s s = 0 (A.23) t s=t P t,s s P s s Xt γ −1αA N (i)α−1 s s s where W is the wage index s (cid:26)(cid:90) (cid:27) 1 W = [w (j)]1−γndj 1−γn (A.24) s s An analogous problem for the foreign producers yield Y∗ (i) (cid:20) γ W∗ (cid:21) E Σ∞ ζs−tΛ Fs P ¯∗ (i)− s = 0 (A.25) t s=t P t,s P Pt γ −1αA∗N∗(i)α−1 s s s Y (i) (cid:20) 1 γ W∗ (cid:21) E Σ∞ ζs−tΛ Fs (1+ςx∗)P ¯ (i)− s = 0 (A.26) t s=t P t,s P ε s X∗t γ −1αA∗N∗(i)α−1 s s s s where (1+τm)P ¯ (i) P (i) = s X∗t Fs (1−τv) s A.2 Equilibrium equations Equations (A.27) − (A.58) below determine the equilibrium process {Ψ(st)} for any st∈(S)t,t≥0 initial value (M ,s ) where s is the policy regime at time 0 and M collects bond holdings −1 0 0 −1 and the distribution of prices and wages: M = {A ,P } −1 −1 −1 (cid:8) (cid:9) A = B R ,B R∗ ,B∗ R∗ ,B∗ R . −1 H,−1 −1 F,−1 −1 F,−1 −1 H,−1 −1 (cid:110) (cid:111) (cid:8) (cid:9) (cid:8) (cid:9) P = P (j),P∗ (j) ,{W (i)} , P∗ (j),P (j) ,{W∗(i)} −1 P,−1 X,−1 j∈J i∈I P,−1 X∗,−1 j∈J∗ i∈I∗ For ease of exposition we group elements of Ψ into variables that we associate with house- A.3

holds optimality conditions,Ψ and Ψ∗ abroad, retailers optimality conditions, Ψ and HH HH RE Ψ∗ , firms optimality conditions, Ψ and Ψ∗ , price indexes, Ψ and Ψ∗ , and market clear- RE FI FI PI PI ing conditions, Ψ . We have that Ψ = {Ψ ,Ψ∗ ,Ψ ,Ψ∗ ,Ψ ,Ψ∗ ,Ψ ,Ψ∗,Ψ } MC HH HH RE RE FI FI P P MC Households optimality (cid:8) ¯ (cid:9) Ψ = w (i),W ,n (i),C ,B (leaving out budget constraint and B ) HH t t t t Ht Ft (cid:26) w (i) w.p. ζ w (i) = t−1 W (A.27) t W ¯ w.p. 1−ζ t W (cid:88) (cid:20) [n (i)]η γ W ¯ (cid:21) E ζs−t C−σ s n − t n (i) = 0 (A.28) t W s C−σ (γ −1) P s s n s (cid:18) w (i) (cid:19)−γn t n (i) = N (A.29) t t W t (cid:20) C−σ P (cid:21) 1 = βE t+1 t R (A.30) t C−σ P t t t+1 (cid:20) C−σ P ε (cid:21) 1+χ (cid:0) B (i)−B ¯ (cid:1) = βE t+1 t t+1 R∗ (A.31) Ft F t C−σ P ε t t t+1 t and symmetric conditions for Ψ∗ = (cid:8) w∗(i),W ¯ ∗,n∗(i),C∗,B∗ (cid:9) abroad HH t t t t Ft Retailers optimality Ψ = {Y ,Y ,Y (i),Y (i)} RE Ht Ft Ht Ft (cid:20) P (cid:21)−θ Ht Y = ω C (A.32) Ht t P t (cid:20) P (cid:21)−θ Ft Y = (1−ω) C (A.33) Ft t P t (cid:18) P (i) (cid:19)−γ Pt Y (i) = Y (A.34) Ht Hs P Pt (cid:18) P (i) (cid:19)−γ Ft Y (i) = Y (A.35) F Ft P Ft and symmetric conditions for Ψ = {Y∗ ,Y∗ ,Y∗ (i),Y∗ (i)} RE Ft Ht Ft Ht Firms optimality (cid:110) (cid:111) Ψ = P∗ (i),P (i),P (i),P∗ (i),P (i),P ∗ (i),P ¯∗ (i),P ¯∗ (i),P∗ (i),P (i) FI Hs Ft Pt Pt Pt Pt Xt X∗t Xt X∗t P∗ (i) = (1+τm∗)P∗ (i) (A.36) Ht t Xt 1+τm P (i) = t P (i) (A.37) Ft 1−τv X∗t t (cid:26) P (i) w.p. ζ P (i) = Pt−1 p (A.38) Pt P ¯ (i) w.p. 1−ζ Pt p A.4

(cid:26) P∗ (i) w.p. ζ P∗ (i) = Pt−1 p (A.39) Pt P ¯∗ (i) w.p. 1−ζ Pt p (cid:20) (cid:21) E Σ∞ ζs−tΛ (cid:2) Y (i)+ s∗Y∗ (i) (cid:3) 1 P (i)− γ (1−ςs p)Ws = 0 PCP t s=t P t,s Hs s Hs Ps Pt γ−1αAsNs(i)α−1 (A.40a) (cid:20) (cid:21) E Σ∞ ζs−tΛ YHs(i) P ¯ (i)− γ (1−ςs p)Ws = 0 LCP t s=t P t,s Ps Pt γ−1αAsNs(i)α−1 (A.40b) (cid:104) (cid:105) E Σ∞ ζs−tΛ∗ (cid:2) s Y (i)+Y∗ (i) (cid:3) 1 P ∗ (i)− γ W s ∗ = 0 PCP t s=t P t,s s∗ Fs Fs P s ∗ Pt γ−1αAsN s ∗(i)α−1 (A.41a) (cid:104) (cid:105) E Σ∞ ζs−tΛ∗ Y F ∗ s (i) P ∗ (i)− γ W s ∗ = 0 LCP t s=t P t,s P s ∗ Pt γ−1αAsN s ∗(i)α−1 (A.41b) P∗ (i) = (1+τ t m∗)PPt(i) PCP Ht (1+ς t x) εt (A.42a) (cid:20) (cid:21) E Σ∞ ζs−tΛ Y H ∗ s (i) ε (1+ςx)P ¯∗ (i)− γ (1−ςs p)Ws = 0 LCP t s=t P t,s Ps s s Xt γ−1αAsNs(i)α−1 (A.42b) A.5

P (i) = 1+τ t mP P ∗ t (i)εt PCP Ft 1−τv (1+ςx∗) t t (A.43a) (cid:104) (cid:105) E Σ∞ ζs−tΛ∗ Y H ∗ s (i) (1+ς s x∗)P ¯ (i)− γ W s ∗ = 0 LCP t s=t P t,s Ps εs X∗t γ−1αAsN s ∗(i)α−1 (A.43b) ¯ P (i) = P (i) PCP X∗t X∗t (A.44a) (cid:26) P (i) w.p. ζ P (i) = X∗t W LCP X∗t+1 P ¯ (i) w.p. 1−ζ X∗t+1 W (A.44b) (cid:110) (cid:111) and symmetric conditions for Ψ∗ = N∗(i),P (i),P∗ (i),P ∗ (i),P ¯ (i),P (i) FI t Ft Pt Pt X∗t X∗t Price indexes Ψ = {P ,P ,P ,P ,W } PI t Ht Pt Ft t (cid:2) (cid:3) 1 P = ωP1−θ +(1−ω)P1−θ 1−θ (A.45) t Ht Ft (cid:20)(cid:90) 1 (cid:21) 1− 1 γ P = P (i)1−γdi (A.46) Ht Ht 0 P = P (1−τv) (A.47) Pt Ht t (cid:20)(cid:90) 1 (cid:21) 1− 1 γ P = P (i)1−γdi (A.48) Ft Ft 0 (cid:20)(cid:90) (cid:21) 1 W = [w (j)]1−γndj 1−γn (A.49) s s and symmetric conditions for Ψ∗ = {P∗,P∗ ,P∗ ,P∗ ,W∗} PI t Ft Pt Ht t Market Clearing Ψ = {N (i),N∗(i),N ,N∗,B ,B∗ ,ε ,R ,R∗} MC t t t t Ft Ht t t t s∗ Y (i)+ Y∗ (i) = A Nα(i) (A.50) Ht s Ht t t A.6

s Y∗ (i)+ Y (i) = A N∗α(i) (A.51) Ft s∗ Ft t t (cid:90) N = N (j)dj (A.52) t t j∈F (cid:90) N∗ = N∗(j)dj (A.53) t t j∈F B +B∗ = 0 (A.54) Ft Ft B +B∗ = 0 (A.55) Ht Ht B∗ B∗ P (cid:20) (1+ςx) P∗ (cid:21) B − Ht = B R∗ − Ht−1R + Pt Y∗ − t ε PtY (A.56) Ft ε Ft−1 t−1 ε t−1 (1+ςx)ε Ht (1+ςx∗) t P Ft t t t t t Pt 1 (cid:18) P∗ (cid:19)φπ (cid:32) Y +Y∗ (cid:33)φy (cid:18) ε (cid:19)φ∗ ε R∗ = pt Ft Ft t (A.57) t β P∗ Yflex +Y∗flex ε¯ pt−1 Ft Ft t 1 (cid:18) P (cid:19)φπ (cid:32) Y +Y∗ (cid:33)φy (cid:18) ε (cid:19)φε R = pt Ht Ht t (A.58) t β P Yflex +Y∗flex ε¯ pt−1 t Ht Ht A.3 Proof of Proposition 1 We let the policy regime s be a vector collecting all policy variables at time t t s = (τm,ςx,τv,ςp,ϵ¯,τm∗,ςx∗) t t t t t t t t We start by giving defining what it means to implement a new policy in our Markov Switching regime framework. Definition 1. Assume that s is governed by {S,Ω} from t = 0,...,t∗. A new policy from t∗ is t (cid:110) (cid:111) ˜ ˜ ˜ defined by a new stochastic process S,Ω and a function σ˜ : S → S that determines how the policy configuration at t∗ changes, s˜ = σ˜(s∗), upon introduction of the new policy. t∗ t We next define neutrality of a policy and equivalence between policies. (cid:110) (cid:111) Definition 2. Assume that a new policy S ˜ ,Ω ˜ ;σ˜ is implemented at time t∗ replacing {S,Ω}. The implementation of the policy has no allocative effects, i.e. it is neutral, if for any endogenous state M and any (continuation) equilibrium process {Ψ(st)} under t∗−1 st∈(S)t+1−t∗ ,t≥t∗ (cid:110) (cid:111) (cid:110) (cid:111) {S,Ω}, there is an equilibrium process, Ψ ˜ (s˜t) under S ˜ ,Ω ˜ that induces the s˜t∈(S˜)t+1−t∗ ,t≥t∗ same probability distribution for the real allocation. That is, letting (cid:8) (cid:0) (cid:1) (cid:0) (cid:1) (cid:8) (cid:0) (cid:1) (cid:0) (cid:1) (cid:0) (cid:1) (cid:0) (cid:1) (cid:0) (cid:1) (cid:0) (cid:1)(cid:9)(cid:9) Ξ= C st ,C∗ st , n i,st ,n∗ i,st ,Y i,st ,Y i,st ,Y∗ i,st ,Y∗ i,st H F H F st∈(S)t+1−t∗ ,t≥t∗ (cid:110) (cid:110) (cid:111)(cid:111) Ξ(cid:101)= C ˜(cid:0) s˜t (cid:1) ,C ˜∗ (cid:0) s˜t (cid:1) , n˜ (cid:0) i,s˜t (cid:1) ,n˜∗ (cid:0) i,s˜t (cid:1) ,Y ˜ (cid:0) i,s˜t (cid:1) ,Y ˜ (cid:0) i,s˜t (cid:1) ,Y ˜∗ (cid:0) i,s˜t (cid:1) ,Y ˜∗ (cid:0) i,s˜t (cid:1) H F H F s˜t∈(S˜)t+1−t∗ ,t≥t∗ A.7

(cid:110) (cid:111) denote the real allocation under {Ψ(st)} and Ψ ˜ (s˜t) respectively. st∈(S)t+1−t∗ ,t≥t∗ s˜t∈(S˜)t+1−t∗ ,t≥t∗ For any s¯ ∈ S i (cid:110) (cid:111) (cid:8) (cid:9) Pr Ξ(cid:101)(s˜n+1) = ξ| s˜ t∗ = σ˜(s¯ i ) = Pr Ξ(sn+1) = ξ| s t∗ = s¯ i ) (S˜,Ω˜) (S,Ω) (cid:110) (cid:111) (cid:110) (cid:111) ˆ ˆ ˜ ˜ We also say that two policies described by S,Ω,σˆ and S,Ω,σ˜ are equivalent if they induce the same probability distribution for the real allocation. Finally we give a definition of IX and VP policies. Definition 3. Assume that s is governed by {S,Ω} from t = 0,...,t∗. A unilateral implement (cid:8) (cid:9) tation of IX of size δ is described by GPIX,ΩIX,σIX with GPIX = S ∪SIX where the new δ set of states is  (cid:12) (cid:12) 1+τ˜m = 1+ς˜x = 1+δ   (cid:12) 1+τm 1+ςx  SIX = s˜= (τ˜m,ς˜x,τv,ςp,ϵ¯,τm∗,ςx∗)(cid:12) , (cid:12)  (cid:12) ∃s = (τm,ςx,τv,ςp,ϵ¯,τm∗,ςx∗) ∈ S  the transition matrix (cid:20) (cid:0) (cid:1) (cid:21) 1−πIX Ω πIXΩ ΩIX = (A.59) (1−ρ)Ω ρΩ allows for the possibility that the tax change is anticipated with probability πIX and then reversed with probability ρ. The implementation of IX is anticipated if πIX > 0 and σIX is the identity function, i.e. δ σIX(s) = s for any s ∈ S. δ The implementation of IX is unanticipated if πIX = 0 and σIX maps each element of S δ to its associated element in SIX. That is for any s = (τm,ςx,τv,ςp,ϵ¯,τm∗,ςx∗) ∈ S σIX (s) = (τ˜m,ς˜x,τv,ςp,ϵ¯,τm∗,ςx∗) δ s.t. (A.60) 1+τ˜m = 1+ς˜x = 1+δ 1+τm 1+ςx We define an anticipated and unanticipated VP policy analogously. The policy is described by (cid:8) (cid:9) GPVP,ΩVP,σVP with GPVP = S ∪SVP where the new set of states is δ  (cid:12) (cid:12) 1−τ˜v = 1−ς˜p = 1   (cid:12) 1−τv 1−ςp 1+δ  SVP = s˜= (τm,ςx,τ˜v,ς˜p,ϵ¯,τm∗,ςx∗)(cid:12) , (cid:12)  (cid:12) ∃s = (τm,ςx,τv,ςp,ϵ¯,τm∗,ςx∗) ∈ S  the transition matrix is (cid:20) (cid:0) (cid:1) (cid:21) 1−πVP Ω πVPΩ ΩVP = , (A.61) (1−ρ)Ω ρΩ A.8

and the function describing the unanticipated transition to VP is given by σVP (s) = (τm,ςx,τ˜v,ς˜p,ϵ¯,τm∗,ςx∗) δ s.t. (A.62) 1−τ˜v = 1−ς˜p = 1 . 1−τv 1−ςp 1+δ (cid:8) (cid:9) Notice that the process GPIX,ΩIX does not encompass the possibility of retaliation which we will introduce below. Proposition 1. In an economy with flexible exchange rates (φ = 0) a unilateral IX policy of ε size δ and a unilateral VP policy of size δ are both neutral and cause a δ− percent appreciation 1+δ of the real exchange rate if 1. The policy is permanent and unanticipated; 2. Foreign holdings of home-currency-denominated bonds are always zero (χ∗ = ∞); 3. Export prices are set in the producer’s currency (PCP), or prices are flexible. Proof. Condition 1 implies that πIX = πVP = 0 and ρ = 1. In this case the transition matrices in A.59 and A.61 are simply (cid:20) (cid:21) Ω 0 ΩIX = ΩVP = (A.63) 0 Ω Let {Ψ(st)} denote an equilibrium process before the implementation of the new st∈(S)t,t≥0 policy, i.e. when s is governed {S,Ω}. Assume without loss of generality that the new policy t is implemented at t∗ = 0. Neutrality of IX Let {µIX} be a sequence of function that map histories in which IX is implemented into t t≥0 a histories in which IX is not implemented: i.e. ∀s˜t = (s˜ ,...,s˜) ∈ (cid:0) GPIX (cid:1)t+1 , µ (s˜t) = st = 0 t t (s ,...,s ) ∈ (S)t+1 where ∀i ≥ 1 0 t (cid:26) s˜ if s˜ ∈ S i i s = i (cid:0) σIX (cid:1)−1 (s˜) if s˜ ∈ SIX δ i i where σIX is as defined in A.60. δ (cid:110) (cid:111) Considernowaprocess Ψ ˜IX (st) withanunanticipatedpermanentIXsuchthat, st∈(S˜)t ,t≥0 for each element κ˜IX of Ψ ˜IX, other than the nominal exchange rate, ε˜IX,and home currency t producer prices of foreign exporters, P ˜IX (i), we have X∗t κ˜IX (cid:0) s˜t (cid:1) = κ (cid:0) µIX (cid:0) s˜t (cid:1)(cid:1) ∀s˜t ∈ (cid:0) GPIX (cid:1)t , ∀t ≥ 0 (A.64) t where κ is the corresponding element of the equilibrium process Ψ without IX. For ease of notation in what follows, for any s˜t = (s˜ ,....,s˜) ∈ (cid:0) GPIX (cid:1)t+1 , we let κ˜IX = κ˜IX (s˜t) and 0 t t (cid:0) (cid:1) κ = κ µIX (s˜t) . t t A.9

The nominal exchange rate and the home currency producer prices of foreign exporters are ∀s˜t = (s˜ ,....,s˜) ∈ (cid:0) GPIX (cid:1)t+1 0 t (cid:26) ε if s˜ ∈ S ε˜IX = t t (A.65) t εt if s˜ ∈ SIX 1+δ t  P (i) if s ∈ S  X∗t t P ˜IX (i) = (A.66) X∗t  1 P (i) if s ∈ SIX 1+δ X∗t t (cid:110) (cid:111) We want to show that Ψ ˜IX (st) is an equilibrium. st∈(GPIX)t+1,t≥0 WefirstshowthatΨ ˜IX (st)satisfiesalloftheequationsdirectlyaffectedbythetariffsandexportsubsidychangewhens˜ ∈ SIX.Theseequationsarethelawsofoneprice(A.42a)−(A.43a), t thetaxpass-throughequations(A.37)−(A.36),andthebalanceofpaymentequilibrium(A.56). Considering the law of one price for domestic goods at an history s˜t such that s˜ ∈ SIX and t letting (cid:0) σIX (cid:1)−1 (s˜) ∈ S we see that δ t 1+τm∗ 1 P ˜∗IX (i) = P∗ (i) = P (i) t (A.67) H,t H,t H,t 1+σx ε t t 1+τm∗ 1 = P ˜IX (i) t (A.68) H,t (1+σ˜x)ε˜IX t t where the first and third equalities follow from (A.64), (A.65) and (A.60) and the second from the fact that Ψ is an equilibrium. An analogous arguemt holds for (A.43a) and (A.37) . Consider now the balance of payment equilibrium which, under condition 2 is (cid:34) (cid:35) P ˜IX P ˜∗IX B ˜IX = B ˜IX R ˜∗IX + Pt Y ˜∗IX −(1+ς˜x)ε˜IX Pt Y ˜IX Ft Ft−1 t−1 (1+ς˜x)ε˜IX Ht t t P ˜IX Ft t t Pt to see that this is satisfied, let again (cid:0) σIX (cid:1)−1 (s˜) = s ∈ S to get δ t t P (cid:20) P∗ (cid:21) B ˜IX = B = B R∗ + Pt Y∗ −(1+ςx)ε PtY Ft Ft Ft−1 t−1 (1+ςx)ε Ht t t P Ft t t Pt (cid:34) (cid:35) P ˜IX P ˜∗IX = B ˜IX R ˜∗IX + Pt Y ˜∗IX −(1+ς˜x)ε˜IX Pt Y ˜IX Ft−1 t−1 (1+ς˜x)ε˜IX Ht t t P ˜IX Ft t t Pt where the first and third equality follow from (A.64) (A.65) and (A.60) and the second from the fact that Ψ is an equilibrium. We then need to check that the adjustment of the nominal exchange rate and local currency producer prices of exports in (A.65) − (A.66) does not induce violations in other equilibrium equations. Under PCP P ˜IX∗(i) and P ˜IX (i) only affect (A.37) and (A.36), i.e. they are Xt X∗t definitions. The exchange rate ε affects optimal holdings of foreign bonds (A.31) and an t analogous condition abroad. As long as πIX = 0 and ρ = 1 we have that ∀st ∈ (cid:0) GPIX (cid:1)t , if st+1 ∈ (cid:0) GPIX (cid:1)t has positive probability, Pr{st+1|st} > 0, the appreciation is identical across A.10

equilibria: ε˜ ε t+1 t+1 = ε˜ ε t t and since these conditions only depend on exchange rate appreciation they are satisfied. Neutrality of VP Let {µVP} be a sequence of function that map histories in which VP is implemented into t t≥0 a histories in which VP is not implemented: i.e. ∀s˜t = (s˜ ,...,s˜) ∈ (cid:0) GPVP (cid:1)t+1 , µ (s˜t) = st = 0 t t (s ,...,s ) ∈ (S)t+1 where ∀i ≥ 1 0 t (cid:26) s˜ if s˜ ∈ S i i s = i (cid:0) σVP (cid:1)−1 (s˜) if s˜ ∈ SVP δ i i where σVP is as defined in A.60. δ (cid:110) (cid:111) Consider the process Ψ ˜VP (st) with an unanticipated permanent VP implest∈(GPVP)t,t≥0 (cid:16) (cid:17) mentationsuchthat,foreachelementκ˜VP ofΨ ˜VP,otherthandomesticprices P ˜VP (i),P ˜VP (i),P ˜VP (i) Ht Ft t (cid:16) (cid:17) (cid:16) (cid:17) and wages w¯ VP (i),w˜VP (i),W ˜ VP and the associated price indexes P ˜VP,P ˜VP,P ˜VP , (cid:101)t t t Ht Ft t κ˜VP (cid:0) s˜t (cid:1) = κ (cid:0) µVP (cid:0) s˜t (cid:1)(cid:1) ∀s˜t ∈ (cid:16) S ˜VP (cid:17)t , ∀t ≥ 0 (A.69) t where κ is the corresponding element of the equilibrium process Ψ without VP. Prices and wages satisfy ∀s˜t = (s˜ ,....,s˜) ∈ (cid:0) GPVP (cid:1)t 1 t  P ˜VP (i) P ˜VP (i) P ˜VP (i)  1 if s˜ t ∈ S H,t = F,t = t = (A.70) P (i) P (i) P (i) H,t F,t t  (1+δ) if s˜ ∈ SVP t  w¯ VP (i) w˜VP (i) W ˜ VP  1 if s˜ t ∈ S (cid:101)t = t = t = (A.71) w¯ (i) w˜ (i) W t t t  (1+δ) if s˜ ∈ SVP t (cid:110) (cid:111) We want to show that Ψ ˜VP (st) is an equilibrium, which given (A.70) and st∈(GPVP)t,t≥0 the fact that ε is unaffected also implies that the real echange rate appreciates by δ. t As discussed in section 3, VP instruments directly effect the two equations determining the labor market equilibrium and the dynamic Euler equations for consumption. Consider the optimality condition for the price of the domestic good at home at an history s˜t ∈ (cid:0) GPVP (cid:1)t such that s˜ ∈ SVP: t (cid:88) (1−ςp) γ W P ¯VP (i) = P ¯ (i) = (1−ςp)E Λ ˜ (i) s s Pt Pt t t t,s (1−ςp)γ −1αA Nα−1(i) s≥t t s s (cid:88) (1−ς˜p) γ WVP = (1−ς˜p)E Λ ˜VP (i) s s (A.72) t t t,s (1−ς˜p)γ −1αA (NVP)α−1(i) s≥t t s s where the first equality follows from A.69, the second from the fact that Ψ is an equilibrium A.11

and the third from A.62 and A.71 together with the fact that with ρ = 1, we have P˜ s VP = Ps W˜ s VP = (1−ςs p) = 1+δ w.p. 1. Notice that the permanent effect on consumer price inflation is Ws (1−ς˜s p) need to ensure that Λ ˜VP = Λ ˜VP state by state, as can be seen by 28. t,s t,s With flexible wages, optimal labor supply is also satisfied since real wages are unaffected: (cid:2) n˜VP (i) (cid:3)η γ w¯ VP (i) [n (i)]η γ w¯ (i) t n − (cid:101)t = t n − t = 0 C ˜VP−σ (γ −1) P ˜VP C−σ (γ −1) P t n t t n t Morevoer, since the transition from s ∈ S to s ∈ SVP is unanticipated, the different t−1 t inflation dynamic ex post does not affect optimal bond holdings ex ante. On the other hand since the policy is permanent, future inflation is unaffected by its implementation as is clear from (A.70)■ A.4 Proof of Proposition 2 Westartbygivingadefinitionofapermanentunexpectedappreciationofthenominalexchange rate. Definition 4. Assume that s is governed by {S,Ω} from t = 0,...,t∗. A currency devaluation t of size δ is described by {GPϵ,Ωϵ,σϵ} with GPϵ = S ∪Sϵ where the new set of states is δ  (cid:12)   (cid:12) ϵ˜¯ = 1+δ   (cid:12)   ϵ¯   (cid:12)  Sϵ = s˜= (τm,ςx,τv,ςp,ϵ˜¯,τm∗,ςx∗)(cid:12) , (cid:12)  (cid:12)      (cid:12) ∃s = (τm,ςx,τv,ςp,ϵ¯,τm∗,ςx∗) ∈ S   (cid:12) the transition matrix is   (1−πϵ)Ω πϵΩ Ωϵ =   (1−ρ)Ω ρΩ and the function describing the unanticipated transition to VP is given by σϵ(s) = (τm,ςx,τv,ςp,ϵ˜¯,τm∗,ςx∗) δ s.t. (A.73) ϵ˜¯ = 1+δ. ϵ¯ Proposition 2. In a fixed exchange rate regime (φ = ∞), under assumptions 1.- 3. of Propo- ε A.12

sition 1, an IX policy of size δ has the same allocative effects as a once-and-for-all unexpected currency devaluation of size δ. A VP policy of the same size δ has no effect on the allocation 1+δ but causes the real exchange rate to appreciate by δ. Proof. The fact that VP is still neutral even under fixed exchange rates is a straightforward consequence of the proof of Proposition 2. Since under flexible exchange rates VP is neutral and the nominal exchang rate is unaffected by its implementation, it follows that even if monetary policy targets a given fixed exchange rate the policy still remains neutral. Turning to the equivalence between a currency devaluation and IX, let {µϵ} be a set t≥0 quence of functions that map histories in which IX is implemented into histories in which a currnecy devaluation is implemented instead: i.e. ∀s˜t = (s˜ ,...,s˜) ∈ (cid:0) GPIX (cid:1)t+1 , µϵ(s˜t) = st = 0 t t (s ,...,s ) ∈ (GPϵ)t+1 where ∀i ≥ 1 0 t   s˜ if s˜ ∈ S i i s = i  σε (cid:16) (cid:0) σIX (cid:1)−1 (s˜) (cid:17) if s˜ ∈ SIX δ δ i i where σIX is as defined in A.60 and σϵ is as defined in A.73. δ δ Let {Ψε(st)} denote an equilibrium process under {GPε,Ωε,σϵ} and consider now st∈(ST)t,t≥0 δ (cid:110) (cid:111) the process Ψ ˜IX (st) with an unanticipated permanent IX such that, for each st∈(GPIX)t,t≥0 element κ˜IX of Ψ ˜IX, apart from the nominal exchange rate, we have κ˜IX (cid:0) s˜t (cid:1) = κε (cid:0) µε (cid:0) s˜t (cid:1)(cid:1) ∀s˜t ∈ (cid:0) GPIX (cid:1)t , ∀t ≥ 0 (A.74) t where κε is the corresponding element of the equilibrium process Ψε. The exchange rate satisfies ∀s˜t = (s˜ ,....,s˜) ∈ (cid:0) GPIX (cid:1)t 1 t   εε if s˜ ∈ S ε˜IX = t t (A.75) t  εε t if s˜ ∈ SIX 1+δ t (cid:110) (cid:111) To show that Ψ ˜IX (st) is an equilibrium we can follow the same steps as in the st∈(GPIX)t,t≥0 proof Proposition 1. At s˜t = (s˜ ,....,s˜) ∈ (cid:0) GPIX (cid:1)t such that s˜ ∈ SIX, the laws of one price and the balance of 1 t t A.13

payment equilibrium equations are satisfied since ε˜ϵ (1+σ˜x) (1+τ˜m) t = t = t ε˜IX (1+σx) (1+τm) t t t and the only other equations in which the exchange rate appears only depend on its expected appreciation which is the same in the two processes.■ A.5 Reversal of IX policies and retaliation We have asserted that the IX policy with reversal considered in the text has very similar effects to an IX policy subject to possible retaliation, meaning in the latter case that agents expect that the foreign government may retaliate in kind sometime in the future. Here we make this argument formally. First we introduce a new variable, TI, that measures international transfers from the foreign t to the home country. The introduction of these transfers allows us to measure the distance between the allocations under reversal and under retaliation in a very simple way. The only equilibrium equation that is modified by the introduction of this transfer is the balance of payment equation A.56 which becomes B∗ B∗ P (cid:20) (1+ςx) P∗ (cid:21) B − Ht = B R∗ − Ht−1R + Pt Y∗ − t ε PtY +TI. (A.76) Ft ε Ft−1 t−1 ε t−1 (1+ςx)ε Ht (1+ςx∗) t P Ft t t t t t t Pt (cid:8) (cid:9) Consider an IX policy subject to policy reversal and characterized by ST,ΩT where (cid:8) (cid:9) (cid:0) (cid:1) (cid:0) (cid:1) ST = sNT,sIX . In state sNT no country levies any taxes and in the second state sIX the home country unilaterally raises import tariffs and export subsidies by the same amount δ. The transition matrix is   1 0 ΩT =   (A.77) 1−ρ ρ (cid:8) (cid:9) Consider also an IX policy that triggers retaliation and characterized by SR,ΩR , where (cid:8) (cid:9) SR = ST,sTW . ST includes the same two states as described above but in sTW the foreign country retaliates with a symmetric policy ( i.e. τm = ςx = τm∗ = ςx∗ = δ). In this case the t t t t A.14

transition probability matrix is:   1 0 0   ΩR =  (1−π)(1−ρ) ρ π(1−ρ)  (A.78)     1−φ 0 φ Lemma 1 If export prices are set in producer currency, a unilateral implementation of IX (cid:8) (cid:9) with policy reversal, i.e. s governed by ST,ΩT , implements the same equilibrium allocation t (cid:8) (cid:9) as a unilateral implementation of IX that triggers retaliation, i.e. s governed by SR,ΩR , t coupled with international transfers that satisfy: δ (cid:2) (cid:3) TI = − B R∗ ε +B R t1 1+δ F,t1−1 t1−1 t1 H,t1−1 t1−1 (cid:20) (cid:21) R TI = δ B R∗ ε +B t2−1 t2 F,t2−1 t2−1 t2 H,t2−1 π t2 where t is the first time the economy transits to the retaliation state sTW and t > t is the 1 2 1 first time it leaves the retaliation state sTW. The intuition of this lemma can be easily understood by considering the special case of a permanent transition to a trade war regime starting from balanced trade. In this case, TI = 0 t1 and TI never occurs so that Lemma 1 implies that the effects of starting a trade war are t2 identical to the effects of abolishing all tariffs and subsidies in both countries. The reason can be easily understood by inspecting equation (A.43a),where export subsidies in the foreign country exactly offset import tariffs in the home country, and, symmetrically, equation (A.42a). When the home country has a positive net foreign asset position, however, a transition to a trade war regime will not be equivalent to a transition to a state with no taxes. Given that a positive net foreign asset position implies that the home country is expected to run trade deficits in the future, import tariff revenues will exceed export subsidy expenditures, implying a positive wealth effect and an associated appreciation of the home currency. Symmetrically, the foreigneconomywillsufferwealthlossesfromitsimplementationofIX.Consequently, atransfer of resources that corrects this international wealth redistribution is needed to implement the same allocation under policy reversal and retaliation. Under our assumption of balanced trade in the long run, however, the economic effects of these transfers are of second order. A.15

Proof. Let {Ψ(st)} be an equilibrium with no international transfers and no st∈(ST)t,t≥0 retaliation, i.e. TI (st) = 0 ∀st ∈ (cid:0) ST (cid:1)t . (cid:110) (cid:111) Consider now the process Ψ ˜ (st) such that, for each element κ˜ of Ψ ˜ , other than st∈(SR)t,t≥0 bond holdings and local currency producer prices of exports, we have κ˜ (cid:0) st (cid:1) = κ (cid:0) µ (cid:0) st (cid:1)(cid:1) ∀st ∈ (cid:0) SR (cid:1)t , ∀t ≥ 0 (A.79) t where κ is the corresponding element of the equilibrium process Ψ without trade wars and function µ maps all histories in which a trade war occurs into a history in which no taxes are t levied: that is ∀st = (s ,...,s ) ∈ (cid:0) SR (cid:1)t , µ (st) = s˜t = (s˜ ,...,s˜) ∈ (cid:0) ST (cid:1)t where ∀i ≥ 1 1 t t 1 t   s if s ̸= sTW i i s˜ = . i  sNT if s = sTW i For ease of notation in what follows, for any st = (s ,....,s ) ∈ (cid:0) SR (cid:1)t , we let κ˜ = κ˜(st) and 1 t t κ = κ(µ(st)). t Bondholdingsandlocalcurrencyproducerpricesofexportssatisfy∀st = (s ,....,s ) ∈ (cid:0) SR (cid:1)t 1 t   1 if s ̸= sTW B ˜ B ˜    t F,t H,t = = (A.80) B B F,t H,t     1 if s = sTW 1+δ t   1 if s ̸= sTW P ˜ P ˜∗    t X∗t = Xt = (A.81) P P∗ X∗t Xt     1 if s = sTW 1+δ t (cid:110) (cid:111) We want to show that Ψ ˜ (st) is an equilibrium when international transfers satisfy st∈(SR)t,t≥0    0 if s t−1 ̸= sTW and s t ̸= sTW         (cid:104) (cid:105) T ˜I (cid:0) st (cid:1) = − δ B ˜ R ˜∗ ε˜ +B ˜ R ˜ if s ̸= sTW and s = sTW . (A.82) 1+δ F,t−1 t−1 t H,t−1 t−1 t−1 t         (cid:104) (cid:105)   δ B ˜ R ˜∗ ε˜ +B ˜ R ˜ if s = sTW and s ̸= sTW 1+δ F,t−1 t−1 t H,t−1 t−1 t−1 t A.16

˜ It is straightforward to check that if Ψ is an equilibrium then Ψ satisfies all equilibrium t t equations other than (A.56). When s = sTW the only conditions that need to be checked are t the laws of one price (A.42a) − (A.43a) and the tax pass-through equations (A.37) − (A.36) which are satisfied under (A.81). All the other equations are clearly satisfied by construction of ˜ Ψ, and by the fact that the probability of leaving the unilateral IX state is the same in (A.77) and (A.78). Consider now the balance of payment equilibrium (A.56) which we rewrite as follows A ˜ = A ˜ r˜a +NX ˜ +T ˜I t t−1 t t t where ˜ ˜ ˜ A = B ε˜ +B t−1 F,t−1 t−1 ht−1 (cid:104) (cid:105) B ˜ R ˜∗ ε˜ +B ˜ R ˜ F,t−1 t−1 t ht−1 t−1 ra = t ˜ A t−1 P∗ s∗ (1−τv)P NX ˜ = ε Ht Y∗ − t Ft Y t t 1+τm∗ s Ht (1+τm) Ft t t Take any history s˜∞ = (s˜ ,...,s˜,...) ∈ (cid:0) SR (cid:1)∞ such that s = sTW ∃i. Let t and t satisfy 1 t i 1 2 s = sTW, s ̸= sTW,s ̸= sTW,s = sTW. At t we have t1 t1−1 t2 t2−1 1 A A ˜ = t1 (A.83) t1 1+δ A ra +NX = t1−1 t1 t1 1+δ NX δ = A ra + t1 − A ra t1−1 t1 1+δ 1+δ t1−1 t1 = A ˜ r˜a +NX ˜ +T ˜I t1−1 t1 t1 t1 where, the first follows from (A.80) given s = sTW; the second from the fact that Ψ is an t1 equilibrium; and the last follows from the fact that (A.80) imply A ra = A ˜ r˜a given t1−1 t1 t1−1 t1 s ̸= sTW together with the fact that s = sTW implies NX ˜ = NXt1 and that T ˜I is given t1−1 t1 t1 1+δ t1 by (A.82). A.17

As long as the trade war is in place (A.80) readily imply that ∀s and t < s < t 1 2 A ˜ s A = (A.84) s 1+δ = A ˜ r˜a +NX ˜ s−1 s s And when it ends, at t , we have 2 ˜ A = A (A.85) t2 t2 = A ra +NX t2−1 t2 t2 A ra δ = t2−1 t2 +NX + A ra 1+δ t2 1+δ t2−1 t2 = A ˜ r˜a +NX ˜ +T ˜I t2−1 t2 t2 t2 where we are using again (A.80) as in (A.83). A.6 Anticipation Effects of IX WhilewehaveshownthatIXpoliciesmayboostoutputiftheirimplementationisasurprise, the anticipation that such policies may be implemented sometime in the future can have immediate contractionary effects. The importance of anticipation effects was recognized by Krugman (1982) in a setting in which agents were certain about the future implementation date, but is useful to revisit in our Markov-switching framework given that it provides a convenient way of capturing uncertainty about the implementation date. In this vein, Figure A.1 shows the response of the economy when agents learn that IX policies will be introduced in the future, but are unsure about the timing. Specifically, as long as IX policies are not implemented, agents believe that there is a 10 percent chance that IX policies will be implemented in the subsequent period (i.e., a = 0.10 ), and that – once implemented – the policies will not be reversed (ρ = 1.0). The anticipation effects of IX policies work through an exchange rate channel: The expectation that the exchange rate must appreciate in the long-run causes the exchange rate to appreciate in the near-term, when agents first come to believe that IX policies will eventually be implemented (first panel). The stronger currency leads to a decline in competitiveness for domestic firms, a drop in exports, and an output contraction. A.18

A.7 Trade in home currency bonds The neutrality result presented in Proposition 1 requires the strong condition that asset market incompleteness takes the form of no international trade in home currency denominated bonds. To understand the role of this restriction, note that the implementation of IX induces changes in two different components of households wealth. First, the IX policy generates fiscal revenues whenever the home country has a trade deficit since in this case revenues from tariffs exceed subsidies to exporters. The wealth increase associated with a permanent IX policy of size δ, GF (δ), is then given by the present discounted value of the fiscal revenues it generates t (cid:32) (cid:33) (cid:88) (cid:89) i π∗ δ (cid:18) P P∗ (cid:19) GF (δ) = E t,t+j Ft+i Y −Q (0) Ht+iY∗ t t R∗ 1+δ P Ft+i t+i P∗ Ht+i i≥0 j=1 t+j t+j t+j δ (cid:20) B R∗ B∗ R (cid:21) = Q (0) Ft−1 t−1 − Ht−1 t−1 (A.86) 1+δ t P∗ π∗ P π t−1 t t−1 t where the second equality uses the fact that in equilibrium the present discounted value of future trade deficits is equal to the net foreign asset position of the home country, that is, (cid:104) (cid:105) the difference between home country holdings of foreign bonds Q (0) BFt−1 R t ∗ −1 and foreign t P∗ π∗ (cid:104) (cid:105) t−1 t country holdings of home bonds B H ∗ t−1Rt−1 . Pt−1 πt Second, the exchange rate appreciation decreases the value of home holdings of foreign bonds. Denote with LB(δ) the losses on foreign bond holdings under an appreciation of size δ, t then B R∗ δ B R∗ LB(δ) = [Q (δ)−Q (0)] Ft−1 t−1 = − Q (0) Ft−1 t−1 (A.87) t t t P∗ π∗ 1+δ t P∗ π∗ t−1 t t−1 t Equations (A.86) and (A.87) imply: δ B∗ R LB(δ) = GF (δ)+ Ht−1 t−1 . (A.88) t t 1+δ P π t−1 t Expression (A.88) summarizes the wealth effects associated with IX policies. When there is no international trading of bonds denominated in home currency (B∗ = 0), as required in Ht Proposition1, wealthgainsthroughhigherfiscalrevenuesGF (δ)areexactlyoffsetbythewealth t losses induced by lower valuations of foreign holdings LB(δ), thus preserving neutrality of IX t (cid:0) (cid:1) policies. In contrast, when the home country borrows in home currency bonds B∗ > 0 Ht−1 and invests in foreign currency bonds (B > 0), it acquires a leveraged exposure to foreign Ft−1 A.19

exchange variations and the sensitivity of wealth in the home country to an exchange rate appreciation is bigger than its net foreign asset position. Consequently, given an unchanged pathforfuturetradedeficits,anexchangerateappreciationofthesamesizeofthepolicyreduces wealth in the home country as the increase in fiscal revenues is not large enough to offset the capital losses on foreign bonds holdings implied by equation (A.88). These wealth losses induce households to reduce their savings and, in equilibrium, the exchange rate appreciates less while the trade balance increases. Figure A.2 shows the response of the economy to a permanent unilateral IX policy when the home country has a leveraged exposure to exchange rate fluctuations. In particular, this experiment assumes that in the initial state international trade is balanced but countries hold off- (cid:0) (cid:1) setting positions in domestic and foreign currency denominated bonds i.e. B = B∗ > 0 F−1 H−1 scaledtobetwiceaslargeasthevalueofannualGDP.Asanticipatedinourpreviousdiscussion, when foreign holdings of home currency denominated bonds are positive the implementation of a permanent IX lowers households wealth, consumption, and savings, thus dampening the appreciation of the exchange rate (solid lines). As a result, the home country runs a permanently positive trade balance to pay interest on its negative net foreign asset position. For comparison, we also plot the response of the baseline economy when there is no international trade in domestic currency bonds, as required in Proposition 1, and a permanent IX policy is neutral (dashed lines). A.8 Departing from Producer’s Currency Pricing We conclude this section with a brief discussion on the requirement of producer’s currency pricing (PCP) in Proposition 1 to deliver neutrality of IX policies. We follow the literature and compare the transmission of policies under PCP, local currency pricing (LCP), and dominant currency pricing (DCP).49 Figure A.3 compares the effects of an IX policy under PCP (dotted lines), LCP (solid lines), and DCP (dashed lines), assuming that all other conditions in Proposition 1 are satisfied. As discussed before, under PCP international relative prices are insulated by the immediate appreciation of the exchange rate and the allocation is unaffected. In contrast, when foreign 49For a discussion of transmission under PCP and LCP see, for instance, Devereux and Engel (2002). In our two-country model, under DCP the home country adopts PCP and the foreign country adopts LCP. A.20

exporters prices are sticky in the currency of the home country the IX policy has allocative effects: Imports contract, inflation jumps, and output experiences a very small boost. The source of non-neutrality, both for LCP and DCP, is the asymmetric pass-through of tariff changes and exchange rate movements to import prices. As shown by the expression for the price of imported goods in the home country P = (1+τm)P (A.89) Ft t X t ∗ changes in import tariffs are fully passed through to import prices (P ) whereas movements Ft in the exchange rate only pass-through gradually as foreign exporters adjust their prices in (cid:0) (cid:1) the home market P infrequently under our Calvo pricing assumption. Hence, the rise in X∗ t import prices reduces the demand for imported varieties and boosts output through importsubstitution channels. The effects under DCP are nearly identical to the effects under LCP. The only difference is that with full exchange rate pass-through, home exports become more expensive causing exports to contract sligthly and, accordingly, output to expand less. A.9 Government Expenditure in Germany in 2007 Our key assumption in the quantitative analysis of section 5.4 is that the VP is responsible for the differential macroeconomic behavior of Germany with respect to other euro-area countries over the 2006Q3-2007Q4 period. A possible objection to this assumption is that government expendituregrewlessinGermanyduringthisperiodthanintherestofEurope. Hereweaddress this point by showing that the quantitative relevance of government expenditure dynamics in this period appears to be in fact negligible. To calibrate the size of government shocks we assume that government expenditure is constant in the Euro area and in Germany it follows an AR(1) process given by: g = ρgg +εg (A.90) t t−1 t Given the observed behavior of government expenditure in the euro area and in Germany, we can use equation (A.90) to back out a time series for government expenditure shocks, under the assumption that ρg = .95. FigureA.4comparesourbaselinemodelresponsestothemodelresponseswheregovernment A.21

shocks are added on top of our VP shocks. Overall, this experiment suggests that the observed pattern of government expenditure in Germany did not have a material impact on the German economy. A.10 Data Sources and Calculation for the Quantitative Section ”2007 Fiscal Devaluation In Germany” Macroeconomic data for Germany and the euro area (EA) are from Haver (EU and Germany Database). Mnemonics and details about the construction of the series are provided below. Germany. Consumption is real private final consumption (J134PCT) and investment is real gross fixed capital formation (J134IFT). Net exports to the euro area are the difference between nominal goods exports to the euro area (DESIXEZ) and nominal goods imports form the euro area (DESIMEZ). We construct real GDP as the sum of nominal private consumption (J134PCN) divided by the consumption deflator (J134PCP), nominal gross fixed capital formation (J134IFN) divided by its deflator (J134IFP), plus nominal exports to the euro area (DESIXEZ) divided by the export deflator (J134EXPP) minus nominal import from the euro area (DESIMEZ) divided by the import deflator (J134IMPP). Consumer price inflation is the four-quarter change in the price level of the core HICP series, which excludes energy, food, alcohol, and tobacco (H134HOEF). Wage inflation is the four-quarter change in the series “Total Labor Cost” (S134LTBN). Labor input is total hours worked from the National Accounts (DEBNHT). EA ex-Germany. Variables are constructed by subtracting the nominal German counterparts from the EA nominal data and then deflating the resulting series using the adjusted NIPA deflators. Specifically, consumption is EA nominal private final consumption (J025PCN) less Germany’s nominal private final consumption (J134PCN) divided by the EA ex-Germany consumption deflator. Investment is EA nominal gross fixed capital formation (J025IFN) less Germany’s nominal gross fixed capital formation (J134IFT) divided by the EA ex-Germany investment deflator (J025IFP). Real GDP is consumption plus investment less Germany’s real net exports to the euro area. The inflation series is the four-quarter change in the price level of the EA ex-Germany core HICP series, which excludes energy, food, alcohol, and tobacco (H023HOEF), and the corresponding series for Germany. We use the HICP weights of Ger- A.22

many in total EA HICP (P134BE11) to construct the EA ex-Germany series. Wage inflation constructed as the (weighted) difference between the four-quarter change in the series “EA: Total Labor Cost” (S025 LTBN) and the corresponding series for Germany. We use the HICP weights of Germany in total EA HICP (P134BE11) to construct the EA ex-Germany series. Labor input is total hours worked from the National Accounts (J025OETE). Fiscal data. Data on social security contributions are from the OECD Tax - Tax Wedge Database obtained through Haver (OECD Government Statistics Database). Data for Germany refer to the average social security tax rate as a percent of total labor costs for workers with income equal to the average wage and include both employer (A132ME2) and employee (A132MS2) taxes. The aggregate for the EA ex-Germany is constructed as a GDP-weighted averagetheaveragesocialsecuritytaxratesofBelgium(A124ME2,A124MS2),France(A132ME2, A132MS2), Italy (A134ME2, A134MS2), the Netherlands (A138ME2, A138MS2), and Spain (A184ME2, A184MS2). DataonVATtaxratesrefertothestandardVATrateforGermanyand for the EA ex-Germany as in European Commission (2019), “VAT rates applied in the member States of the European Union”. On a GDP basis, the countries of Belgium, France, Italy, the Netherlands, and Spain altogether account for about 85 percent of the EA ex-Germany region. A.23

Figure A.1: Macroeconomic Effects of an Anticipated Permanent IX Nominal Exchange Rate Imports Exports Nominal Wage 15 10 5 2 S S S S8 S S S S 1 m10 m6 m 0 m0 o rf o rf 4 o rf o rf -1 % 5 % 2 % -5 % - - 3 2 0 0 -10 -4 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Home Inflation Home Policy Rate Home Consumption Home Output )q 4 ( S S m o tc r p f - - 1 0 - . . 0 1 5 5 .r.a S S m o tc r p f - 0 0 . . 0 5 5 S S m o % rf 0 1 . . 1 2 5 5 S S m o % rf - 0 0 . . 0 5 5 -2 -1 0 -1 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Foreign Inflation Foreign Policy Rate Foreign Consumption Foreign Output )q 4 2 .r.a 1 1 1 ( S S m o rf - 0 1 1 S S m o rf 0. 0 5 S S m o rf - - 0 2 1 S S m o rf - - 0 2 1 tc p - - 3 2 tc p -0 - . 1 5 % - - 4 3 % - - 4 3 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Quarters Quarters Quarters Quarters Anticipated Permanenent IX Unanticipated Permanent IX A.24

Figure A.2: Permanent IX with Foreign Holdings of Home Currency Bonds Nominal Exchange Rate Imports Exports Nominal Wage 15 5 5 2 S S S S1 S S S S m10 m m m0 o rf o rf 0 o rf 0 o rf -1 % 5 % % % -2 -3 0 -5 -5 -4 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Home Inflation Home Policy Rate Home Consumption Home Output )q 4 ( S S m o tc r p f - 0 0 . . 0 1 5 5 .r.a S S m o tc r p f - 0 0 . . 0 5 5 S S m o % rf - 0 0 . . 0 1 5 5 S S m o % rf - 0 0 . . 0 1 5 5 -1 -1 -1 -1 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Foreign Inflation Foreign Policy Rate Foreign Consumption Foreign Output )q 4 2 .r.a 1 1 1 ( S S m o rf - 0 1 1 S S m o rf 0. 0 5 S S m o rf - - 0 2 1 S S m o rf - - 0 2 1 tc p - - 3 2 tc p -0 - . 1 5 % - - 4 3 % - - 4 3 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Quarters Quarters Quarters Quarters B* =2 times Annual GDP B =0 Note: In both experiments we assume that prices are sticky, wages are flexible, and the exchange rate is flexible. The solid line shows the case in which, in the initial state, the home country has offsetting bond holdings in domestic and foreign currency equal to two times annual GDP. The dashed line is the case in which countries hold no bonds in the initial state. The figure shows the (expected) path of each variable after the policy is implemented and given that it is (expected to be) permanent. A.25

Figure A.3: Permanent IX: LCP, DCP and PCP Nominal Exchange Rate Imports Exports Nominal Wage 15 5 5 2 1 0 0 S S10 S S S S S S0 m m m m o rf o rf -5 o rf -5 o rf -1 %5 % % %-2 -10 -10 -3 0 -15 -15 -4 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Home Inflation Home Policy Rate Home Consumption Home Output 2 1 1 1 0.8 0.8 1.5 0.5 )q 4 ( S S m o tc r p f 0. 0 1 5 .r.a S S m o tc r p f - - - 0 0 0 0 0 0 . . . . . . 0 2 4 6 6 4 2 S S m o % rf -0 - . 0 1 5 S S m o % rf - - - 0 0 0 0 0 0 . . . . . . 0 2 4 6 6 4 2 -0.5 -1.5 -0.8 -0.8 -1 -1 -2 -1 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 LCP DCP PCP Note: In all the experiments we assume that prices are sticky, wages are flexible, and the exchange rate is flexible. The solid line shows the case in which both domestic and foreign exporters adopt LCP. The dashed line shows the case in which domestic exporters adopt PCP and foreign exporters adopt LCP. The dotted line shows the case in which both foreign and domestic exporters adopt PCP. The figure shows the (expected) path of each variable after the policy is implemented and given that it is (expected to be) permanent. A.26

Figure A.4: VP with and without Government Expenditure Shocks VAT taxes Payroll subsidies Government Expenditure 1.5 1.5 1 = g - .95 * g 0.5 t t-1 1 1 0 -0.5 0.5 0.5 -1 0 0 -1.5 Net Exports to EA Consumption Investment 2 2 5.5 1 5 0 0 4.5 -1 -2 -2 4 -3 -4 3.5 Hours GDP (including G) GDP (G fixed) 2 2 2 1 1 1 0 0 0 -1 -1 -1 -2 -2 -2 -3 -3 -3 Q3 Q4 Q1 Q2 Q3 Q4 Q3 Q4 Q1 Q2 Q3 Q4 Q3 Q4 Q1 Q2 Q3 Q4 2006 2006 2007 2007 2007 2007 2006 2006 2007 2007 2007 2007 2006 2006 2007 2007 2007 2007 Note: The data line (black crossed) and the baseline (blue solid) are as in figure 7. The dashed blue line includes the effects of government spending shocks. All experiments assume µ=µ∗ and ρ=ρ∗. A.27