The Macroeconomic Effects of Trade Policy

K.7 The Macroeconomic Effects of Trade Policy Erceg, Christopher, Andrea Prestipino, and Andrea Raffo Please cite paper as: Erceg, Christopher, Andrea Prestipino, and Andrea Raffo (2018). The Macroeconomic Effects of Trade Policy. International Finance Discussion Papers 1242. https://doi.org/10.17016/IFDP.2018.1242 International Finance Discussion Papers Board of Governors of the Federal Reserve System Number 1242 December 2018

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 1242 December 2018 The Macroeconomic Effects of Trade Policy Christopher Erceg, Andrea Prestipino, and Andrea Raffo NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. 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.

The Macroeconomic E⁄ects of Trade Policy (cid:3) Christopher Erceg Andrea Prestipino Andrea Ra⁄o Federal Reserve Board Federal Reserve Board Federal Reserve Board First version: March 20, 2017. This version: October 1, 2018 Abstract Westudytheshort-runmacroeconomice⁄ectsoftradepoliciesthatareequivalentinafrictionless economy, namely a uniform increase in import tari⁄s and export subsidies (IX), an increase in value-added taxes accompanied by a payroll tax reduction (VP), and a border adjustment of corporate pro(cid:133)t taxes (BAT). Using a dynamic New Keynesian open-economy framework, we summarize conditions for exact neutrality and equivalence of these policies. Neutrality requires therealexchangeratetoappreciateenoughtofullyo⁄setthee⁄ectsofthepoliciesonnetexports. Wearguethatacombinationofhigherimporttari⁄sandexportsubsidiesislikelytotriggeronly a partial exchange rate o⁄set and thus boosts net exports and output (with the output stimulus largely due to the subsidies). Under full pass-through of taxes, IX and BAT are equivalent but VP is not. We show that a temporary VP can increase intertemporal prices enough to depress aggregate demand and output, even when wages are sticky. These contractionary e⁄ects are especially pronounced under (cid:133)xed exchange rates. JEL classi(cid:133)cation: E32, F30, H22 Keywords: Trade Policy, Fiscal Policy, Exchange Rates, Fiscal Devaluation 1 Introduction There is a longstanding debate about how trade policies can stimulate the macroeconomy. In considering di⁄erent ways of alleviating a deep economic recession within the con(cid:133)nes of the gold standard, Keynes (1931) argued that the U.K. could derive a similar degree of stimulus from raising import tari⁄s and providing export subsidies as through devaluing the pound against gold.1More recently, We thank our discussants Ralph Ossa, Matteo Cacciatore, Nora Traum, Fiorella Di Pace, and Emmanuel Farhi (cid:3) for very insightful comments as well as seminar participants at the Federal Reserve Board, Federal Reserve Banks of Boston and Philadelphia, Macroeconomic Meetings of the Federal Reserve System, XXIX Villa Mondragone International Economic Seminar, NBER Summer Institute, ITAM-PENN Macroeconomic Meetings, Melbourne Institute MacroeconomicPolicyMeetings,theCEBRA-BOEIFMAnnualMeeting,theNBERIFMFallMeetings,theEuropean CentralBank,theXXIn(cid:135)ationTargetingConferenceoftheCentralBankofBrazil,andtheSEDMeetings. Theviews in this paper are solely the responsibility of the authors and should not be interpreted as re(cid:135)ecting the views of the BoardofGovernorsoftheFederalReserveSystemorofanyotherpersonassociatedwiththeFederalReserveSystem. 1Eichengreen (1981) provides a detailed account ofthe contentious politicaldebate that preceded the United Kingdom(cid:146)s shift towards protectionist trade policies in the early 1930s. 1

there has been renewed interest in the question of how countries constrained by membership in a currency union can implement tax policies with economic e⁄ects akin to a currency depreciation (e.g. Calmfors 1998 and Farhi, Gopinath, and Itskhoki 2014). The approach of cutting payroll taxes to lowerdomesticrelativetoforeignprices,andthusboostexternalcompetitiveness,hasstrongintuitive appeal. In this vein, a number of countries have reduced payroll taxes and (cid:133)nanced these cuts with VAT increases. However, even if these policies can provide stimulus under (cid:133)xed exchange rates, it is unclear to what extent they would do so under (cid:135)exible exchange rates. Mundell (1961) questioned whether the mercantilist prescription of higher import tari⁄s and export subsidies would stimulate demand in economies with (cid:135)oating exchange rates, as (cid:147)equilibrium in the balance of payments is automatically maintained by variations in the price of foreign exchange(cid:148). Similarly, Feldstein (2017) and Auerbach, Devereux,Keen,andVella(2017)havearguedthataborderadjustmentofcorporatetaxation that (cid:0) in e⁄ect taxes imports and subsidies exports would not a⁄ect the trade balance provided that the (cid:0) nominal exchange rate was free to adjust. Inthispaper,weexaminetheshort-runmacroeconomice⁄ectsofthreealternativepoliciesthatare equivalentinafrictionlesseconomy, namelyauniformincreaseinimporttari⁄sandexportsubsidies, a reduction in employer payroll taxes (cid:133)nanced by an increase in VAT rates, and a border adjustment of corporate pro(cid:133)t taxation. To do so, we use a New Keynesian open-economy framework that builds on contributions by Gal(cid:236) and Monacelli (2005) and Corsetti, Dedola, and Leduc (2010). We analyze the extent to which these three policies elicit equivalent macroeconomic e⁄ects under both (cid:135)exible (cid:0) and (cid:133)xed exchange rates as well as their e¢ cacy in providing cyclical stimulus. (cid:0) The (cid:133)rst key (cid:133)nding of our analysis is that the combination of import tari⁄s and export subsidies (IX henceforth) induces expenditure-switching towards domestic goods that tend to boost domestic output and in(cid:135)ation even under (cid:135)exible exchange rates. While IX policies clearly stimulate demand under (cid:133)xed exchange rates (cid:150)as hypothesized by Keynes and corroborated by Farhi, Gopinath, and Itskhoki(2014)(cid:150)our(cid:133)ndingthatthesepoliciesarestimulativeunder(cid:135)exibleexchangeratescontrasts sharply with the conventional view, in which the exchange rate appreciates enough to fully o⁄set any allocative e⁄ects of import tari⁄s and export subsidies on the domestic economy.2 We lay out the conditions under which the conventional view holds and IX policies are (cid:147)neutral,(cid:148) 2See,forinstance,the orginalcontribution by Lerner(1936) and,more recently,Costinot and Werning (2017). 2

i.e., havenoallocativee⁄ects, andarguethattheseconditionsappearextremelyrestrictiveandhence unlikely to hold in practice. Crucially, the neutrality of IX policies hinges on the expectation that the real exchange rate will appreciate permanently, re(cid:135)ecting the public(cid:146)s belief that trade actions will remain in place forever and not induce foreign retaliation (even in the long run). 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;3 alternatively, they may result from an electoral shift towards a political party more supportive of free trade.4 Moreover, although some trade policy legislation has been enacted with the expectation that it will remain in e⁄ect for a long time as in the Great (cid:0) Depression the tari⁄wars that ensued during the 1930s (especially in response to Smoot-Hawley) (cid:0) serve to underscore the high likelihood of foreign retaliation under such circumstances. Given this motivation, we use a Markov-switching framework to consider two mechanisms that cause the exchange rate to revert to its initial level in the long-run: (cid:133)rst, an eventual abandonment of the policy; and second, retaliation by foreign countries.5 In both cases, we (cid:133)nd that the policy boosts output so long as the unilateral actions remain in e⁄ect (that is, before the foreign retaliation occurs). Intuitively,whentheexchangerateisexpectedtoeventuallyreverttoitspre-shocklevel,the immediate appreciation of the currency falls short of completely o⁄setting the expenditure-switching e⁄ects of the policy on imports and exports. While the expectation that the policy will be reversed raises the relative price of current consumption since tari⁄s are expected to decline the resulting (cid:0) (cid:0) fall in consumption due to this intertemporal substitution channel is swamped by the boost to net exports, so that output expands. As a matter of fact, a key insight of our paper is that the output stimulus of unexpected IX policies is largely driven by the export subsidy whereas tari⁄s, depending 3 In this vein, Irwin (2013) discusses how President Nixon favored the imposition of a 10 percent across-the-board tari⁄ in 1971 partly to enhance his electoral prospects in the 1972 election, as well as to put pressure on foreign tradingpartnerstorevaluetheirexchangerates. Asitturnedout,thetari⁄swereliftedfairlyquicklywhentheforeign policy objectives were viewed as largely achieved, as well as from pressure coming even from some members of the Administration. 4For example, in the U.S. experience, President Wilson, a free-trade Democrat, strongly supported the passage of the Underwood Tari⁄ Act of 1913 which scaled back the high tari⁄s that had prevailed under previous Republican Administrations (see Irwin 2017). 5In standard DSGE models,expectationsabouthow tradepolicy willbesetin thedistantfuture(cid:150)by a⁄ectingthe exchange rate that must prevail in the long-run to satisfy intertemporal trade balance (cid:150)can exert powerful e⁄ects on the exchange rate today. However, such implications rest on the doubtful premise that agents have a high degree of con(cid:133)dence about the stance ofpolicy farin the future. 3

on parameter values, have a negligible or even contractionary e⁄ect on output.6;7 We then turn our attention to the analysis of a reduction in payroll taxes (cid:133)nanced by an increase in VAT (VP policy), an alternative tax policy that is often considered either equivalent or a close substitutetoIX.SomeEuropeangovernmentshaveattemptedtoprovidemacroeconomicstimulusby implementing such "(cid:133)scal devaluations", including the governments of Denmark in 1988, Sweden in 1993,Germanyin2007,andPortugalinthecontextofthe2011-2014EU-IMFEconomicStabilization Program.8 Our second key (cid:133)nding is that, in general, the e⁄ects of IX policies diverge markedly from VP, evenqualitatively. Toillustratethedi⁄erentgeneralequilibriumresponsetothesepoliciesitishelpful to consider the same conditions under which IX is neutral namely, when policies are implemented (cid:0) permanentlyandexchangeratesare(cid:135)exible. Inthiscase,neutralityofIXoccursthroughanimmediate jumpintheexchangeratewhichensuresthatthepriceofimportedgoodsremainsunchangedrelative todomestically-producedgoods;nochangeinfactorprices,includingthewage,isrequired. WhileVP alsoturnsouttobeneutral(cid:150)atleastifwagesare(cid:135)exible(cid:150)astrikingdi⁄erenceisthatnoadjustment intheexchangerateisrequiredtokeeptherelativepriceoftradedgoodsconstant,re(cid:135)ectingthatthe VAT applies to both imported and domestic goods. Moreover, the wage must jump under VP, both to o⁄set the competitiveness-enhancing e⁄ect of the subsidy on (cid:133)rm marginal cost, and to induce households to keep their labor supply unchanged. A direct consequence of these di⁄erent relative price responses is that any departure from the speci(cid:133)c conditions that deliver allocative equivalence (and neutrality) will result in markedly di⁄erent macroeconomic e⁄ects. For instance, in the special case in which wages are (cid:135)exible but exchange rates are (cid:133)xed, IX has expansionary e⁄ects while VP remains neutral. An important open question remains whether a temporary implementation of VP can provide stimulus in the event of cyclical downturns. We (cid:133)nd that a VP policy can easily have contractionary e⁄ects on aggregate demand and in(cid:135)ation, even when wages are sticky. While the payroll subsidy to employers increases competitivenes by reducing marginal costs, the temporary increase in VAT rates 6OuremphasisonintertemporalsubstitutionchannelsisinthespiritofearlierworkbySvenssonandRazin(1983), who use a two-period model to illustrate how a temporary tari⁄ a⁄ects the current account through intertemporalsubstitution e⁄ects on consumption. 7Barattieri,Cacciatore,andGhironi(2017)incorporateadditionalsupply-sidechannels,includingendogenousentry andexitof(cid:133)rms,thatamplifythenegativee⁄ectsoftari⁄s. Theseauthors,however,focusexclusivelyonthee⁄ectsof tari⁄s ratherthan the combination ofimport tari⁄s and export subsidies (IX policies),as we do here. 8A number of quantitative and empirical papers have tried to gauge the e⁄ects of (cid:133)scal devaluations on trade, including Lipi·nska and Von Thadden (2012),de Mooijand Keen (2012),Franco (2013),and Gomes et al. (2016). 4

raises the price of current consumption relative to future consumption, thus depressing aggregate demand. The latter intertemporal substitution e⁄ect exerts a strong contractionary impetus unless monetary policy cuts interest rates su¢ ciently. Hence, VP tends to be sharply contractionary under (cid:133)xed exchange rates and may well cause output to fall even under (cid:135)exible exchange rates. Theseresultsmayseemsurprisinginlightoftheexistingliterature,includingtheseminalworkby Farhietal. (2014), whichshowsthat, under(cid:133)xedexchangerates, VPprovidesequivalentstimulusto output and in(cid:135)ation as IX or an exchange rate devaluation. A critical assumption responsible for the contractionarye⁄ectsofVPisthat,inourframework,pre-taxpricesaresticky,sothatVATincreases are immediately passed through to consumer prices. Given the centrality of this assumption about VAT pass-through for our theoretical results, we discuss some empirical evidence in support of our speci(cid:133)cationthatshowsthatconsumerpricestendtoincreasequicklyinresponsetoVATincreases. A particularlyapplicablecasewastheimplementationoftheGerman(cid:133)scaldevaluationin2007 arare (cid:0) case of a VAT increase accompanied by an equally-sized payroll subsidy in which the pass-through (cid:0) of VAT increases was large and immediate. While our analysis focuses heavily on IX and VP policies, we also study the e⁄ects of a border adjustment of corporate taxes (BAT). Several authors, including Feldstein (2017) and Auerbach et al. (2017), have recently argued that a border adjustment of corporate taxation, that amounts to taxingimportsandsubsidizingexports, wouldnota⁄ectthetradebalanceprovidedthatthenominal exchange rate was free to adjust. A key theoretical insight of our analysis is that, with nominal rigidities and full pass-through of taxes, the BAT is equivalent to IX. Consequently, the BAT would provide macroeconomic stimulus exactly like IX policies and have no allocative e⁄ects only under fairly extreme assumptions. A few authors, including Barbiero, Gopinath, Farhi, and Itshoki (2018) and Linde and Pescatori (2018), have recently provided quantitative assessments of a possible adoption of a BAT by the United States. These papers mainly consider a unilateral permanent implementation of the BAT which implies a large jump in the exchange rate. They focus on incomplete pass-through of exchange ratechangestoimportpricesasakeysourceofnon-neutrality,andshowhow,undertheseconditions, the BAT can have large e⁄ects on both trade prices and volumes. While our analysis has clear complementarities with this research, we focus on features (cid:150)such as the possibility of retaliation or reversal as captured by our Markov-switching framework (cid:150)that greatly diminish the scope for trade 5

policiestoexertlargee⁄ectsonthelong-runleveloftheexchangerate.Asemphasized,thesefeatures cause trade policies to have allocative e⁄ects by damping the near-term movement in the exchange rate. Although we retain a standard in(cid:133)nite-horizon general equilibrium framework, our use of a Markov-switching framework to limit the role of long-run expectations in determining the economic e⁄ects of trade policies is in the same spirit as a recent literature that attempts to damp the role of beliefs about future policies on current outcomes.9 Thepaperisorganizedasfollows. Section2describesthemodel. Section3developssomeintuition about the e⁄ects of IX, VP, and BAT policies by discussing their partial equilibrium e⁄ects. Section 4 discusses the macroeconomic e⁄ects of IX policies, including conditions for neutrality. Section 5 investigates the relation between IX, VP, and BAT policies. Section 6 concludes. 2 Model The economy consists of a home (H) country and a foreign (F) country that are isomorphic in structure. Foreignvariablesaredenotedwithanasterisk. Agentsineacheconomyincludehouseholds, 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 producercurrencypricing(PCP),fully(cid:135)exiblewages,andasimple(cid:133)nancialmarketstructureinwhich 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 (cid:133)nancial market structure, as well as for di⁄erences in country size; all of the theoretical results are derived within the context of this general framework. 2.1 Households Householdsinthehomecountryderiveutilityfroma(cid:133)nalgoodconsumption(C )anddisutilityfrom t labor (N ). They maximize expected lifetime utility t E0 (cid:6) 1t=0 (cid:12)tU(C t ;N t ) (1) 9See,forinstance,researchonthe(cid:147)forwardguidancepuzzle(cid:148)byMcKay,Nakamura,andSteinsson(2014),Fahriand Werning (2018),and Angeletosand Lian (2017),aswellasrelated analysisofthe e⁄ectsof(cid:133)nite planning horizonsby Woodford (2018). 6

subject to the budget constraint (cid:31) P C +B +" B + B B(cid:22) 2 =R B +" R B +W N +(cid:5) +T (2) t t Ht t Ft 2 Ft (cid:0) F t (cid:0) 1 Ht (cid:0) 1 t t(cid:3) (cid:0) 1 Ft (cid:0) 1 t t t t h (cid:0) (cid:1) i e where P is the consumer price index, B are noncontingent nominal bond holdings denominated in t Ht domestic currency, B are noncontingent nominal bond holdings denominated in foreign currency, Ft R is the foreign nominal interest rate, " is the nominal exchange rate (de(cid:133)ned as the price of one t(cid:3) 1 t (cid:0) unit of foreign currency in terms of units of home currency), W is the wage rate, (cid:5) is the aggregate t t pro(cid:133)tofthehome(cid:133)rmsassumedtobeownedbythehomeconsumers,T isalump-sumtransferfrom t e the government. The parameter (cid:31) 0 allows for the possibility that home households face quadratic (cid:21) costs of adjusting their holdings of foreing bonds.10 In our baseline calibration we focus on the case, often considered in the literature, in which foreign households cannot invest in the domestic bond so that only the foreign bond is traded internationally.11 We assume that the period utility function takes the form 1 1 U(C;N)= C1 (cid:27) N1+(cid:17) (3) 1 (cid:27) t(cid:0) (cid:0) (cid:17)+1 t (cid:0) Optimality requires W N(cid:17)C(cid:27) = t (4) t t P t P 1=(cid:12)Et (cid:3) t;t+1P t R t (5) (cid:20) t+1 (cid:21) P " 1=(cid:12)Et (cid:3) t;t+1P t t " +1R t(cid:3) (6) (cid:20) t+1 t (cid:21) (cid:27) where(cid:3) = Ct istherealstochasticdiscountfactorofthehomehousehold. Thecorrespondt;t+1 Ct+1 (cid:16) (cid:17) ing optimality condition for foreign household holdings of the foreign bond is P 1=(cid:12)Et (cid:3) (cid:3)t;t+1P t(cid:3) R t(cid:3) (7) (cid:20) t(cid:3)+1 (cid:21) Combining the optimality conditions for bond holdings (6) and (7), one obtains the risk-sharing 10Allofourtheoreticalresults go through irrespective ofthe value of(cid:31)provided that (cid:31)=0:Forsimplicity,the (cid:133)rst orderconditionswereportinthetextassume(cid:31)=0:Inoursimulationsweintroduceverysmallcostsofadjustmentto ensure stability ofa (cid:133)rst orderapproximation. See Neumeyerand Perri(2001) and Schmitt-Grohe and Uribe (2003). 11That is,the budget constraint forforeign households is given by P t(cid:3) C t(cid:3) +B F(cid:3)t + " 1 t B H(cid:3)t + (cid:31) 2 (cid:3) B H(cid:3)t(cid:0) B(cid:22) H 2 =R t(cid:3) (cid:0) 1 B F(cid:3)t (cid:0) 1 + " 1 t Rt (cid:0) 1B H(cid:3)t (cid:0) 1 +W t(cid:3) N t(cid:3) +(cid:5) (cid:3)t +T t(cid:3) In our baseline anahlysis we set(cid:0)(cid:31) (cid:3) = 1 so(cid:1)thiat only foreign currency bonds are traded int e ernationally. We consider relaxing this assumption in Section 4.4. 7

condition Q P Et (cid:3) t;t+1 Q t+1 (cid:0) (cid:3) (cid:3)t+1 P t(cid:3) =0 (8) (cid:26)(cid:20) t (cid:21) t(cid:3)+1(cid:27) where Q is the real exchange rate expressed as the price of the foreign consumption bundle in home t currency relative to the price of the domestic consumption bundle, that is P Q =" t(cid:3) (9) t t P t 2.2 Retailers Competitive home retailers combine home and foreign intermediate goods to produce the (cid:133)nal consumption good according to the constant-elasticity-of-substitution (CES) aggregator (cid:18) C t = ! H (cid:18) 1 Y H (cid:18) (cid:0) t (cid:18) 1 +(1 (cid:0) ! H )(cid:18) 1 Y F (cid:18) t (cid:0)(cid:18) 1 (cid:18) (cid:0) 1 (10) h i where (cid:18) 0 determines the elasticity of substitution between home and foreign intermediate goods (cid:21) and! [0:5;1]governshomebias. Thehomegood(Y )andtheforeigngood(Y )consistofCES H Ht Ft 2 aggregators over home and foreign varieties (cid:13) Y Ht = 1 Y Ht (i) (cid:13) (cid:0)(cid:13) 1 di (cid:13) (cid:0) 1 (11) (cid:20)Z0 (cid:21) (cid:13) Y Ft = 1 Y Ft (i) (cid:13) (cid:0)(cid:13) 1 di (cid:13) (cid:0) 1 (12) (cid:20)Z0 (cid:21) where (cid:13) 0 determines the elasticity of substitution across varieties. (cid:21) Pro(cid:133)t for the home retailers are P (cid:5)R =(1 (cid:28)v)(1 (cid:28)(cid:25)) P C P Y Ft Y (13) t (cid:0) t (cid:0) t t t (cid:0) Ht Ht (cid:0) (1 (cid:28)(cid:25)BAT ) Ft (cid:20) (cid:0) t t (cid:21) where P and P are the price indexes of the home and foreign goods, (cid:28)v is the value-added tax Ht Ft t rate, (cid:28)(cid:25) is the tax rate on pro(cid:133)ts, and BAT 0;1 indicates whether pro(cid:133)t taxes are adjusted at t t 2 f g the border or not. The border adjustment implies that the cost of imported goods (Y ) cannot be Ft deducted from pro(cid:133)ts. Prices are inclusive of value-added taxes and, in the case of imported goods, are also inclusive of home tari⁄s ((cid:28)m). t 8

Given the CES structure of these aggregators, the home and foreign good demand functions are characterized by Y =! P Ht (cid:0) (cid:18) C (14) Ht t P (cid:20) t (cid:21) Y =(1 !) P Ft (cid:0) (cid:18) C (15) Ft (cid:0) (1 (cid:28)(cid:25)BAT )P t (cid:20) (cid:0) t t t(cid:21) Y (i)= P Ht (i) (cid:0) (cid:13) Y (16) Ht Ht P (cid:20) Ht (cid:21) Y (i)= P Ft (i) (cid:0) (cid:13) Y (17) Ft Ht P (cid:20) Ht (cid:21) The zero pro(cid:133)t conditions for home retailers imply that price indexes satisfy: 1 P = !P1 (cid:18)+(1 !) P Ft 1 (cid:0) (cid:18) 1 (cid:0) (cid:18) (18) t " H(cid:0)t (cid:0) (cid:18) 1 (cid:0) (cid:28)(cid:25) t BAT t(cid:19) # 1 1 1 (cid:13) P Ht = P Ht (i)1 (cid:0) (cid:13)di (cid:0) (19) (cid:20)Z0 (cid:21) 1 1 1 (cid:13) P Ft = P Ft (i)1 (cid:0) (cid:13)di (cid:0) (20) (cid:20)Z0 (cid:21) 2.3 Producers Each country features a continuum i [0;1] of monopolistically-competitive (cid:133)rms that produce dif- 2 ferent varieties of intermediate goods. Producers use the technology Y (i)+Y (i)=A N(cid:11)(i) (21) Ht H(cid:3)t t t where Y (i) and Y (i) are (cid:133)rm is sales in the domestic and foreign market, respectively, A is the Ht H(cid:3)t 0 t aggregate level of technology, and (cid:11) (0;1) controls the curvature of the production function. 2 Inourbenchmarkspeci(cid:133)cationweassumeproducercurrencypricing(PCP),thatis,producersset prices in the domestic currency while letting prices in the foreign market adjust to ensure that unit revenues are equalized across markets. We can then write (cid:133)rm is pro(cid:133)ts as 0 (cid:5)P(i)=(1 (cid:28)(cid:25)) P (i)[Y (i)+Y (i)] (1 &v)W N (i) (22) t (cid:0) t f Pt Ht H(cid:3)t (cid:0) (cid:0) t t t g where P (i) denotes the unit revenue from domestic sales of the home variety. Pt 9

Thepresenceofvalue-addedtaxesintroducesawedgebetweenunitrevenuesP (i)andtheprice Pt paid by domestic retailers for P (i): Ht P (i)=(1 (cid:28)v)P (i) (23) Pt (cid:0) t Ht Similarly, import tari⁄s, export subsidies, and the deductability of export sales from the corporate pro(cid:133)t tax when the border adjustment is in place (i.e. BAT =1) create a wedge between the foreign currency price paid by foreign retailers, P (i); and (cid:133)rm is foreign currency unit revenue from H(cid:3)t 0 exports, PPt(i): "t (1 (cid:28)(cid:25)BAT )(1+(cid:28)m )P (i) P H(cid:3)t (i)= (cid:0) t (1+ t &x) t (cid:3) P " t (24) t t Producers set prices in staggered contracts following a Calvo-style timing assumption and with full pass-through of value added taxes. That is, a domestic (cid:133)rm that adjusts its price at time t sets the unit revenues P (i) and, absent any price adjustment until time s > t; changes in value-added Pt taxes are fully re(cid:135)ected in retailer(cid:146)s costs of purchasing the home variety P (i) P (i)= Pt : (25) Hs (1 (cid:28)v) (cid:0) s Each (cid:133)rm that reoptimizes at time t will then choose P(cid:22) to solve Pt; P(cid:22) (i)[Y (i)+Y (i)] (1 &v)W N (i) maxE t (cid:16)s P(cid:0) t(cid:3) t;s (1 (cid:0) (cid:28)(cid:25) s ) Pt Hs H(cid:3)s P (cid:0) (cid:0) s s s (26) s t (cid:26) s (cid:27) X(cid:21) where (cid:16) is the probability that the (cid:133)rm won(cid:146)t be able to adjust its price in any given period, labor P demand satis(cid:133)es (21); and domestic and foreign sales are determined by retailers(cid:146)demand schedules in both the home and foreign market (i.e., equation (16) and its foreign analogue, respectively). The reset price P (i) satis(cid:133)es the usual optimality condition: Pt 1 (cid:13) (1 &v)W Et (cid:6) 1s=t (cid:16)s P(cid:0) t(cid:3) t;s [Y Hs (i)+Y H(cid:3)s (i)](1 (cid:0) (cid:28)(cid:25) s ) P P Pt (i) (cid:0) (cid:13) 1(cid:11)A (cid:0) N s (i)(cid:11) s 1 =0 (27) s (cid:20) (cid:0) s s (cid:0) (cid:21) Equation(27)indicatesthatthecontractpriceP (i)issetasa(cid:133)xedmarkupovertheappropriately Pt discounted measure of (cid:133)rm marginal costs that takes into account the expected duration that the contract price will remain in e⁄ect. We let the producer price index P be de(cid:133)ned in a way that Pt mimics the consumer price index in (19): 1 P Pt = P Pt (i)1 (cid:0) (cid:13)di 1 (cid:0) (cid:13) ; (28) (cid:20)Z (cid:21) 10

our Calvo-style pricing assumption then implies that producer price in(cid:135)ation is given by 1 (cid:25) = (cid:16) +(1 (cid:16) ) P(cid:22) P;t 1 (cid:0) (cid:13) 1 (cid:0) (cid:13) (29) Pt " P (cid:0) P (cid:18) P P;t (cid:0) 1(cid:19) # Expression (29) indicates that producer price in(cid:135)ation depends on future marginal costs through the optimal reset price P(cid:22) ; which is identical across all (cid:133)rms that reset at time t: Combining equations P;t (27) and (29) one obtains the familiar New Keynesian Phillips Curve linking domestic price in(cid:135)ation to current and future marginal costs. Similarly, foreign (cid:133)rm j sells its good in the foreign country at a price of P (j) and in the home F(cid:3)t country according to the PCP condition12 (1+(cid:28)m) P (j)= t " P (j) (30) Ft (1+&x )(1 (cid:28)v) t P(cid:3)t t(cid:3) (cid:0) t Foreign (cid:133)rms that are allowed to reset their price choose their contract price P(cid:3) (j) so that Ft (cid:13) W Et (cid:6) 1s=t (cid:16) (cid:3)P s (cid:0) t(cid:3) (cid:3)s;t [Y F(cid:3)s (j)+Y Fs (j)] P(cid:3) Pt (j) (cid:0) (cid:13) 1(cid:11)A Z (i) s N (cid:3) (j)(cid:11) 1 =0 (31) (cid:20) (cid:0) (cid:3)s s(cid:3) (cid:3) s(cid:3) (cid:0) (cid:21) 2.4 Government Policy Fiscal policy in the home and in the foreign country is characterized by a vector of (cid:133)scal instruments s =((cid:28)m;&x;(cid:28)v;&v;(cid:28)(cid:25);BAT ;(cid:28)m ;&x ) (32) t t t t t t t t (cid:3) t(cid:3) that are assumed to follow a Markov chain as described below. The home government balances its budget in every period through levying lump-sum taxes T t (cid:28)m+(cid:28)v " P (cid:28)(cid:25) t t P Y +(cid:28)vP Y &x t H(cid:3)t Y + t (cid:5)(cid:25) &vW N +TI =T (33) 1+(cid:28)m Ft Ft t Ht Ht (cid:0) t 1+(cid:28)m H(cid:3)t 1 (cid:28)(cid:25) t (cid:0) t t t t t (cid:20) t (cid:21) t (cid:3) (cid:0) t e where TI are net international transfers. t Monetary policy follows a Taylor-style interest rate rule: 1 R = ((cid:25) )’ (cid:25)(y~)’ y(" )’ " (34) t Pt t t (cid:12) where ’ is the weight on producer price in(cid:135)ation ((cid:25) ); ’e the weight on the output gap (y~); and (cid:25) Pt y t ’ determines how policy rates respond to deviations of the nominal exchange rate from an exchange " 12As we specify later, we assume that the foreign governments does not make use of VP and BAT policies. Hence, unit revenues to producers equalretailers cost in the foreign country (i.e. P =P ): F(cid:3);t P(cid:3);t 11

rate target i.e. " = "t .13 When ’ =0; the home interest rate responds exclusively to (cid:135)uctuations t (cid:22)" " in output ga(cid:0)ps and dom(cid:1)estic in(cid:135)ation. This speci(cid:133)cation implies that the central bank looks through e changes in in(cid:135)ation due to the direct e⁄ects of tari⁄s and value-added taxes. When ’ =M, with M " large, the interestrateis set sothatthecountrypegs its exchange rate toapredetermined target((cid:22)"). 2.5 Market Clearing and Equilibrium Labor market clearing equates household supply of labor with aggregate (cid:133)rms(cid:146)demand N = N (i)di: (35) t t Z Bond market clearing requires B +B =0 (36) Ft F(cid:3)t B +B =0 (37) Ht H(cid:3)t Combining home and foreign households budget constraints and using the bond market clearing conditions we get a balance of payment equilibrium equation " B =" B R +NX (38) t Ft t Ft 1 t(cid:3) 1 t (cid:0) (cid:0) whichrequiresthathomehouseholdsincreasetheirholdingsofforeignbondstomeetthetotalamount of new borrowing demand from abroad, given by home net exports: " P NX = t H(cid:3)t (Y S Y ) (39) t (1+(cid:28)m ) H(cid:3)t(cid:0) t Ft t (cid:3) where S denotes the terms of trade t (1+(cid:28)m )(1 (cid:28)v)P S = t (cid:3) (cid:0) t Ft (40) t (1+(cid:28)m) " P t t H(cid:3)t which is the key relative price determining the behavior of the trade balance. Let the initial condition for home holdings of bonds and individual producer prices in the home and foreign market be: x = B R ;P (i);P (i) 0 F 1 (cid:3)1 H 1 F(cid:3) 1 (cid:0) (cid:0) (cid:0) (cid:0) (cid:2) (cid:3) De(cid:133)nition. Given an initial state x ; a stochastic process for (cid:133)scal policy s and international 0 t f g transfers TI ;anequilibriumconsistsof (i)anallocationathome,(cid:4)= C ;B ;N ;Y ;Y ;Y (i); t f t F t Ht Ft Ht 13See Ben(cid:8)igno(cid:9)et al. (2007) fora discussion ofinterest rate rules that maintain a (cid:133)xed exchange rate. 12

Y (i) ;andabroad (cid:4) ;(ii)(cid:133)rm-levelpricesandproductiondecisionsathome,(cid:8)= P(cid:22) (i);N (i); Ft gt 0 (cid:3) Pt t (cid:21) P (i);P (i) ;andabroad (cid:8) ; (iii)aggregatepricesathome (cid:0)= P ;P ;P ;P (cid:8);(cid:25)P;W ;R Ht H(cid:3)t gt 0 (cid:3) t Ht Ft Pt t t t t 0 (cid:21) (cid:21) and abroad (cid:0) ;(iv)(domestic)bond holdings, net exports, currency exc(cid:8)hange rates and terms of trad(cid:9)e (cid:3) B ;B ;NX ;" ;S such that: f Ht F(cid:3)t t t t g 1. The allocation (cid:4) satis(cid:133)es households and retail (cid:133)rms optimality conditions (4) (6) and (cid:0) (14) (17) as well as the analogous conditions in the foreign country; (cid:0) 2. Individual producer prices and production decisions (cid:8) maximize (cid:133)rm pro(cid:133)ts, i.e. they satisfy conditions (21),(23);(24) and (27) as well as the analogous conditions in the foreign country; 3. Prices (cid:0) clear all markets. That is, price indexes, P ;P ;P ;P ;(cid:25)P ; satisfy (18) t Ht Ft Pt t t 0 (cid:0) (cid:21) (20);(28) (29); wages clear the labor market, i.e. ((cid:8)35)is satis(cid:133)ed; and n(cid:9)ominal interest rates (cid:0) are determined according to (34): Analogous conditions pin down (cid:0) : (cid:3) 4. The bond market clears, i.e. equations (36) (40) are satis(cid:133)ed. (cid:0) 2.6 Calibration In our discussion of the transmission of trade policies, we calibrate the model using fairly standard values in the literature.14 Table 1 shows our baseline parameter values. Table 1. Calibration Parameter Value Households Discount factor (cid:12) 0:99 Risk aversion (cid:27) 1:00 Frisch elasticity of labor supply (cid:17) 1 1:00 (cid:0) Producers Labor share (cid:11) 0:36 Price stickiness (cid:16) 0:90 P Trade elasticity (cid:18) 1:25 Import share ! 0:15 H Monetary Policy Output gap weight in the rule ’ 0:125 y In(cid:135)ation weight in the rule ’ 1:50 (cid:25) 14See,forinstance,Gal(cid:236)(2008). 13

3 Partial equilibrium e⁄ects of trade and (cid:133)scal policies The trade and (cid:133)scal tax instruments considered in this paper directly a⁄ect three key margins determining the equilibrium allocation in our model economy, namely relative demand for home and foreign varieties, for consumption and leisure, and for consumption at di⁄erent dates. In this section, we focus on these margins to show how the e⁄ects of IX and BAT di⁄er markedly from VP in partial equilibrium - i.e. holding (cid:133)xed nominal interest rates, exchange rates, wages, and producer prices. This analysis will prove helpful in understanding the di⁄erent general equilibrium e⁄ects of these policies under various assumptions about nominal rigidities and monetary policy. Starting with the relative demand for home and foreign varieties, the PCP conditions (30) and (25) allow us to express the relative price of imports as P (1+(cid:28)m)" P (1+(cid:28)m) Ft = t t P(cid:3)t = t Q (41) P (1+&x ) P (1+&x ) Pt Ht t(cid:3) Pt t(cid:3) where " P Q = t P(cid:3)t (42) Pt P Pt is the home relative to the foreign level of producer prices (henceforth, the producer real exchange rate). Note that this relative price is not directly a⁄ected by changes in taxes. Equations (14), (15); and (41) imply that the relative demand for imported goods in the home country can be rewritten as Y Ft = P Ft (cid:0) (cid:18) = (1+(cid:28)m t ) Q (cid:0) (cid:18) (43) Y P (1 (cid:28)(cid:25)BAT ) (1+&x )(1 (cid:28)(cid:25)BAT ) Pt Ht (cid:20) Ht (cid:0) t t (cid:21) (cid:20) t(cid:3) (cid:0) t t (cid:21) This equation shows that the imposition of a tari⁄ raises the relative price of imports for any given level of the producer real exchange rate, and hence shifts demand away from imports towards domestically-producedgoods. Similarly,thenon-deductibilityofimportsfromcorporatepro(cid:133)tsunder the BAT operates like a tari⁄by raising the e⁄ective price of imports: The foreign subsidy to exports (&x ) has a countervailing e⁄ect, by allowing foreign exporters to decrease their price and hence t(cid:3) stimulate the home demand for imports. In contrast, changes in the VAT have no e⁄ect on relative import prices provided that the producer real exchange rate is unchanged, re(cid:135)ecting that the VAT has equal-sized e⁄ects on both the price of imported as well as domestically-produced goods (see e.g. Feldstein and Krugman (1982) for a similar argument). 14

Foreign relative demand can be expressed in a symmetric way as (cid:18) Y (1+(cid:28)m ) 1 (cid:0) H(cid:3)t = t (cid:3) (44) Y (1+&x) Q F(cid:3)t (cid:20) t Pt(cid:21) whichshowsthattheimpositionofanexportsubsidyinthehomecountry(&x)boostsforeigndemand t for home exports, while higher tari⁄s abroad reduce them. Once again, the VAT has no direct e⁄ect on this margin: foreign demand for home exports is una⁄ected by changes in VAT rates (holding the producer real exchange rate constant). Turning to the consumption-leisure margin, we can rewrite the labor supply schedule (4) in terms of a product real wage, de(cid:133)ned as the nominal wage in terms of producer prices Wt ; as follows: Ppt (cid:16) (cid:17) W P t = t C(cid:27)N(cid:17) (45) P P t t pt pt where 1 P t = 1 !+(1 !) (1+(cid:28)m t ) Q 1 (cid:0) (cid:18) 1 (cid:0) (cid:18) (46) P pt 1 (cid:0) (cid:28)v t ( (cid:0) (cid:20) (1+&x t(cid:3) )(1 (cid:0) (cid:28)(cid:25) t BAT t ) Pt (cid:21) ) Equations (45) and (46) show that the imposition of import tari⁄s, the BAT adjustment, and an increase of VAT rates all induce a contraction in labor supply by causing an increase in the relative price of the consumption bundle (i.e., a rise in Pt ) holding (cid:133)xed the producer real exchange rate. As Ppt consumption becomes more expensive, households(cid:146)willingness to supply labor, at any given product real wage, falls. Notably, this e⁄ect is larger in the case of VAT increases as these taxes raise the priceofbothdomesticandforeigngoodswhereasimporttari⁄sandtheBATraisepricesonlyforthe share(1 !)ofimportedgoods. InthecaseofVPpolicies,payrollsubsidies(&v)alsoa⁄ectthelabor (cid:0) t market equilibrium by increasing (cid:133)rms(cid:146)labor demand at any given level of the product real wage, as implied by equation (27): Finally, to see how these policies a⁄ect the intertemporal margin, we can rewrite the optimal consumption-saving condition (5) by using (41) and (46) to express consumer price in(cid:135)ation (cid:25) in t+1 termsofproducerpricein(cid:135)ation((cid:25) ),theproducerrealexchangerate(Q ),andthetaxinstruments pt Pt as: 1 1 (cid:18) (cid:12)E 8 C t (cid:27) R t 1 (cid:0) (cid:28)v t+1 2 !+(1 (cid:0) !) (1+&x t(cid:3) ( ) 1 ( + 1 (cid:0) (cid:28)m t (cid:28)(cid:25) t ) BATt) Q Pt 1 (cid:0) (cid:18) 3 (cid:0) 9 =1 (47) t>>>>< C t (cid:27) +1 (cid:25) pt+1 1 (cid:0) (cid:28)v t 6!+(1 !) (cid:16) (1+(cid:28)m t+1 ) Q (cid:17) 1 (cid:0) (cid:18) 7 >>>>= 6 6 (cid:0) (cid:18) (1+&x t+(cid:3)1 )(1 (cid:0) (cid:28)(cid:25) t+1 BATt+1 ) Pt+1 (cid:19) 7 7 >>>>: 4 5 >>>>; 15

Equation(47)showsthatconsumptiondependscruciallyonagents(cid:146)expectationsabouttheevolutionofthesepolicies. Forinstance,whenagentsexpectthesepoliciestobetemporary,thepriceofthe consumptionbundleinthefuturewillbelowerthanthecurrentprice,makingsavingsmoreattractive. Once again, while IX and BAT policies generate in(cid:135)ationary pressure through only higher prices of imported goods, VP policies make the entire consumption bundle more expensive. The implication of this di⁄erence is that expected dynamics of VAT changes have stronger e⁄ects on internal demand than the dynamics of IX and BAT tax changes. 4 Macroeconomic E⁄ects of IX Policy Inthissection,weanalyzethemacroeconomice⁄ectsofanincreaseinimporttari⁄sandexportsubsidies in the home country (IX policy) assuming that other tax policies (BAT, VP) remain unchanged. We begin by brie(cid:135)y describing the speci(cid:133)cation of trade policy regimes. We then provide conditions under which IX policies are neutral, and explore how various departures from these conditions, especially in terms of agents(cid:146)beliefs about the persistence of tax changes and the risk of retaliation, can induce IX policies to exert sizable allocative e⁄ects. 4.1 Trade Policy Shocks: Retaliation and Policy Reversal Inourbenchmarkmodel,weassumethattradepolicyactionss Sfollowa(cid:133)nitestateMarkovchain, t 2 which provides a convenient way of capturing the possibility that foreign economies may retaliate, or thatthepoliciesmaybereversed.Speci(cid:133)cally,thetradepolicyregimecanbecategorizedasbelonging tooneofthreedi⁄erentstatess SR = sNT;sIX;sTW :Inthe(cid:133)rststate sNT ;nocountrylevies t 2 anytaxes,tari⁄s,orprovidesexportsubs(cid:8)idies((cid:147)NoTax(cid:148)(cid:9)state). Inthesecon(cid:0)dsta(cid:1)te sIX ;thehome country unilaterally adopts an IX policy that raises import tari⁄s and export subsid(cid:0)ies b(cid:1)y the same amount (cid:14): In the third state sTW ; the foreign country retaliates in a symmetric way by raising its own tari⁄s and subsidies by t(cid:0)he sam(cid:1)e amount as the home country, that is, (cid:28)m =&x =(cid:28)m =&x =(cid:14) t t t (cid:3) t(cid:3) ("TradeWar"state):15 Allothertaxes,includingtheVAT,thepayrollsubsidy,andthecorporatetax rate, are held unchanged (we consider shocks to these tax rates in Section 5). 15Althoughwerestrictouranalysistosymmetricretaliatoryactionsbytheforeigngovernment,wealsoexperimented with departures from this assumption (e.g.,the foreign government retaliates by only imposing a tari⁄). 16

The transition probability matrix (cid:10) can be expressed: 1 a a 0 (cid:0) (cid:10)R = (1 (cid:25))(1 (cid:26)) (cid:26) (cid:25)(1 (cid:26)) (48) 2 (cid:0) (cid:0) (cid:0) 3 (1 ’) 0 ’ (cid:0) 4 5 with element(cid:10) indicatingtheprobabilityofmoving from state itostate j. The(cid:133)rstrow ofmatrix i;j (cid:10)R 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,givenanimplementationofIX,theeconomyremainsinthestatesIX withprobability(cid:26),returns to the no-tax state with probability (1 (cid:25))(1 (cid:26)); and transitions to the retaliation state sTW with (cid:0) (cid:0) probability (cid:25)(1 (cid:26)): Once the foreign country retaliates, the economy returns to a no-tax state with (cid:0) probability 1 ’; while with probability ’ it remains in the trade war regime. In this speci(cid:133)cation, (cid:0) theforeigncountrydoesnotabandonitsretaliatorypoliciesunilaterally, sothatatradewarcanonly end through a coordinated policy reversal by both countries.16 This general speci(cid:133)cation for the trade policy regime is helpful for considering a wide range of policy con(cid:133)gurations and dynamics as special cases, including permanent unilateral tari⁄s, trade (or tax) policies that are expected to eventually be reversed, and foreign retaliation. Moreover, the Markovstructurewillproveveryusefulinanalyzinghowuncertaintyaboutprospectivetradepolicies a⁄ects current macroeconomic outcomes.17 4.2 Neutrality of IX Policies A large literature has analyzed the Lerner Symmetry Theorem (Lerner, 1936) establishing conditions under which changes in import tari⁄s and export subsidies do not have allocative e⁄ects on the equilibriumallocation.18 Whilemostoftheliteraturehasfocusedontaxchangeswithinstaticmodels of international trade, here we enumerate conditions that generalize Lerner(cid:146)s result in the context of our dynamic monetary framework.19 Proposition1. Inaneconomywith(cid:135)exibleexchangerates(’ =0), aunilateralimplementation " 16In our calibration the exact value of ’ does not have material e⁄ects on outcomes (see the discussion in Section 4.3.2). Thus,in our experiments,we set ’equalto (cid:26): 17Ossa(2014,2016)presentestimatesaboutthee⁄ectsofcooperativeandnoncooperativecommercialpoliciesinmulticountry and multi-industry general equilibrium models of international trade. Although Ossa is able to characterize the optimaltrade policies,his analysis abstracts from dynamic considerations which are the focus ofthis paper. 18See, for instance, McKinnon (1966) and, more recently, Costinot and Werning (2017). The Lerner(cid:146)s Symmetry Theorem is also a relevant result for the neutrality of border tax adjustments, as in Meade (1974), Grossman (1980), and Auerbach et al. (2017),LindØ and Pescatori(2017),and Barbiero et al. (2018). 19Eichengreen (2018) provides an intuitive discussion ofthese neutrality conditions. 17

of IX of size (cid:14) (i.e. (cid:28)m = &x = (cid:14) and (cid:28)m = &x = 0) causes a (cid:14) percentage appreciation of the t t t (cid:3) t(cid:3) (cid:0) exchange rate and has no allocative e⁄ect if 1. Itispermanent,unanticipated,andthereisnoprobabilityofretaliation(a=(cid:25) =0;and(cid:26)=1); 2. Foreign holdings of home currency-denominated bonds are always zero ((cid:31) = ); (cid:3) 1 3. Export prices are set in the producer(cid:146)s currency (PCP) or prices are (cid:135)exible. Theformalproofofproposition1isinAppendixB.20 Themainintuitionbehindthisproposition, however, can be summarized by the observartion that, under conditions 1.- 3., a permanent and immediate jump in the real exchange rate is su¢ cient to insulate international relative prices and quantities, and thus the entire allocation, from the e⁄ects of IX policies. Recallfromsection(3)thatIXpoliciesa⁄ectdirectlytherelativedemandofdomesticandforeign varieties in the home and foreign country through the relative prices P Ft =(1+(cid:28)m)Q (49) P t Pt Ht P 1 H(cid:3)t = (50) P (1+&x)Q F(cid:3)t t Pt whereQ istheproducerrealexchangerateasde(cid:133)nedinequation(42). Theserelativepricesremain Pt unchanged if a (cid:14)-percentage increase in both import tari⁄s 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 o⁄set the increase in tari⁄s and lowers the revenues from sales of domestic varieties in the foreign country by as much as the higher export subsidy. Ina(cid:135)exibleexchangerateregime(’ =0);anappreciationofthenominalexchangeratedelivers " neutrality. Thatis,inresponsetoanIXpolicyofsize(cid:14) implementedattime0;thenominalexchange rate " ((cid:14)) satis(cid:133)es t " ((cid:14)) 1 t = ; (51) " (0) 1+(cid:14) t and all other prices and quantities are una⁄ected.21 To give a sketch of the proof, note (cid:133)rst that expressions (49) and (50) imply that this permanent appreciation of the exchange rate leaves relative 20While we do not prove that these conditions are necessary, we illustrate in sections 4.3 - 4.5 that they are tight in the sense that relaxing any one ofthem breaks the neutrality ofIX. 21Note that Proposition 1 does not impose any restriction on wage setting, as neutrality of IX does not require any adjustment in wages. As we discuss later,this result is in stark contrast with the case ofVP. 18

prices PFt and P H(cid:3)t unchanged. Itisthenimmediatetoverifythatthethreemarginsdiscussedin PHt P F(cid:3)t (cid:16) (cid:17) (cid:16) (cid:17) section(3) therelativedemandforhomeandforeignvarieties(equations43and44),forconsumption (cid:0) and leisure (equation 45), and for consumption at di⁄erent points in time (equation 47) are also (cid:0) una⁄ected by the policy change: In addition, the two optimality conditions for holdings of foreign currency denominated bonds, (equations 6 and 7); are una⁄ected as these holdings depend on future exchange rate changes while the IX policy causes a permanent appreciation of the exchange rate.22 Finally, after substituting equations (39) and (40); the expression for the balance of payment B =B R +P [Y S Y ] (52) Ft Ft (cid:0) 1 t(cid:3) (cid:0) 1 H(cid:3)t H(cid:3)t(cid:0) t Ft showsthattheexternalbalanceisalsouna⁄ectedasthepermanentappreciationoftheexchangerate insulates the terms of trade 1 P S = Ft (53) t (1+(cid:28)m)" ((cid:14))P t t H(cid:3)t 4.3 Policy Reversal, Retaliation, and Anticipation: The Role of Exchange Rate Dynamics TheneutralityofIXpoliciesinourdynamicframeworkrequiresthattherealexchangeratejumpstoa new long-run value, re(cid:135)ecting the public(cid:146)s belief that trade actions will be permanent and not induce foreign retaliation, even in the future. However, as argued in the introduction, these assumptions seem at odds with historical experience. Given these considerations, we next apply our benchmark model to study the e⁄ects of IX policies that have no long-run e⁄ect on the real exchange rate. Through the lens of the Markov structure presented earlier, the e⁄ects on the exchange rate may prove temporary because the policy action is reversed, or alternatively, because the home country(cid:146)s implementationofIXpoliciespromptstheforeigngovernmenttoretaliatebyadoptingsimilarpolicies. As the implications of either type of policy turn out to be nearly identical, for expositional simplicity 22ThisdiscussionimpliesthatapermanentIXpolicywouldnotbeneutralundercompletemarkets,absenttheuseof additionaltaxinstruments(suchasappropriatelychosenconsumptiontaxes). Therisk-sharingconditionwouldimpose atightlinkbetween theratioof(marginalutilityof)consumption acrosscountriesand thecurrentrealexchangerate. Thus,anymovementinthecurrentrealexchangeratewouldhaveallocativee⁄ects. LindØandPescatori(2017)explore a similarinsight in the context oftheiranalysis ofthe e⁄ects ofBAT policies. 19

webeginbyfocusingonthecaseinwhichaunilateralIXpolicyisexpectedtobereversed(1 (cid:26)>0, (cid:0) (cid:25) =0) and later discuss di⁄erences between policy reversal and retaliation ((cid:25) >0). 4.3.1 Reversal of IX policies In our benchmark framework, a unilateral IX policy of size (cid:14) that is expected to be reversed with probability1 (cid:26)>0exertsallocativee⁄ectsbyboostingrealnetexports, astheassociatedexchange (cid:0) rateappreciationonlypartiallyinsulatesinternationalrelativeprices. Inordertoexplaintheintuition behind this result, it is helpful to proceed by way of contradiction. Assume that the allocation is una⁄ected and that the exchange rate appreciates by (cid:14) as in (51) for as long as the policy (cid:0) (cid:0) remains in e⁄ect. This exchange rate movement su¢ ces to completely o⁄set the e⁄ects of IX on relative prices (49) and (50). However, the expectation that the IX policy will eventually be reversed impliesthattheexchangeratedepreciatesinthefuture, whichinturnrequiresanincreaseinthereal interest rate to satisfy the uncovered interest parity condition C(cid:27) P " Et C(cid:27) t P t R t (cid:0) t " +1R t(cid:3) =0 (54) (cid:20) t+1 t+1 (cid:18) t (cid:19)(cid:21) Asariseintheinterestrateclearlyhasallocativee⁄ects, thiscontradictsthehypothesisofneutrality of a transitory IX. The increase in the demand for foreign bonds associated with the expected depreciation of the currency turns out to lead to a smaller simultaneous appreciation of the exchange rate and an expansion of net exports.23 Notably, transitory IX policies are non-neutral both under (cid:135)exible prices as wellas under stickyprices, although speci(cid:133)c assumptions aboutthe formof nominal rigidities and the monetary policy rule are of course key to determining how the stimulus to net exports is transmitted to the rest of the economy. In this vein, the solid lines in Figure 1 show the expected paths of key variables after the home countryadoptsaunilateralIXpolicyinourbenchmarkmodelwithstickyprices.TheIXpolicyconsists ofa10percentagepointsincreaseinimporttari⁄sandexportsubsidiesthatisexpectedtobereversed with probability (1 (cid:26)) = 0:05 by the following quarter: The policy causes a small appreciation of (cid:0) the exchange rate that does not fully insulate relative prices and, as a consequence, imports fall and exports rise. In our general equilibrium model, monetary policy reacts to the stronger external demandbyraisinginterestrates,whichreduceshomeconsumptionandcontributestotheappreciation 23The use of appropriately targeted capital controls, i.e. designed so that equation (54) holds without requiring an adjustment in the interest rate;restores neutrality. We thank ourdiscussant EmmanuelFarhiforthis observation. 20

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 GDP and in(cid:135)ation decline. To clarify the transmission channels through which IX policies that are expected to be reversed a⁄ect the economy (cid:150)and highlight the distinction between import tari⁄s and export subsidies in violating Lerner(cid:146)s symmetry (cid:150)it is helpful to consider the following log-linearized equations of the model: y~ !y~ +(1 !)y~ =c~ +(1 !)nxq (55) t (cid:17) ht (cid:0) h(cid:3)t t (cid:0) t f nxq =y~ y~ =(cid:18)![((cid:28)m+(cid:27)x)+2q~ ]+(c~ c~) (56) t h(cid:3)t(cid:0) ft t t pt (cid:3)t (cid:0) t f (cid:1)q~ =(r~ (cid:25)~ ) (r~ (cid:25)~ )+(cid:30) b (57) pt+1 t (cid:0) pt+1 (cid:0) t(cid:3) (cid:0) (cid:3)pt+1 b t 1 c~ =c~ r~ (cid:25)~ (1 !) (cid:1)(cid:28)m +(cid:1)q~ (58) t t+1 (cid:0) (cid:27) t (cid:0) pt+1 (cid:0) (cid:0) t+1 pt+1 (cid:2) (cid:0) (cid:1)(cid:3) where a (cid:145)tilde(cid:146)denotes the percent or percentage point deviation of a variable from its steady state level. Equation (55) speci(cid:133)es that output may be allocated to consumption c or to real net exports t nxq,wherethelatteristhedi⁄erencebetweenexportsandimports(evaluatedatsteadystateprices). t e Equation (56) states that real net exports rise in response to higher import tari⁄s ((cid:28)m) or export f t subsidies ((cid:27)x), a depreciation of the producer real exchange rate (i.e., a rise in q ); or to a rise t pt in foreign relative to home consumption. The direct e⁄ects of the trade policy shocks on aggregate e demand are stronger if technology allows higher substitution between domestic and foreign varieties (i.e. higher trade elasticity (cid:18)) and if the country is more open (i.e. higher !): Equation (57) is the uncovered interest parity condition, linking the evolution of the real exchange rate to the di⁄erence between real interest rates between countries, with the (cid:133)nal term (cid:30) b capturing that investors are b t willing to accept a relatively lower real return on home bonds if net foreign assets b are positive: e t Finally, using the Euler equation (47); expression (58) links consumption changes to the producer e realinterestrate(r~ (cid:25)~ )aswellastochangesinimporttari⁄sandintheproducerrealexchange t pt+1 (cid:0) rate (with the strength of the latter changes controlled by the import share). This expression reveals thatIXpoliciesoperatenotonlythroughtradechannels, butalsothroughintertemporalchannels, as 21

anincreaseinimporttari⁄s thatisexpectedtobereversed raisesthecostofcurrentconsumption (cid:0) (cid:0) relative to future consumption: These dynamic e⁄ects of tari⁄s contrast sharply with the e⁄ects of export subsidies, which do not a⁄ect the consumer real interest rate directly (but only through the strength of the monetary policy response). This intertemporal substitution e⁄ect of import tari⁄s that pushes down consumption is consequential. Returning to Figure 1, the dashed lines show the e⁄ects of import tari⁄s only: An increase inimporttari⁄shasessentiallynoe⁄ectonoutputunderourbaselinecalibration((cid:27) =1;(cid:18) =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 blue and red lines). The quasi-invariance of output to the tari⁄increase re(cid:135)ects that the expenditure-switching e⁄ect, which pushes up the desired share of consumption spent on home goods, iso⁄setbytheintertemporal-substitution e⁄ect, thatpushesdownoverallconsumption. Stepping beyond our speci(cid:133)c calibration, the output e⁄ects of higher import tari⁄s depend on the relative strength of these two e⁄ects. If the intertemporal elasticity of substitution is low relative to the trade price elasticity, higher tari⁄s would tend to boost output (as the expenditure-switching e⁄ect dominates), whereas the tari⁄would reduce output if the intertemporal elasticity is relatively high relative to the trade elasticity. Even so, under reasonable assumptions about intertemporal substitution and trade elasticities, a combination of import tari⁄s 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 policyaswell. Forinstance,alargerinterestrateresponsetoproducerpricein(cid:135)ation(higher’ inthe (cid:25) policy rule) and, consequently, to the external demand stimulus would imply smaller output e⁄ects. By contrast, when monetary policy gives high weight to stabilization of the exchange rate (high ’ " in the policy rule), the output stimulus is larger, with a (cid:133)xed 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 (cid:133)xed to that of the foreign economy (solid lines). Home output rises signi(cid:133)cantly more in this case than under (cid:135)exible exchange rates. This larger output expansion largelyre(cid:135)ectsthatconsumptionexpandsrobustly ratherthancontracts asthehomepolicyrate (cid:0) (cid:0) declines in lockstep with the foreign policy rate. The rise in output is also reinforced by a smaller appreciation of the real exchange rate, which boosts net exports relatively more. 22

4.3.2 Reversal of IX policies and retaliation We have asserted that the IX policy with reversal considered so far has very similar e⁄ects to an IX policy subject to possible retaliation, meaning in the latter case that agents expect that the foreign governmentmayretaliateinkindsometimeinthefuture.Asshownbythelemmabelow,thedi⁄erence betweentheequilibriumallocationunderretaliationandtheequilibriumallocationwithpolicyreversal is attributable to wealth e⁄ects that can be o⁄set by appropriate international transfers. Lemma 1 If prices are (cid:135)exible or set in the producer(cid:146)s currency, a unilateral implementation of IX with policy reversal implements the same equilibrium allocation as a unilateral implementation of IX that triggers retaliation coupled with international transfers that satisfy: (cid:14) TI = B R " +B R t1 (cid:0)1+(cid:14) F;t1(cid:0) 1 t(cid:3) 1(cid:0) 1 t1 H;t1(cid:0) 1 t1(cid:0) 1 (cid:2) (cid:3) R T t I 2 =(cid:14) (cid:20) B F;t2(cid:0) 1 R t(cid:3) 2(cid:0) 1 " t2 +B H;t2(cid:0) 1 (cid:25) t2 t (cid:0) 2 1 (cid:21) where t is the (cid:133)rst time the economy transits to the retaliation state sTW and t > t is the (cid:133)rst 1 2 1 time it leaves the retaliation state sTW. Proof. See Appendix C. Theintuitionofthislemmacanbeeasilyunderstoodbyconsideringthespecialcaseofapermanent transition to a trade war regime starting from balanced trade. In this case, TI = 0 and TI never t1 t2 occurs so that Lemma 1 implies that the e⁄ects of starting a trade war are identical to the e⁄ects of abolishing all tari⁄s and subsidies in both countries. The reason can be easily understood by inspecting equation (43);where export subsidies in the foreign country exactly o⁄set import tari⁄s in the home country, and, symmetrically, equation (44): 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 de(cid:133)cits in the future, import tari⁄revenues will exceed export subsidy expenditures, implying a positive wealth e⁄ect and an associated appreciation of the home currency. Symmetrically, the foreign economy will su⁄er wealth losses from its implementation of IX. Consequently, a transfer of resources that corrects this international wealth redistribution is needed to implement the same allocation under policy reversal 23

and retaliation. Under our assumption of balanced trade in the long run, however, the economic e⁄ects of these transfers are of second order. 4.3.3 Anticipation E⁄ects of IX While we have shown that IX policies may boost output if their implementation is a surprise, the anticipation that such policies may be implemented sometime in the future can have immediate contractionary e⁄ects. The importance of anticipation e⁄ects 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 abouttheimplementationdate.Inthisvein,Figure3showstheresponseoftheeconomywhenagents learn that IX policies will be introduced in the future, but are unsure about the timing. Speci(cid:133)cally, 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 (cid:150)once implemented (cid:150)the policies will not be reversed ((cid:26)=1:0). The (cid:133)gure plots a realized simulation path in which IX policies are not actually implemented in the 5-year period shown, even though agents continue to see a substantial likelihood that they will be put into e⁄ect in the near term. The anticipation e⁄ects 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 (cid:133)rst come to believe that IX policies will eventually be implemented ((cid:133)rst panel). The stronger currency leads to a decline in competitiveness for domestic (cid:133)rms, a drop in exports, and an output contraction. 4.4 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 di⁄erentcomponentsofhouseholdswealth. First,theIXpolicygenerates(cid:133)scalrevenueswheneverthe home country has a trade de(cid:133)cit since in this case revenues from tari⁄s exceed subsidies to exporters. The wealth increase associated with a permanent IX policy of size (cid:14), GF ((cid:14)); is then given by the t 24

present discounted value of the (cid:133)scal revenues it generates GF ((cid:14)) = E i (cid:25) (cid:3)t;t+j (cid:14) P Ft+iY Q (0) P H(cid:3)t+iY t t i 0 0 j=1 R t(cid:3)+j 11+(cid:14) P t+j Ft+i (cid:0) t+i P t(cid:3)+j H(cid:3)t+i ! X(cid:21) Y (cid:14) @ B AR B R = Q t (0) Ft (cid:0) 1 t(cid:3) (cid:0) 1 H(cid:3)t (cid:0) 1 t (cid:0) 1 (59) 1+(cid:14) P (cid:25) (cid:0) P (cid:25) (cid:20) t(cid:3) (cid:0) 1 (cid:3)t t (cid:0) 1 t (cid:21) where the second equality uses the fact that in equilibrium the present discounted value of future trade de(cid:133)cits is equal to the net foreign asset position of the home country, that is, the di⁄erence between home country holdings of foreign bonds Q (0)BFt 1 R t(cid:3) 1 and foreign country holdings of t P t(cid:3) (cid:0) 1 (cid:25)(cid:0) (cid:3)t (cid:0) home bonds B H(cid:3)t 1Rt 1 : h i Pt (cid:0) 1 (cid:25)(cid:0) t (cid:0) h i Second, the exchange rate appreciation decreases the value of home holdings of foreign bonds. Denote with LB((cid:14)) the losses on foreign bond holdings under an appreciation of size (cid:14), then t B R (cid:14) B R LB t ((cid:14))=[Q t ((cid:14)) (cid:0) Q t (0)] P Ft (cid:0) 1 (cid:25) t(cid:3) (cid:0) 1 = (cid:0)1+(cid:14) Q t (0) P Ft (cid:0) 1 (cid:25) t(cid:3) (cid:0) 1 (60) t(cid:3) 1 (cid:3)t t(cid:3) 1 (cid:3)t (cid:0) (cid:0) Equations (59) and (60) imply: (cid:14) B R LB t ((cid:14))=GF t ((cid:14))+ 1+(cid:14) P H(cid:3)t (cid:0) 1 (cid:25) t (cid:0) 1: (61) t 1 t (cid:0) Expression (61) summarizes the wealth e⁄ects associated with IX policies. When there is no international trading of bonds denominated in home currency (B =0), as required in Proposition H(cid:3)t 1, wealth gains through higher (cid:133)scal revenues GF ((cid:14)) are exactly o⁄set by the wealth losses induced t by lower valuations of foreign holdings LB((cid:14)), thus preserving neutrality of IX policies. In contrast, t whenthehomecountryborrowsinhomecurrencybonds B >0 andinvestsinforeigncurrency H(cid:3)t 1 (cid:0) bonds(B >0);itacquiresaleveragedexposuretofor(cid:0)eignexchan(cid:1)gevariationsandthesensitivity Ft 1 (cid:0) of wealth in the home country to an exchange rate appreciation is bigger than its net foreign asset position. Consequently, given an unchanged path for future trade de(cid:133)cits, an exchange rate appreciation of the same size of the policy reduces wealth in the home country as the increase in (cid:133)scal revenuesisnotlargeenoughtoo⁄setthecapitallossesonforeignbondsholdingsimpliedbyequation (61). Thesewealthlossesinducehouseholdstoreducetheirsavingsand, inequilibrium, theexchange rate appreciates less while the trade balance increases. Figure 4 shows the response of the economy to a permanent unilateral IX policy when the home countryhasaleveragedexposuretoexchangerate(cid:135)uctuations. Inparticular,thisexperimentassumes that in the initial state international trade is balanced but countries hold o⁄setting positions in 25

domestic and foreign currency denominated bonds i.e. B =B >0 scaled to be twice as F 1 H(cid:3) 1 (cid:0) (cid:0) large as the value of annual GDP. As anticipated in(cid:0) our previous discussi(cid:1)on, the implementation of a permanent IX when foreign holdings of home currency denominated bonds are positive lowers households wealth and reduces 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 negativenetforeignassetposition. Forcomparison,wealsoplottheresponseofthebaselineeconomy when there is no international trade in domestic currency bonds, as required in Proposition 1, and a permanent IX policy is neutral (dashed lines). 4.5 Departing from Producer(cid:146)s Currency Pricing We conclude this section with a brief discussion on the requirement of producer(cid:146)s currency pricing (PCP) in Proposition 1 to deliver neutrality of IX policies. We follow the literature and compare the transmissionofpoliciesunderPCPandlocalcurrencypricing(LCP).24 UnderLCP,producersineach country set a price for the home market in domestic currency and a (pre-tari⁄) price for the foreign market in foreign currency, with both prices adjusted infrequently because of the Calvo friction.25 Figure 5 compares the e⁄ects of an IX policy under PCP (dashed lines) and under LCP (solid lines), assuming that all other conditions in Proposition 1 are satis(cid:133)ed. As discussed before, under PCP international relative prices are insulated by the immediate appreciation of the exchange rate andtheallocationisuna⁄ected. UnderLCP,incontrast,theIXpolicyhasallocativee⁄ects: Imports contract, in(cid:135)ation jumps, while exports and output experience a very small boost. The source of non-neutrality is the asymmetric pass-through of tari⁄changes and exchange rate movementstoimportprices. Asshownbytheexpressionforthepriceofimportedgoodsinthehome country P =(1+(cid:28)m)P (62) Ft t X t(cid:3) changes in import tari⁄s are fully passed through to import prices (P ) whereas movements in the Ft exchangerateonlypass-throughgraduallyasforeignexportersadjusttheirpricesinthehomemarket P infrequently under our Calvo pricing assumption: Hence, the rise in import prices reduces the X t(cid:3) (cid:0)24Fo(cid:1)radiscussionoftransmissionunderPCPandLCPsee,forinstance,DevereuxandEngel(2002). Seesection5.4 for a discussion of alternative pricing assumptions that also considers the "Dominant Currency Paradigm" (DCP). If the dominant currency is the currency of the country that implements IX, IX would still not be neutral for the same reasons described in this section. 25Appendix A presents a fullderivation ofthe optimization conditions ofproducers underthe LCP assumption. 26

demand for imported varieties and boosts output through import-substitution channels. 5 Can Alternative Tax Policies Substitute for Trade Policy Actions? In this section, we compare IX policies to tax policies that are often considered as having similar macroeconomic e⁄ects. These tax policies include "(cid:133)scal devaluation" (cid:150)implemented through a rise intheVATthatiscoupledwithapayrollsubsidytoemployers(VP)(cid:150)aswellasaborder-adjustment of corporate pro(cid:133)t taxes (BAT). Our main contribution is to provide conditions under which these three policies are equivalent and to investigate their transmission when they are not. To that end, we (cid:133)rst show that under the (quite stringent) conditions of Proposition 1, all three policies in our baseline framework are equivalent and neutral. We next present a general result stating that while IX and BAT remain equivalent when the conditions required by Proposition 1 are relaxed, IX and VP are generically not equivalent. Our analysis thus emphasizes that the equivalence of these policies often ascribed in the existing literature and among many policymakers relies crucially on a very speci(cid:133)c assumption about how VAT changes are assumed to be passed through to consumer prices. In particular, under our preferred speci(cid:133)cation of full and immediate passthrough of VAT changes to consumer prices (cid:150)for which we provide some empirical evidence at the end of this section (cid:150)we show that the e⁄ects of IX policies often diverge markedly from VP, even qualitatively. Given these di⁄erences, we conclude that alternative assumptions about tax passthrough are highly consequential for the macroeconomic e⁄ects of VP, a result reminiscent of Poterba et al. (1986). 5.1 A Special Case: Equivalence and Neutrality To understand the di⁄erences between IX (and BAT) and VP policies, it is helpful to (cid:133)rst consider a special case in which the e⁄ects of these policies look beguilingly similar (cid:150)namely, the case in which the policies are implemented permanently, exchange rates are (cid:135)exible, and monetary policy follows the benchmark Taylor-style rule that responds only to producer price in(cid:135)ation and the output gap: 1 R = ((cid:25) )’ (cid:25)(y~)’ y (63) t Pt t (cid:12) Under these conditions, VP, IX, and BAT policies have no allocative e⁄ects (cid:150)meaning no e⁄ects on output, employment, or in(cid:135)ation (cid:150)and hence may be regarded as equivalent and neutral. These 27

results are formalized in the following proposition. Proposition 2. If monetary policy is described by (63); wages are (cid:135)exible, and conditions 1.- 3. of Proposition 1 are satis(cid:133)ed, the following policies are equivalent, neutral, and induce the real exchange rate to appreciate by (cid:14): 1. A permanent unexpected IX policy of size (cid:14); 2. A permanent unexpected BAT policy with corporate taxes (cid:28)(cid:25) = (cid:14) ; 1+(cid:14) 3. A permanent unexpected VP policy of size (cid:14) ; 1+(cid:14) The formal proof of this proposition is relegated to Appendix D. It is immediate to conclude why the IX policy is neutral as the conditions of Proposition 1 apply. Given that IX and BAT are always equivalent in our environment, as we show later in Section (5:2), here we focus on the relation between IX and VP.26 In particular, we provide intuition for why VP is neutral in this special case andunderscorekeydi⁄erencesintransmissionwithrespecttotheneutralityofIX.Figure6compares the economic adjustment that delivers neutrality under IX (solid blue lines) and VP policies (dashed red lines). The three partial-equilibrium margins discussed in section (3) are a useful starting point to understand why VP has no allocative e⁄ects in this special case. Inspection of equations (43) and (44) revealsthatVPhasnodirecte⁄ectonrelativedemandofhomeandforeignvarieties,asVATchanges a⁄ect equally the price of imported and domestically-produced goods. Consequently, under VP no generalequilibriumadjustmentoftheproductrealexchangerate(Q )isrequiredtoinsulaterelative Pt prices from the e⁄ects of the policy. This transmission of VP contrasts sharply with IX where, as shown in Figure 6, the nominal exchange rate has to jump to insulate relative prices. Turning to the labor market equilibrium, the increase in the payroll subsidy and the VAT hike have o⁄setting e⁄ects on labor demand and labor supply. Under our assumption of full pass-through of taxes, at (cid:133)xed producer prices, a VAT hike induces consumer prices (P ) to jump by (cid:14) percent (see t 26Inindependentworkdevelopedaroundthesametimeasourpaper,Barbieroetal. (2018)providesimilarconditions requiredfortheBATtobeneutral. Theirneutralityresult,however,isslightlydi⁄erentfromoursbecauseofadi⁄erent assumption about the response of import prices to the adoption of the BAT, which allows them to relax condition 3 in the proposition. In particular, these authors assume that under LCP, the actual cost of imports, inclusive of the e⁄ectofthe non-deductibility from corporate pro(cid:133)ts underBAT i:e: PFt ,remains (cid:133)xed absentprice adjustment (cid:18) (1 (cid:0) (cid:28)(cid:25) t ) (cid:19) by foreign exporters (whereas this cost jumps in our environment as the price PFt remains (cid:133)xed). This assumption implies that neutrality goes through underLCP as wellin theirsetup. 28

equation46). Inorderforthehouseholdlaborsupplytoremainunchanged,equation(45)requiresan adjustment in the (cid:147)product(cid:148)real wage Wt of the same exact percentage of the VAT hike. That PPt is, in response to a VP policy of size (cid:14)(cid:16) ; the (cid:17) nominal wage W ((cid:14)) satis(cid:133)es 1+(cid:14) t W ((cid:14)) t =1+(cid:14): (64) W (0) t while producer prices are una⁄ected. In addition, as evident from the optimal pricing decision of producers (27), the commensurate increase in payroll subsidies (&v) ensures that (cid:133)rms are willing to t pay this higher wage. As shown in Figure 6, the increase in consumer prices and in the nominal wage under VP is also in sharp contrast to IX, where the nominal exchange rate is the only price that neutralizes the e⁄ects of the policy. Finally, the intertemporal optimality condition in (47) clari(cid:133)es why the consumption pro(cid:133)le is una⁄ected by VP, as long as the implementation of the policy is unexpected and permanent. We havealreadynotedthatunderVPboththeproducerrealexchangerate(Q )andtheproducerprice Pt in(cid:135)ation ((cid:25) ) do not need to adjust. Given that VAT rates jump permanently to a higher level (i.e., Pt (cid:28)v = (cid:28)v), a constant nominal interest rate keeps consumption growth constant. This result hinges t+1 t critically on the assumption that the monetary policy rule responds to producer price in(cid:135)ation and thus "sees through" rising consumer prices. Insum,IXandVParebothequivalentandneutralundertherestrictiveconditionsofProposition 2. That said, while IX policies achieve allocative neutrality through an adjustment in the nominal exchange rate, VP policies achieve neutrality through a jump in consumer prices and nominal wages without requiring any nominal exchange rate adjustment. This observation turns out to be the basis for the main result of this section, namely that IX and VP policies generically implement di⁄erent allocations. 5.2 The General Case We begin this section with a more precise de(cid:133)nition of the the three policies that we consider. De(cid:133)nition. An IX , a VP; and a BAT policy of size (cid:14) and probability of reversal (cid:26) are describedbystochasticprocesses SIX;(cid:10)IX ; SVP;(cid:10)VP ; SBAT;(cid:10)BAT respectively,withSIX = sNT;sIX as de(cid:133)ned above;S nVP = sNoT;s nVP where o in n state sVP all o taxes are zero apart from e e e e e e e (cid:8)value-adde(cid:9)d taxes and payroll subsidi(cid:8)es given by(cid:9) (cid:28)v = &v = (cid:14) ; SBAT = sNBAT;sBAT where e 1+(cid:14) in state sNBAT all taxes are zero apart from corporate pro(cid:133)t taxes given by(cid:8)(cid:28)(cid:25) = (cid:14) and(cid:9)in state e 1+(cid:14) 29

sBAT corporate pro(cid:133)t taxes are adjusted at the border (i.e. BAT =1 and (cid:28)(cid:25) = (cid:14) ). The transition 1+(cid:14) matrix is given by 1 0 (cid:10)i = (65) 1 (cid:26) (cid:26) (cid:20) (cid:0) (cid:21) where i=IX;VP;BAT: e Our main result, summarized in Proposition 3, is that while IX and BAT always implement the same allocation, VP does not (as long as prices are sticky). Proposition 3. Under full pass-through of taxes, an unexpected IX policy of size (cid:14) and an unexpected BAT policy of size (cid:14) implement the same allocation. Generically, a VP policy of size (cid:14) 1+(cid:14) does not implement the same allocation as IX or BAT. Equivalence of the three policies requires that policies are permanent, i.e. (cid:26)=1; or that prices are (cid:135)exible. Appendix E provides a formal proof showing that BAT and IX policies have identical allocative e⁄ects if there is full pass-through of tari⁄s, irrespective of the speci(cid:133)c assumptions about price and wage settings. Intuitively, recall from Section (3) that the non-deductibility of imports from (cid:133)rm pro(cid:133)ts under the BAT is similar to an import tari⁄, whereas the exemption of export sales acts like an export subsidy. Hence, a BAT policy of size (cid:14) exerts the same e⁄ects on trade prices and, more generally, on the allocation as an IX policy of the same size. The equivalence of BAT and IX policies relies importantly on the assumption of full pass-through of tari⁄s. For instance, it is immediate to show that if import tari⁄s were not fully passed through, thenBATandIXpolicieswouldbenolongerequivalentwhenforeignexporterspriceinlocalcurrency. HavingestablishedtheequivalencebetweentheBATandIXpoliciesinourbaselinemodel, inthe remainderofthissectionwestudytherelationbetweenVPandIX(orBAT)bydiscussingcasesthat make di⁄erences in transmission more evident. 5.2.1 Fixed Exchange Rates Proposition 4. In a (cid:133)xed exchange rate regime (’ = ); under assumptions 1.- 3. of Proposition " 1 1, an IX policy of size (cid:14) and a BAT policy of size (cid:14) have the same allocative e⁄ects as a once-and- 1+(cid:14) for-all unexpected currency devaluation of size (cid:14): A VP policy of the same size (cid:14) has no e⁄ect on 1+(cid:14) the allocation but causes the real exchange rate to appreciate by (cid:14): AppendixEcontainsaformalproofofProposition4. TheequivalencebetweenIXandacurrency devaluation in this framework con(cid:133)rms Keynes(cid:146)original argument and has already been formally 30

establishedinFarhietal(2014). Underourassumptionoffullpass-throughofimporttari⁄s,however, thisresultislessgeneralasitrequiresthatchangesintheexchangeratesarealsofullypassedthrough: Condition 3. of Proposition 1 ensures that this is the case by assuming producer currency pricing. Here we make use of Figure 7 to compare the e⁄ects of VP (dashed red lins) and IX (solid blue lines) under (cid:133)xed exchange rates and provide intuition for the di⁄erent e⁄ects. The neutrality of VP is a direct consequence of the neutrality result discussed in Proposition 2: Given that VP does not cause changes in relative demand and thus does not require any adjustment in the producer real exchange rate (Q ), the (cid:133)xed exchange rate regime does not pose any constraint to achieving the Pt same outcome as under (cid:135)exible exchange rates that was described above. This outcome contrasts sharply with the large output stimulus provided by IX policies under (cid:133)xed exchange rates. As shown in Figure 7, absent an appreciation of the nominal exchange rate, the IX policy boosts net exports and, with nominal interest rates unchanged, domestic consumption expands as well. ThelackofequivalencebetweenIXandVPpoliciesunder(cid:133)xedexchangeratesappearsincontrast with recent results in the (cid:133)scal devaluation literature, such as Farhi et al. (2014). The key di⁄erence between the two frameworks is that our analysis assumes that pre-tax prices are sticky and taxes are fully passed through, so that consumer prices jump immediately after the implementation of a VP policy. In the (cid:133)scal devaluation literature, in contrast, prices are typically assumed to be sticky inclusive of taxes (and hence pre-tax prices are free to adjust). Therefore, a permanent VP in thisenvironmentexactlyreplicatesthee⁄ectsofanIXpolicyasthesluggishadjustmentinconsumer pricesisassociatedwithadeclineinrealinterestratesthatboostsconsumption.Whileweconsiderour contributionaslargelytheoretical,welaterdiscusssomeevidencepointingtofairlyrapidpassthrough of VAT changes to consumer prices, in line with our benchmark speci(cid:133)cation. Nevertheless, it is plausible that this policy could have some delayed e⁄ects on consumer prices so that the contrast between IX and VP would not be quite as stark as in our baseline model. 5.2.2 Alternative wage settings Wenextexaminetheimplicationsofdepartingfromtheassumptionof(cid:135)exiblewagesforthemacroeconomicconsequencesofIXandVPpolicies. Alargemacroeconomicliteratureassumesthathouseholds set nominal wages in Calvo-style staggered contracts that are similar in form to the price contracts outlined in Section 2.27 We choose the parameter controlling the degree of wage stickiness to imply 27See,forinstance,Erceg et al. (2000). 31

that wages are adjusted with the same frequency as prices. Figure 8 shows the response of the economy to unexpected and permanent VP (dashed red lines) and IX (solid blue lines) policies under (cid:135)exible exchange rates. Recall from our discussion of Proposition 2 that IX policies do not rely on adjustment in wages to achieve neutrality. Hence, IX policies continue to have no allocative e⁄ects when wages are sticky, as shown by the blue lines in Figure 8. Given that VP policies required a jump in the product real wage to have no allocative e⁄ects, it follows that when wages are sticky VP policies are not neutral. The nominal wage rises only gradually under VP, and the product real wage follows a similar pattern, thus preventing labor supply fromfalling. However, thehigherpayrollsubsidypersistentlyreducesproducers(cid:146)marginalcosts, thus pushing producer price in(cid:135)ation down and increasing labor demand. As monetary policy cuts the policy rate in response to below-target producer price in(cid:135)ation, consumption expands. The increase in consumption and the rise in (net) exports due to the induced decline in the terms of trade (cid:0) (cid:0) contribute to an expansion in home country output. Anequallyimportantmacroeconomicliteratureconsidersformulationsofdownwardwagerigidities of the form W t >(cid:24)W t 1 ; (cid:24) >0 (66) (cid:0) where(cid:24)governsthedegreeofdownwardwagerigidity.28 GiventhatbothIXandVPpolicieseither do not a⁄ect nominal wages or increase them, it is immediate to conclude that our non-equivalence results would go through when wages are downwardly rigid. 5.2.3 IX and VP with Reversal WeconcludeouranalysisofVPandIXpolicieswithacomparisonoftheire⁄ectswhenagentsperceive that these policies will be reversed according to the transition matrix in equation (41). When agents expectpoliciestobereversed,changesinthepriceoftheconsumptionbundleovertimecanhavestrong intertemporalsubstitutione⁄ectsonconsumption,asshownbythelinearizedversionofequation(47) 1 c =c r~ (cid:25)~ (cid:1)(cid:28)v (1 !) (cid:1)q~ +(cid:1)(cid:28)m (67) t t+1 (cid:0) (cid:27) t (cid:0) pt+1 (cid:0) t+1(cid:0) (cid:0) pt+1 t+1 (cid:2) (cid:0) (cid:1)(cid:3) Equation (67) showes theat this intertemporal substitution e⁄ect is much stronger in the case of temporary VP as this policy, under full pass-through of taxes, induces direct in(cid:135)ationary pressure on 28See,forinstance,Schmitt-GrohØ and Uribe (2016). 32

the entire consumption bundle. IX policies, in contrast, generate in(cid:135)ationary pressure through only higher prices of imported goods. Figure 9 compares VP (dashed red lines) and IX (solid blue lines) policies of size (cid:14) = 10 percent that are reversed with probability (1 (cid:26)) = 0:05 by the following quarter. For simplicity, we focus (cid:0) here on the case in which wages are sticky and exchange rates are (cid:135)exible. The higher consumption real interest rate under VP depresses consumption markedly, causing a contraction in output. As output declines, the central bank lowers policy rates, which depreciates the exchange rate and boosts net exports. The contractionary e⁄ects of VP contrast substantially with the expansion of output under IX. While the two policies have similar e⁄ects of trade quantities, this outcome re(cid:135)ects very di⁄erent channels. TheIXpolicyhasdirect(cid:147)competitiveness-enhancing(cid:148)e⁄ectsonrelativetradepriceswhich 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 the depreciation of the exchange rate induced by the fall in policy rates in the face of lower aggregate demand. The disparity between VP and IX policies under full pass-through of taxes is not a⁄ected by di⁄erentassumptionsaboutwagesettingsandbecomesevengreaterunder(cid:133)xedexchangerates(since theinterestratecutunderVPshowninthe(cid:133)gurewouldbeprecluded,aswouldtheinterestratehike under IX). Taken together, our results underscore that VP and IX operate through substantially di⁄erent transmission channels. Given the importance of intertemporal substitution channels in shaping the macroeconomic e⁄ects of VP, the imposition of VP on a temporary basis runs the risk of providing a contractionary impetus to output, especially if the policy interest rate and exchange rates cannot adjust much. 5.3 Survey of Empirical Evidence on the Pass-through of Tax Changes Our (cid:133)nding that an increase in VAT accompanied by a commensurate increase in payroll subsidies has signi(cid:133)cantly di⁄erent macroeconomic e⁄ects relative to a increase in import tari⁄s and export subsidiesappearsinsharpcontrastwiththeconventionalwisdomestablishedinthe(cid:133)scaldevaluation literature. The key insight of our analysis is that assumptions about the pass-through of tax changes 33

critically determine the equivalence of these policies as nominal rigidities alter the incidence of these taxes. While the theoretical literature typically assumes that prices are rigid inclusive of taxes, our analysishasassumedthatpre-taxpricesarerigidandVATincreasesarefullyandimmediatelypassed through to consumer prices. In this section, we brie(cid:135)y review some evidence in support of the assumption of full pass-through of taxes. Nevertheless, rather than viewing this evidence as dispositive in favor of our speci(cid:133)cation of price-setting, we view our main contribution as highlighting the sensitivity of the equivalence results ofIXandVPpoliciestoassumptionsabouttaxpass-throughwhen(cid:133)rmpricescannotbeimmediately adjusted. Severalstudiespresentestimatesoflargepass-throughfromtheanalysisofcountry-speci(cid:133)cepisodes of VAT changes. Carbonnier (2006) reports that two large reductions in French VAT rates for car and housing services were associated with pass-through of between 60 and 75 percent, with most of the price adjustment completed within two months. Cashin and Unayama (2016) use the 1997 VAT increase in Japan to derive estimates of the intertemporal elasticity of substitution using information about the response of very detailed consumption expenditure categories. They (cid:133)nd that the passthrough oftheVATincreaseinto consumer prices was fulland that prices adjusted within one month of the tax change. Karadi and Rei⁄ (2016) investigate the response of prices to two increases and one decrease in VATrates thatwere implemented in Hungarybetween 2004 and 2006 across di⁄erent categories of goods. In their data, positive increases in VAT rates elicited immediate adjustments of prices (within one month) with very high pass-through (between 75 and 99 percent). The response to reduction in VAT rates, in contrast, was signi(cid:133)cantly smaller, pointing to an asymmetric response of prices to positive and negative VAT changes. Afewcross-countrystudiesalsopresentevidenceoflargeandquickpass-throughofVATchanges. Benedek et al. (2015) analyze the response of prices to VAT changes that took place in euro-area countriesovertheyears1999-2013and(cid:133)ndcompletepass-throughforchangesinstandardVATrates. Exploiting a di⁄erent identi(cid:133)cation strategy on similar data, Benzarti and Carloni (2017) (cid:133)nd that the pass-through of standard VAT rate changes to prices is about 39 percent for VAT increases and only 11 percent for VAT decreases. Despite this asymmetry, in both cases the passthrough happens in the (cid:133)rst month after the implentation of the VAT change.29 29ThetaxshiftofsaletaxesacrossU.S.statesalsoappearstobeveryhighandimmediate,asdiscussedinBesleyand Rosen (1999), although it bears noting that the nature of the sales tax base and incidence of the tax di⁄er somewhat 34

Directevidenceon(cid:133)scaldevaluationsalsopointtolargeVATpass-throughs. Forinstance,in2007 theGermangovernmentraisedthestandardVATrateby3percentagepointsandloweredthemarginal rate for social security contributions by a similar amount. Figure 10 shows the evolution of German core in(cid:135)ation and motor vehicle in(cid:135)ation (blue lines in the top panels) around the implementation of thesetaxchanges. Forcomparison,the(cid:133)gurealsopresentsthebehaviorofin(cid:135)ationinothereuro-area countries where no changes in VAT rates orpayroll contributions were implemented (red lines). Both panels clearly show a discrete jump in German in(cid:135)ation in the month January 2007, when the tax changes went into e⁄ect, whereas in(cid:135)ation in other euro-area countries does not reveal any outsized change throughout the 2007 year. This observation suggests that the spike in German in(cid:135)ation is likely to re(cid:135)ect the increase in value-added taxes. The immediate pass-through to core in(cid:135)ation is around 50 percent, a large number if one considers that the good categories a⁄ected by the VAT change accounted for just half of the consumption basket.30 Consequently, the VAT pass-through must have been very high for a large number of consumption items, as exempli(cid:133)ed by the evolution of car prices. The bottom panels of Figure 10 provide some evidence on the macroeconomic e⁄ects of the 2007 (cid:133)scal devaluation in Germany. In particular, data on various measures of nominal wages (e.g. negotiatied, compensation per hour) show a substantial pick up in labor costs in the aftermath of VAT changes,possiblyre(cid:135)ectingworkers(cid:146)requestsforstabilityinafter-taxrealwages. Finally,privateconsumption in Germany underperformed consumption in other euro-area countries, suggesting, at least qualitatively, that VAT hikes may have adverse e⁄ects on aggregate demand even when accompanied by commensurate reductions in payroll taxes. All told, evidence from country-speci(cid:133)c episodes as well as cross-sectional analysis suggests that VATchangestendtobepassedthroughtoconsumerpricesquicklyand, inmanycases, nearlyinfull. Within the context of theoretical frameworks where producer prices are adjusted infrequently, this empirical observation appears easier to reconcile with the assumption that pre-tax prices are sticky and valued added tax changes are fully passed through. from value-added taxes. 30The 2007 VAT hike did not apply to goods taxed at a reduced rate (such as food,entertainement,and books). 35

5.4 Alternative Pricing Assumptions For ease of exposition, we described the transmission of the IX (and BAT) and VP policies under the assumption of producer currency pricing (PCP) and, thus, full pass-through of exchange rate changes to traded good prices. In this section we study the e⁄ects of these policies under alternative pricing assumptions. In particular, we present simulations of transitory IX and VP policies under local currency pricing (or LCP, when exporters set prices in the destination currency) and under dominant currency pricing (or DCP, when exporters both in the home and the foreign country set prices in the home currency).31;32 There are two key takeaways from these experiments. First, given that IX policies directly a⁄ect trade prices, di⁄erent assumptions about pass-through change their e⁄ectsonexportpricesandhencea⁄ecttransmissiononimportsandexports. Nonetheless,compared to the PCP case, the overall macroeconomic e⁄ects of IX remain qualitatively similar. Second, the transmission of VP policies is very little changed under di⁄erent assumptions on exchange rate passthrough. This observation should come as no surprise given that, as we argued above, VP policies do not operate by directly a⁄ecting relative trade prices. Figure 11 shows the response of the economy to a transitory implementation of IX under PCP (solid lines), DCP (crossed lines), and LCP (dashed lines). While the response of exports is virtually identicalunderDCPasunderPCP,DCPimpliessomewhatgreaterexpenditureswitchingawayfrom imports, re(cid:135)ecting that foreign exporters under DCP are slow to adjust their (cid:145)(cid:146)at the dock(cid:148)prices (P in equation 62) so that home (cum-tari⁄) import prices rise by more. Accordingly, output rises X t(cid:3) a tad more under DCP than PCP. LCP is similar to DCP in inducing larger expenditure-switching away from imports than PCP. However, under LCP domestic exporters do not immediately reduce thepricesatwhichtheysellthedomesticgoodintheforeigncountry(P )inresponsetotheexport H(cid:3)t subsidy, leading to a much more limited boost to domestic exports under LCP than PCP (or DCP). The smaller export boost under LCP translates into a smaller output rise than under PCP or DCP, though the qualitative responses are clearly aligned. Figure 12 shows the response of the economy to a transitory implementation of VP under PCP (solid lines), LCP (dashed lines), and DCP (crossed lines). In all cases, monetary policy cuts interest 31We focus on policies that are eventually reversed given our interest in assessing the scope for IX and VP policies to provide macroeconomic stimulus. Our simulations allow wages to be sticky: As discussed before, when wage are stickyVPinducesthecompetitive-enhancinge⁄ectswhichtypicallymotivatetheuseofsuchpolicies(see,forexample, Calmfors 1998). 32Casas,Diez,Gopinath,andGourinchas(2016)studytheimplicationsofDCPinastandardNewKeynesianmodel. 36

rates in response to weaker domestic demand, thus contributing to a depreciation of the exchange rate. Compared to PCP, the slower responsiveness of trade prices to such depreciation under LCP results in a smaller boost to net exports, so that output initially contracts even more. The drop in output, in contrast, is very similar to PCP under DCP as exporters bene(cid:133)t from the depreciation of the home currency. Notwithstanding these minor di⁄erences, the overall transmission of VP is very similar across pricing assumptions as these policies do not directly alter trade prices. 6 Conclusions Our paper has presented a systematic analysis of the short-run e⁄ects of trade policies that are equivalent in a frictionless economy, namely a uniform increase in import tari⁄s and export subsidies (IX), an increase in value-added taxes accompanied by a payroll tax deduction (VP), and a border adjustmentofcorporatetaxation(BAT).UsingaNewKeynesiandynamicgeneralequilibriummodel, we have studied the transmission of these policies and summarized conditions for their equivalence and neutrality. Our paper has shown that the conventional view that trade policies do not stimulate output under (cid:135)exible exchange rates (cid:150)on the grounds that long-run balance of payment equilibrium should induce an immediate currency appreciation large enough to insulate trade prices (cid:150)rests on fragile assumptions. Speci(cid:133)cally, we argue that an increase in import tari⁄s and export subsidies is likely to elicit a much smaller response of the exchange rate than required for (cid:147)full insulation(cid:148)to hold, so that expenditure-switching e⁄ects show through to higher output. This output stimulus is largely drivenbytheexportsubsidywhereastari⁄stendtohaveanegligibleorevencontractionarye⁄ecton output. We have also shown how VP can di⁄er substantially from either IX or the BAT under full passthrough of taxes. VP tends to have contractionary e⁄ects on output if implemented on a temporary basis,re(cid:135)ectingthatthecompetitiveness-enhancinge⁄ectsofproducersubsidies(cid:150)thetypicalemphasis inthe(cid:133)scaldevaluationliterature(cid:150)areoutweighedbythedragonconsumptionfromtheimpliedrise in the real interest rate (since the VAT is expected to decrease through time). We caution that our results should not be interpreted as implying that IX policies are likely to provide a reliable and e⁄ective way of providing macroeconomic stimulus relative to other (cid:133)scal 37

measures. Indeed, given that the stimulus is due to expenditure-switching, it is contingent on foreign economies refraining from retaliation, which seems unlikely if the IX policies are put in place for very long. Conversely,ouranalysisofVPshouldnotbeinterpretedasdismissiveofthepossibilityofusing these policies to boost the economy; rather, in doing so, the program should be designed to pay keen attention to intertemporal substitution e⁄ects in addition to the competitiveness e⁄ects emphasized in the literature. Whilewehaveusedaworkhorseopen-economymodeltofacilitatecomparisonbetweenthepolicies considered, trade policies in practice have widely divergent e⁄ects across di⁄erent industries and economicsectors,withpoliticaleconomyconsiderationsoftenplayingaparamountroleindetermining thestructureoftari⁄sorsubsidies. Infuturework,itwouldbeofinteresttouseamedium-scalemodel with a broader array of frictions and more sectoral di⁄erentiation to revisit some of the questions we have considered here. 38

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7 Appendix A. Model Equations 7.1 Households Household i H =[0;1] chooses w(cid:22) (i);w (i);n (i);c (i);a (i);B (i);B (i) to maximize t t t t t;t+1 Ht Ft 2 f g maxE0 (cid:6) 1t=0 (cid:12)t " [c t 1 (i)]1 (cid:27) (cid:0) (cid:27) (cid:0) [ 1 n t + (i (cid:17) )]1+(cid:17) # (68) (cid:0) s:t P c (i)+(cid:6) q a (i)+B (i)+" B (i)+ (cid:31) B (i) B(cid:22) 2 = t t t+1 t;t+1 t;t+1 Ht t Ft 2 Ft (cid:0) F (69) R t 1 B Ht 1 (i)+" t R t(cid:3) 1 B Ft 1 (i)+P t a t h 1;t (i)+w t (i (cid:0) )n t (i)+(cid:5) t + (cid:1) Ti t (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) w (i) w:p: (cid:16) w t (i)= w t (cid:22) (cid:0) 1 (i) w:p: 1 W (cid:16) e (70) (cid:26) t (cid:0) W n (i)= w t (i) (cid:0) (cid:13) n N (71) t t W (cid:20) t (cid:21) where W is a wage index (descrobed below) and q is the price of a state contingent Arrow t t;t+1 securitypayingoneunitofconsumptioninaspeci(cid:133)cstateattimet+1:Weassumethatacompleteset of Arrow securities is traded domestically so that perfect risk sharing within each country allows for simpleaggregation. Equation(70)statesthathousheholdscanonlyadjusttheirwagewithprobability (cid:16) : Equation (71) is the (cid:133)rms(cid:146)demand schedule for labor variety i; derived below. W Optimality conditions are 1=(cid:12)Et " C C t t (cid:0) (cid:0) + (cid:27) (cid:27) 1 P P t+ t 1 R t # (72) 1+(cid:31) B Ft (i) (cid:0) B(cid:22) F =(cid:12)Et " C C t t (cid:0) (cid:0) + (cid:27) (cid:27) 1 P P t+ t 1 " t " + t 1R t(cid:3) # (73) (cid:0) (cid:1) [n (i)](cid:17) (cid:13) W(cid:22) E (cid:16)s t C (cid:27) s n t n (i)=0 (74) t W(cid:0) s(cid:0) C (cid:27) ((cid:13) 1) (cid:0) P s (cid:26) s(cid:0) n(cid:0) s(cid:27) X 7.2 Retailers The problem of retailers is as described in the main text. 43

7.3 Producers 7.3.1 PCP pricing Producer i F = [0;1] chooses an optimal reset price P (i); export prices P (i) quantities 2 Pt f H(cid:3)s gs t (cid:21) Y (i);Y (i) and employment N (i); n (j;i) to maximize f Hs H(cid:3)s gs (cid:21) t s f s gj s t n o (cid:21) P(cid:22) (i) Y (i)+ s(cid:3)Y (i) (1 &v) w (j)n (j;i)dj maxE (cid:16)s t(cid:3) (1 (cid:28)(cid:25)) Pt Hs s H(cid:3)s (cid:0) (cid:0) s s s (75) t P(cid:0) t;s (cid:0) s 8 h iP s R 9 X s (cid:21) t < = s:t: : ; s Y (i)+ (cid:3)Y (i)=A N(cid:11)(i) (76) Hs s H(cid:3)s s s (cid:13)n N s (i)= [n s (j;i)] (cid:13)n (cid:13)n (cid:0) 1 dj (cid:13)n(cid:0) 1 (77) (cid:26)Z (cid:27) Y (i)= P(cid:22) Pt (i) (cid:0) (cid:13) Y (78) Hs Hs P (cid:20) Ps (cid:21) Y (i)= P H(cid:3)s (i) (cid:0) (cid:13) Y (79) H(cid:3)t P H(cid:3)t (cid:20) H(cid:3)s (cid:21) (1 (cid:28)(cid:25)BAT )(1+(cid:28)m )P(cid:22) (i) P H(cid:3)s (i)= (cid:0) s (1+ s &x) s (cid:3) P " t (80) t s where s and s are the size of the foreign and home country respectively. (cid:3) Theoptimalityconditionsforthisproblemareconstraints(76) (80)aswellasanoptimalpricing (cid:0) condition as in the text: s 1 (cid:13) (1 &v)W Et (cid:6) 1s=t (cid:16)s P(cid:0) t(cid:3) t;s Y Hs (i)+ s (cid:3)Y H(cid:3)s (i) (1 (cid:0) (cid:28)(cid:25) s ) P P Pt (i) (cid:0) (cid:13) 1(cid:11)A (cid:0) N s (i)(cid:11) s 1 =0 (81) (cid:20) (cid:21) s (cid:20) (cid:0) s s (cid:0) (cid:21) where W is the wage index s 1 W s = [w s (j)]1 (cid:0) (cid:13) ndj 1 (cid:0) (cid:13)n (82) (cid:20)Z (cid:21) 7.3.2 LCP pricing Producer i chooses optimal reset prices P(cid:22) (i) and P(cid:22) (i); where P(cid:22) (i) is the foreign currency Pt X(cid:3)t X(cid:3)t price of domestic export net of tari⁄s, export prices P (i) ; quantities Y (i);Y (i) and f H(cid:3)s gs t f Hs H(cid:3)s gs t (cid:21) (cid:21) employment N (i); n (j;i) to maximize s f s gj s t n o (cid:21) P(cid:22) (i)Y (i)+" P (i) (1+&x s ) s(cid:3)Y (i) (1 &v) w (j)n (j;i)dj maxE t (cid:16)s P(cid:0) t(cid:3) t;s (1 (cid:0) (cid:28)(cid:25) s ) 8 Pt Hs s X(cid:3)t (1 (cid:0) (cid:28)(cid:25) s BATs) P s s H(cid:3)s (cid:0) (cid:0) s R s s 9 X s (cid:21) t < = (83) : ; 44

s:t: s Y (i)+ (cid:3)Y (i)=A N(cid:11)(i) (84) Hs s H(cid:3)s s s (cid:13)n N s (i)= [n s (j;i)] (cid:13)n (cid:13)n (cid:0) 1 dj (cid:13)n(cid:0) 1 (85) (cid:26)Z (cid:27) Y (i)= P(cid:22) Pt (i) (cid:0) (cid:13) Y (86) Hs Hs P (cid:20) Ps (cid:21) Y (i)= P H(cid:3)s (i) (cid:0) (cid:13) Y (87) H(cid:3)t P H(cid:3)t (cid:20) H(cid:3)s (cid:21) P (i)=(1+(cid:28)m )P (i) (88) H(cid:3)s s (cid:3) X(cid:3)t The optimality conditions for this problem are constraints (84) (88) and optimal pricing condi- (cid:0) tions for domestic and foreign markets: Y (i) (cid:13) (1 &v)W Et (cid:6) 1s=t (cid:16)s P(cid:0) t(cid:3) t;s (1 (cid:0) (cid:28)(cid:25) s ) H P s P(cid:22) Pt (i) (cid:0) (cid:13) 1(cid:11)A (cid:0) N s (i)(cid:11) s 1 =0 (89) s (cid:20) (cid:0) s s (cid:0) (cid:21) Y (i) (1+&x) (cid:13) (1 &v)W Et (cid:6) 1s=t (cid:16)s P(cid:0) t(cid:3) t;s (1 (cid:0) (cid:28)(cid:25) s ) H(cid:3) P s " s (1 (cid:28)(cid:25)B s AT ) P X(cid:3)t (i) (cid:0) (cid:13) 1(cid:11)A (cid:0) N s (i)(cid:11) s 1 =0 (90) s (cid:20) (cid:0) s s (cid:0) s s (cid:0) (cid:21) where W is the wage index s 1 W s = [w s (j)]1 (cid:0) (cid:13) ndj 1 (cid:0) (cid:13)n (91) (cid:26)Z (cid:27) An analogous problem for the foreign producers yield Y (i) (cid:13) W Et (cid:6) 1s=t (cid:16)s P(cid:0) t(cid:3) t;s F(cid:3) P s P(cid:22) P(cid:3)t (i) (cid:0) (cid:13) 1(cid:11)A N s ( (cid:3) i)(cid:11) 1 =0 (92) s (cid:20) (cid:0) (cid:3)s s(cid:3) (cid:0) (cid:21) Y (i) 1 (cid:13) W Et (cid:6) 1s=t (cid:16)s P(cid:0) t(cid:3) t;s F P s " (1+&x s(cid:3) )P(cid:22) X (cid:3) t (i) (cid:0) (cid:13) 1(cid:11)A N s ( (cid:3) i)(cid:11) 1 =0 (93) s (cid:20) s (cid:0) (cid:3)s s(cid:3) (cid:0) (cid:21) where (1+(cid:28)m)P(cid:22) (i) P (i)= s X (cid:3) t Fs (1 (cid:28)v) (cid:0) s 8 Equilibrium equations Equations(94) (125)determinetheequilibriumprocess (cid:9)(st) . Foreaseofexpositionwe (cid:0) f gst (S)t;t 0 2 (cid:21) we group elements of (cid:9) into variables that we associate with households optimality conditions,(cid:9) HH and (cid:9) abroad, retailers optimality conditions, (cid:9) and (cid:9) ; (cid:133)rms optimality conditions, (cid:9) (cid:3)HH RE (cid:3)RE FI 45

and (cid:9) ; price indexes, (cid:9) and (cid:9) ; and market clearing conditions, (cid:9) : We have that (cid:9) = (cid:3)FI PI (cid:3)PI MC (cid:9) ;(cid:9) ;(cid:9) ;(cid:9) ;(cid:9) ;(cid:9) ;(cid:9) ;(cid:9) ;(cid:9) f HH (cid:3)HH RE (cid:3)RE FI (cid:3)FI P (cid:3)P MC g Households optimality (cid:9) = w (i);W(cid:22) ;n (i);C ;B (leaving out budget constraint and B ) HH t t t t Ht Ft (cid:8) (cid:9) w (i) w:p: (cid:16) w (i)= t W (94) t+1 W(cid:22) w:p: 1 (cid:16) (cid:26) t+1 (cid:0) W [n (i)](cid:17) (cid:13) W(cid:22) E (cid:16)s t C (cid:27) s n t n (i)=0 (95) t W(cid:0) s(cid:0) C (cid:27) ((cid:13) 1) (cid:0) P s (cid:20) s(cid:0) n(cid:0) s(cid:21) X n (i)= w t (i) (cid:0) (cid:13) n N (96) t t W (cid:18) t (cid:19) 1=(cid:12)Et " C C t t (cid:0) (cid:0) + (cid:27) (cid:27) 1 P P t+ t 1 R t # (97) 1+(cid:31) B Ft (i) (cid:0) B(cid:22) F =(cid:12)Et " C C t t (cid:0) (cid:0) + (cid:27) (cid:27) 1 P P t+ t 1 " t " + t 1R t(cid:3) # (98) (cid:0) (cid:1) and symmetric conditions for (cid:9) = w (i);W(cid:22) ;n (i);C ;B abroad (cid:3)HH t(cid:3) t(cid:3) (cid:3)t t(cid:3) F(cid:3)t Retailers optimality (cid:8) (cid:9) (cid:9) = Y ;Y ;Y (i);Y (i) RE Ht Ft Ht Ft f g Y =! P Ht (cid:0) (cid:18) C (99) Ht t P (cid:20) t (cid:21) Y =(1 !) P Ft (cid:0) (cid:18) C (100) Ft (cid:0) (1 (cid:28)(cid:25)BAT )P t (cid:20) (cid:0) t t t(cid:21) Y (i)= P Pt (i) (cid:0) (cid:13) Y (101) Ht Hs P (cid:18) Pt (cid:19) Y (i)= P Ft (i) (cid:0) (cid:13) Y (102) F Ft P (cid:18) Ft (cid:19) and symmetric conditions for (cid:9) = Y ;Y ;Y (i);Y (i) RE f F(cid:3)t H(cid:3)t F(cid:3)t H(cid:3)t g Firms optimality (cid:9) FI = P H(cid:3)s (i);P Ft (i);P Pt (i);P P(cid:3)t (i);P Pt (i);P(cid:3) Pt (i);P(cid:22) X(cid:3)t (i);P(cid:22) X(cid:3) (cid:3) t (i);P X(cid:3)t (i);P X (cid:3) t (i) n o P (i)=(1+(cid:28)m )P (i) (103) H(cid:3)t t (cid:3) X(cid:3)t 1+(cid:28)m P (i)= t P (i) (104) Ft 1 (cid:28)v X (cid:3) t (cid:0) t 46

P (i) w:p: (cid:16) P (i)= Pt p (105) Pt+1 P(cid:22) (i) w:p: 1 (cid:16) (cid:26) Pt+1 (cid:0) p P (i) w:p: (cid:16) P (i)= P(cid:3)t p (106) P(cid:3)t+1 P(cid:22) (i) w:p: 1 (cid:16) (cid:26) P(cid:3)t+1 (cid:0) p Et (cid:6) 1s=t (cid:16)s P(cid:0) t(cid:3) t;s Y Hs (i)+ s s (cid:3)Y H(cid:3)s (i) P 1 s P Pt (i) (cid:0) (cid:13) (cid:0) (cid:13) 1(cid:11)A (1 s (cid:0) N & s v s ( ) i W )(cid:11) s (cid:0) 1 =0 PCP h i h i (107a) Et (cid:6) 1s=t (cid:16)s P(cid:0) t(cid:3) t;s YH P s s (i) P(cid:22) Pt (i) (cid:0) (cid:13) (cid:0) (cid:13) 1(cid:11)A (1 s (cid:0) N & s v s ( ) i W )(cid:11) s (cid:0) 1 =0 LCP h i (107b) Et (cid:6) 1s=t (cid:16)s P(cid:0) t(cid:3) (cid:3)t;s s s (cid:3) Y Fs (i)+Y F(cid:3)s (i) P 1 s(cid:3) P(cid:3) Pt (i) (cid:0) (cid:13) (cid:0) (cid:13) 1(cid:11)AsN W s(cid:3) s ( (cid:3) i)(cid:11) (cid:0) 1 =0 PCP (cid:2) (cid:3) h i (108a) Et (cid:6) 1s=t (cid:16)s P(cid:0) t(cid:3) (cid:3)t;s Y F P (cid:3)s s(cid:3) (i) P(cid:3) Pt (i) (cid:0) (cid:13) (cid:0) (cid:13) 1(cid:11)AsN W s(cid:3) s ( (cid:3) i)(cid:11) (cid:0) 1 =0 LCP h i (108b) P H(cid:3)t (i)= (1 (cid:0) (cid:28)(cid:25)B ( A 1+ T & t) x t ( ) 1+(cid:28)m t (cid:3))PP " t t (i) PCP (109a) Et (cid:6) 1s=t (cid:16)s P(cid:0) t(cid:3) t;s Y H(cid:3) P s s (i) " s(1 (cid:0) ( (cid:28) 1 (cid:25) + B &x s A ) Ts) P(cid:22) X(cid:3)t (i) (cid:0) (cid:13) (cid:0) (cid:13) 1(cid:11)A (1 s (cid:0) N & s v s ( ) i W )(cid:11) s (cid:0) 1 =0 LCP h i (109b) P (i)= 1+(cid:28)m t P P(cid:3)t (i)"t PCP Ft 1 (cid:0) (cid:28)v t (1+&x t(cid:3)) (110a) Et (cid:6) 1s=t (cid:16)s P(cid:0) t(cid:3) (cid:3)t;s Y H(cid:3) P s s (i) (1+ " & s x s(cid:3))P(cid:22) X (cid:3) t (i) (cid:0) (cid:13) (cid:0) (cid:13) 1(cid:11)AsN W s(cid:3) s ( (cid:3) i)(cid:11) (cid:0) 1 =0 LCP h i (110b) 47

P (i)=P(cid:22) (i) PCP X t X t (cid:3) (cid:3) (111a) P (i) w:p: (cid:16) P (i)= X (cid:3) t W LCP X (cid:3) t+1 P(cid:22) (i) w:p: 1 (cid:16) (cid:26) X (cid:3) t+1 (cid:0) W (111b) and symmetric conditions for (cid:9) (cid:3)FI = N t(cid:3) (i);P Ft (i);P P(cid:3)t (i);P(cid:3) Pt (i);P(cid:22) X (cid:3) t (i);P X (cid:3) t (i) n o Price indexes (cid:9) = P ;P ;P ;P ;W PI t Ht Pt Ft t f g 1 P = !P1 (cid:18)+(1 !) P Ft 1 (cid:0) (cid:18) 1 (cid:0) (cid:18) (112) t " H(cid:0)t (cid:0) (cid:18) 1 (cid:0) (cid:28)(cid:25) t BAT t(cid:19) # 1 1 1 (cid:13) P Ht = P Ht (i)1 (cid:0) (cid:13)di (cid:0) (113) (cid:20)Z0 (cid:21) P =P (1 (cid:28)v) (114) Pt Ht (cid:0) t 1 1 1 (cid:13) P Ft = P Ft (i)1 (cid:0) (cid:13)di (cid:0) (115) (cid:20)Z0 (cid:21) 1 W s = [w s (j)]1 (cid:0) (cid:13) ndj 1 (cid:0) (cid:13)n (116) (cid:20)Z (cid:21) and symmetric conditions for (cid:9) = P ;P ;P ;P ;W (cid:3)PI f t(cid:3) F(cid:3)t P(cid:3)t H(cid:3)t t(cid:3) g Market Clearing (cid:9) = N (i);N (i);N ;N ;B ;B ;" ;R ;R MC f t t(cid:3) t t(cid:3) Ft H(cid:3)t t t t(cid:3) g s Y (i)+ (cid:3)Y (i)=A N(cid:11)(i) (117) Ht s H(cid:3)t t t s Y (i)+ Y (i)=A N (cid:11)(i) (118) F(cid:3)t s Ft t t(cid:3) (cid:3) N = N (j)dj (119) t t Zj 2 F N = N (j)dj (120) t(cid:3) t(cid:3) Zj 2 F 48

B +B =0 (121) Ft F(cid:3)t B +B =0 (122) Ht H(cid:3)t s P (1 (cid:28)v)P " t B Ft +B Ht =" t B Ft (cid:0) 1 R t(cid:3) (cid:0) 1 +B Ht (cid:0) 1 R t (cid:0) 1 + s (cid:3)" t 1+ H(cid:3) (cid:28) t m t (cid:3) Y H(cid:3)t(cid:0) ( (cid:0) 1+ t (cid:28)m t ) FtY Ft (123) R = 1 P p(cid:3)t ’ (cid:25) Y Ft +Y F(cid:3)t ’ y " t ’(cid:3)" (124) t(cid:3) (cid:12) P p(cid:3)t 1! Y F f t lex+Y F(cid:3)t flex ! (cid:18) (cid:22)" t(cid:19) (cid:0) 1 P ’ (cid:25) Y +Y ’ y " ’ " R = pt Ht H(cid:3)t t (125) t (cid:12) (cid:18) P pt (cid:0) 1(cid:19) Y H fl t ex+Y H(cid:3) f t lex ! (cid:18) (cid:22)" t(cid:19) 9 Appendix B. Proof of Proposition 1 We start by giving a formal de(cid:133)nition of neutrality of a policy and equivalence between policies. De(cid:133)nition 1.Let the evolution of the policy regime s before the implementation of a given policy t be determined by the stochastic process S;(cid:10) and let S~;(cid:10)~ describe the process for policy after the f g n o implementation of the policy. We say that the implementation of the policy has no allocative e⁄ects or that it is neutral if for any equilibrium process (cid:9)(st) before the implementation of the f gst (S)t;t 0 2 (cid:21) policy there is an equilibrium process (cid:9)~ (st) under which the real allocation st (S~)t;t 0 n o 2 (cid:21) (cid:4)= C~ st ;C~ st ; n~ i;st ; n~ i;st ; Y~ i;st ; Y~ i;st ; Y~ i;st ; Y~ i;st (cid:3) (cid:3) H F H(cid:3) F(cid:3) st (S~)t;t 0 n (cid:0) (cid:1) (cid:0) (cid:1) (cid:8) (cid:0) (cid:1)(cid:9) (cid:8) (cid:0) (cid:1)(cid:9) n (cid:0) (cid:1)o n (cid:0) (cid:1)o n (cid:0) (cid:1)o n (cid:0) (cid:1)oo 2 (cid:21) e t is una⁄acted: that is there exists a sequence of functions (cid:22) : S~ (S)t such that for each element t ! (cid:16) (cid:17) {~ in (cid:4) t e {~ st ={ (cid:22) t st for any st 2 S~ ;t (cid:21) 0 (cid:0) (cid:1) (cid:0) (cid:0) (cid:1)(cid:1) (cid:16) (cid:17) where { is the corresponding element in the real allocation (cid:4) which is part of equilibrium process (cid:9): We also say that the two policies described by S;(cid:10) and S~;(cid:10)~ are equivalent. f g n o De(cid:133)nition2givesade(cid:133)nitionofaunilateralIXpolicythatgeneralizestheexampleusedinLemma 1. De(cid:133)nition 2. Let the evolution of trade policy at home and abroad s =((cid:28)m;&x;(cid:28)m ;&x ) before t t t t (cid:3) t(cid:3) the IX implementation be determined by the stochastic process S;(cid:10) : A unilateral implementation f g of IX of size (cid:14) that is anticipated w.p. (cid:25)IX and is reversed w.p. (cid:26); is described by a new stochastic process GPIX;(cid:10)IX such that GPIX =S SIX where the set of states is given by [ (cid:8) (cid:9) SIX =(cid:27)IX([S]) (126) (cid:14) 49

where ((cid:28)m;&x;(cid:28)m ;(cid:28)x ) S the function (cid:27)IX((cid:28)m;&x;(cid:28)m ;(cid:28)x )=((cid:28)~m;~&x;(cid:28)m ;(cid:28)x ) with 8 t t t (cid:3) t(cid:3) 2 (cid:14) t t t (cid:3) t(cid:3) t t t (cid:3) t(cid:3) 1+(cid:28)~m 1+~&x t = t =1+(cid:14) (127) 1+(cid:28)m 1+&x t t and 1 (cid:25)IX (cid:10) (cid:25)IX(cid:10) (cid:10)IX = (cid:0) (128) (1 (cid:26))(cid:10) (cid:26)(cid:10) (cid:20) (cid:0) (cid:0) (cid:1) (cid:21) where the ordering of states in the matrix (cid:10)IX is the obvious one. Notice that the process GPIX;(cid:10)IX does not encompass the possibility of retaliation. Proposition 1. In an e(cid:8)conomy with(cid:9)(cid:135)exible exchange rates, a unilateral implementation of IX of size (cid:14) has no allocative e⁄ect if 1. It is unanticipated, permanent, and there is no probability of retaliation; 2. Foreign holdings of home currency are always zero; 3. Export prices are set in producer currency (PCP) or prices are (cid:135)exible The only e⁄ect of the policy is to cause a (cid:14) percent appreciation of the currency " : t Proof. Condition 1 implies that (cid:25)IX =0 and (cid:26)=1: In this case the transition matrix is simply (cid:10) 0 (cid:10)IX = (129) 0 (cid:10) (cid:20) (cid:21) Let (cid:9)(st) denote an equilibrium process before the IX implementation, i.e. when s f gst (ST)t;t 0 t 2 (cid:21) is governed S;(cid:10) : f g Consider now a process (cid:9)~ (st) with an unanticipated permanent IX such that, for st (S~)t;t 0 each element {~ of (cid:9)~; other th n an the o nom 2 inal (cid:21) exchange rate, ~" t ; and home currency producer prices of foreign exporters, P~ (i); we have X t (cid:3) {~ s~t ={ (cid:22) t s~t 8 s~t 2 GPIX t ; 8 t (cid:21) 0 (130) (cid:0) (cid:1) (cid:0) (cid:0) (cid:1)(cid:1) (cid:0) (cid:1) where { is the corresponding element of the equilibrium process (cid:9) without IX and function (cid:22) t maps all histories in which IX is implemented into a history in which IX is not implemented: i.e. s~t =(s~ ;:::;s~) GPIX t ; (cid:22) (s~t)=st =(s ;:::;s ) (S)t where i 1 8 1 t 2 t 1 t 2 8 (cid:21) (cid:0) (cid:1) s~ if s~ S i i s = 2 i ( (cid:27)I (cid:14) X (cid:0) 1 (s~ i ) if s~ i 2 GPIX (cid:0) (cid:1) 50

For ease of notation in what follows, for any s~t = (s~ 1 ;::::;s~ t ) GPIX t ; we let {~ t = {~(s~t) and 2 {t ={ (cid:22)I t X(s~t) : (cid:0) (cid:1) The(cid:0)nominal(cid:1)exhange rate and the home currency producer prices of foreign exporters are s~t = 8 (s~ ;::::;s~) GPIX t 1 t 2 " if s~ S (cid:0) (cid:1) ~" t = "t t if s~ t 2 SIX (131) ( 1+(cid:14) t 2 P (i) if s =sTW X t t (cid:3) 6 P~ (i)= (132) X t (cid:3) 8 < 1+ 1 (cid:14) P X (cid:3) t (i) if s t =sTW We want to show that (cid:9)~ (st) : is an equilibrium. st (GPIX)t;t 0 We (cid:133)rst show that n (cid:9)~ (st) s o atis 2 (cid:133)es all of (cid:21) the equations directly a⁄ected by the tari⁄s and export subsidychangewhens~ =((cid:28)~m;~&x;(cid:28)m ;(cid:28)x ) SIX:Theseequationsarethelawsofoneprice(109a) t t t t (cid:3) t(cid:3) 2 (cid:0) (110a), the tax pass-through equations (104) (103); and the balance of payment equilibrium (123) (cid:0) Consideringthelawofonepricefordomesticgoodsatanhistorys~t suchthats~ =((cid:28)~m;~&x;(cid:28)m ;(cid:28)x ) t t t t (cid:3) t(cid:3) 2 SIX and letting (cid:27)I (cid:14) X (cid:0) 1 (s~ t )=((cid:28)m t ;(cid:28)x t ;(cid:28)m t (cid:3) ;(cid:28)x t(cid:3) ) 2 S we see that (cid:0) (cid:1) 1+(cid:28)m 1 P~ (i) = P (i)=P (i) t (cid:3) (133) H(cid:3);t H(cid:3);t H;t 1+(cid:27)x " t t 1+(cid:28)m 1 = P~ (i) t (cid:3) (134) H;t (1+(cid:27)~x)~" t t where the (cid:133)rst and third equalities follow from (130), (131) and (127) and the second from the fact that (cid:9) is an equilibrium. An analogous arguemt holds for (110a) and (104) . Consider now the balance of payment equilibrium which, under condition 2 B = 0 = B(cid:22) and H(cid:3) 1 (cid:0) (cid:31)= ; is 1 P~ P~ B~ =B~ R~ + H(cid:3)t Y~ Ft Y~ Ft Ft (cid:0) 1 t(cid:3) (cid:0) 1 1+(cid:28)m t (cid:3) H(cid:3)t(cid:0) (1+(cid:28)~m t )~" t Ft to see that this is satis(cid:133)ed, let again (cid:27)I (cid:14) X (cid:0) 1 (s~ t )=((cid:28)m t ;(cid:28)x t ;(cid:28)m t (cid:3) ;(cid:28)x t(cid:3) ) 2 S to get (cid:0) (cid:1) P P B~ = B =B R + H(cid:3)t Y Ft Y Ft Ft Ft (cid:0) 1 t(cid:3) (cid:0) 1 1+(cid:28)m t (cid:3) H(cid:3)t(cid:0) (1+(cid:28)m t )" t Ft P~ y~ = B~ R~ + H(cid:3)t Y~ P~ Ft Ft (cid:0) 1 t(cid:3) (cid:0) 1 1+(cid:28)m t (cid:3) H(cid:3)t(cid:0) Ft (1+(cid:28)~m t )~" t wherethe(cid:133)rstandthirdequalityfollowfrom(130)(131)and(127)andthesecondfromthefactthat (cid:9) is an equilibrium : We then need to check that the adjustment of the nominal exchange rate and local currency producer prices of exports in (131) (132) does not induce violations in other equilibrium equations. (cid:0) 51

Under PCP P~ (i) and P~ (i) only a⁄ect (104) and (103); i.e. they are de(cid:133)nitions:The exchange X(cid:3)t X (cid:3) t rate " a⁄ects optimal holdings of foreign bonds (98) and an anlogous condition abroad. As long t as (cid:25)IX = 0 and (cid:26) = 1 we have that st GPIX t ; if st+1 GPIX t has positive probability, 8 2 2 Pr st+1 st >0; the appreciation is identica(cid:0)l across(cid:1)equilbria: (cid:0) (cid:1) j (cid:8) (cid:9) ~" " t+1 = t+1 ~" " t t and since these conditions only depend on exchange rate appreciation they are satis(cid:133)ed. 10 Appendix C. Proof of Lemma 1 ConsideranIXpolicysubjecttopolicyreversalandcharacterizedby ST;(cid:10)T whereST = sNT;sIX : Instate sNT nocountryleviesanytaxesandinthesecondstate sI(cid:8)X theh(cid:9)omecountryu(cid:8)nilaterally(cid:9) raises im(cid:0)port(cid:1)tari⁄s and export subsidies by the same amount (cid:14):(cid:0)The(cid:1)transition matrix is 1 0 (cid:10)T = (135) 1 (cid:26) (cid:26) (cid:20) (cid:0) (cid:21) Consider also an IX policy that triggers retaliation and characterized by SR;(cid:10)R ; where SR = ST;sTW :ST includesthesametwostatesasdescribedabovebutinsTW t(cid:8)heforeig(cid:9)ncountryretal- (cid:8)iateswith(cid:9)asymmetricpolicy( i.e. (cid:28)m =&x =(cid:28)m =&x =(cid:14)):Inthiscasethetransitionprobability t t t (cid:3) t(cid:3) matrix is: 1 0 0 (cid:10)R = (1 (cid:25))(1 (cid:26)) (cid:26) (cid:25)(1 (cid:26)) (136) 2 (cid:0) (cid:0) (cid:0) 3 1 ’ 0 ’ (cid:0) 4 5 Lemma 1 If export prices are set in producer currency, a unilateral implementation of IX with policy reversal, i.e. s governed by ST;(cid:10)T ; implements the same equilibrium allocation as a unit lateral implementation of IX that t(cid:8)riggers r(cid:9)etaliation, i.e. s governed by SR;(cid:10)R ; coupled with t international transfers that satisfy: (cid:8) (cid:9) (cid:14) TI = B R " +B R t1 (cid:0)1+(cid:14) F;t1(cid:0) 1 t(cid:3) 1(cid:0) 1 t1 H;t1(cid:0) 1 t1(cid:0) 1 (cid:2) (cid:3) R T t I 2 =(cid:14) (cid:20) B F;t2(cid:0) 1 R t(cid:3) 2(cid:0) 1 " t2 +B H;t2(cid:0) 1 (cid:25) t2 t (cid:0) 2 1 (cid:21) where t is the (cid:133)rst time the economy transits to the retaliation state sTW and t > t is the (cid:133)rst 1 2 1 time it leaves the retaliation state sTW. 52

Proof. Let (cid:9)(st) be an equilibrium with no international transfers and no retaliaf gst (ST)t;t 0 2 (cid:21) tion, i.e. T (st)=0 st ST t . 8 2 Consider now the proc(cid:0)ess(cid:1) (cid:9)~ (st) such that, for each element {~ of (cid:9)~; other than st (SR)t;t 0 n o 2 (cid:21) bond holdings and local currency producer prices of exports, we have {~ st ={ (cid:22) t st 8 st 2 SR t ; 8 t (cid:21) 0 (137) (cid:0) (cid:1) (cid:0) (cid:0) (cid:1)(cid:1) (cid:0) (cid:1) where { is the corresponding element of the equilibrium process (cid:9) without trade wars and function (cid:22) maps all histories in which a trade war occurs into a history in which no taxes are levied: that is t st =(s ;:::;s ) SR t ; (cid:22) (st)=s~t =(s~ ;:::;s~) ST t where i 1 8 1 t 2 t 1 t 2 8 (cid:21) (cid:0) (cid:1) s if s (cid:0) = (cid:1) sTW s~ i = sN i T if s i 6 =sTW : (cid:26) i For ease of notation in what follows, for any st = (s 1 ;::::;s t ) SR t ; we let {~ t = {~(st) and 2 {t ={((cid:22)(st)): (cid:0) (cid:1) Bond holdings and local currency producer prices of exports satisfy st =(s ;::::;s ) SR t 1 t 8 2 (cid:0) (cid:1) 1 if s =sTW B~ F;t = B~ H;t = t 6 (138) B B 8 F;t H;t < 1+ 1 (cid:14) if s t =sTW : 1 if s =sTW P~ X (cid:3) t = P~ X(cid:3)t = t 6 (139) P P 8 X (cid:3) t X(cid:3)t < 1+ 1 (cid:14) if s t =sTW We want to show that (cid:9)~ (st) is a:n equilibrium when international transfers satisfy st (SR)t;t 0 n o 2 (cid:21) 0 if s =sTW and s =sTW t 1 t (cid:0) 6 6 8 T~ st =>>>>>>< (cid:0)1+ (cid:14) (cid:14) h B~ F;t (cid:0) 1 R~ t(cid:3) (cid:0) 1 ~" t +B~ H;t (cid:0) 1 R~ t (cid:0) 1 i if s t (cid:0) 1 6 =sTW and s t =sTW : (140) (cid:0) (cid:1) (cid:14) B~ R~ ~" +B~ R~ if s =sTW and s =sTW Itisstraightf >>>>>>: orwa 1+ rd (cid:14) h toc F h ;t e (cid:0) c 1 kt t(cid:3) h (cid:0) a 1 ti t f(cid:9) i H s ; a t (cid:0) n 1 eq t u (cid:0) il 1 i i briumth t e (cid:0) n 1 (cid:9)~ satis(cid:133)esall t e 6 quilibriumequations t t other than (123). When s = sTW the only conditions that need to be checked are the laws of one t price(109a) (110a)andthetaxpass-throughequations(104) (103)whicharesatis(cid:133)edunder(139). (cid:0) (cid:0) All the other equations are clearly satis(cid:133)ed by construction of (cid:9)~; and by the fact that the probability of leaving the unilateral IX state is the same in (135) and (136): 53

Consider now the balance of payment equilibrium (123) which we rewrite as follows A~ =A~ r~a+NX~ +T~ t t 1 t t t (cid:0) where A~ =B~ ~" +B~ t 1 F;t 1 t 1 ht 1 (cid:0) (cid:0) (cid:0) (cid:0) B~ R~ ~" +B~ R~ F;t 1 t(cid:3) 1 t ht 1 t 1 ra = (cid:0) (cid:0) (cid:0) (cid:0) t h A~ i t 1 (cid:0) P s (1 (cid:28)v)P NX~ t =" t 1+ H(cid:3) (cid:28) t m s (cid:3)Y H(cid:3)t(cid:0) ( (cid:0) 1+ t (cid:28)m) FtY Ft t (cid:3) t Takeanyhistorys~ 1 =(s~ 1 ;:::;s~ t ;:::) 2 SR 1 suchthats i =sTW 9 i:Lett 1 andt 2 satisfys t1 =sTW; s =sTW;s =sTW;s =sTW:(cid:0)At t(cid:1) we have t1(cid:0) 1 6 t2 6 t2(cid:0) 1 1 A A~ = t1 (141) t1 1+(cid:14) A ra +NX = t1(cid:0) 1 t1 t1 1+(cid:14) NX (cid:14) = A ra + t1 A ra t1(cid:0) 1 t1 1+(cid:14) (cid:0) 1+(cid:14) t1(cid:0) 1 t1 = A~ r~a +NX~ +T~ t1(cid:0) 1 t1 t1 t1 where,the(cid:133)rstfollowsfrom(138)givens =sTW;thesecondfromthefactthat(cid:9)isanequilibrium; t1 and the last follows from the fact that (138) imply A ra = A~ r~a given s =sTW together t1(cid:0) 1 t1 t1(cid:0) 1 t1 t1(cid:0) 1 6 with the fact that s t1 =sTW implies NX~ t1 = N 1 X +(cid:14) t1 and that T~ t1 is given by (140). As long as the trade war is in place (138) readily imply that s and t <s<t 1 2 8 A A~ = s (142) s 1+(cid:14) = A~ r~a+NX~ s 1 s s (cid:0) And when it ends, at t ; we have 2 A~ = A (143) t2 t2 = A ra +NX t2(cid:0) 1 t2 t2 A ra (cid:14) = t 1 2(cid:0) + 1 (cid:14) t2 +NX t2 + 1+(cid:14) A t2(cid:0) 1 r t a 2 = A~ r~a +NX~ +T~ t2(cid:0) 1 t2 t2 t2 where we are using again (138) as in (141). 54

11 Appendix D. Proof of Proposition 2 We start by giving a de(cid:133)nition of a permanent unexpected implemnation of BAT and VP: De(cid:133)nition 2. Let the evolution of trade policy at home and abroad s =((cid:28)m;&x;(cid:28)v;&v;(cid:28)(cid:25);BAT ;(cid:28)m ;&x ) t t t t t t t t (cid:3) t(cid:3) be determined by the stochastic process S;(cid:10) that satis(cid:133)es BAT = 0 s S: A unilateral imf g 8 2 plementation of BAT and an implementation VP of size (cid:14) are described by stochastic processes 1+(cid:14) GPBAT;(cid:10)BAT and GPVP;(cid:10)VP respectively such that GPBAT = S SBAT and GPVP = [ S(cid:8) SVP where(cid:9)SBAT (cid:8)= (cid:27)BAT ([S])(cid:9)and SVP = (cid:27)VP ([S]): The functions (cid:27)BAT and (cid:27)VP satsify [ (cid:14) (cid:14) (cid:14) (cid:14) ((cid:28)m;&x;(cid:28)v;&v;(cid:28)(cid:25);0;(cid:28)m ;&x ) S 8 t t t t t t (cid:3) t(cid:3) 2 (cid:27)BAT ((cid:28)m;&x;(cid:28)v;&v;(cid:28)(cid:25);0;(cid:28)m ;&x )=((cid:28)m;&x;(cid:28)v;&v;(cid:28)(cid:25);1;(cid:28)m ;&x (cid:28)m ;&x ) (cid:14) t t t t t t (cid:3) t(cid:3) t t t t t t (cid:3) t(cid:3) t (cid:3) t(cid:3) (cid:27)VP ((cid:28)m;&x;(cid:28)v;&v;(cid:28)(cid:25);0;(cid:28)m ;&x )=((cid:28)m;&x;(cid:28)~v;~&v;;(cid:28)(cid:25);1;(cid:28)m ;&x (cid:28)m ;&x ) (cid:14) t t t t t t (cid:3) t(cid:3) t t t t t t (cid:3) t(cid:3) t (cid:3) t(cid:3) with 1 (cid:28)~v 1 ~&v 1 (cid:0) t = (cid:0) t = 1 (cid:28)v 1 &v 1+(cid:14) (cid:0) t (cid:0) t The transition matrices are given by 1 (cid:25)BAT (cid:10) (cid:25)BAT(cid:10) (cid:10)BAT = (cid:0) (144) (1 (cid:26)BAT)(cid:10) (cid:26)BAT(cid:10) (cid:20) (cid:0) (cid:0) (cid:1) (cid:21) 1 (cid:25)VP (cid:10) (cid:25)VP(cid:10) (cid:10)VP = (cid:0) (145) 1 (cid:26)VP (cid:10) (cid:26)VP(cid:10) (cid:20) (cid:0) (cid:0) (cid:1) (cid:21) where the ordering of states in the transition(cid:0)probabil(cid:1)ity matrices is the obvious one. Proposition 2. If monetary policy is described by (63); wages are (cid:135)exible, and the three conditions of Proposition 1 are satis(cid:133)ed, the following policies are equivalent and neutral: 1. A permanent unexpected IX policy of size (cid:14); 2. A permanent unexpected BAT policy when corporate taxes are (cid:28)(cid:25) = (cid:14) ; 1+(cid:14) 3. A permanent unexpected VP policy of size (cid:14) ; 1+(cid:14) These three policies have no e⁄ect on the real allocation and induce the real exchange rate to appreciate by (cid:14): 55

Proof. Neutrality of IX under the assumptions of Proposition 1 was already proved. Therefore, we just need to prove that a BAT and a VP implementations of size (cid:14) are neutral and generate a real 1+(cid:14) exchange rate appreciation of size (cid:14). Let (cid:9)(st) denote an equilibrium process before the implementation of any policy, i.e. f gst (S)t;t 0 2 (cid:21) when s is governed S;(cid:10) : t f g Consider now the process (cid:9)~BAT (st) with an unanticipated permanent BAT st (GPBAT)t;t 0 such that, for each element {~ n of (cid:9)~BAT; o o the 2 r than retai (cid:21) lers and producers import prices, P~ F B t AT (i) and P~ (i); and the nominal exchange rate, " , we have X t t (cid:3) {~BAT s~t ={ (cid:22)B t AT s~t 8 s~t 2 GPBAT t ; 8 t (cid:21) 0 (146) (cid:0) (cid:1) (cid:0) (cid:0) (cid:1)(cid:1) (cid:0) (cid:1) where{ isthecorrespondingelementoftheequilibriumprocess(cid:9)and s~t =(s~ 1 ;::::;s~ t ) GPBAT t 8 2 the function (cid:22) (s~t)=st =(s ;:::;s ;:::) (S)t where i 1 (cid:0) (cid:1) t 1 t 2 8 (cid:21) s~ if s~ S i i s = 2 : i ( (cid:27)B (cid:14) AT (cid:0) 1 (s~ i ) if s~ i 2 SBAT (cid:0) (cid:1) . Import prices and the exchange rate satisfy s~t =(s~ ;::::;s~) GPBAT t 1 t 8 2 P~BAT (i) P~BAT P~BAT (i) 1 (cid:0) if s~ (cid:1) S F;t = F;t = X (cid:3) ;t = t 2 (147) P (i) P P (i) (1 (cid:28)(cid:25)) if s~ SBAT F;t F;t X (cid:3) ;t (cid:26) (cid:0) t t 2 ~"BAT 1 if s~ S t = t 2 (148) " (1 (cid:28)(cid:25)) if s~ SBAT t (cid:26) (cid:0) t t 2 We want to show that (cid:9)~BAT (st) is an equilibrium which, given (148) and the fact st (GPBAT)t;t 0 n o 2 (cid:21) that P and P are una⁄ected also implies that the real echange rate appreciates by (cid:14). t t(cid:3) The conditions that are directly a⁄ected by BAT are the law of one price for domestic exporters, (109a); retailers optimal demand of imports, (100); and the domestic price index, (112): Fix an history s~t =((cid:28)m;&x;(cid:28)v;&v;(cid:28)(cid:25);1;(cid:28)m ;&x (cid:28)m ;&x ) GPBAT t : Equation (109a) is satis(cid:133)ed since: t t t t t t (cid:3) t(cid:3) t (cid:3) t(cid:3) 2 (1+(cid:28)m(cid:0) )(1 (cid:28) (cid:1)v)P (i) P~ H(cid:3) B t AT = P H(cid:3)t = (1 t + (cid:3) &x) (cid:0) t H " t (149) t t (1+(cid:28)m )(1 (cid:28)v)(1 (cid:28)(cid:25))P~BAT(i) = t (cid:3) (cid:0) t (cid:0) Ht (1+&x) ~"BAT t t the last equality from (148) and (cid:28)(cid:25) = (cid:14) . t 1+(cid:14) 56

Retailers optimal demand of imports is satis(cid:133)ed since Y~BAT = Y =(1 !) P Ft (cid:0) (cid:18) C (150) Ft Ft (cid:0) P t (cid:20) t (cid:21) (cid:18) P~BAT 1 (cid:0) = (1 !) Ft C~BAT (cid:0) "P~ t BAT 1 (cid:0) (cid:28)(cid:25) t # t where the last equality follows from (147): And analogously for the price index: 1 P~ t BAT = P t = !P H 1 (cid:0)t (cid:18)+(1 (cid:0) !)(P Ft )1 (cid:0) (cid:18) 1 (cid:0) (cid:18) h i 1 1 (cid:18) P~BAT 1 (cid:0) (cid:18) 1 (cid:0) (cid:18) = ! P~BAT (cid:0) +(1 !) Ft (151) 2 (cid:16) Ht (cid:17) (cid:0) 1 (cid:0) (cid:28)(cid:25) t ! 3 4 5 Moreover to make sure that the adjustment in import prices is still consistent with (cid:133)rms optimality conditions we also need to check the law of one price for foreign exporters: (1+(cid:28)m) P~BAT = P (1 (cid:28)(cid:25))= t P " (1 (cid:28)(cid:25)) Ft Ft (cid:0) t (1+&x )(1 (cid:28)v) F(cid:3)t t (cid:0) t t(cid:3) (cid:0) t (1+(cid:28)m) = t P~ BAT~"BAT (1+&x )(1 (cid:28)v) F(cid:3)t t t(cid:3) (cid:0) t Finally we need to check the balance of payment equilibrium P s (1 (cid:28)v)P Y B~ F B t AT = B Ft =B Ft (cid:0) 1 R t(cid:3) (cid:0) 1 + 1+ H(cid:3) (cid:28) t m t (cid:3) s (cid:3)Y H(cid:3)t(cid:0) ( (cid:0) 1+ t (cid:28)m t ) Ft " F t t P~ BAT s (1 (cid:28)v)P~BAT y~BAT = B~ F B t A (cid:0) T 1 R~ t(cid:3) (cid:0) B 1 AT + 1+(cid:28) H(cid:3) m t t (cid:3) BAT s (cid:3)Y~ H(cid:3) B t AT (cid:0) (cid:0) (1+ t (cid:28)m t F ) t ~" F B t t AT where the third equality uses P~ F B t AT =P ; (cid:28)(cid:25) = (cid:14) and ~"BAT (1+(cid:14))=" : (1 (cid:28)(cid:25)) Ft 1+(cid:14) t t (cid:0) Inspecting all of the other dynamic equations we observe that since BAT adjustemnts and import prices do not enter any of those equations and the exchange rate only enters through the future appreciation which by (148) and under conditions of Proposition 1 is identical across allocations with probability one, all equations will be satis(cid:133)ed by (cid:9)~BAT since they are satis(cid:133)ed by (cid:9): Let(cid:146)s now turn to equivalence with VP. Considertheprocess (cid:9)~VP (st) withanunanticipatedpermanentVPimplementast (GPVP)t;t 0 tionsuchthat,foreachel n ement{~VP o o 2 f(cid:9)~VP;oth (cid:21) erthandomesticprices P~ H V t P (i);P~ F V t P (i);P~ t VP (i) and wages w(cid:22) VP (i);w~VP (i);W~VP and the associated price indexes (cid:16) P~VP;P~VP;P~VP , (cid:17) t t t Ht Ft t (cid:16) (cid:17) (cid:16) (cid:17) e {~VP s~t ={ (cid:22)V t P s~t 8 s~t 2 S~VP t ; 8 t (cid:21) 0 (152) (cid:0) (cid:1) (cid:0) (cid:0) (cid:1)(cid:1) (cid:16) (cid:17) 57

where{ isthecorrespondingelementoftheequilibriumprocess(cid:9)~ withIXand s~t =(s~ 1 ;:::;s~ t ;::::) 8 2 GPVP t ; (cid:22) (s~t)=st =(s ;:::;s ;:::) (S)t where i 1 t 1 t 2 8 (cid:21) (cid:0) (cid:1) s~ if s~ S i i s = 2 i ( (cid:27)V (cid:14) P (cid:0) 1 (s~ i ) if s~ i 2 SIX (cid:0) (cid:1) Prices and wages satisfy s~t =(s~ ;::::;s~) GPVP t 1 t 8 2 (cid:0) (cid:1) P~ H V ; P t (i) = P~ F V ;t P (i) = P~ t VP (i) = 1 if s~ t 2 S (153) P (i) P (i) P (i) 8 H;t F;t t < (1+(cid:14)) if s~ t SVP 2 : w(cid:22) VP (i) w~VP (i) W~VP 1 if s~ t 2 S t = t = t = (154) w(cid:22) (i) w~ (i) W 8 e t t t < (1+(cid:14)) if s~ t 2 SVP Wewanttoshowthat (cid:9)~VP (st) i:sanequilibrium,whichgiven(153)andthefact st (GPVP)t;t 0 n o 2 (cid:21) that " is una⁄ected also implies that the real echange rate appreciates by (cid:14). t The two laws of one price and the balance of payment are again straightforward: (cid:133)x an history s~t GPVP t such that s~ =((cid:28)m;&x;(cid:28)~v;~&v;(cid:28)(cid:25);1;(cid:28)m ;&x (cid:28)m ;&x ) SVP: We have 2 t t t t t t t (cid:3) t(cid:3) t (cid:3) t(cid:3) 2 (cid:0) (cid:1) (1+(cid:28)m )(1 (cid:28)v)P (i) P~ H(cid:3) V t P (i) = P H(cid:3)t (i)= (1 t + (cid:3) &x) (cid:0) t H " t (155) t t (1+(cid:28)m )(1 (cid:28)~v)P~VP(i) = t (cid:3) (cid:0) t Ht (156) (1+&x) ~"VP t t where we are making use of (153) and 1 1 (cid:0) (cid:28) (cid:28) ~v t v = 1+ 1 (cid:14) :And similarly for foreign producers. For the (cid:0) t balance of payment equilibrium condition we use the same argument as well: P s (1 (cid:28)v)P B~ F V t P = B Ft =B Ft (cid:0) 1 R t(cid:3) (cid:0) 1 + 1+ H(cid:3) (cid:28) t m t (cid:3) s (cid:3)Y H(cid:3)t(cid:0) (1 (cid:0) +(cid:28) t m t )" F t tY Ft P~ VP s (1 (cid:28)~v)P~VP B~ F V t P (cid:0) 1 R~ t(cid:3) (cid:0) V 1 P + 1+ H(cid:3) (cid:28) t m t (cid:3) s (cid:3)Y~ H V t P (cid:3) (cid:0) (1 (cid:0) +(cid:28) t m t ) F ~" t t Y~ F V t P Now consider the optimality condition for the price of the domestic good at home an history s~t 2 GPVP t such that s~ =((cid:28)m;&x;(cid:28)~v;~&v;(cid:28)(cid:25);1;(cid:28)m ;&x (cid:28)m ;&x ) SVP: t t t t t t t (cid:3) t(cid:3) t (cid:3) t(cid:3) 2 (cid:0) (cid:1) s 1 VP (cid:13) (1 ~&v)W~VP E ~V t P(cid:6) 1s=t (cid:16)s P(cid:0) t(cid:3)~V t;s P (cid:20) Y~ H V s P (i)+ s (cid:3)Y~ H(cid:3) V s P (i) (cid:21) P~ s VP " P~ Pt (i) (cid:0) (cid:13) (cid:0) 1(cid:11)A s (cid:0) N~ s V s P(i) s (cid:11) (cid:0) 1# = (157) Et (cid:6) 1s=t (cid:16)s P(cid:0) t(cid:3) t;s (cid:20) Y Hs (i)+ s s (cid:3)Y H(cid:3)s (i) (cid:21) 1 P + s (cid:14) (cid:20) P V Pt P (i) (cid:0) (cid:13) (cid:0) (cid:13) 1(cid:11) ( A 1 s (cid:0) N~ & s V v s P )W (i) s V (cid:11) (cid:0) P 1 (cid:21) = 0(158) where the (cid:133)rst equality follows from P~ P s V s P = W~ W s V s P = ( ( 1 1 (cid:0) (cid:0) ~ & & v s v s ) ) =1+(cid:14) w.p. 1. 58

With (cid:135)exible wages, optimal labor supply is also satis(cid:133)ed since real wages are una⁄ected: n~VP (i) (cid:17) (cid:13) w(cid:22) VP (i) [n (i)](cid:17) (cid:13) w(cid:22) (i) t n t = t n t =0 (cid:2) C~ t VP (cid:0) (cid:27) (cid:3) ((cid:13) n(cid:0) 1) (cid:0) P~ t VP C t(cid:0) (cid:27) ((cid:13) n(cid:0) 1) (cid:0) P t e Morevoer, since the transition from s S to s SVP is unanticipated, the di⁄erent in(cid:135)ation t 1 t (cid:0) 2 2 dynamic ex post does not a⁄ect optimal bond holdings ex ante. On the other hand since the policy is permanent, future in(cid:135)ation is una⁄ected by its implementation as is clear from (153): 12 Appendix E. Proof of Proposition 3 Westartbygivingade(cid:133)nitionofapermanentunexpectedappreciationofthenominalexchangerate: De(cid:133)nition 3. Let the evolution of trade policy and monetary policy at home and abroad s =((cid:28)m;&x;(cid:28)v;&v;(cid:28)(cid:25);BAT ;(cid:28)m ;&x ;(cid:22)" ) t t t t t t t t (cid:3) t(cid:3) t bedeterminedby the stochasticprocess S;(cid:10) that satis(cid:133)es BAT =0 s S: A currency devaluation f g 8 2 ofsize (cid:14) startingfrom S;(cid:10) isdescribedbyastochasticprocesses GP";(cid:10)" suchthat GP" =S S" f g f g [ where S" =(cid:27)"([S]) (159) (cid:14) (cid:27)BAT ((cid:28)m;&x;(cid:28)v;&v;(cid:28)(cid:25);0;(cid:28)m ;&x ;(cid:22)" )=((cid:28)m;&x;(cid:28)v;&v;(cid:28)(cid:25);0;(cid:28)m ;&x ;(cid:22)" (1+(cid:14))) (cid:14) t t t t t t (cid:3) t(cid:3) t t t t t t t (cid:3) t(cid:3) t and the transitiong matrix is (1 (cid:25)")(cid:10) (cid:25)"(cid:10) (cid:10)" = (cid:0) (160) (1 (cid:26)")(cid:10) (cid:26)"(cid:10) (cid:20) (cid:0) (cid:21) where the ordering of states in the transition probability matrices is the obvious one. Proposition 3. If monetary policy is described by (34)in a (cid:133)xed exchange rate regime (’ = ) " 1 and assumptions 1.-3. of Proposition 1 hold, an unexpected IX policy of size (cid:14) and an expected BAT policyofsize (cid:14) havethesameallocativee⁄ectsofaonceandforallunexpectedcurrencydevaluation 1+(cid:14) of size (cid:14):An unexpected VP policy of the same size (cid:14) has no e⁄ect on the real allocation but causes 1+(cid:14) the real exchange rate to appreciate by (cid:14): Proof. Let (cid:9)"(st) denote an equilibrium process under GP";(cid:10)" : f gst (ST)t;t 0 f g 2 (cid:21) Consider now the process (cid:9)~IX(st) with an unanticipated permanent IX such st (GPIX)t;t 0 that, for each element {~IX of (cid:9)~nIX, apart o fro 2 m the no (cid:21) minal exchange rate, we have {~IX s~t ={ " (cid:22)" t s~t 8 s~t 2 GPIX t ; 8 t (cid:21) 0 (161) (cid:0) (cid:1) (cid:0) (cid:0) (cid:1)(cid:1) (cid:0) (cid:1) 59

where { " is the corresponding element of the equilibrium process (cid:9)" and s~t = (s~ 1 ;:::;s~ t ;::::) 8 2 GPIX t ; (cid:22)"(s~t)=st =(s ;:::;s ;:::) (GP")t where i 1 t 1 t 2 8 (cid:21) (cid:0) (cid:1) s~ if s~ S i i s i = ( (cid:27)" (cid:14) (cid:27)I (cid:14) X (cid:0) 1 (s~ i ) if s~ i 2 2 SIX : For ease of notation in what follows, (cid:16) f (cid:0) or an (cid:1) y s~t = (cid:17) (s~ 1 ;::::;s~ t ) 2 GPIX t ; we let {~ t IX = {~IX(st) and {t " ={((cid:22)" t (st)): (cid:0) (cid:1) The exchange rate satis(cid:133)es s~t =(s~ ;::::;s~) GPIX t 1 t 8 2 "" (cid:0) if s~(cid:1) S ~"I t X = ( 1 " + " t t (cid:14) if s~ t 2 t 2 SIX (162) Toshowthat (cid:9)~IX(st) isanequilibriumwecanfollowthesamestepsasintheproof st (GPIX)t;t 0 n o 2 (cid:21) Proposition 1. At s~t = (s~ ;::::;s~) GPIX t such that s~ SIX; the laws of one price and the balance of 1 t t 2 2 payment equilibrium equat(cid:0)ions are(cid:1)satis(cid:133)ed since ~"IX (1+(cid:27)~x) (1+(cid:28)~m) t = t = t ~"IX (1+(cid:27)x) (1+(cid:28)m) 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. The argument for the BAT policy is analogous but in that case optimal import demands and the price index need to be checked as well just as in the proof of Proposition 2.33 Finally, the fact that VP is still neutral even under (cid:133)xed exchange rates is a straightforward consequence of the proof of Proposition 2. Since under (cid:135)exible exchange rates VP is neutral and the nominal exchang rate is una⁄ected by its implementation, it follows that even if monetary policy targets a given (cid:133)xed exchange rate the policy still remains neutral. 13 Appendix F. Proof of Proposition 4 Proposition 4. Underfullpass-throughoftaxes, anunexpectedIXpolicyofsize (cid:14) andanunexpected BAT policy of size (cid:14) implement the same allocation. Generically, a VP policy of size (cid:14) does not 1+(cid:14) implement the same allocation as IX or BAT. Equivalence of the three policies requires that policies are permanent, i.e. (cid:26)=1; or that prices are (cid:135)exible. 33The equivalence result between BAT and IX in Proposition 4 also delivers taht BAT is equivalent to IX in this context and hence it is equivalent to an exchange rate devaluation. 60

Proof. Let (cid:9)IX(st) denote an equilibrium process with IX: st (GPIX)t;t 0 2 (cid:21) Cons(cid:8)ider the p(cid:9)rocess with BAT GPBAT;(cid:10)BAT and de(cid:133)ne a sequence of functions (cid:22)BAT;IX : t GPBAT t (S)t as follows: s~t =(cid:8)(s~ ;:::;s~;::::) (cid:9)GPBAT t ; (cid:22)BAT;IX(s~t)=st =(s ;:::;s ;:::) ! 8 1 t 2 t 1 t 2 ((cid:0)S)t wher(cid:1)e i 1 (cid:0) (cid:1) 8 (cid:21) s~ if s~ S i i s i = ( (cid:27)I (cid:14) X (cid:27)B (cid:14) AT (cid:0) 1 (s~ i ) if s~ i 2 2 SBAT that is function (cid:22)BAT;IX maps all histor (cid:16) ie(cid:0)s in w(cid:1)hich BA (cid:17) T has occurred into histories in which IX has t occurred instead. Consider now a process (cid:9)~BAT (st) with an unanticipated permanent BAT such st (GPBAT)t;t 0 that, for each element {~BAT n of (cid:9)~BAT; o oth 2 er than imp (cid:21) ort prices, P~ F B t AT (i);P~ F B t AT , we have (cid:16) (cid:17) {~BAT s~t ={ IX (cid:22)B t AT;IX s~t 8 s~t 2 GPBAT t ; 8 t (cid:21) 0 (163) (cid:0) (cid:1) (cid:16) (cid:0) (cid:1)(cid:17) (cid:0) (cid:1) where { IX is the corresponding element of the equilibrium process (cid:9)IX and s~t = (s~ 1 ;:::;s~ t ) 8 2 GPBAT t ; (cid:22)BAT;IX(s~t)=st =(s ;:::;s ) (S)t where i 1 t 1 t 2 8 (cid:21) (cid:0) (cid:1) s~ if s~ S i i s i = ( (cid:27)I (cid:14) X (cid:27)B (cid:14) AT (cid:0) 1 (s~ i ) if s~ i 2 2 SBAT : Import prices satisfy s~t =(s~ ;::::;s~ (cid:16)(cid:0) ) GP (cid:1) BAT t (cid:17) 1 t 8 2 P~BAT (i) P~BAT (cid:0) (cid:1) 1 if s~ S F;t = F;t = t 2 (164) P (i) P (1 (cid:28)(cid:25)) if s~ SBAT F;t F;t (cid:26) (cid:0) t t 2 We want to show that (cid:9)~BAT (st) is an equilibrium. st (GPBAT)t;t 0 n o 2 (cid:21) Under PCP the equilibrium equations that are directly a⁄ected by BAT and IX are the laws of one price for exporters, (109a) and (110a); the tax passthrough equation, (104);retailers optimal demand of imports, equation (100); the price index (115); and the balance of paymet equilibrium (??) Fix an history s~t GPBAT t with s~ = ((cid:28)m;&x;(cid:28)v;&v;(cid:28)(cid:25);1;(cid:28)m ;&x (cid:28)m ;&x ) SBAT and let 2 t t t t t t t (cid:3) t(cid:3) t (cid:3) t(cid:3) 2 st =(cid:22)BAT;IX(s~t) where (cid:0)s =((cid:28)~m;(cid:1)~&x;(cid:28)v;&v;(cid:28)(cid:25);0;(cid:28)m ;&x (cid:28)m ;&x ) has IX in place instead of BAT: t t t t t t t t (cid:3) t(cid:3) t (cid:3) t(cid:3) Under LCP instead of (109a) and (110a) we only need to check equation (109b): The laws of one price (109a) and (110a) are satis(cid:133)ed since: (1+(cid:28)m )(1 (cid:28)v)PIX P~ H(cid:3) B t AT = P H(cid:3) I t X = (1 t + (cid:3) ~&x) (cid:0) t "I H X t t t (1+(cid:28)m )(1 (cid:28)v)(1 (cid:28)(cid:25))P~BAT = t (cid:3) (cid:0) t (cid:0) t Ht (165) (1+&x) ~"BAT t t 61

(1 (cid:28)(cid:25))(1+(cid:28)~m)"IX P~ F B t AT (i) = (1 (cid:0) (cid:28)(cid:25))P F IX t (i)= ( (cid:0) 1+&x )(1 t (cid:28)v) t P F(cid:3) I t X(i) t(cid:3) (cid:0) t (1+(cid:28)m)~"BAT = t t P~ BAT (i) (1+&x )(1 (cid:28)v) F(cid:3)t t(cid:3) (cid:0) t Under LCP, equation (109b) is satsi(cid:133)ed since: Y (i) (cid:13) (1 &v)W Et (cid:6) 1s=t (cid:16)s P(cid:0) t(cid:3) t;s H(cid:3) P s " s (1+~&x s )P(cid:22) X(cid:3)t (i) (cid:0) (cid:13) 1(cid:11)A (cid:0) N s (i)(cid:11) s 1 = s (cid:20) (cid:0) s s (cid:0) (cid:21) Y (i) (1+&x) (cid:13) (1 &v)W Et (cid:6) 1s=t (cid:16)s P(cid:0) t(cid:3) t;s H(cid:3) P s " s (1 (cid:28)(cid:25)B s AT ) P(cid:22) X(cid:3)t (i) (cid:0) (cid:13) 1(cid:11)A (cid:0) N s (i)(cid:11) s 1 = 0 s (cid:20) (cid:0) s (cid:0) s s (cid:0) (cid:21) and similarly for equations and (104) (1 (cid:28)(cid:25))(1+(cid:28)~m) (1+(cid:28)m) P~BAT =(1 (cid:28)(cid:25))PIX = (cid:0) t PIX(i)= t P~BAT (i) Ft (cid:0) Ft (1 (cid:28)v) X t(cid:3) (1 (cid:28)v) X t(cid:3) (cid:0) t (cid:0) t Retailers optimal demand of imports is satis(cid:133)ed since PIX (cid:0) (cid:18) y~BAT = yIX =(1 !) Ft CIX (166) Ft Ft (cid:0) PIX t (cid:20) t (cid:21) (cid:18) P~BAT 1 (cid:0) = (1 !) Ft C~BAT (cid:0) "P~ t BAT 1 (cid:0) (cid:28)(cid:25) t # t And analogously for the price index: 1 P~BAT = PIX = ! PIX 1 (cid:0) (cid:18) +(1 !) PIX 1 (cid:0) (cid:18) 1 (cid:0) (cid:18) (167) t t Ht (cid:0) Ft h (cid:0) 1 (cid:18) (cid:1) P~B (cid:0) AT (cid:1)1 (cid:0) (cid:18) i 1 (cid:0) 1 (cid:18) = ! P~BAT (cid:0) +(1 !) Ft (168) 2 (cid:16) Ht (cid:17) (cid:0) 1 (cid:0) (cid:28)(cid:25) t ! 3 4 5 Finally we need to check the balance of payment equilibrium: P IX s (1 (cid:28)v)PIX B~ F B t AT = B F IX t =B F IX t (cid:0) 1 R t(cid:3) (cid:0) IX 1 + 1+ H(cid:3) (cid:28) t m t (cid:3) s (cid:3)Y H(cid:3) I t X (cid:0) (1 (cid:0) +(cid:28)~ t m t )" F I t X t Y F I t X P~ BAT s (1 (cid:28)v)P~BAT = B~ F B t A (cid:0) T 1 R~ t(cid:3) (cid:0) B 1 AT + 1+ H(cid:3)t (cid:28)m t (cid:3) s (cid:3)Y~ H(cid:3) B t AT (cid:0) (1 (cid:0) +(cid:28) t m t )~" F B t t AT Y~ F B t AT Given that import prices, BAT adjustments and IX policies don(cid:146)t enter any other equilibrium equations and (cid:9)IX is an equilibrium, than (cid:9)BAT is an equilibrium as well. ToseethatVPwillgenericallyimplementadi⁄erentallocationnoticethatthe(cid:133)rstordercondition for optimal reset price of domestic (cid:133)rms can be rewritten as P Ht (i) = (cid:13) Et (cid:6) 1s=t( ( 1 1 (cid:0) (cid:0) (cid:28) &v s v t ) ) (cid:16) P s (cid:0) t(cid:3) t;s Y Hs (i) (cid:11)AsZs(i) 1 Ns(i)(cid:11) (cid:0) 1 W Ps s (169) P t (cid:13) (cid:0) 1 Et (cid:6) 1s=t (cid:16)s P(cid:0) t(cid:3) (cid:25)t t ; ; s sY Hs (i) 62

whichimpliesthataslongastherearepricerigidities,i.e. & (0;1);andpoliciesarenotpermanent, P 2 i.e. ( ( 1 1 (cid:0) (cid:28) &v s v ) ) isnotequaltounityw.p. 1,theintroductionofVATtaxesandpayrollsubsidieswillinduce (cid:0) t adi⁄erentoptimallevelofrelativepricesandhenceproductionbydomestic(cid:133)rms. Sowithinoursetup equivalence can only old if (cid:26)=1 or when prices are (cid:135)exible: 14 Appendix G. Data Sources We report below details on the data used in Figure 10. In the case of price series, the "Euro-area excluding Germany" aggregate refers to the weighted average of data for Belgium, France, Italy, the Netherlands,andSpain(thesecountriesaccountfornearly80percentoftheactualeuro-areaaggregate excluding Germany). All series were obtained from Haver Analytics and corresponding mnemonics are reported in parenthesis. Core In(cid:135)ation. In(cid:135)ationseriesinthe(cid:133)rstpanelrefertoseasonally-adjustedcoreHICPdata(i.e. excluding energy, food, alcohol, and tobacco) for Germany (EUDATA(cid:146)H134HOEF), Belgium (EU- DATA(cid:146)H124HOEF), France (EUDATA(cid:146)H132HOEF), Italy (EUDATA(cid:146)H136HOEF), the Netherlands (EUDATA(cid:146)H138HOEF), and Spain (EUDATA(cid:146)H184HOEF). Data are plotted in 12-month percent changes. Motor Vehicle In(cid:135)ation. The price series in the second panel refer to seasonally-adjusted new and used automobiles prices for Germany (EUDATA(cid:146)H134H711), Belgium (EUDATA(cid:146)H124H711), France (EUDATA(cid:146)H132H711), Italy (EUDATA(cid:146)H136H711), the Netherlands (EUDATA(cid:146)H138H711), and Spain (EUDATA(cid:146)H184H711). WageIn(cid:135)ation. ThewageseriesforGermanyinthethirdpanelrefertoseasonally-adjustednegotiatedhourlywages(GERMANY-DENEDBS),wagesintheproductionandservicesector(GERMANY- DENE6I), total labor costs in all sectors excluding agriculture (GERMANY(cid:146)DESLTXA), and gross wages in all sectors excluding agriculture (GERMANY(cid:146)DESLEXA). Data are presented in 4-quarter percent changes. Real Consumption. The consumption series in the fourth panel refer to Households and Nonpro(cid:133)t Final Consumption Expenditures (SWDA, millions of chained 2010 euros) for Germany (EU- DATA(cid:146)J134PCT) and the euro area (EUDATA(cid:146)J025PCT). 63

Figure 1. Macroeconomic Effects of IX with Retaliation Nominal Exchange Rate Imports Exports Nominal Wage 10 5 10 10 S S S S S S S S 0 5 m m m m 5 o o o o 5 r r r r f f f f " " -5 " 0 " % % % % 0 -10 -5 0 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 3 ) . r 1 1 4 4 ( S 2 . a ( S 0.5 S S 0 S S 3 S S m m 2 m 1 m 0 o o r r o o f f 1 r f " 0 r f " -0.5 % " -1 % " 0 % % -1 -1 -2 -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 2 ) . r 1 2 1 4 ( S 1 . a ( S 0.5 S S 1 S S 0 S 0 S m m -1 m m 0 o o r r o -1 o f f -2 r f " -2 r f " -0.5 % " 0 % " -3 % % -3 -1 -1 -4 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Quarters Quarters Quarters Quarters IX Tariff Only

Figure 2. Macroeconomic Effects of IX with Retaliation: Fixed Exchange Rates Nominal Exchange Rate Imports Exports Nominal Wage 10 5 15 10 S S S S S S S 10 S 0 m m m m 5 o o o o 5 5 r r r r f f f f " " -5 " " 0 % % % % 0 -10 -5 0 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 3 ) . r 1 1 4 4 ( S 2 . a ( S 0.5 S S 0 S S 3 S S m m 2 m 1 m 0 o o r r o o f f 1 r f " 0 r f " -0.5 % " -1 % " 0 % % -1 -1 -2 -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 2 ) . r 1 3 1 4 ( S 1 . a ( S 0.5 S S 2 S S 0 S 0 S m m -1 m m 0 o o r r o -1 o f f -2 r f " -2 r f " -0.5 % " 1 % " -3 % % -3 -1 0 -4 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Quarters Quarters Quarters Quarters Fixed Exchange Rate Flexible Exchange Rate

Figure 3. Anticipation Effects of Permanent IX Nominal Exchange Rate Imports Exports Nominal Wage 15 10 5 2 S S S S S S S S 10 0 0 m m m m o o o o 5 r r r r f f f f " 5 " " -5 " -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 0 ) . r 0.5 2 0.5 4 . a S S ( S -0.5 ( S 0 S 1.5 S 0 S S m m m -1 m o 1 o r r o o f f r f " -1.5 r f " -0.5 % " 0.5 % " -0.5 % % -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 2 ) . r 1 1 1 4 ( S 1 . a ( S 0.5 S S 0 S S 0 S 0 S m m -1 m m 0 o o r r o -1 o f f -2 r f " -2 r f " -0.5 % " -1 % " -3 % % -3 -1 -2 -4 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Quarters Quarters Quarters Quarters Anticipation of IX Unanticipated IX

Figure 4. Permanent IX With and Without Foreign Holdings of Home Currency Bonds Real Exchange Rate 15 S S 10 m o r f " 5 % 0 0 2 4 6 8 10 12 14 16 18 20 Quarters Net Exports 1 0.5 P D G 0 f o % -0.5 -1 0 2 4 6 8 10 12 14 16 18 20 Quarters Home Output 1 S 0.5 S m o 0 r f " % -0.5 -1 0 2 4 6 8 10 12 14 16 18 20 Quarters * * B = 2.0 GDP B = 0 GDP h h

Figure 5. Permanent IX: LCP vs. PCP Nominal Exchange Rate Imports Exports Nominal Wage 15 2 1 0.25 0 0.8 0.2 S S -2 S 0.6 S S 10 S S S 0.15 m m -4 m 0.4 m o o o o 0.1 r r r r f f f f -6 0.2 " " " " % 5 % % % 0.05 -8 0 0 -10 -0.2 0 -12 -0.4 -0.05 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 4 1 1 4 0.5 ) q 3 ) . r 0.5 ) . r 3 4 . a S . a ( S 2 ( S S 0 ( S 2 S S m S m m 0 o -0.5 m r o o f o r f " 1 r f " % " -1 r f " 1 % % -0.5 % 0 0 -1.5 -1 -1 -2 -1 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Quarters Quarters Quarters Quarters LCP PCP

Figure 6. Permanent IX vs. VP: Neutrality Nominal Exchange Rate Imports Exports Nominal Wage 10 1 1 15 8 ) ) . . r 0.5 r 0.5 . . S a a 10 S 6 ( ( P S S D m S S G o r f 4 m o 0 m o 0 f o " r f r f % 5 % 2 " " % -0.5 % -0.5 0 0 -2 -1 -1 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 15 1 1 1 ) q 0.5 0.5 ) . r 0.5 4 S S . a ( S 10 S S ( S S m m S m o 0 o 0 m 0 r r o f f o r f " 5 % " % " r f " % -0.5 -0.5 % -0.5 0 -1 -1 -1 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Quarters Quarters Quarters Quarters IX VP

Figure 7. Permanent IX and VP: Fixed Exchange Rates Nominal Exchange Rate Imports Exports Nominal Wage 10 0.5 10 25 8 ) ) 8 20 . . r 0 r . . S a a S 6 ( ( P S S 6 D 15 m S S G o r f 4 m o -0.5 m o f o " r f r f 4 % 10 % 2 " " % -1 % 2 5 0 -2 -1.5 0 0 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 12 1 8 10 10 ) q 0 6 ) . r 8 4 8 S S . a ( S S -1 S 4 ( S 6 S 6 m m S m o o m r r o 4 f f o r f " % " -2 % " 2 r f " 4 % 2 % -3 0 2 0 -2 -4 -2 0 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Quarters Quarters Quarters Quarters IX VP

Figure 8. Permanent IX and VP: Sticky Wages Nominal Exchange Rate Imports Exports Nominal Wage 10 1 10 15 8 ) ) 8 . . r 0.5 r . . S a a S 6 ( ( P 10 S S 6 D m S S G o r f 4 m o 0 m o f o " r f r f 4 % % 2 " " 5 % -0.5 % 2 0 -2 -1 0 0 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 10 1 8 10 8 ) q 0 6 ) . r 8 4 6 S S . a ( S S -1 S 4 ( S 6 S 4 m m S m o o m r r o 2 f f o r f " % " -2 % " 2 r f " 4 % 0 % -3 0 2 -2 -4 -4 -2 0 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Quarters Quarters Quarters Quarters IX VP

Figure 9. Temporary IX vs. VP: Stick Wages (PCP) Nominal Exchange Rate Imports Exports Nominal Wage 15 2 10 10 0 ) ) 8 5 . . 10 r r S . a -2 . a S ( ( P S S 6 D 0 m S -4 S G o r f 5 m o -6 m o f o " r f r f 4 % -5 % " " -8 0 % % 2 -10 -10 -5 -12 0 -15 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 10 1 0.5 1.5 0 0 1 ) q 5 -1 ) . r 4 S S . a ( S S -2 S -0.5 ( S 0.5 S m m S m 0 o -3 o -1 m 0 r r o f f o r f " % " -4 % " -1.5 r f " -0.5 % -5 -5 % -2 -1 -6 -10 -7 -2.5 -1.5 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Quarters Quarters Quarters Quarters IX VP

2.5 2 1.5 1 0.5 0 % Core Inflation 4 3.5 3 2.5 2 1.5 1 0.5 0 -0.5 % Motor Vehicle Inflation 4 3 2 1 0 % Figure 10. Fiscal Devaluation in Germany (2007) June 06 June 07 June 08 June 06 June 07 June 08 Wage Inflation Real Consumption 103 Negotiated Wage Wage Index 102 Total Labor Cost Gross Wage 101 100 99 98 97 -1 96 2006q1 2007q1 2008q1 2006q1 2007q1 2008q1 Germany Euro Area (excl. Germany)

Figure 11. Temporary IX with Sticky Wages: PCP vs LCP vs DCP Nominal Exchange Rate Imports Exports Nominal Wage 6 5 10 0.5 0 4 ) ) 8 . . r 0 r S . a . a -0.5 S 2 ( ( P S S 6 D m S S -1 G o r f 0 m o -5 m o f o -1.5 " r f r f 4 % % -2 " " -2 % -10 % 2 -4 -2.5 -6 -15 0 -3 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 10 1 0.5 1.5 0 0 1 ) q -1 ) . r 4 S S -0.5 . a ( S 5 S -2 S ( S 0.5 S m m -1 S m o -3 o m 0 r r o f f -1.5 o r f " 0 % " -4 % " r f " -0.5 % -5 -2 % -1 -2.5 -6 -5 -7 -3 -1.5 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Quarters Quarters Quarters Quarters PCP LCP DCP

Figure 12. Temporary VP with Sticky Wages: PCP vs LCP vs DCP Nominal Exchange Rate Imports Exports Nominal Wage 6 2 10 1 0 4 ) ) 8 . . r r 0 S . a -2 . a S 2 ( ( P S S 6 D m S -4 S G o r f 0 m o -6 m o f o -1 " r f r f 4 % % -2 " " -8 % % -2 2 -4 -10 -6 -12 0 -3 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 10 1 0.5 1.5 0 0 1 ) q -1 ) . r 4 S S -0.5 . a ( S 5 S -2 S ( S 0.5 S m m -1 S m o -3 o m 0 r r o f f -1.5 o r f " 0 % " -4 % " r f " -0.5 % -5 -2 % -1 -2.5 -6 -5 -7 -3 -1.5 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Quarters Quarters Quarters Quarters PCP LCP DCP