Financial Heterogeneity and Monetary Union

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Financial Heterogeneity and Monetary Union Simon Gilchrist, Raphael Schoenle, Jae Sim, and Egon Zakrajˇsek 2018-043 Please cite this paper as: Gilchrist, Simon, Raphael Schoenle, Jae Sim, and Egon Zakrajˇsek (2018). “Financial Heterogeneity and Monetary Union,” Finance and Economics Discussion Series 2018-043. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2018.043. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Financial Heterogeneity and Monetary Union Simon Gilchrist∗ Raphael Schoenle† Jae Sim‡ Egon Zakrajˇsek§ June 17, 2018¶ Abstract We analyze the economic consequences of forming a monetary union among countries with varying degrees of financial distortions, which interact with the firms’ pricing decisions because of customer-market considerations. In response to a financial shock, firms in financially weak countries (the periphery) maintain cashflows by raising markups—in both domestic and export markets—while firms in financially strong countries (the core) reduce markups, undercutting their financially constrained competitors to gain market share. When the two regions are experiencing different shocks, common monetary policy results in a substantially higher macroeconomic volatility in the periphery, compared with a flexible exchange rate regime; this translates into a welfare loss for the union as a whole, with the loss borne entirely by the periphery. By helping firms from the core internalize the pecuniary externality engendered by the interaction of financial frictions and customer markets, a unilateral fiscal devaluation by the periphery can improve the union’s overall welfare. JEL Classification: E31, E32, F44, F45 Keywords: eurozone; financial crisis; monetary union; inflation dynamics; markups; fiscal devaluation WethankIsabelCorreia,JulianBengui,RobertKollmann,FabrizioPerri,RicardoReis,andMatthiasTrabandt forhelpfulcomments. Wealsothankparticipantsatnumerousuniversities,centralbanks,andconferencesforuseful suggestions. George Gu, Matthew Klepacz, Gerardo Sanz-Maldonado, Clay Wagar, and Rebecca Zhang provided outstanding research assistance at various stages of the project. The views expressed in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of anyone else associated with the Federal Reserve System. ∗Department of Economics New York University and NBER. Email: sg40@nyu.edu †Department of Economics Brandeis University. Email: schoenle@brandeis.edu ‡Research and Statistics, Federal Reserve Board. Email: jae.w.sim@frb.gov §Monetary Affairs, Federal Reserve Board. Email: egon.zakrajsek@frb.gov ¶This version of the paper contains the correct mathematical expressions for the current account that appear on pages 22 and 23.

1 Introduction The consensus in both the academic and policy circles is that the eurozone’s recent financial crisis was a classic balance-of-payment crisis, which can be traced to the toxic mix of excessive credit growth and loss of competitiveness in the euro area periphery. Following the introduction of the euro in early 1999, periphery countries such as Greece, Ireland, Italy, Spain, and Portugal went on a borrowing spree, the proceeds of which were used largely to finance domestic consumption and housing investment. Foreign investors’ widespread reassessment of risks during the 2008–2009 globalfinancialcrisis,alongwithagrowingrecognitionofanunsustainablefiscalsituationinGreece, precipitated a sharp pullback in private capital from the periphery in early 2010. This further tightening of financial conditions exacerbated the already painful process of deleveraging through which the periphery economies were attempting to bring domestic spending—both government and private—back into line with domestic incomes.1 In a monetary union comprised of countries experiencing different economic and financial conditions—with limited labor mobility and no common fiscal policy—the financial crisis would have to be resolved largely through a downward adjustment of the overvalued real exchange rates in the periphery. In the euro area, however, this adjustment has occurred very slowly. Although the periphery has endured notable disinflation since 2010, an appreciable gap remains, on balance, between the general level of prices in the core and periphery. As a result, real effective exchange rates in the periphery have tended to remain above those of the core euro area countries.2 What economic forces are responsible for such a slow adjustment in the price levels between the core and periphery countries? Why have firms in the periphery—given the degree of resource underutilizationintheseeconomies—beensoslowtocutprices? Bythesametoken,whyhavefirms in the core been reluctant to increase prices, despite an improvement in the economic outlook and highly stimulative monetary policy? In fact, some prominent commentators have argued that it is the core countries that are exporting deflationary pressures into the periphery, a dynamic contrary to that needed to reverse the real exchange rate appreciation that has eroded the periphery’s competitiveness (see Krugman, 2014). To help answer these questions, we build on Gilchrist et al. (2017), GSSZ hereafter, and introduce the interaction of customer markets and financial frictions into an otherwise standard international macroeconomic framework. Specifically, we augment the conventional two-country general equilibrium model with nominal rigidities and incomplete risk sharing with two new assumptions: 1The tightening of financial conditions was not as severe as might have been expected given the scale of capital flight from the periphery. The withdrawal of capital was tempered importantly by cross-border credits to central banksindeficitcountriesextendedbyothereuroareacentralbanksthroughtheTARGET2system,amechanismfor managing payment imbalances among eurozone countries. In combination with policies to supply liquidity to banks in the periphery, this balance-of-payments financing helped offset the drain of funds abroad (see Auer (2014)). 2Throughout the paper, we use the following definition of the euro area core and periphery. Core countries: Austria,Belgium,Finland,France,Germany,andNetherlands. Peripherycountries: Greece,Ireland,Italy,Portugal, and Spain. We omit the Eastern European countries (Estonia, Latvia, Lithuania, Slovakia, and Slovenia) from the periphery because they adopted the euro relatively recently. Our analysis also excludes Cyprus, Luxembourg, and Malta because of limited data in some instances and because of their very specialized economies. 1

First, we assume that firms operate in customer markets—both domestically and abroad.3 And second, we assume that foreign and domestic financial markets are subject to differing degrees of frictions. We then show that in such an environment firms from the core—that is, firms with a relatively unimpeded access to external finance—have a strong incentive to expand their market shareathomeandabroadbyundercuttingpriceschargedbytheirperipherycompetitors,especially when the latter are experiencing financial distress. By contrast, firms from the periphery have an incentive to increase markups in order to preserve internal liquidity, even though doing so means forfeiting some of their market share in the near term. The idea that firms operating in customer markets and facing financial frictions set prices to actively manage current versus expected future demand is not new to macroeconomics (see Gottfries, 1991; Chevalier and Scharfstein, 1996). Our contribution lies in bringing the interplay of customer markets and financial frictions into the international context and studying the implications of this interaction within a two-country dynamic stochastic general equilibrium model. As shown below, this pricing mechanism generates time-varying markups and import price dynamics that differ significantly from those in the standard literature (see Dornbusch, 1987; Kimball, 1995; Yang, 1997; Bergin and Feenstra, 2001; Atkeson and Burstein, 2008; Gopinath and Itskhoki, 2010a,b;Burstein and Gopinath,2014;Auer and Schoenle,2016). Specifically,thisliteratureshows that following an adverse exchange rate shock, firms do not fully pass the resulting cost increase into import prices, but instead absorb some of this cost shock in their profits by lowering markups. Inourmodel,bycontrast,financiallyconstrainedfirms,whenhitbyadverseshocks,trytomaintain their cashflows by increasing markups in both the domestic and export markets, in effect trading off future market shares for current profits. The interaction of customer markets and financial frictions helps explain several aspects of the eurozone financial crisis that are difficult to reconcile using conventional open-economy macro models. Most importantly, the pricing mechanism implied by this interaction is consistent with our empirical evidence, which shows that the acute tightening of financial conditions in the euro area periphery between 2008 and 2013 significantly attenuated the downward pressure on prices arising from the emergence of substantial and long-lasting economic slack. The tightening of financial conditions during this period is also strongly associated with a notable increase in markups in the periphery, which is exactly the pattern predicted by our model. Ourframework,therefore,canhelpexplainwhytheperipherycountrieshavemanagedtoavoida potentiallydevastatingFisheriandebt-deflationspiralinthefaceofmassiveandpersistenteconomic slack and high levels of indebtedness. It also helps us understand the chronic stagnation in the euro areaperipheryandhowthe“pricewar”betweenthecoreandperipheryhasimpededtheadjustment process through which the latter economies have been trying to regain external competitiveness. As such, the interaction of customer markets and financial frictions provides a complimentary economic mechanism to the recent work of Schmitt-Groh´e and Uribe (2013, 2016), who emphasize 3Bycustomermarkets,wemeanmarketsinwhichacustomerbaseis“sticky”andthusanimportantdeterminant of firm’s assets and its ability to generate profits (see GSSZ for a thorough discussion). 2

the fact that nominal wages in the eurozone periphery failed to adjust downward after 2008 despite a significant increase in unemployment. In our model, the divergent economic trajectories between the core and periphery in response to a financial shock in the periphery present a dilemma for the union’s central bank because monetary policy cannot be targeted to just one region. Common monetary policy in a situation where members of the union are at different phases of the business cycle increases the volatility of consumption and hours worked in the periphery significantly above the levels registered under flexible exchange rates. This translates into a welfare loss for the union as a whole, with the loss borne entirely by the periphery. With flexible exchange rates, in contrast, monetary authorities in the periphery are able to largely offset the real effects of an asymmetric financial shock by cutting policy rates, inducing a depreciation of nominal exchange rates in the periphery. This policy-induced currency devaluation causes the real exchange rate to depreciate, thereby boosting exports of firms in the periphery and helping to stabilize the contraction in output. In a monetary union, this policy option is, of course, not available. The pricing behavior of firms in the core in response to an asymmetric financial shock implies a real exchange rate appreciation for the periphery, which causes an export-driven boom in the core countries and a deepening of the recession in the periphery. Given the union’s problem with a “one-size-fits-all” monetary policy, we consider the macroeconomic implications of a fiscal devaluation, a policy that has received considerable attention from academic economists and policymakers during the eurozone crisis. For example, Adao et al. (2009) and Farhi et al. (2014) explore the stabilization properties of certain fiscal policy mixes, intended to replicate the effects of a nominal devaluation in a fixed exchange rate regime. What makes such policies desirable is that they can be implemented unilaterally by the periphery countries encountering economic weakness. However, it is not clear why the core countries should welcome such unilateral policy interventions, as they have, in many instance, joined the monetary union precisely to avoid the manipulation of nominal exchange rates by the monetary authorities in the periphery. Thus, a natural question that emerges is whether the periphery can carry out a unilateral fiscal devaluation without worrying about a retaliatory reaction from the core. We show that a fiscal devaluation by the periphery can be welfare enhancing even to the core. Because firms in the core take aggregate prices and the real exchange rate as given when setting prices, they do not take into account the effect of their pricing behavior on the union-wide aggregate demand. As shown by Farhi and Werning (2016), a distortionary taxation can help agents internalize such externalities, and in our model, fiscal devaluations provide an effective means of achieving this goal. 2 Financial Conditions, Prices, Wages, and Markups In this section, we document how financial conditions influenced the dynamics of prices, wages, and markups in the eurozone core and periphery during the 2008–2013 period. We begin by examining the extent to which price and wage inflation forecast errors implied by the canonical Phillips curve 3

relationships during this period are systematically related to differences in the tightness of financial conditions across countries. We do so in two steps. First, we use a panel euro area countries to estimate the following two Phillips curve specifications: π = α +ρπ +λ(u −u¯ )+φ∆VAT +ψ1[i ∈ e]+ǫ ; (1) i,t i i,t−1 i,t i,t i,t i,t πw = α +ρπ +λ(u −u¯ )+φ∆z˜ +ψ1[i ∈ e]+ǫ , (2) i,t i i,t−1 i,t i,t i,t i,t where i indexes countries and t represents time (in years).4 In terms of notation, π denotes price i,t inflation measured by the log-difference of the GDP price deflator, while πw denotes wage inflation i,t measured by the log-difference of nominal compensation per employee. These two specifications are the textbook price and wage Phillips curves, which assume that inflation expectations are proportional to past inflation and where labor market tightness—measured by the difference of the unemployment rate u from its corresponding natural rate u¯ —is a fundamental determinant of i,t i,t price and wage dynamics.5 We also consider a New Keynesian variant of the Phillips curve (NKPC), which incorporates into the process of price inflation determination both rational expectations as well as more explicit microfoundations (see Gal´ı and Gertler, 2000; Gal´ı et al., 2001). In that case, we estimate, π = α +β E π +β π +λmc +φ∆VAT +ψ1[i ∈ e]+ǫ , (3) i,t i f t i,t+1 b i,t−1 i,t i,t i,t where mc denotes a proxy for marginal cost. Incaddition to a country fixed effect α , all three i,t i specifications also include 1[i ∈ e], an indicator variable that equals one when country i adopts c the euro and thereafter; specifications (1) and (3) also control for the pass-through of changes in the effective value-added tax (VAT) rate to aggregate price inflation. To ensure that the parameter estimates are not unduly influenced by the extraordinary events surrounding the eurozone crisis, we end the estimation in 2007, that is, well before the onset of the crisis in the euro area. In columns (1) and (4) of Table 1, we report estimates of the coefficients of the standard price and wage Phillips curves, respectively; in columns (2) and (5), we repeat the same exercise, except that we allow the coefficients on the unemployment gap (u −u¯ ) to differ i,t i,t across countries. And lastly, column (3) reports coefficient estimates of the NKPC with common coefficients, using the output gap (y −y¯ ) as a proxy for marginal cost.6 i,t i,t 4The panel includes six core countries (Austria, Belgium, Finland, France, Germany, and Netherlands) and five periphery countries (Greece, Ireland, Italy, Portugal, and Spain); together, these 11 countries account for about 95 percent of the eurozone’s total economic output. The annual macroeconomic data for these countries, including the estimates of the natural rate of unemployment and potential GDP, were obtained from the AMECO database maintained by the European Commission. 5ThewagePhillipscurve(2)alsoincludesthegrowthrateoftrendlaborproductivity(∆z˜ ),therebyallowingfor i,t alinkbetweenrealwagebargainingandlaborproductivity(seeBlanchard and Katz,1999). Trendlaborproductivity is estimated by regressing the log of labor productivity on a constant and a third-order polynomial in time. 6Specifications(1),(2),(4),and(5)areestimatedbyOLS;inthecaseofspecifications(2)and(5),wereportthe averageofthecoefficientontheunemploymentgapacrossthe11countriesinourpanel. TheNKPCisestimatedby GMM,treating(y −y¯ )andE π asendogenousandinstrumentedwithlags1to3of(y −y¯ )andπ ,and i,t i,t t i,t+1 i,t i,t i,t lags 0 to 2 of the log-difference of commodity prices. 4

Table 1: Price and Wage Phillips Curves in the Euro Area Pricesa Wagesb Explanatory Variables (1) (2) (3) (4) (5) (u −u¯ ) −0.273 −0.529 . −0.559 −0.659 i,t i,t (0.117) (0.127) (0.096) (0.118) (y −y¯ ) . . 0.134 . . i,t i,t (0.084) . . π 0.845 0.813 0.561 0.763 0.745 i,t−1 (0.046) (0.046) (0.078) (0.057) (0.050) E π . . 0.407 . . t i,t+1 (0.085) ∆z˜ . . . 0.689 0.668 i,t (0.127) (0.104) ∆VAT 0.091 0.072 0.035 . . i,t (0.040) (0.039) (0.057) 1[i ∈ e] −0.631 −0.657 −0.315 −1.529 −1.230 (0.300) (0.298) (0.202) (0.358) (0.286) Adj. R2 0.839 0.845 . 0.858 0.872 Pr > Jc . . 0.109 . . Equal coeff. on (u −u¯ )d . <.001 . . <.001 i,t i,t Note: In columns (1), (2), and (3), the dependent variable is π , the log-difference of the GDP price deflator i,t of country i from year t−1 to year t; in columns (4) and (5), the dependent variable is πw, the log-difference of i,t (nominal) compensation per employee of country i from year t−1 to year t. Explanatory variables: (u −u¯ )= i,t i,t unemployment gap; (y −y¯ ) = output gap; ∆z˜ = growth rate of trend labor productivity; VAT = effective i,t i,t i,t i,t VAT rate; and 1[i ∈ e] = indicator variable that equals 1 once country i joined the eurozone. All specifications include country fixed effects; those in columns (1), (2), (4), and (5) are estimated by OLS, while the specification in column (3) is estimated by GMM. In columns (2) and (5), the coefficients on the unemployment gap are allowed to differ across countries, and the entries correspond to the average of the estimated OLS coefficients across the 11 countries. Asymptotic standard errors reported in parentheses are clustered in the time (t) dimension. aAnnual data: from 1970 to 2007 (T¯=29.7); No. of countries = 11; Obs. = 327. aAnnual data: 1971 to 2007 (T¯=26.1); No. of countries = 11; Obs. = 287. cp-value for the Hansen (1982) J-test of the over-identifying restrictions. dp-value for the test of equality of country-specific coefficients on (u −u¯ ). i,t i,t As shown in columns (1), (2), (4), and (5), the degree of labor market slack is an economically and statistically important determinant of price and wage inflation dynamics in all four standard Phillips curve specifications. The estimated sensitivity of both price and wage inflation to tightness oflabormarketconditionsis,onaverage,somewhathigherinspecifications(2)and(5),whichallow for a greater degree of heterogeneity in the price and wage inflation processes across countries. All four specifications, however, explain about the same proportion of the variability in annual price and wage inflation rates across our sample of 11 euro area countries. The estimates of the NKPC in column (3) also indicate an economically significant effect of the output gap—our proxy for marginal cost—on inflation outcomes. This effect, however, is estimated with considerably less precision, compared with the estimated sensitivity of inflation to labor market slack implied by the standard Phillips curve specifications. 5

Figure 1: Sovereign CDS Spreads in the Euro Area (2006–2015) Periphery countries Core countries Percentage points (log scale) Percentage points (log scale) Quarterly Quarterly 150 4 50 2 1 10 0.5 2 0.5 Austria 0.1 Italy Belgium Greece France Portugal Germany Spain Netherlands Ireland Finland 0 0 2006 2008 2010 2012 2014 2006 2008 2010 2012 2014 Note: Thefiguredepictssovereign(5-year)CDSspreadsoneuro-denominatedcontracts;eachseriesisaquarterly average of the daily quotes. Source: Markit North America, Inc., Credit Default Swaps (CDS). Asnotedabove,ourinterestisnotintheseestimatesperse. Rather,weareinterestedinwhether deviations of actual price and wage inflation from the trajectories implied by these Phillips curves during the crisis are systematically related to differences in the tightness of financial conditions across countries. To test this hypothesis, we use spreads on sovereign credit default swap (CDS) contractstomeasurethedegreeoffinancialstrainsineachcountry.7 AsemphasizedbyLane(2012), the European sovereign debt crisis originated over concerns related to the solvency of national banking systems in the periphery. Accordingly, sovereign CDS spreads likely provide an accurate gauge of pressures faced by the national banking systems in the eurozone during the crisis. Given the bank-centric nature of the euro area, variation in CDS spreads should thus reflect differences in the tightness of financial conditions faced by businesses and households in different countries.8 Figure 1 shows the evolution of sovereign CDS spreads in the euro area from 2006 to 2015. Clearly evident is the tightening of financial conditions in the eurozone periphery (left panel): First in 2008, as the escalating financial turmoil in the U.S. led to investors’ widespread reassessment of risks globally; and then again in 2010, when a growing recognition of an unsustainable fiscal situation in Greece led to a massive outflow of private capital from the periphery. To stabilize the economic and political situation that was spiraling out of control, EU leaders and the ECB responded in early 2012 with a number of aggressive policy measures, and by the end of 2013, the riskoffinancialcontagionthatinvestorsthoughtwouldhavelikelyledtoabreak-upoftheeurozone receded notably. 7We use premiums implied by the 5-year, euro-denominated contracts because they are the most liquid segment of the credit derivatives market. 8ThisassumptionisconsistentwiththeevidenceofGilchrist and Mojon(2018),whodocumentastrongrelationship between sovereign risk and credit spreads on bonds issued by financial institutions in the euro area countries. 6

Table 2: Financial Conditions and Phillips Curve Prediction Errors Explanatory Variable PC Specification lnCDS lnCDS ×1[i ∈ P] R2 i,t−1 i,t−1 (a) Without time fixed effects 1. Prices (homogeneous) 0.043 0.601 0.198 [−0.139,0.227] [0.218,0.985] 2. Prices (heterogeneous) 0.204 0.593 0.258 [0.028,0.372] [0.156,1.030] 3. Hybrid NK 0.028 0.299 0.110 [−0.100,0.156] [0.022,0.577] 4. Wages (homogeneous) −0.008 −0.776 0.254 [−0.266,0.251] [−1.425,0.100] 5. Wages (heterogeneous) 0.085 −2.075 0.425 [−0.190,0.360] [−3.082,−1.069] (b) With time fixed effects 1. Prices (homogeneous) 0.044 0.453 0.329 [−0.239,0.327] [0.092,0.814] 2. Prices (heterogeneous) 0.684 0.275 0.419 [0.369,0.999] [0.031,0.519] 3. Hybrid NK 0.125 0.200 0.205 [−0.051,0.301] [−0.031,0.410] 4. Wages (homogeneous) −1.364 −0.495 0.352 [−2.221,−0.506] [−1.359,0.369] 5. Wages (heterogeneous) −2.196 −1.469 0.542 [−2.731,−1.661] [−2.550,−0.389] Note: Annualdatafrom2008to2013;No.ofcountries=11;Obs.=66. Thedependentvariableisǫˆ ,apriceor i,t wageinflationpredictionerrorofcountryiinyeartimpliedbythespecifiedPhillipscurve. HomogeneousPhillips curvespecificationsimposethesamecoefficientontheunemploymentgap,whereasinheterogeneousspecifications, the coefficient on the unemployment gap is country specific (see the text and notes to Table 1 for details). The entriesdenotetheOLSestimatesofthecoefficientsassociatedwiththelog-levelofsovereign(5-year)CDSspreads at the end of year t−1. All specifications include a constant and 1[i ∈ P], an indicator for whether country i is in the euro area periphery (not reported). The 95-percent confidence intervals reported in brackets are based on theempiricaldistributionofcoefficientsacross5,000replications,usingthewildbootstrapclusteredinthetime(t) dimension (see Cameron et al., 2008). To gauge the effects of these financial strains on price and wage dynamics, we first use the estimates in Table 1 to generate price and wage inflation prediction errors from 2008 to 2013. In the second step, we estimate the following regression: ǫˆ = θ +θ lnCDS +θ lnCDS ×1[i ∈ P]+χ1[i ∈ P]+u , (4) i,t 0 1 i,t−1 2 i,t−1 i,t where ǫˆ denotes a residual from one of the estimated Phillips curves in Table 1 and 1[i ∈ P] i,t is an indicator variable that equals one if country i is in the periphery and zero otherwise. The parameters θ and θ thus measure the extent to which differences in financial conditions between 1 2 the core and periphery countries during the crisis can explain deviations of price and wage inflation 7

Figure 2: Price Markups in the Euro Area (1999–2015) Periphery countries Core countries Percent Percent 25 25 Annual Annual 20 20 15 15 10 10 5 5 0 0 -5 -5 -10 -10 2000 2005 2010 2015 2000 2005 2010 2015 Note: The solid lines depict the cross-sectional median of price markups, while the shaded bands denote the corresponding cross-sectional range. The price markup is defined as minus (100 times) the log of real unit labor costs (2008 = 1). Periphery countries: Greece, Ireland, Italy, Portugal, and Spain. Core countries: Austria, Belgium, Finland, France, Germany, and Netherlands. Source: European Commission, AMECO database. trajectories from those implied by the various Phillips curve specifications.9 As shown in panel (a) of Table 2, differences in financial conditions across the euro area during thisperiodaresystematicallyrelatedtothedeviationsofpriceandwageinflationfromthedynamics implied by canonical Phillips curve-type relationships. Turning first to prices (rows 1, 2, and 3), the positive estimates of θ , the coefficient on the interaction term lnCDS ×1[i ∈ P], imply 2 i,t−1 that a widening of sovereign CDS spreads in the eurozone periphery is associated with subsequent inflation rates that exceed those predicted by our various estimated Phillips curves. With regards to wages (rows 4 and 5), on the other hand, negative estimates of θ imply that increased sovereign 2 riskintheperipheryleadstosubsequentwagegrowththatisbelowthatpredictedbytheestimated Phillips curves. The 95-percent confidence intervals bracketing the point estimates of θ exclude 2 zero, an indication that these relationships are statistically significant at conventional levels. In panel (b), we repeat the same exercise, except we add time fixed effects to specification (4), so that θ and θ are identified using only variation between countries. As before, the results 1 2 indicate that an increase in CDS spreads in the eurozone periphery is associated with rates of price inflation that lie systematically above those predicted by the estimated Phillips curves, whereas such tightening of credit conditions leads to rates of wage inflation that run systematically below those implied by the corresponding estimated wage Phillips curve. Taken together, these findings indicate that the deterioration in financial conditions may have significantly influenced price-cost 9Weestimateequation(4)byOLS.However,theassociatedstatisticalinferencethatreliesontheusualasymptotic arguments is likely to be unreliable, given a relatively small number of observations, especially in the time-series dimension. Accordingly, we report the 95-percent confidence intervals for coefficients θ and θ , based on the time- 1 2 clusteredwildbootstrapprocedureofCameron et al.(2008),whichisdesignedforsituationsinwhichthenumberof clusters or the number of observations within each cluster is relatively small. 8

Table 3: Financial Conditions and Price Markups Explanatory Variable Specification lnCDS lnCDS ×1[i ∈ P] R2 i,t−1 i,t−1 (a) Aggregate markupsa 1. Without time fixed effects −0.205 1.378 0.256 [−0.944,0.534] [0.557,2.220] 2. With time fixed effects −0.312 1.148 0.681 [−0.528,−0.095] [0.926,1.372] (b) Sectoral markupsb 1. Without time fixed effects −0.442 2.556 0.057 [−2.135,1.252] [0.913,4.198] 2. With time fixed effects −0.331 1.974 0.152 [−1.915,1.254] [1.244,2.704] Note: In panel (a), the dependent variable is the change in the aggregate price markup in country i from year t−1toyeart,whileinpanel(b)thedependentvariableisthechangeinthecountry-specificsectoralpricemarkup over the same period. The entries denote the OLS estimates of the coefficients associated with the log-level of sovereign (5-year) CDS spreads at the end of year t−1. All specifications include a constant and 1[i ∈ P], an indicator for whether country i is in the euro area periphery (not reported); specifications in panel (b) also include sector fixed effects. The 95-percent confidence intervals reported in brackets are based on the empirical distribution of coefficients across 5,000 replications, using the wild bootstrap clustered in the time (t) dimension (see Cameron et al., 2008). aAnnual data from 2008 to 2013; No. of countries = 11; Obs. = 66. bAnnual data from 2008 to 2013; No. of countries = 11; No. of sectors = 5 (Agriculture, Forestry & Fishing; Building & Construction; Industrial; Manufacturing; and Services); Obs. = 328. margins and hence the behavior of markups in the periphery. Figure 2 shows the evolution of price markups in the eurozone periphery and core since the introduction of the euro in 1999.10 The divergence in markups between the core and periphery during the crisis is striking: The median markup in the periphery increased about 5 percentage points between 2009 and 2013, while in the core, the median markup fell about the same amount during this period. To examine how differences in financial strains across countries affected the behavior of markups in the euro area during the crisis, we re-estimate regression (4) using the change in markups as the dependent variable. As indicated in panel (a) of Table 3, a widening CDS spreads in the periphery is associated with a statistically significant subsequent increase in markups, whereas in the euro area core, such a tightening of financial conditions has no effect on markups; note that this effect is robust to the inclusion of time fixed effects. In panel (b), we improve on the power of this test by considering markups at the sectoral level. Adding this dimension to our data further strengthens the relationship between financial conditions and subsequent changes in price markups. Using the “between” estimates in row 2 as a benchmark, a periphery country with CDS spreads at the 90th percentile of the distribution would see its markups increase more than 5.5 percentage points, 10As shown by Gal´ı et al. (2007), the price markup can, under reasonable assumptions, be measured (up to an additive constant) as minus the log of real unit labor costs. 9

compared with a country whose CDS spreads are at the 10th percentile of the distribution. The above results add to the growing empirical evidence, which supports the notion that financial conditions of firms in the euro area affected their pricing decisions during the global financial crisisanditsaftermath(seeMontero and Urtasun,2014;Antoun de Almedia,2015;Montero,2017; Duca et al., 2017). Combining the theory of customer markets with financial frictions provides a natural way to understand these new findings. The pricing mechanism implied by this interaction predicts exactly the differences in the behavior of prices and markups between the eurozone core and periphery documented above: In response to a financial shock in the periphery, the tightening ofcreditconditions causesfirms—inanefforttopreserveinternalliquidity—toboost pricesbyraising markups. The following quote from Sergio Marchionne, the CEO of Fiat Chrysler, in mid-2012 paints a visceral picture of the price dynamics implied by our theory: Mr.MarchionneandotherautoexecutivesaccuseVolkswagenofexploitingthecrisis to gain market share by offering aggressive discounts. “It’s a bloodbath of pricing and it’s a bloodbath on margins,” he said. The New York Times, July 25, 2012 3 Model The model consists of two countries—referred to as home (h) and foreign (f)—and where foreign country variables carry a superscript “*.” We think of home and foreign countries as representing the periphery and core countries of the euro area, respectively. 3.1 Preferences and Technology In each country, there exists a continuum of households indexed by j ∈ N = [0,1], c = h,f. Each c household consumes two types, h and f, of differentiated varieties of consumption goods, indexed byi ∈ N = [0,1]inthehomecountryandbyi ∈ N = [1,2]intheforeigncountry. Consistentwith h f the standard assumption used in international macroeconomics, the home country only produces the h-type goods, while the foreign country only produces the f-type goods. In this two-country j setting, c denotes the consumption of product i of type f by a home country household j, while i,f,t j∗ c denotes its foreign counterpart—that is, the consumption of product i of type f by a foreign i,f,t country household j.11 The preferences of household j in the home country are given by ∞ E δsU(x j −ω ,h j ); (0 < δ < 1). (5) t t+s t+s t+s s=0 X Thehousehold’sper-periodutilityfunctionU(·,·)isstrictlyincreasingandconcaveintheconsumpj j tion bundle x and strictly decreasing and concave in hours worked h . The preference shock ω t t t 11In our notation, cj denotes consumption of an imported good by a home country household j, while cj∗ i,f,t i,f,t denotes consumption of a domestically produced good by a foreign household j. 10

j affectsthemarginalutilityofconsumingthebundlex todayandisusedtoexploretheimplications t of an aggregate demand shock in our framework. For simplicity, we assume that labor is perfectly immobile. Standardopeneconomymodelsallowforhome-biasinconsumptionbycombiningDixit-Stiglitz preferences with an Armington aggregator of home and foreign goods. We introduce into this framework a sticky customer base via the “deep habits” preference structure of Ravn et al. (2006). This yields the consumption/habit aggregator 1−1/ε 1 1−1/ε x j ≡ Ξ c j /sθ 1−1/η di 1−1/η , t k i,k,t i,k,t−1 " k=h,f (cid:20)ZNk (cid:21) # X (cid:0) (cid:1) whereη > 1andε > 1arethe elasticitiesofsubstitution within atypeofgoodsproducedinagiven countryandbetween thetwotypesofgoods, respectively. TheparameterΞ > 0governsthedegree k of home bias in the household’s consumption basket in the steady state, with Ξε = 1. k=h,f k 1 j Let c = c dj denote the average level of consumption of good i in country k. As in i,k,t 0 i,k,t P Ravn et al. (2006), let s denote the good-specific habit, which evolves according to R i,k,t s = ρs +(1−ρ)c ; k = h,f (0 < ρ < 1). i,k,t i,k,t−1 i,k,t In the above formulation, habits are external to the household and country specific. When θ < 0, the stock of habit formed by past consumption of the average household has a positive effect on the utility derived from today’s consumption, making the household desire more of the same good. In equilibrium, all households within a given country choose the same consumption basket. Going forward, we thus omit the household index j. The cost minimization associated with equation (5) implies the following demand function for good i (of type h or f) in the home country: P −η i,k,t θ(1−η) c = s x ; k = h,f, i,k,t P˜ i,k,t−1 k,t (cid:18) k,t (cid:19) where the habit-adjusted price index P˜ and the habit-adjusted consumption bundle x are given k,t k,t by 1 1 1−η 1−1/η P˜ = (P sθ )1−ηdi and x = (c /sθ )1−1/ηdi ; k = h,f. k,t i,k,t i,k,t−1 k,t i,k,t i,k,t−1 " ZNk # " ZNk # In equilibrium, the consumption/habit basket x is equal to k,t 1 P˜ −ε 1−ε x = Ξε k,t x ; k = h,f, with P˜ = Ξ P˜1−ε , (6) k,t k (cid:18) P˜ t (cid:19) t t " k=h,f k k,t # X whereP˜ denotesthewelfare-basedaggregatepriceindexofthehomecountry. Duetothesymmetric t 11

structure of the two countries, the foreign country analogues of c , x , and P˜ can be expressed i,k,t k,t t simply by adding a superscript “*” to each variable. For later use, we also define the consumer price index (CPI) as 1 1 1−ε 1−η P = Ξ P1−ε , where P = P 1−ηdi ; k = h,f, (7) t k k,t k,t i,k,t " k=h,f # " ZNk # X is the CPI corresponding to a k-type category of goods. On the production side, we abstract from capital and assume that labor is the only input. The technologies in the home and foreign countries are given by A α A∗ α y = t h −φ and y∗ = t h∗ −φ∗; (0 < α ≤ 1), i,t a i,t i,t a∗ i,t (cid:18) i,t (cid:19) (cid:18) i,t (cid:19) where φ,φ∗ > 0 denote fixed operating costs; A and A∗ are the country-specific aggregate techt t nology shocks, and a and a∗ are the idiosyncratic “cost” shocks affecting home and foreign i,t i,t firms, respectively. We assume that the idiosyncratic cost shocks are distributed according to a log-normal distribution: lna ,lna∗ i ∼ id N(−0.5σ2,σ2). We denote the CDF of the idiosyncratic i,t i,t shocks by F(a). The presence of fixed costs makes it possible for firms to incur operating losses and hence to find themselves in a liquidity squeeze if external financing is costly or, as during the height of the eurozone sovereign debt crisis, essentially unavailable. 3.2 Frictions For fixed costs to play a role in creating liquidity risk, we introduce several frictions to the firm’s flow-of-funds constraint. First, we adopt a timing convention, whereby in the first half of period t firms collect information about the aggregate state of the economy. Based on this aggregate information, firms post prices, take orders from customers, and plan production based on expected marginal cost. In the second half of the period, idiosyncratic cost uncertainty is resolved, and firms realize their actual marginal cost. They then hire labor to fulfill the agreed-upon orders and produce period-t output. Wealsoassumethatfirmspayoutalloperatingprofitsasdividendswithinagivenperiod—that is, we rule out corporate savings.12 Because of fixed costs, the firm’s revenues may, ex post, be insufficienttocoverthetotalcostofproduction. Inthatcase, thefirmmustissuenewshareswithin that period. Due to agency problems, such equity financing involves a constant dilution cost per share issued, denoted by 0 < ϕ,ϕ∗ < 1. Hence when a home country firm issues a notional amount of equity d < 0, the actual amount of funds raised is given by −(1 − ϕ)d . Consistent with i,t i,t the fact that core euro area countries have deeper and more developed capital markets than the eurozone periphery, the dilution costs in the home country are assumed to exceed those in foreign 12Ruling out precautionary savings limits the dimension of the state space. However, this assumption does not mean that firms do not engage in any form of risk management. Rather, as shown below, the firms’ liquidity risk management involves the accumulation and decumulation ofmarket shares, a central facet oftheir pricing behavior. 12

country—that is, 0 < ϕ∗ < ϕ. This implies that firms in the home country are more exposed to liquidity risk than their foreign counterparts.13 In addition to financial frictions, we also allow for nominal rigidities by assuming that firms incur costs when adjusting prices. Following Rotemberg (1982), these costs are given by γ P 2 γ Q P∗ P∗ 2 p i,h,t −1 c + p t t i,h,t −1 c∗; (γ > 0), 2 P t 2 P P∗ t p (cid:18) i,h,t−1 (cid:19) t (cid:18) i,h,t−1 (cid:19) where Q denotes the nominal exchange rate. We assume the same degree of price stickiness (γ ) t p in both countries and let the price adjustment costs be proportional to local consumption—that is, c and c∗—an assumption made solely to preserve the homogeneity of the firm’s problem and one t t that has no first-order consequences for dynamics of the model. Note also that we assume local currency pricing rather than producer currency pricing. 3.3 The Firm’s Problem The firm’s objective is to maximize the present value of its dividend flow, E ∞ m d , t s=0 t,t+s i,t+s where d = D /P is the real dividend payout when positive and real equity issuance when i,t i,t t (cid:2)P (cid:3) negative. Firms are owned by households, and they discount future cashflows using the stochastic discount factor of the representative household, denoted by m , in their respective country. t,t+s Before formally stating the firm’s optimization problem, we define relative prices. The real product prices relative to the CPIs in home and foreign countries can be written as P P P P∗ P∗ P∗ i,h,t = i,h,t h,t ≡ p p and i,h,t = i,h,t h,t ≡ p∗ p∗ . P P P i,h,t h,t P∗ P∗ P∗ i,h,t h,t t h,t t t h,t t Note that p and p∗ are prices charged by home country firm i relative to the average price i,h,t i,h,t level chosen by the home country firms in the home and foreign markets, respectively; p and p∗ , h,t h,t on the other hand, are the average price levels relative to the CPI in the home and foreign markets, respectively and as such are taken as given by individual firms. From the perspective of firms in the foreign country, the relative prices p , p∗ , p , and p∗ are interpreted in the same way. i,f,t i,f,t f,t f,t A home country firm maximizes the present value of real dividends, subject to a flow-of-funds constraint: d = p p c +q p∗ p∗ c∗ −w h +ϕmin 0,d i,t i,h,t h,t i,h,t t i,h,t h,t i,h,t t i,t i,t − γ p p i,h,t π −1 2 c − γ p q p∗ i,h,t π∗ − (cid:8) 1 2 c (cid:9) ∗, 2 p h,t t 2 t p∗ h,t t (cid:18) i,h,t−1 (cid:19) (cid:18) i,h,t−1 (cid:19) where w = W /P is the real wage, q = Q P∗/P is the real exchange rate, and π = P /P t t t t t t t h,t h,t h,t−1 and π∗ = P∗ /P∗ are the market-specific (gross) inflation rates faced by firms in the home h,t h,t h,t−1 13Implicitly, we are assuming that the stock markets of the two countries are fully segmented—only domestic (foreign) households invest in the shares of domestic (foreign) firms. Empirical evidence of significant home bias in equityholdingsisprovidedbyFrench and Poterba(1991),Tesar and Werner(1995),andObstfeld and Rogoff(2000). 13

country. Formally, the firm is choosing the sequence d ,h ,c ,c∗ ,s ,s∗ ,p ,p∗ ∞ to i,t i,t i,h,t i,h,t i,h,t i,h,t i,h,t i,h,t t=0 optimize the following Lagrangian: (cid:8) (cid:9) ∞ α A L = E m d +κ t h −φ−(c +c∗ ) 0 0,t i,t i,t a i,t i,h,t i,h,t t=0 ( " (cid:18) i,t (cid:19) # X +ξ p p c +q p∗ p∗ c∗ −w h −d +ϕmin{0,d } i,t i,h,t h,t i,h,t t i,h,t h,t i,h,t t i,t i,t i,t " γ p 2 γ p∗ 2 − p i,h,t π −1 c − p q i,h,t π∗ −1 c∗ (8) 2 p h,t t 2 t p∗ h,t t (cid:18) i,h,t−1 (cid:19) (cid:18) i,h,t−1 (cid:19) # +ν (p )−ηp˜ η s θ(1−η) x −c +ν∗ (p∗ )−ηp˜ ∗η s ∗θ(1−η) x∗ −c∗ i,h,t i,h,t h,t i,h,t−1 h,t i,h,t i,h,t i,h,t h,t i,h,t−1 h,t i,h,t (cid:20) (cid:21) (cid:20) (cid:21) +λ ρs +(1−ρ)c −s +λ∗ ρs∗ +(1−ρ)c∗ −s∗ , i,h,t i,h,t−1 i,h,t i,h,t i,h,t i,h,t−1 i,h,t i,h,t ) (cid:20) (cid:21) (cid:20) (cid:21) where p˜ = P˜ /P and p˜∗ = P˜∗ /P∗ ; κ and ξ are the Lagrange multipliers associated h,t h,t h,t h,t h,t h,t i,t i,t with the production constraint and the flow-of-funds constraint, respectively; ν and ν∗ are i,h,t i,h,t the Lagrange multipliers associated with the domestic and foreign demand constraints; and λ i,h,t andλ∗ arethemultipliersassociatedwiththedomesticandforeignhabitaccumulationprocesses. i,h,t We begin by describing the firm’s optimal choice of labor hours and dividends (or equity issuance), two decisions that are made after the realization of the idiosyncratic cost shock a . In i,t contrast to these two decisions, the optimality conditions for prices (p ,p∗ ), production orders i,h,t i,h,t (c ,c∗ ), andhabitstocks(s ,s∗ )inthedomesticandforeignmarketsaredeterminedprior i,h,t i,h,t i,h,t i,h,t to the realization of the idiosyncratic cost shock. For maximum intuition, we focus on the case without sticky prices. We then discuss the implications of our model for inflation and the Phillips curve in an environment where firms face quadratic costs of changing prices. The efficiency condition for labor hours in problem (8) is given by α−1 A t a ξ w = κ αA h , (9) i,t i,t t i,t t i,t a (cid:18) i,t (cid:19) where given the production function, labor hours satisfy the conditional labor demand:14 a h i,t = A i,t (φ+c i,h,t +c∗ i,h,t )α 1 . (10) t Our timing assumptions imply that c and c∗ are determined prior to the realization of the i,h,t i,h,t idiosyncratic cost shock a . Combining equations (9) and (10), applying the expectation operator i,t Ea[x] ≡ xdF(a) to both sides of the resulting expression, and dividing through by Ea[ξ ] yields t t i,t 14This cRonditional labor demand ensures a symmetric equilibrium, in which all firms produce an identical level of output regardless of their productivity. Relatively inefficient firms, however, have to hire more labor to produce the same level of output than their more efficient counterparts, which exposes them to ex post liquidity risk. 14

the following expression for the expected real marginal cost normalized by the expected shadow value of internal funds: Ea[κ ] Ea[a ξ ] w E t a[ξ i,t ] = E t a[ i ξ ,t i ] ,t αA t (φ+c i,h,t +c∗ i,h,t ) 1− α α . (11) t i,t t i,t t To understand the economic content behind this expression, consider first the case with no financial frictions. In this case, the shadow value of internal funds ξ = 1, for all i and t, implying i,t that Ea[ξ ] = 1 and Ea[a ξ ] = Ea[a ]Ea[ξ ] = 1. With constant returns-to-scale for example, t i,t t i,t i,t t i,t t i,t Ea[κ ] = w /A and expected marginal cost equals unit labor costs. t i,t t t In the presence of financial frictions, however, the shadow value of internal funds is not always equaltooneandbecomesstochastic,accordingtotherealizationoftheidiosyncraticcostshocka , i,t which influences the liquidity position of the firm. The first-order condition for dividend payouts (or equity issuance) implies that 1 if d ≥ 0; i,t ξ = (12) i,t ( 1/(1−ϕ) if d i,t < 0. In other words, the shadow value of internal funds is equal to one when the firm’s revenues are sufficiently high to cover labor and fixed costs, and thus the firm pays dividends. If, however, the firm incurs an operating loss, it must issue new equity, and the shadow value of internal funds jumps to 1/(1−ϕ). Intuitively, given the equity dilution costs, a firm must issue 1/(1−ϕ) units of equity to obtain one unit of cashflow. These conditions imply that Ea[ξ ] > 1. t i,t It is also the case that the realized shadow value of internal funds covaries positively with the idiosyncratic cost shock a , as profits and hence dividends are negative when costs are high. i,t Because Ea[a ] = 1, this implies t i,t Ea[ξ a ] Cov[ξ ,a ] t i,t i,t = 1+ i,t i,t > 1. Ea[ξ ] Ea[ξ ] t i,t t i,t Becauseofthispositivecovariance,thefirm’sexanteinternalvaluationofmarginalcost,Ea[ξ a ], t i,t i,t exceeds its ex ante valuation of marginal revenue, Ea[ξ ], and financial frictions raise the real t i,t marginal cost given by equation (11). In effect, the firm must be compensated for the liquidity premium associated with costly external finance, and this required compensation increases its marginal cost, inclusive of financing costs. 3.4 Optimal Pricing in a Symmetric Equilibrium With risk-neutral firms and i.i.d. idiosyncratic costs shocks, our timing assumptions imply that all firms in a given country are identical ex ante. As a result, we focus on an equilibrium that has a number of symmetric features. Specifically, all home country firms choose identical relative prices (p = 1 and p∗ = 1), scales of production (c = c and c∗ = c∗ ), and habit i,h,t i,h,t i,h,t h,t i,h,t h,t stocks (s = s and s∗ = s∗ ). The symmetric equilibrium condition p = p∗ = 1 i,h,t h,t i,h,t h,t i,h,t i,h,t 15

implies that firms in the home country set the same relative prices in domestic and foreign markets vis-a`-vis other competitors from the same origin.15 Similarly, foreign firms make pricing decisions among themselves, both in the domestic and foreign markets, such that p = p∗ = 1. The i,f,t i,f,t asymmetricnatureoffinancialconditionsinducesdifferencesinthefirms’internalliquiditypositions andcauseshomeandforeignfirmstoadoptdifferentpricingpolicies. Asaresult,p = P /P 6= 1, h,t h,t t p∗ = P∗ /P∗ 6= 1, p = P /P 6= 1, and p∗ = P∗ /P∗ 6= 1, implying that p 6= p and h,t h,t t f,t f,t t f,t f,t t h,t f,t p∗ 6= p∗ , in general. As we show below, the relatively weaker financial position of home firms h,t f,t forcesthemtomaintainhigherpricesandmarkupsintheneighborhoodofthenonstochasticsteady state, such that p > p and p∗ > p∗. h f h f Imposing the relevant symmetric equilibrium conditions, the firm’s internal funds are given by revenues less production costs: p c +q p∗ c∗ −w a i,t φ+c +c∗ α 1 , h,t h,t t h,t h,t t A h,t h,t t (cid:0) (cid:1) where we substituted the conditional labor demand (10) for h . The firm resorts to costly external t finance—that is, issues new shares—if and only if a > aE ≡ A t p h,t c h,t +q t p∗ h,t c∗ h,t . (13) i,t t w t" (φ+c h,t +c∗ h,t )α 1 # Using the above definition of the equity issuance threshold aE, we can express the first-order t conditions for dividends (12) as 1 if a ≤ aE; ξ = i,t t i,t ( 1/(1−ϕ) if a i,t > aE t , which states that because of costly external financing, the shadow value of internal funds jumps from one to 1/(1 − ϕ) > 1 when the realization of the idiosyncratic cost shock a exceed the i,t threshold value aE. Let zE denote the standardized value of aE (i.e, zE = (lnaE + 0.5σ2)/σ). t t t t t Taking expectations, the expected shadow value of internal funds is given by Ea[ξ ] = aE t dF(a)+ ∞ 1 dF(a) = 1+ ϕ 1−Φ(zE) ≥ 1, t i,t 1−ϕ 1−ϕ t Z0 ZaE t (cid:2) (cid:3) where Φ(·) denotes the standard normal CDF. Thus, the expected shadow value of internal funds is strictly greater than one as long as equity issuance is costly (ϕ > 0) and future costs are uncertain (σ > 0). In our context, Ea[ξ ] directly captures the firm’s ex ante valuation of an additional unit t i,t of cashflow obtained from increasing marginal revenue. To streamline notation, we define the markup—denoted by µ˜ —as the inverse of real marginal t 15Recall that p and p∗ are relative prices measured against average prices charged by firms in the home i,h,t i,h,t country. These are different from the relative prices against local and foreign CPIs, which are averages of prices of both domestic and imported goods (see equation (7)). 16

cost inclusive of financing costs: −1 µ˜ = Ea t [a i,t ξ i,t ] w t φ+c +c∗ 1− α α , t Ea[ξ ] αA h,t h,t " t i,t t # (cid:0) (cid:1) where Ea[ξ a ] Cov[ξ ,a ] 1−ϕΦ(zE −σ) t i,t i,t = 1+ i,t i,t = t > 1 Ea[ξ ] Ea[ξ ] 1−ϕΦ(zE) t i,t t i,t t follows from properties of the log-normal distribution.16 Imposingthesymmetricequilibriumconditions, wecanexpress(seeSectionAoftheAppendix) the firm’s optimal pricing strategies in the domestic and foreign markets as η 1 ∞ Ea[ξ ] 1 p = +(1−ρ)θηE β s i,s p − ; (14) h,t η−1µ˜ t h,t,sEa[ξ ] h,s µ˜ t " s=t+1 t i,t (cid:18) s(cid:19) # X η 1 ∞ Ea[ξ ] 1 q p∗ = +(1−ρ)θηE β∗ s i,s q p∗ − , (15) t h,t η−1µ˜ t h,t,sEa[ξ ] s h,s µ˜ t " s=t+1 t i,t (cid:18) s(cid:19) # X where the growth-adjusted, compounded discount factors, β and β∗ , are given by h,t,s h,t,s m g if s = t+1; s−1,s h,s β = h,t,s s−(t+1) ( m s−1,s g h,s × j=1 (ρ+χg h,t+j )m t+j−1,t+j if s > t+1; β∗ = m s−1,s g h ∗ ,s Q if s = t+1; h,t,s ( m s−1,s g h ∗ ,s × s j= − 1 (t+1) (ρ+χg h ∗ ,t+j )m t+j−1,t+j if s > t+1, Q and where g = sh,t/sh,t−1 −ρ , g∗ = s∗ h,t /s∗ h,t−1 −ρ , and χ = (1−ρ)θ(1−η) > 0. h,t 1−ρ h,t 1−ρ In the absence of customer-market relationships (i.e., θ = 0), the second term on the right-hand sides of equations (14) and (15) disappears, and we obtain the standard pricing equation for a static monopolist facing isoelastic demand: The price is equal to a constant markup, η , over η−1 current marginal cost, inclusive of financing costs. With customer markets (i.e., θ < 0), prices are, on average, strictly lower than those that would have been set by the static monopolist because firms have an incentive to lower prices in order to expand their market shares. Financial frictions create a tension between the firm’s desire to expand its market share and its desiretomaintainadequateinternalliquidity. Thetermsinsidethesquarebracketsofequations(14) and (15) represent the present values of future profits. When expanding market shares becomes moreimportant, whichhappensthroughtheincreaseinthegrowth-adjusted, compoundeddiscount factors β and β∗ , the firm has a greater incentive to reduce prices because θ < 0. However, h,t,s h,t,s when the firm faces a liquidity problem in the sense that the shadow value of internal funds today is strictly greater than its future values—that is, Ea[ξ ] > Ea[ξ ], for s > t—the firm discounts t i,t t i,s 16From the assumption that lna i∼idN(−0.5σ2,σ2), it follows that Cov[ξ ,a ]= ϕ Φ(zE)−Φ(zE−σ) >0; i,t i,t i,t 1−ϕ t t see Kotz et al. (2000) for details. (cid:2) (cid:3) 17

future profits more heavily. This in turn leads to a higher price than would otherwise prevail. Intuitively, the short-run demand elasticity in our model is less than its long-run counterpart because of customer markets. If the firm discounted the future completely, it would set price as a constant markup, η , over its current marginal cost µ˜ . Such a markup reflects entirely the η−1 t low short-run demand elasticity. A firm that fully disregards financial considerations, in contrast, would set a substantially lower markup, consistent with the lower long-run demand elasticity that prevails because of the competition for future market share. As the firm encountering a liquidity problem begins to discount the future more heavily, its pricing strategy shifts towards the higher markup associated with the inelastic short-run demand, relative to the optimal long-run markup that fully captures these customer market considerations.17 3.5 Inflation Dynamics Adding nominal rigidities to the model does not alter the nature of the optimal pricing problem in any fundamental way. The inherent tension between the maximization of market shares and the maximization of current profits that arises from the interaction of financial frictions and customer markets is also present in a version of the model with sticky prices. Therefore, instead of repeating the analysis, we simply close this section by showing how the well-known, log-linearized Phillips curve is modified owing to financial frictions and customer-market relationships. Using equation (7), we can express the log-linearized dynamics of national CPIs as πˆ = Ξ p (pˆ +πˆ )+Ξ p (pˆ +πˆ ); (16) t h h h,t−1 h,t f f f,t−1 f,t πˆ∗ = Ξ∗p∗(pˆ∗ +πˆ∗ )+Ξ∗p∗(pˆ∗ +πˆ∗ ), (17) t h h h,t−1 h,t f f f,t−1 f,t where the variables with the “hat” denote log-linearized deviations from their respective steadystate values, which correspond to variables without the time subscript. Equations (16) and (17) illustrate how import prices affect the inflation dynamics of national CPIs. A full characterization 17Note that in the steady state, β = δ(ρ+χ) s−t. The pricing equation (14) then becomes h,t,s (cid:2) (cid:3) η 1 δ(ρ+χ)(1−ρ)θη 1 p = + p − h η−1µ˜ 1−δ(ρ+χ) (cid:18) h µ˜(cid:19) η δ(ρ+χ)(1−ρ)θη 1 δ(ρ+χ)(1−ρ)θη = − + p . (cid:20)η−1 1−δ(ρ+χ) (cid:21)µ˜ 1−δ(ρ+χ) h Defining δ(ρ+χ)(1−ρ)θη Θ= , 1−δ(ρ+χ) and solving the above expression for p , yields h 1 1 p = 1+ , h (cid:20) (η−1)(1−Θ)(cid:21)µ˜ which shows that the long-run relative price p is equal to the gross markup over real marginal cost, where the net h markup is equal to 1 . For the net markup to be positive, we need to impose a condition 1 > 0; (η−1)(1−Θ) (η−1)(1−Θ) because η > 1, this is equivalent to Θ < 1. Under our baseline calibration of the model (see Section 4 below), this condition is easily satisfied, and the long-run net markup is about seven percent substantially below its short-run value of η , that is, 100 percent η−1 18

of these dynamics requires a construction of Phillips curves for πˆ , πˆ , πˆ∗ , and πˆ∗ . For the h,t f,t h,t f,t sake of space, we focus on the first and the third. The log-linearization of the first-order conditions for p and p∗ implies: i,h,t i,h,t 1 p c πˆ = h h pˆ −(νˆ −ξˆ) +δE [πˆ ]; (18) h,t h,t h,t t t h,t+1 γ c p 1 c∗(cid:2) (cid:3) πˆ∗ = qp∗ h qˆ +pˆ∗ −(νˆ∗ −ξˆ) +δE [πˆ∗ ], (19) h,t γ hc∗ t h,t h,t t t h,t+1 p (cid:2) (cid:3) whereνˆ , νˆ∗ , andξˆ arethelog-deviationsofEa[ν ], Ea[ν∗ ], andEa[ξ ]fromtheirrespective h,t h,t t t i,h,t t i,h,t t i,t steady-state values. In the absence of customer markets, the terms in brackets are exactly equal to the log-deviation of the financially adjusted real marginal cost µ˜−1, and we recover the standard t forward-looking Phillips curve for each market. Withcustomermarkets,however,weobtainaconsiderablyrichersetofinflationdynamics. Substituting the log-linear dynamics of νˆ −ξˆ and νˆ∗ −ξˆ into equations (18) and (19), respectively, h,t t h,t t yields the following Phillips curve for the domestic market: ∞ 1 p c µˆ µˆ πˆ = h h pˆ −η pˆ + t −ηχE δ˜s−t pˆ + s h,t h,t h,t t h,s γ c p µ˜ p µ˜ p " (cid:18) h (cid:19) s=t+1 (cid:18) h (cid:19) # X ∞ ηχp c 1 + h h 1− E δ˜s−t (ξˆ −ξˆ)−βˆ +δE [πˆ ]; t t s h,t,s t h,t+1 γ c p µ˜ p (cid:18) h (cid:19) s=t+1 X (cid:2) (cid:3) and for the foreign market: 1 c∗ µˆ ∞ µˆ πˆ∗ = qp∗ h qˆ +pˆ∗ −η (qˆ +pˆ )+ t +ηχE δ˜s−t (qˆ +pˆ∗ )+ s h,t γ hc∗ t h,t t h,t qp∗µ˜ t s h,s qp∗µ˜ p " (cid:18) h (cid:19) s=t+1 (cid:18) h (cid:19) # X ηχ c∗ 1 ∞ + qp∗ h 1− E δ˜s−t (ξˆ −ξˆ)−βˆ∗ +δE [πˆ∗ ], γ hc∗ qp∗µ˜ t t s h,t,s t h,t+1 p (cid:18) h (cid:19) s=t+1 X (cid:2) (cid:3) where δ˜ = δ(ρ + χ). Because χ > 0, the firm’s heightened concern about its current liquidity position, as manifested by the fact that ξˆ −ξˆ > 0, will result in higher inflation in both markets. t s In contrast, the increased importance of future market shares at home and abroad, as captured by βˆ > 0 and βˆ∗ > 0, leads to lower inflation in both markets. The terms (ξˆ −ξˆ)−βˆ and h,t,s h,t,s t s h,t,s (ξˆ −ξˆ)−βˆ∗ , therefore, capture the fundamental tension between the maximization of current t s h,t,s profits andthe maximizationoflong-runmarketshares, atensionthat importantly shapes inflation dynamics in periods of financial turmoil. 3.6 The Household’s Problem We now turn to the optimization problem of the representative household in the home country. First, we formulate this problem in an environment of flexible exchange rates. We then impose 19

restrictions that deliver the baseline model of a monetary union. 3.6.1 Flexible Exchange Rates The representative household in the home country works h hours. It allocates its savings between t shares of the home country firms and international bonds that are not state contingent. We denote the home country’s holdings of international bonds issued in home and foreign currency units by B and B , respectively, while B∗ and B∗ denote their foreign counterparts.18 The h,t+1 f,t+1 h,t+1 f,t+1 respective (gross) nominal interest rates on these securities are denoted by R and R∗. t t We assume that investors in both countries face identical portfolio rebalancing costs, denoted by τ > 0. Focusing on the home country, these costs are given by τ B 2 B 2 h,t+1 f,t+1 P +q . 2 t P t P∗ " (cid:18) t (cid:19) (cid:18) t (cid:19) # Under these assumptions, the marginal cost of borrowing in home currency is given by R /(1+ t τB /P ), which is strictly greater than R if B < 0. The marginal return on foreign lending h,t+1 t t h,t+1 inhomecurrencyisgivenbyR (Q /Q )/(1+τB∗ /P∗),whichisstrictlylessthanR (Q /Q ) t t t+1 h,t+1 t t t t+1 ifB∗ > 0. Thus, (1+τB /P )−1 representsawelfareloss, notonlytotheborrowers, butalso h,t+1 h,t+1 t to the lenders. As pointed out by Ghironi and Melitz (2005), the role of such portfolio rebalancing costs is to pin down the steady-state levels of international bond holdings, as varying τ does not modify the model dynamics in any significant way. The number of outstanding shares of home country firm i is denoted by S , while PS is the i,t i,t−1,t period-t per-share value of the shares outstanding as of period t−1 and PS is the (ex-dividend) i,t per-share value of shares in period t. Using the fact that P c di = P˜ x , for k = h,f, Nk i,k,t i,k,t k,t k,t we can express the household’s budget constraint as R 0 = W h +R B +Q R∗ B + max{D ,0}+PS SS di t t t−1 h,t t t−1 f,t i,t i,t−1,t i,t ZNh (cid:2) (cid:3) (20) τ B 2 B 2 −P˜x −B −Q B − P h,t+1 +q f,t+1 − PSSS di. t t h,t+1 t f,t+1 2 t P t P∗ i,t i,t+1 " (cid:18) t (cid:19) (cid:18) t (cid:19) # ZNh The consumption expenditure problem is expressed as purchasing the habit-adjusted consumption bundle x using the price index P˜, which is possible because P˜ is a welfare-based price index. t t t The representative household maximizes the life-time utility given by equation (5) subject to the budget constraint (20). Letting Λ denote the Lagrange multiplier associated with the budget t constraint, the first-order condition for x is then given by Λ = U /P˜ = U /(P˜/P )P = t t x,t t x,t t t t (U /p˜)/P . We can then express the first-order condition for hours worked as U w /p˜ = −U . x,t t t x,t t t h,t 18OurnotationimpliesthatB +B∗ =0,whereB andB∗ aredenominatedinhomecurrency—as h,t+1 h,t+1 h,t+1 h,t+1 denoted by the subscript h—and are held by the home and foreign country residents, respectively. If B < 0 h,t+1 (B <0), the home country borrows money in home currency units (in foreign currency units) from the foreign f,t+1 country, whose claim is B∗ >0 (B∗ >0). h,t+1 f,t+1 20

The two equity valuation terms that appear in the budget constraint are related to each other through an accounting identity PS = PS +ES , where ES is the per-share value of new equity i,t i,t−1,t i,t i,t issued by a firm i in period t. Because of equity dilution costs, ES = −(1 − ϕ)min{D ,0}. i,t i,t Substituting PS = PS − ES = PS + (1 − ϕ)min{D ,0} into the budget constraint (20), i,t−1,t i,t i,t i,t i,t we obtain the optimality conditions governing the household’s holdings of international bonds and shares of firms: U /p˜ R 1 1 = δE x,t+1 t+1 t ; (21) t U /p˜ π 1+τb " x,t t (cid:18) t+1 h,t+1(cid:19) # U /p˜ q R∗ 1 1 = δE x,t+1 t+1 t+1 t ; (22) t U /p˜ q π∗ 1+τb " x,t t (cid:18) t t+1 f,t+1(cid:19) # U /p˜ 1 Ea [D˜ ]+PS 1 = δE x,t+1 t+1 t+1 i,t+1 t+1 , (23) t U /p˜ π PS " x,t t t+1(cid:18) t (cid:19) # where D˜ = max{D ,0}+(1−ϕ)min{D ,0}, b = B /P , and b = B /P∗.19 In i,t i,t i,t h,t+1 h,t+1 t f,t+1 f,t+1 t deriving the first-order condition (23), we exploited the fact that the ex ante value of the firm—the value prior to the realization of the idiosyncratic cost shock—is the same for all firms; that is, Ea [PS ] = PS in the symmetric equilibrium. t+1 i,t+1 t+1 The bond market clearing conditions are given by 0 = b +b∗ and 0 = b +b∗ , (24) h,t+1 h,t+1 f,t+1 f,t+1 where foreign holdings of international bonds denominated in home and foreign currencies—b∗ h,t+1 and b∗ , respectively—satisfy the foreign counterparts of equations (21) and (22):20 f,t+1 U∗ /p˜∗ q R 1 1 = δE x,t+1 t+1 t t ; t U∗ /p˜∗ q π 1+τb∗ " x,t t t+1 t+1 h,t+1# U∗ /p˜∗ R∗ 1 1 = δE x,t+1 t+1 t . t U∗ /p˜∗ π∗ 1+τb∗ " x,t t t+1 f,t+1# Assuming that the portfolio rebalancing costs are transferred back to the household in a lumpsum fashion, imposing the stock market equilibrium condition S = S = 1, i ∈ N , and i,t i,t+1 h dividing the budget constraint through by P , equation (20) then implies the following law of t 19Equitydilutioncostsdonotaffecttheresourceconstraintbecausetheexistingshareholders’lossisexactlyoffset bythecorrespondinggainofnewshareholders;bothtypesofshareholdersare,ofcourse,therepresentativehousehold and thus are the same. 20Notethatinequation(24),b andb∗ arenormalizedbythehomecountry’spricelevel. Thisimpliesthat h,t+1 h,t+1 b∗ enters the foreign country’s budget constraint as b∗ /q . In contrast, b and b∗ are normalized by h,t+1 h,t+1 t f,t+1 f,t+1 the foreign country’s price level, and b enters the home country’s budget constraint as q b . f,t+1 t f,t+1 21

motion for the bond holdings in the home country: R R∗ b +q b = t−1 b + t−1q b +w h +d˜ −p˜x , (25) h,t+1 t f,t+1 π h,t π∗ t f,t t t t t t t t where d˜ = D˜ /P ; the corresponding law of motion for the bond holdings in the foreign country is t t t given by 1 R R∗ b∗ +b∗ = t−1 b∗ + t−1b∗ +w∗h∗+d˜∗−p˜∗x∗, (26) q h,t+1 f,t+1 q π h,t π∗ f,t t t t t t t t t t where d˜∗ = D˜∗/P∗. Multiplying equation (26) by q , subtracting the resulting expression from t t t t equation (25), and imposing the bond market clearing conditions given in equation (24) yields R R∗ 1 1 1 b +q b = t−1 b + t−1q b + (w h −q w∗h∗)+ (d˜ −q d˜∗)− (p˜x −q p˜∗x∗). (27) h,t+1 t f,t+1 π h,t π∗ t f,t 2 t t t t t 2 t t t 2 t t t t t t t This condition, together with bond market clearing conditions (24), should hold for the balanceof-payments between the two countries. Note that the current account of home country—denoted by ca —is defined as the change in its international bond holdings: t R R∗ ca = b +q b − t−1 b + t−1q b . t h,t+1 t f,t+1 π h,t π∗ t f,t (cid:18) t t (cid:19) The current account of foreign country is then given by ca∗ = −ca . t t Closing the model requires us to specify a monetary policy rule. In the case of flexible exchange rates, we assume that monetary authorities in the home and foreign countries set prices of government bonds in their respective countries using interest-rate rules of the form: y ψy π ψπ y∗ ψy π∗ ψπ R = R t t and R∗ = R∗ t t , t y π t y∗ π∗ (cid:18) (cid:19) (cid:18) (cid:19) (cid:18) (cid:19) (cid:18) (cid:19) where the reaction coefficients ψ and ψ are assumed to be the same across the two countries. We y π do not assume any policy inertia because such an inertial term is frequently a source of inefficiency in the conduct of monetary policy.21 3.6.2 Monetary Union Inamonetaryunion,allproductsandfinancialassetsaredenominatedinunitsofcommoncurrency. As a result, the nominal exchange rate Q is not defined. In addition, a single monetary authority t sets the interest rate, denoted by RU, and all investors, regardless of their country of origin and t 21The output gap in the monetary policy rule does not correspond to the deviation of actual output from the efficient level of output—that is, the level of output that would prevail in the absence of nominal rigidities and inefficient sources of output fluctuations. However, when inefficient sources of output fluctuations are the primary driverofbusinesscycles,whichisthecaseinourcalibration,ourdefinitionoftheoutputgapworksinthesameway as the output gap implied by flexible prices. 22

currentlocation,earnthesamenominalreturnontheirbondholdings.22 Weassumethatmonetary policy in the union is conducted in a manner that reflects the economic fundamentals of both countries: yU ψy πU ψπ RU = RU t t , t yU πU (cid:18) (cid:19) (cid:18) (cid:19) where the union-wide variables are constructed as weighted averages of country-specific aggregates, with the weights given by the steady-state share of output: y qy∗ y qy∗ yU = y +q y∗ and πU = π +π∗ . t t y+qy∗ t t y+qy∗ t t y+qy∗ t y+qy∗ (cid:18) (cid:19) (cid:18) (cid:19) (cid:18) (cid:19) (cid:18) (cid:19) Because there is no longer any distinction between bonds issued in home or foreign currency, we replace the bond market clearing conditions (see equation (24)) by b +b∗ = 0, (28) t+1 t+1 whereb andb∗ denoteholdingsofinternationalbondsinthesinglecurrencyunitsbyhomeand t+1 t+1 foreign countries, respectively. Now there are two, instead of four, Euler equations characterizing the equilibrium in the international bond market: U /p˜ RU 1 1 = δE x,t+1 t+1 t ; (29) t U /p˜ π 1+τb " x,t t t+1 t+1# U∗ /p˜∗ q RU 1 1 = δE x,t+1 t+1 t t . (30) t U∗ /p˜∗ q π∗ 1+τb∗ " x,t t t+1 t+1 t+1# Note that q /q = (Q /Q )(π /π∗ ) = π /π∗ in a monetary union. Finally, a monet t+1 t t+1 t+1 t+1 t+1 t+1 tary union implies that the combined law of motion for the international bond holdings given in equation (27) can be expressed as RU 1 1 1 b = t−1b + (w h −q w∗h∗)+ (d˜ −q d˜∗)− (p˜x −q p˜∗x∗). (31) t+1 π t 2 t t t t t 2 t t t 2 t t t t t t In this case, the home country’s current account is given by RU ca = b − t−1b . t t+1 t π t 22However, the real returns on international bond holdings will differ in equilibrium, depending on the reference location of investors. This divergence in real returns reflects two factors. First, the two countries have different consumption baskets in the long run, owing to the presence of home bias in consumption. Second, at any point in time,thelawofonepricedoesnotholdinthemonetaryunionbecausetwoconsumersresidingindifferentcountries have accumulated different stocks of habit for an identical product. Because firms price their products to markets— theso-calledpricingtohabitsasinRavn et al.(2007)—inflationratesarenotequalizedacrosscountries,despitethe adoption of a single currency and common monetary policy. 23

4 Calibration There are three sets of parameters in the model: (1) parameters related to preferences and technology; (2) parameters governing the strength of nominal rigidities and the conduct of monetary policy; and (3) parameters determining the degree of financial market distortions, including portfolio rebalancing costs. In setting their values, our calibration strategy closely follows GSSZ, while expanding the set of parameters to the international environment. Because the model is quarterly, we set the time discount factor equal to 0.996. The CRRA parameter in the household’s utility function is set equal to two. As we explain below, we specify the same degree of persistence (0.90) for all exogenous shock processes (i.e., aggregate demand shocks, aggregate technology shocks, and financial shocks). We then adjust the volatilities of shocks to match the variance-decomposition shares of output fluctuations. We set the deep habit parameter θ to −0.86, a value similar to that used by Ravn et al. (2006). The key tension between the maximization of a long-run market share and the maximization of current profits does not exist when θ = 0. In such an environment, the financial shock we consider has considerably smaller effect on economic outcomes. It is in this sense that our model owes a lot tocustomer-marketconsiderationsascapturedbydeephabits. Consequently, wefollowRavn et al. (2006) and choose a fairly persistent habit-formation process, so that only 15 percent of the habit stockdepreciatesinagivenquarter(ρ = 0.85), achoicethat highlights firms’incentivestocompete for market share. The elasticity of substitution η is a key parameter in the customer-markets model because the greater the firm’s market power, the greater the incentive to invest in customer base. We set η equal to two, a value consistent with Broda and Weinstein (2006), who provide a range of estimates of η for the U.S. economy; their estimates lie between 2.1 and 4.8, depending on the characteristics of products (commodities vs. differentiated goods) and sub-samples (before 1990 vs. after1990). Ourchoiceofη = 2correspondscloselytothemedianvalueoftheestimatedelasticities for differentiated goods for the post-1990 period, a class of products that is most relevant for the deep habits framework; this choice is also broadly consistent with Ravn et al. (2010), who estimate η equal to 2.48 within a context of the deep habits model. RegardingΞ andΞ (andΞ∗ andΞ∗),theweightsofhomeandforeigngoodsinthehousehold’s h f f h utility function, we choose their values so that the share of imported goods in the steady-state consumption basket is equal to 0.4 in both countries, a value in the middle of the range of the import-to-GDP ratios for the euro area countries since 2000.23 As for the Armington elasticity, we set ε equal to 1.5, in order to stay close to the near-unit elasticity estimated by Feenstra et al. (2014).24 23Note that Ξ itself is not equal to the share of imported goods in the GDP of the home country; rather Ξ is f f chosen such that Ξε =p c / p c =0.4. f f f k=h,f k k 24As long as ε > 1, a valuePlower than 1.5 does not affect our main results. For example, setting ε close to one reducestheimpactofafinancialshockonaggregateoutputinamonetaryuniontotwo-thirdsofthatimpliedbyour baseline calibration. This is because the lower elasticity of cross-border substitution implies a less intense price war between firms of the two countries. However, even in this extreme case, the qualitative features of the equilibrium 24

The fixed operating costs φ and φ∗ are another two key parameters in our model. In our baseline calibration, we assume φ = φ∗, which implies that differences in the degree of financial distortions are the sole source of heterogeneity between the two countries. We calibrate φ in conjunction with the returns-to-scale parameter α. Specifically, we set α first and then choose φ so that the dividend-payout ratio (relative to operating income) hits 2.5 percent, the mean of this ratio in the U.S. since 1945, which is close to the average dividends-and-buyback ratio of three percentfortheEuropeanOECDcountriesduringthe2002–2015period. Followingtheinternational macroeconomics literature, we set α = 1; in turn, this implies that φ = 0.1. With α = 1, φ = 0.1, and η = 2, the average short-run gross markup in our model comes out at 1.19, while the long-run gross markup is equal to 1.07. In calibrating the degree of financial distortions faced by domestic firms, we set the equity dilution cost parameter ϕ equal to 0.2, a value that is in the middle of the range typically used in the corporate finance literature. The degree of financial frictions faced by foreign firms ϕ∗ is then calibrated to be one-tenth of ϕ (i.e., ϕ∗ = 0.1ϕ), implying a considerably more accommodative financial conditions for foreign country firms in the steady state. The volatility of the idiosyncratic cost shock σ is set to 0.2 at a quarterly frequency. With ϕ = 0.2 and φ = 0.1, this level of idiosyncratic volatility implies that the expected shadow value of internal funds equals 1.16 for home country firms in the steady state. For the parameters related to nominal rigidities, we set γ , the quadratic adjustment costs of p nominal prices, equal to 10 in both countries. In presenting the model, we treated nominal wages as completely flexible. However, given the importance of (downward) nominal wage rigidities in periphery economies during the eurozone crisis (see Schmitt-Groh´e and Uribe, 2013, 2016), we introduce(symmetric)nominalwagerigiditiesintheactualsimulationsalongthelinesofBordo et al. (2000) and Erceg et al. (2000). Specifically, we assume market power for households that supply labor to production firms and a quadratic cost of adjusting nominal wages. In this case, assuming a 1/ζ separable, constant elasticity of labor supply U = −h , the efficiency condition for labor hours h,t t becomes 1/ζ h /U η t x,t = η −1+γ (π −π )π w w w w,t w w,t w /p˜ t t U /p˜ π h −δE x,t+1 t+1 γ (π −π )π w,t+1 t+1 , t w w,t+1 w w,t+1 U /p˜ π h (cid:20) x,t t t+1 t (cid:21) where π = W /W , γ is the coefficient of nominal wage adjustment costs, and ζ is the labor w,t t t−1 w supply elasticity, which we set equal to five. In symmetry with our assumptions regarding nominal price rigidities, we set η = 2 and γ = 30 in both countries.25 Finally, we assume that monetary w w remain the same. 25Our choice for the degrees of price and wage stickiness are comparable to the point estimates of γ = 14.5 and p γ =41obtainedbyRavn et al.(2010),whoshowthatdeephabitssubstantiallyenhancethepersistenceofinflation w without the need to impose an implausibly large degree nominal price stickiness. The addition of nominal wage rigiditiesdoesnotmateriallymodifyanyofourmainresults. Itdoes,however,leadtoanotablygreatervolatilityof the real exchange rate because the countercyclical markups in the country where firms face acute financial distress 25

policy is conducted using an interest-rate rule proposed by Taylor (1999). (Table B-1 in Section B of the Appendix conveniently summarizes our baseline calibration.) 5 Model Simulations Inthissection, weusethemodeltoanalyzequantitativelythemacroeconomicimplicationsofhome and foreign countries forming a monetary union—that is, adopting a common currency and hence common monetary policy—in an environment of asymmetric financial shocks. 5.1 Currency Regimes and the Impact of Asymmetric Financial Shocks To analyze the effects of financial instability under various currency regimes, we posit an external financial shock, which temporarily raises the cost of outside equity capital for firms in the two countries. Specifically, the cost of issuing new shares is assumed to be subject to a “cost-of-capital” shock of the form: ϕ = ϕf ; where lnf = ρ lnf +ǫ , with ǫ ∼ N(−0.5σ2,σ2); t t t f t−1 f,t f,t f f ϕ∗ = ϕ∗f∗; where lnf∗ = ρ lnf∗ +ǫ∗ ,with ǫ∗ ∼ N(−0.5σ2,σ2). t t t f t−1 f,t f,t f f We calibrate the size of the shock ǫ such that ϕ jumps to 1.5ϕ upon impact and then returns to f,t t itsnormallevelofϕ = 0.2, accordingtotheautoregressivedynamicsspecifiedabove.26 Becauseour baseline calibration assumes that ϕ∗ = 0.1ϕ, the above formulation results in asymmetric financial conditions between the two countries, with home country firms facing a significantly higher cost of external finance. To further underscore the effects of differences in financial conditions faced by domestic and foreign firms, we keep the cost of external equity capital in the foreign country at ϕ∗ = 0.1ϕ, for all t. t In this experiment, the financial shock increases the expected shadow value of internal funds for firms in the home country from 1.16 to 1.32 upon impact. Figure 3 displays the macroeconomic effects of such an asymmetric financial shock when the two countries share a common currency. As shown in panel (f), home country firms raise prices significantly in response to an adverse financial shock. Foreign inflation also increases somewhat because of the increase in import prices. At the same time, the burst of inflation in the home country is accompanied by an economic slump: Production declines notably in the immediate aftermath of the shock (panel (a)), as does consumption (panel (b)) and hours worked (panel (c)). Because the nominal exchange rate is unable to respond to the shock, the differential behavior of inflation in the two countries implies a notable appreciation of the real exchange rate (panel (e)). As a result, exports from the home country drop (panel (g)), and the home country registers a notable trade deficit in the near term aredrivenmorebyanincreaseinproductpricesasopposedtoanimmediatedeclineinnominalwages,whichwould have occurred in an environment with flexible wages. In the latter case, the more stable final product prices result in a less volatile real exchange rate, which runs counter to intuition, in addition to being at odds with the data. 26As noted in Section 4, the persistence of all exogenous shock processes is set to 0.9; thus, we set ρ =0.9. f 26

Figure 3: Asymmetric Financial Shock in Monetary Union (a) Production (b) Consumption (c) Hours worked (d) Interest rate pct. pct. pct. pps. 2 0.8 2 2.0 Home Foreign 1.5 1 0.4 1 1.0 0 0.0 0 0.5 -1 -0.4 -1 0.0 -2 -0.8 -2 -0.5 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 ( e ) Exchange rate ( f ) Inflation ( g ) Exports ( h ) Net exports pct. pps. pct. pct. of GDP 6 1.6 1.6 1.2 1.2 0.8 Real 4 0.8 Nominal 0.4 0.8 2 0.0 0.0 0.4 -0.4 0 0.0 -0.8 -0.8 -0.4 -2 -1.6 -1.2 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 Note: The panels of the figure depict the model-implied responses of selected variables to an adverse financial shock in the home country in period 0. Unless noted otherwise, the solid lines show responses of variables in the home country, while the dashed lines show those of the foreign country. Exchange rates are expressed as home currency relative to foreign currency. (panel (h)). Strikingly, the downturn in the home country is accompanied by a robust boom in the foreign country: Production, consumption, hours worked, and exports all increase significantly, and the foreign country’s trade balance improves significantly. As shown in Figure 4, the pattern of international macroeconomic adjustment in response to such a shock looks dramatically different when the two countries have their own currencies and are able to pursue independent monetary policies responding to their respective domestic economic developments. As in the monetary union case, home country firms again raise prices in response to an adverse financial shock (panel (f)), and foreign inflation rises slightly, reflecting the passthrough of higher import prices. With flexible exchange rates, however, the nominal exchange rate strongly depreciates (panel (e)). In fact, the depreciation is so large that the real exchange rate also depreciates, despite the inflation differential moving in the “wrong” direction. As in the data, therefore, the short-run dynamics of the real exchange rate are dominated by fluctuations in the nominal exchange rate, rather than by changes in the relative price levels.27 27Thenominalexchangerateshowninpanel(e)appearstoreturntoitssteady-statevalueinthelongrun. However, thisissimplyacoincidencebecauseourNewKeynesianframeworkdoesnothaveapredictionforthelevelofnominal exchange rate, just as it does not have one for the price level. In all simulations, we assume that the initial value of 27

Figure 4: Asymmetric Financial Shock with Flexible Exchange Rates (a) Production (b) Consumption (c) Hours worked (d) Interest rate pct. pct. pct. pps. 2 0.8 2 2.0 Home Foreign 1.5 1 0.4 1 1.0 0 0.0 0 0.5 -1 -0.4 -1 0.0 -2 -0.8 -2 -0.5 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 ( e ) Exchange rate ( f ) Inflation ( g ) Exports ( h ) Net exports pct. pps. pct. pct. of GDP 6 1.6 1.6 1.2 Real Nominal 1.2 0.8 4 0.8 0.4 0.8 2 0.0 0.0 0.4 -0.4 0 0.0 -0.8 -0.8 -0.4 -2 -1.6 -1.2 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 Note: The panels of the figure depict the model-implied responses of selected variables to an adverse financial shock in the home country in period 0. Unless noted otherwise, the solid lines show responses of variables in the home country, while the dashed lines show those of the foreign country. Exchange rates are expressed as home currency relative to foreign currency. As shown in panel (g), the depreciation of the real exchange rate significantly boosts the home country’s exports. However, because firms in the home country respond to the shock by raising prices and are facing downward-sloping demand curves, domestic production declines in response to the financial shock (panel (a)). Consequently, hours worked in the home country also decline (panel(c)). Inthehomecountry,therefore,thefinancialshockhasrealconsequencesintermsofthe foregoneoutputandemployment,thoughtheeffectsarerelativelysmall,giventheassumedseverity and persistence of financial distress. The economic forces responsible for this stark difference in the internationalmacroeconomicdynamicsacrossthetwocurrencyregimescanbefoundinpanels(d)– (f) of Figure 3. First, note that the behavior of inflation in the two countries when they are in a monetary union (panel (f) of Figure 3) is quite similar to that under a flexible exchange rate regime (panel (f) of Figure 4). This result reflects the fact that regardless of the currency arrangement, firms in the home country, when confronted with a tightening of financial conditions, have a strong incentive to raise prices compared with their foreign counterparts. the nominal exchange rate is equal to one, an arbitrary but innocuous assumption, as only changes in the nominal exchange rate are a well-defined concept in our model. 28

What differs between the two currency frameworks is, of course, the behavior of the real exchangerate. Theinternationalbond-holdingconditions(21)and(22)imply,toafirst-orderapproximation, the following no-arbitrage condition: R /π −(q /q )(R∗/π∗ ) = 0. Taking logs and t t+1 t+1 t t t+1 solvingthisequationforward, thecurrentrealexchangerate, q , reflectstherealinterestratediffert entialonlong-termbondsofthetwocountries—thatis, ∞ ln(R∗ /π∗ )−ln(R /π ) . s=0 t+s t+s+1 t+s t+s+1 In a monetary policy regime that only targets inflation, those interest rate differentials are deter- P (cid:2) (cid:3) minedsolelybythedifferencesininflationtrajectoriesbetweenthetwocountries. UndertheTaylor principle, real interest rates in the home country will thus be higher than in the foreign country, causing the real exchange rate to appreciate. Allowing monetary policy to respond also to the output gap reverses this real interest rate differential and causes the exchange rate to depreciate. With the two countries sharing a common currency, such an adjustment is, of course, not possible. The real exchange rate reflects the terms of trade, and as a result, differences in inflation ratestranslatedirectlyintomovementsintherealexchangerate. Becausefirmsinthehomecountry optimally choose higher markups and relative prices in response to the tightening of financial conditions, the real exchange rate appreciates substantially, and production and exports by home country firms drop sharply. In comparison, the decline in consumption is noticeably less severe because international borrowing—while subject to costly portfolio rebalancing—allows consumers in the home country to smooth the effects of the financial shock to a certain extent. The foreign economic boom is simply a mirror image of the home country’s economic plight and is reminiscent of the dichotomy in economic outcomes between the eurozone core and periphery during the recent financial crisis. As shown in panels (a) and (d) of Figure 5, the financial shock in the home country induces a significant dispersion in relative prices in both countries, regardless of the currency regime. The increase in the cost of external finance causes home country firms to raise relative prices in both their domestic and export markets. Foreign country firms, in contrast, optimally follow the opposite strategy and lower relative prices in both markets in order to steal market share from their financially constrained home country counterparts (panels (b) and (e)). This “predatory” price war is noticeably more intense when the two countries share a common currency, as home country firms are unable to rely on the depreciation of their currency to improve their internal liquidity positions. And lastly, financial distress leads to a strongly countercyclical markup in the home country, irrespective of the currency regime (panel (f)). The model-implied dynamics of markups in the home country in response to a financial shock are thus consistent with the behavior of the price markups in the eurozone periphery during the recent financial crisis and its aftermath shown in Figure 2.28 28Asshowninpanels(b)and(e)ofFigure5,animportantpredictionofthemodelconcernstherelativebehaviorof marketsharesduringthefinancialcrisis. InSectionCoftheAppendix,weshowthatthesemodel-implieddynamics are consistent with the available data. 29

Figure 5: Asymmetric Financial Shock, Relative Prices, and Markups (a) Relative prices (b) Market share (c) Wage inflation Home country Home country pct. pps. pps. 1.2 0.4 1.0 0.9 0.5 0.6 0.2 0.0 0.3 -0.5 0.0 0.0 Home - union Foreign - union -0.3 H Fo o r m ei e g n - f - l e fl x e ib xi l b e le -1.0 -0.2 -0.6 -1.5 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 ( d ) Relative prices ( e ) Market share ( f ) Markup Foreign country Foreign country pct. pps. pps. 1.0 0.4 3 0.5 2 0.0 0.0 1 -0.4 -0.5 0 -1.0 -0.8 -1 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 Note: The panels of the figure depict the model-implied responses of selected variables to an adverse financial shock in the home country in period 0. The solid lines show responses when the two countries are in a monetary union, while the dashed lines show responses under flexible exchange rates. 5.2 The Boom-Bust Cycle AnaspectofthemacroeconomicdynamicsshowninFigure3thatappearsatoddswiththecrisisin the euro area periphery is the fact that following the financial shock, imports to the home country (that is, exports from the foreign country) increase notably, which would cause the current account deficit of the home country to increase. After about eight quarters, this pattern is reversed, and the home country begins to register an improvement in its external position. The current account deficits in the periphery countries, however, started to improve immediately with the onset of the crisis in 2009, owing primarily to a sharp decline in imports. This discrepancy in the timing of external adjustment patterns should not be taken as evidence that the model-implied crisis dynamics are inconsistent with the data. The impulse responses are expressed as deviations from the steady state—that is, our simulations assume that the two economies are at their respective steady states prior to the home country being hit by a shock, a situation that is unlikely to have characterized the euro area on the eve of the crisis. In fact, with our model, it is straightforward to generate external adjustment patterns in the home country that closely resemble those experienced by the eurozone periphery in the period surrounding the sovereign debt crisis. 30

Figure 6: Boom-Bust Cycle in the Home Country (a) Imports (b) Exports (d) Real exchange rate pct. of GDP pct. of GDP pct. 2 0.5 2.5 Financial shock Financial shock Financial shock 2.0 0.0 1 1.5 -0.5 0 1.0 -1.0 0.5 -1 0.0 -1.5 -0.5 -2 -2.0 -1.0 -3 -2.5 -1.5 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 Note: The solid lines depict the model-implied responses of selected variables in the home country, when the countryexperiencesasequenceofpositivedemandshocksinperiods0,...,11andinperiod12ishitbyafinancial shock. The real exchange rate is expressed as home currency relative to foreign currency. As noted at the outset, periphery countries borrowed heavily in the years preceding the crisis, primarily to finance domestic consumption and housing investment. Consequently, real exchange rates in the eurozone periphery appreciated significantly, eroding these countries’ competitiveness. Thesedevelopmentsalsoproducedlargetradedeficitsamongperipherycountries,whichintheyears leading to the crisis were easily financed by foreign capital inflows, facilitated by the convergence in domestic interest rates across the euro area. To capture the buoyant economic sentiment that prevailedintheeurozoneperipherypriortothecrisis,weconsideranexperiment,wherebythehome country first experiences a sequence of gradually increasing positive demand shocks ω —the pret crisis economic boom—which is then followed by an asymmetric financial shock. In implementing thisscenario, weassumeasequenceofdemandshocksinperiods0,1,...,11, suchthatω gradually t increases to five percent of its steady-state value; in period 12, we hit the home country with a large and persistent financial shock, which increases the equity dilution costs ϕ from 0.2 to 0.35 t upon impact. As shown in Figure 6, this sequence of events generates external adjustment patterns in the home country that correspond closely to those experienced in the eurozone periphery in the period surrounding the crisis. In the years immediately preceding the financial shock, imports-to-GDP increase notably (panel (a)), while exports-to-GDP fall (panel (b)), trade dynamics that are consistent with the erosion in the home country’s competitiveness as evidenced by the appreciation of therealexchangerateduringthisperiod(panel(c)). Whenthehomecountryishitbythefinancial shock, these patterns are abruptly reversed: With imports falling and exports rising, the current account deficit will begin to shrink immediately. Thus with an economically plausible sequence of shocks, the model is to able replicate the kind of current account reversal dynamics experienced by the eurozone periphery during the crisis. 31

Figure 7: Financial Heterogeneity and Monetary Union (a) Real GDP (b) Consumption (c) Inflation (d) Markup Home country Home country Home country Home country pct. pct. pps. pps. 0.5 0.3 2.5 1.6 2.0 1.2 0.0 0.0 1.5 0.8 1.0 0.4 Baseline -0.5 -0.3 Symmetric 0.5 0.0 0.0 -1.0 -0.6 -0.4 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 ( e ) Real GDP ( f ) Consumption ( g ) Inflation ( h ) Markup Foreign country Foreign country Foreign country Foreign country pct. pct. pps. pps. 1.6 0.8 2.5 1.6 Baseline 1.2 2.0 Symmetric 0.4 1.2 0.8 1.5 0.8 0.4 0.0 1.0 0.4 0.0 -0.4 0.5 -0.4 0.0 0.0 -0.8 -0.8 -0.4 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 Note: Thesolidlinesdepictthemodel-impliedresponsesofselectedvariablestoanadversefinancialshockinthe home country in period 0 under the baseline calibration of the model. The dashed lines depict the corresponding responsesunderthealternativecalibration ofhomogeneousfinancialcapacityandwhenbothcountriesarehitby an adverse financial shock in period 0. 5.3 “Kill My Neighbor’s Cow Too” An old Slovenian joke tells of two neighboring peasants who each own a cow. One day, out of the blue, a lighting strikes and kills one of the cows. The poor peasant whose cow—his most prized possession—has been killed cries to God in anguish, begging for justice. When God replies and asks him what he wants Him to do, the peasant replies, “kill my neighbor’s cow too.” Inourmodel,thepoorpeasant’ssituationresemblesthatofcash-strappedfirmsintheperiphery, who in the midst of a financial crisis are fending off competitors from the core that are trying to increase their market shares by engaging in predatory pricing behavior. Asking to “kill the neighbor’s cow too” is akin to asking how would the periphery fare in a situation where the core has equally distorted financial markets and its firms are subjected to the same degree of financial distress, compared with the asymmetric set-up, whereby only the periphery’s financial markets are distorted and only the periphery is hit by a financial shock. To shed light on this question, we consider an experiment in which firms in both countries face the same degree of financial frictions in the steady state (ϕ = ϕ∗ = 0.2) and both economies are perturbed by a financial shock of the type described above (ǫ = ǫ∗ > 0). The dashed lines t t 32

in Figure 7 show the impulse responses of selected variables under this alternative “symmetric” calibration, while the solid lines show the corresponding responses under our baseline calibration and when only the home country is hit by a financial shock (see Figure 3). The comparison of these two experiments clearly indicates that the home country would prefer the alternative economic environment, as evidenced by a much smaller impact on domestic output and consumption (panels (a) and (b)). As shown in panel (h), foreign firms—in response to the deterioration in their own financial conditions—raise markups significantly to maintain current cashflows. In other words, the symmetric financial distress does not allow foreign firms to engage in predatory pricing behavior. As a result, foreign inflation dynamics mirror those in the home country(panels(c)and(g)), andthereisnomovementintherealexchangerate. Hence,theforeign country undergoes the same contraction in economic activity as the home country (panels (a) and (e)), a result that stands in stark contrast to the baseline monetary union case, in which the foreign country experiences an export-driven boom, while the home country falls into a recession. 6 Welfare Analysis and Policy Implications Simulations in Section 5 show that when financial markets of countries in a monetary union are subject to a differing degree of financial distortions, the financially weaker members of the union undergo a much more severe recession when hit by an external shock, compared with a flexible exchange rate regime. In this section, we examine formally the welfare implications of forming a monetary union among countries with different financial capacities. To highlight the welfare effects of such a political choice, we adopt a calibration strategy, which assumes that the home and foreign countries are subject to only two types of aggregate shocks: technology shocks (ǫ and ǫ∗ ) and A,t A,t financial shocks (ǫ and ǫ∗ ). We set the standard deviation of aggregate technology shocks to f,t f,t one percent and then calibrate the standard deviation of financial shocks so that they account for 10 times as much of the variance of real GDP of the home country as technology shocks (see Jermann and Quadrini, 2012).29 6.1 Welfare Consequences of Joining a Monetary Union To compare welfare across the different currency regimes in such an environment, we approximate the value functions of the representative households in the two countries up to a second order and report their analytic first moments under our baseline calibration in the top panel of Table 4 (see Schmitt-Groh´e and Uribe, 2004). In addition, we calculate the certainty-equivalent changes in consumption (CE), which are required to make the welfare levels of the households in two countries in the monetary union equal to those under the flexible exchange rate regime. As evidenced by these entries, joining a monetary union results in a significant welfare loss for the home country: 29Consistent with our calibration strategy, we set ρA =ρ f =0.9. With financial shocks playing such an outsized role in economic fluctuations, this calibration clearly does not provide the most realistic representation of the two economies. However, our main conclusions are qualitatively the same under alternative calibrations, whereby the business cycles are driven primarily by aggregate technology shocks. 33

Table 4: Welfare Analysis Welfare Comparison Monetary Union Flexible FX CE (pct.) Home country −259.23 −254.16 2.53 Foreign country −254.05 −254.26 −0.11 Memo: Both countries −513.28 −508.42 . Moments Comparison µ(cU)/µ(cF) σ(cU)/σ(cF) σ(hU)/σ(hF) Home country 0.99 1.55 2.92 Foreign country 1.01 1.51 4.31 Note: In the top panel, CE denotes the certainty-equivalent change in the average consumption per period (holdinghoursworkedconstant)thatisrequiredtomaketherepresentativehouseholdinthespecifiedcountry no worse off when the two countries choose to abandon flexible exchange rates and independent monetary policiesandformamonetaryunion. Inthebottompanel,µ(c)=averageconsumptionlevel;σ(c)=volatility of consumption; and σ(h) = volatility of hours worked. Currency arrangement: U = monetary union; and F = flexible exchange rates. Therepresentativehouseholdinthehomecountryshouldbegivenanincreaseof2.5percentoftheir steady-state consumption level per quarter in order to be as well off in the union as they were with flexible exchange rates. In contrast, the representative household in the foreign country is notably better off in the monetary union, given that typical estimates of the welfare cost of business cycles are on the order of 0.2 percent, according to the CE metric. The bottom panel compares the selected moments of consumption and hours worked across the two currency frameworks. Abandoning its own currency and independent monetary policy to join the union results in a lower average level of consumption for the representative household in the home country and a correspondingly higher average consumption for the representative household in the foreign country. This result is due to the fact that in the monetary union home country firms lose market share to their foreign competitors in the long run. Interestingly, the volatilities of consumption and hours worked in both countries are appreciably higher when the two countries share a common currency. The result that the welfare of the foreign country is higher in the monetary union than with flexible exchange rates runs counter to the conventional view in the international macroeconomics literature. This view, however, does not take into account the role that heterogeneity in financial capacitiesofcountriescomprisingtheunionplaysinincentivizingfirmstocompeteformarketshare by engaging in predatory pricing behavior. When a country with distorted and inefficient financial markets forms a monetary union with a country with a relatively frictionless financial system, the formerishighlyvulnerabletothebeggar-thy-neighborpricingpoliciesoffirmsinthelattercountry, especiallyinperiodsoffinancialdistress. Thisisthemainreasonwhyindependentmonetarypolicy is such a valuable macroeconomic stabilization tool for the financially weak country and why the welfare of the home country is lower in the monetary union than with flexible exchange rates.30 30The welfare calculations reported in Table 4 are not predicated on optimal monetary policy. It is unlikely, however, that the welfare ordering would be reversed under optimal monetary policy because the Ramsey planner maximizing the joint welfare with two instruments—two short-term interest rates—can never do worse than the 34

In Section D of the Appendix, we show that the welfare results in Table 4 are robust across the differentcombinationsofparametersgoverningthestrengthandpersistenceofthecustomer-market relationships. Specifically, for nearly all configurations of the parameters θ and ρ, the welfare of the home country improves with the exit from the monetary union, whereas the welfare of the foreign country is greater in the monetary union.31 Thus, the welfare implications of a monetary union under our baseline calibration shown in Table 4 are not a knife-edged result, as they are robust for most of the combinations of the parameters θ and ρ. 6.2 Fiscal Devaluations Given the union’s problem with a one-size-fits-all monetary policy, we now examine the welfare implications of a frequently advocated policy option in the context of the European sovereign debt crisis: a revenue-neutral fiscal devaluation by the periphery countries.32 Adao et al. (2009) and Farhi et al. (2014) have shown that various combinations of fiscal measures can replicate the effects of a nominal exchange rate depreciation in a fixed exchange rate system. Such fiscal measures can, for example, include a combination of import tariffs and export subsidies or a shift from labor to consumption taxes.33 As discussed above, the welfare of the foreign country is lower in a flexible exchange rate regime across most of the (θ,ρ) parameter space. Hence, the home country cannot carry out a unilateral fiscal devaluation without the fear of retaliation if such a policy recovers the allocation implied by flexible exchange rates. Relatedly, fiscal policies that result in large budget deficits are unlikely to be adopted in situations where financial distress is intertwined with sovereign default risk, as was the case for periphery countries during the eurozone crisis. Accordingly, we study the extent to which a revenue-neutral fiscal devaluation by the home country can improve welfare at home and does not leave the representative foreign household in the monetary union any worse off. To provide insight into this question, we consider a scenario in which the home country introduces a payroll subsidy (ςP) that is financed by a VAT (τV).34 This combination of fiscal t t Ramsey planner with only one instrument, namely a union-wide short-term interest rate. 31The one exception is a small region of the parameter space characterized by a very strong and persistent deephabit mechanism (θ < −0.9 and ρ > 0.9). In this region of the parameter space, the monetary union results in a welfare loss even for the foreign country due to the heightened volatility of consumption and hours worked. 32It is worth emphasizing that the lower joint welfare in the monetary union reported in Table 4 has nothing to dowiththepossibleinefficiencyofthepositedTaylor(1999)interest-raterule. AsshowninFigureD-1inSectionD of the Appendix, the macroeconomic dynamics in the two countries in response to an asymmetric financial shock in the home country under the Ramsey monetary policy are virtually the same as those under the Taylor (1999) rule, indicating that even the Ramsey planner is unable to overcome the limitations of a one-size-fits-all monetary policy. 33Farhi et al.(2014)provideanin-depthanalysisofvariousfiscalpolicymixesthatcanundervariousassetmarket conditionsreplicatetheeffectsofanominalexchangeratedepreciation. Inprinciple,acompleterisk-sharingarrangement that could improvethe union’s overall welfarecould be achieved byforming a fiscal union, a point emphasized byFarhi and Werning(2017). However,theresultsreportedinTableE-1inSectionEoftheAppendixindicatethat inourenvironment,theformationofsuchaunioninvolveslargestate-contingenttransfersofwealthfromtheforeign country to the home country. In combination with the euro area’s institutional setup, this result underscores the elusive goal of further European integration, as such transfers are unlikely to enjoy broad public support. 34We stress the qualitative nature of this exercise because the effectiveness of a fiscal devaluation depends on a varietyofcountry-specificfactors: thedegreeofprice/wagerigidities,thedegreeofpricepass-through,theelasticity of labor supply, the size of the economy, its trade openness, and the share of labor as variable production input. 35

measures—a reduction in employers’ social security contributions, coupled with an increase in the VAT rate imposed in a revenue-neutral manner—received considerable attention in policy circles during the crisis (see Puglisi, 2014). Under these policies, the marginal revenue of a home country firm selling its product in the domestic market becomes (1−τV)p , while its marginal labor cost t h,t is equal to (1−ςP)w . We assume that the home country firms are not subject to the same VAT t t in the foreign country and that the foreign country does not retaliate in response to the unilateral adoption of these fiscal measures by the home country. In addition, we assume that the home government implements these measures to stabilize the economy using the following Taylor-type fiscal rule: ∆ y τV = t , with ∆ = −αFDln t , t 1+∆ t y t (cid:18) (cid:19) and where αFD > 0 is the fiscal reaction coefficient. To pin down the level of the payroll subsidy ςP, we impose the following revenue-neutrality t constraint: ςPw h = τV(p c +p c ), t t t t h,t h,t f,t f,t where the left side represents the home government’s payroll subsidy expenditures, and the right side is the revenue generated by the VAT. When the home country enters a recession, ∆ > 0, t which makes the export sales of foreign country firms and the domestic sales of the home country firms subject to a VAT rate of τV > 0. At the same time, the revenue-neutrality constraint implies t a payroll subsidy ςP > 0, which lowers the marginal labor cost for home country firms to a fraction t 1−ςP of the level that prevailed before the implementation of these measures. t To understand how this fiscal devaluation affects the pricing behavior of firms, it is useful to consider how such a policy modifies the equity issuance threshold aE, given in equation (13); recall t that the higher this threshold, the lower is the likelihood that home country firms will have to issue new equity, With the fiscal devaluation, the threshold becomes aE = A t p h,t 1−τ t V c h,t +q t p∗ h,t c∗ h,t . t 1−ς t P w t  (cid:0) φ+c h (cid:1) ,t +c∗ h,t α 1  (cid:0) (cid:1)   (cid:0) (cid:1) An increase in the payroll subsidy ςP improves the internal liquidity positions of home country t firms, while raising the VAT rate τV worsens their liquidity positions. However, because the VAT t is applied only to the domestic sales, whereas the payroll subsidy affects the entire wage bill, the improvement in the firms’ financial conditions resulting from the payroll subsidy outweighs the negative impact of the VAT. As a result, home country firms do not have to raise relative prices as much as they are forced to do so in the baseline monetary union case without a fiscal devaluation.35 Notethesimilaritybetweenthefiscaldevaluationandtheactualexchangeratedevaluationwithno fiscaladjustment. Inthelattercase, thedevaluation—ahigherrealexchangerateq —alsoimproves t the firms’ internal liquidity positions. 35If this mix of fiscal policies is not constrained by revenue neutrality and the home country can run a temporary 36

Figure 8: Asymmetric Financial Shock, Relative Prices, Markups, and Fiscal Devaluation (a) Relative prices (b) Market share (c) Wage inflation Home country Home country pct. pps. pps. 1.2 0.4 1.0 0.9 0.5 0.6 0.2 0.0 0.3 -0.5 0.0 0.0 Home - baseline union Foreign - baseline union -0.3 H Fo o r m ei e g n - u - n u i n o i n o n w / w F / D FD -1.0 -0.2 -0.6 -1.5 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 ( d ) Relative prices ( e ) Market share ( f ) Markup Foreign country Foreign country pct. pps. pps. 1.0 0.4 3 0.5 2 0.0 0.0 1 -0.4 -0.5 0 -1.0 -0.8 -1 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 Note: The panels of the figure depict the model-implied responses of selected variables to an adverse financial shockinthehomecountryinperiod0, whenthetwocountriesareinamonetaryunion. Thesolidlinesshowthe responsesfromthebaselinemonetaryunioncase(seeFigure5). Thedashedlinesshowthecorrespondingresponses when the home country pursues a unilateral fiscal devaluation, with the fiscal reaction coefficient αFD =3. ThesepricedynamicsareshowninFigure8, inwhichwereproducetheeffectsofanasymmetric financial shock in the home country shown in Figure 5, but we set the fiscal reaction coefficient αFD = 3, thus allowing the home country to engage in a unilateral fiscal devaluation.36 As shown by the solid lines in panels (a) and (d), home country firms, in response to the pricing behavior of foreignfirms, raiserelativepricestomaintaincashflows, thussacrificingtheirmarketshareathome and abroad (panels (b) and (e)). To the extent that the fiscal devaluation improves the financial conditionofhomecountryfirms, such“defensive”pricehikesshouldbelesspronouncedinboththe domestic and foreign markets. As shown by the corresponding dashed lines that is indeed the case, and as a result, the loss in the corresponding market shares is noticeably less severe. Furthermore, foreign firms do not lower relative prices as much as in the baseline case because such actions would reduce their after-tax revenue too much. These differences in price dynamics are also reflected in the differential behavior of markups, as home country firms set lower markups, while their foreign budget deficit, such a unilateral fiscal devaluation can provide even greater liquidity support to home country firms. 36We set αFD = 3 for illustrative purposes only. As we show below, this coefficient value lies between the values that maximize the welfare of the two countries. 37

Figure 9: Asymmetric Financial Shock, Monetary Union, and Fiscal Devaluation (a) Production (b) Hours worked (c) Consumption (d) Cons. of h-type goods Home country Home country Home country Home country pct. pct. pct. pct. 1.0 0.9 0.5 0.5 0.5 0.6 0.0 0.0 0.0 0.3 -0.5 -0.5 -0.5 0.0 -1.0 -1.0 -1.0 -0.3 -1.5 -1.5 Baseline union -1.5 Union w/ FD -2.0 -0.6 -2.0 -2.0 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 ( e ) Production ( f ) Hours worked ( g ) Consumption ( h ) Cons. of f-type goods Foreign country Foreign country Foreign country Home country pct. pct. pct. pct. 2.0 2.0 1.0 2.5 2.0 1.5 1.5 Baseline union 1.5 Union w/ FD 1.0 1.0 0.5 1.0 0.5 0.5 0.5 0.0 0.0 0.0 0.0 -0.5 -0.5 -0.5 -1.0 -1.0 -1.0 -0.5 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 (i) Fiscal position w/ FD (j) Net exports (k) Real exchange rate (l) Current account Home country Home country Home country pct. of GDP pct. of GDP pct. pct. of GDP 2.0 0.5 0.5 0.2 1.5 1.0 0.0 0.1 0.0 0.5 0.0 0.0 -0.5 -0.5 Baseline union Revenues -0.5 Union w/ FD -0.1 Expenditures -1.0 -1.0 -1.5 -0.2 -2.0 -1.0 -1.5 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 Note: The panels of the figure depict the model-implied responses of selected variables to an adverse financial shockinthehomecountryinperiod0, whenthetwocountriesareinamonetaryunion. Thesolidlinesshowthe responsesfromthebaselinemonetaryunioncase(seeFigure3). Thedashedlinesshowthecorrespondingresponses when the home country pursues a unilateral fiscal devaluation, with the fiscal reaction coefficient αFD = 3. The real exchange rate is expressed as home currency relative to foreign currency. counterparts choose higher markups than in the baseline case (panel (f)).37 Figure 9 shows how such a unilateral fiscal devaluation leads to greater macroeconomic stabil- 37Thefactthathomecountryfirmschooselowermarkupsdoesnotimplythattheyalsosetlowerpricesinabsolute terms. TheimpositionoftheVATimpliesthatapartofthetaxispaidbytherepresentativehomecountryhousehold. Thismeansthattheactualpricelevelinthehomecountrycanbehigherunderthefiscaldevaluationcomparedwith thebaselinemonetaryunioncase;andindeed,theinitialresponseofinflationinthehomecountryisslightlygreater than in the baseline case. 38

ity in both countries. According to panels (a) and (b), the policy is very effective at stabilizing production and hours worked in the home country, relative to the baseline monetary union case. The stabilization gains in the home country are due primarily to the payroll subsidy, which increases domestic employment and wages, the most important source of income in the steady state. Importantly, the payroll subsidy is paid for by an increase in the VAT rate, which is only partially financed by domestic consumers. Panel (i) shows that under revenue neutrality, fiscal expenditures due to the payroll subsidy (expressed as negative cashflow for the home country’s government) are exactly offset by an increased revenue from the introduction of the VAT. Given the small degree of home bias in our baseline calibration, roughly one-half of the revenue raised by the VAT is paid for by domestic consumers, with the other half being paid for by foreign firms. On balance, therefore, the combination of the payroll subsidy and VAT results in a positive income shock in the home country—the unilateral fiscal devaluation by the home country is akin to an expansionary domestic fiscal policy under a balanced budget trajectory. Asshowninpanel(c), thisexpansionaryfiscalpolicyprovidesasignificantstimulustodomestic consumption. Despite the imposition of the VAT, the decline in consumption of domestically produced (i.e., h-type) goods is considerably attenuated relative to the baseline case, while the consumption of imported (i.e., f-type) goods increases further (panels (d) and (h)). As a result, the home country’s trade deficit worsens and the real exchange rate appreciates even more than in the baseline monetary union case (panels (j) and (k)). However, as shown on panel (l), the home country’s current account balance (expressed as a percent of initial level of GDP) registers a modest surplus under this policy. Because the marginal propensity to consume in response to a temporary increase in income is less than unity, the fiscal devaluation leads to an increase in domestic savings. It also leads to an appreciation of the real exchange rate, a deterioration in the trade balance, and an improvement in the home country’s external capital position, a pattern of adjustment that stands in stark contrast to that registered under flexible exchange rates. When the home country is experiencing financial distress, the foreign economic boom leads to anexpansioninforeigndemand,whichunderflexibleexchangerates,leadstoatighteningofforeign monetary policy. A similar dynamic is at work in the monetary union, when the home country pursues a unilateral fiscal devaluation. In the baseline case, the negative output gap in the home country is roughly offset by the positive gap in the foreign country, and the union’s central bank is responding largely to an increase in inflation in both countries. As shown in panels (e)–(f), the fiscal devaluation also helps to stabilize foreign economic activity, though to a lesser extent than in thehomecountry. Thecombinationofanappreciablylessnegativeoutputgapinthehomecountry and a smaller positive gap in the foreign country resulting from the fiscal devaluation implies a stronger monetary policy response relative to the baseline case. At the same time, lower foreign inflation—reflecting lower markups of both foreign firms and home country exporters—results in a higher real interest rate in the foreign country (about 80 basis points at an annual rate) relative to the baseline case. In turn, this reduces the volatility of consumption and hours worked and points to potential foreign welfare gains as the home country pursues a unilateral fiscal devaluation in 39

Figure 10: Customer Markets, Fiscal Devaluations, and Union Welfare ( a ) D e e p h a b i t s : θ = − 0 . 3 ; ρ = 0.3 ( b ) D e e p h a b i t s : θ = − 0 . 8 6 ; ρ = 0.85 ( c ) D e e p h a b i t s : θ = − 0 . 9 5 ; ρ = 0.95 Change in welfare Change in welfare Change in welfare 6 6 6 Home Foreign 4 4 4 2 2 2 0 0 0 0 10 20 30 0 10 20 30 0 10 20 30 αFD αFD αFD Note: ThelinesdepictchangesinwelfareforthehomeandforeigncountriesasafunctionofαFD,theparameter governing the size of a unilateral fiscal devaluation by the home country. The “•” symbol marks the value of αFD that maximizes the welfare of the foreign country. Welfare differentials are measured relative to a baseline monetary union case with no fiscal devaluation—that is, αFD =0. order to stabilize its macroeconomy in the wake of a financial shock. In light of this observation, we now analyze the welfare implications of a unilateral fiscal devaluation by the home country, both domestically and abroad. To do so, we consider a set of experiments, where we set the fiscal reaction coefficient αFD to a value that maximizes the welfare of a representative household in either country. Figure 10 traces out the implications of such an exercise on the welfare of the two countries under three different calibrations of the deep-habit mechanism: “weak” deep habits (panel (a)); baseline deep habits (panel (b)); and “strong” deep habits (panel (c)). In general, this analysis indicates that the macroeconomic stabilization benefits from a unilateral fiscal devaluation by the home country are shared by both countries of the union. However, the magnitude of potential welfare gains depends critically, especially for the foreign country, on the strength of customer market relationships in the two economies. As shown in panel (a), when the strength and persistence of deep habits are fairly weak, the foreign country realizes only a minuscule welfare gain from such a unilateral fiscal devaluation— in fact, too much fiscal activism may result in a small welfare loss for the foreign country. As indicated by the “•” symbol, the foreign welfare reaches the maximum when the home country sets αFD ≈ 1, and even in this case, the maximal foreign welfare is essentially indistinguishable from the baseline. This result suggests that when foreign firms have relatively little incentive to engage in predatory pricing to capture market share from their home country competitors, it may be difficult for the home country to make a compelling argument for a unilateral fiscal devaluation within the monetary union, even though such a policy is clearly beneficial domestically. Under our baseline calibration shown in panel (b), by contrast, we reach a very different conclusion. In this case, a fiscal devaluation that maximizes the foreign welfare calls for an aggressive 40

Figure 11: Financial Frictions, Fiscal Devaluations, and Union Welfare Home country Foreign country Change in welfare Change in welfare 6 6 ϕ= 0.10 ϕ= 0.20 4 ϕ= 0.10 ϕ= 0.20 4 ϕ= 0.15 ϕ= 0.25 ϕ= 0.15 ϕ= 0.25 2 2 0 0 0 10 20 30 0 10 20 30 αFD αFD Note: The left (right) panel depicts changes in welfare for the home (foreign) country as a function of αFD, the parameter governing the size of a unilateral fiscal devaluation by the home country, for different values of the steady-stateequitydilutioncostsϕ. The“•”symbolintheleftpanelmarksthevalueofαFD thatmaximizesthe welfare of the home country, while in the right panel, the “•” symbol marks the value of αFD that maximizes the welfare of the foreign country. Welfare differentials are measured relative to a baseline monetary union case with no fiscal devaluation—that is, αFD =0. policy setting of αFD ≈ 15.38 Even more interestingly, the maximal foreign welfare is attained at the value of αFD that is substantially greater than that preferred by the home country—the latter’s welfare is maximized at αFD ≈ 1. Thus, with a more powerful deep-habit mechanism, the foreign country has a strong incentive to support an aggressive unilateral fiscal devaluation by the home country. In the case of the strong deep habits shown in panel (c), there is more room for welfare gains by the foreign country, as that configuration of the deep-habits parameters lies in the region where even the foreign country is worse off in the monetary union. AsshowninthebottompanelofTable4, joiningthemonetaryunionincreasestheaveragelevel of consumption in the foreign country by one percent. Despite this economically large gain in the steady-state consumption level, the welfare gain for the representative foreign household—in terms ofthecertainty-equivalentchangesintheaverageconsumption—amountstoonly0.11percent. This is because joining the union significantly increases the volatility of consumption—and especially of 38The large reaction coefficient αFD preferred from the perspective of the foreign country under our baseline calibrationofthedeep-habitmechanismdoesnotnecessarilyimplylargechangesintheVATorpayrollsubsidyrates. Our posited fiscal policy rule—just like the interest-rate rule governing the conduct of monetary policy—responds to an endogenous variable and to the extent that such fiscal measures are effective in stabilizing the output gap, the effectiveVATandpayrollsubsidyrateswillnotfluctuateverymuchinresponsetochangesinthedegreeofeconomic slack. A fiscal rule that responds aggressively to the output gap sends a signal to the agents that deviations of real GDP from its potential will be countered by large changes in the tax and subsidy rates. Because such a policy is credible, effective rates do not need to change much in equilibrium and do not result in overly protectionist trade policy. In fact, both the payroll subsidy and VAT rates peak at less than three percent in response to our standard financial shock, when the optimal value of αFD is applied to the baseline economy. 41

hours worked—in the foreign country. A fiscal devaluation by the home country effectively removes these deleterious welfare side-effects without eliminating the sizable steady-state gains in foreign consumption. According to our calculations, the volatility of foreign consumption is reduced by two-thirds—relative to the baseline monetary union case—as a result of the fiscal devaluation by the home country, while the volatility of hours worked declines by almost 40 percent. In both countries, the magnitude of any potential welfare gains (or losses) arising from a unilateral fiscal devaluation by the home country will also depend on the degree of financial market frictions. Becausethelimitedcapacityofthefinancialsysteminthehomecountrymakespredatory pricing strategies of foreign firms profitable, the greater the degree of financial market imperfections in the home country, the greater are the potential benefits from pursuing a unilateral fiscal devaluation. The left panel of Figure 11 shows the welfare gains from such a fiscal policy for the home country, as we vary the steady-state value of equity dilution costs ϕ, while the right panel displays the same information for the foreign country. As expected, increasing the severity of financial frictions monotonically increases the welfare gains from a unilateral fiscal devaluation for both countries. Moreover, the optimal degree of fiscal activism by the home country also increases, as financial distortions become more severe. 7 Conclusion In this paper, we present a two-country dynamic stochastic general equilibrium model and use it to analyze the business cycle and welfare consequences of forming a monetary union among countries, whose financial markets are subject to varying degrees of distortions. Because of customer-market considerations, financial shocks affect the firms’ pricing decisions, thereby influencing the dynamics of markups and market shares—and therefore patterns of external adjustment—across countries. When applied to the eurozone crisis, the interaction of customer markets and financial frictions helps explain several phenomena that are difficult to reconcile using conventional models. First, the pricing mechanism implied by this interaction is consistent with our empirical evidence, which shows that the tightening of financial conditions in the euro area periphery between 2008 and 2013 significantly attenuated the downward pressure on prices arising from the emergence of substantial and long-lasting economic slack. And second, this tightening of financial conditions is strongly associated with an increase in price markups in the periphery. Hence our framework can explain why the periphery countries have managed to avoid a debt-deflation spiral in the face of persistent economic weakness and high indebtedness and how the price war between the core and periphery has impeded the adjustment process through which the latter economies have been trying to regain external competitiveness. In our model, the pricing behavior of firms in the core in response to a financial shock in the periphery implies a real exchange rate depreciation vis-a`-vis the periphery, which causes an export-driven boom in the core and a deepening of the recession in the periphery. The one-sizefits-all aspect of monetary policy in a common currency regime is especially ill-suited to address 42

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Appendix A Optimal Pricing This section derives the firm’s optimal pricing strategies in the domestic and foreign markets, given byequations(14)and(15)inthemaintext. Giventhesymmetricnatureoftheprofit-maximization problems faced by home and foreign firms, we present the pricing rules from the vantage point of a firm in the home country. The full set of first-order conditions implied by the optimization of the Lagrangian (8) in the main text is given by: With respect to d : i,t 1 if d ≥ 0; ξ = i,t (A-1) i,t 1/(1−ϕ) if d < 0. i,t (cid:26) With respect to h : i,t α−1 A t ξ w = ακ h , (A-2) i,t t i,t i,t a (cid:18) i,t (cid:19) where the conditional demand for labor is given by h = a i,t φ+c +c∗ α 1 . (A-3) i,t A i,h,t i,h,t t (cid:0) (cid:1) With respect to c and c∗ : i,h,t i,h,t Ea[ν ] = Ea[ξ ]p p −Ea[κ ]+(1−ρ)λ ; (A-4) t i,h,t t i,t i,h,t h,t t i,t i,h,t Ea[ν∗ ] = Ea[ξ ]q p∗ p∗ −Ea[κ ]+(1−ρ)λ∗ . (A-5) t i,h,t t i,t t i,h,t h,t t i,t i,h,t With respect to s and s∗ : i,h,t i,h,t c λ = ρE [m λ ]+θ(1−η)E m Ea ν i,h,t+1 ; (A-6) i,h,t t t,t+1 i,h,t+1 t t,t+1 t+1 i,h,t+1 s " (cid:20) i,h,t (cid:21) # c∗ λ∗ = ρE [m λ∗ ]+θ(1−η)E m Ea ν∗ i,h,t+1 . (A-7) i,h,t t t,t+1 i,h,t+1 t t,t+1 t+1 i,h,t+1 s∗ " " i,h,t ## With respect to p and p∗ : i,h,t i,h,t Ea[ν ] π p η t i,h,t c = Ea[ξ ] p c −γ h,t π i,h,t −1 c p i,h,t t i,t h,t i,h,t p p h,t p t i,h,t (cid:20) i,h,t−1 (cid:18) i,h,t−1 (cid:19) (cid:21) (A-8) p p +γ E m Ea [ξ ]π i,h,t+1 π i,h,t+1 −1 c ; p t t,t+1 t+1 i,t+1 h,t+1 p2 h,t+1 p t+1 " i,h,t (cid:18) i,h,t (cid:19) # Ea[ν∗ ] q π∗ p∗ η t i,h,t c∗ = Ea[ξ ] q p∗ c∗ −γ t h,t π∗ i,h,t −1 c∗ p∗ i,h,t t i,t t h,t i,h,t p p∗ h,tp∗ t i,h,t " i,h,t−1 i,h,t−1 ! # (A-9) p∗ p∗ +γ E m Ea [ξ ]q π∗ i,h,t+1 π∗ i,h,t+1 −1 c∗ . p t t,t+1 t+1 i,t+1 t+1 h,t+1 p∗2 h,t+1 p∗ t+1 " i,h,t i,h,t ! # 47

In the absence of nominal price rigidities, the first-order conditions (A-8) and (A-9) reduce to Ea[ν ] p p = η t i,h,t ; (A-10) i,h,t h,t Ea[ξ ] t i,t and Ea[ν∗ ] q p∗ p∗ = η t i,h,t . (A-11) t i,h,t h,t Ea[ξ ] t i,t Dividing the first-order conditions (A-4) and (A-5) by the expected shadow value of internal funds yields Ea[ν ] Ea[κ ] λ t i,h,t = p p − t i,t +(1−ρ) i,h,t ; (A-12) Ea[ξ ] i,h,t h,t Ea[ξ ] Ea[ξ ] t i,t t i,t t i,t and Ea[ν∗ ] Ea[κ ] λ∗ t i,h,t = q p∗ p∗ − t i,t +(1−ρ) i,h,t . (A-13) Ea[ξ ] t i,h,t h,t Ea[ξ ] Ea[ξ ] t i,t t i,t t i,t Similarly, dividing the first-order-conditions (A-6) and (A-7) by the expected shadow value of internal funds we obtain λ Ea [ξ ] λ i,h,t = ρE m t+1 i,t+1 i,h,t+1 Ea[ξ ] t t,t+1 Ea[ξ ] Ea [ξ ] t i,t (cid:20) t i,t t+1 i,t+1 (cid:21) (A-14) Ea [ξ ]Ea [ν ]c +θ(1−η)E m t+1 i,t+1 t+1 i,h,t+1 i,h,t+1 ; t t,t+1 Ea[ξ ] Ea [ξ ] s (cid:20) t i,t t+1 i,t+1 i,h,t (cid:21) and λ∗ Ea [ξ ] λ∗ i,h,t = ρE m t+1 i,t+1 i,h,t+1 Ea[ξ ] t t,t+1 Ea[ξ ] Ea [ξ ] t i,t (cid:20) t i,t t+1 i,t+1 (cid:21) (A-15) Ea [ξ ] Ea [ν∗ ]c∗ +θ(1−η)E m t+1 i,t+1 t+1 i,h,t+1 i,h,t+1 . t t,t+1 Ea[ξ ] Ea [ξ ] s∗ " t i,t t+1 i,t+1 i,h,t # Updating equations (A-12) and (A-13) one period and substituting the resulting expressions into the right-hand sides of equations (A-14) and (A-15), we obtain λ Ea [ξ ] c λ i,h,t = E m t+1 i,t+1 ρ+θ(1−η)(1−ρ) i,h,t+1 i,h,t+1 Ea[ξ ] t t,t+1 Ea[ξ ] s Ea [ξ ] t i,t " t i,t (cid:18) i,h,t (cid:19) t+1 i,t+1 # Ea [ξ ]c Ea [κ ] +θ(1−η)E m t+1 i,t+1 i,h,t+1Ea p p − t+1 i,t+1 ; t t,t+1 Ea[ξ ] s t+1 i,h,t+1 h,t+1 Ea [ξ ] " t i,t i,h,t (cid:20)(cid:18) t+1 i,t+1 (cid:19)(cid:21) # (A-16) and λ∗ Ea [ξ ] c∗ λ∗ i,h,t = E m t+1 i,t+1 ρ+θ(1−η)(1−ρ) i,h,t+1 i,h,t+1 Ea[ξ ] t t,t+1 Ea[ξ ] s∗ Ea [ξ ] t i,t " t i,t i,h,t ! t+1 i,t+1 # Ea [ξ ]c∗ Ea [κ ] +θ(1−η)E m t+1 i,t+1 i,h,t+1Ea q p∗ p∗ − t+1 i,t+1 . t t,t+1 Ea[ξ ] s∗ t+1 t+1 i,h,t+1 h,t+1 Ea [ξ ] " t i,t i,h,t (cid:20)(cid:18) t+1 i,t+1 (cid:19)(cid:21) # (A-17) 48

Wethenimposethesymmetricequilibriumconditions,c = c ,s = s ,λ = λ , i,h,t+1 h,t+1 i,h,t h,t i,h,t h,t p = 1, c∗ = c∗ , s∗ = s∗ , λ∗ = λ∗ , and p∗ = 1, for all i, to obtain i,h,t+1 i,h,t+1 h,t+1 i,h,t h,t i,h,t h,t i,h,t+1 λ Ea [ξ ] s /s −ρ λ h,t = E m t+1 i,t+1 ρ+θ(1−η)(1−ρ) h,t+1 h,t h,t+1 Ea[ξ ] t t,t+1 Ea[ξ ] 1−ρ Ea [ξ ] t i,t " t i,t (cid:18) (cid:19) t+1 i,t+1 # (A-18) Ea [ξ ]s /s −ρ 1 +θ(1−η)E m t+1 i,t+1 h,t+1 h,t Ea p − ; t t,t+1 Ea[ξ ] 1−ρ t+1 h,t+1 µ˜ " t i,t (cid:20)(cid:18) t+1(cid:19)(cid:21) # and λ∗ Ea [ξ ] s∗ /s∗ −ρ λ∗ h,t = E m t+1 i,t+1 ρ+θ(1−η)(1−ρ) h,t+1 h,t h,t+1 Ea[ξ ] t t,t+1 Ea[ξ ] 1−ρ Ea [ξ ] t i,t " t i,t ! t+1 i,t+1 # (A-19) Ea [ξ ]s∗ /s∗ −ρ 1 +θ(1−η)E m t+1 i,t+1 h,t+1 h,t Ea q p∗ − , t t,t+1 Ea[ξ ] 1−ρ t+1 t+1 h,t+1 µ˜ " t i,t (cid:20)(cid:18) t+1(cid:19)(cid:21) # whereweusedthefactthatc /s = (s /s −ρ)/(1−ρ) ≡ g ,c∗ /s∗ = (s∗ /s∗ − h,t+1 h,t h,t+1 h,t h,t+1 h,t+1 h,t h,t+1 h,t ρ)/(1 − ρ) ≡ g∗ , and Ea [κ ]/Ea [ξ ] = µ˜−1 . We can define the growth-adjusted, h,t+1 t+1 i,t+1 t+1 i,t+1 t+1 compounded discount factors, β and β∗ , as h,t,s h,t,s m g if s = t+1; s−1,s h,s β = (A-20) h,t,s s−(t+1) m g × (ρ+χg )m if s > t+1; ( s−1,s h,s j=1 h,t+j t+j−1,t+j β∗ = m s−1,s g h ∗ ,s Q if s = t+1; (A-21) h,t,s m g∗ × s−(t+1) (ρ+χg∗ )m if s > t+1, ( s−1,s h,s j=1 h,t+j t+j−1,t+j Q where χ = θ(1−η)(1−ρ). Rational expectations solutions to equations (A-18) and (A-19) can then be found by iterating the two equations forward as λ ∞ Ea[ξ ] 1 h,t = θ(1−η)E β s i,s p − ; (A-22) Ea[ξ ] t h,t,sEa[ξ ] h,s µ˜ t i,t " s=t+1 t i,t (cid:18) s(cid:19) # X and λ∗ ∞ Ea[ξ ] 1 h,t = θ(1−η)E β∗ s i,s q p∗ − . (A-23) Ea[ξ ] t h,t,sEa[ξ ] s h,s µ˜ t i,t " s=t+1 t i,t (cid:18) s(cid:19) # X After imposing the symmetric equilibrium conditions, we substitute equations (A-12) and (A-13) into equations (A-10) and (A-11), which yields 1 λ h,t p = ηp −η +(1−ρ)η ; (A-24) h,t h,t µ˜ Ea[ξ ] t t i,t and 1 λ∗ q p∗ = ηq p∗ −η +(1−ρ)η h,t . (A-25) t h,t t h,t µ˜ Ea[ξ ] t t i,t Finally, substituting equations (A-22) and (A-23) into equations (A-24) and (A-25) and solving the resulting expressions for p and q p∗ yields the firm’s optimal pricing strategies in the domestic h,t t h,t and foreign markets, given by equations (14) and (15) in the main text. 49

B Calibration Summary The entries in the table denote the values of the model parameters used in the baseline calibration of the model. Table B-1: Baseline Calibration Model Parameters Value Preferences & technology time discount factor (δ) 0.996 constant relative risk aversion (γ ) 2.000 x elasticity of labor supply (ζ) 5.000 elasticity of substitution between differentiated labor (η ) 2.000 w strength of deep habits (θ) −0.860 persistence of deep habits (ρ) 0.850 elasticity of substitution between differentiated goods (η) 2.000 Armington elasticity (ε) 1.500 home bias (Ξε,Ξ∗ε) (0.600,0.600) h f returns-to-scale (α) 1.000 fixed operating costs (φ,φ∗) (0.10,0.10) Nominal rigidities & monetary policy price adjustment costs (γ ) 10.00 p wage adjustment costs (γ ) 30.00 w Taylor rule inflation gap coefficient (ψ ) 1.500 π Taylor rule output gap coefficient (ψ ) 1.000 y Financial frictions & shocks equity dilution costs (ϕ,ϕ∗) (0.20,0.02) std. deviation of idiosyncratic cost shock (σ) 0.200 portfolio rebalancing costs (τ) 0.150 persistence of aggregate financial shocks (ρ ) 0.900 f persistence of aggregate technology shocks (ρ ) 0.900 A persistence of aggregate demand shocks (ρ ) 0.900 ω C Market Share Dynamics During the Financial Crisis As noted in the main text, an important prediction of our model concerns the relative behavior of market shares in response to an adverse financial shock in the home country. According to panels (b) and (e) in Figure 5, foreign firms, by undercutting prices charged by their home country counterparts, significantly expand market shares in both the domestic and export markets. At the same time, home firms increase relative prices in their domestic and export markets, and their corresponding market shares fall. Our model, therefore, shares with conventional international macroeconomic models the prediction that increases in relative prices lead to decreases in market shares. Totestthispredictionofthemodel, wewouldfirsthavetodefinewhatconstitutesamarketand then show that changes in relative prices in those markets are inversely related to changes in the corresponding market shares and that those changes are driven by changes in financial conditions. A lack of data on destination-specific, disaggregated producer prices and the corresponding data 50

on the firms’ financial conditions limits the analysis of how market shares respond to changes in relative prices induced by financial shocks. As an alternative, we use the Eurostat trade data to construct relative importer shares by major product groups—defined on the basis of Broad EconomicCategories(BECs)—fortheeurozonecoreandperiphery.39 Specifically,foreacheurozone region—that is, core (C) and periphery (P)—and BEC (indexed by k), we calculate an importer share as Impk Impk ImpShrk = t,P→C and ImpShrk = t,C→P, t,P→C Impk t,C→P Impk t,C t,P whereImpk isthenominalvalueofimports(inBECk)bythecorecountriesfromtheperiphery t,P→C (P → C) in year t, Impk is the nominal value of imports (in BEC k) by the periphery countries t,C→P from the core (C → P) over the same period, and Impk and Impk denote total imports (in t,C t,P BEC k) by the core and periphery countries, respectively. Our definition of the market, therefore, is the total euro-volume of sectoral imports in region j ∈ {C,P}, originating from any of the region’s trading partners, including those outside the eurozone. Given the available data, this definition of the market is the narrowest available to us. It brings withittheadvantagethatitabstractsfromchangesinmarketsharesthatarenotduetochangesin relative prices at more aggregated levels. For example, if we defined market shares relative to GDP, sectoral shocks, such as the sharp drop in residential investment in the eurozone’s periphery during the crisis, might spuriously show up as higher market shares. To abstract from such dynamics, we consider reallocation among imported goods only. Under the assumption that sectoral import price inflation between the euro area core and periphery comoves, relative changes in sectoral importer shares will primarily reflect changes in relative prices charged by firms in two regions regions.40 To see this, consider a general demand setting, in which the sector k importer share in the regions j and j′ depends on sectoral import prices, according to Pk −ηk ImpShrk = t,j→j′ , t,j′→j P t k ,j ! where η > 0 is the sector-specific demand elasticity, and Pk and Pk denote the price index k t,j→j′ t,j of sector k imports from j′ into j and the overall import price index prevailing in j, respectively. Then, the assumption that ∆lnPk ≈ ∆lnPk implies that t,j t,j′ ∆lnImpShrk −∆lnImpShrk ≈ −η πk −πk . t,j′→j t,j→j′ k t,j′→j t,j→j′ Letting j′ = P, that is, the financially distressed periphery, (cid:0) and j = C, that (cid:1) is, the financially strong core, our model predicts that πk < 0 and πk > 0, which implies a negative difference t,C→P t,P→C in the growth of importer shares of the periphery relative to the core. In other words, the periphery loses importer market shares, while the core gains importer market shares, when the periphery is hitbyanadversefinancialshock. Notethatthesignofthispredictionisnotaffectedbytheimplicit assumption that η = η = η . k k,P k,C The left panel of Figure C-1 shows the cumulative relative growth in importer market shares between the periphery and core for the seven BECs. With the exception of BEC-2 (Industrial 39The seven categories are BEC-1: Food & Beverages; BEC-2: Industrial Supplies; BEC-3: Fuels & Lubricants; BEC-4: Capital Goods (excluding transport equipment); BEC-5: Transport Equipment; BEC-6: Consumer Goods; and BEC-7: Goods, not elsewhere specified. 40This assumption is in fact borne out by the data. Using Eurostat “Import Prices in Industry,” we find that import price inflation between the eurozone core and periphery exhibits a strong positive comovement. 51

Figure C-1: Relative Importer Shares in the Euro Area (2008–2015) By broad economic categories Trade-weighted aggregates Index(2008=100) Index(2008=100) Index(2008=100) 200 120 105 Annual Annual BEC-1 (RHS) BEC-2 (RHS) BEC-3 (LHS) BEC-4 (RHS) BEC-5 (RHS) BEC-6 (RHS) 150 BEC-7 (LHS) 110 100 100 100 95 Average Median 50 90 90 0 80 85 2008 2010 2012 2014 2008 2010 2012 2014 Note: Theleftpaneldepictsthebehaviorofrelativeimportersharesbetweentheeurozoneperipheryandcorein seven broad economic categories (BECs): BEC-1 = Food & Beverages; BEC-2 = Industrial Supplies; BEC-3 = Fuels & Lubricants; BEC-4 = Capital Goods (excluding transport equipment); BEC-5 = Transport Equipment; BEC-6=ConsumerGoods;andBEC-7=Goods,notelsewherespecified. Therightpaneldepictsthecumulative trade-weightedaverageandthetrade-weightedmedianoftherelativegrowthinimportermarketsharesacrossthe seven BECs, using total trade flows between the two regions as weights. Source: Eurostat. Supplies)—a category of goods for which the relative importer market share between the eurozone periphery and core was about unchanged—the relative importer market shares for all other categories declined markedly during the crisis. Although in BEC-7 (Goods, not elsewhere classified), the sharp drop in the relative importer market share was fairly transient, the relative importer market shares in the remaining categories registered appreciably more persistent declines.41 To gauge the aggregate implications of these trade patterns, the right panel shows the cumulative trade-weighted average and the trade-weighted median of the relative growth in importer market shares across the seven BECs, using total trade flows between the two regions as weights. Both measures paint the same picture: As the crisis in the euro area unfolded, imports by the periphery countries from the core countries—normalized by the periphery’s total imports—declined by considerably more than the imports by the core countries from the periphery, normalized by the total imports of the core countries.42 Such dynamics in relative importer market shares are consistent with our model, which predicts that in periods of financial distress, firms in the home country will lose importer market share, while their financially stronger foreign competitors will gain importer market share. D Optimal Monetary Policy and Welfare in the Monetary Union As noted in the main text, the welfare calculations for the monetary union reported in Table 4 are not predicated on optimal monetary policy because we assume that the union’s central bank conducts monetary policy according to the Taylor (1999) interest-rate rule. To show that the 41Wealsoverifiedthatthesemovementsarenotdrivenbyincreasesinthedifferenceofthetotalvolumeofimports, but rather mainly by the declines in the size of relative flows. 42The aggregate patterns are qualitatively the same if instead of total imports by each region, imports from the periphery and core and vice versa are normalized by the relevant region’s nominal GDP. 52

lower joint welfare in the monetary union is not due to the suboptimality of the assumed interestrate rule, the solid lines in Figure D-1 depict the responses of selected variables to our standard asymmetric financial shock in the home country in the case of optimal monetary policy conducted by the Ramsey planner, whose objective is to maximize the joint welfare of the two countries using a union-wide short-term interest rate; for comparison purposes, the dashed lines show the corresponding responses from the baseline monetary union experiment, in which the monetary authorities follow the Taylor (1999) interest-rate rule (see Figure 3). The fact that the dynamics of key macroeconomic aggregates are virtually the same across these two simulations indicates that even the Ramsey planner is unable to overcome the limitations of a one-size-fits-all aspect of monetary policy in the monetary union. Figure D-1: Asymmetric Financial Shock in Monetary Union With Optimal Monetary Policy (a) Production (b) Consumption (c) Hours worked (d) Interest rate pct. pct. pct. pps. 2 0.8 2 2.0 Home - Ramsey Foreign - Ramsey H Fo o r m ei e g n - T - a T y a lo yl r o ’ r 9 ’ 9 99 R Ta a y m lo s r e ’ y 99 1.5 1 0.4 1 1.0 0 0.0 0 0.5 -1 -0.4 -1 0.0 -2 -0.8 -2 -0.5 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 ( e ) Exchange rate ( f ) Inflation ( g ) Exports ( h ) Net exports pct. pps. pct. pct. of GDP 6 1.6 1.6 1.2 1.2 0.8 Real - Ramsey 4 0.8 R N e o a m l in - a T l aylor ’99 0.8 0.4 2 0.0 0.0 0.4 -0.4 0 0.0 -0.8 -0.8 -0.4 -2 -1.6 -1.2 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 0 8 16 24 32 Note: Thesolidlinesdepictthemodel-impliedresponsesofselectedvariablestoanadversefinancialshockinthe home country in period 0, when the two countries are in a monetary union and monetary policy is conducted by the Ramsey planner. The dashed lines show the corresponding responses when the union-wide monetary policy follows the Taylor (1999) interest-rate rule. Exchange rates are expressed as home currency relative to foreign currency. Figure D-2 show the robustness of the welfare results reported in Table 4 across the different combinations of parameters θ and ρ, which govern the strength and persistence of the customermarket relationships. The symbol “o” indicates that the welfare of the representative household is greater under a flexible exchange rate regime, while the symbol “x” indicates higher welfare when the two countries are in a monetary union. According to the left panel, the welfare of the home country improves with the exit from the monetary union for all configurations of the parameters θ and ρ. As shown in the right panel, by contrast, the welfare of the foreign country is greater in the monetary union across most of the (θ,ρ)-space, the exception being a small region of the parameter 53

Figure D-2: Welfare Gains and Losses From Dissolving Monetary Union Home country Foreign country 1.0 1.0 ooooooooooooooooooo ooox x x x x x x x x x x x x x x x ooooooooooooooooooo ooox x x x x x x x x x x x x x x x ooooooooooooooooooo oox x x x x x x x x x x x x x x x x 0.8 ooooooooooooooooooo 0.8 ox x x x x x x x x x x x x x x x x x ooooooooooooooooooo ox x x x x x x x x x x x x x x x x x ooooooooooooooooooo x x x x x x x x x x x x x x x x x x x ooooooooooooooooooo x x x x x x x x x x x x x x x x x x x 0.6 ooooooooooooooooooo 0.6 x x x x x x x x x x x x x x x x x x x ooooooooooooooooooo x x x x x x x x x x x x x x x x x x x ρ ooooooooooooooooooo ρ x x x x x x x x x x x x x x x x x x x ooooooooooooooooooo x x x x x x x x x x x x x x x x x x x 0.4 ooooooooooooooooooo 0.4 x x x x x x x x x x x x x x x x x x x ooooooooooooooooooo x x x x x x x x x x x x x x x x x x x ooooooooooooooooooo x x x x x x x x x x x x x x x x x x x ooooooooooooooooooo x x x x x x x x x x x x x x x x x x x 0.2 ooooooooooooooooooo 0.2 x x x x x x x x x x x x x x x x x x x ooooooooooooooooooo x x x x x x x x x x x x x x x x x x x ooooooooooooooooooo x x x x x x x x x x x x x x x x x x x ooooooooooooooooooo x x x x x x x x x x x x x x x x x x x 0.0 0.0 −1.0 −0.8 −0.6 −0.4 −0.2 0.0 −1.0 −0.8 −0.6 −0.4 −0.2 0.0 θ θ O = welfare greater under flexible exchange rates X = welfare greater under monetary union Note: Thetwopanelsshowthechangeinwelfareoftherepresentativehousehold—overtherelevant(θ,ρ)-space— inthehomeandforeigncountries,inthecasethatthetwocountriesdissolvethemonetaryunionandadoptflexible exchangerates. Thesymbol“o”indicatesthatthewelfareoftherepresentativehouseholdisgreaterunderaflexible exchange rate regime, while the symbol “x” indicates higher welfare when the two countries are in a monetary union. space characterized by a very strong and persistent deep-habit mechanism (θ < −0.9 and ρ > 0.9). In this region of the parameter space, the monetary union results in a welfare loss even for the foreign country due to the heightened volatility of consumption and hours worked. One concern with the welfare analysis is that the second-order exact solution implies a substantially higher average premium on external funds than is implied by the nonstochastic steady state. To account for this difference, we have redone the analysis shown in Figure D-2 under a calibration in which the average premium on external funds is equal to that implied by the nonstochastic steady state under our baseline calibration. Again, the resulting welfare results shows that over a wide range of the (θ,ρ)-space, the home country prefers flexible exchange rates, while the foreign country’s welfare is higher in the monetary union. E Welfare Consequences of a Fiscal Union The Online Technical Appendix shows the details of how the introduction of complete risk sharing between the two countries—a de facto fiscal union—modifies the model’s key equations and equilibrium conditions. Table E-1 compares the representative households’ welfare—with and without risk sharing—when the two countries share a common currency. Under our baseline calibration shown in panel (a), both countries can potentially reap large welfare gains by forming a fiscal union, according to the certainty-equivalent changes in consumption, which are required to make the welfare levels of the households in the monetary union with risk sharing equal to those in the 54

union without risk sharing. Table E-1: Welfare Consequences of Forming a Fiscal Union Welfare Comparison Calibration w/o Risk Sharing w/ Risk Sharing CE (pct.) (a) θ = −0.86, ρ = 0.85, φ∗ = φ Home country −259.23 −257.61 0.79 Foreign country −254.05 −253.15 0.45 Memo: Both countries −513.28 −510.76 . (b) θ = −0.95, ρ = 0.95, φ∗ = φ Home country −283.64 −279.86 1.71 Foreign country −278.47 −274.94 1.66 Memo: Both countries −562.11 −554.80 . (c) θ = −0.86, ρ = 0.85, φ∗ = 0.9φ Home country −261.00 −254.69 3.13 Foreign country −248.73 −249.81 −0.56 Memo: Both countries −509.73 −504.50 . Note: CE denotes the certainty-equivalent change in the average consumption per period (holding hours worked constant)thatisrequiredtomaketherepresentativehouseholdinthespecifiedcountrynoworseoffwhenthetwo countriesinthemonetaryunionabandonacompleterisk-sharingarrangement. Inpanels(a)and(b),φ∗ =φ=0.1, as in our baseline calibration. Asshowninpanel(b),thepotentialwelfaregainsfromformingafiscalunionareevenlargerwith very strong and persistent deep habits, an environment where the interaction between customer markets and financial distortions leads to an especially powerful propagation of financial shocks when the two countries share a common currency. Recall that this configuration of θ and ρ lies in the region of parameter space that is associated with a lower welfare for the foreign country in a monetary union (see Figure D-2). Thus in these more extreme circumstances, the macroeconomic stabilizationpropertiesofafiscalunionmayalsoconfersignificantbenefitsonthefinanciallystrong members of the union. The calibration in panel (c), by contrast, indicates that the formation of a fiscal union when the twocountriesalreadyshareacommoncurrency—aprogressionenvisionedbytheEuropeanpolitical establishment—is not necessarily Pareto improving. This calibration differs from our baseline in only one dimension: We assume that foreign firms are slightly more efficient—in terms of fixed operating costs—than their domestic counterparts; that is, φ∗ = 0.9φ, where φ = 0.1, our baseline value. In this case, the welfare of the foreign country is significantly lower with complete risk sharing, according to the certainty-equivalent consumption metric. A useful way to think about this result is to interpret the fixed operating costs as capturing the quality of the firms’ balance sheets. That is, these costs can include long-term debt payments, a couponpayment to perpetualbond holders andcanthus capture the possibility ofadebt overhang. Under this interpretation, the country with high fixed operating costs can be viewed as highly indebted, as is the eurozone periphery; for instance, the debt-to-GDP ratio averaged 130 percent in the eurozone periphery in 2013, about 55 percentage points higher than the corresponding average for the core. In our model, this differential translates into φ∗ = 0.6φ, and our welfare calculations implythattherepresentativeforeignhouseholdwouldseeitssteady-stateconsumptionleveldecline seven percent per quarter in the fiscal union, compared with a situation in which the two countries 55

only share a common currency. By the same token, the representative home country household would see an increase of nine percent in certainty-equivalent consumption were the two countries form a fiscal union. While admittedly crude, these welfare calculations underscore the political difficulties of forming a fiscal union, as residents of the foreign country are unlikely to agree with the size of such wealth transfers. 56