Asymmetric Shocks in a Currency Union with Monetary and Fiscal Handcuffs

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 1012 December 2010 Asymmetric Shocks in a Currency Union with Monetary and Fiscal Handcuffs Christopher J. Erceg and Jesper Lindé NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/.

Asymmetric Shocks in a Currency Union with Monetary and Fiscal Handcu⁄s (cid:3) Christopher J. Erceg Jesper LindØ (cid:3)(cid:3) Federal Reserve Board Federal Reserve Board December 2010 Abstract This paper investigates the impact of the asymmetric shocks within a currency union in a framework that takes account of the zero bound constraint on policy rates, and also allows for constraints on (cid:133)scal policy. In this environment, we document that the usual optimal currency argument showing that the e⁄ects of shocks are mitigated to the extent that they are common across member states can be reversed. Countries canbeworseo⁄whentheirneighborsexperiencesimilarshocks,includingpolicy-driven reductions in government spending. JEL Classi(cid:133)cation: E32, F41 Keywords: Monetary Policy, Fiscal Policy, Liquidity Trap, Zero Bound Constraint, Open Economy Macroeconomics, DSGE Model. ThispaperwaspreparedfortheNBER(cid:146)sInternationalSeminaronMacroeconomics(ISOM)Conference (cid:3) inAmsterdamonJune18-19,2010. WewouldliketothankourdiscussantsBiancaDePaoliandHans-Helmut Kotz for very helpful comments. Comments by other conference participants and by seminar participants at the National Bank of Belgium, Sveriges Riksbank, IMF research department, Federal Reserve Bank of Richmond,MONFISPOLworkshopattheLondonMetropolitanUniversityandtheFederalReserveBankof Chicagowerealsohelpful. TheauthorsareparticularlygratefultoRaymondZhongforoutstandingresearch assistance. The views expressed in this paper are solely the responsibility of the authors and should not be interpreted as re(cid:135)ecting the views of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System. Corresponding Author: Telephone: 202-452-2575. (cid:3)(cid:3) Fax: 202-263-4850 E-mail addresses: christopher.erceg@frb.gov and jesper.l.linde@frb.gov

1. Introduction Following the intensi(cid:133)cation of the (cid:133)nancial crisis in the fall of 2008, many countries implemented large (cid:133)scal stimulus packages aimed at mitigating the e⁄ects of the recession. A number of in(cid:135)uential papers were supportive of these policy actions on the premise that (cid:133)scal multipliers were likely to be especially large in an environment in which monetary policy was unlikely to respond by raising interest rates.1 However, the rise in sovereign spreads in a number of European countries since late 2009, especially those with high government debt or de(cid:133)cit levels, has spurred plans for substantial and accelerated (cid:133)scal consolidation in those countries. Moreover, even some countries that have access to capital markets on very favorable terms appear committed to (cid:133)scal retrenchment. This paper uses an open economy DSGE model to analyze how asymmetric shocks that are concentrated in a subset of member countries of a currency union a⁄ect the union both at an aggregate level, and di⁄erentially across member states. While this question has a long history in the optimal currency area literature, our framework takes explicit account of possible constraints on both monetary and (cid:133)scal policy. In particular, we assume that monetary policy is constrained by the zero lower bound (ZLB) on policy rates, and also consider the possibility that (cid:133)scal policy in at least some member countries may be constrained to react aggressively to debt or de(cid:133)cits. Our model consists of two country blocks that are integrated into a currency union, and hence share a single currency. The model structure inherits many of the features of a broad class of new open economy macro models. These include the various nominal and real fric- 1 Eggertsson (2008), Eggertsson (2009), and Christiano, Eichenbaum, and Rebelo (2009) argue that the (cid:133)scal multiplier is likely to be very large in a liquidity trap; Cogan et al (2009) o⁄er a contrasting view. 1

tions that have been identi(cid:133)ed as empirically important in the closed economy models of Christiano, Eichenbaum, and Evans (2005) and Smets and Wouters (2003), as well as analogous frictions relevant in an open economy framework, such as costs of adjusting trade (cid:135)ows. The model also incorporates (cid:147)rule of thumb(cid:148)households which consume all of their after-tax income as in Erceg, Guerrieri, and Gust (2006), and a (cid:133)nancial accelerator channel following the approach of Bernanke, Gertler, and Gilchrist (1999). Fiscal policy is determined separately by each country block, and includes rules for adjusting an endogenous component of government spending or taxes in response to government debt. We calibrate the model to the euro area, identifying one country block as the (cid:147)South(cid:148), and the other the (cid:147)North.(cid:148)Our analysis focuses on a (cid:147)Large South(cid:148)calibration in which the GDP of the South is half as large as of the North. We also examine an alternative (cid:147)Small South(cid:148)calibration in which the GDP of the South is a tiny fraction of the North(cid:146)s GDP. The latter closely approximates the case of a small open economy. We begin by examining the e⁄ects of a contraction in government spending in the South. Under (cid:147)normal conditions(cid:148)in which monetary policy is unconstrained, the e⁄ects of (cid:133)scal contraction in a single small economy are considerably more severe than if a sizeable group of its neighbors also reduced spending (based on comparing our Small South and Large South calibrations). This re(cid:135)ects that the monetary authority essentially leaves interest rates unchanged in response to a contraction in a small economy, while reducing interest rates considerably in the case of a concerted (cid:133)scal contraction. Thus, as familiar from a standard optimal currency area rationale, a small country such as Portugal would be better o⁄if it cut spending at the same time as its larger neighbors; and the smaller GDP decline would translate into a more rapid fall in the stock of debt. The (cid:133)scal contraction under the 2

Large South calibration actually causes output to rise slightly in the North. These implications contrast starkly with the case in which monetary policy is unable to reduce interest rates due to the ZLB constraint. In this environment, the impact of the (cid:133)scal shock on the South depends on agents(cid:146)perceptions about how long the liquidity trap would last in the absence of additional shocks, and the severity of the associated recession. As a benchmark, we choose initial conditions to imply that the liquidity trap would last two years in the absence of an additional shock. Against this backdrop, a (cid:133)scal contraction in the Large South case has a considerably more negative impact than when a single small country reduces spending (cid:150)so that a small country in the South is impacted more if its neighbors cut government spending at the same time. The implication that the (cid:133)scal multiplier is larger when monetary policy is constrained is consistent with previous closed economy analysis by Eggertsson (2008), Christiano, Eichenbaum, and Rebelo (2009), Woodford (2010), and Erceg and LindØ (2010). The spillover e⁄ects to the North of the South(cid:146)s (cid:133)scal contraction to the North are negative and very sizeable, and cause a substantial deterioration in the North(cid:146)s government budget position. The implication of large spillover e⁄ects given the ZLB constraint has a close parallel to previous work by Bodenstein, Erceg, and Guerrieri (2009). However, the latter examined cross country spillovers in a two country framework in which each country conducted an independent monetary policy, and in which nominal exchange rates were free toadjust. Inourmodel, spilloverstotheNortharelargeandnegativewhenmonetarypolicy is constrained by the zero bound, even though the North(cid:146)s exchange rate remains (cid:133)xed in nominal terms (rather than appreciate, as would occur in the BEG framework). The implication that the GDP contraction grows nonlinearly with the size of the South(cid:146)s 3

spending shock makes it di¢ cult to achieve progress in reducing government debt. Government debt in the South actually increases in the size of the spending contraction over a three year horizon. The impact on the currency union is exacerbated considerably if (cid:133)scal policy in the North aims to keep government debt stock fromexpanding. Such a policy turns out to be counterproductive, reducing currency union output and lengthening the period in which government debt rises. Our results on the impact of monetary and (cid:133)scal constraints also applies to other shocks, including (cid:133)nancial shocks. A rise in borrowing costs in the South turns out to have small spillover e⁄ects to the North under normal conditions, but can have vastly ampli(cid:133)ed e⁄ects when both monetary and (cid:133)scal policy are constrained. Moreover, reacting to cyclical deterioration in the budget position by tightening (cid:133)scal policy turns out to be counterproductive as long as the economy remains in a liquidity trap: the recession deepens in both South and North, and government budget positions deteriorate further. Anextensiveliteratureonexpansionary(cid:133)scalconsolidationoriginatingwithGiavazziand Pagano (1990) and Alesina and Perotti (1995,1997) has shown that sharp and durable cuts in government expenditure have appeared to boost output under certain conditions. The likelihood of achieving an output expansion is clearly enhanced to the extent that the (cid:133)scal consolidation reduces borrowing spreads. To examine this possibility, we amend our model to let credit spreads depend inversely on the government de(cid:133)cit, and stock of debt (on the premise that private borrowing costs are heavily in(cid:135)uenced by the creditworthiness of the sovereign). In this environment, the adverse impact of (cid:133)scal consolidation in the "Large South" is greatly ameliorated, as are spillover e⁄ects to the North. If the (cid:133)nancial spread is su¢ ciently sensitive to the government debt/de(cid:133)cit, the decline in spreads can even be large 4

enough that the risk-free interest rate actually rises in response to (cid:133)scal consolidation, and output also rises after a few quarters. Under such conditions, the zero bound constraint has no material consequence for the South(cid:146)s GDP response, or for spillover e⁄ects to the North. Taken together, our results suggest that the usual optimal currency area argument suggesting that the e⁄ects of shocks are mitigated to the extent that they are common across member states is not valid in an environment with monetary and (cid:133)scal constraints. As an upshot, coincident cuts in government spending across a large subset of member states (cid:150)the South (cid:150)can have an especially large contractionary e⁄ect if they occur when the monetary authority is likely to be constrained by the ZLB for a substantial period, with large adverse spillover e⁄ects to the North. Even so, while there appear to be substantial bene(cid:133)ts of delaying the implementation of consolidation to a period when monetary policy is no longer constrained for countries that can already borrow on favorable terms, our analysis provides some rationale for aggressive andpreemptive consolidationfor countries that standto reduce borrowing spreads markedly through rapid action. The reminder of the paper is organized as follows. In the next Section, we present the two country open economy model. In Section 3, we discuss how we calibrate and compute the solution of the model under the zero lower bound for nominal interest rates. The results for the benchmark parameterization of the model are reported in Section 4. In Section 5, we assess the sensitivity of the results for alternative parameterizations of the model. Finally, we provide some conclusions in Section 6. 5

2. The Model Our model consists of two country blocks that di⁄er in size, but are otherwise isomorphic. The (cid:133)rst country block is called the (cid:147)South(cid:148), and the second country block the (cid:147)North.(cid:148) The country blocks share a common currency, and monetary policy is conducted by a single central bank. During (cid:147)normal(cid:148)times when the zero bound constraint on policy rates is not binding, the central bank adjusts policy rates in response to the aggregate in(cid:135)ation rate and output gap of the currency union. By contrast, (cid:133)scal policy may di⁄er across the two blocks. Given the isomorphic structure, our exposition below largely focuses on the structure of the South. It is important to recall, however, that di⁄erences in country size translate into di⁄erence in steady state trade shares. Thus, the standard small open economy paradigm emerges as a special case in which the population size of the South is calibrated to be an arbitrarily small fraction of the population of the currency union. Our speci(cid:133)cation of the (cid:133)nancial accelerator channel closely parallels earlier work by Bernanke, Gertler, andGilchrist(1999)andChristiano, Motto, andRostagno(2008). Given that the mechanics underlying the (cid:133)nancial accelerator are well-understood, we simplify our exposition by focusing on a special case of our model which abstracts from a (cid:133)nancial accelerator. We conclude our model description with a brief description of how the model is modi(cid:133)ed to include the (cid:133)nancial accelerator (Section 2.6). 6

2.1. Firms and Price Setting 2.1.1. Production of Domestic Intermediate Goods There is a continuum of di⁄erentiated intermediate goods (indexed by i [0;1]) in the 2 South block, each of which is produced by a single monopolistically competitive (cid:133)rm. In the domestic market, (cid:133)rm i faces a demand function that varies inversely with its output price P (i) and directly with aggregate demand at home Y : Dt Dt (1+(cid:18)p) P Dt (i) (cid:0) (cid:18)p Y (i) = Y ; (1) Dt Dt P (cid:20) Dt (cid:21) where (cid:18) > 0, and P is an aggregate price index de(cid:133)ned below. Similarly, in the North p Dt block, (cid:133)rm i faces the demand function: (1+(cid:18)p) X (i) = P M(cid:3) t (i) (cid:0) (cid:18)p M ; (2) t P t(cid:3) (cid:20) M(cid:3) t (cid:21) where X (i) denotes the quantity demanded of domestic good i in the North block, P (i) t M(cid:3) t denotes the price that (cid:133)rm i sets in the North market, P is the import price index in the M(cid:3) t North, and M is an aggregate of the North(cid:146)s imports (we use an asterisk to denote the t(cid:3) North block(cid:146)s variables). Each producer utilizes capital services K (i) and a labor index L (i) (de(cid:133)ned below) t t to produce its respective output good. The production function is assumed to have a constant-elasticity of substitution (CES) form: (cid:26) 1 (cid:26) 1 1+(cid:26) Y t (i) = ! K 1+(cid:26)K t (i)1+(cid:26) +! L1+(cid:26)(Z t L t (i))1+(cid:26) : (3) (cid:16) (cid:17) Theproductionfunctionexhibitsconstant-returns-to-scaleinbothinputs,andz isacountryt speci(cid:133)c shock to the level of technology. Firms face perfectly competitive factor markets for 7

hiring capital and labor. Thus, each (cid:133)rm chooses K (i) and L (i), taking as given both t t the rental price of capital R and the aggregate wage index W (de(cid:133)ned below). Firms can Kt t costlessly adjust either factor of production, which implies that each (cid:133)rm has an identical marginal cost per unit of output, MC . t We assume that each intermediate goods producer sets the same price P (i) in both Dt blocks of the currency union, implying that P (i) = P (i) and that P = P . The prices M(cid:3) t Dt M(cid:3) t Dt of the intermediate goods are determined by Calvo-style staggered contracts (see Calvo, 1983). Ineachperiod,a(cid:133)rmfacesaconstantprobability,1 (cid:24) ,ofbeingabletoreoptimizeits p (cid:0) price(P (i)). Thisprobabilityofreceivingasignaltoreoptimizeisindependentacross(cid:133)rms Dt and time. If a (cid:133)rm is not allowed to optimize its prices, we follow Christiano, Eichenbaum and Evans (2005) and Smets and Wouters (2003), and assume that the (cid:133)rm must reset its home price by a weighted combination of the lagged and steady state rate of in(cid:135)ation P (i) = (cid:25) (cid:19)p (cid:25)1 (cid:19)pP (i) for the non-optimizing (cid:133)rms. When (cid:19) is set close to unity, this Dt t 1 (cid:0) Dt 1 p (cid:0) (cid:0) formulation introduces structural inertia into the price-setting equation. When a (cid:133)rm i is allowed to reoptimize its price in the domestic market in period t, the (cid:133)rm maximizes j 1 Et (cid:24)j p t;t+j " (cid:25) t+h (cid:0) 1 P Dt (i)Y Dt+j (i) (cid:0) MC t+j Y Dt+j (i) # : (4) j=0 h=1 X Y The operator Et represents the conditional expectation based on the information available to agents at period t. The (cid:133)rm discounts pro(cid:133)ts received at date t+j by the state-contingent discount factor ; for notational simplicity, we have suppressed all of the state indices.2 t;t+j 2 We de(cid:133)ne (cid:24) to be the price in period t of a claim that pays one dollar if the speci(cid:133)ed state occurs t;t+j in period t+j (see the household problem below); then the corresponding element of equals (cid:24) t;t+j t;t+j divided by the probability that the speci(cid:133)ed state will occur. 8

The (cid:133)rst-order condition for setting the contract price of good i in the home market is Et 1 t;t+j (cid:24)j p j h= ( 1 1 (cid:25) + t+ (cid:18) h (cid:0) ) 1 (i) (cid:0) MC t+j Y Dt+j (i) = 0: (5) j=0 Q p ! X 2.1.2. Production of the Domestic Output Index BecausehouseholdshaveidenticalDixit-Stiglitzpreferences, itisconvenienttoassumethata representativeaggregatorcombinesthedi⁄erentiatedintermediateproductsintoacomposite home-produced good Y : Dt 1 1+(cid:18)p 1 Y Dt = Y Dt (i)1+(cid:18)p di : (6) (cid:20)Z0 (cid:21) The aggregator chooses the bundle of goods that minimizes the cost of producing Y , taking Dt the price P (i) of each intermediate good Y (i) as given. The aggregator sells units of Dt Dt each sectoral output index at its unit cost P : Dt 1 (cid:18)p 1 (cid:0) P Dt = P Dt (i)(cid:0)(cid:18)p di : (7) (cid:20)Z0 (cid:21) We also assume a representative aggregator in the foreign economy who combines the di⁄erentiated home products X (i) into a single index for foreign imports: t 1 1+(cid:18)p 1 M t(cid:3) = X t (i)1+(cid:18)p di ; (8) (cid:20)Z0 (cid:21) and sells M at price P : t(cid:3) M(cid:3) t 1 (cid:18)p 1 (cid:0) P M(cid:3) t = P M(cid:3) t (i)(cid:0)(cid:18)p di : (9) (cid:20)Z0 (cid:21) 2.1.3. Production of Consumption and Investment Goods Final consumption goods are produced by a representative consumption goods distributor. This (cid:133)rm combines purchases of domestically-produced goods with imported goods to pro- 9

ducea(cid:133)nalconsumptiongood(C )accordingtoaconstant-returns-to-scaleCESproduction At function: C At = ! C 1+ (cid:26)C (cid:26)CC D 1+ t 1 (cid:26)C +(1 (cid:0) ! C )1+ (cid:26)C (cid:26)C (’ Ct M Ct )1+ 1 (cid:26)C 1+(cid:26) C ; (10) (cid:18) (cid:19) whereC denotestheconsumptiongooddistributor(cid:146)sdemandfortheindexof domestically- Dt produced goods, M denotes the distributor(cid:146)s demand for the index of foreign-produced Ct goods, and ’ re(cid:135)ects costs of adjusting consumption imports. The (cid:133)nal consumption Ct good is used by both households and by the government. The form of the production function mirrors the preferences of households and the government sector over consumption of domestically-produced goods and imports. Accordingly, the quasi-share parameter ! C may be interpreted as determining the preferences of both the private and public sector for domestic relative to foreign consumption goods, or equivalently, the degree of home bias in consumption expenditure. Finally, the adjustment cost term ’ is assumed to take the Ct quadratic form: ’ MCt 2 ’ = 1 MC CDt 1 : (11) Ct 2 (cid:0) 2 M CD C t t (cid:0) 1 1 (cid:0) ! 3 (cid:0) 4 5 This speci(cid:133)cation implies that it is costly to change the proportion of domestic and foreign goods in the aggregate consumption bundle, even though the level of imports may jump costlessly in response to changes in overall consumption demand. Giventhepresenceofadjustmentcosts, therepresentativeconsumptiongoodsdistributor chooses (a contingency plan for) C and M to minimize its discounted expected costs of Dt Ct 10

producing the aggregate consumption good: 1 min Et t;t+k 8(P Dt+k C Dt+k +P Mt+k M Ct+k ) (12) CDt+k;MCt+k X k=0 > > < +P Ct+k C A;t+k (cid:0) ! C 1+ (cid:26)> > : C (cid:26)CC D 1+ t 1 + (cid:26)C k +(1 (cid:0) ! C )1+ (cid:26)C (cid:26)C (’ Ct+k M Ct+k )1+ 1 (cid:26)C 1+(cid:26) C : " #) (cid:18) (cid:19) The distributor sells the (cid:133)nal consumption good to households and the government at a price P , which may be interpreted as the consumption price index (or equivalently, as the Ct shadow cost of producing an additional unit of the consumption good). We model the production of (cid:133)nal investment goods in an analogous manner, although we allow the weight ! in the investment index to di⁄er from that of the weight ! in the I C consumption goods index.3 2.2. Households and Wage Setting We assume a continuum of monopolistically competitive households (indexed on the unit interval), each of which supplies a di⁄erentiated labor service to the intermediate goodsproducing sector (the only producers demanding labor services in our framework). A representative labor aggregator (or (cid:147)employment agency(cid:148)) combines households(cid:146)labor hours in the same proportions as (cid:133)rms would choose. Thus, the aggregator(cid:146)s demand for each household(cid:146)s labor is equal to the sum of (cid:133)rms(cid:146)demands. The aggregate labor index L has t the Dixit-Stiglitz form: 1 1+(cid:18)w 1 L t = ((cid:16)N t (h))1+(cid:18)w dh ; (13) (cid:20)Z0 (cid:21) where(cid:18) > 0 andN (h) is hours workedbyatypical memberof householdh. Theparameter w t (cid:16) is the size of a household of type h, and e⁄ectively determines the size of the population in 3 Notice that the (cid:133)nal investment good is not used by the government. 11

the South. The aggregator minimizes the cost of producing a given amount of the aggregate labor index, taking each household(cid:146)s wage rate W (h) as given, and then sells units of the t labor index to the production sector at their unit cost W : t 1 (cid:18)w 1 (cid:0) W t = W t (h)(cid:18)(cid:0) w dh : (14) (cid:20)Z0 (cid:21) The aggregator(cid:146)s demand for the labor services of a typical member of household h is given by 1+(cid:18)w W t (h) (cid:0) (cid:18)w N (h) = L =(cid:16): (15) t t W (cid:20) t (cid:21) We assume that there are two types of households: households that make intertemporal consumption, labor supply, and capital accumulation decisions in a forward-looking manner by maximizing utility subject to an intertemporal budget constraint (FL households, for (cid:147)forward-looking(cid:148)); and the remainder that simply consume their after-tax disposable income (HM households, for (cid:147)hand-to-mouth(cid:148)households). The latter type receive no capital rental income or pro(cid:133)ts, and choose to set their wage to be the average wage of optimizing households. We denote the share of FL households by & and the share of HM households by 1 &. (cid:0) We consider (cid:133)rst the problem faced by FL households. The utility functional for an optimizing representative member of household h is Et 1 (cid:12)j 1 1 (cid:27) C t O +j (h) (cid:0) {C t O +j 1 (cid:0) (cid:23) ct 1 (cid:0) (cid:27) + (cid:0) j=0 (cid:26) (cid:0) X (cid:0) (cid:1) (cid:31) 0 Z t 1 +(cid:0)j (cid:27) (1 N (h))1 (cid:31) + (cid:22) 0 MB t+j+1 (h) 1 (cid:0) (cid:22) ; (16) t+j (cid:0) 1 (cid:31) (cid:0) 1 (cid:22) P (cid:0) (cid:0) (cid:18) Ct+j (cid:19) ) where the discount factor (cid:12) satis(cid:133)es 0 < (cid:12) < 1: As in Smets and Wouters (2003, 2007), we allow for the possibility of external habit formation in preferences, so that each household 12

member cares about its consumption relative to lagged aggregate consumption per capita of optimizing agents, CO . The period utility function depends on an each member(cid:146)s current t 1 (cid:0) leisure 1 N (h), his end-of-period real money balances, MBt+1(h), and a preference shock, (cid:0) t PCt (cid:23) . The inclusion of money in the model - which is a zero nominal interest asset - provides ct a rationale for the zero lower bound on nominal interest rates in the model. Household h faces a (cid:135)ow budget constraint in period t which states that its combined expenditure on goods and on the net accumulation of (cid:133)nancial assets must equal its disposable income: P CO(h)+P I (h)+MB (h) MB (h)+ (cid:24) B (h) Ct t It t t+1 (cid:0) t s t;t+1 Dt+1 B (h)+P B B + P B(cid:3)t BFt+1(h) B (h) (cid:0) Dt Bt Gt+1 (cid:0) Gt (cid:30) bt R (cid:0) Ft (17) = (1 (cid:28) )W (h)N (h)+(cid:0) (h)+TR (h) T (h)+(1 (cid:28) )R K (h)+ Nt t t t t t Kt Kt t (cid:0) (cid:0) (cid:0) P (cid:28) (cid:14)K (h) P (cid:30) (h): It Kt t Dt It (cid:0) Investment in physical capital augments the per capita capital stock K (h) according to a t+1 linear transition law of the form: K (h) = (1 (cid:14))K (h)+I (h); (18) t+1 t t (cid:0) where (cid:14) is the depreciation rate of capital. Financial asset accumulation of a typical member of FL household h consists of increases in nominal money holdings (MB (h) MB (h)) and the net acquisition of bonds. While t+1 t (cid:0) the domestic (cid:133)nancial market is complete,4 cross-border asset trade is restricted to a single non-state contingent bond issued by the government of the North economy. The terms B and B represents each household member(cid:146)s net purchases of the Gt+1 Ft+1 government bonds issued by the South and North governments, respectively. Each type 4 These contingent claims are in zero net supply from the standpoint of the South as a whole; hence, we omit them from the budget constraint for expositional simplicity. 13

of bond pays one currency unit (e.g., euro) in the subsequent period, and is sold at price (discount) of P and P , respectively. To ensure the stationarity of foreign asset positions, Bt B(cid:3)t we follow Turnovsky (1985) by assuming that domestic households must pay a transaction cost when trading in the foreign bond. The intermediation cost depends on the ratio of economy-wide holdings of net foreign assets to nominal GDP, P Y , and are given by: t t B Ft+1 (cid:30) = exp (cid:30) : (19) bt (cid:0) b P Y (cid:18) (cid:18) t t (cid:19)(cid:19) If the South is an overall net lender position internationally, then a household will earn a lower return on any holdings of foreign (i.e., North) bonds. By contrast, if the South has a net debtor position, a household will pay a higher return on its foreign liabilities. Given that the domestic government bond and foreign bond have the same payo⁄, the price faced P by domestic residents net of the transaction cost is identical, so that P = B(cid:3)t: Bt (cid:30) bt Each member of FL household h earns after-tax labor income, (1 (cid:28) )W (h)N (h), Nt t t (cid:0) where (cid:28) is a stochastic tax on labor income. The household leases capital at the after-tax Nt rental rate (1 (cid:28) )R , where (cid:28) is a stochastic tax on capital income. The household Kt Kt Kt (cid:0) receives a depreciation write-o⁄of P (cid:28) (cid:14) per unit of capital. Each member also receives an It Kt aliquot share (cid:0) (h) of the pro(cid:133)ts of all (cid:133)rms and a lump-sum government transfer, TR (h) t t and pays a lump-sum tax T (h). Following Christiano, Eichenbaum and Evans (2005), we t assume that it is costly to change the level of gross investment from the previous period, so that the acceleration in the capital stock is penalized: 1 (I (h) I (h))2 t t 1 (cid:30) (h) = (cid:30) (cid:0) (cid:0) : (20) It 2 I I (h) t 1 (cid:0) In every period t, each member of FL household h maximizes the utility functional (16) with respect to its consumption, investment, (end-of-period) capital stock, money balances, 14

holdings of contingent claims, and holdings of domestic and foreign bonds, subject to its labor demand function (15), budget constraint (17), and transition equation for capital (18). In doing so, a household takes as given prices, taxes and transfers, and aggregate quantities such as lagged aggregate consumption and the aggregate net foreign asset position. Forward-looking (FL) households set nominal wages in staggered contracts that are analogous to the price contracts described above. In particular, with probability 1 (cid:24) , each w (cid:0) member of a household is allowed to reoptimize its wage contract. If a household is not allowed to optimize its wage rate, we assume each household member resets its wage according to: W (h) = !(cid:19)w !1 (cid:19)wW (h); (21) t t 1 (cid:0) t 1 (cid:0) (cid:0) where ! is the gross nominal wage in(cid:135)ation in period t 1, i.e. W =W , and ! = (cid:25) t 1 t t 1 (cid:0) (cid:0) (cid:0) is the steady state rate of change in the nominal wage (equal to gross price in(cid:135)ation since steady state gross productivity growth is assumed to be unity). Dynamic indexation of this form introduces some element of structural persistence into the wage-setting process. Each member of household h chooses the value of W (h) to maximize its utility functional (16) t subject to these constraints. Finally, we consider the determination of consumption and labor supply of the hand-tomouth (HM) households. A typical member of a HM household simply equates his nominal consumption spending, P CHM (h), to his current after-tax disposable income, which con- Ct t sists of labor income plus net lump-sum transfers from the government: P CHM (h) = (1 (cid:28) )W (h)N (h)+TR (h) T (h): (22) Ct t (cid:0) Nt t t t (cid:0) t The HM households set their wage to be the average wage of the forward-looking house- 15

holds. Since HM households face the same labor demand schedule as the forward-looking households, each HM household works the same number of hours as the average for forwardlooking households. 2.3. Monetary Policy We assume that the central bank follows a Taylor rule for setting the policy rate of the currency union, subject to the zero bound constraint on nominal interest rates. Thus: i = max i;(1 (cid:13) )((cid:25)~ +(cid:13) ((cid:25)~ (cid:25))+(cid:13) x~ )+(cid:13) i (23) t i t (cid:25) t x t i t 1 f(cid:0) (cid:0) (cid:0) (cid:0) g In this equation, i is the quarterly nominal interest rate expressed in deviation from its t steady state value of i. Hence, imposing the zero lower bound then implies that i cannot t fall below i. (cid:25)~ is price in(cid:135)ation rate of the currency union, (cid:25) the in(cid:135)ation target, and x~ t t (cid:0) is the output gap of the currency union. The aggregate in(cid:135)ation and output gap measures are de(cid:133)ned as a GDP-weighted average of the in(cid:135)ation rates and output gaps of the South and North. Finally, the output gap in each member is here de(cid:133)ned as the deviation of actual output from its potential level, where potential is the level of output that would prevail if wages and prices were completely (cid:135)exible. 2.4. Fiscal Policy Government purchases have no direct e⁄ect on the utility of households, nor do they a⁄ect the production function of the private sector. To capture the possibility of implementation lags in spending, we assume that government spending follows an AR(2) process as in Uhlig 16

(2009): g g = (cid:26) (g g ) (cid:26) g +" ; (24) t (cid:0) t (cid:0) 1 g1 t (cid:0) 1 (cid:0) t (cid:0) 2 (cid:0) g2 t (cid:0) 1 g;t The government does not need to balance its budget each period, and issues nominal debt to (cid:133)nance its de(cid:133)cits according to: P B B = P G +TR T (cid:28) W L ((cid:28) R (cid:14)P )K Bt Gt+1 Gt Ct t t t Nt t t Kt Kt It t (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (25) (MB MB ): t+1 t (cid:0) (cid:0) Equation (25) aggregates the capital stock, money and bond holdings, and transfers and 1 taxes over all households so that, for example, T = (cid:16) T (h)dh. The capital tax (cid:28) is t t 0 t Kt R assumed to be (cid:133)xed, and the ratio of real transfers to (trend) GDP, tr = TRt, is also (cid:133)xed. t PtY Given that the central bank uses the nominal interest rate as its policy instrument, the level of seigniorage revenues are determined by nominal money demand. The distortionary tax on labor income (cid:28) adjusts in response to both the debt/GDP Nt ratio, b , and to the total government de(cid:133)cit, b b : Gt+1 Gt+1 Gt (cid:0) (cid:28) = (cid:23) (cid:28) +(cid:23) (b b )+(cid:23) (b b ); (26) Nt 0 N;t 1 1 Gt+1 G 2 Gt+1 Gt (cid:0) (cid:0) (cid:0) where b = BGt+1 and b is the government(cid:146)s target value for the ratio of government Gt+1 PtY G debt to nominal (trend) output. 2.5. Resource Constraint and Net Foreign Assets The domestic economy(cid:146)s aggregate resource constraint can be written as: Y = C +I +(cid:30) ; (27) Dt Dt Dt It 17

where (cid:30) is the adjustment cost on investment aggregated across all households. The (cid:133)nal It consumption good is allocated between households and the government: C = C +G ; (28) At t t where C is total private consumption of FL (optimizing) and HM households: t C = CO +CHM: (29) t t t Totalexportsmaybeallocatedtoeithertheconsumptionortheinvestmentsectorabroad: M = M +M : (30) t(cid:3) C(cid:3)t I(cid:3)t Finally, at the level of the individual (cid:133)rm: Y (i) = Y (i)+X (i) i: (31) t Dt t 8 The evolution of net foreign assets can be expressed as: P B B(cid:3);t F;t+1 = B +P M P M : (32) (cid:30) F;t M(cid:3) t t(cid:3) (cid:0) Mt t bt This expression can be derived from the budget constraint of the FL households after imposing the government budget constraint, the consumption rule of the HM households, the de(cid:133)nition of (cid:133)rm pro(cid:133)ts, and the condition that domestic bonds (B ) are in zero net Dt+1 supply. Finally, we assume that the structure of the foreign country (the North) is isomorphic to that of the home country (the South). 2.6. Production of capital services We incorporate a (cid:133)nancial accelerator mechanism into both country blocks of our benchmark model following the basic approach of Bernanke, Gertler and Gilchrist (1999). Thus, 18

the intermediate goods producers rent capital services from entrepeneurs (at the price R ) Kt rather than directly from households. Entrepeneurs purchase capital from competitive capital goods producers, with the latter employing the same technology to transform investment goods into (cid:133)nished capital goods as described by equations 18) and 20). To (cid:133)nance the acquisition of physical capital, each entrepreneur combines his net worth with a loan from a bank, for which the entrepreneur must pay an external (cid:133)nance premium (over the risk-free interestratesetbythecentralbank)duetoanagencyproblem. WefollowChristiano,Motto and Rostagno (2008) by assuming that the debt contract between entrepreneurs and banks is written in nominal terms (rather than real terms as in Bernanke, Gertler and Gilchrist, 1999). Banks obtain funds to lend to the entrepreneurs by issuing deposits to households at the interest rate set by the central bank. By assuming perfect competition and free entry among banks and that all bank portfolios are well diversi(cid:133)ed (i.e., that each bank lends out to a continuum of entrepreneurs, whose default risk is independently distributed), it follows that banks make zero pro(cid:133)ts in each state of the economy and that there is no credit risk to households associated with bank deposits.5 3. Solution Method and Calibration To analyze the behavior of the model, we log-linearize the model(cid:146)s equations around the non-stochastic steady state. Nominal variables are rendered stationary by suitable transformations. To solve the unconstrained version of the model, we compute the reduced-form solution of the model for a given set of parameters using the numerical algorithm of Ander- 5 We refer to Bernanke, Gertler and Gilchrist (1999) and Christiano, Motto and Rostagno (2008) for further details. An excellent exposition is also provided in Christiano, Trabandt and Walentin (2007). 19

son and Moore (1985), which provides an e¢ cient implementation of the solution method proposedbyBlanchardandKahn(1980). Whenwesolvethemodelsubjecttothenon-linear monetary policy rule (23), we use the techniques described in Hebden, LindØ and Svensson (2009). An important feature of the Hebden, LindØ and Svensson algorithm is that the duration of the liquidity trap is endogenous, and is a⁄ected by shocks hitting the model economy. The model is calibrated at a quarterly frequency. Structural parameters are set at identical values for each of the two country blocks, except for the parameter (cid:16) determining population size (as discussed below), and the parameters determining trade shares. We assume that the discount factor (cid:12) = 0:995, consistent with a steady-state annualized real interest rate r of 2 percent. By assuming that gross in(cid:135)ation (cid:25) = 1:005 (i.e. a net in(cid:135)ation of 2 percent in annualized terms), the implied steady state nominal interest rate i = equals 0:01 at a quarterly rate, and 4 percent at an annualized rate. The utility functional parameter (cid:27) is set equal to 2, while the parameter determining the degree of habit persistence in consumption { = 0:8. We set (cid:31) = 4, implying a Frisch elasticity of labor supply of 1/2, which is roughly consistent with the evidence reported by Domeij and FlodØn (2006). The utility parameter (cid:31) is set so that employment comprises 0 one-third of the household(cid:146)s time endowment, while the parameter (cid:22) on the subutility 0 function for real balances is set at an arbitrarily low value (given the separable speci(cid:133)cation, variation in real balances has no impact on other variables). We choose & = 0:25 so that 75 percent of households are Ricardian FL agents. This share implies that consumption of HM households equals about 10 percent of total consumption in steady state. The lower share of total consumption re(cid:135)ects that HM households consume less on average than FL households 20

as they are assumed not to save and accumulate any capital. The depreciation rate of capital (cid:14) is set at 0.025. (consistent with an annual depreciation rate of 10 percent). The parameter (cid:26) in the CES production function of the intermediate goods producers is set to 2. This implies an elasticity of substitution between capital and (cid:0) labor, (1+(cid:26))=(cid:26), of 1/2, somewhat below the unity elasticity implied by the Cobb-Douglas speci(cid:133)cation. The quasi-capital share parameter ! (cid:150)together with the price markup pa- K rameter of (cid:18) = 0:20 is chosen to imply a steady state investment to output ratio of 20 P percent. We set the cost of adjusting investment parameter (cid:30) = 3, slightly below the value I estimated by Christiano, Eichenbaum and Evans (2005). The calibration of the parameters determining the (cid:133)nancial accelerator follows Bernanke, Gertler and Gilchrist (1999), and is identical across country blocks. In particular, the monitoring cost, (cid:22), expressed as a proportion of entrepreneurs(cid:146)total gross revenue, is set to 0:12. The default rate of entrepeneurs is 3 percent per year, and the variance of the idiosyncratic productivity shocks to entrepreneurs is 0:28: We maintain the assumption of a relatively (cid:135)at Phillips curve by setting the price contract duration parameter (cid:24) = 0:9. We allow for some intrinsic persistence by setting the p price indexation parameter (cid:19) = 0:65. It bears emphasizing that our choice of (cid:24) does not p p necessarily imply an average price contract duration of 10 quarters. Altig et al. (2010) show that even a model with a low slope of the Phillips curve can be consistent with frequent price reoptimization. Our choice of (cid:24) implies a Phillips curve slope of about 0:007. This is p somewhat lower than the median estimates of literature, which cluster in the range of about 0.009-.014, but well within standard con(cid:133)dence intervals provided by empirical studies (see e.g. Adolfson et al (2005), Altig et al. (2010), Gal(cid:237) and Gertler (1999), Gal(cid:237), Gertler, and 21

L(cid:243)pez-Salido(2001), LindØ (2005), andSmets andWouters (2003; 2007). As arguedinErceg and LindØ (2010), a low slope of the Phillips curve is consistent with the development during the recent crisis where in(cid:135)ation and in(cid:135)ation expectations have fallen very moderately despite large contractions in output. Given strategic complementarities in wage-setting across households, the wage markup in(cid:135)uences the slope of the wage Phillips curve. Our choices of a wage markup of (cid:18) = W 1=3 and a wage contract duration parameter of (cid:24) = 0:85 along with a wage indexation w (cid:0) parameterof (cid:19) = 0:65 -implythatwagein(cid:135)ationisaboutasresponsivetothewagemarkup w as price in(cid:135)ation is to the price markup. The parameters pertaining to (cid:133)scal policy are set as follows. The share of government spending of total expenditure is set equal to 20 percent. The government debt to GDP ratio, b , is set to 0:75, about equal to the average level of debt in euro area countries at end-2008. G The lump-sum tax revenue to GDP ratio is set to a small value of 0.02. Given that the capital tax (cid:28) is set to zero, the government(cid:146)s intertemporal budget constraint implies that K the labor income tax rate (cid:28) equals 0:27 in steady state. N Using Eurostat data for 2008, the average share of imports of the South countries (of Greece, Ireland, Portugal, Italy, and Spain) from the remaining countries of the euro area comprised about 14 percent of GDP in 2008. This pins down the trade share parameters ! and ! for our large South calibration under the additional assumption that the import C I intensity of consumption is equal to 3/4 that of investment. These South countries comprise about 1/3 of euro area GDP, or are half as large as the North countries, so that (cid:16) = 0:5. Given that trade is balanced in steady state, this parameterization implies an export and import share of the North countries of 7 percent of GDP. 22

Our small South calibration is based on data for the Greek economy. The import share of the Greek economy from the rest of the euro area is also around 14 percent, so that the trade parameters ! and ! remain unchanged across these calibrations; however, since Greece C I only comprises about 2 percent of euro area GDP, we adjust (cid:16) so that its trade share of the North block is only about 0.3 percent. We assume that (cid:26) = (cid:26) = 2, consistent with a long-run price elasticity of demand for C I importedconsumptionandinvestmentgoodsof1.5. Whilethisishigherthanmostempirical estimates using macro data, the presence of adjustment costs reduces the near-term relative price sensitivity. In particular, we set the adjustment cost parameters ’ = ’ = 3, MC MI implying a half-life of adjustment of about half a year. We choose a small value (0.00001) for the (cid:133)nancial intermediation cost (cid:30) , which is su¢ cient to ensure the model has a unique b steady state. We set the parameters of the monetary rule so that (cid:13) = 1:5, (cid:13) = 0:125, and (cid:13) = (cid:25) x i 0:7. Relative to the standard Taylor rule, this rule is more aggressive in responding to in(cid:135)ation, and incorporates considerable interest rate inertia; these features seem a relevant characterization of ECB monetary policy. For the tax rate reaction function, we choose (cid:23) = 0:9, (cid:23) = 0:02, (cid:23) = 0:05. This benchmark tax rule is not very aggressive, and has 0 1 2 similar implications to adjustment via lump-sum taxes in the short to medium-run. 4. Results Given the nonlinear zero bound constraint, the e⁄ects of shocks depend on the perceived depth and duration of the underlying liquidity trap. Accordingly, we begin by using our 23

model to generate initial macroeconomic conditions that roughly capture some features of the recent recession in the euro area, including a large decline in output relative to trend, and extended period of near-zero policy rates. The solid lines in Figure 1 depict a (cid:147)Euro area recession scenario (cid:148)under the benchmark calibration of our model when the zero lower bound is imposed on the policy rule. The underlying shocks are identical negative consumption taste shocks ((cid:23) and (cid:23) ) to each C;t (cid:3)C;t country block. The taste shocks are assumed to follow an AR(1) with persistence of 0.9, and sincetheparameterizationiscompletelysymmetricandwemaketheassumptionof producer currency pricing, the e⁄ects on both the South and the North is completely symmetric. For comparison purposes, we also include results in Figure 1 when policy is not constrained by the zero lower bound. The shocks induceasharpcontractioninaggregateGDPof about 6 percent belowsteady state at its peak, compared with a 4 percent decline that would occur if policy was unconstrained by the zero bound. In the constrained case, policy rates fall quickly to their lower bound of zero, and remain at zero for eight quarters (in this (cid:133)gure, nominal variables are shown in levels to highlight the zero bound constraint on interest rates). Thus, given perfect foresight, agents expect the liquidity trap would last eight quarters in the absence of additional shocks. In(cid:135)ation falls from its steady state level of 2 percent to a trough of -1 percent, and remains below zero for a sustained period. 4.1. Fiscal Consolidation in the South We begin by assessing the impact of a front-loaded contraction in government spending in the South under the Small South calibration, which approximates the e⁄ects on a small open 24

economy. The government spending shock follows an AR(1) with a persistence of 0.99 and is scaled to equal one percent of steady state GDP. The impulse response functions shown in Figure 2 are computed as the di⁄erence between this scenario which includes both the consumption taste shocks and government spending shock, and the previous scenario with only the taste shocks to each country (shown in Figure 1). Under normal conditions in which monetary policy can react (labeled (cid:147)currency union: normal(cid:148)), the nearly permanent contraction in government spending has a substantial and highly persistent e⁄ect on the South(cid:146)s GDP. The South(cid:146)s output falls about 1 percent initially, consistent with an impact multiplier of about unity, and remains below baseline for a very prolonged period. The protracted output decline re(cid:135)ects that the monetary policy essentially leaves nominal interest rates unchanged in response to the South(cid:146)s output decline given its tiny weight in aggregate GDP (the policy rate falls only 1 basis point). With in(cid:135)ation falling, real interest rates rise in the short-run in the South. Output gradually recoversasprivateconsumptionisboostedthroughapositivewealthe⁄ect, therealexchange rate gradually depreciates as prices fall, and the real interest rate declines (re(cid:135)ecting that prices overshoot, and eventually start rising again). It is useful to contrast the protracted output decline under a currency union with the alternative in which the South had an independent monetary policy and (cid:135)exible exchange rate, again assuming that monetary policy can react (labeled (cid:147)(cid:135)exible exchange rate: normal(cid:148)). In this case, interest rates would drop immediately, and the real exchange rate would depreciate, substantially reducing the persistence of the GDP contraction in the South. For example, the South(cid:146)s GDP is only 0.3 percent below baseline after 2 years, compared with 0.7 percent in the currency union case. The faster output rebound also allows the spending 25

reduction to translate into a much more rapid decline in the government debt/GDP ratio. The contraction in the South under a currency union is invariant to whether monetary policyisconstrainedorunconstrainedbytheZLB(asseenbycomparingthetwocasesshown in Figure 2). As discussed below, this re(cid:135)ects that shocks to a small country have a tiny e⁄ect on the potential real interest rate in the currency union as a whole, and do not a⁄ect the duration of the liquidity trap in the union. Figure 3 presents a parallel analysis for the case of the Large South calibration. Under (cid:147)normal conditions(cid:148)in which monetary policy is unconstrained, the output response under a currency union is much less persistent than for the Small South calibration analyzed in Figure 2. This re(cid:135)ects that the monetary authority reduces interest rates considerably in the case of a concerted (cid:133)scal contraction. The speed of the recovery in GDP still isn(cid:146)t as rapid as would occur if the Large South(cid:146)s exchange rate was (cid:135)exible, re(cid:135)ecting that interest rates fall by somewhat less, and the real exchange rate depreciates gradually rather than immediately (comparing the (cid:147)(cid:135)exible exchange rate: normal(cid:148)with the (cid:147)currency union: normal(cid:148)calibrations); nevertheless, the disparity is relatively modest. Thus, as familiar from a standard optimal currency area rationale, a small country such as Portugal would be better o⁄ if it cut spending at the same time as Italy and Belgium. Moreover, GDP in the North actually rises, as the stimulative e⁄ect of lower interest rates outweighs the contractionary impact of the fall in exports to the South; and the government debt/GDP ratio falls a bit. Wenowturntothecaseinwhichthecurrencyunionisconstrainedfromreducinginterest ratesduetothezerolowerboundonnominalinterestrates((cid:147)currencyunion: ZLB(cid:148)inFigure 3). In this case, the South(cid:146)s GDP shows a much more protracted contraction than under 26

normal times, with output remaining close to 1 percent below baseline for six quarters. The prolongedoutputdeclinere(cid:135)ectsthatthesluggishreactionofpolicyratescausesrealinterest rate to rise for a period of about two years. GDP in the North contracts by 0.3 percent at trough, in striking contrast to the case in which monetary policy adjusts. The GDP decline in the North re(cid:135)ects that the fall in the North(cid:146)s real net exports to the South is reinforced by a rise in the North(cid:146)s real interest rates. The highly persistent decline in the North(cid:146)s GDP induces the North(cid:146)s government debt/GDP ratio to rise by almost 0.7 percent of GDP after two years. Our (cid:133)nding that (cid:133)scal multipliers are enhanced in a liquidity trap relative to normal conditions is consistent with the empirical VAR panel evidence provided by Corsetti, M(cid:252)ller and Meier (2010), who argues that (cid:133)scal contractions have more negative e⁄ects on output in crisis periods. Figure4considersthee⁄ectsofagovernmentspendingcontractionofprogressivelylarger magnitude in the South, ranging from 1 percent of the South(cid:146)s GDP (as in Figure 3) to 3 percent. The response of both the South and North(cid:146)s GDP increases in a nonlinear fashion with the size of the spending cuts, implying an increasing marginal impact. Thus, cutting reducing South spending by 2 percent of GDP reduces South output by a little more than 2 percent, and North output by about 1 percent; by an additional spending cut of 1 percent of GDP has almost as large a depressing impact on both the South(cid:146)s and North(cid:146)s output. The increasing marginal impact parallels the analysis of a (cid:133)scal expansion in the closed economy analysis of Erceg and Linde (2010), except with the reverse sign. In the Erceg and Linde analysis, a (cid:133)scal expansion has a diminished marginal impact on output as the size of the expansion grows larger. Because (cid:133)scal stimulus shrinks the duration of the liquidity trap, monetary policy responds relatively more quickly to any incremental stimulus. In the 27

simulations shown in Figure 4, the 3 percent (cid:133)scal contraction in the South extends the duration of the currency union(cid:146)s liquidity trap by two quarters, compared with the eight quarter trap for a 1 percent of GDP consolidation. This increases the multiplier, in part because the expected in(cid:135)ation response is sensitive to the duration of the trap (falling more as the trap lengthens). Given that the 3 percent of GDP output decline in the South translates into a 1 percent declineingovernmentspendingasafractionofcurrencyunionoutput, theimpliedmultiplier fortheunionasawholeisabout2(asseenfromtheaggregatecurrencyunionoutputresponse in Figure 4). Because the North comprises 2/3 of currency union output, the contraction in the North actually accounts for almost half of the aggregate output decline in the currency union. The more adverse impact on output means that it is di¢ cult for a (cid:133)scal consolidation to achieve progress in reducing the government debt. Figure 4 shows that the South(cid:146)s government debt actually rises by more at horizons of up to 1-1/2 years as spending is cut by larger amounts. Government debt in the North countries rises by almost 3 percent of GDP. Progress in reducing government debt only becomes apparent once monetary policy has latitude to reduce interest rates. There is clearly a high value in a discretionary (cid:133)scal expansion in the North to help o⁄set (cid:133)scal contraction in the South. Even so, it is possible that (cid:133)scal policy in the North may be aimed at keeping the government debt stock from expanding through balanced budget rules that adjust spending or taxes very aggressively to keep debt near its target. In Figure 5, we proxy for such a rule by examining the impact of a spending cut in the North block that is similar in magnitude to that in the South. This policy turns out to be counterproductive by 28

further reducing currency union output, and by extending the period over which government debt rises (due to the (cid:133)scal consolidation in North and South) to more than 2 years. 4.2. Financial Shock in the South Wenextconsiderthee⁄ectsofa(cid:133)nancialshockintheSouth. Inourlog-linearizedframework, the(cid:133)nancialacceleratormechanisminourmodelimpliesthatthecorporate(cid:133)nancepremium in each country depends on the degree of leverage of the non-(cid:133)nancial corporate sector, plus an exogenous disturbance. Thus, for the South: icorp = i +#l +" : (33) t t t t where icorp i is the spread of the nominal corporate bond rate over the policy rate, l is the t t t (cid:0) leverage ratio (the ratio of the value of the capital stock to the net worth of entrepreneurs), and " is an exogenous (cid:133)nancial spread shock. A similar relation holds for the North. t To examine the implications of the zero bound constraint, we construct initial conditions for both the (cid:147)Small South(cid:148)and (cid:147)Large South(cid:148)calibrations that produce identical macroeconomic e⁄ects as those depicted in Figure 1. In particular, the same adverse taste shock in each country causes output to decline substantially, and generates a liquidity trap lasting 8 quarters. Figure 6 shows the e⁄ects of a (cid:133)nancial shock in the South that causes (cid:133)nancial spreads to rise persistently (i.e., with a root of 0.99) by around 50 basis points under our (cid:147)Small South(cid:148)calibration. The spread shock reduces the South(cid:146)s output by boosting the cost of capital. Under normal conditions in which monetary policy is unconstrained, output falls more sharply under a currency union (dash-dotted red lines) than it would if the South had 29

an independent monetary policy (solid black lines). In the context of a currency union, it makes little di⁄erence whether the ZLB binds monetary policy given the small size of the South. Figure 7 shows the e⁄ects of the same-sized (cid:133)nancial shock in the South under our (cid:147)Large South(cid:148)calibration. In a currency union unconstrained by the ZLB, the (cid:133)nancial shock depresses the South(cid:146)s output much less sharply than in the small open economy case, re(cid:135)ecting a much larger induced decline in policy rates. The more accommodative policy stance causes output in the North to expand slightly. Paralleling our previous analysis of the (cid:133)scal shock, the e⁄ects on the South are dramatically di⁄erent when monetary policy is constrained by the ZLB (dashed green lines). The South(cid:146)s output contracts more persistently and by a greater degree, and the spillover e⁄ect to the North are sizeable. In particular, given that the North is twice the size of the South, almost half of the decline in currency union output is attributable to the fall in the North(cid:146)s output. The output declines result in a rise in government debt in North and South that is substantially larger than in normal times. Figure 8 analyzes (cid:133)nancial shocks to the Large South of varying size, ranging from the 50 basis point increase (from Figure 7) to 150 basis points. The e⁄ects on output in both the South and North increase in a nonlinear manner, again re(cid:135)ecting that large shocks extend the duration over which monetary policy is constrained to respond to the ZLB. The 150 basis point shock raises the South(cid:146)s government debt by 6 percentage points after two years, and by almost half as much in the North. Finally, Figure 9 examines the case in which a 50 basis point rise in spreads in the Large South is ampli(cid:133)ed by (cid:133)scal consolidation in the South. Given the ZLB, the (cid:133)scal 30

consolidation in the South (cid:150)equal to 1 percent of GDP (cid:150)results in a much more sizeable output decline in both South and North (the red dotted lines) than if (cid:133)scal policy simply followed the non-aggressive rule implied by our benchmark calibration (the solid black lines). Moreover, in addition to restraining aggregate currency union output, (cid:133)scal consolidation boosts government debt in both the South and North for roughly two years relative to the case of no (additional) (cid:133)scal response. 5. Sensitivity Analysis In this section, we examine the robustness of the results for alternative parameterizations of the model. We begin by showing that the e⁄ects of a government spending cut on output in a liquidity trap can be mitigated considerably by an aggressive tax rule that rapidly reduces labor tax rates. Second, we show that government spending cuts have much smaller contractionary e⁄ects on output in a liquidity trap when they are implemented gradually, and that gradual cuts induce a faster improvement in the government debt/GDP ratio than a front-loaded spending reduction. While these simulations show how the contractionary e⁄ects of government spending cuts on output may be mitigated, we next explore conditions suggested by the literature on "expansionary (cid:133)scal consolidations(cid:148)following Giavazzi and Pagano (1990) and Alesina and Perotti (1995, 1997). In particular, we show that a (cid:133)scal cut can expand output even in the near-term for a country facing unfavorable initial borrowing conditions provided that interest rate spreads are su¢ ciently responsive to lower future expected debt and de(cid:133)cits levels. Finally, we conclude by examining the sensitivity of our results to a key parameter determining the share of hand-to-mouth households. 31

5.1. Labor-income tax rule Under our benchmark calibration, the labor-income tax rule is largely unresponsive to the evolution to government debt and de(cid:133)cits. We now assess the e⁄ects of a government spendingcut underamore aggressive taxrule withcoe¢ cients (cid:23) and(cid:23) that are tentimes as high 1 2 in the benchmark calibration (i.e. we set (cid:23) = 0:2 and (cid:23) = 0:5 in equation 26). A more 1 2 aggressive tax rule in normal times would cushion the output e⁄ects of (cid:133)scal contraction, as the more rapid fall in taxes eventually raises potential output by boosting labor supply and capital spending. The results of Eggertsson (2009), however, suggest that such e⁄ects might not obtain when the economy is constrained by the ZLB. In particular, Eggertsson (2009) shows in the context of a stylized New Keynesian model that a tax cut actually decreases output when the economy is in a liquidity trap. Figure 10 compares the e⁄ects of a persistent cut in government consumption in the large South calibration of the model under both the benchmark ((cid:147)unresponsive(cid:148)) and more aggressive labor income tax rule (under normal conditions and for an 8 quarter liquidity trap). As expected, the more aggressive tax rule damps the fall in the South(cid:146)s GDP under normal conditions. However, the disparity between the tax rules is much larger when the economy is in a liquidity trap, with the fall in the South(cid:146)s GDP only about half as large after 2-3 years under the aggressive rule as under our benchmark. The GDP response under the aggressive rule in a liquidity trap is in fact only a bit more negative than under normal conditions. This re(cid:135)ects that the promise of near-term tax cuts provides a strong impetus to domestic demand, and mitigates the sharp fall in the potential real rate that occurs in response to an immediate spending cut. As a result, monetary policy would not cut interest 32

rates much even if unconstrained, so the ZLB constraint has a comparatively small impact. The smaller output e⁄ects on the South under the aggressive tax rule imply much smaller spillover e⁄ects to the North. Clearly, aggressive tax adjustment implies less longer-term improvement in government debt, andthusmaynotbeanappealingoptiontogovernmentswhichaimtomarkedlyreduce thelonger-rundebtstock. Evenso, ouranalysisshowsthatpolicieswhichreducegovernment spending in a liquidity trap can have much more modest e⁄ects on output when combined withaggressivetax-cutting. Themaindi⁄erencebetweenourresultsandEggertsson(cid:146)sisthat thelatterconsidersthee⁄ectsofafront-loadedtemporarytaxcutinanenvironmentwithout saving or investment possiblities. Because the tax cut has a positive front-loaded e⁄ect on potential output, it raises desired saving, and hence reduces the potential real interest rate (in contrast to our aggressive tax rule, which o⁄sets some of the fall in the potential real interest rate arising from the spending decline). Given that the economy is in a liquidity trap, the lower potential real interest rate causes output to decline in Eggertsson(cid:146)s model: the larger gap between the actual real interest rate (which rises due to a fall in expected in(cid:135)ation) and the potential real interest rate more than o⁄sets the stimulative e⁄ect of the tax cut on potential output. 5.2. Aggressiveness of spending cut Figure 11 compares the e⁄ects of a gradual reduction in government spending to our benchmark case in which government spending is cut immediately. In the former case, the maximum decline in spending (cid:150)of 1 percent of GDP (cid:150)occurs after about 5 years (the (cid:147)gradual cut(cid:148)case in the (cid:133)gure). This gradual decline in spending is achieved by adjusting (cid:26) .and (cid:26) g1 g2 33

in equation 24) to ensure that the undiscounted net present value of the spending cut, i.e. (cid:6) g , equals the spending cut under the benchmark calibration. The path of government 1t=0 t spending is in all cases assumed to be fully credible upon announcement of the consolidation. We also examine the e⁄ects of a concerted spending cut in all members of the currency union (cid:150)both North and South (cid:150)in order to emphasize the crucial role of the path of spending when monetary policy is constrained by the ZLB. From Figure 11, it is clear that a more gradual spending cut induces a much slower improvement in the government debt to GDP ratio than a front-loaded cut in normal times. By contrast, the government debt/GDP ratio actually improves much more rapidly in the caseofthegradualspendingcutwhentheeconomyisinaliquiditytrap! Thisratherstartling implication re(cid:135)ects that the more gradual spending cut tends to greatly reduce the fall in the potential real interest rate that occurs in response to (cid:133)scal consolidation compared with the case of an immediate cut. Intuitively, the expectation that government spending will be low in the future helps crowd in private demand even holding the interest rate constant. Thus, because the central bank would not adjust interest rates very much even if unconstrained (the (cid:147)gradual cut: normal(cid:148)case), the output response in a liquidity trap isn(cid:146)t much di⁄erent than in normal times. This contrasts sharply to the large di⁄erences in normal times and times of a liquidity trap for a front-loaded cut. Our analysis of how a gradual spending cut mitigates e⁄ects on output and induces a quickerimprovementinthegovernmentdebtisessentiallythe(cid:147)mirrorimage(cid:148)oftheresultsof ErcegandLindØ(2010)andWoodford(2010). Theseauthorsshowhowlagsinimplementing (cid:133)scal stimulus plans in a liquidity trap can markedly dampen the multiplier. 34

5.3. Endogeneous Risk Premium In the benchmark calibration of the model, we assumed that interest rates faced by the government and banks in South and North were equal to the currency area interest rate set by the central bank (notwithstanding a tiny di⁄erence to imply stationary dynamics). To examine conditions under which (cid:133)scal consolidation may be expansionary, we amend our model and instead assume that the interest rate faced by the government and banks in the South equals the interest rate set by the central bank plus a risk-spread that depends positively on the government de(cid:133)cit and debt level. If we let iS denote the interest rate in t South, we thus have iS i = (b b )+ (b b ); (34) t (cid:0) t b Gt+1 (cid:0) G d Gt+1 (cid:0) Gt where we recall that b is the end-of-period t government debt level and i the interest Gt+1 t rate set by the central bank. The speci(cid:133)cation in (34) is motivated by the spread equation estimated by Laubach (2010) for the Euro area, and captures the idea that countries with high government de(cid:133)cits and debt levels face higher spreads due to a higher risk of default. There is a substantial empirical literature that has examined the question of whether higher de(cid:133)cits and debt lead to increasing interest rates, but it has provided at best mixed evidence in favor of positive values of and , see e.g. Evans (1985, 1987). However, the papers in b d this literature have typically used data from both crisis periods and non-crisis periods, and asarguedbyLaubach(2010)basedoncross-countryevidence, this islikelytobiasdownward the estimates, as the parameters tend to be close to zero in non-crisis periods and positive in crisis periods only. As we are examining the e⁄ects of (cid:133)scal consolidations in crisis periods, we entertain the assumption that and are both positive. b d 35

As a tentative calibration, we set = 0:05 and = 0:10, implying that a one percent b d decline in government debt decreases the spread by 5 basis points, and that a one percent declineinthebudgetde(cid:133)citdecreasesthespreadwith10basispoints. Whiletheseelasticities are somewhat on the upper side relative to the evidence reported by Laubach (2010), they are nevertheless useful to help gauge the potential implications of this channel. In Figure 12, we report the results of this experiment. The model where interest rates spreads for South is given by (34) is referred to as (cid:147)Endo Spread(cid:148)in the model, and the benchmark model is referred to as the (cid:147)No Endo Spread(cid:148). From the (cid:133)gure, it is clear that the existence of strong risk spreads has the potential of generating much more favorable e⁄ects on output and government debt, even when the economy is in a deep liquidity trap. Under our calibration for the endogenous risk spread, we (cid:133)nd that output in South expands after only a little more than a year, which stands in sharp contrast to the model without the endogenous risk premium in (34) which output in the South contracts for more than 5-years in response to the same spending cut. The stark di⁄erence in results is driven by the large andpersistentdeclineinthespreadongovernmentbondsinSouth,iS i , whichisvisualized t (cid:0) t in the lower right panel in Figure 12. The spread declines by more than 200 basis points, and the key parameter behind the persistent decline is the , as this parameter implies that b the government spread will be closely tied to the persistent decline in the government debt level. 5.4. Share of HM households In Figure 13, we examine the sensitivity of our results to the share of hand-to-mouth (HM) agents, considering both a cut in government spending in the South alone, and a coordinated 36

cut in both North and South. In our model, a higher value of & is crucial for generating a initial decline in private consumption after a contraction in government spending in normal times. Under the benchmark calibration of the model, we used & = 0:25 so that 75 percent of households are Ricardian agents. Although not shown, our benchmark calibration of & implies that the model generates an initial decline in private consumption following a contraction in government spending. In Figure 13, we consider varying & between 0 and 0:50. & = 0:50 implies that consumption of HM households equals about 21 percent of total consumption (recalling that our benchmark calibration of & = 0:25 implies a share of 0.11). As seen from Figure 13, the results for a non-coordinated cut are not very sensitive to the share of HM households, but the results for a coordinated cut in government expenditures are rather sensitive to the share of HM households. This is due to the fact that a larger share of HM households in the model implies a larger decline in the potential real interest rate in response to a coordinated spending cut, which extends the duration of the liquidity trap considerably. In particular, the liquidity trap is extended from 8 to 11 quarters, and the marginal impact of an extra decrease in spending is hence larger (as in Figure 4) when & is higher. Erceg and LindØ (2010) also provide a detailed discussion of how the presence of HM agents a⁄ects the (cid:133)scal multiplier through this channel. 6. Conclusions Our analysis has shown that the usual optimal currency area argument suggesting that the e⁄ects of shocks are mitigated to the extent that they are common across member states is not valid in an environment with monetary and (cid:133)scal constraints. Coincident cuts in 37

government spending across a large subset of member states can have an especially large contractionary e⁄ect if they occur when the monetary authority is likely to be constrained by the ZLB for a substantial period, with large adverse spillover e⁄ects to other member states. Accordingly, there appear to be substantial bene(cid:133)ts of delaying the implementation of consolidation to a period when monetary policy is no longer constrained for countries that can already borrow on favorable terms. Ina liquidity trap, progress inreducing government debt is actually faster when spending cuts are implemented gradually, re(cid:135)ecting a less contractionary near-term impact on output. Evenso,ouranalysisdoesprovidesomerationaleforaggressiveandpreemptiveconsolidation for countries that stand to reduce borrowing spreads markedly through rapid action. The framework adopted in this paper has the limitation that the currency union as a whole is modeled as a closed economy. Thus, it does not allow for the possibility that the e⁄ects of (cid:133)scal consolidation could be assuaged by currency depreciation. Clearly, it would be of interest to extend our analysis to a three country framework. In addition, we solve our model under the assumption of perfect foresight, and thus abstract from the e⁄ects of future shockuncertaintyonprivate sectorbehavior. Auseful extensionwouldinvolve incorporating the e⁄ects of shock uncertainty into the analysis along the lines suggested by Adam and Billi (2008). 38

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Figure 1: Baseline Scenario When Monetary Policy is Unconstrained and Subject to the Zero Lower Bound South: Nominal Interest Rat e ( A P R ) 3 2 1 0 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Nominal Interest Rate (APR) 3 2 1 0 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Real Interest Rate (APR) 3 2 1 0 −1 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Real Interest Rate (APR) 3 2 1 0 −1 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: CPI Inflation (APR) 1 0 −1 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: CPI Inflation (APR) 1 0 −1 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Output 0 −2 −4 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Output 0 −2 −4 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Govt Debt as Share of GDP 80 75 70 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Government Debt as Share of GDP 80 75 70 0 4 8 12 16 20 24 28 32 36 40 tnecreP South/North: Demand Shock −1 −2 −3 −4 0 4 8 12 16 20 24 28 32 36 40 tnecreP 3 2 1 0 −1 0 4 8 12 16 20 24 28 32 36 40 Quarter Quarter tnecreP South/North: Nominal Exchange Rate Unconstrained Zero Lower Bound

Figure 2: Responses to a Front−Loaded Decrease in Government Spending in Small South under Flexible Exchange Rate and in a Currency Union South: Nominal Inte r e s t R a t e ( A P R ) 0 −0.1 −0.2 −0.3 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Nominal Interest Rate (APR) 0 −0.1 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Real Interest Rate (APR) 0.4 0.2 0 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Real Interest Rate (APR) 0.2 0 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: CPI Inflation (APR) 0 −0.2 −0.4 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: CPI Inflation (APR) 0 −0.1 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Output −0.2 −0.4 −0.6 −0.8 −1 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Output 0 −0.2 −0.4 0 4 8 12 16 20 24 28 32 36 40 tnecreP South/North: Real Exchange Rate 1 0.8 0.6 0.4 0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP South/North: Nominal Exchange Rate 0.8 0.6 0.4 0.2 0 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Govt Debt as Share of GDP 0 −2 −4 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Govt Debt as Share of GDP 0.8 0.6 0.4 0.2 0 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Govt Spend (trend GDP share) 0.5 0 −0.5 −1 0 4 8 12 16 20 24 28 32 36 40 tnecreP 4 2 0 0 4 8 12 16 20 24 28 32 36 40 Quarter Quarter tnecreP North: Govt Spend (trend GDP share) Flex ex rate: Normal Curr Union: Normal Curr Union: ZLB

Figure 3: Responses to a Front−Loaded Decrease in Government Spending in Large South under Flexible Exchange Rate and in a Currency Union South: Nominal Inte r e s t R a t e ( A P R ) 0 −0.1 −0.2 −0.3 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Nominal Interest Rate (APR) 0 −0.1 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Real Interest Rate (APR) 0.4 0.2 0 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Real Interest Rate (APR) 0.2 0 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: CPI Inflation (APR) 0 −0.2 −0.4 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: CPI Inflation (APR) 0 −0.1 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Output −0.2 −0.4 −0.6 −0.8 −1 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Output 0 −0.2 −0.4 0 4 8 12 16 20 24 28 32 36 40 tnecreP South/North: Real Exchange Rate 1 0.8 0.6 0.4 0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP South/North: Nominal Exchange Rate 0.8 0.6 0.4 0.2 0 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Govt Debt as Share of GDP 0 −2 −4 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Govt Debt as Share of GDP 0.8 0.6 0.4 0.2 0 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Govt Spend (trend GDP share) 0.5 0 −0.5 −1 0 4 8 12 16 20 24 28 32 36 40 tnecreP 4 2 0 0 4 8 12 16 20 24 28 32 36 40 Quarter Quarter tnecreP North: Govt Spend (trend GDP share) Flex ex rate: Normal Curr Union: Normal Curr Union: ZLB

Figure 4: Responses to Government Spending Cuts of Different Magni− tudes for Large South Currency Union Member in a Liquidity Trap South: Nominal Intere s t R a t e ( A P R ) 0.2 0 −0.2 −0.4 −0.6 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Nominal Interest Rate (APR) 0.2 0 −0.2 −0.4 −0.6 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Real Interest Rate (APR) 1.5 1 0.5 0 −0.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Real Interest Rate (APR) 1.5 1 0.5 0 −0.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: CPI Inflation (APR) 0 −0.5 −1 −1.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: CPI Inflation (APR) 0 −0.5 −1 −1.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Output −1 −2 −3 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Output −1 −2 −3 0 4 8 12 16 20 24 28 32 36 40 tnecreP South/North: Real Exchange Rate 1 0.8 0.6 0.4 0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP Aggregate Currency Union Output −1 −2 −3 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Govt Debt as Share of GDP 0 −5 −10 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Govt Debt as Share of GDP 5 0 −5 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Govt Spend (trend GDP share) −1 −2 −3 0 4 8 12 16 20 24 28 32 36 40 tnecreP 1 0 −1 0 4 8 12 16 20 24 28 32 36 40 Quarter Quarter tnecreP North: Govt Spend (trend GDP share) 1% decrease: ZLB 2% decrease: ZLB 3% decrease: ZLB

Figure 5: Responses to Government Spending Cut in Large South Currency Union Member With and Without North Spending Adjustment South: Nominal Intere s t R a t e ( A P R ) 0.2 0 −0.2 −0.4 −0.6 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Nominal Interest Rate (APR) 0.2 0 −0.2 −0.4 −0.6 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Real Interest Rate (APR) 1 0.5 0 −0.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Real Interest Rate (APR) 1 0.5 0 −0.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: CPI Inflation (APR) 0 −0.5 −1 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: CPI Inflation (APR) 0 −0.5 −1 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Output −0.5 −1 −1.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Output −0.5 −1 −1.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP South/North: Real Exchange Rate 0.3 0.2 0.1 0 0 4 8 12 16 20 24 28 32 36 40 tnecreP Aggregate Currency Union Output −0.5 −1 −1.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Govt Debt as Share of GDP 0 −2 −4 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Govt Debt as Share of GDP 0 −2 −4 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Govt Spend (trend GDP share) 0.5 0 −0.5 −1 0 4 8 12 16 20 24 28 32 36 40 tnecreP 0.5 0 −0.5 −1 0 4 8 12 16 20 24 28 32 36 40 Quarter Quarter tnecreP North: Govt Spend (trend GDP share) No North Fiscal Adj: ZLB North Fiscal Adj: Normal North Fiscal Adj: ZLB

Figure 6: Responses to a Financial Spread Increase in Small South under Flexible Exchange Rate and in a Currency Union South: Nominal Interest R a t e ( A P R ) 0 −0.1 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Nominal Interest Rate (APR) 0 −0.1 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Real Interest Rate (APR) 0.2 0 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Real Interest Rate (APR) 0.2 0.1 0 −0.1 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: CPI Inflation (APR) 0.1 0 −0.1 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: CPI Inflation (APR) 0 −0.1 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Output −0.2 −0.4 −0.6 0 4 8 12 16 20 24 28 32 36 40 tnecreP 0 −0.1 −0.2 −0.3 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Output Flex ex rate: Normal Curr Union: Normal Curr Union: ZLB South/North: Real Exchange Rate 0.2 0 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP South/North: Nominal Exchange Rate 0.2 0 −0.2 −0.4 −0.6 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Govt Debt as Share of GDP 3 2 1 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Govt Debt as Share of GDP 0.6 0.4 0.2 0 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Spread Shock (APR) 0.5 0.45 0.4 0.35 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: 5−Year Nom Int Rate (APR) 0.45 0.4 0.35 0.3 0 4 8 12 16 20 24 28 32 36 40 Quarter tnecreP Quarter

Figure 7: Responses to a Financial Spread Increase in Large South under Flexible Exchange Rate and in a Currency Union South: Nominal Interest R a t e ( A P R ) 0 −0.1 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Nominal Interest Rate (APR) 0 −0.1 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Real Interest Rate (APR) 0.2 0 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Real Interest Rate (APR) 0.2 0.1 0 −0.1 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: CPI Inflation (APR) 0.1 0 −0.1 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: CPI Inflation (APR) 0 −0.1 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Output −0.2 −0.4 −0.6 0 4 8 12 16 20 24 28 32 36 40 tnecreP 0 −0.1 −0.2 −0.3 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Output Flex ex rate: Normal Curr Union: Normal Curr Union: ZLB South/North: Real Exchange Rate 0.2 0 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP South/North: Nominal Exchange Rate 0.2 0 −0.2 −0.4 −0.6 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Govt Debt as Share of GDP 3 2 1 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Govt Debt as Share of GDP 0.6 0.4 0.2 0 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Spread Shock (APR) 0.5 0.45 0.4 0.35 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: 5−Year Nom Int Rate (APR) 0.45 0.4 0.35 0.3 0 4 8 12 16 20 24 28 32 36 40 Quarter tnecreP Quarter

Figure 8: Responses to Financial Spread Increases of Different Sizes in Large South in a Currency Union in a Liquidity Trap South: Nominal Interes t R a t e ( A P R ) 0.2 0 −0.2 −0.4 −0.6 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Nominal Interest Rate (APR) 0.2 0 −0.2 −0.4 −0.6 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Real Interest Rate (APR) 1 0.5 0 −0.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Real Interest Rate (APR) 1 0.5 0 −0.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: CPI Inflation (APR) 0 −0.5 −1 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: CPI Inflation (APR) 0 −0.5 −1 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Output −0.5 −1 −1.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Output −0.5 −1 −1.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP South/North: Real Exchange Rate 0.2 0 −0.2 −0.4 −0.6 −0.8 0 4 8 12 16 20 24 28 32 36 40 tnecreP Aggregate Currency Union Output −0.5 −1 −1.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Govt Debt as Share of GDP 10 8 6 4 2 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Govt Debt as Share of GDP 10 8 6 4 2 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Spread Shock (APR) 1.5 1 0.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP 1.5 1 0.5 0 4 8 12 16 20 24 28 32 36 40 Quarter Quarter tnecreP South: 5−Year Nom Int Rate (APR) 0.5% increase: ZLB 1% increase: ZLB 1.5% increase: ZLB

Figure 9: Responses to a Financial Spread Increase in Large South Currency Union Member With and Without Spending Adjustment South: Nominal Intere s t R a t e ( A P R ) 0 −0.2 −0.4 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Nominal Interest Rate (APR) 0 −0.2 −0.4 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Real Interest Rate (APR) 0.6 0.4 0.2 0 −0.2 −0.4 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Real Interest Rate (APR) 0.6 0.4 0.2 0 −0.2 −0.4 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: CPI Inflation (APR) 0 −0.2 −0.4 −0.6 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: CPI Inflation (APR) 0 −0.2 −0.4 −0.6 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Output 0 −0.5 −1 −1.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Output 0 −0.5 −1 −1.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP South/North: Real Exchange Rate 0.4 0.2 0 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP Aggregate Currency Union Output 0 −0.5 −1 −1.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Govt Debt as Share of GDP 2 0 −2 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Govt Debt as Share of GDP 2 0 −2 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Corporate Spread (APR) 1 0.8 0.6 0.4 0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP 0.5 0 −0.5 −1 0 4 8 12 16 20 24 28 32 36 40 Quarter Quarter tnecreP South: Govt Spend (trend GDP share) No Fiscal Adj: ZLB Fiscal Adj: Normal Fiscal Adj: ZLB

Figure 10: Responses to Government Spending Cut in Large South For Alternative Labor−Income Tax Rules South: Nominal Interest Ra t e ( A P R ) 0.05 0 −0.05 −0.1 −0.15 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Nominal Interest Rate (APR) 0.05 0 −0.05 −0.1 −0.15 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Real Interest Rate (APR) 0.4 0.2 0 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Real Interest Rate (APR) 0.2 0.1 0 −0.1 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: CPI Inflation (APR) 0 −0.2 −0.4 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: CPI Inflation (APR) 0 −0.1 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Output 0 −0.2 −0.4 −0.6 −0.8 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Output 0 −0.1 −0.2 −0.3 0 4 8 12 16 20 24 28 32 36 40 tnecreP South/North: Real Exchange Rate 0.4 0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP Aggregate Currency Union Output 0 −0.2 −0.4 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Govt Debt as Share of GDP 0 −2 −4 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Govt Debt as Share of GDP 0.6 0.4 0.2 0 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP 0.5 South: Govt Spend (trend GDP share) 0 −0.5 −1 0 4 8 12 16 20 24 28 32 36 40 tnecreP 1 0 −1 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Govt Spend (trend GDP share) Unresponsive tax−rule: Normal Unresponsive tax−rule: ZLB Aggressive tax−rule: Normal Aggressive tax−rule: ZLB South: Labor Income Tax Rate −0.5 −1 −1.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Labor Income Tax Rate 0.05 0 −0.05 −0.1 −0.15 0 4 8 12 16 20 24 28 32 36 40 Quarter tnecreP Quarter

Figure 11: Responses to Coordinated Front−loaded and Gradual Government Spending Cuts in Currency Union in Normal times and in a Liquidity Trap South: Nominal Inte r e s t R a t e ( A P R ) 0.2 0 −0.2 −0.4 −0.6 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Nominal Interest Rate (APR) 0.2 0 −0.2 −0.4 −0.6 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Real Interest Rate (APR) 1 0.5 0 −0.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Real Interest Rate (APR) 1 0.5 0 −0.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: CPI Inflation (APR) 0 −0.5 −1 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: CPI Inflation (APR) 0 −0.5 −1 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Output −0.5 −1 −1.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Output −0.5 −1 −1.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP 1 0 −1 0 4 8 12 16 20 24 28 32 36 40 tnecreP South/North: Real Exchange Rate Aggregate Currency Union Output Front−Loaded Cut: Normal −0.5 Front−Loaded Cut: ZLB Gradual Cut: Normal −1 Gradual Cut: ZLB −1.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Govt Debt as Share of GDP 0 −2 −4 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Govt Debt as Share of GDP 0 −2 −4 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Govt Spend (trend GDP share) −0.2 −0.4 −0.6 −0.8 −1 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Govt Spend (trend GDP share) −0.2 −0.4 −0.6 −0.8 −1 0 4 8 12 16 20 24 28 32 36 40 Quarter tnecreP Quarter

Figure 12: Responses to Government Spending Cut in Large South Currency Union Member With and Without Endogenous Risk−Spread South: Nominal Inte r e s t R a t e ( A P R ) 0.2 0.1 0 −0.1 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Nominal Interest Rate (APR) 0.2 0.1 0 −0.1 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Real Interest Rate (APR) 0.4 0.2 0 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Real Interest Rate (APR) 0.4 0.2 0 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: CPI Inflation (APR) 0.2 0 −0.2 −0.4 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: CPI Inflation (APR) 0.2 0 −0.2 −0.4 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Output 2 1 0 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Output 2 1 0 0 4 8 12 16 20 24 28 32 36 40 tnecreP South/North: Real Exchange Rate 0.8 0.6 0.4 0.2 0 −0.2 0 4 8 12 16 20 24 28 32 36 40 tnecreP Aggregate Currency Union Output 2 1 0 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Govt Debt as Share of GDP 0 −5 −10 0 4 8 12 16 20 24 28 32 36 40 tnecreP 0 −5 −10 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Govt Debt as Share of GDP No Endo Spread: Normal No Endo Spread: ZLB Endo Spread: Normal Endo Spread: ZLB South: Govt Spend (trend GDP share) 0 −1 −2 −3 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Government Spread (APR) 0 −1 −2 −3 0 4 8 12 16 20 24 28 32 36 40 Quarter tnecreP Quarter

Figure 13: Responses to Coordinated and Uncoordinated Govt Spending Cuts in Large South Currency Union Member for Different Shares of HM Households South: Nomina l I n t e r e s t R a t e ( A P R ) 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Nominal Interest Rate (APR) 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Real Interest Rate (APR) 1 0 −1 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Real Interest Rate (APR) 1 0 −1 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: CPI Inflation (APR) 0 −0.5 −1 −1.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: CPI Inflation (APR) 0 −0.5 −1 −1.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Output −0.5 −1 −1.5 −2 −2.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Output −0.5 −1 −1.5 −2 −2.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP South/North: Real Exchange Rate 0.3 0.2 0.1 0 0 4 8 12 16 20 24 28 32 36 40 tnecreP Aggregate Currency Union Output −0.5 −1 −1.5 −2 −2.5 0 4 8 12 16 20 24 28 32 36 40 tnecreP South: Govt Debt as Share of GDP 2 0 −2 −4 0 4 8 12 16 20 24 28 32 36 40 tnecreP North: Govt Debt as Share of GDP 2 0 −2 −4 0 4 8 12 16 20 24 28 32 36 40 tnecreP 0.5 0 −0.5 −1 0 4 8 12 16 20 24 28 32 36 40 Quarter tnecreP South: Govt Spend (trend GDP share) North: Govt Spend (trend GDP share) 0.5 South Cut, 0% HM: ZLB South Cut, 50% HM: ZLB 0 Coordinated Cut, 0% HM: ZLB −0.5 Coordinated Cut, 50% HM: ZLB −1 0 4 8 12 16 20 24 28 32 36 40 tnecreP Quarter