Spillover Effects of Fiscal Policy under Flexible Exchange Rates

Transcription

1 Spillover Effecs of Fiscal Policy under Flexible Exchange Raes Ingo Pierle Dirk Seffen 13h February 2004 ABSTRACT The paper analyzes he ransmission mechanisms of fiscal shocks in a wo-counry general equilibrium model wih sicky prices in line wih he new open economy macroeconomics (NOEM) approach. Specifically, he model allows for boh marke segmenaion and asymmeric preferences. We inroduce money via a cash-in-advance consrain: Households need cash in order o purchase consumpion goods and o pay axes. Therefore, governmen expendiures are relevan for overall money demand. Providing closed form soluions, we find ha a balanced budge fiscal expansion resuls in an appreciaion of he exchange rae. This resul sands in sharp conras o sandard open economy models wih money-in-he-uiliy (MIU), ha predic depreciaions. The exchange rae movemen is all he more pronounced, he higher he degree of pricing-o-marke and he sronger he bias for domesically produced goods. As an appreciaion of he shor run exchange rae implies lower compeiiveness of domesic firms, producion is emporarily shorened. Therefore, he deerioraion of he rade balance is exacerbaed when compared wih MIU models. We show ha he erms of rade depend qualiaively and quaniaively on he degree of pricing-o-marke, whereas a home bias in consumpion only rules is ampliude. A rigorous welfare analysis reveals ha a fiscal expansion is a prosper-hy-neighbor insrumen. A higher share of PTM goods reinforces he prosper-hy-neighbor effec while a home bias in consumpion ends o reduce he posiive spillover effecs. Keywords: Fiscal Shocks, Flexible Exchange Raes, Cash-in-Advance, Pricing-o-Marke, Home Bias, Prosper-hy-Neighbor JEL Classificaion: F31, F32, F41 and F42 Universiy of Frankfur, pierle@wiwi.uni-frankfur.de. Universiy of Frankfur, seffen@wiwi.uni-frankfur.de. The auhors wish o express heir appreciaion o Uwe Walz and Fabrice Collard and paricipans of he DEGIT VIII conference in Helsinki and of he VIII Jornadas de Economía Inernacional in Ciudad Real for helpful commens. The auhors graefully acknowledge financial suppor of he German Science Foundaion.

2 1 INTRODUCTION Wha are he welfare implicaions of moneary and fiscal policy in a globalized world? Since Mundell (1963) and Fleming (1962) economiss ry o address he issue by formal models. While well esablished no only in he scienific arena bu also in pracice, Keynesian-ype of inernaional macro-models have a severe draw back: he enire absence of microfoundaions resuls in he use of ad hoc welfare crieria. Evenually, Obsfeld and Rogoff (1995a) inroduced he now famous Redux model ino he lieraure on open macroeconomics. The model incorporaes explici microfoundaions and hereby improves he welfare analysis of moneary and fiscal shocks subsanially. One of he mos prominen opics in inernaional finance is he poenial role of fiscal shocks for exchange rae movemens, inernaional price level differenials and welfare effecs. However, he vas majoriy of he lieraure on new open economy macroeconomics (NOEM) emanaing from he Redux model has concenraed on he ransmission mechanisms of moneary shocks, as poined ou by Ganelli and Lane (2002). There are a few noable excepions, hough. Ganelli (2003) analyzes useful governmen spending in he Redux framework while Tille (2001) focuses on he role of consumpion subsiuabiliy in he inernaional ransmission of fiscal shocks. Corsei and Peseni (2001) sress he poenial beggar-hy-neighbor propery of fiscal expansions when naional governmen purchases fall exclusively on domesically produced goods. Following his line of research, we analyze fiscal policy in a wo-counry general equilibrium model wih sicky prices. Specifically, we focus on he compeing welfare effecs of pricing-omarke (PTM) and a home bias in consumpion in a cash-in-advance economy where governmen expendiures rigger addiional money demand. Tracing back o Mankiw and Summers (1986), empirical research suggess ha governmen purchases are relevan for money demand. Our model capures his effec as households need cash in order o purchase consumpion goods and o pay axes such ha money demand is absorpion raher han consumpion based. As a consequence, expansive fiscal policy leads o an appreciaion of he exchange rae, which sands in sharp conras o he sandard money-in-he-uiliy (MIU) approach. As boh he reacion of he erms-of-rade and he expendiure swiching effec depend on he exchange rae movemen, he implicaions of PTM and a home bias in consumpion are very differen from hose in a MIU seing. We demonsrae ha a higher share of PTM goods reinforces 1

3 prosper-hy-neighbor effecs of fiscal expansions while a home bias in consumpion ends o reduce posiive spillovers. The role of pricing-o-marke in inernaional economics has been inensively sudied in he las years. Seminal papers on pricing-o-marke are Krugman (1987), and Dornbusch (1987) while empirical suppor for PTM is provided by Kneer (1993). In he conex of NOEM wih money-in-he-uiliy, Bes and Devereux (2000) provide an innovaive sudy of pricing-omarke behavior and is implicaions for he inernaional ransmission of asymmeric shocks. However, hey neiher consider a home bias in consumpion nor do hey analyze he welfare effecs of fiscal policy explicily. As for biased preferences, recen empirical sudies by Mc- Callum (1995), Helliwell (1996), and Wei (1996), ha invesigae so called border effecs in inernaional rade, confirm ha here is a persising home bias in consumpion despie he opening up of he indusrial counries. Warnock (1999) offers an analysis of fiscal policy in a MIU model agains he backdrop of idiosyncraic ases bu leaves ou he possibiliy of PTM and does no provide a deailed welfare analysis. Pierle and Seffen (2004) invesigae he effecs of a home bias in consumpion in a moneary union seing. The paper shows ha he absence of he exchange rae channel leads o an increased imporance of demand composiion effecs for he inernaional ransmission of fiscal policy. The underlying model of our analysis is perhaps closes o Carré and Collard (2003) who analyze fiscal and echnology shocks in cash-in-advance economy under alernaive exchange rae regimes. However, our approach differs mehodologically, since we provide closed form soluions. We achieve his as we leave ou capial accumulaion and consider exogenous price rigidiies. 1 The analyical soluion idenifies he main mechanisms a work and provides a deeper undersanding of fiscal policy inerdependencies. We find ha a domesic balanced budge fiscal expansion resuls in an appreciaion of he equilibrium exchange rae. The very reason for his lies in he feaure ha increased governmen expendiures raise overall domesic money demand because axes have o be paid wih cash and privae consumpion is only parially crowded ou. As we do no consider an accommodaing moneary policy and prices of domesically produced goods are fixed in he shor run, he required increase of real balances can only be brough abou hrough cheaper impors. This in urn implies ha he exchange rae has o appreciae. As an appreciaion of 1 The inclusion of capial accumulaion and endogenous price rigidiies impedes ha he model economy reach a new seady sae quickly afer unanicipaed shocks. Therefore, an analyical soluion canno be derived. 2

4 he shor run exchange rae implies lower compeiiveness of domesic firms, home producion is shorened. Therefore, our resuls cauion abou possible oupu simulaing effecs of expansive fiscal policy in he shor run. Furhermore, he exchange rae movemen raher exacerbaes he deerioraion of he rade balance while MIU models predic a miigaing effec. The exchange rae response is all he more pronounced, he higher he degree of pricing-omarke and he sronger he bias for domesically produced goods. We show ha he shor run response of he erms of rade depends qualiaively and quaniaively on he degree of pricingo-marke, whereas a home bias in consumpion only rules is ampliude. The incorporaion of biased preferences implies ha purchasing power pariy does no hold even in he long run. This capures he empirical evidence of persisen price level deviaions of counries ha face similar moneary policy. A prominen example for his phenomenon is he regional inflaion experience of he European Moneary Union (EMU). The incorporaion of an explici opimizaion problem of he households allows us o conduc a rigorous welfare analysis. Aggregaing shor and long run welfare for he foreign households reveals ha a domesic fiscal expansion acs as a prosper-hy-neighbor insrumen. We idenify hree major ransmission mechanisms: he expansion of world demand, he change of he erms of rade and expendiure swiching. A deailed analysis of he compeing effecs demonsraes ha a higher share of PTM goods reinforces he prosper-hy-neighbor effec. Even hough he posiive welfare effecs from expendiure swiching decrease wih more producers pursuing pricing-o-marke, he simulaneous improvemen of he erms of rade dominaes. In conras, a home bias in consumpion ends o reduce he posiive spillover effecs because of he lower relevance of inernaional rade for boh economies. The paper is organized as follows. Secion 2 gives a descripion of he model. Secion 3 provides long run and shor run soluions of he linearized sysem, while secion 4 explores he welfare implicaions of fiscal shocks. Secion 5 concludes. 2 MODEL SETUP The considered model consiss of wo counries, home and foreign, of equal size. This feaure is mandaory because households display a home bias in consumpion. Differen populaion sizes lead o a srucure of world demand such ha an analyical soluion for he seady sae is precluded. We normalize he populaion size in each counry o one. Producers in 3

5 boh counries are spli ino wo groups. A fracion s of producers are capable of segmening markes as arbirage for hese goods is ruled ou. They se prices for home and foreign markes in he respecive buyer s currency, i.e. hey pursue local currency pricing. Following Bes and Devereux (2000), we call ha kind of pricing behavior pricing-o-marke (PTM). To be more precise, he pricing behavior we label PTM comprises segmening markes and local currency pricing. The remaining (1 s) producers price goods in he currency of he seller. There is no resricion on rade in hese goods. Hence, markes canno be segmened, and only one price may be se by he producers. This behavior - producer-currency-pricing (PCP) from now on - is consisen wih he law of one price ha shows up in more radiional models of inernaional macroeconomics. 2.1 Households The descripion of he model will be carried ou in deail for he home counry. As for he foreign counry, mos of he equaions are defined analogously, while all foreign variables are denoed wih an aserisk. Households derive uiliy from consumpion and leisure. As we are ineresed in obaining a manageable closed form soluion of he model, we use a special case of he general isoelasic uiliy funcion: The elasiciy of ineremporal subsiuion is se o one and equal weigh is aached o consumpion and leisure. Thus, households maximize heir discouned uiliy given by U = β ( log c + log(1 h ) ), (1) =0 where β [0, 1] denoes he discoun facor, (1 h ) represens leisure enjoyed by he household, and c is a consan elasiciy of subsiuion (CES) real consumpion index. The laer consiss of a baske of goods produced in he domesic economy, c h, and a baske of goods produced in he foreign counry, c f : c = [ω 1θ c h θ 1 θ ] + (1 ω) 1 θ c f θ 1 θ θ 1 θ (2) By deermining he weigh of he domesically produced goods in he consumpion index, 4

6 ω [0.5, 1) serves as a measure of a possible home bias in consumpion. 2 If ω > 0.5, home and foreign households have biased demand for goods ha are produced in heir own counry, whereas he fracion of impored goods in he consumpion bundle is smaller han 0.5. The parameer θ > 1 denoes he elasiciy of subsiuion beween he wo consumpion baskes which are defined as: ( s c h = 0 c f = ( s 0 1 ) θ c m (h) θ 1 θ dh + c a (h) θ 1 θ 1 θ dh s 1 ) θ c m (f) θ 1 θ df + c a (f) θ 1 θ 1 θ df s (3) (4) c h aggregaes over he consumpion of individual PTM goods c m (h) and PCP goods c a (h) ha are produced in he domesic economy. c f aggregaes over he consumpion of individual PTM goods c m (h) and PCP goods c a (h) ha are produced in he foreign economy. To keep he preference srucure simple, we follow Obsfeld and Rogoff (1995a) and assume he same cross-counry and wihin-counry subsiuabiliy of goods. 3 Consumpion maximizaion yields domesic demand funcions for he respecive goods: ( ) p c a a (h) = (h) θ ωc p ( ) p c m m (h) = (h) θ ωc c a (f) = p ( e p a p ) (f) θ (1 ω)c (5) ( ) p c m m (f) = (f) θ (1 ω)c (6) p The demand funcions are specified for goods produced a home (h) and abroad (f). A furher disincion has o be made for goods of PCP producers, indicaed by a, and goods offered by PTM producers, indicaed by m. The difference beween pricing-o-marke and producercurrency-pricing shows up mos clearly in he demand funcions (5) and (6) for foreign goods. While foreign PCP producers se a foreign currency price ha has o be muliplied by he 2 Warnock (2003) models a home bias in consumpion using a similar specificaion of consumpion preferences. 3 Tille (2001) invesigaes he effecs of differing subsiuabiliies on he welfare implicaions of fiscal and moneary shocks. 5

7 exchange rae, e, o yield domesic currency prices, 4 foreign PTM producers segmen markes and se he price direcly in he currency of he domesic consumer. Hence, in imes of fixed prices and exchange rae movemens i is only he prices of PCP goods ha may change. The possibiliy of pricing-o-marke hereby ends o limi he exchange rae pass-hrough ino impor prices. A home bias in consumpion implies ha, for any given relaive price, households always demand relaively more domesic goods han foreigners do. The price indexes ha correspond o he consumpion bundles (2)-(4) are obained by expendiure minimizaion: p = ( ωp h1 θ ) + (1 ω)p f 1 θ 1 1 θ (7) wih ( s p h = p m (h) 1 θ dh s ) 1 p a (h) 1 θ 1 θ dh (8) and ( s p f = p m (f) 1 θ df s (e p a ) 1 (f)) 1 θ 1 θ df (9) Again, he aggregae price level (7) is a home biased funcion of impor prices (f), and prices of domesic goods (h). The price index for domesic goods (8) and he impor price index (9) aggregae over he prices of (1 s) individual PCP goods, and over a fracion of s goods ha are priced o marke. The household s opimizaion problem is consrained by m + R f +1 f + p w h + Π (10) m p (c + T ) (11) The budge consrain (10) says ha nominal expendiure on cash holdings and bond purchases canno exceed income derived from remuneraion of labor effor, profis and mauring bonds. In order o smooh consumpion, households may purchase nominal one-period bonds f +1, ha are denominaed in domesic currency unis. The bond price R is inversely relaed o 4 We use price noaion as i is sandard. 6

8 he nominal ineres rae. Our iming convenion is he following: Bonds denoed wih + 1 are acquired a he beginning of period and maure a he beginning of period + 1. The specificaion of he budge consrain is a shor cu o Helpman (1981) as money holdings are no carried over from he previous period, hough i is heoreically possible o do so. As Helpman poins ou, households will no find i reasonable o hold money over periods in he presence of ineres yielding bonds. Money hereby reduces o money o spend. Anoher imporan aspec of he budge consrain is he iming of paymens. Households receive nominal labor income, p w h, and profis, Π, insananeously. As a resul, neiher firms nor households hold money longer han an insan. We hereby avoid an addiional source of disorion ha would blur our analysis of nominal rigidiies. 5 Addiionally, households face a cash-in-advance consrain (11) à la Helpman (1981) and Lucas (1982). Households need money in order o carry ou consumpion goods purchases and ax paymens. Our specificaion avoids possible disorions of he consumpion decision by unexpeced inflaion as households decide on money demand afer he occurrence of shocks. In he ligh of posiive nominal ineres raes he consrain is binding. In conras o he NOEM lieraure, we are quie aware of he fac ha he specificaion of money demand alers he oucome of our analysis subsanially. 6 The effec of fiscal shocks on he exchange rae, for example, will be radically differen in a sandard model wih money in he uiliy or models wih CIA consrains where axes do no have o be paid wih cash. The very reason for his lies in he feaure ha, in our model, money demand depends no only on he consumpion level, bu on oal absorpion. Thus, ax-financed governmen expendiure increases ceeris paribus demand for money in equilibrium. Households maximize heir ineremporal uiliy (1) subjec o (10) and (11). The decision variables a ime are f +1, h, and c. Opimal bond holdings yield sandard Euler equaions of he form β p c = R p +1 c +1 (12) Tha is, marginal uiliy of consumpion oday equals marginal uiliy of fuure consumpion, discouned by he ime preference β and muliplied by he real ineres rae 1 + r +1 = 1 R 5 Thanks o Fabrice Collard who gave us some clarifying remarks on ha subjec. 6 See for a deailed discussion Chang and Lai (1997). p p +1. 7

9 Noe ha due o our definiion of bonds, real ineres raes may differ inernaionally. As opposed o Obsfeld and Rogoff (1995a), real bond payoffs depend on possible inflaion, and in he case of he foreign counry also on exchange rae movemens. The opimal labor supply decision is characerized by he labor leisure rade off 1 1 h = w c, (13) A he margin, an addiional uni of leisure yields he same uiliy as he exra consumpion possibiliies derived from an addiional uni of work ha is remuneraed wih he curren real wage. The cash-in-advance consrain (11) may be inerpreed as he money demand funcion m d = p (c + T ) Noe ha his implies a consumpion elasiciy of money demand equal o one in he absence of axes. 2.2 Governmen The governmen decides in every period on purchases of public goods g. Le he public consumpion indexes be defined analogously o he real consumpion indices of he households. 7 Governmen spending is assumed o be purely dissipaive, i.e. he public good does no ener he household s uiliy funcion a all. 8 The governmen finances is expendiures via lump sum axes T. The governmen budge consrain herefore reduces o g = T 7 Some auhors, e.g. Tille (2001) consider a complee home bias in governmen expendiure. However, under his specificaion, he demand simulaing effecs of fiscal policy only fall on he home counry and he foreign counry is likely o be worse off. 8 Ganelli (2003) invesigaes he implicaions of welfare enhancing governmen spending under he assumpion of non-separabiliy. Take Beesma and Jensen (2002) for he general preference case. In heir model, he uiliy of public spending is addiively separable from privae consumpion. This is also rue for Corsei and Peseni (2001). 8

10 As we focus exclusively on fiscal policy, we assume ha he cenral bank leaves he money supply unchanged m s = m s 1 = m s 2.3 Firms Suppose ha producion is linear in he only producion facor labor. We absrac from echnology shocks and hus define he producion funcions for PTM producers h [0, s] and PCP producers h [s, 1] in is simples form: y a (h) = h a (h) y m (h) + y m (h) = h m (h) PCP producers maximize profis ha are given by 9 max p a (h) Π a (h) = p a (h)y a (h) p w h a (h) subjec o ( ) p y a a (h) = (h) θ ( ) p a ω(c + g ) + (h) θ p e p (1 ω)(c + g ) In he PTM case, producers maximize a profi funcion ha disinguishes explicily beween home and foreign demand: p m max (h), pm (h) Π m (h) = p m (h)y m (h) + e p m (h)y m (h) p w h m (h) subjec o ( ) p y m m (h) = (h) θ ω(c + g ) p 9 The opimizaion problem of he producers is essenially saic because we assume exogenous price rigidiies. Models ha endogenize price rigidiies via explici price adjusmen coss like Hairaul and Porier (1993) or use Calvo (1983) syle price deerminaion as in Kollmann (2001a, 2001b) yield more dynamic opimizaion problems of he firm. Though hese approaches are richer in srucure hey hamper he finding of analyical soluions. 9

11 y m (h) = ( p m p (h) ) θ (1 ω)(c + g ) Though PTM producers are free o pursue price discriminaion hey will se he same domesic currency price for home and foreign consumers. To see his, we derive he opimal price seing rule of any home producer h by solving he respecive maximizaion problems. I urns ou ha he opimal price is always given as a markup on nominal marginal producion coss: p h = θ θ 1 w p (14) Noe ha a higher θ implies a lower mark up. Tha is, he degree of monopolisic disorion decreases wih he degree of subsiuabiliy of goods. As a resul of he assumed consan elasiciy of subsiuion (CES) consumpion baskes he level of overall demand does no influence he opimal price. Therefore, PTM producers will no charge differen prices across counries, even if he demand levels differed. Furhermore, boh ypes of producers face he same marginal producion coss, and will herefore se he same price. However, if prices are rigid PCP and PTM consumer prices differ when he exchange rae changes. In order o analyze he disribuion of gains in inernaional rade i is convenien o define he erms of rade which describe he relaion beween domesic expor and impor price indexes in domesic currency: τ = e p h p f (15) where he domesic impor price index p f index denominaed in foreign currency may be saed as p h = ( s 0 p m (h) 1 θ dh + 1 s ( p a (h) e is given by equaion (9). The domesic expor price ) 1 θ dh) 1 1 θ 10

12 3 POSITIVE ANALYSIS OF FISCAL SHOCKS 3.1 Seady sae To ge a firs feel for he characerisics of he model i is useful o sar wih he calculaion of a seady sae. To achieve a closed form soluion we choose he mos simple form of he seady sae, where iniial bond holdings and governmen expendiure equal zero. A he same ime, he seady sae exercise yields he flexible price version of he model which serves as a saring poin for he following shock analysis in he presence of price rigidiies. From a echnical perspecive, we need he seady sae of he model as we evaluae he dynamic sysem around a saionary equilibrium. In fac, he propagaion of shocks will be analyzed only locally. In he sequel, seady sae values of he variables are barred. One of he mos imporan feaures of Redux syle models is he incorporaion of monopolisic compeiion. This faciliaes demand driven welfare improvemens in he shor run, because producion is inefficienly low in he iniial seady sae. We may derive he oupu level from he seady sae labor markes: h = h = ȳ = ȳ = θ 1 θ 1 + θ 1 θ whereas he socially opimal employmen (producion) level would be 1 2. The inverse markup θ 1 θ, ha defines he marke power of firms, eners he labor marke equilibrium hrough he (disored) real wage ha workers receive for an hour worked, see pricing equaion (14). Seady sae consumpion may be derived from barred versions of he curren accoun = ph p ȳ = ph p h = h Obviously, an inefficienly low level of hours worked ranslaes ino inefficienly low producion and hereby lower consumpion. Barred versions of he Euler equaion (12) link he seady sae real ineres rae o he ime-preference facor β r = 1 β β Finally, money marke clearing reveals ha he seady sae exchange rae hinges on relaive 11

13 money supplies and he inernaional consumpion raio ē = m m c c Inuiively, a loose relaive moneary policy precipiaes a depreciaion of he exchange rae while a higher relaive consumpion level yields an appreciaion. 3.2 Long run equilibrium We now urn o he policy experimen of an unanicipaed asymmeric fiscal shock. Wha will happen o he key variables if he governmen raises is ax-financed expendiures? For welfare analysis purposes i is crucial o deermine he dynamic response of consumpion and hours worked because boh ener he uiliy funcion of he represenaive agen. The movemen of he exchange rae is a he cener of our analysis as i deermines consumpion, hours worked, and he erms of rade. The laer are in urn decisive for he disribuion of gains in rade and herefore have srong implicaions for he welfare effecs of fiscal shocks. Though our se of equaions is complex, i is possible o solve for he individual variables, because he dynamic sysem reaches is new seady sae righ afer he shock period. This feaure is due o he special form of price rigidiies - prices have o be se before he occurrence of shocks bu may be changed in he following period - and some more suble issues such as he lack of capial accumulaion. Given his special srucure, we may spli he algebraic problem ino wo pars ha can be reaed (almos) independenly. Firs, we solve for he long run (pos shock, flexible price) values of he inernaional consumpion differenial and he exchange rae. I urns ou ha hese depend on exogenous variables and endogenous bond holdings ha are deermined in he shor run (pos shock, rigid prices). Second, we solve for he shor run equilibrium given he long run values of he variables. The combinaion of he shor run (period ) and long run (period + 1) soluion finally yields he soluion for exchange raes, consumpion levels, hours worked, price levels and so forh. The essenial link beween he shor and long run sysem will be he bond holdings acquired in he shock period. 10 The following sysem of equaions includes he marke clearing and opimaliy condiions ha define he long run equilibrium. 10 The imporance of he curren accoun as a main channel of inernaional ransmission of shocks is sressed by he ineremporal approach o he curren accoun, see Obsfeld and Rogoff (1995b). 12

14 Money markes m s +1 p +1 = md +1 p +1 = c +1 + g +1 (16) m s +1 p +1 = md +1 p +1 Curren accouns = c +1 + g +1 (17) p +1 (c +1 + g +1 ) + R +1 f +2 = p h +1y +1 + f +1 (18) p +1(c +1 + g +1) + R +1 e +1 f +2 = p f +1 y +1 + f +1 e +1 (19) Goods markes y +1 = ( p h +1 p +1 ) θ ω(c +1 + g +1) + ( ) p h θ +1 p (1 ω)(c +1 + g+1) (20) +1 y +1 = Euler equaions ( ) p f θ ( ) +1 p f θ p ω(c +1 + g+1) +1 + (1 ω)(c +1 + g +1) (21) +1 p +1 β p +1 c +1 = R +1 p +2 c +2 (22) β p +1 c +1 = R +1 e +2 e +1 p +2 c +2 (23) Labor markes p h +1 1 = θ 1 (24) 1 h +1 θ p +1 c h +1 = θ 1 θ p f +1 p +1 c +1 (25) Equaions (16) and (17) assure ha money markes in boh counries clear. The naional 13

15 Table 1: Linearized long run price indexes p +1 = ω p h +1 + (1 ω) pf +1 p h +1 = s pm +1 (h) + (1 s) pa +1 (h) p +1 = ω pf +1 + (1 ω) ph +1 pf +1 = s pm +1 (f) + (1 s) pa +1 (f) p f +1 = s pm +1 (f) + (1 s)( pa +1 (f) + ẽ +1) p h +1 = s pm +1 (h) + (1 s)( pa +1 (h) ẽ +1) budge consrains are described by (18) and (19): Nominal expendiures on privae and governmen consumpion and on home-currency denominaed bonds mus equal nominal income from goods sales plus pay-offs derived from mauring bonds acquired in he previous period. (20) and (21) represen he goods marke clearing condiions. As prices are flexible in he long run and all producers face he same marginal producion coss, we do no have o disinguish beween PCP and PTM goods markes. Equaions (22) and (23) are he Euler equaions, describing he opimal pah of consumpion growh in boh counries. Finally, (24) and (25) represen he labor markes, which combine he households opimal labor supply decision and he firms pricing rule, i.e. he opimal price as a markup over wages. Since he model we consider is non-linear we have o recur o a mehod of linearizaion before proceeding. As i is sandard in he NOEM lieraure we log-linearize he model around he seady sae. 11 From now on, le he percenage deviaion 12 of a variable x from is seady sae value x be defined as x = dx x. As we assume zero bond holdings and no governmen expendiure in he iniial seady sae, he respecive deviaion of hese variables will be relaed o seady sae domesic consumpion. An imporan feaure of our model are he long run implicaions of fiscal shocks for he price levels. Due o he home bias in privae and public consumpion, changes in he marginal producion cos differenial are refleced in a deviaion from purchasing power pariy. To derive his effec, consider he linearized versions of he domesic price indices (7), (8), (9), and is foreign counerpars, ha are saed in Table This implies ha we may no consider shocks o he sysem ha are oo big as he approximaion error would grow oo much once you leave he seady sae. See Corsei and Peseni (2001) for a NOEM model ha does no rely on log-linearizaion. However, he applied Cobb-Douglas specificaion of he consumpion baskes rules ou curren accoun imbalances. 12 For he sake of lean exposiion, we will always refer o he deviaion of a variable, if no oherwise saed. 14

16 In he long run, producers are free o se heir prices and PTM producers may sill segmen markes. Anyhow, he law of one price will hold for all ypes of goods, because he opimal price across producers is derived as a markup on marginal producion coss. Therefore, PTM producers will se prices for foreign markes in he same way as PCP producers do. Tha is, hey calculae he opimal price in he producer s currency and hen muliply (divide) i by he exchange rae. The law of one price, hough, does no imply purchasing power pariy, as marginal producion coss across counries may differ. For example, if he real wage a home is higher han abroad, domesic producers - PTM and PCP ypes alike - will se a higher price han heir foreign compeiors. Then, i is no only he exchange rae, bu also he mix of domesic and foreign goods in he consumpion bundles ha governs he inernaional price level differenial: p +1 p +1 = ẽ +1 + (2ω 1)( p h +1 p f +1 ) (26) Obviously, in a world of symmeric preferences, i.e. ω = 0.5, equaion (26) reduces o he familiar log-linear form of purchasing power pariy, p +1 p +1 = ẽ +1. Following Obsfeld and Rogoff (1995a) and Aoki (1981) we now solve for he differences of he linearized variables and hen calculae he individual variables. Combining he difference of he linearized long run money markes, (16) and (17), and remembering ha boh cenral banks leave he money supply unchanged, we can derive he following expression for he long run exchange rae: ẽ +1 = ( c +1 c +1) dg +1 dg +1 (2ω 1)( p h +1 p f +1 ) (27) Equaion (27) reveals ha he endogenous price differenial of home and foreign goods only eners he exchange rae equaion if here is a home bias in consumpion. As already menioned, he reason for his lies in he lack of purchasing power pariy in he long run. Once we se ω o 0.5 we arrive immediaely a an exchange rae equaion ha only depends on exogenous variables and he long run consumpion differenial. Using linearized versions of equaions (18)-(25) we may derive he long run consumpion 15

17 differenial following some deviaions from he seady sae in he shor run: 13 c +1 c +1 = θ 2(1 β)df ( θ 1 p 2ω 1 2ω(θ 1) + 1 θ ) dg+1 dg+1 2θ 1 (28) The evoluion of he long run consumpion differenial is governed by nominal bond holdings f +1 and long run governmen expendiure g +1. The sign of domesic bond holdings will be deermined by he shor run soluion of he model. Assume domesic households acquire deb in he shor run responding o a domesic fiscal expansion. Negaive domesic bond holdings hen reduce he consumpion differenial as home residens face permanen ineres paymens ha allow for a higher relaive consumpion of foreign residens. A posiive long run governmen spending differenial yields a furher reducion of he consumpion differenial. 14 This is due o he permanen reducion of disposable income in he home counry as governmen expendiures are ax-financed. Once we absrac from home bias concerns, he coefficien ha deermines he impac of governmen spending on consumpion reduces o θ θ+(θ 1), which is always less han one. This illusraes he model feaure of limied crowding ou of privae consumpion, i.e. domesic households reduce heir consumpion by less han he increased ax burden. 15 Thus, a domesic fiscal expansion simulaes overall domesic demand. Finally, we may ake a look a he effecs of a home bias in privae consumpion and governmen spending on he long run consumpion differenial. While he coefficien of bond holdings remains unaffeced, he coefficien of he public spending differenial depends on he size of ω. Wih dg +1 dg +1 wih respec o ω is posiive, > 0, he parial derivaive of he consumpion differenial ( c +1 c +1 ) ω > 0. Therefore, a rising home bias miigaes he negaive effec of an asymmeric domesic fiscal expansion on he consumpion differenial. The explanaion for his kind of smoohing is sraighforward, once you consider he goods markes. Domesic demand increases relaively o foreign demand because of he limied crowding ou effec of he fiscal expansion. As boh, public and privae demand, are ruled by a home bias, he overall increase in world demand falls primarily on home goods, hereby increasing domesic relaive income compared wih a siuaion of symmeric preferences. 13 See Appendix A for deails. 14 To see his, we may rewrie he governmen expendiure erm as θ 1 2θ 1 + 2(1 ω)θ (2(θ 1)ω+1)(2θ 1). 15 This behavior is reinforced by he way we model governmen consumpion as privae uiliy remains unaffeced. 16

18 3.3 Shor run equilibrium We can now proceed o he analysis of he shor run (period ) equilibrium, which is characerized by sicky prices. Producers fix heir prices before he occurrence of he fiscal shock and canno change hem bu in he nex period. Consequenly, producion becomes enirely demand deermined. This in urn implies ha we do no have o consider labor markes in he shor run equilibrium sysem, which can be described by he following equaions: Money markes m = (c + g )p (29) m = (c + g )p (30) Curren accouns p (c + g ) + R f +1 = (1 s)p a (h)y a (h) + s ( p m (h)y m (h) + e p m (h)y m (h) ) (31) p (c + g ) + R f+1 = (1 s)p a e ( (f)y a (f) + s p m (f)y m (f) + pm (f) e ) y m (f) (32) Goods markes ( ) p y a a (h) = (h) θ ( ) p a ω(c + g ) + (h) θ p e p (1 ω)(c + g ) y a (f) = ( p a p (f) ) θ ω(c + g ) + ( ) p y m m (h) = (h) θ ω(c + g ) y m (h) = p ( p m p (h) ( p a ) θ (1 ω)(c + g ) ( ) p y m m (f) = (f) θ (1 ω)(c + g ) y m (f) = p ( p m p (f) ) θ ω(c + g ) (f)e p ) θ (1 ω)(c + g ) 17

19 Euler equaions β p c = R p +1 c +1 β p c = R e +1 e p +1 c +1 The shor run equilibrium sysem differs in wo main aspecs from he long run equilibrium. Firs, here are separaed goods marke clearing condiions for PCP and PTM goods. In case of he laer, a furher disincion has o be made beween demand ha sems from he respecive domesic markes and demand faced in he foreign markes. Second, as usual in his ype of model, he labor marke clearing condiion is no binding because, as explained above, firms adjus producion somehow passively o he demand consisen wih he previously fixed prices. The linearized version of he shor run equilibrium is saed in Appendix B. We are now ready o derive he shor run exchange rae response. Using shor erm versions of he linearized price indexes saed in Table 1 and remembering ha prices are sicky in he shor run, i becomes clear ha a change in he overall price index can only be brough abou hrough a variaion of he exchange rae: p = (1 ω)(1 s)ẽ (33) p = (1 ω)(1 s)ẽ. (34) Obviously, he overall price indexes do no respond o an exchange rae movemen if here is eiher full pricing o marke (s = 1) or a very srong home bias (ω 1). Taking linearized differences of he money marke equaions (29) and (30), subsiuing for he price levels and keeping in mind ha money supplies do no vary, we ge he following expression for he exchange rae: ẽ = ( c c ) ( dg dg ) 2(1 ω)(1 s) (35) Thus, he movemen of he exchange rae depends on he ineracion of he governmen expendiure differenial and he endogenous privae consumpion differenial. In a nex sep, we solve for he linearized difference beween he home and foreign budge 18

20 consrains (31) and (32). Subsiuing for he resuling differences beween goods demands and for he difference beween he overall price levels, we obain he following expression for he exchange rae: ẽ = ( c c ) + βdf +1 p(1 ω) + dg dg 2s 1 + 2ωθ(1 s) (36) These wo exchange rae equaions conain wo endogenous erms, c c and df +1, and he exogenous governmen expendiure differenial dg dg. In he following, we have o eliminae he shor run consumpion differenial and he inernaional bond holdings from he exchange rae equaions. For his purpose, we firs solve he long run consumpion differenial (28) for df +1 p. Nex, we use linearized versions of he Euler equaions in order o eliminae he long run consumpion differenial. Then, subsiuing for he inernaional bond holdings in (36) and combining i wih exchange rae equaion (35) so as o eliminae he shor run consumpion differenial, gives us he shor run response of he exchange rae o an unanicipaed fiscal shock. 16 As we are mainly ineresed in he impac of a permanen shock, we assume here ha dg +1 = dg = dg p : 17 θ(θ 1)2ω (θ 1)2ω + 1 ẽ = r ( (θ 1)(1 s)2ω + 1 )( 2ω 1 + 2(1 ω)θ ) dg p dgp + 2θ 1 (37) From now on, we consider an asymmeric domesic fiscal expansion where dg p > 0 and dg p = 0. For he parameer range given above, an unanicipaed permanen posiive shock o home governmen expendiure will lead o a nominal appreciaion of he exchange rae. The driving force behind his resul is an increase in he relaive domesic demand for real balances. Consider he following adjusmen process: A higher level of governmen expendiure is financed by an increase in axes. Therefore, he disposable income of domesic households decreases, which forces hem o reduce consumpion, leading o a higher marginal uiliy of consumpion. In he shor run, oupu and consequenly hours worked are compleely demand deermined. In he long run, however, home residens are inclined o work more so as o achieve 16 Appendix B provides a deailed descripion of he soluion process. 17 Following a emporary fiscal shock, he exchange rae appreciaion would be more pronounced because he long run governmen spending differenial eners he shor run exchange rae equaion wih a posiive sign. 19

21 he opimal labor leisure rade off. The marginal uiliy of leisure rises while he addiional income spen on consumpion lowers he marginal uiliy of consumpion unil equilibrium is resored. In ha case, he long run labor marke will clear a a higher equilibrium work effor faciliaing a re-increase of consumpion. Via he Euler equaions ha describe he households desire for consumpion smoohing - absracing from real ineres rae effecs - a higher long run consumpion level implies higher shor run consumpion. Then, due o he cash in advance consrain 18 domesic households are in he conjecured need of exra real balances in order o finance he re-increase of consumpion. As boh money supply and domesic prices are fixed in he shor run, an increase of real balances can only be brough abou hrough cheaper impors. This requires an appreciaion of he exchange rae. We can now proceed o analyze how he degree of PTM and he home bias affec he response of he nominal exchange rae in he ligh of a domesic fiscal expansion. In he case of PTM, i is easy o see via he parial derivaive, e s, ha a higher value of s leads o a larger appreciaion. A higher share of PTM goods implies ha less goods are affeced by a variaion of he exchange rae. Consequenly, he prices of he goods no subjec o PTM have o change more srongly o resore equilibrium, which means ha he appreciaion of he exchange rae has o be more pronounced. Likewise, a higher value of ω, represening a sronger bias for domesically produced goods, should reinforce he appreciaion of he exchange rae. Again, he explanaion is sraighforward: A smaller proporion of impored goods in he consumpion baske of he household implies ha he prices of hese goods have o change more srongly o obain he required change of he overall price level. Ye, he sign of he parial derivaive of he exchange rae wih respec o ω is no unique. However, for reasonable parameer values our reasoning is validaed. Figure 1 illusraes he effec of a variaion in ω on he exchange rae for differen values of s when domesic governmen expendiure dg p is increased by one percen. For he numerical simulaion we picked sandard parameer values, namely θ = 6 and β = The value of θ yields a relaively high mark up rae suiable for counries ha are less compeiive han he Unied Saes, see Hairaul and Porier (1993). We are now prepared o solve he model for he consumpion and oupu responses. Saring 18 Remember ha governmen expendiures leave domesic money demand unchanged if here is full crowding ou of privae consumpion. 19 See for example Warnock (2003). 20

22 shor run exchange rae response omega s=0 s=0.5 s=1 Figure 1: Effec of ω [0.5, 1) on he shor run exchange rae. wih he shor run world consumpion response, we add up linearized versions of he shor run money markes (29) and (30): c w = 1 dg 2 Noe ha price deviaions cancel ou by (33) and (34). The effec of fiscal expansions on overall world consumpion is unambiguously negaive and i does no maer wheher he expansion is emporary or permanen. 20 This is due o he fac ha overall world demand has o remain unchanged as world real money balances are fixed in he shor run. The level of any individual variable may be saed as a combinaion of is world aggregae and is differenial: c = c w ( c c ) = c w 1 dg 2 (1 ω)(1 s)ẽ = dg (1 ω)(1 s)ẽ (38) where he consumpion differenial is deduced from exchange rae equaion (35), ha sems 20 In Bes and Devereux (2000) he shor run world consumpion level is affeced if and only if fiscal expansions are permanen. 21

23 from money marke clearing. We see ha he effec of a governmen spending shock on shor run consumpion a home can be decomposed ino wo pars. As menioned before, he direc effec of an increase in ax financed governmen spending is - ceeris paribus - a complee crowding ou of privae consumpion. A he same ime, however, here is an indirec price effec hrough he response of he exchange rae. An appreciaion lowers he home price level, which allows - hrough he money marke condiions - consumpion o fall by less han he amoun of axes paid. In he same way, we derive he foreign consumpion response: c = c w 1 2 ( c c ) = c w + 1 dg 2 + (1 ω)(1 s)ẽ = (1 ω)(1 s)ẽ The only effec on foreign s shor run consumpion sems from he movemen of he nominal exchange rae. The appreciaion reduces he amoun of real balances available o households, which in urn requires a fall in consumpion. The indirec effecs on he consumpion responses hinges boh on he degree of pricing o marke and on he home bias in consumpion. I can be shown ha a higher degree of PTM always reduces domesic consumpion and raises foreign consumpion. This is due o he fac ha he limied pass-hrough effec associaed wih PTM dominaes he amplified appreciaion of he exchange rae. The PTM reasoning also applies for he home bias effec. For he above reasons world demand and consequenly world producion are no affeced by a domesic fiscal expansion in he shor run. As for he respecive individual oupu responses, domesic employmen is deermined by he condiion h = (1 s)y a (h) + s(y m (h) + y m (h)), and foreign employmen analogously by h = (1 s)y a (f) + s(y m (f) + y m (f)). Linearizing hese condiions and subsiuing for he respecive demands via he linearized goods marke equilibria we ge h = ω c + (1 ω) c + ω dg + (1 s)(1 ω)2ωθ ẽ (39) and h = ω c + (1 ω) c + (1 ω) dg (1 s)(1 ω)2ωθ ẽ (40) 22

24 Furhermore, subsiuing for he individual consumpion variables c and c we arrive a: h = (1 s)(1 ω)(2ω(θ 1) + 1) ẽ (41) and h = (1 s)(1 ω)(2ω(θ 1) + 1) ẽ In he shor run, hours worked only depend on he movemen of he exchange rae which deermines he compeiiveness of he respecive goods. An appreciaion of he exchange rae lowers demand for home goods as he relaive price ends o rise. Home consumers face cheaper impors whereas home expors become less aracive for foreign consumers. The opposie is rue for foreign goods, hence he reducion (rise) of home (foreign) producion and hours worked. Again, an increasing fracion s of PTM goods and a sronger home bias limi he expendiure swiching effec as a greaer share of good prices are no subjec o exchange rae movemens. Solving he exchange rae equaion (36) for he rade balance response yields: βdf +1 p ( = (1 ω) [2s 1 + 2ωθ(1 s)]ẽ ( c c ) dg ) (42) As can be seen from (42), he appreciaion of he exchange rae and a posiive domesic fiscal expansion work in he same direcion, whereas a negaive consumpion differenial miigaes he deerioraion of he rade balance. Replacing he shor run consumpion differenial defined by he exchange rae equaion (35) we ge a rade balance effec ha only depends on he exchange rae movemen: βdf +1 p = (1 ω) [(1 s)2 ω(θ 1) + 1] ẽ Thus, alogeher a permanen governmen expendiure shock causes a deerioraion of he rade balance via he exchange rae appreciaion. Wih oupu emporarily falling due o a decline in compeiiveness, and he sum of privae and governmen consumpion demand rising, domesic households resor o selling bonds so as o finance he gap beween ne shor run income and consumpion expendiures. A higher degree of PTM or of he home bias dampen his effec. 23

25 4 WELFARE ANALYSIS So far, we have esablished he effecs of an unanicipaed permanen fiscal shock on he shor run variables of ineres. Remember he main shor run resuls: The driving force of he model is he exchange rae which appreciaes. Domesic consumpion decreases, bu by less han he increased ax burden, while foreign consumpion decreases by he domesic re-increase. Domesic households work less whereas foreign households work more in spie of he demand composiion effecs. Toaling hese effecs, he home counry runs a curren accoun defici. In his secion we analyze he welfare implicaions of his adjusmen process. Wih he microfoundaions of our model a hand, we do no have o rely any longer on ad hoc welfare crieria as for example oupu simulaion per se. However, due o subopimally low seady sae producion levels, fiscal policy may improve welfare when producion is simulaed and he ne presen value of producion in consumpion unis exceeds he accompanying loss of uiliy semming from a higher working effor. We idenify hree welfare driving effecs which depend boh on he degree of PTM and on he home bias in consumpion: an overall demand effec, a erms-of-rade effec, and an expendiure swiching effec. To he end of a horough shor, long run and overall welfare quanificaion we oally differeniae he uiliy funcion (1): du = c θ 1 h θ Shor run domesic uiliy depends posiively on consumpion of he households, and negaively on heir working effor. Subsiuing for c and h using equaions (38) and (41) we arrive a: du = dg ( 2θ 1 (1 ω)(1 s) + θ ) 2ω(θ 1)2 ẽ (43) θ The fiscal expansion reduces domesic welfare via he amoun of axes paid. On he oher hand, he appreciaion of he exchange rae has an unambiguously posiive effec on welfare as i leads o he aforemenioned re-increase in consumpion and a reducion of hours worked. Wih oal PTM or ω 1, here is no miigaing effec of he exchange rae a all. We may carry ou he same exercise for he foreign counry. Then, he change of foreign 24

26 uiliy in he shor run is given by ( 2θ 1 du = (1 ω)(1 s) + θ ) 2ω(θ 1)2 ẽ (44) θ Comparing (43) and (44) reveals ha he home counry - while sill suffering he ax induced welfare loss - may raise shor run uiliy a he expense of he foreign counry. Adding up he individual changes in welfare we deduce ha he oal effec on world welfare is dg. The ineresing aspec of he shor run model lies in he inernaional disribuion of he welfare loss ha is associaed wih a ax-financed domesic fiscal expansion. Obviously, while welfare enhancing in he shor run, he curren accoun defici of he home counry has negaive welfare implicaions in he long run via permanen ineres rae paymens. Addiionally, a permanen fiscal expansion raises long run overall demand and affecs he long run erms of rade. In order o assess he overall welfare impac, we have o calculae welfare effecs for subsequen periods + i wih i = 1, 2,...,. From he long run home and foreign curren accouns and labor markes we derive he world consumpion response ( ) θ 1 1 c w dg +i +i = 2θ 1 2 and he response of world hours worked h w +i = ( ) θ 1 dg +i 2θ 1 2 In he subsequen periods, world consumpion of he privae secor will be reduced while world oupu is simulaed. As boh effecs are welfare reducing, world uiliy will decrease in he long run. Calculaing he long run consumpion differenial and he differenial of hours worked, and combining hese resuls wih he respecive world responses, we arrive a he following expression for he change of home uiliy from period + 1 onwards: ( ) θ 1 ωθ 2ω + 1 dg+i ( ) du +i = + + r(1 ω) (1 s)2ω(θ 1) + 1 ẽ 2θ 1 2ωθ 2ω + 1 In he same manner, we can show ha he long run impac on foreign uiliy is given as ( du+i θ(1 ω) = (2θ 1)(2ωθ 2ω + 1) ) dg+i ( ) r(1 ω) (1 s)2ω(θ 1) + 1 ẽ 25

27 As can easily be seen, he permanen fiscal expansion lowers domesic welfare from period + 1 on, and increases foreign welfare. Domesic households consume less and work more in he long run han in he iniial seady sae in order o finance governmen expendiure and o mee he permanen ineres paymens on deb accumulaed in he shor run. In he foreign counry, he siuaion is he oher way around: Employmen decreases, while consumpion increases. All in all, he foreign households are beer off in he long run. To obain he full impac of he fiscal shock we now combine he shor and long erm uiliy effecs. Using dv = du + (1/r)dU +1 and he analogous expression for he foreign counry, we ge he overall welfare effecs for he households in he wo counries: dv = dg 1 ( ) θ 1 ωθ 2ω + 1 dg+1 + +(1 ω) (2s 1+ 1 ) r 2θ 1 2ωθ 2ω + 1 θ (1 s)(2ωθ 2ω +1) ẽ dv = 1 r θ(1 ω) dg +1 (1 ω) (2s ) (2θ 1)(2ωθ 2ω + 1) θ (1 s)(2ωθ 2ω + 1) ẽ For he range of parameer values we consider, he erm preceding he exchange rae variaion is always posiive. The overall welfare effecs of he fiscal expansion are hus unambiguous: Households in he home counry suffer a welfare loss, whereas he foreign households welfare improves. A fiscal expansion becomes a prosper-hy-neighbor insrumen in our model. Figure 2 illusraes he welfare effecs of a one percen increase of domesic governmen expendiure dg p depending on ω for differen values of s. For he numerical simulaion we picked he parameer values saed above. A permanen fiscal expansion always lowers domesic welfare as he domesic households have o finance he overall expansion of demand while he welfare effecs semming from he inernaional ransmission of he fiscal shock are second order. The evoluion of foreign welfare (Figure 2(b)) gives a clearer picure of he underlying adjusmen process because foreign governmen expendiures are unchanged and do no blur he analysis. I is helpful o disinguish beween he anicipaed and he unanicipaed componen of he permanen fiscal shock. The dominaing effec on foreign overall welfare is he anicipaed simulaion of world demand in he long run (Overall Demand Effec), which explains he rough picure given in Figure 2(b). Increased world demand ranslaes eiher in higher foreign producion or higher relaive foreign producer prices boh of which are welfare enhancing. A 26