Segmented Asset Markets and Optimal Exchange Rate. Regimes 1

Transcription

1 Segmened Asse Markes and Opimal Exchange Rae Regimes 1 Amarya Lahiri Federal Reserve Bank of New York amarya.lahiri@ny.frb.org Rajesh Singh Iowa Sae Universiy rsingh@iasae.edu Carlos Vegh UCLA and NBER cvegh@ucla.edu Revised: Ocober We would like o hank Andy Akeson, Mick Devereaux, Hubero Ennis, Andy Neumeyer, Mark Spiegel, and seminar paricipans a Duke, FRB Cleveland, FRB NY, Penn Sae, UBC, UCLA, UC Sana Cruz, USC, Warwick, ITAM-FBBVA Summer Camp 2003, SED 2003, NBER IFM meeing Fall 2003, for helpful commens and suggesions. The usual disclaimer applies. Lahiri and Végh would like o hank he UCLA Academic Senae for research suppor. The views expressed here do no necessarily reflec he views of he Federal Reserve Bank of New York or he Federal Reserve Sysem.

2 Absrac This paper revisis he issue of he opimal exchange rae regime in a flexible price environmen. The key innovaion is ha we analyze his quesion in he conex of environmens where only a fracion of agens paricipae in asse marke ransacions (i.e., asse markes are segmened). We show ha flexible exchange raes are opimal under moneary shocks and fixed exchange raes are opimal under real shocks. These findings are he exac opposie of he sandard Mundellian prescripion derived under he sicky price paradigm wherein fixed exchange raes are opimal if moneary shocks dominae while flexible raes are opimal if shocks are mosly real. Our resuls hus sugges ha he opimal exchange rae regime should depend no only on he ype of shock (moneary versus real) bu also on he ype of fricion (goods marke fricion versus financial marke fricion). Keywords: Opimal exchange raes, asse marke segmenaion JEL Classificaion: F1,F2

3 1 Inroducion Fify years afer Milon Friedman s (1953) celebraed case for flexible exchange raes, he debae on he opimal choice of exchange rae regimes rages on as fiercely as ever. Friedman argued ha, in he presence of sicky prices, floaing raes would provide beer insulaion from foreign shocks by allowing relaive prices o adjus faser. In a world of capial mobiliy, Mundell s (1963) work implies ha he opimal choice of exchange rae regime should depend on he ype of shocks hiing an economy: real shocks would call for a floaing exchange rae, whereas moneary shocks would call for a fixed exchange rae. Ulimaely, however, an explici cos/benefi comparison of exchange rae regimes requires a uiliy-maximizing framework, as argued by Helpman (1981) and Helpman and Razin (1979). In such a framework, Engel and Devereux (1998) reexamine his quesion in a sicky prices model and show how resuls are sensiive o wheher prices are denominaed in he producer s or consumer s currency. On he oher hand, Cespedes, Chang, and Velasco (2000) incorporae liabiliy dollarizaion and balance shees effecs and conclude ha he sandard prescripion in favor of flexible exchange raes in response o real shocks is no essenially affeced. An implici assumpion in mos, if no all, of he lieraure is ha economic agens have unresriced and permanen access o asse markes. 1 This, of course, implies ha in he absence of nominal rigidiies, he choice of fixed versus flexible exchange raes is irrelevan. In pracice, however, access o asse markes is limied o some fracion of he populaion (due o, for example, fixed coss of enry). This is likely o be paricularly rue in developing counries where asse markesaremuchsmallerinsizehaninindusrialcounries. Table1showshaevenforheUnied Saes, he degree of segmenaion in asse markes is remarkably high. The able reveals ha 59 percen of U.S. households did no hold any ineres bearing asses (defined as money marke accouns, cerificaes of deposi, bonds, muual funds, and equiies). More srikingly, 25 percen 1 There are some excepions when i comes o he relaed issue of he coss and benefis of a common currency area (see, for example, Neumeyer (1998) and Ching and Devereux (2000), who analyze his issue in he presence of incomplee asse markes). 1

4 of households did no even have a checking accoun as lae as in Given hese facs for a developed counry like he Unied Saes, i is easy o anicipae ha he degree of asse marke segmenaion in emerging economies mus be considerably higher. Since asse markes are a he hear of he adjusmen process o differen shocks in an open economy, i would seem naural o analyze how asse marke segmenaion affecs he choice of exchange rae regime. 2 Table 1: US Household ownership of financial asses, 1989 Ineres-bearing asses Checking accoun No Yes Toal No 19% 6% 25% Yes 40% 35% 75% Toal 59% 41% 100% Source: Mulligan and Sala-i-Marin (2000). Daa from he Survey of Consumer Finance. This paper absracs from any nominal rigidiy and focuses on a sandard moneary model of an economy subjec o sochasic real and moneary (i.e., velociy) shocks in which he only fricion is ha an exogenously-given fracion of he populaion can access asse markes. The analysis makes clear ha asse marke segmenaion inroduces a fundamenal asymmery in he choice of fixed versus flexible exchange raes. To see his, consider firs he effecs of a posiive velociy shock in a sandard one-good open economy model in he absence of asse marke segmenaion. Under flexible exchange raes, he velociy shock ges refleced in an excess demand for goods, which leads o an increase in he price level (i.e., he exchange rae). Under fixed exchange raes, 2 In closed economy macroeconomics, asse marke segmenaion has received widespread aenion ever since he pioneering work of Grossman and Weiss (1983) and Roemberg (1984) (see also Chaerjee and Corbae (1992) and Alvarez, Lucas, and Weber (2001)). The key implicaion of hese models is ha open marke operaions reduce he nominal ineres rae and hereby generae he so-called liquidiy effec. In an open economy conex, Alvarez and Akeson (1997) and Alvarez, Akeson, and Kehoe (2002) have argued ha asse marke segmenaion models help in resolving ousanding puzzles in inernaional finance such as volaile and persisen real exchange rae movemens as well as excess volailiy of nominal exchange raes. 2

5 he adjusmen mus ake place hrough an asse marke operaion whereby agens exchange heir excess money balances for foreign bonds a he cenral bank. In eiher case, he adjusmen akes place insananeously wih no real effecs. How does asse marke segmenaion affec his adjusmen? Under flexible raes, he same adjusmen akes place. Under fixed exchange raes, however, only hose agens who have access o asse markes (called raders ) may ge rid of heir excess money balances. Non-raders who are shu off from asses markes canno do his. Non-raders are herefore forced o buy excess goods. The resulan volailiy of consumpion is cosly from a welfare poin of view. Hence, under asse marke segmenaion and in he presence of moneary shocks, flexible exchange raes are superior han fixed exchange raes. Asse marke segmenaion also has dramaic implicaions for he opimal exchange rae regime when shocks come from he goods marke. We show ha when oupu is sochasic, non-raders in he economy unambiguously prefer fixed exchange raes o flexible exchange raes because pegs provide a form of risk pooling. Under a peg, household consumpion is a weighed average of curren period and las period s oupu which implies ha he consumpion risk of non-rading households is pooled across periods. Under flexible raes, however, he real value of consumpion is always curren oupu which implies no ineremporal risk sharing. Trading households, on he oher hand, prefer flexible exchange raes o fixed exchange raes since mainaining an exchange rae peg involves injecing or wihdrawing money from raders which makes heir consumpion more volaile under a peg. However, using a populaion share weighed average of he welfare of he wo ypes, we show ha under fairly general condiions, he non-raders preferences dominae he social welfare funcion. Hence, he opimal exchange rae regime when oupu is sochasic is an exchange rae peg. 3 We derive he resuls in he ex under incomplee markes, which is he more realisic assumpion (see Burnside, Eichenbaum, and Rebelo (1999) for a relaed discussion.) In he appendix 3 We derive he resuls in he ex under incomplee markes, which is he more realisic assumpion (see Burnside, Eichenbaum, and Rebelo (1999) for a relaed discussion.) We show in he appendix ha he same resuls obain under complee markes (and, are in fac, even sarker). 3

6 we show ha he same resuls obain under complee markes (and, are in fac, even sarker). Moreover, in he appendix we also derive he moneary policy rule which implemens he firs-bes allocaion. Ineresingly, his rule involves a procyclical moneary policy. In he process, we show ha in an environmen wih only velociy shocks, flexible exchange raes successfully implemen he firs-bes allocaion. However, when oupu shocks are he only source of uncerainy, he fixed exchange rae regime fails o implemen he firs-bes even hough i welfare dominaes he flexible exchange rae regime. In sum, he paper shows ha asse marke segmenaion may be a criical fricion in deermining he opimal exchange rae regime. More crucially, resuls under asse marke segmenaion run couner o he Mundellian prescripion ha if moneary shocks dominae hen fixed raes are preferable, while if real shocks dominae flexible raes are preferable. This discrepancy reflecs he difference in he underlying fricion. In he Mundell-Fleming world, sicky prices presumably reflec some imperfecion in goods markes, whereas in our model asse marke segmenaion capures some imperfecion in asse markes (for example, fixed cos of enry). Of course, which fricion dominaes in pracice is ulimaely an empirical issue. However, our resuls sugges ha policy judgemens regarding he choice of exchange rae regimes need o be based on a broader se of analyical facors han jus he sandard sicky price-based Mundell insigh. In paricular, aside from a judgemen regarding he relaive imporance of alernaive shocks (e.g., moneary or real shocks), his decision should also be based on a judgemen regarding he relaive imporance of alernaive fricions (e.g., sicky prices or asse marke segmenaion) since differen fricions have conflicing implicaions. Lasly, we also sudy he implicaions of asse marke segmenaion for he debae regarding inflaion argeing versus money argeing. Since mos of he exising work on his opic has been done in a closed economy conex, we sudy he quesion in ha conex as well. Mirroring he resuls in he open economy version, we find ha under asse marke segmenaion, money-argeing is welfare superior o inflaion argeing when shocks are moneary while inflaion argeing is he superior policy if shocks are real. The paper proceeds as follows. Secion 2 presens he model and he equilibrium condiions 4

7 while Secion 3 describes he allocaions under alernaive exchange rae regimes and derives he opimal regime under moneary and oupu shocks. Secion 4 sudies he implicaions of asse marke segmenaion for he inflaion argeing versus money argeing debae in a closed economy conex. Finally, Secion 5 concludes. Algebraically edious proofs are consigned o an appendix. The appendix also derives he complee markes case. 2 Model The basic model is an open economy varian of he model oulined in Alvarez, Lucas, and Weber (2001). Consider a small open economy perfecly inegraed wih world goods markes. There is a uni measure of households who consume an inernaionally-raded good. The world currency price of he consumpion good is fixed a one. The households ineremporal uiliy funcion is ( ) X W = E β s u(c s ), (1) s= where β is he households ime discoun facor, c s is consumpion in period s, while E denoes he expecaion condiional on informaion available a ime. The households face a cash-in-advance consrain. As is sandard in hese models, he households are prohibied from consuming heir own endowmen. We assume ha a household consiss of a seller-shopper pair. While he seller sells he household s own endowmen, he shopper goes ou wih money o purchase consumpion goods from oher households. There are wo poenial sources of uncerainy in he economy. Firs, each household receives a random endowmen y of he consumpion good in each period. We assume ha y is an independenly and idenically disribued random variable wih mean ȳ and variance σ 2 y. 4 Second, following Alvarez e al, we assume ha he shopper can access a proporion v of he household s curren period () sales receips, in addiion o he cash carried over from he las period (M ),o purchase consumpion. We assume ha v is an independenly and idenically disribued random variable wih mean v [0, 1] and variance σ 2 v. Only a fracion of he populaion, called raders, 4 We could allow for differen means and variances for he endowmens of raders and non-raders wihou changing our basic resuls. 5

8 have access o he asse markes, where The res, 1, called non-raders, can only hold domesic money as an asse. In he following we shall refer o hese v shocks as velociy shocks. 6 The iming runs as follows. Firs, boh he endowmen and velociy shocks are realized a he beginning of every period. Second, he household splis. Sellers of boh households say a home and sell heir endowmen for local currency. Shoppers of he non-rading households are excluded from he asse marke and, hence, go direcly o he goods marke wih heir overnigh cash o buy consumpion goods. Shoppers of rading households firs carry he cash held overnigh o he asse marke where hey rade in bonds and receive any money injecions for he period. They hen proceed o he goods marke wih whaever money balances are lef afer heir porfolio rebalancing. Afer acquiring goods in exchange for cash, he non-rading-shopper reurns sraigh home while.he rading-shopper can re-ener he asse marke o exchange goods for foreign bonds. Afer all rades for he day are compleed and markes close, he shopper and he seller are reunied a home. 5 Noe ha hough raders do have access o asse markes, hese markes are incomplee. More specifically, raders do no have access o asse markes where hey can rade in sae coningen asses spanning all saes. Hence, as will become clear below, random shocks can induce wealh effecs and consumpion volailiy for raders as well, despie heir access o compeiive world capial markes. In he appendix, we analyze he complee markes case and show how he same key resuls obain. Hence, our resuls on he opimal exchange rae regime under asse marke segmenaion do no depend on wheher asse markes for raders are complee or no. 6 There are alernaive ways in which one can hink abou hese velociy shocks. Following Alvarez, Lucas, and Weber (2001) one can hink of he shopper as visiing he seller s sore a some ime during he rading day, empying he cash regiser, and reurning o shop some more. The uncerainy regarding v can be hough of as he uncerainy regarding he oal volume of sales a he ime ha he shopper accesses he cash regiser. Alernaively, one can hink of his as represening an environmen where he shopper can purchase goods eiher hrough cash or credi. However, he mix of cash and credi ransacions is uncerain and flucuaes across periods. 6

9 2.1 Households problem Non-raders The non-rader s cash-in-advance consrain is given by: M NT + v S y = S c NT, (2) where M NT is he beginning of period nominal money balances while S is he period exchange rae (he domesic currency price of foreign currency). Equaion (2) shows ha for consumpion purposes, he non-raders can augmen he beginning of period cash balances by wihdrawals from curren period sales receips v (he velociy shocks). Money balances a he beginning of period +1are given by sales receips ne of wihdrawals for period consumpion: M NT +1 = S y (1 v ), (3) where S denoes he domesic currency price of consumpion goods a ime. The usual flow consrain follows from combining (2) and (3): M+1 NT = M NT + S y S c NT. (4) Given he cash-in-advance (2), i follows ha: c NT = M NT + v S y S. (5) Traders The raders begin any period wih asses in he form of money balances and bond holdings carried over from he previous period. Armed wih hese asses he shopper of he rader household visis he asse marke where she rebalances he household s asse posiion and also receives he lump sum asse marke ransfers from he governmen. Thus, for any period, he accouning ideniy for he asse marke ransacions of a rader household is given by ˆM T = M T +(1+i 1 ) B B +1 + S (1 + r)f S f +1 + T, (6) 7

10 where ˆM T denoes he money balances wih which he rader leaves he asse marke and M T denoes he money balances wih which he rader enered he asse marke. Also, B denoes aggregae one-period nominal governmen bonds, i is he ineres rae on hese nominal bonds, f are foreign bonds (denominaed in erms of he consumpion good), r is he exogenous and consan world real ineres rae, and T are aggregae (nominal) lump-sum ransfers (i.e., negaive axes) from he governmen. 7,8 Noe ha nominal bonds mauring a dae pay an ineres rae i 1 since his rae was conraced in 1. 9 Afer asse markes close, he shopper proceeds o he goods marke wih ˆM T in nominal money balances o purchase consumpion goods. Like non-raders, raders can also augmen hese saring money balances wih random wihdrawals from curren sales receips o carry ou goods purchases. Thus, he cash-in-advance consrain for a rader is given by 10 S c T = ˆM T + v S y. (7) Combining equaions (6) and (7) gives M T + T + v S y = S c T + B +1 (1 + i 1) B + S f +1 S (1 + r)f, (8) In his se-up he only reason ha raders hold money overnigh is he separaion beween markes. In paricular, if he seller could access he asse marke a he end of he day, hen he 7 We assume ha hese ransfers are made in he asse markes, where only he raders are presen. Noe ha since B and T denoe aggregae bonds and aggegae ransfers, heir corresponding per rader values are B/ and T/ since raders comprise a fracion of he populaion. 8 The assumpion of endogenous lump-sum ransfers will ensure ha any moneary policy may be consisen wih he ineremporal fiscal consrain. This becomes paricularly imporan in his sochasic environmen where hese endogenous ransfers will have o adjus o ensure ineremporal solvency for any hisory of shocks. To make our life easier, hese ransfers are assumed o go only o raders. If hese ransfers also wen o non-raders, hen (5) would be affeced. 9 Alernaively, we could work wih one period discoun bonds so ha he ime price of a bond paying one uni 1 1+i. of he local a ime +1 would be 10 Throughou he analysis we shall resric aenion o ranges in which he cash-in-advance consrain binds for boh raders and non-raders. In general, his would enail checking he individual opimaliy condiions o infer he parameer resricions for which he cash-in-advance consrains bind. 8

11 rading household would use all heir remaining sales receips from he period o buy ineres bearing bonds. However, since asse markes close before he opening of he goods marke, raders are forced o hold money overnigh. Thus, period- sales receips ne of wihdrawals become beginning of nex period s money balances M+1 T = S y (1 v ). (9) Noe ha since v, S, and y are all exogenous, he raders money holdings evolve exogenously over ime. A rader chooses c, B +1 and f +1 o maximize (1) subjec o he flow consrain (8). Combining firs-order condiions, we obain: u 0 (c T )=β(1 + r)e u 0 (c T +1) ª, (10) " u 0 (c T ) u 0 (c T +1 = β (1 + i ) E ) #. (11) S S +1 Equaion (10) is he sandard Euler equaion for he rader which relaes he expeced marginal rae of consumpion subsiuion beween oday and omorrow o he reurn on savings (given by 1+r) discouned o oday. Equaion (11), on he oher hand, deermines he opimal holdings of nominal bonds. Equaions (10) and (11) joinly deermine he modified ineres pariy condiion for his economy which reflecs he sandard porfolio choice beween safe and risky asses. 2.2 Governmen The governmen in his economy holds foreign bonds (reserves) which earn he world rae of ineres r. The governmen can sell nominal domesic bonds, issue domesic money, and make lump sum ransfers o he raders. Thus, he governmen s budge consrain is given by S h +1 (1 + r)s h +(1+i 1 )B B +1 + T = M +1 M, (12) where B denoes he amoun of nominal governmen bonds held by he privae secor, h are foreign bonds held by he governmen, M is he aggregae money supply, and T is governmen ransfers o he raders. Equaion (12) makes clear ha he money supply can be alered in hree ways: 9

12 hrough open marke operaions, hrough inervenions in he foreign exchange marke, or hrough ransfers. Imporanly, all hree mehods impac only he raders since hey are he only agens presen in he asse marke. 2.3 Equilibrium condiions Equilibrium in he money marke requires ha M = M T +(1 )M NT. (13) The flow consrain for he economy as a whole (i.e., he curren accoun) follows from combining he flow consrain for non-raders (equaion (4)), raders (equaions (7) and (9)), and he governmen (equaion (12)) and money marke equilibrium (equaion (13)): c T +(1 )c NT = y +(1+r)k k +1, (14) where k h + f denoes per-capia foreign bonds for he economy as a whole. To obain he quaniy heory, combine (3), (9) and (13) o ge: M +1 1 v = S y. (15) Noice ha he sock of money relevan for he quaniy heory is end of period money balances (i.e., M +1 ). This reflecs he fac ha, unlike sandard CIA models (in which he goods marke is open before he asse marke and shoppers canno wihdraw curren sales receips for consumpion), in his model (i) asse markes open and close before goods marke open (which allows raders o change his period s money balances for consumpion purposes); and (ii) boh raders and nonraders can access curren sales receips. Combining (3) and (5) gives he consumpion of non-raders: c NT = S 1y 1 +(v S y v 1 S 1 y 1 ) S. (16) To derive he consumpion of raders, we use equaion (9) o subsiue for M T in equaion (8). Then, subracing S y from boh sides allows us o rewrie (8) as (1 + r)f f +1 + (1 + i 1) B B +1 + T + y c T = M +1 M, S S 10

13 wherewehaveusedequaion(15)ogem +1 M =[(S y S 1 y 1 ) (v S y v 1 S 1 y 1 )]. Using equaion (12) in he equaion above gives k +1 (1 + r)k = y c T + µ µ 1 M+1 M S, (17) where k 0 is given exogenously. Equaion (17) gives he rader s flow consrain in equilibrium. The lef hand side capures he ne acquisiion of foreign asses (per rader) by he economy while he righ hand side gives periodic rader income ne of consumpion. Given he precise moneary regime, we can ierae forward equaion (17) and impose he rader household s firs order condiion for opimal consumpion (equaion (10)) o derive he rader s policy funcion for consumpion along a raional expecaions equilibrium pah. I is worh noing ha he las erm on he righ hand side of (17) capures he source of redisribuion in his economy. Any changes of money supply occur hrough cenral bank operaions in he asse marke where only raders are presen. Hence, he raders receive he enire incremenal money injecion while heir own increase in money balances is only a fracion of he oal. This leads o redisribuion of ³ 1 M +1 M S from non-raders o raders. Noe ha as 1 his erm goes o zero. I is imporan o noe ha his channel exiss solely due o asse marke segmenaion. 3 Alernaive exchange rae regimes Having described he model and he equilibrium condiions above, we now urn o allocaions under specific exchange rae regimes. We will look a wo pure cases:flexible exchange raes and fixed exchange raes. The end goal, of course, is o evaluae he welfare implicaions under he wo regimes. In all he policy experimens below, we shall assume ha he iniial disribuion of nominal money balances across he wo ypes of agens is invarian. In paricular, we assume ha M T 0 = M NT 0 = M. In order o make he analyics of he welfare comparisons racable, we shall also assume from 11

14 hereon ha he periodic uiliy funcion of boh agens is quadraic: u(c) =c ζc 2. (18) To focus our resuls, we shall proceed by analyzing he effec of each shock in isolaion. In paricular, we firs sudy an environmen where he only shock is he velociy shock and hen go o he oher case where he only shock is he real shock. 3.1 Velociy shocks only In his subsecion we focus solely on velociy shocks. Hence, we se σ 2 y =0. Thus, here is no uncerainy abou he endowmen process. Every period all households receive he fixed endowmen ȳ Flexible exchange raes under velociy shocks We assume ha under flexible exchange raes, he moneary auhoriy ses a consan pah of he money supply: M = M. Furher, he governmen does no inervene in foreign exchange markes and, for simpliciy, we assume ha iniial foreign reserves are zero. Then, he governmen s flow consrain reduces o: (1 + i 1 )B B +1 + T =0. (19) The quaniy heory equaion (15) deermines he exchange rae: S = M (1 v )ȳ. (20) The exchange rae will hus follow he velociy shock and be high (low) when he shock v is high (low). Using (20), consumpion of non-raders (given by equaion(16)) under flexible exchange raes can be wrien as: c NT,flex =ȳ, 0. (21) 12

15 Equaion (21) shows ha consumpion of non-raders remains consan a all imes. Inuiively, under floaing exchange raes, prices change in proporion o he velociy shocks. Since he velociy shock is common o all agens, here is no redisribuion of purchasing power beween agens. To deermine consumpion of raders under he floaing exchange rae regime, we can ierae forward equaion (17) under he condiion M = M o ge c T,flex = r k 0 +ȳ, 0, (22) where we have used he fac ha under he quadraic uiliy specificaion adoped above, equaion (10) which describes he opimal consumpion plans for raders reduces o c 0 = E 0 (c ) for all >0. Hence, under flexible exchange raes, consumpion of raders is also consan over ime. The inuiion is he same as before. Since, prices change in proporion o heir velociy shock, here are no real balance effecs on he raders. Hence, heir consumpion remains invarian over ime Fixed exchange raes under velociy shocks Under fixed exchange raes, he moneary auhoriy ses a consan pah of he exchange rae equal o S. In paricular, we assume ha he nominal exchange rae is fixed a S = M (1 v)ȳ. (23) In effec, we are assuming ha a ime =0he moneary auhoriy pegs he exchange rae a he deerminisic equilibrium level. Under his specificaion, i is easy o see from equaion (16) ha consumpion of non-raders under a fixed exchange rae is given by c NT,peg =ȳ [1 + (v v 1 )], (24) c NT,peg 0 =ȳ [1 + (v 0 v)]. (25) Equaion (24) shows ha under an exchange rae peg, consumpion of non-raders will flucuae by he full amoun of heir velociy shock. Inuiively, velociy shocks change he nominal balances 13

16 ha non-raders have available for consumpion. Since he price level is now fixed, any change in nominal balances also implies a one-for-one change in real balances and, hence, affecs he consumpion of non-raders. To deermine he consumpion of raders we again ierae forward on equaion (17) by using he Euler equaion c 0 = E 0 (c ) and afer imposing he condiion S = S for all, wege " c T,peg 0 = r k µ 0 +ȳ " ( r X µ 1 (v 0 v)+e 0 (v v 1))##. (26) 1+r 1+r In deriving (26) we have used he fac ha under pegged exchange raes, equaion (15) implies ha M +1 M = (v v 1 ) Sȳ. 11 To undersand he consumpion funcion of raders, noe ha under fixed exchange raes, =1 he nominal value of GDP remains unchanged, i.e., S ȳ = Sȳ for all. The quaniy heory relaionship requires ha aggregae nominal money balances plus he aggregae wihdrawal from curren period sales be sufficien o purchase curren nominal oupu. To keep nominal oupu unchanged over ime, any change in cash wihdrawals from curren receips, i.e., v 6= v 1,mus be me by he moneary auhoriy wih an offseing change in aggregae nominal money balances. This inervenion mus happen hrough ransacions in he asse marke where only raders are presen. On a per rader basis hen, he proporional change in nominal money balances needed for keeping he exchange rae fixed is 1 (v v 1 ). Thus, under fixed exchange raes, a velociy shock of v no only changes real balances of raders by he full amoun bu also changes heir real balances by 1 due o cenral bank inervenion. The ne effec is 1 1 which is he erm ha shows up in he coefficien on he velociy shocks in equaion (26) Opimal exchange rae regime Having described allocaions under he alernaive exchange rae arrangemens, we now urn o he key focus of he paper: deerminaion of he opimal exchange rae regime. We shall conduc our 11 More generally, consumpion of raders under fixed exchange raes a any poin in ime >1 is given by " c T,peg = r k µ + y ( X µ s 1 E (v s v s 1))#. 1+r s= 14

17 analysis by comparing he uncondiional expecaion of lifeime welfare a ime =0(i.e., before he revelaion of any informaion a ime 0). In erms of preliminaries, i is useful o define he following: ½ X ³ W i,j = E β c i,j ζ c i,j 2 ¾, i = T,NT, j = flex, peg, (27) W j = W T,j +(1 )W NT,j, j = flex, peg. (28) Equaion (27) gives he welfare for each agen under a specific exchange rae regime where he relevan consumpion for each ype of agen is given by he consumpion funcions derived above for each regime. Equaion (28) is he aggregae welfare for he economy under each regime which is he sum of he regime specific individual welfares weighed by heir populaion shares. Noe ha he quadraic uiliy specificaion implies ha he expeced value of periodic uiliy can be wrien as where var(c) denoes he variance of consumpion. E c ζc 2 = E(c) ζ [E(c)] 2 ζv ar(c). (29) Proposiion 1 When velociy shocks are he only source of uncerainy in he economy, he flexible exchange rae regime welfare-dominaes he fixed exchange rae regime for boh agens and hence, is he opimal exchange rae regime for he economy. Proof. I is easy o see ha E(c NT,flex )=E(c NT,peg )=ȳ while E(c T,flex 0 )=E(c T,peg 0 )=r k 0 +ȳ. Hence, for boh ypes of agens, expeced consumpion under he wo regimes is idenical. However, Var(c T,peg ) > Var(c T,flex ) = 0 and Var(c NT,peg ) > Var(c NT,flex ) = 0 for all. From he expression for expeced periodic uiliy given by (29), i hen follows direcly ha W i,flex >W i,peg, i = T,NT. Hence, welfare under flexible exchange raes is greaer han welfare under fixed exchange raes for boh agens. Thus, aggregae welfare under flexible exchange raes is unambiguously greaer han under fixed raes. 15

18 Inuiively, under flexible exchange raes he adjusmen of he price level is proporional o he velociyshockofbohagens. Hence,flexible exchange raes compleely insulae he real balances of boh agens which allows hem o smooh consumpion compleely. Under fixed exchange rae on he oher hand, a wealh redisribuion occurs across agens due o velociy shocks. Specifically, in order o keep he exchange rae unchanged, he moneary auhoriy inervenes in he asse marke o accommodae he average effec of he velociy shock. This affecs ransfers o raders which induces redisribuions. Hence, consumpion of non-raders flucuaes over ime while consumpion of raders is affeced by a wealh effec coming from asse marke ransfers. We should noe ha in he special case where all agens are raders, i.e., =1, our model reduces o a sandard represenaive agen, small open economy model wih perfec capial mobiliy. To deermineheopimalexchangeraeregimeinhiscasewecanfocusexclusivelyonhewelfare comparison for raders across he wo exchange rae regimes. Proposiion 2 When all agens in he economy are raders, i.e., =1,hefixed and flexible exchange rae regimes are welfare equivalen. Proof. For =1i follows direcly from equaions (22) and (26) ha c T,flex 0 = c T,peg 0 = rk 0 +ȳ. Hence, for =1, consumpion for raders is idenical under boh regimes. Moreover, since no sochasic erms ener he consumpion funcion, welfare of raders (and hence aggregae welfare as well) mus be idenical under boh regimes. Thus, welfare is independen of he exchange rae regime. This resul is similar o he well known resul of Helpman and Razin (1979) who showed he welfare equivalence beween fixed and flexible exchange raes for represenaive agen economies wih perfec capial mobiliy where agens are subjec o cash-in-advance consrains. Inuiively, under flexible exchange raes he price level adjuss exacly in proporion o he rader s velociy shock which leaves her real balances unchanged and hereby insulaes her compleely from any wealh effecs due o real balance flucuaions. Symmerically, when exchange raes are fixed, 16

19 he moneary auhoriy pegs he exchange rae by exacly offseing he aggregae velociy shock hrough a corresponding inervenion in asse markes. When all agens are in he asse marke, he inervenion amoun in asse markes corresponds exacly o he size of he rader s velociy shock which leaves heir real balances unchanged. As in he flexible exchange rae case, his inervenion effecively insulaes raders from any wealh effecs due o heir velociy shocks. Hence, he wo regimes are idenical from a welfare sandpoin. 3.2 Oupu shocks only We now urn o he issue of real shocks and heir effecs in his model. To focus on his issue, we assume ha v = v for all and σ 2 v =0. In oher words, here is no uncerainy regarding he velociy realizaion. However, we now assume ha oupu, y, is i.i.d. wih mean ȳ and variance σ 2 y. To analyze he welfare rade-offs underfixed and flexible exchange raes we shall coninue o assume ha under flexible exchange raes M = M for all while under fixed exchange raes S = S (= M/(1 v)ȳ). The quaniy heory equaion in his case is given by M +1 1 v = S y. Noe ha M = M implies ha under a flexible exchange rae regime, nominal income is consan over ime. Hence, nominal money balances of boh ypes are also consan over ime. The above implies ha consumpion allocaions for non-raders under he wo regimes, using equaion (16), are given by c NT,flex = y, (30) c NT,peg =(1 v) y 1 + vy. (31) Noe ha in deriving equaion (30) we have used he fac S 1 y 1 = S y under flexible raes. Similarly, ieraing forward on he periodic budge consrain for he rading households, equaion 17

20 (17), and imposing he relevan moneary regime on he resul gives he consumpion allocaions for raders under he wo regimes: c T,flex = r k +(1 β)y + βȳ, (32) c T,peg = r k µ µ Ω +(1 β) y 1 + β + 1 β µ Ω y + β β + 1 β Ω ȳ, (33) ³ where Ω =[1 (1 ) v]. I iseasy o checkha E(c NT,flex )=E(c NT,peg )=ȳ and E c T,flex = ³ E c T,peg = r k 0 +ȳ. Hence, expeced consumpion of boh ypes is idenical under he wo regimes. However he variance of consumpion is differen. Specifically, Var(c NT,flex )=σ 2 y, (34) Var(c NT,peg )=σ 2 y [1 2 v (1 v)] <σ 2 y, (35) Var(c NT,peg 0 )= v 2 σ 2 y <σ 2 y (36) Hence, for non-rading households, consumpion volailiy is lower under a peg relaive o a flexible exchange rae regime. Given ha expeced consumpion is idenical under he wo regimes while volailiy is lower under a peg, i follows ha non-raders always prefer a fixed exchange rae regime o a flexible rae regime when shocks are real. 12 To undersand he inuiion, noe ha under flexible exchange raes, a consan pah of nominal money balances implies ha he real value of las period s sales (in erms of curren prices) is always equal o curren oupu. Hence, curren consumpion (which is a weighed average of curren and las period s real sales revenues) is jus curren oupu. Thus, he enire variance of curren oupu is refleced in he variance of curren consumpion. Under an exchange rae peg on he oher hand, he real value of las period s sales is always las period s oupu. is a weighed average of las period and curren period s oupu. Hence, curren consumpion The resuling lower variance of consumpion under a peg reflecs a form of risk pooling: he consumpion risk is pooled across periods. 12 We should noe ha his resul is crucially dependen on he household being able o consume some fracion of curren sales, i.e., v>0. If v =0hen c NT,flex he variance of consumpion would be idenical under he wo regimes. = y and c NT,peg = y 1. Hence, boh expeced consumpion and 18

21 The variance of consumpion of rading households also differs across he wo regimes. In he appendix (6.1) we show ha ³ Var c T,peg ³ Var ³ Var c T,peg 0 c T,flex = =(1 β) 2 µ h r 2 β 2 +(1 β) 2i σ 2 y, (37) β + 1 β 2 Ω σ 2 y, (38) = r 2 h³ ( 1) (βa + C) 2 + r 2 C 2 +(1 β) 2 A 2 + B 2 +2r (1 β) AC i σ 2 y, (39) where A = Ω, B = β + 1 β Ω,andC = Ω (1 β) B. Our welfare meric is given, as before, by equaion (28). In order o compare welfare across regimes we define W W flex W peg. Subsiuing equaions (34-39) in (27) and (28) gives W = W T +(1 ) W N = 1 c2 2 + c 1 + c 0, (40) ³ ³ ³ ³ where c 2 = a 2 (1 β) 2 1+β 1 β +2a 1 1 β (1 β) ; c 1 = a 2 2(1 β) 2 1+β 1 β 2a 1 1 β (1 β) ; c 0 = a 2 (1 β) 2 ; and where a =1 v. Lemma 1 Equaion (40) has wo roos: 1 =1 and 2 = Proof. See Appendix. ³ a 2 (1 β) 2 ³ (1 β) a 2 (1 β) 2 1+β +2a 1. 1 β 1 β Lemma 2 β (0.5, 1] and v >0 are joinly sufficien condiions for 2 (0, 1). Proof. See Appendix. Proposiion 3 When endowmen shocks are he only source of uncerainy in he economy and he condiions of Lemma 2 apply, he opimal exchange rae regime is a fixed exchange rae for all > 2 while flexible exchange raes are opimal for all < 2. Proof. See Appendix. Thus, Proposiion 3 shows ha whenever he share of raders is above a criical hreshold, fixed exchange raes are he opimal regime under real shocks. Noe ha his lower hreshold goes o zero as v ends o uniy. The sriking feaure of his resul is ha i is he opposie of he convenional wisdom derived under sicky prices. Recall ha under sicky prices and real shocks, flexible exchange raes are opimal. Hence, once again he well-known opimal exchange 19

22 rae resuls due o Mundell appear o be urned on heir heads. Noe ha he condiions of Lemma 2 are quie non-resricive. To undersand he inuiion behind his resul, i is helpful o noe ha while boh ypes of agens face he same shock, heir abiliy o cope wih hem is asymmeric. In paricular, rading households have an exra insrumen financial asses wih which o smooh ou heir consumpion flow in response o shocks. Thus, he welfare losses of raders in shifing from a flexible exchange rae regime o a peg is always smaller han he corresponding loss of a nonrading household moving from a peg o a flexible exchange rae regime. Thus, he preferences of non-raders ypically dominaes he overall welfare crierion. The only cavea o his inuiion occurs for very small values of. In paricular, when < 2, a very small number of rading households have o bear he burden of mainaining an exchange rae peg for he enire economy by acceping all he moneary injecions or wihdrawals. Due o heir very small numbers, he resulan consumpion volailiy of raders under a peg becomes very big. A he limi, consumpion volailiy of raders goes o infiniy as ends o zero. However, our simulaions show ha for mos realisic parameer values, 2 is very small (ypically in he second or hird decimal poin). 13 Moreover, we also know ha for =0he opimal regime is a peg since non-rading households unambiguously prefer exchange rae pegs o flexible regimes. Hence, ypically he range in which flexible raes are opimal is very small. This suggess ha exchange rae pegs are, in general, he opimal regime under oupu shocks. 4 Closed economy case We now urn our aenion from exchange rae policy in an open economy o moneary policy in a closed economy conex. Over he pas decade, an ongoing debae in moneary policy design has been he relaive meri of inflaion argeing versus money argeing. Laely a consensus appears o be emerging in favor of inflaion argeing. Mos such conclusions are however derived from environmens wih nominal sickiness (eiher prices or wages) (see Clarida, Gerler and Gali (1999) 13 The simulaion resuls are available from he auhors on reques. 20

23 for an overview of his lieraure). The framework sudied in his paper provides an alernaive srucure wihin which his quesion can be asked. The reason he answers may be differen is because he key fricion here is an asse marke fricion as opposed o he sicky price fricion analyzed by mos of he exising lieraure on he opic. The model is he same as he one analyzed above. In paricular, he closed economy version is idenical o he model analyzed by Alvarez e al (2001). Relaive o he open economy case, he key difference is ha in he closed economy version goods markes mus clear inernally. Hence, c T +(1 )c NT = y, for all. (41) The non-rading household s consrains remain unchanged relaive o he open economy case. Hence, consumpion of non-raders is he same as before: c NT =(1 v 1 ) S 1y 1 S + v y, (42) where S denoes he domesic nominal price level. The marke clearing condiion hen gives consumpion of he raders: c T = 1+ µ 1 µ1 cnt y y. (43) The rading household s budge consrain is he same as before excep for he absence of foreign bonds. Thus, M T + T + v S y = S c T + B +1 (1 + i 1) B. (44) Opimal behavior by raders now enails saisfying jus one condiion (equaion (11)) which deermines he nominal ineres i. I is easy o check ha he quaniy heory equaion derived earlier coninues o hold. Hence, he price level is deermined by equaion (15). Lasly, he governmen s budge consrain is now given by (1 + i 1 )B B +1 + T = M +1 M, (45) which is idenical o he open economy case excep for he fac ha here are no foreign reserves, h, in he closed economy case. 21

24 4.1 Inflaion argeing versus money argeing In order o sudy he welfare meris of inflaion argeing as opposed o money argeing, we assume ha he wo regimes are characerized by he following policy rules: Inflaion Targeing: S +1 =(1+µ)S, S 0 = (1 + µ) M (1 v)ȳ, (46) Money Targeing: M +1 =(1+µ)M, M 0 = M. (47) Noe ha under inflaion argeing we assume ha he cenral bank also announces (and delivers hrough an appropriae choice of M 1 ) he iniial price level S 0. The precise number for S 0 ha we have assumed guaranees ha he wo regimes are symmeric in erms of he expeced firs period price level. Moreover, o keep he regimes symmeric, we have also assumed ha he rae of growh of he relevan policy arge is he same for boh regimes Velociy shocks only As before, we sar by sudying environmens where he only source of uncerainy is he velociy shock. Hence, we se σ 2 y =0. Under our assumpions i is easy o check ha consumpion allocaions under inflaion argeing are given by 1 = c NT,π c NT,π 0 = µ 1+µ + v v 1 ȳ, 1+µ µ 1 1+µ + v 0 v ȳ. 1+µ Noe ha once c NT is known, c T is deermined from he marke clearing condiion (41). Similarly, under money argeing consumpion allocaions are given by 1 = c NT,m c NT,m 0 = 1+µ + µ 1+µ v ȳ, 1 1+µ + µ 1+µ v 0 ȳ. 22

25 I can easily be checked ha E(c NT,π )=E(c NT,m )= Var(c NT,π )=ȳ 2 1+ Var(c NT,m )=ȳ 2 µ µ 1+µ Hence, Var(c NT,π ) >Var(c NT,π 0 ) >Var(c NT,m µ 1+µ v ȳ, 1+µ 1 (1 + µ) 2 σ 2 v, 2 σ 2 v = Var(c NT,m 0 ). Var(c NT,π 0 )=ȳ 2 σ 2 v, )=Var(c NT,m 0 ). Since expeced consumpion is idenical under he wo regimes while he variance of consumpion is greaer under inflaion argeing, equaion (18) implies ha all agens unambiguously prefer money argeing o inflaion argeing under moneary shocks Oupu shocks only The second case of ineres is where he only randomness in he economy is due o uncerainy abou he endowmen realizaion. Hence, we now assume ha σ 2 v =0. I is again sraighforward o verify ha in his case he consumpion allocaions of he non-rading households under he inflaion argeing regime of equaion (46) are given by c NT,π = 1 v 1+µ y 1 + vy, c NT,π 0 = 1 v 1+µȳ + vy 0. Correspondingly, under he money-argeing policy given by equaion (47), he consumpion allocaions are c NT,m = c NT,m 0 = 1 v 1+µ + v y, 1 v 1+µ + v y 0. h i I is easy o check ha E(c NT,π )=E(c NT,m )= 1 v 1+µ + v ȳ for all 0. Thus, expeced consumpion is idenical across regimes for boh agens. However, he variance of consumpion is h 14 Noe ha in he closed economy case, consumpion of raders is given by c T = 1+ 1 ³ 1 cnt ȳ greaer consumpion volailiy for non-raders also implies greaer consumpion volailiy for raders. 23 i ȳ. Hence,

26 differen. In paricular, i follows from he above ha " µ # Var(c NT,π 1 v 2 )= + v 2 σ 2 1+µ y, µ Var(c NT,m 1 v )= 1+µ Var(c NT,π 0 )= v 2 σ 2 y, 2 + v σ 2 y = Var(c NT,m 0 ). Hence, Var(c NT,m ) >Var(c NT,π ) for all 0 from which i follows ha boh ypes unambiguously prefer inflaion argeing o money argeing under real shocks. 5 Conclusion The deerminaion of he opimal exchange rae regime for an open economy is one of he oldes issues in inernaional economics. The single mos influenial idea in his conex has been he Mundellian prescripion ha if shocks facing he counry are mosly moneary hen fixed exchange raes are opimal whereas flexible raes are opimal if he shocks are mosly real. The key fricion underlying Mundell s resuls was he assumpion of sicky prices in he goods marke. In his paper we have invesigaed he implicaions of fricions in he asse marke as opposed o he goods marke. We have shown ha when only a fracion of agens rade in asse markes (i.e., asse markes are segmened), he Mundellian prescripion ges urned on is head. Fixing exchange raes enails cenral bank inervenions in he asse marke where only a fracion of agens are presen. Hence, moneary shocks (shocks o velociy in our conex) under fixed exchange rae regimes cause redisribuions across agens hereby generaing consumpion volailiy. On he oher hand, when exchange raes are flexible, moneary shocks cause changes in he price level which insulae agens real balances. Thus, asse marke segmenaion causes an inheren welfare bias owards flexible exchange rae regimes when shocks are moneary. We have also derived general condiions under which fixed exchange raes unambiguously welfare dominae flexible raes when he economy faces only oupu shocks, hereby overurning he well-know Mundellian prescripion once again. We believe ha he key imporance of our resuls lies in heir calling ino quesion he convenional wisdom regarding he choice of exchange rae regimes. The convenional hinking on his 24

27 opic has followed he sicky-price insighs of Mundell (1963). We believe ha nominal fricions are bu one of many possible fricions in any economy. More roublingly, we have shown ha an alernaive fricion whereby here is segmenaion in asse markes leads o he opposie conclusion regarding he choice of exchange rae regimes. Since a judgemen regarding which fricion is more imporan is ulimaely an empirical issue and likely o be counry-specific, he main implicaion of his paper is ha an evaluaion of he relaive srenghs of alernaive fricions mus be a key inpu ino any policy debae regarding he choice of exchange rae regimes. Blanke conclusions based on jus he sicky-price paradigm are likely o be misleading a bes and plain wrong a wors. More generally, given ha an opimal exchange rae regime will depend no only on he ype of shock bu also on wha ype of fricion prevails in he economy, i makes i more likely ha inermediae exchange rae regimes may be opimal, hus providing a raionale for Calvo and Reinhar s (2002) fear of floaing. The paper has also explored, in a closed-economy conex, he implicaions of our flexible price segmened asse markes model for he policy debae regarding inflaion argeing versus money argeing. We have shown ha under moneary shocks, money argeing unambiguously welfaredominaes a policy of inflaion argeing. On he oher hand, under oupu shocks he opposie is rue: inflaion argeing welfare dominaes money argeing. I bears repeaing ha relaive o sandard resuls in his area which use he sicky price paradigm, our resuls reflec a very differen fricion in he form of asse marke segmenaion. I is worh noing ha in he main ex we have ignored sae coningen rules, which provides an ineresing area of fuure research. In he appendix we have shown ha in he conex of his model here exiss a sae coningen rule which can implemen he firs-bes and ha such a rule involves a procyclical moneary policy. Noice, however, ha unless here are some coss or impedimens o implemening and/or operaing a sae coningen rule, such a rule would, by consrucion, dominae any deerminisic rule. Hence, he ineresing quesion is eiher o sudy he opimal sae coningen rule wihin some general class of sae coningen rules or explicily model some cos of having such rules and compare hem wih deerminisic rules (along he lines 25

28 of he rules versus discreion debae). In his paper we have ignored he issue of endogeneiy of marke segmenaion. In paricular, one would expec ha agens endogenously choose o be raders or non-raders wih he choice being sensiive o he cos of paricipaing in asse markes as well as he prevailing exchange rae and/or moneary regime. However, we see no reason o believe ha his would change our key resuls. As should be clear from he inuiion provided in he paper, wha maers for our resuls is ha, a every poin in ime, some agens have access o asses marke while ohers do no. Wha paricular agens have access o asse markes and wheher his group changes over ime should no aler he essenial argumens. A formal check of his conjecure is lef for fuure work. 26

29 6 Appendix 6.1 Expressions for variances under oupu shocks Firs, from equaion (33), we obain Furher, for any >0 h Var c T,peg h Var i = r 2 Var c T,peg 0 i =(1 β) 2 µ β + 1 β 2 Ω σ 2 y. (48) k +(1 β) 2 A 2 + B 2 σ 2 y +2rA (1 β) Cov[ k,y 1], (49) where A = Ω and B = β + 1 β Ω. From equaions (33) and (17), we ge k +1 = k + βay 1 + Cy βbȳ, (50) where C = Ω (1 β) B. Ieraing on equaion (50), i can be shown ha Then, from equaion (51), we obain k 1 = k 0 + βay 1 + Cy 0 βbȳ, k = k X 0 + βay 1 +(βa + C) y s 2 + Cy 1 βbȳ. (51) Combining equaion (52) wih (49) yields h Var c T,peg s=2 Var[ k 1 ]=C2 σ 2 y, k Var = ³( 2 1) (βa + C) 2 + C σ 2 y, k Cov,y 1 = Cσ 2 y. (52) i ³³ 2 = r 2 ( 1) (βa + C) + r 2 C 2 +(1 β) 2 A 2 + B 2 +2r (1 β) AC σ 2 y. (53) Using equaions (48) and (53), he variance erm of raders life-ime discouned uiliy under fixed exchange raes is obained as ζ µ(1 β) B 2 + C2 β + βa2 +2AC σ 2 y. (54) 27

30 For he case of flexible exchange raes, from equaion (32), we ge h Var c T,flex Then, from equaions (17) and (32), we ge i = r 2 Var k +(1 β) 2 σ 2 y. (55) k +1 = k + βy βȳ. (56) >From equaion (56) i direcly follows ha Var k = β 2 σ 2 y. (57) Using equaions (55) and (57), he variance erm of raders life-ime discouned uiliy under flexible exchange raes is obained as 6.2 Proof of Lemma 1 ζσ 2 y. (58) Since boh raders and non-raders have he same expeced consumpion under he wo exchange rae regimes, he welfare gain is solely deermined by he variance erms of life-ime uiliies. Using equaions (34) - (36), for non-raders he welfare gains under he flexible exchange rae regime relaive o he fixed exchange rae regime is W N = ζ For raders, we use equaions 54) and 58) o obain W T = ζσ 2 y Ã! σ 2 y v 2 + β(1 v) 2 1. (59) 1 β µµ(1 β) B 2 + C2 β + βa2 +2AC 1. (60) Using equaions (59) and (60) i can be easily shown ha he weighed uiliy gain is a funcion of and v: W = W T +(1 ) W N = 1 c2 2 + c 1 + c 0, (61) 28