"Exchange Rate Determination in a Small Open Economy and the Exchange Rate Disconnect"

Transcription

1 "Exchange Rae Deerminaion in a Small Open Economy and he Exchange Rae Disconnec" Miroslava Jindrová Absrac The purpose of his paper is o discuss he differences beween models wih wo alernaive assumpions allowing for deviaions of, i.e. model wih nonraded goods and pricingo-marke and o survey alernaive approaches of explaining deerminaion of exchange raes. The key quesion is, wheher he local currency pricing migh be he reason for he high level of exchange rae volailiy. Crucial poin in undersanding real exchange rae flucuaions is o capure he link beween marke srucure and sources of deviaions from purchasing power pariy (especially in a small open economy). We can hink of exchange rae overshooing as being special ype of so called exchange rae disconnec, because here is shor-run disconnecing of he level of he nominal exchange rae from is long-run equilibrium level corresponding o he level. In he case of exchange rae disconnec i seems, ha here is only a limied feedback no only wih price levels, bu eiher wih oher curren macroeconomics variables, such as money supply of GD, so ha exchange raes have lives of heir own and radiional exchange rae models have failed when rying o forecas shor o medium exchange rae movemens even ex-pos. Inroducion The deerminaion of he real and nominal exchange raes is sill dominan problem among he moneary economics. The idea ha moneary shocks generae addiional dynamics in he exchange rae has a long sanding radiion in inernaional macroeconomics. The well-known Mundell-Fleming model (based on he IS-LM) criicism had led o a naural exension by incorporaing he supply side. The resuling medium run model wih raional expecaions is known as he Mundell-Fleming- Dornbusch (MFD) model. A nex sep forward was o inroduce he microfoundaions of he supply side and allowing for making he model ruly dynamic wih he implicaions of ineremporal uiliy maximizaion. This has been done by Obsfeld and Rogoff (995) by changing he framework o a monopolisic compeiion marke. Therefore, he Obsfeld-Rogoff model can be considered he successor of he MFD model. Since he fall of Breon-Woods sysem in 970s and he inroducion of floaing exchange raes, he exchange raes have in some cases become exremely volaile wihou no corresponding link o changes in is macroeconomic fundamenals. This Universiy of Economics, rague, jindrovm@vse.cz

2 has led o higher ineres in exchange rae modeling as he quesion of exchange rae deerminaion reveals o be one of he mos imporan problems on heoreical field of moneary macroeconomics. Srucural moneary models have been inroduced and used in exchange rae modeling in a quie successful way in he early 970s, especially when concerning wihin-sample comparisons. However, hand o hand o his boom of exchange rae deerminaion heory, a number of empirical anomalies and so called puzzles have arisen since he end of he 970s. Several empirical puzzles have revealed during he ime. The nice overview of he six major puzzles in he inernaional macroeconomics can be found for example in Obsfeld and Rogoff (2000)2. The las wo menioned here are he so called purchasing power pariy and disconnec puzzle, boh price anomalies dealing wih he fac ha he exchange rae movemens doesn respond consisenly o he movemens of he underlying macroeconomic fundamenals, e.g. according o heir heoreic values and direcions. In las few years, researchers are rying o resolve he price puzzles in he inernaional economics, especially he puzzle and so called exchange-rae disconnec puzzle. The exchange rae disconnec puzzle in a sense of Obsfeld and Rogoff (2000) is a missing link beween exchange raes and he macroeconomic fundamenals ha inernaional macroeconomics heory suggess should be he driving force of he exchange raes. In paricular, i seems ha macroeconomic variables are no able o explain no only a curren level of exchange raes bu even heir volailiy. I should be menioned ha he disconnec puzzle in his meaning is a general erm ha includes also anoher well known puzzles: forward bias puzzle and purchasing power pariy () puzzle. The disconnec puzzle is o some exen similar o he puzzle, in which he moves of exchange raes don correspond o moves in relaive price levels. As one can hink of exchange rae overshooing as being special ype of exchange rae disconnec, because shor-run disconnecing of he level of he nominal exchange rae from is long-run equilibrium level corresponding o he level is allowed here. In he case of exchange rae disconnec i seems, ha here is only a limied feedback no only wih price levels, bu eiher wih oher curren macroeconomics variables, such as money supply of GD, so ha exchange raes have 2 For he review of six empirical inernaional puzzles see for example Obsfled (2000). (he home bias in rade puzzle, Feldsein and Horioka puzzle, he home bias porfolio puzzle and he low consumpion correlaion puzzle, he purchasing power pariy puzzle, he exchange rae disconnec puzzle)

3 lives of heir own and radiional exchange rae models have failed when rying o forecas shor o medium exchange rae movemens even ex-pos. In order o ge closer o answers o hose quesions, i seems o be necessary o modify he baseline Obsfeld and Rogoff model in several direcions 3. The rough insigh ino he problem of exchange rae deerminaion puzzle gives us he following able abou he variabiliy of some key macroeconomic fundamenals in he CR. Sandard deviaions, (where available) of he growh raes of fundamenals Sandard deviaion whole sample ( m ) ( i ) ( y ) m i y d s (EUR/CZK _end) d s (EUR/CZK _avg) d q (EUR/CZK _end) d q (EUR/CZK _avg) Source: CNB and own compuaion (normalized ime series, in log deviaions) Daa available since /996, ( m m ) is he money sock differenial growh, ( i i ) ineres rae differenial, ( y ) is he oupu growh differenial (using indusry as a proxy), y is he d s is d he nominal exchange rae growh and q is he real exchange rae. See Appendix for more deails abou he variabiliy of macroeconomic fundamenals. Those daa brings us quie surprising insigh: even when here were several differen moneary policy regimes during he las decade in he CR, he variabiliy of he growh of he imporan macroeconomic fundamenals differenials remains (roughly said) 3 M. Duare and A. Sockman have modified he OR (995) wo counry model, when assuming he concep of goods marke segmenaion, local-currency pricing o marke, incomplee asse markes and auonomous changes in risk premium should be incorporaed ino he model.

4 unchanged 4, excep for he pre- and pos-crisis period (around 997), where, however, he money growh differenial says sable oo. Tha fac can be inerpreed as he evidence for disconnec, bu on he oher hand, hese findings seems o be quie surprising. The purpose of his paper is o discuss poenial ways, in which i is possible o srucure ineremporal model of (small) open economy. Being more specific, we discuss he differences beween models wih wo alernaive assumpions allowing for deviaions of, i.e. model wih nonraded goods and TM, in a dynamic behaviour of exchange rae of a small open economy. We invesigae Dornbusch's overshooing resul in a new open economy macro seing, sressing ou he use of ineremporal opimizaion and including he nominal rigidiies inheren he Mundell-Fleming approach hrough monopolisically compeiive produc markes. The key quesion is, wheher he local currency pricing (LC) migh be he reason for he high level of exchange rae volailiy. In principal, by inroducing LC, he linkage of goods prices across counries is being impeding, which migh (ogeher wih some oher assumpions) explain he high exchange rae volailiy. This paper is organized as follows. The firs secion provides a brief skech of he small open economy version of he so called redux model inroduced in Obsfeld- Rogoff (995), where he exchange rae dynamics is possible due o he exisence of nonradable goods, while he second par of he paper inroduce anoher varian, where we assumed local currency pricing. Secion hree brings alernaive compeing approach o he resuls of exchange raes dynamics in hese models and he las secion concludes. 2 The Obsfeld-Rogoff model wih nonradables The firs direcion of he research ries o learn abou disconnec from sudying sicky price model based on Obsfeld and Rogoff s (995) exchange rae dynamics redux. As was menioned in he inroducion, in he case of exchange rae disconnec i seems, ha here is only a limied feedback no only wih price levels, bu eiher wih oher curren macroeconomics variables, such as money supply of GD, so ha exchange raes have lives of heir own and radiional exchange rae models have failed when rying o forecas shor o medium exchange rae movemens even ex-pos. In order o 4 See Appendix for he graphical exposiion of he variabiliy of macroeconomic fundamenals.

5 ge closer o answers o hose quesions, i would be necessary o modify he baseline OR model in several direcions. This sor of model is based on a dynamic general equilibrium framework wih well specified micro foundaions, which allows for incorporaing he assumpions of imperfec compeiion, incomplee asse markes and alernaive pricing adjusmens (as well as differen ypes of nominal rigidiies). The original model of Obsfeld and Rogoff does no allowed for he CI-based deviaions of purchasing power pariy, as i assumes all goods o be radables and complee pass-hrough of exchange rae changes o impor prices (e.g. prices of radables are se in buyer s currency). In he appendix o he Obsfeld-Rogoff (995) is, however, skeched he small open economy version of heir model, where he presence of nonraded consumpion goods allows for he deviaions of he purchasing power pariy. Thus his makes exchange rae overshooing possible. Because of he fac ha heir model could be aken as a benchmark o any oher small scale open economies, we inroduce i here. While he main lieraure focus on wo-counry global economy models ha are able o explain, beyond ohers, macroeconomic inerdependence and inernaional rnasmission chanells, hose models are no very useful in analysing small open economies. In he appendix o he Obsfeld-Rogoff (995) is, however, skeched he small open economy version of heir model, where he presence of nonraded consumpion goods makes exchange rae overshooing possible. Their model could be aken as a benchmark o any oher small scale open economies, hus we skeched ha here. Similar o any oher DGE model, we assume ha here is a coninuum of consumerproducers ha produce nonradable goods and consume boh, he nonradables and he radables. Each represenaive household is consider o have monopoly over producion of one of he nonradables [ 0,] good each period, y T, z and is endowed a consan quaniy of he raded The represenaive household j seeks o maximize lifeime uiliy funcion of he form = 0 s U E β u, which on heir seup akes following paricular form s=

6 U j = s= β s γ logc j T, s + χ ε M s ε j s 2 ( γ ) logc + log y ( j) N, s j κ 2 N, s, () where 0<β< is he discoun facor, C N is nonraded goods consumpion index defined by CT sands for consumpion of he raded good and C N = 0 θ θ θ [ c ] θ dz. N (2) Noe ha real balances ener uiliy funcion direcly and ha he parameer has showed o be crucial elemen of wheher overshooing can occur or no. The CI index in eq. γ N γ γ γ () is he defined by T / γ ( γ ), wih T being he price of radables. In radables i is assumed ha he law of one price holds, so ha he equaliy = E T T holds (under assumpion he index N is given by T is exogenous and consan). The nonraded goods price N { [ ( )] } θ θ pn z, = dz 0 wih p N being he price of nonraded good z in money erms. As a consequence of given preferences i is assumed ha he demand curve for nonraded goods is downward sloping and has he form (3) y d N ( j) p = ( j) θ N, A C N pn,, (4) A C N is aggregae per capia nonraded goods consumpion, here aken as a given. As bonds are denominaed in radables and r denoes he consan world ne ineres rae in radables and β ( + r) = defined as, he ypical j s period budge consrain in money erms is T, B ( + r) B + M p y + y + τ, + M + N, C N, + T, CT, = T, + N, N, T, (5) where per capia axes τ are denominaed in radables.

7 Since Obsfeld and Rogoff assume ha Ricardian equivalence holds, hey absrac from governmen spending and inroduce balanced governmen budge in each period. The governmen budge consrain, in unis of radables, is herefore given by τ = M M T,. (6) Opimaliy Condiions By choosing he opimal level of consumpion, money and bond holdings and he oupu of nonraded goods, he individuals solves heir ineremporal maximizaion problem. Sricly speaking, firs order condiions are found by maximizing eq. () subjec o consrains given by eq. (4) and (5). Afer some calculaions, we ge C = C C T, + T,, γ = γ N, T, CT, N., (7) (8) M χ T, C = γ T, + i i / ε, (9) y N, θ γ / N, N θκ ( ) ( θ + ) / θ ( )( ) A θ j = C ( C ). (0) The erm i sands for nominal ineres rae and is defined by he Fisher ideniy ( + r) T, / T i = +, + Equaion (7) is he so called Euler equaion resolving opimal ineremporal allocaion of radables, whils eq. (8) governs he opimal inraremporal levels of consumion of nonradables and radables. Equaion (9) is he money marke equilibrium condiion, where he money demand is he posiive funcion of consumion and negsive funcion of he ineres rae. Equaion (0) is he opimal labour-leisure choice, where he marginal disuiliy of producing one exra uni of a nonraded goods is equal he marginal uiliy of consuming one. Following Obsfeld-Rogoff (995) 5, we derive he symmeric seady sae in which all exogenous variables are consan and he iniial level sock of ne foreign asses is zero. Then he model is solved for log-linearized deviaions of iniial seady sae. One can

8 derive, ha he equaion for he long run equilibrium level of exchange rae, money supply and price level is (he variables wih overbars/has sands for log-linear deviaion of iniial seady sae) ˆ T = Eˆ = β + β + ( β ) ε ( β )( γ + γε ) Mˆ. () As long as law of one price holds only for radables in small open economy manner, he price of raded goods changes in proporion o he exchange rae. From eq. () we see ha, if ε >, he nominal exchange rae overshoos is long run level. Why does i hold? When hinking of he erm / ε as being he consumpion elasiciy of money demand, one can imagine wha happen when he siuaion is differen from ha when ˆ = Mˆ (i.e. when here is neiher over- nor undershooing). If T for example he supply of real balances would have o rise by M = ( γ ) M, be derived ha in his case he demand for real balances will rise by ( / )( γ )Mˆ ˆ ˆ ˆ i can ε. This means, ha when ε >, he demand for real balances will rise by less han he supply and he price of radables (he exchange rae) would have o rise furher o reach equilibrium. Therefore he exchange rae overshoos is long run equilibrium level. 3 The modificaion of he baseline model LC approach There is now a huge lieraure exending he OR model, usually referred o as he New Open Economy Macroeconomics. While OR (995) assume complee pass hrough of exchange raes o prices because hey assume ha nominal prices are se in he currency of he producer, a lo of heir successors have exended heir framework o he local currency pricing case. The assumpion of LC has become one of he sronges compeing explanaion of he disconnec puzzle, because his explanaion of excessice exchange rae volailiy concerns he behaviour of radables prices. Under LC firms se prices in heir own currency for sale o households locaed in heir counry, bu se a price in foreign currency for sales o foreign households. They believe ha wihin his framework i is possible o sudy and learn much more abou he naure of exchange rae volailiy when moving from one exchange rae regime o anoher. For example Duare and Sockman (2005) came ou wih a modified version of OR (995), 5 For deails of derivaion of seady sae see Appendix o Obsfeld-Rogoff (995)

9 when assuming he concep of goods marke segmenaion, local-currency pricing o marke, incomplee asse markes and auonomous changes in risk premium ha have been incorporaed ino he model. The Redux model assumes ha he law of one price holds for all goods, ha aggregaing across goods implies purchasing-power pariy, = E. However, generally does no hold and even if he inroducion of nonraded goods would allow for deviaions from purchasing-power pariy, deviaions from he law of one price for raded goods appear o explain he majoriy of flucuaions in real exchange raes. This is why alernaive pricing srucures are o be explored. The Redux model assumed ha firms se prices in he sellers currency, wha has come o be called producer currency pricing (C). When assuming an alernaive assumpion ha firms se prices in he buyers currency or local currency pricing (LC). Srucure of he Model, Building blocks if he model A simple model of Localcurrency ricing The purpose of his par is o inroduce he main building blocks of he pricing-omarke (local currency pricing) small-scale version of he general equilibrium model given in Obsfeld and Rogoff (995). There are wo counries, domesic and foreign. Foreign counry variables are denoed wih an aserisk. The parameerizaion of he model allows he relaive size of he wo counries o be varied. The wo counries are inhabied by a coninuum of infiniely lived individual consumers and producers. Households in each counry consume a coninuum of differeniaed radable goods of oal measure uniy. These goods, produced by firms, are indexed by z, z [ 0,]. A fracion n of hese goods is produced by firms locaed in he home counry, and he remaining fracion -n is produced by firms locaed in he foreign counry 6. According o similariy of preferences beween counries, only he equaions relaing o he domesic economy are described below. 6 These fracions also represen he relaive size of home and foreign counries, respecively.

10 references and ricing Srucure Home and foreign counry consumers have he same preferences, defined as before over a consumpion index, real money balances and labour supply. A represenaive domesic counry residen j maximises he lifeime uiliy funcion ha depends on consumpion C, real money balances M/ and labour supplied L: In he home counry, hese preferences are defined by he lifeime uiliy funcion of represenaive household U j = s= β s j χ M logc +, s log ε s j s ε κ L µ µ s, (2) Wih 0<β<, σ>0, ε>0 and µ>. Leing C be a domesic agen s oal consumpion and θ be he elasiciy of demand for consumpion goods, he consumpion index C is: C = 0 θ θ θ [ C ] θ dz. This aggregaes he consumpion of all differeniaed goods, c. The parameer θ is he elasiciy of subsiuion beween any wo differeniaed goods, and for values of θ greaer han, differen goods are imperfec subsiues in consumpion. Besides consumpion, he consumer s momenary uiliy also depends on leisure (hours worked), (3) -L, and real money balances held during he period. and is he home counry consumpion price index. M, where M is nominal balances Domesic consumers face a consumer price index represening he minimum expendiure necessary o buy one uni of composie good c defined as: = n { [ ( )] [ ( )] } θ θ θ p z dz E p z dz, + 0 n (4) Wih produce currency pricing, movemens in he exchange rae will affec he consumer price index, as in OR (995). On he oher hand, wih full LC here is no pass-hrough from he exchange rae o prices of impored goods, which implies ha he

11 price level is compleely unaffeced by exchange rae movemens in he shor run. Thus, when assuming ha foreign price is exogenous and fixed, he price index (eq. 3) may be wrien in a form: = n { [ ( )] [ ( )] } θ θ θ p z dz p z dz, + 0 n The domesic counry s CI is made up of a combinaion of p (z) represening he home currency price of he home produced good and ( ) he foreign currency price p f, z of a foreign non-tm good. rices wihou aserisks are for domesic goods and hose wih aserisks are for foreign goods. E is he exchange rae in erms of he domesic uni cos of foreign currency. World capial markes are assumed o be perfecly inegraed, so here is a single world bond marke. This implies uncovered ineres pariy as follows: E+ ( + i ) = ( + i ) E where i denoes he domesic nominal ineres rae. Given he aggregae consumpion index, he household s opimal allocaion of consumpion across each differeniaed goods yields he demand funcions c = p θ c, z [ 0,. ] Noe ha home demand funcions for foreign goods, z [ n,] (5) c do no depend on he nominal exchange rae. As we shall see, his follows from he fac ha he home price of foreign goods is denominaed in he home currency. As oulined above, home and foreign markes are segmened, effecively allowing firms o price discriminae across wo markes. Therefore, home firm i, i [ 0, n], will choose separaely he price for is goods in he home counry, p, and in he foreign counry, p, in order o maximize is oal profis.

12 The governmen in each counry prins money and makes lump sum ransfers τ. Consumers receive income from wages w L and profis Π of domesic firms, and are resrained o he following flow budge consrain: B ( + i ) B + M M C + w L + Π + τ, = (6) where lump sum ransfers τ are defined by τ = M M. (7) Households Maximisaion roblem Domesic households maximise lifeime uiliy (2) subjec o heir holdings of wealh in forms of domesic currency and bonds. The firs order condiions are: C+ = C β ( + i ), (8) + M + i = χc i / ε, (9) ( µ ) / w L =. (20) κc Equaion (8) is again he sandard consumpion Euler equaion. Given he aggregae consumpion index, he household s opimal allocaion of consumpion across each differeniaed goods yields he demand funcions c = a θ c, z [ 0,. ] (2) Where a (z) can be p (z) or E p f, depending on he ype of good. Noe ha home demand funcions for foreign goods, z [ n,] c do no depend on he nominal exchange rae. As we shall see, his follows from he fac ha he home price of foreign goods is denominaed in he home currency.

13 The household s opimal money demand schedule is given by (9) which equae he marginal rae of subsiuion of composie consumpion for real money balances o he opporuniy cos of holding real balances. The household s opimal labour supply decision is shown by (20), his equaes he marginal disuiliy of labour effor o he marginal uiliy of he real wage. Labour markes are assumed o be compleely segregaed wih real wages deermined by marke clearing in each labour marke. Firms and rice Deerminaion Home firm z operaes he producion funcion y = l, where worked, and period profis are defined as l represens hours π = p c + e p c w ( c + c ). (22) And aggregaing i leads o: Π = p θ C ( p w ) + p θ C ( E p w ) Noe he erm w is he real wage and he nominal exchange rae, e, convers he revenues from sales in he foreign counry ino home currency. rofi maximizaion is made subjec o he firm s producion funcion and home and foreign demand funcions for is goods (eq. 4 and he analogous expression for he foreign consumer). p When nominal prices are flexible, home firm z ses is price as = e p = w, θ θ i.e., he opimal pricing funcion rule for each firm is o se is price in each marke as a consan markup over marginal cos. Therefore, he law of one price holds for each good, even hough firms have abiliy o price discriminae across markes. The model wih flexible prices (and an assumpion of idenical demand elasiciies in boh counries) does no generae deviaions from. Nex suppose ha firms se prices in advance a a level ha achieves he opimal markup and he absence of shocks. Firms canno adjus prices wihin he period in response o shocks, accommodaing ex-pos demand a he prese prices. rices adjus

14 fully afer one period. As before, firms are assumed o se prices in he local currency of sale. Therefore, in his case, unanicipaed changes in he exchange rae lead o he deviaions in he law of one price. In his model, deviaions from resul only from deviaions from he law of one price, i.e. from movemens in he relaive price of similar goods across counries. 4 The alernaive approach o he disconnec puzzle Several differen approaches of explaining he disconnec puzzle have revealed over ime. Quie inspiring is he direcion leading in leaving of raional behaviour of individual agens. Quie large group of researchers is rying o answer he quesion of excessive volailiy in resignaion o raionaliy of agens behaviour in exchange rae modelling and explore models wih heerogeneous agens srucure saring from he microsrucure of he foreign exchange marke. This approach represens quie huge deparure from radiional macroeconomic approach relaxing is key underlying assumpions. We can menion Devereux and Engel (2002) among ohers, who believes ha here are swings in expecaions abou fuure values of he exchange raes ha sand behind so volaile exchange raes, which are (in his view) unrelaed o prices and ineres differenials. There are several issues ha suppor his view: he fac ha exchange rae expecaions are inconsisen and seem o fail in forecasing fuure values, he failure of UI ha could be due o he non-raional behaviour of economic agens, failing of efficien marke hypohesis. Las bu no leas, issues arising from swiching from one exchange rae regime or moneary policy framework o anoher, which is generally followed by he changing of he way how expecaions in he economy is made. Under fixed exchange rae regime he governmen is obliged o sabilize he exchange rae a some predefined value. Counries moving from fixed o floaing exchange raes face a remarkable change in he behaviour of real exchange raes 7. They are much more volaile under floaing exchange rae regimes, where expecaions are no ied down by he hrea of poenial cenral bank inervenion. However under he assumpion ha expecaions are based on fundamenals, he relaionship beween 7 See Appendix for he evidence in he case of he CR.

15 fundamenals and exchange raes should be he same if here is no corresponding change in underlying fundamenals. One non-raional direcion of resolving exchange rae deerminaion puzzle is he inroducion of irraional behaviour of one group of agens in he foreign exchange marke. The represenaive non-raional approach is for example he model wih ineracion of chariss and fundamenaliss, where agens have differen beliefs abou he fuure changes of exchange raes. The simple chariss-fundamenaliss model could have for example following srucure: Fundamenaliss excess demand depends on he deviaions beween he curren exchange rae and is fundamenal value 8 ED F = γ ( s s ), f Where α is he coefficien for he sensiiviy o deviaions of s f and s. The chariss excess demand will generally depend on he expecaions over fuure depreciaion of he exchange rae, i.e. on he expeced fuure change of he exchange rae. 9 ED CH ( E [ p ] p ) = α E( s& ) = r = α + α where γ is again he sensiiviy parameer. The depreciaion of he exchange rae (he change of he exchange rae) is he oucome of he overall excess demand, as well as ineracion beween he agens: s & ( ED + ED ) = λ( γ ( s s ) + E( s& )) = λ α F CH f Under he assumpion ha chariss adjus heir expecaions adapively o acual change in exchange rae, i.e. ha r& = β ( s& r ), where β is he speed of adjusmen of adapively made expecaions. Their behaviour may be like his due o lack of experience, which leads o heir irraional behaviour. 8 This value migh be given by value as an example; i is he fundamenal value ha should be known o he fundamenaliss. The charis and fundamenaliss approach was inroduced by Frankel and Froo (986) 9 In coninuous ime seing he difference beween expeced and he acual exchange rae can be replaced by he expeced differenial of exchange rae wih respec o ime.

16 The non-raional behaviour of agens is he consequence of chariss adapive expecaions on one hand and he neglecing of he exisence of chariss by fundamenalis on he oher hand. The previous equaions consiue following sysem of wo differenial equaions: ( γ ( s s ) + r ) s& = λ α f r& = β ( s& r ) = β ( λ( γ ( s s ) + α r ) r ), f Under dynamic equilibrium boh s& = 0 and r& = 0, wha obviously means ha he equilibrium price is equal o is fundamenal value ( s f = s ) and expeced depreciaion of he exchange rae is equal o zero ( r& = 0 ). Using graphical perspecive he previous sysem is shown in Figure and Figure 2: The sable soluion wih overshooing (γ =0.07, α =0.8, β =0.3, λ =., s f =)

17 The unsable soluion wih explosive flucuaions (γ =0.0, α =, β =0.4, λ =., s f =0) As we can see, his kind of model is able o bear high volailiy of exchange raes, as well as he well known Dornbusch-ype of overshooing wih mean reversion. As for example De Grauwe and M. Grimaldi (2005) have poined ou, models of exchange rae ha incorporae heerogeneous beliefs of agens (and herefore nonlineariies in he exchange rae dynamics) are able o explain several puzzles, including he disconnecions (in all heir meanings). They disinguish wo agen ypes: i.e. chariss wih a posiive feedback rule and fundamenaliss wih a negaive one. The nonlineariies came ino he model hrough he ransacion coss and nonlinear adjusmen in he goods marke. They have shown ha he disconnecion of acual exchange rae from is long run fundamenal value is he naural consequence of nonlineariies in he model. Moreover, he nonlineariy of he model can produce endogenous regime shifs (srucural changes) such ha he link beween he exchange rae and is fundamenals could be broken even when here is no change in he policy regime. Despie of he promising naure of hese kinds of models, heir pracical usage is quie quesionable. As Duare and Sockman (2005) have poined ou, one should no resign o find explanaions of he disconnec puzzle wihin he radiional class of models. The reason is, ha you can always build up a model, which is able o explain he daa, bu here is a quesion wheher he model is able o provide reasonable policy implicaions.

18 5 Conclusion In his paper, we show he main feaures of a wo-counry dynamic general equilibrium model building upon Obsfeld and Rogoff (995), which is used o analyze he effec of change in money supply o he behaviour of he nominal exchange rae in a small open economy framework. Whereas he baseline redux model and mos of he subsequen lieraure on new open economy macroeconomics are based on a wocounry framework, which allows an explici analysis of inernaional ransmission channels and he endogenous deerminaion of ineres raes and asse prices, he similar, bu simpler models may be consruced under he assumpion of a small open economy, which enable us o easier o make a disincion beween radable and nonradable goods in he analysis. Moreover, he implicaions of small open economy models of his class seem o be plausible for mos counries, counries, including The Czech republic. One imporan conclusion of his analysis is ha a crucial poin in undersanding real exchange rae flucuaions is o capure he link beween marke srucure and sources of deviaions from purchasing power pariy (especially in a small open economy). The model wih local currency pricing as well as he model wih nonradable has a number of implicaions for exchange rae deerminaion and in a combinaion wih sicky prices here are shor-erm deviaions from. Also, hose models produce Dornbusch (976) ype overshooing and are able o parially explain increased volailiy of real and nominal exchange raes. To fully undersand he disconnec puzzle, however, a more complex approach is needed. Boh of ha feaures should be pu ogeher wih an assumpion of consumpion home-bias (i.e. he hird channel of deviaion of ) and allowing for oher imperfecions in goods and labour marke, as well as he assumpion of complee financial markes. The deerminaion of he real and nominal exchange raes is sill dominan problem among he moneary economics, especially due o he exisence of quie large number of puzzles ha he conemporaneous research has been unable o resolve. One of hem, he disconnec puzzle, saes ha he enormous exchange rae volailiy seems o have no corresponding counerpar in he variabiliy of macroeconomic fundamenals. In las few years, researchers are rying o resolve his puzzle ogeher wih anoher price

19 puzzle in he inernaional economics, he purchasing power pariy puzzle ha could be in some sense considered o be a special form of he disconnec puzzle. In any cases i is worh o say, however, ha he role of macroeconomic fundamenals in explaining exchange rae behaviour is undoubedly conroversial and open issue in inernaional macroeconomics. References [] Benigno, G.- Thoenissen, Ch. (2003): Equlibrium Exchange Raes and Supply- Side erformance. The Economic Journal, Vol. 3 (March), p [2] Borondo, C. (2003): Inernaional Transmission of Moneary Shocks: Mundell- Fleming vs Obsfeld-Rogoff. in Oscar Bajo (ed) Macroeconomic olicy in an Open Economy. Applicaions of he Mundell-Fleming Model. Nova Science ublisher, New York [3] Campbell, D.(2006): Why Are Exchange Raes Ou of Sync Wih Oher Economic Indicaors? Region Focus, [4] De Grauwe,. and M. Grimaldi (2005): The Exchange Rae and is Fundamenals in a Complex World. Review of Inernaional Economics, 3(3), [5] Duare, M and A.C. Sockman (2005): Raional Speculaion and Exchange Rae. Journal of Moneary Economics, Vol. 52, No., [6] Duare, M. (200): Inernaional ricing in New Open-Economy Models. Federal Reserve Bank of Richmond Economic Quaerly, Vol. 87, No 4, p ? [7] Engel, C. and K.D. Wes (2005), Exchange raes and fundamenals. Journal of oliical economy, Vol. 3, issue 3, p (2005) [8] Hogan, L. (986): A Comparison of Alernaive Exchange Rae Forecasing Models. Economic Record, Vol. 62, Issue 77, [9] Cheung, Y., Chinn, M. and A.G. ascual (2005): Empirical Exchange Rae Models of he Nineies: Are Any Fi o Survive? Journal of Inernaional Money and Finance, 24, [0] Kempa, B. (2005): Exchange Rae Disconnec in a Sandard Open-Economy Macro Model. Open Economies Review, Vol. 6, [] Meese, R. and K. Rogoff (983): Empirical Exchange Rae Models of he Sevenies: Do hey Fi Ou of sample? Journal of Inernaional economics 4, [2] Obsfeld, M. and K. Rogoff (995): Exchange Rae Dynamics Redux. Journal of oliical Economy, Vol.03, s [3] Obsfeld, M. and K. Rogoff (2000): The Six Major uzzles in Inernaional Macroeconomics: Is here a Common Cause?, NBER Macroeconomics Annual

20 [4] Obsfeld, M. Rogoff, K. (998): Foundaions of Inernaional Macroeconomics. The MIT ress [5] Sarno, L (2005): Viewpoin: Towards a Soluion o he uzzles in Exchange Rae Economics: Where Do We Sand? Canadian Journal of Economics, Vol. 38, No. 3, [6] Taylor, M.. (995): The Economics of Exchange Raes. Journal of Economic Lieraure, Vol. XXXIII, Appendix: The variabiliy of major fundamenals in he CR The variabiliy of nominal exchange rae EUR(ECU)/CZK,2,5 EUR(ECU)/CZK (monh average),,05 0,95 0,9 0,85 II.93 II.94 VIII.93 II.95 VIII.94 II.96 VIII.95 II.97 VIII.96 II.98 VIII.97 II.99 VIII.98 II.00 VIII.99 II.0 VIII.00 II.02 VIII.0 II.03 VIII.02 II.04 VIII.03 II.05 VIII.04 II.06 VIII.05 II.07 VIII.06,25,2,5 EUR(ECU)/CZK (monh end),,05 0,95 0,9 0,85 0,8 II.93 II.94 VIII.93 II.95 VIII.94 II.96 VIII.95 II.97 VIII.96 II.98 VIII.97 II.99 VIII.98 II.00 VIII.99 II.0 VIII.00 II.02 VIII.0 II.03 VIII.02 II.04 VIII.03 II.05 VIII.04 II.06 VIII.05 II.07 VIII.06

21 The variabiliy of ineres raes and he ineres rae differenial,25,2,5,,05 0,95 0,9 0,85 0,8 ribor 3M Euroraes 3M II.93 II.94 VIII.93 II.95 VIII.94 II.96 VIII.95 II.97 VIII.96 II.98 VIII.97 II.99 VIII.98 II.00 VIII.99 II.0 VIII.00 II.02 VIII.0 II.03 VIII.02 II.04 VIII.03 II.05 VIII.04 II.06 VIII.05 VIII.06 0,25 0,2 0,5 0, 0,05 0-0,05-0, -0,5-0,2-0,25 II.02 VIII.0 II.0 VIII.00 II.00 VIII.99 II.99 VIII.98 II.98 VIII.97 II.97 VIII.96 II.96 VIII.95 II.95 VIII.94 II.94 IR_diff VIII.06 II.06 VIII.05 II.05 VIII.04 II.04 VIII.03 II.03 VIII.02 The variabiliy of indusry growh and he indusry growh differenial,3,2, 0,9 0,8 0,7 I.93 VII.02 I.02 VII.0 I.0 VII.00 I.00 VII.99 I.99 VII.98 I.98 VII.97 I.97 VII.96 I.96 VII.95 I.95 VII.94 I.94 VII.93 IND_Euroarea VII.06 I.06 VII.05 I.05 VII.04 I.04 VII.03 I.03 IND_cze 0,3 0,2 0, 0-0, -0,2-0,3 II.98 VIII.97 II.97 VIII.96 II.96 II.02 VIII.0 II.0 VIII.00 II.00 VIII.99 II.99 VIII.98 VIII.02 II.03 IND_diff VIII.06 II.06 VIII.05 II.05 VIII.04 II.04 VIII.03

22 The variabiliy of growh of moneary aggregaes and he money growh differenial,06,04,02 0,98 0,96 CZE_m2 Euroarea_m2 II.93 II.94 II.95 II.96 II.97 II.98 II.99 II.00 II.0 II.02 II.03 II.04 II.05 II.06 0,03 0,02 0,0 0-0,0-0,02-0,03-0,04-0,05 M2_diff II.99 VIII.98 II.98 VIII.97 II.97 VIII.96 II.96 II.0 VIII.00 II.00 VIII.99 II.03 VIII.02 II.02 VIII.0 VIII.06 II.06 VIII.05 II.05 VIII.04 II.04 VIII.03 Source: CNB, own compuaion Noe: The ime series are in growh of logarihms and normalized using maximum and minimum of he series. The daa are from CNB and Eurosa daabase. The EUR/CZK ime series is he monhly average and he end of he monh value. The ineres rae ime series compares he 3 monh ribor rae for he Czech Republic and 3M eurorae for Euro area. Due o he fac ha he oupu daa are no provided on he monhly basis, he seasonally adjused indusry producion index is used as a proxy. As a money supply he naional defined moneary aggregae M2 is used (he ECB definiion aggregaes have shorer ime series).