Revisiing exchange rae puzzles Charles Engel and Feng Zhu Absrac Engel and Zhu (207) revisi a number of major exchange rae puzzles and conduc empirical ess o compare he behaviour of real exchange raes among pairs of economies ha have rigidly fixed nominal exchange raes wih heir behaviour among pairs of economies under floaing raes. They find ha some of hese puzzles become less puzzling for counries wihin he euro area, and regions in China and Canada, han for he non-euro-area OECD economies. Their resuls may have implicaions for exchange rae modelling. Keywords: consumpion correlaion puzzle; excess volailiy, exchange rae disconnec, exchange rae regime, real exchange rae, purchasing power pariy, uncovered ineres rae pariy. JEL classificaion: E43, F3. Charles Engel: Deparmen of Economics, Universiy of Wisconsin a Madison. E-mail: cengel@ssc.wisc.edu. Feng Zhu: BIS Represenaive Office for Asia and he Pacific, Hong Kong SAR. Email: feng.zhu@bis.org. We hank Luca Dedola and Michael Devereux for houghful commens and suggesions, and Jimmy Shek and Seve Pak Yeung Wu for excellen research assisance. The views expressed here belong o he auhors alone and do no represen hose of he Bank for Inernaional Selemens (BIS). BIS Papers No 96 3
. Inroducion The lieraure has named several exchange rae puzzles and has offered many poenial explanaions for hese puzzles. 2 This paper summarises our recen work (Engel and Zhu (207)), which focuses on six major exchange rae puzzles and invesigaes wheher he naure of hese puzzles differs under fixed and under freefloaing exchange rae regimes. These puzzles include he excess volailiy of real exchange raes; heir excess reacion o he real ineres rae differenials; he uncovered ineres rae pariy (UIP) puzzle; he excess persisence of real exchange raes; he exchange rae disconnec puzzle; and he consumpion correlaion puzzle. We sudy which of he puzzles may be significanly differen under rigidly fixed exchange raes versus floaing exchange raes. We compare he degree o which he puzzles hold among pairs of economies wih floaing exchange raes (eg among he pairs of OECD member counries ha are no in he euro area) wih pairs of economies which have rigidly fixed exchange raes (such as Hong Kong SAR vis-à-vis he Unied Saes and counry pairs wihin he euro area). We also exend he analysis o inra-naional daa, such as for US saes and Canadian and Chinese provinces, and examine a leas some of hese proposiions, depending on daa availabiliy. Wihin he naional borders, nominal exchange raes are irrevocably fixed, providing he bes example of fixed exchange raes. Engel and Zhu (207) sugges ha, under a rigidly fixed nominal exchange rae regime, he excess volailiy puzzle of real exchange raes pracically disappears or becomes minor for he vas majoriy of he fixed-rae economies; here is less evidence for an excess reacion of he real exchange rae o he real ineres rae differenial; here is less disconnec beween he real exchange rae and he economic fundamenals; and uncovered ineres rae pariy appears o hold more frequenly in hese economies. However, real exchange raes are as persisen in hese economies as in he floaing-rae economies, and he evidence for risk-sharing shows lile difference among counries wih fixed versus floaing nominal exchange raes. This evidence may provide clues o he ypes of model ha are useful for resolving he puzzles and herefore, he ypes of model ha are mos useful for open-economy macroeconomic analysis. The res of his summary is organised as follows. Secion II describes he six major exchange rae puzzles and our ess. In Secion III, we presen he empirical resuls. Secion IV concludes. 2. Six exchange rae puzzles A vas lieraure exiss on each of he six exchange rae puzzles we examine. A key focus of Engel and Zhu (207) is he behaviour of such puzzles under a rigidly fixed nominal exchange rae regime. There are many open-economy macroeconomic models in which here is sickiness in nominal prices or wages of varying degrees. In hese models, he behaviour of he nominal exchange rae does maer for he real 2 Obsfeld and Rogoff (200) lis six challenging puzzles in inernaional macroeconomics, namely he home-bias-in-rade puzzle, he Feldsein-Horioka (980) puzzle, he home-bias porfolio puzzle, he consumpion correlaions puzzle, he purchasing-power-pariy puzzle, and he exchange-rae disconnec puzzle. They sugges ha rade coss could help resolve he core quaniy puzzles. 4 BIS Papers No 96
exchange raes, and he real exchange rae behaves very differenly under fixed han i does under floaing nominal exchange raes. Engel and Zhu (207) sudy six major exchange rae puzzles under differen nominal exchange rae regimes. Define he real exchange rae Q as Q SP P where S is he nominal exchange rae (he price of he foreign currency in home currency or he amoun of he home currency ha can be bough wih one uni of foreign currency), P is he consumer price level in he home counry, and P is he consumer price level in he foreign counry. The real exchange rae is he price of he consumer baske in he foreign counry relaive o he price in he home counry. Using lower case leers o denoe he logs of variables wrien in upper case leers, we have q s p p () A rise in q hen indicaes a real depreciaion of he home currency. Noe ha under a rigidly fixed nominal exchange rae regime, he real exchange rae becomes he relaive foreign-o-home price, ie q p p. One of he main puzzles of real exchange rae behaviour is he excess volailiy of real exchange raes (see, for example, Rogoff (996) and Evans (20)). We define real exchange rae volailiy as var q or var q q, ie he variance of he log of he real exchange rae and he variance of he change in he log of he real exchange rae, respecively. Wrie: p p p N N, N T, where p and N, p are he log of he prices of non-raded and raded goods in he T, home counry, respecively, and N is he weigh of raded goods in he consumpion baske. Then, T, T, T, N N, T, N, T, q s p p p p p p (2) Under he assumpion of no home bias in consumpion and no pricing-o-marke for raded goods, since, we mus have var N var N, T, N, T, q p p p p, and N, T, N, T, var q var p p p p (3) Besides (3), Engel and Zhu (207) propose hree alernaive ess of excess volailiy, one of which is derived based on a simple version of he Harrod-Balassa- Samuelson model. The second puzzle ha Engel and Zhu (207) examine is he excess reacion of he real exchange rae o he real ineres rae differenial. Engel (206) noes ha, under uncovered ineres pariy (UIP), he covariance of he real ineres rae BIS Papers No 96 5
differenial wih he real exchange rae should be equal o ha wih he real exchange rae consisen wih he UIP assumpion. Ye for many floaing-rae economies, here ends o be excess co-movemen beween he real exchange rae and he real ineres rae differenial. We compare hese wo covariances by esimaing he UIP-consisen real exchange raes from VAR models, in erms of boh levels and firs differences. The hird, uncovered ineres rae pariy puzzle can be illusraed in he well known Fama (984) regression: 0 0 0, s s i i u (4) where i and i are nominal ineres raes in he home and foreign counries. The UIP relaionship posulaes ha i E s s i (5) Under UIP, he null hypohesis is ha 0 0 and 0. Ye, in pracice, for many pairs of economies under a floaing exchange rae regime, he empirics acually sugges ha 0 and frequenly 0 0, hence he UIP puzzle. Engel (204, 206) poins ou ha mos models offered as explanaions for he UIP puzzle, paricularly hose based on foreign exchange risk premiums, acually accoun for he co-movemen of he excess reurn wih he real ineres rae differenial. In pracice, he exising models presen heories consruced on real exchange raes in order o explain he UIP puzzle based on reurns expressed in nominal erms. Bu under a fixed nominal exchange rae, he only source of variaion in he real exchange rae resides in inflaion movemens. Recognising ha he counries ha have fixed nominal exchange raes do no fi he paradigm of he lieraure which assumes ha each bond pays off a riskless reurn in unis of he bond-issuing counry s consumpion baske, we modify he UIP regression. Given he fixed nominal exchange raes, he change in he real exchange rae is simply he differen beween foreign and home inflaion raes, ha is, i E i E u (6) For counry pairs wih rigidly fixed nominal exchange raes, he risk characerisics of he wo bonds should be idenical. Even for risk-averse invesors, he wo bonds should have equal expeced real raes of reurn. This implies ha UIP should hold ex ane. Tha is, we should find 0 and. We es he null hypohesis of. The fourh puzzle we sudy relaes o he excess persisence of real exchange raes, or he purchasing power pariy (PPP) puzzle. Rogoff (996) defines he puzzle as how can one reconcile he enormous shor-erm volailiy of real exchange raes wih he exremely slow rae a which shocks appear o damp ou? He argues ha he high volailiy of real exchange raes migh be explained in a moneary model wih sicky prices, implying ha he real exchange rae s persisence is deermined by he speed of adjusmen of nominal prices. Rogoff (996) noes ha consensus esimaes sugges half-lives for shocks o real exchange raes o be of approximaely hree o five years for floaing-rae counries, seemingly far oo long o be explained 6 BIS Papers No 96
by nominal rigidiies. Indeed, measures of price sickiness sugges ha he half-life of nominal price levels is closer o nine monhs. For economies under a rigidly fixed nominal exchange rae regime, one direc es of excess persisence is o examine wheher he half-life of real exchange raes is closer o nine monhs. Alernaively, we compare he half-life of real exchange raes o ha of he difference beween foreign and domesic relaive prices of non-radable o radable goods. The fifh, he exchange rae disconnec puzzle relaes o he seemingly raher weak relaionship beween he exchange rae and any economic fundamenals. Engel and Zhu (207) consider wo differen expressions for he fundamenals. The firs approach, based on a simple Harrod-Balassa-Samuelson model, is o sudy he shorrun and long-run relaionship beween real exchange raes and relaive non-radedo-raded produciviy, by esimaing an error correcion model. Alernaively, we examine he correlaion beween he real exchange rae q and IP q, he rae ha is consisen wih UIP, which capures he effec of measurable economic fundamenals on he real exchange rae. Tha is, facors such as moneary policy, fiscal policy, produciviy changes, or indeed anyhing ha affecs he real exchange rae hrough he real ineres rae channel raher han hrough he deviaions from UIP. The sixh, he consumpion correlaion puzzle relaes o he earlier lieraure on wheher financial markes deliver risk-sharing across counries. In he presence of financial inegraion and some capial mobiliy, one would expec some degree of consumpion-smoohing across counries, implying higher correlaion in he growh in real consumpion han ha in oupu growh. Ye Backus e al (992) find lower consumpion growh correlaion relaive o oupu growh correlaion. Engel and Zhu (207) insead examine he correlaion of he income available for consumpion, ie oal income minus invesmen and governmen spending in he home counry, wih ha in he foreign counry. These variables represen income made available for privae consumpion in he home and foreign counries, if hey were closed. Bu even wih complee financial markes, we migh no see high consumpion correlaion across counries, because financial asses are denominaed in currencies, no in unis of aggregae consumpion. Assuming a consan relaive risk-aversion uiliy funcion, if PPP does no hold, hen relaive consumpion growh raes should be perfecly posiively correlaed wih he growh rae of he real exchange rae. However, a fairly large empirical lieraure, including Backus and Smih (993), has found ha, among pairs of counries wih floaing nominal exchange raes, he correlaion is acually low and negaive, hence he consumpion correlaion puzzle or consumpion-real-exchange-rae anomaly. In realiy, PPP does no hold. Assuming a logarihmic uiliy funcion, hen growh raes of nominal consumpion ha are expressed in a common currency should be perfecly correlaed if markes are incomplee. The radiional es of he consumpion correlaion puzzle becomes one of comparing he correlaion of nominal domesic and foreign consumpion wih ha of nominal and foreign domesic income available for consumpion. BIS Papers No 96 7
3. Empirical resuls We summarise our resuls on he exchange rae volailiy puzzle in Table, based on he variance bound ess (3). For he economies under a fixed nominal exchange rae arrangemen, including 9 euro area counries, he variance bound (3) in levels are saisfied in 54 ou of 72 cases, bu only 42 ou of 423 cases for he non-euro area OECD economies wih floaing raes. 3 The difference in erms of he changes in he real exchange rae is even more sriking. Clearly, excess real exchange rae volailiy is much less an issue for he economies under a rigidly fixed nominal exchange rae regime, bu i remains a puzzle in hose economies wih floaing exchange raes. The same analysis on inra-naional daa for 0 provinces in Canada, 3 provinces in China and 27 meropolian areas in he Unied Saes furher srenghen he oucome we obained from he inernaional comparisons. The resuls for he alernaive variance bounds are similarly sriking and sugges a broadly similar picure o he paerns we observe in Table. The excess volailiy puzzle of real exchange raes pracically disappears or becomes minor for he vas majoriy of he economies which have adoped a rigidly fixed nominal exchange rae arrangemen. The puzzle remains for mos of he counries wih floaing nominal exchange raes such as he non-euro area OECD economies. Excess volailiy of real exchange raes: variance bounds (3) Table Boh fixed 2 Pairs of economies wih rigidly fixed exchange raes In levels Boh floaing 3 Fixed vs floaing 4 Boh fixed 2 In changes Boh floaing 3 Fixed vs floaing 4 Wihin he bound 54 3 39 72 0 3 Above he bound 8 6 265 0 9 273 Toal of pairs 72 9 304 72 9 304 Regions in Canada, China and he Unied Saes 5 In levels In changes Canada 6 China 7 US 8 Canada 6 China 7 US 8 Wihin he bound 4 4 293 45 454 35 Above he bound 4 54 58 0 0 Toal of pairs 45 465 35 45 465 35 Variance of real exchange raes relaive o he variance of relaive prices. 2 For he 9 euro area counries, here are a oal of (9 9 9)/2 = 7 pairs. In addiion, we have he US-HK pair. 3 Four of he 9 non-euro area OECD counries (Ausralia, Israel, Korea 4 and New Zealand) have incomplee daa. Hence, we have (5 5 5)/2 = 05 pairs. Plus 4 pairs wih HK. Wih daa for 9 euro area 5 counries and 4 non-euro area OECD counries, here are a oal of 9 5 = 285 pairs. Plus 9 pairs wih HK. Based on regional daa 6 7 for Canada, China and he Unied Saes. For he 0 Canadian provinces, here are a oal of (0 0 0)/2 = 45 pairs. For he 3 8 Chinese provinces, here are a oal of (3 3 3)/2 = 465 pairs. For he 27 Meropolian area pairs, here are a oal of (27 27 27)/2 = 35 pairs. Sources: Eurosa; OECD; auhors calculaions. Empirical resuls are similar for he puzzle of excess reacion o he real ineres rae differenial. Boh in levels and changes, our covariance bound is saisfied for he 3 In he laer calculaion, we group ogeher he boh floaing and he fixed vs floaing counries, since in fac he exchange rae floas beween all counry pairs in boh groups. 8 BIS Papers No 96
vas majoriy of counry pairs wihin he euro area for which we have daa, bu for only a small fracion of floaing exchange rae pairs. This implies ha here is an excess reacion of he real exchange rae for mos floaing-rae pairs, while he puzzle largely dissipaes for he economies wih rigidly fixed nominal exchange raes. To analyse he UIP puzzle, Engel and Zhu (207) esimae he coefficiens and in regression (6). Table 2 summarises he es resuls for he null hypohesis of. For he 2 euro area economies wih fixed exchange raes, he null can be rejeced in 27 ou of 66 cases a he % significance level and in 3 cases a he 0% significance level. Even hough he esimaed coefficiens are close o one, he sandard errors of he coefficien esimaes end o be very small for he counries wih fixed exchange raes, leading o rejecion of he null a he 0% level in nearly half he counry pairs. The null can be rejeced in 86 ou 32 counry pairs a a % significance level and in 267 cases a he 0% significance level among he floaing rae pairs. Uncovered ineres rae pariy puzzle, null H 0 : Table 2 Boh fixed Boh floaing Fixed vs floaing 3 0% 5% % 0% 5% % 0% 5% % Do no rejec H0: 35 37 39 8 3 55 27 39 7 Rejec H0: 3 29 27 02 89 65 65 53 2 Toal 66 20 92 Noe: he numbers indicae he couns of observaions for which he p-values are greaer han 0.0, 0.05 and 0.0, respecively. 2 For he 2 euro area counries, here are a oal of (2 2 2)/2 = 66 pairs. Three of he 9 non-euro zone OECD counries (Iceland, 3 Israel and Korea) have incomplee daa. Therefore, we have (6 6 6)/2 = 20 pairs. Wih daa for he 2 euro area counries and 6 non-euro zone OECD counries, here are a oal of 2 6 = 92 pairs. Sources: Eurosa; OECD; auhors calculaions. Because he esimaed slope coefficiens are much smaller han for he fixed nominal exchange rae counry pairs, and he rejecion of he null is much more frequen, we can conclude ha here mus be somehing else driving he rejecions of UIP among counry pairs ha have floaing nominal exchange raes. To examine he PPP puzzle or excess persisence of real exchange raes, Engel and Zhu (207) follow Rogoff (996) and compue he half-life of real exchange raes based on he esimaes of he AR() coefficiens for he raes. Their resuls sugges ha he real exchange rae is quie persisen under boh fixed and floaing nominal exchange raes, bu i is no any more persisen han he relaive foreign-o-home and non-radable-o-radable prices. We sudy he exchange rae disconnec puzzle by esimaing he coinegraing relaionship beween he real exchange rae and he relaive produciviy variables, focusing on pairs of counries for which we have a leas 5 years of daa. We find ha, proporionally, far more pairs of euro area counries have he correc posiive sign han hose counry pairs wih floaing exchange raes. In addiion, for hose counry pairs ha have he correc posiive sign, esimaed error correcion models sugges ha he speed of adjusmen is acually lower in he euro area counries on average. BIS Papers No 96 9
IP We find ha q and q are very highly correlaed in he counry pairs wih rigidly fixed nominal exchange raes, boh in levels and firs differences, bu much less for he floaing-rae counries. Wih boh measures of fundamenals, here appears o be less disconnec beween he real exchange rae and he economic variables under rigidly fixed nominal exchange raes han under floaing raes. In erms of he consumpion correlaion puzzle, a key resul is ha he primary difference does no involve he nominal exchange rae sysem, bu raher counry borders. While here appears o be evidence of some risk-sharing for abou half of he euro area pairs and OECD counry pairs, consumpion correlaion is higher han income correlaion for all 45 Canadian provinces, wheher we look a oal income or income available for consumpion. In addiion, we compare he correlaion beween relaive consumpion growh raes and he growh rae of he real exchange rae for pairs of counries wih fixed exchange raes, o ha of floaing-rae pairs. Across counries, wheher wihin he euro area, or among floaing-rae pairs, he average and median correlaion is close o zero. In conras, he real exchange raes among Canadian provinces are mosly posiively correlaed wih he relaive consumpion growh. Comparing he correlaion of nominal domesic and foreign consumpion wih he correlaion of nominal and foreign domesic available consumpion, we find srong evidence of risk-sharing by consumers among differen counries and regions, wheher or no exchange raes are floaing. 4. Conclusion Engel and Zhu (207) examine six exchange rae puzzles focusing on counries wihin he euro area, regions in China and Canada, and Hong Kong SAR vis-à-vis he Unied Saes. Their empirical ess yield resuls which sugges ha some of hese puzzles are less puzzling, ie less severe, under a rigidly fixed exchange rae regime, while oher puzzles remain. This evidence may provide clues o he ypes of model ha would be useful for resolving he puzzles and herefore, he ypes of model ha are mos useful for open-economy macroeconomic analysis. References Backus, D, P Kehoe and F Kydland (992): Inernaional real business cycles, Journal of Poliical Economy, vol 00, no 4, pp 745 75. Backus, D and G Smih (993): Consumpion and real exchange raes in dynamic economies wih non-raded goods, Journal of Inernaional Economics, vol 35, no 3, pp 297 36. Engel, C (204): Exchange rae sabilizaion and welfare, Annual Review of Economics, vol 6, pp 55 77. (206): Exchange raes, ineres raes, and he risk premium, American Economic Review, vol 06, pp 436 74. Engel, C and F Zhu (207): Exchange rae puzzles: evidence from rigidly fixed nominal exchange rae sysems, BIS Working Papers, forhcoming. 0 BIS Papers No 96
Evans, M (20): Exchange-rae dynamics, Princeon Series in Inernaional Economics, Princeon Universiy Press. Fama, E (984): Forward and spo exchange raes, Journal of Moneary Economics, vol 4:3, pp 39-338. Feldsein, M and C Horioka (980): Domesic saving and inernaional capial flows, Economic Journal, vol 90, no 358, pp 34 29. Obsfeld, M and K Rogoff (200): The six major puzzles in inernaional macroeconomics: is here a common cause?, NBER Macroeconomics Annual 2000, vol 5, pp 339 42. Rogoff, K (996): The purchasing power pariy puzzle, Journal of Economic Lieraure, vol 34, pp 647 68. BIS Papers No 96