The Long-Run Volailiy Puzzle of he Real Exchange Rae Ricardo Hausmann Kennedy School of Governmen Harvard Universiy Ugo Panizza Research Deparmen Iner-American Developmen Bank Robero Rigobon * Sloan School of Managemen Massachuses Insiue of Technology Absrac This paper documens large cross-counry differences in he long run volailiy of he real exchange rae. In paricular, i shows ha he real exchange rae of developing counries is approximaely hree imes more volaile han he real exchange rae in indusrial counries. The paper ess wheher his difference in volailiy can be explained by he fac ha developing counries face larger shocks (boh real and nominal) and recurren currency crises or by differen elasiciies o hese shocks. I finds ha he magniude of he shocks and he differences in elasiciies can only explain a small par of he difference in RER volailiy beween developing and indusrial counries. Resuls from ARCH esimaions confirm ha here is a subsanial difference in long erm volailiies beween hese wo ses of counries and indicae ha here is also a much higher persisence of deviaions of he variance of he RER from is long run value when he economy suffers shocks of various kinds. JEL Codes: F31, F41 Keywords: Real Exchange Rae, Volailiy * RICARDO_HAUSMANN@HARVARD.EDU; UGOP@IADB.ORG; RIGOBON@MIT.EDU. We would like o hank he paricipans a he Lunch on Inernaional Economic Policy a he KSG, Harvard for helpful commens and suggesions and Alejandro Riaño and Monica Yañez for excellen research assisance. The usual caveas apply. 1
1. Inroducion Developing counries are more volaile han indusrial counries. This is rue when we look across counries a differences in he volailiy of oupu, consumpion, ineres raes, or exchange raes. The purpose of his paper is o documen cross-counry differences in long run volailiy of he real exchange rae (RER). We show ha he real exchange rae ends o be much more volaile in developing counries han in indusrial counries, even a long horizons, and ha his difference in volailiy canno be aribued o sandard explanaions based on he fac ha developing counries face larger shocks (eiher real or nominal), or ha hey are more sensiive o hese shocks. The paper finds ha par of he explanaion lies in he fac ha volailiy swings are more persisen in developing counries. Since he seminal conribuion by Cassel (1922), Purchasing Power Pariy (PPP) has been one of he mos sudied opics in inernaional economics. In is simples form, PPP implies ha he price level of consumpion baskes across counries is he same. This is he absolue version of PPP which, by expressing all variables in logs, can be wrien as: p + s = p * where p is he price of he domesic consumpion baske, * p is he price of he foreign baske, and s represen he exchange rae. The idea is ha if goods are raded freely hen deviaions from PPP would imply flow of goods o arbirage he differences. Absolue PPP is only saisfied under very srong assumpions and he presence of non-radable goods, ransporaion coss, and monopolisic compeiion are among he main reasons used in he lieraure o accoun for deviaions from absolue PPP. Relaive PPP enails weaker assumpions and, raher han requiring price equalizaion across consumpion baskes, i only assumes ha changes in he price of hose consumpion baskes are arbiraged away. Formally, relaive PPP requires ha: p = p * + s Boh absolue and relaive PPP have implicaions for he behavior of he real exchange rae. Absolue PPP implies ha he real exchange rae is always equal o one, while relaive PPP implies ha deviaions of he real exchange rae from is seady sae are zero. q = s + p * p 2
PPP is an appealing heory. So much so, ha i is one of he mos imporan building blocks of he models in inernaional economics. PPP, however, was never mean o characerize he shor-erm dynamics of counries. Prices do no adjus o monhly flucuaions of he exchange rae, and in mos counries, no even o yearly movemens. Dornbusch s (1976) seminal paper explained exchange rae overshooing in he shor run as he consequence of differenial arbirage speeds beween he fas financial markes and he slower goods markes. In all hese heories, arbirage in he goods markes will evenually ake place and PPP can be hough as a he long run characerisic of a mean revering process. There are, however, heoreical models ha by assuming permanen real shocks can accoun for an RER ha follows a random walk. In fac, mos of he aenion of he empirical lieraure on PPP has focused on esing wheher he RER is beer described by a random walk or by a mean revering process. In mos cases his is done by concenraing on he sochasic properies of real exchange rae deviaions from some rend and by esimaing variaions of he following regression: q = α 1 + ε (1) q where he focus of he analysis has ended o concenrae on he coefficien α. While a survey of he exensive lieraure on he empirics of PPP is beyond he purpose of his paper, i is worh noing ha Froo and Rogoff (1995) find ha he consensus in he lieraure is ha PPP holds in he long run, and ha he half-life of he deviaions ranges beween 3 and 4 years. 1 I should be poined ou ha his is a consensus, no an agreemen (Kilian and Zha, 2002). For example, he area coninues o be invesigaed and recenly Imbs, e.al. (2002) sugges ha he average half-life is smaller han a year. They argue ha he longer esimaes found in he previous lieraure were due o aggregaion bias. Their findings, however, have been recenly challenged by Chen and Engel (2004). 2 While he lieraure has mosly concenraed on he serial correlaion coefficien α in equaion (1), his paper sudies cross-counry differences in he variance of he innovaions o he 1 Froo and Rogoff (1995), Rogoff (1996), and Chen and Engle (2004) offer excellen surveys of he empirical and heoreical lieraure. The survey of economiss reporing he consensus view was conduced by Kilian and Zha (2002). 2 There are imporan small sample problems in he esimaion of auo correlaion models. There are wo alernaives: one is o use exremely long daa ses and he oher one is o perform he esimaion on a panel. Abuaf and Jorion (1990), Diebold, Hused, and Rush (1991), Frankel (1986, 1990), Glen (1992), Lohian and Taylor (1996), and Mark (1995), look a very long daa ses. Frankel and Rose (1996), Lohian (1997), Oh (1996), and Wu (1996) esimae he auoregressive coefficien using panels. Recenly, some papers have sudied non-lineariies (Obsfeld and Taylor, 1997, Taylor, Peel and Sarno, 2001, and Taylor and Peel, 2000). 3
PPP equaion ε. 3 We find ha some counries have innovaions whose variance is more han 20 imes larger han ohers. And more imporanly, we find ha hese differences are only very parially explained by he higher variance of heir erms of rade, moneary and oupu shocks, by differences in he sensiiviies o hese shocks or by differences in exchange rae regimes. These differences are also no accouned for by differen speeds of mean reversion in he PPP equaion. We consisenly find ha indusrialized economies have, on average, a lower sandard deviaion of he innovaions o he RER (developing economies are 2.5 imes more volaile han indusrial counries). 4 Conrolling for various shocks and allowing for differen parameers by counry groups explains a very small fracion of he RER volailiy. Esimaing counry-bycounry equaions can explain up o 60 percen of he variance in he long run RER. However, none of hese equaions can reduce he raio of he residual long run RER volailiies, which remains beween 2 and 2.5. We also find ha he difference in residual RER volailiy is srongly associaed wih he level of developmen (eiher economic, as measured by GDP per capia, or insiuional, as measured by rule of law) and o a lesser exen o he degree of expors diversificaion, as measured by he Hirschman-Herfindahl concenraion indexes. Furher invesigaion sugges ha differences in long run RER volailiy are no due o he magniude or frequency of he shocks bu o differences in persisence of he volailiy indicaing ha he way in which he RER adjuss o shocks end o imply more persisen swings in volailiy. The paper is organized as follows. Secion 2 shows he basic facs abou cross-counry differences in RER volailiy and ess differen heories aimed a explaining hese differences. Secion 3 uses an ARCH model o show ha par of he difference in RER volailiy beween developing and indusrial counries can be explained by differences in persisence. Secion 4 concludes. 3 While here is a large lieraure ha uses cross counry daa o gauge he consequences of RER volailiy (especially on rade, for a recen survey see Hau, 2002), here are almos no papers ha use cross-counry daa o sudy he causes of long run RER volailiy. One excepion is Hau (2002) who focuses on how openness affecs RER volailiy. 4 In a paper ha is somewha relaed o ours, Cashin and McDermo (2004) find ha he speed of reversion o PPP is faser for developed counries han for indusrial counries. 4
2. The Puzzle The purpose of his secion is o documen he presence of large cross-counry differences in real effecive exchange rae (RER) volailiy and show ha in developing counries he real exchange rae ends o be much more volaile han in indusrial counries, even afer conrolling for differences in exernal and domesic shocks. Our sample covers up o 74 indusrial and developing counries for which we have annual daa on real effecive exchange rae over he 1980-2000 period. 5 We sar wih he simples possible measure of volailiy: he sandard deviaion of he growh rae of he RER. Formally, our firs measure of volailiy is given by: VOL i ( RER ) ln( RER )) SD ln( n = (2) n We focus on boh one year (n=1) and five-year (n=5) volailiy (he upper bound for sandard esimaes of he real exchange rae half-life is 4 years, Froo and Rogoff, 1995). Figure 1 plos five-year volailiy for our sample of counries (he daa have been normalized so ha he cross-counry average is equal o one). I clearly shows ha indusrial counries (he ligh bars) end o have levels of real exchange rae volailiy ha are much lower han hose of emerging marke and developing counries (dark bars). Porugal is he indusrial counry wih he highes level of volailiy and is volailiy is jus above he cross-counry average; no oher indusrial counry has levels of volailiy ha are above he cross-counry average. We also find very few emerging marke or developing counries in he lef par of Figure 1. The few we find end o be very small (Papua New Guinea, S. Vincen, and The Bahamas). The only large emerging marke counries ha are characerized by low levels of real exchange rae volailiy (i.e., less han half he cross-counry average) are Israel and Taiwan, wo raher advanced economies. Table 1 repors average values for one-year and five-year volailiy for he whole sample of counries and for developing and indusrial counries (no normalized o one) and ess wheher 5 The real exchange rae daa are from J.P. Morgan and he IMF Inernaional Financial Saisics. We use J.P. Morgan daa whenever hey are available and complemen hem wih IMF daa for counries ha are no included in he J.P. Morgan daase. All he resuls are robus o using he IMF as main source or o resricing he sample o only J.P. Morgan or IMF daa. In all cases, we focus on he annual average of he real exchange rae index (he resuls are robus o using end of period daa). An increase in he RER index reflecs a real appreciaion of he currency. 5
he difference in volailiy beween hese wo groups of counries is saisically significan. I shows ha five-year volailiy is only en percen lower han one-year volailiy and ha volailiy in developing counries is always a leas 2.5 imes larger han volailiy in indusrial counries. The las wo rows of he able show ha we can always rejec he hypohesis ha he wo groups of counries have he same level of volailiy. The las four columns of he able also show ha differences in volailiy are no due o a specific sub-period. In fac, we obain similar resuls when we resric our analysis o he 1980s or o he 1990s (even hough he difference beween developing and indusrial counries was slighly larger in he 1980s). We also look a he hird and fourh momens o check wheher differences in volailiy are due o large devaluaion or real appreciaion episodes. Table 2 repors he skewness and kurosis of RER changes. The firs wo columns show ha he disribuion of he real exchange rae is skewed o he lef in boh developing and indusrial counries, indicaing ha large depreciaions are more common han large appreciaion. While column 1 indicaes ha skewness is significanly larger (in absolue value) in developing counries (indicaing ha large depreciaion are more common in his group of counries), column 2 shows ha when we focus on five-year periods here is no significan difference beween he wo samples of counries. This suggess ha large depreciaions and currency crises (ha are more common in developing counries) canno explain why five-year RER volailiy is higher in developing counries. The las wo columns of Table 2 show ha if we focus on one-year volailiy, we find ha he disribuion of RER ends o have faer ails in he sample of developing counries. However, he difference in kurosis beween hese wo groups of counries disappears when we focus on five-year volailiy. Again, his suggess ha exreme episodes canno fully explain he fac ha five-year RER volailiy is much higher in developing han in indusrial counries. 2.1. Trying o Explain he Puzzle Why are developing counries more volaile? Clearly his suggess a misspecificaion error in he AR(1) represenaion of he real exchange rae i.e., here are unobservable shocks ha are more volaile in one sub-sample han in he oher. These forms of misspecificaion should have been expeced. In fac, several of hem are implied by he heories we already have available. There are six sandard explanaions based on he differen ypes of shocks and responses 6 : (i) Developing counries are subjec o larger erms of rade shocks. (ii) Developing counries are 6 The higher volailiy of developing counries and is poenial causes in erms of exernal shocks and insiuional failings is discussed in Iner-American Developmen Bank (1995), Hausmann and Gavin 6
subjec o large volailiy in GDP growh because of heir limied abiliy o conduc counercyclical moneary and fiscal policies. (iii) Developing counries are subjec o large nominal shocks because hey have non-credible moneary insiuions and weak fiscal posiion. (iv) Developing counries are subjec o sudden sops in capial flows ha lead o currency crisis. (v) Differences in volailiy are due o he fac ha developing counries are no as open as indusrial counries. (vi) Differences in volailiy are due o differen exchange rae arrangemens and in paricular o he adopion of non-credible pegs. To check wheher hese heories can help us in explaining away he difference in RER volailiy beween developing and indusrial counries we sar by running various subses of he following regression: DEV + 2 n= 1 * α DEV n = SHOCK n β + + δcrisis + µ + ε i + CC λ + SHOCK Where he variable DEV is he firs difference of he real exchange rae deviaion from is long run equilibrium level (compued as a log-linear rend). 7 Noice ha expressing he dependen variable in erms of deviaion from is long run rend is equivalen o including a counry specific rend in Equaion (2). Such a counry specific rend conrols for he fac ha, because of he Balassa-Samuelson effec, some counries may experience rend appreciaion or depreciaion. SHOCK is a marix ha includes various measures of shocks. Crisis is a dummy variable aimed a capuring he effec of currency crisis. CC is a marix of counry characerisics (openness, exchange rae regime, level of developmen) ha may affec he RER response o shocks. Finally, we include wo lags of he dependen variable o conrol for he possibiliy ha differences in volailiy are driven by differences in persisence. µ i is a counry fixed effec. CC γ + Afer running regression (3), we recover he error erm ( ε ) and use i o compue counry s i one-year and five-year residual RER volailiy as: (3) (1996), De Ferrani e al. (2000), Aizenman and Pino (2004). The role of sudden sops and openness is discussed in Calvo e al (2003). 7 Formally, DEV, i = (ln RER, i ln TREND, i ) (ln RER 1, i ln TREND 1, i ). As (ln TREND, i ln TREND 1, i ) is a consan, he sandard deviaion of DEV, i is equal o he oneyear volailiy as compued in Equaion (1). As we run fixed effec esimaions, we would obain exacly he same resuls if we were o define our dependen variable as ln RER, i ln RER 1, i 7
RESVOL n = SD n 1 j= 0 ε n + j (4) Clearly, when n=1 (one-year volailiy), he residual volailiy is jus equal o he counryspecific sandard deviaion of he regression s residuals. When n=5 (five-year volailiy), he residual volailiy is equal o he sandard deviaion of he five year average of he residuals. Nex, we use RESVOL o check wheher, afer conrolling for all he variables included in Equaion 2, here is sill a difference beween he unexplained volailiy of he real exchange rae in developing and developed counries. 2.2. The Role of Shocks In Table 3, we explore wheher shocks can help in explaining away he difference in RER volailiy beween developing and indusrial counries. In column 1, we conrol for erms of rade shocks (do measures he change in erms of rade and ldo is lagged value). While we find ha erms of rade shocks are posiively and significanly correlaed wih changes in he RER (indicaing ha posiive TOT shocks lead o an appreciaion of he RER), he low R-squared (0.03) suggess ha erms of rade shocks can only explain a very small fracion of he variance of he real exchange rae. Columns 1 of Tables 4 and 5 repor he residual (afer conrolling for erms of rade shocks) one-year and five-year volailiy. They show ha he residual volailiy is basically idenical o he uncondiional volailiy. In he case of developing counries, he oneyear volailiy goes from 0.112 o 0.109 and he five-year volailiy goes from 0.103 o 0.099. In he case of indusrial counries, one-year volailiy goes from 0.044 o 0.042 and five-year volailiy goes from 0.041 o 0.040. Hence, differences in he magniude of erms of rade shocks do no explain he difference in RER volailiy beween developing and indusrial counries. Developing counries remain 2.5 imes more volaile han indusrial counries and he difference beween he wo groups remains highly significan. In he second column of Table 3, we conrol for oupu shocks by including GDP growh (growh). Clearly, GDP growh shocks are no exogenous and may be joinly deermined wih RER innovaions. However, his dual causaion cleads he regression o oversae he explanaory power of GDP growh shocks and hence o leave a smaller residual han is warraned. This biases he resuls agains he poin we are making. This commen is valid for oher endogenous variables ha we consider below as well. Remember ha he problems of endogeneiy will affec he 8
esimaion and inerpreaion of he coefficiens in equaion (1). We are, on he oher hand, concenraing on he properies of he residuals regardless of heir sources. While GDP growh (we use real local currency GDP growh) has a posiive and saisically significan coefficien (indicaing ha posiive oupu shocks are associaed wih real appreciaions), he R-squared of he regression remains exremely low (0.05) and columns 2 of Tables 4 and 5 show ha conrolling for GDP growh neiher reduces RER volailiy nor reduces he difference in RER volailiy beween developing and indusrial counries. In he hird column of Table 3, we include he change in log inflaion (dinf) o conrol for nominal shocks. While inflaion is no saisically significan, column 3 fis he daa beer han he wo previous columns (he R-squared goes o 0.09) and somewha reduces five-year volailiy (in developing counries i goes from 0.099 o 0.092). However, his is due o he fac ha, when we include inflaion in he regression, we lose abou 300 observaions. In any case, columns 3 of Tables 4 and 5 show ha he difference beween developing and indusrial counries remains large and highly significan. In column 4 of Table 3, we include a dummy variable ha akes value 1 during currency crises. The Crisis dummy akes value one when, in any wo-year period, he RER depreciaes by more han wo sandard deviaion of he cross-counry sample (according o his definiion here are no currency crisis in indusrial counries). As his variable is buil using he lef hand-side of he regression, i has a negaive and highly significan coefficien and grealy increases he fi of he regression (he R-squared jumps o 0.3). However, conrolling for currency crisis does no explain away he difference in volailiy beween developing and indusrial counries. Columns 4 of Tables 4 and 5 sill show ha developing counries are a leas wice as volaile as indusrial counries. This suggess ha he difference in volailiy beween indusrial and developing counries is no due o he presence of a few large depreciaions. This is consisen wih our finding ha here is no significan difference beween he five-year skewness of developing and indusrial counries. Column 5 of Table 3 conrols for changes in expors (dexp) in order o check wheher movemens in he real exchange rae are due o sudden jumps demand for a counry s expors. I finds ha he coefficien of dexp is negaive and no saisically significan. Column 6 conrols for openness and Column 7 ineracs openness wih oupu (grop), erms of rade shocks (dop and ldop), and changes in expors (dexpop). The raionale for including hese ineracion erms is ha more open economies could be beer equipped o face exernal shocks. In paricular, Calvo e al. (2003) show ha he real depreciaion brough abou by a sudden sop in capial flows is 9
negaively correlaed wih he degree of openness. 8 We find ha neiher openness nor he ineracion erms are saisically significan. We also find ha he R-squared remains low (a 0.10) and ha he difference in volailiy beween developing and indusrial counries remains large and highly significan (columns 6 and 7 of Tables 4 and 5). In column 8 of Table 3, we inerac he shock variables wih an indusrial counry dummy o conrol for he possibiliy ha shocks may have a differen effec on he real exchange rae in each of he counry ses. We find ha he ineracion erms are rarely significan. The only excepion is he change in expors which is correlaed wih real depreciaions in developing counries and real appreciaions in indusrial counries. In any case, conrolling for hese ineracions neiher reduces he level of real exchange rae volailiy, nor he difference in volailiy beween indusrial and developing counries (column 8 of Tables 4 and 5). In columns 9, 10, and 11 of Table 3, we check wheher differences in RER volailiy can be explained away by he ineracion beween shocks and he exchange rae regime (Broda, 2001 shows ha counries wih a flexible exchange rae regime are beer able o smooh-away erms of rade shocks). In column 9, we include wo dummies based on he de faco measure of he exchange rae regime assembled by Levy-Yeyai and Surzenegger (2000). Lys02 akes value one for counries wih an inermediae regime and Lys03 akes value one for counries wih a fixed exchange rae regime (he excluded dummy is for counries wih a floaing regime). In column 10, we inerac hese dummies wih he oupu, erms of rade, and inflaion shocks discussed above. In column 11, we also include a dummy (swich) ha akes value one when a counry moves o a more flexible exchange rae regime (from inermediae o floaing or from fixed o inermediae or floaing). We find ha, compared wih counries wih floaing and fixed exchange rae regime, erms of rade shocks end o have a larger effec on he RER in counries wih an inermediae regime (all he oher variables are no significan). Conrolling for he exchange rae regime reduces he sample by approximaely 200 observaions and increases he R-squared of he regression o 0.20. However, columns 9, 10 and 11 of Tables 4 and 5 show ha conrolling for he role of he exchange rae regime and is ineracion wih shocks does no explain away he difference in RER volailiy beween developing and indusrial counries. The las hree column of Table 3 inerac shocks wih boh exchange rae regime and growh. As one may expec, we find ha erms of rade shocks have a smaller effec on he RER during periods of high growh (grdo is negaive) bu, again, his does no explain away he 8 Obsfeld and Rogoff (2000) find ha in models wih nominal rigidiies, more open economies should exhibi lower RER volailiy. We es his hypohesis in subsecion 2.4. 10
difference in volailiy beween developing and indusrial counries (columns 12, 13, and 14 of Tables 4 and 5). 2.3. The role of Persisence As we found ha shocks canno explain away he difference in volailiy beween developing and indusrial counries, we now explore he role of persisence by augmening he regression wih lagged values of he dependen variable and allowing for differen persisence in developing and indusrial counries. The idea is ha he variance of he observed variable could be differen across groups because counries have differen persisence and no necessarily because he innovaions have differen variances. This secion explores his possibiliy. In he firs column of Table 6, we include wo lags of he dependen variable. Boh lags have a negaive coefficien (saisically significan for he second lag). While he negaive coefficiens sugges ha, afer a shock, he RER end o rever o is long run rend, he coefficiens are raher small indicaing ha shocks end o be persisen. The ypical esimae in he able implies an auoregressive coefficien of abou 0.8. 9 This is consisen wih he PPP lieraure ha has found average half-lives of abou 3 o 4 years. Columns 1 of Tables 7 and 8 show ha, allowing for persisence does no reduce our measure of RER volailiy and does no eliminae he difference in volailiy beween indusrial and developing counries. In he second column of Table 6, we inerac he lagged values of he dependen variable wih an indusrial counry dummy and hus allow persisence o differ across he wo groups of counries. Ineresingly, we find ha he coefficien on he firs lag becomes posiive in indusrial counries suggesing ha exchange rae shocks are more persisen (a leas in he shor run) in his group of counries. This resul is also consisen wih some evidence of non-lineariy of PPP deviaions. In he daa developing counries have larger deviaions and if he relaionship is nonlinear we should expec hese counries o reurn o he mean faser (Obsfeld and Taylor 1997). However, for he purpose of his paper, allowing for differen degrees of persisence does no affec our basic resul ha RER is more volaile in developing counries (column 2 of Table 7 and 8). In columns 3 hrough 9 we inroduce he variables discussed above (shocks, crisis, openness, and exchange rae regime). Again, we find ha none of hese variables can explain 9 Remember ha we are esimaing an AR(2) which means ha he value of 0.8 repored in he ex is he implied coefficien if we were o fi an AR(1). Or pu i in oher erms, he half-lives of he esimaed AR(2) is he same as an AR(1) wih an auoregressive coefficien of 0.8. 11
away he difference in volailiy beween developing and indusrial counries (see columns 3-9 of Tables 7 and 8). In column 10, we allow boh he shocks and persisence o have a differenial effec in developing and indusrial counries. Column 11 conrols for he exchange rae regime and columns 12 hrough 16 allows for ineracions beween shock and exchange rae regime and shocks and growh. The resuls are similar o hose of Table 3 and show ha none of he specificaions of Table 6 can explain away differences in RER volailiy beween indusrial and developing counries. 10 The resuls of he exercises described above are remarkable. Afer conrolling for a very ample se of shocks and ineracing he shocks wih differen counry characerisics, we could, in he bes of cases (when we inerac shocks wih he exchange rae regime in columns 10, 11, 13 and 14 of Table 3 or include our crisis dummy which is buil using he lef hand side variable, column 4) reduce he residual five-year RER volailiy in developing counries by 30 percen (from 0.103 o 0.07). Even in hese cases, volailiy in developing counries remains 1.7 imes higher han he RER volailiy in indusrial counries (and he difference is saisically significan a he 1 percen confidence level). In all oher cases, our se of explanaory variables can reduce developing counries five-year volailiy by a mos 20 percen. Ineresingly, hese explanaory variables accoun for a smaller reducion in residual volailiy a 5-year horizons han a 1 year. As a final robusness check, we look a wheher our resuls are driven by aggregaion bias or by non-lineariies. We sar by running a se of regressions where all he shocks are ineraced wih counry fixed effecs. This eliminaes any aggregaion bias because his is equivalen o running he regression counry by counry. Afer running hese regressions, we recover he errors in he wo groups, compue he residual volailiy, and compare indusrial wih developing counries. The resuls are repored in Table 9. They show ha even afer running a separae regression for each counry, we sill ge ha he residual volailiy of he RER in developing counries is more han wice as large as he residual volailiy in indusrial counries (he raios beween he volailiies of he wo groups of counries range beween 2.4 and 2.9). Table 10, repors resuls of counry by counry regressions where we also conrol for non-lineariies by enering he squares of various shocks. Again, his does no eliminae differences in RER volailiy beween developing and indusrial counries and he raio beween he volailiy of he wo group of counries remains in he 2.3-2.7 range. 10 To check he robusness of our resuls, we also reesimaed he specificaions of Table 6 by using he GMM esimaor developed by Arellano and Bond (1991) and obained resuls ha are essenially idenical o hose of Table 6. 12
In Figure 2 we illusrae he real exchange rae volailiy puzzle in ye anoher way. We plo summary saisics of all he regressions we have esimaed hus far. For each specificaion we plo he R-squared of he equaion separaely for indusrial and for developing counries, shown respecively in dark and ligh color bars (measured from he lef axis). The idea is o measure how much can be explained by he shocks and ineracions we are including in he regressions. Noe ha as we include more explanaory variables, he R squares go up. However, in general, he equaions do a significanly beer job in explaining he wihin counry volailiy among indusrial counries han among developing counries. Noe also ha as more variables are included, he R-square increases, especially afer equaion 33 when we run counry by counry equaions (his should be expeced because he counry by counry regressions have less han fifeen degrees of freedom). However, he line depiced in he figure indicaes he raio of he residual volailiies beween developing and indusrialized counries is very sable. Noice ha he raio flucuaes beween 2 and 2.5 regardless of he specificaion. Therefore, he puzzle is, hen, ha independenly of how much of he RER volailiy we can explain, we are unable o make any progress in explaining he relaive residual volailiies of hese wo ses of counries. 2.4. Going beyond he indusrial-developing spli So far we compared volailiy beween developing and indusrial counries wihou asking wheher here is any specific characerisic of hese wo groups of counries ha may explain he differences in volailiy we jus documened. In wha follows we use he one-year residual volailiy obained by running he counry by counry regressions ha includes all conrols and wo lags of he dependen variable (column 8 of Table 9) and regress hese volailiies over a se of counry characerisics (measured as averages for he 1980-2000 period unless oherwise noed). In he firs column, we conrol for he log of GDP per capia (o conrol for differences in he level of developmen), he volailiy of erms of rade, and he degree of openness. As expeced, we find ha more developed counries have lower residual RER volailiy (he coefficien of LGDPPC is negaive and saisically significan) and, as suggesed by Obsfeld and Rogoff (2000) and Calvo e al. (2003), we also find ha more open counries have lower residual RER volailiy. A he same ime, we find ha erms of rade volailiy is no correlaed wih residual RER volailiy (his should no be surprising because in compuing residual RER volailiy we already need ou he effec of erms of rade shocks). In he second and hird columns, we also conrol for GDP growh volailiy and volailiy of expors and find an insignifican relaionship (again, his was expeced because in compuing residual volailiy we 13
already need ou he effec of GDP and expor shocks). In he fourh column, we conrol for rule of law (measured over he 1996-2002 period) and we find ha his variable has he expeced negaive sign bu ha i is no saisically significan. We also find ha once we include rule of law, GDP per capia is no longer significan (and he coefficien drops from 0.01 o 0.005). 11 This is due o he fac ha GDP per capia and rule of law are highly correlaed (he correlaion coefficien is 0.89) and a Wald es indicaes ha he wo variables are joinly significan wih a p- value of 0.001. In he fifh and sixh columns we conrol for expor concenraions a he 4 and 10 digis (he idea is ha counries wih less diversified expor srucures migh experience higher volailiy). We use daa on US impors by counry and calculae Hirschman-Herfindahl indexes of concenraion a he 4 (CONC4) and 10 (CONC10) digi levels (he concenraion indexes are measured as averages over he 1990-2000 period). As expeced, he coefficiens are posiive and marginally significan in he case of CONC10. Columns 7, 8, 9 conrol for counry size (measured by oal GDP) and wo measures of financial developmen (DC_GDP is an average over he 1990-2000 period) and find ha none of hese variables are significanly correlaed wih residual volailiy (when we conrol for oal GDP we find ha openness is no longer significan). 12 Equaions 11 hrough 13 pu several of he explanaory variables ogeher. The main message of hese equaions is ha a measure of developmen wheher GDP per capia or rule of law is robusly relaed o he difference in residual RER volailiy. In addiion, expor concenraion is also robus o he inclusion of oher variables. In paricular, i is robus o he inclusion of openness and size, wo variables wih which i is relaed. 13 However, neiher of hese wo laer variables are robusly relaed o RER volailiy. 14 Table 12 uses he equaions esimaed in Table 11 o accoun for he difference in average residual RER volailiy beween indusrial counries (2.3 percen) and developing counries (5.6 percen). The esimaed equaions when applied o he average characerisics of indusrial and developing counries can allow for a decomposiion of he residual volailiies. The equaions 11 I should be poined ou ha, as rule of law is measured in he lae 1990s raher han for he whole period, his variable is more endogenous han GDP per capia. 12 Larger economies end o be more closed and counry size and openness have a negaive correlaion of 0.5 in our daase. Our resuls are in conras wih he finding of Hau (2002) who find ha openness is a robus predicor of long run RER volailiy. One difference beween our and his empirical sraegy is ha we focus on residual volailiy and, in he cross-counry analysis, we also conrol for counry size and expor concenraion. 13 There is a relaively high and negaive correlaion beween CONC10 and LGDP of -0.41 in our daase and here is no correlaion beween CONC10 and openness (0.05). Inclusion of boh size as measured by LGDP and CONC10 makes openness no longer saisically significan. 14 These resuls are robus o esimaion echniques ha pu less weighs on ouliers. 14
explain beween 71 and 100 percen of he difference. In general, he level of developmen, measured eiher as LGDPPC or as he index of Rule of Law or in andem, can explain beween 80 and 100 percen of he difference, depending on he specificaion. Differences in expor concenraion can accoun for abou 18 percen of he difference. Differences in openness do no help explain he differences, as developing counries are on average more open han developed counries. Differences in size also do no explain he RER puzzle as larger counries end o have more residual RER volailiy. Hence, he level of developmen and of expor concenraion seems o be involved in any explanaion of why residual RER volailiy is higher in developing counries. 3. Anoher way o look a persisence and a possible answer o he puzzle So far we compared RER volailiy beween indusrial and developing counries by esing he difference beween average volailiy in he wo groups of counries or by regressing residual volailiy on a series of counry characerisics. We now esimae an ARCH model ha allows us o use a proper regression se up o es wheher here is indeed a difference beween long-run RER volailiy in developing and indusrial counries. We also use he ARCH model o check wheher he difference in RER volailiy beween developing and indusrial counries can be explained by differences in persisence in he ARCH componen of he regression. Formally, we joinly esimae he following wo ARCH (2) equaions: DEV = SHOCK + (1 + d * IND) * h + (1 + δ * IND) * + ψ h = ϕ + SHOCK 1 1 + ψ h 2 2 n= 1 2 a + IND b + SHOCK g n DEV i n i + u 1 α + IND β + SHOCK * IND c + 2 λn DEV n + (6) n= 1 + φ IND * h 1 + φ IND * h 2 i * IND γ + i 2 + ε (5) The firs equaion (mean equaion) measures how shocks and persisence affec he level of he dependen variable (in our case he change of he real exchange rae). The second equaion he variance equaion describes he evoluion of he variance and allows us o measure he difference in he long run variance beween developing and indusrial counries. 15
Equaion 1 in Table 13 esimaes he above model by seing c and d equal o zero in he mean equaion and α, γ, δ, λ1, λ2, ψ1, ψ 2, φ1, φ2 equal o zero in he variance equaion. In his case, he consan (0.0132) measures he long run variance in developing counries and he consan plus β (0.0132-0.0118=0.0014), he long run variance in indusrial counries. Hence, he fac ha he indusrial counry dummy has a negaive and highly significan coefficien indicaes ha he condiional variance of he real exchange rae is significanly higher in developing counries. Noe ha hese numbers reflec he esimaed variances, which are he squares of he sandard deviaions. By aking he square roos of he esimaed long run variances we obain 11.5 percen for developing counries and 3.7 percen for indusrial counries, numbers which are in line wih he resuls obained in he previous secions (Equaion 1 of Table 13 is comparable o Equaion 4 of Table 6; he residual 5 year volailiy of his laer equaion is 1.09 percen in developing counries and 3.5 percen in indusrial counries). In Equaion 2, we explore wheher he wo ses of counries have he same persisence in he variance equaion. We address his issue by adding wo ARCH erms o he previous equaion. The esimaed long run variances of hese equaions are given by ϕ h NONIND = for 1 ψ ψ ϕ + β developing counries and by h IND = for indusrial counries, he esimaed raio 1 ψ ψ 1 2 ϕ beween he long run variance of indusrial and developing counries is given by =5.125 ϕ + β (i.e., long run RER volailiy is five imes higher in developing counries). Taking square roos of his raio we obain 2.264, which is in line wih our esimaed relaive residual volailiies of he previous secion. Equaion 3 allows he variance of developing and indusrial counries o have differen persisence and shows ha persisence is sronger in developing counries. While he ARCH coefficiens are posiive and saisically significan, he ineracion erms are negaive and saisically significan and indicae ha persisence in he variance of he real exchange rae of indusrial counries is a small fracion of ha in developing counries (0.55 vs. 0.20 for ARCH1 and 0.53 vs. 0.04 for ARCH2). In his case, he respecive long run variances are given by: ϕ ϕ + β h NONIND = and h IND =. Noice ha ψ 1 + ψ 2 is very close o 1 ψ ψ 1 ψ ψ φ φ 1 2 1 2 one (1.09) indicaing ha he model could be misspecified because he variance of developing counries could be eiher negaive or explosive. 1 2 1 2 16
In equaion 4 we allow for various shocks and he lagged values of he real exchange rae o have an effec on he variance (i.e., we relax he assumpion ha α, λ, λ 1 2 are equal o zero). In he variance equaion we square all our explanaory variables, so ha he coefficien of, say, erms of rade, should be inerpreed as he effec of erms of rade shock (eiher posiive or negaive) on he variance of he RER. We find ha pas RER shocks increase RER volailiy bu we find no significan effec of erms of rade or oupu shocks (he esimaed effecs are posiive bu no significan). The long run variance of he RER in developing and indusrial counries can be calculaed in he same way as we did in Equaion 2 yielding values of 0.00414 and 0.00072, which correspond o volailiies of 6.4 percen and 2.7 percen and a raio of volailiies of 2.4. In Equaion 5, we reproduce equaion 4 bu now we allow for ineracion in he mean equaion (i.e., we relax he assumpion ha c and d are zero) his allows indusrial and developing counries o have differen slopes in he mean equaion. None of he ineracion erms is saisically significan indicaing ha here is no evidence ha shocks affec he real exchange rae of developing counries differenly from he way hey affec he real exchange rae of indusrial counries. We find almos idenical resuls for he esimaed long run RER volailiies and of he esimaed persisence erms in he variance equaion. Finally in Equaion 6, we also allow for differen persisence in he wo ses of counries of he effecs of he RER, TOT and oupu shocks on he variance equaion (i.e., relax he assumpion ha γ and δ are equal o zero). Several resuls are worh noing. Firs of all, he difference on he ARCH coefficien remains large and highly saisically significan indicaing ha persisence is lower in indusrial counries, even afer allowing he various shocks o have a differenial effec in he wo groups of counries. We find ha erms of rade shocks and he second lag of he dependen variable have a smaller effec on he volailiy of he RER in indusrial counries. Also, we now find ha he IND dummy in he variance equaion is no longer significan. The esimaed raio of long run volailiies beween indusrial and developing counries now declines o 1.57, indicaing ha par of he long run variance of developing counries is explained by difference in persisence. All his poins o he fac ha he difference in real exchange rae volailiy documened in Secion 2 is neiher fully explained by differences in he magniude of he shocks or by how shocks direcly affec he level of he real exchange rae, or heir volailiies. Par of he explanaion is ha he adjusmen of he shifs in he variance ends o be slower in developing counries. As a final robusness analysis, we augmen he ARCH model wih a furher se of ime invarian coninuous variables ha are likely o be correlaed wih he indusrial counry dummy. 17
The resuls are repored in Tables 14 hrough 16. The srucure of he esimaions is similar o ha of Table 10. In Table 14, we include a variable measuring he log of average (over he 1980-2000 period) GDP per capia (GDPPC). This is he bes proxy for economic developmen and i is highly correlaed wih he IND dummy. Column 1 shows ha even conrolling for GDP per capia, he indusrial dummy remains negaive and significan. Columns 2, allows for differences in he ARCH erms beween he wo ses of counries. The esimaed persisence in he indusrial counries is close o nil, while i is large in developing counries. Moreover, allowing for a difference in persisence drasically reduces he value and significance of he coefficien on IND. This resul is essenially repeaed in he res of Table 14 and in he subsequen ables. If we do no allow for differences in he ARCH erms beween he wo ses of counries, we usually ge a large, negaive and significan coefficien on IND. Once we allow for differences in he ARCH erms we find large differences in persisence beween he wo ses of counries. In addiion, he coefficien on he IND erm declines drasically and becomes insignifican. Tables 15 and 16 repea hese experimens using rule of law and financial developmen as coninuous proxies for he indusrial counry dummy. 4. Final Remarks The aim of his paper was o documen he main facs abou long run RER volailiy. I showed ha he long run RER of developing counries is beween 2 and 2.5 imes larger han ha of indusrial counries. We also show ha hese differences are only parially due o he fac ha developing counries face larger shocks (boh real and nominal) or o differences in he sensiiviy of he RER o hese shocks. In fac, afer conrolling for such shocks he raio of he residual volailiies beween he wo ses of counries remains essenially unaffeced. We also show ha differences in residual volailiy (i.e. afer conrolling for shocks and sensiiviies) are srongly correlaed wih he level of developmen and o he degree of diversificaion of he economy (as measured by he concenraion of is expor baske). In addiion, we show ha a significan par of he larger measured RER volailiy in developing counries is associaed wih a much larger persisence of shocks o he variance of he RER iself, as capured by differen ARCH coefficiens. Any model ha aemps o explain he long run RER volailiy puzzle would need o explain no only he poenially larger sensiiviies of he RER o shocks in developing counries, bu also he much longer persisence of shocks boh o he level and volailiy of he RER. 18
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