The well-known analyses of Balassa (1964) and Samuelson (1964) provide an

IMF Staff Papers Vol. 52, Number 3 2005 Internatonal Monetary Fund Real Exchange Rates n Developng Countres: Are Balassa-Samuelson Effects Present? EHSAN U. CHOUDHRI AND MOHSIN S. KHAN* There s surprsngly lttle emprcal research on whether Balassa-Samuelson effects can explan the long-run behavor of real exchange rates n developng countres. Ths paper presents new evdence on ths ssue based on a panel-data sample of 16 developng countres. The paper fnds that the traded-nontraded productvty dfferental s a sgnfcant determnant of the relatve prce of nontraded goods, and the relatve prce n turn exerts a sgnfcant effect on the real exchange rate. The terms of trade also nfluence the real exchange rate. These results provde strong verfcaton of Balassa-Samuelson effects for developng countres [JEL F31, F41] The well-known analyses of Balassa (1964) and Samuelson (1964) provde an appealng explanaton of the long-run behavor of the real exchange rate n terms of the productvty performance of traded relatve to nontraded goods. Bascally, the argument s that as the productvty of traded goods rses relatve to that of nontraded goods, there wll be a tendency for the real exchange rate to apprecate. Balassa-Samuelson effects are generally thought to be the key source of observed cross-sectonal dfferences n real exchange rates (.e., the same currency prces of comparable commodty baskets) between countres at dfferent levels of *Ehsan U. Choudhr s Chancellor s Professor at Carleton Unversty n Canada. Mohsn S. Khan s Drector of the Mddle East and Central Asa Department at the IMF. The authors would lke to thank Robert Flood, Aasm Husan, Jean Le Dem, Gene Leon, Gan Mara Mles-Ferrett, Nkunde Mwase, Sam Oulars, Mguel Savastano, and anonymous referees for helpful comments and suggestons, and Mandana Dehghanan and Tala Khartabl for excellent research assstance. 387

Ehsan U. Choudhr and Mohsn S. Khan ncome per capta. 1 There s consderable emprcal research on Balassa-Samuelson effects based on tme-seres data, but ths research has been confned to ndustral countres. 2 The tme-seres evdence on the workng of the Balassa-Samuelson mechansm for developng countres has been largely unexplored. 3 One reason for ths neglect s that sectoral prce and productvty data are not readly avalable for developng countres. To address ths problem, ths paper makes use of recently avalable data from a number of sources to assemble a sutable data set for developng countres, whch s used to obtan new tme-seres evdence on the operaton of Balassa-Samuelson effects n these countres. Our data set ncludes tme-seres data from 1976 to 1994 for 16 countres. 4 The behavor of the dollar real exchange rate for each country durng ths perod s shown n Fgure 1. The fgure also dsplays the long-run component of the real exchange rate seres based on the Hodrck-Prescott flter. As the fgure shows, the long-run component regsters large changes over the sample perod for a number of countres. It s, thus, nterestng to examne whether Balassa-Samuelson effects have played an mportant role n causng these long-term movements. For many countres, the fgure also exhbts large fluctuatons around the long-term trend. Some of these movements represent currency crses n response to speculatve attacks. Our emprcal analyss attempts to control for the effect of short-run dynamcs n order to dentfy long-run Balassa-Samuelson effects. Balassa-Samuelson effects can be embedded n a varety of models. These effects are typcally derved wthn a statc model, but they can be easly ncorporated n the dynamc framework of the new open economy macroeconomc models. 5 Usng a framework compatble wth the new open economy macroeconomc approach, ths paper derves two steady-state relatons that capture key channels of the Balassa-Samuelson mechansm. The frst relaton lnks the real exchange rate to relatve prces of nontraded goods at home and abroad. Under certan condtons, ths relaton ncludes the terms of trade as an addtonal determnant of the real exchange rate. 6 The second relaton explans the relatve prce of nontraded 1 For a revew of the evdence and a dscusson of alternatve explanatons, see Edwards and Savastano (1999). See also Bergn, Glck, and Taylor (2004), who pont out that although recent data reveal a strong assocaton between natonal prce levels and ncome per capta, ths assocaton dsappears n hstorcal data gong back 50 years or more. 2 See, for example, Canzoner, Cumby, and Dba (1999), and Lane and Mles-Ferrett (2002). 3 See, however, Ito, Isard, and Symansky (1997), who use tme-seres data to explore the Balassa- Samuelson hypothess for Asa-Pacfc Economc Cooperaton (APEC) economes that nclude some developng countres. 4 Ths set ncludes 14 countres at low- and medum-ncome levels and 2 hgh-ncome economes (Republc of Korea and Sngapore) that had lower ncome levels at the begnnng of the sample perod. 5 These models tend to focus on the short- to medum-term dynamcs arsng from nomnal rgdtes and have not pad much attenton to long-run Balassa-Samuelson nfluences. Bengno and Thoenssen (2003), however, do use a new open economy macroeconomc model to explore the effect of a productvty mprovement n the traded-goods sector on the Unted Kngdom real exchange rate. 6The relaton assumes that the law of one prce holds for each traded good n the long run. The real exchange rate for the traded-goods basket, however, need not be statonary and could nfluence the relaton f weghts for ndvdual traded goods dffer between the home and foregn countres. Our emprcal procedure accounts for ths possblty. 388

REAL EXCHANGE RATES IN DEVELOPING COUNTRIES Fgure 1. Selected Developng Countres: Real Exchange Rate Behavor, 1976 94 0.0036 0.0048 Cameroon 0.0044 0.0032 0.0040 0.0028 0.0036 0.0032 0.0024 0.0028 0.0020 0.0024 0.0020 0.0016 0.0016 1976 78 80 82 84 86 88 90 92 94 1976 Chle 78 80 82 84 86 88 90 92 94 0.0020 Colomba 0.0009 Ecuador 0.0008 0.0016 0.0007 0.0006 0.0012 0.0005 0.0004 0.0008 0.0003 1976 78 80 82 84 86 88 90 92 94 1976 78 80 82 84 86 88 90 92 94 0.07 Inda 2.6 2.4 Jordan 0.06 2.2 0.05 2.0 1.8 0.04 1.6 1.4 0.03 1.2 1976 78 80 82 84 86 88 90 92 94 1976 78 80 82 84 86 88 90 92 94 0.028 0.026 0.024 Kenya 0.0014 0.0013 Korea 0.022 0.0012 0.020 0.0011 0.018 0.016 0.0010 0.014 0.0009 1976 78 80 82 84 86 88 90 92 94 1976 78 80 82 84 86 88 90 92 94 Real dollar exchange rate (1994 CPI = 100 for all countres) Long-term component (based on Hodrck-Prescott flter) Source: See Appendx II. 389

Ehsan U. Choudhr and Mohsn S. Khan Fgure 1. (Concluded) 0.56 Malaysa 0.36 Mexco 0.52 0.32 0.48 0.28 0.44 0.40 0.24 0.36 0.20 0.32 0.16 1976 78 80 82 84 86 88 90 92 94 1976 78 80 82 84 86 88 90 92 94 0.20 0.18 Morocco 0.052 0.048 Phlppnes 0.16 0.044 0.14 0.12 0.040 0.036 0.032 0.10 0.028 0.08 0.024 1976 78 80 82 84 86 88 90 92 94 1976 78 80 82 84 86 88 90 92 94 0.40 0.36 0.32 South Afrca 0.66 0.64 0.62 0.60 Sngapore 0.28 0.58 0.24 0.56 0.54 0.20 0.52 0.16 0.50 1976 78 80 82 84 86 88 90 92 94 1976 78 80 82 84 86 88 90 92 94 0.00008 Turkey 0.016 Venezuela 0.00007 0.014 0.00006 0.012 0.010 0.00005 0.008 0.00004 0.006 0.00003 0.004 1976 78 80 82 84 86 88 90 92 94 1976 78 80 82 84 86 88 90 92 94 Real dollar exchange rate (1994 CPI = 100 for all countres) Long-term component (based on Hodrck-Prescott flter) Source: See Appendx II. 390

REAL EXCHANGE RATES IN DEVELOPING COUNTRIES goods. Followng Canzoner, Cumby, and Dba (1999), we use restrctons on producton technology to derve a smple form of the relaton, whch makes the labor productvty dfferental between traded and nontraded goods the man determnant of the relatve prce of nontraded goods. The technology restrcton used to obtan the second relaton s not needed to derve the frst relaton. An mportant lmtaton of the use of labor productvty to represent long-term changes n technology s that the long-run value of ths varable can also be affected by permanent shfts n demand. 7 Ths problem may not be too serous f technology shocks are the key source of permanent shocks affectng labor productvty. Tests of the Balassa-Samuelson hypothess are typcally based on a sngle relaton relatng the real exchange rate drectly to the productvty dfferental. Such a relaton can be derved by combnng our two relatons. However, separate estmaton of the two relatons provdes addtonal tests of the Balassa-Samuelson model and s useful n dentfyng the sources of departures from ths model. As the tme seres for ndvdual countres n our sample are not very long, we pool these seres across countres to estmate our relatons. Recent panel-data econometrc technques are used to dentfy long-run effects n these relatons. The results provde strong evdence that the Balassa-Samuelson mechansm operates n developng countres. Usng the Unted States as the reference country, we fnd that U.S. developng country dfferences n the relatve prce of nontraded goods and the terms of trade are sgnfcant determnants of the real exchange rate n the long run. The dfferences n the labor productvty dfferental, moreover, exert a sgnfcant long-run effect on the relatve-prce dfferences. One puzzlng result s that the estmated effect of the relatve-prce varable s greater and that of the labor productvty varables smaller than the predcted value. We suggest explanatons based on data problems to account for these dscrepances between estmated and predcted values. I. Theoretcal Framework Ths secton outlnes a framework to provde theoretcal underpnnngs for our emprcal analyss. As we are concerned wth long-term effects, we do not model short-run dynamcs but focus on steady-state relatons under complete adjustment of wages and prces. We consder a multcountry framework, wth each country usng fxed endowments of labor and captal to produce traded and nontraded goods under perfect competton. 8 We focus on two specal models of the pattern of traded-goods producton. The frst model follows the standard Balassa-Samuelson formulaton and assumes that each country s dversfed and produces all traded goods. The second model assumes that each country s specalzed n the producton of a country-specfc traded good, as n Armngton s (1969) model. We dscuss 7 One way to deal wth ths problem s to use an ndex of total factor productvty nstead of labor productvty. Data constrants for developng countres, however, prevent us from usng ths approach. 8Our framework can be readly extended to ncorporate monopolstc competton. As such an extenson would make lttle dfference to the long-run relatons derved n the paper, we assume perfect competton for smplcty. 391

Ehsan U. Choudhr and Mohsn S. Khan below only the part of the model that s needed to derve the relatons used n our emprcal analyss. Basc Setup Households n country supply a fxed amount of labor and maxmze the followng expected lfetme utlty: E where δ s the dscount factor, and C τ represents a consumpton ndex for perod τ. The consumpton ndex s defned as T C C C where C T and C N are the subndces for consumpton bundles of traded and nontraded goods, γ s the share of traded goods n aggregate consumpton, and tme subscrpts are dropped for smplcty. The traded-goods basket s also assumed to be a Cobb-Douglas ndex of m (> 1) goods: C where C Tj s the amount consumed of traded good j, and θ j represents the share of the good n the basket. Let P denote the consumer prce ndex, and P T and P N the prce ndces for traded and nontraded goods. Usng equatons (1) and (2), we defne P and P T as the cost-mnmzng prces of C and C T,whch are gven by T P P P P T T The pattern of producton for traded goods s characterzed by ether dversfcaton (wth each country producng all traded goods) or specalzaton (wth each country producng a dfferent traded good). In the case of specalzaton, we use the same ndex for a country and ts traded good (.e., good s produced by country ). Lettng Y N and Y Tj denote outputs of the nontraded and jth traded good, we assume the followng Cobb-Douglas producton functon for these goods: 9 N N N N Y A K L t = t δ τ U ( C ) τ γ = ( ) ( ) ( ( ) ) m Tj j = ( C θ ) θ, ( ) = ( ) γ ( ), τ = t θ j j = 1 4 m Tj = ( P ) α = ( ) ( ) j j= 1 2 N N 1 γ γ γ γ γ 1 1 γ 3, ( ). ( ) N βn 1, ( 1), ( 5) 9The Cobb-Douglas form of the producton functon s used below to derve a smple relaton between the relatve prce of nontraded goods and the labor productvty dfferental. Canzoner, Cumby, and Dba (1999) dscuss more general producton condtons, whch would also mply such a relaton. 392

REAL EXCHANGE RATES IN DEVELOPING COUNTRIES Tj Tj Tj αj Tj β j Y A K L, ( 6) = ( ) ( ) where K N and L N represent the amounts of captal and labor used n the producton of the nontraded good, whle K Tj and L Tj are the correspondng amounts for the traded good j. If there s specalzaton, K Tj = L Tj = 0 for j. Let country 1 be the reference country, and defne S as the exchange rate of country (expressed as the prce of country s currency) wth respect to country 1. We dstngush between the short and long run n the present model. The short run s characterzed by nomnal rgdtes n the form of stcky wages and prces. The long run, on the other hand, represents steady-state equlbrum wth full adjustment of wages and prces. In the short run, nomnal rgdtes can cause departures from the law of one prce and the margnal productvty condton for labor. We assume below that there are no departures from these relatons n steady state. We focus on the steady-state behavor of varables to derve Balassa-Samuelson effects. A tlde over a varable s used to denote the steady-state value of the varable. Assumng that the law of one prce holds n steady state, we can lnk steadystate prces of traded goods n dfferent countres as follows: SP Tj P Tj = 1. ( 7) Also, assume that the margnal productvty condton s satsfed n steady state. Thus, lettng W denote the wage rate, and usng equatons (5) and (6), we have N N N W Y L P Y Tj L Tj P Tj β β, (8) = ( ) = ( ) N j where the second equalty n equaton (8) holds only for traded good under specalzaton. Key Relatons We now derve key relatons n the log-lnear form. Usng lowercase letters to denote values n logs, we defne the consumpton-based log real exchange rate as q s + p p 1. ( 9) Next, we use equaton (3) to decompose the log real exchange rate as T N T N T q = q + ( 1 γ) ( p p ) ( 1 γ 1) ( p1 p1 ), ( 10) where q T s + p T p 1 T s the log real exchange rate for traded goods. Usng equaton (4), we can express ths varable as T m j Tj j Tj q = s + p p j θ ( ) θ = 1 1 1. ( 11) 393

Ehsan U. Choudhr and Mohsn S. Khan The traded-goods prce n logs can be lnked to export and mport prce ndces as T X X p p X M = θ + 1 θ p, ( 12) ( ) where p X and p M are the prce ndces for goods for whch country s, respectvely, a net exporter and net mporter, and θ X s the share of the export good n the tradedgoods bundle. 10 Note that n the specalzaton case, p X = p T and θ X =θ. Let rp denote the log relatve prce of nontraded goods to domestcally produced traded goods. In the dversfcaton case, rp = p N p T, snce all traded goods are produced domestcally. Thus, for ths case, equaton (7) and the steadystate versons of equatons (10) and (11) mply the followng long-run relaton for the real exchange rate: ( ) + ( ) ( ) m j j Tj q p rp r = θ θ1 1 1 γ 1 γ p 1. ( 13) j= 1 1 The Balassa-Samuelson analyss s often smplfed by the assumpton that expendture shares are the same everywhere. In ths smple case, θ j =θ j 1 for all j, γ =γ 1, and equaton (13) can be expressed smply as q = (1 γ 1 )(rp rp 1). In the case of specalzaton, rp = p N p T, snce only traded good s produced n country. Usng equaton (12) and recallng that p T = p X, we obtan rp = p N p T (1 θ X )(p X p M ). Then, lettng tt p X p M denote the log terms of trade and usng equaton (7) along wth equatons (10) and (11) for steady state, we derve the followng long-run relaton for the specalzaton case: ( ) + ( ) ( ) m j j Tj q = θ θ p ( γ rp r j ) ( γ ) = 1 1 1 1 1 1 p1 X X + 1 θ ( 1 γ ) tt 1 θ ( 1 γ ) tt. ( 14) 1 1 1 Note that even f a country has the same expendture shares as the reference country, the terms of trade dfferental (tt tt 1) would affect the long-run real exchange rate n addton to the relatve-prce dfferental (rp rp 1). Ths effect arses because, n each country, the terms of trade nfluence the prce of the traded-goods basket relatve to that of the traded good produced at home. The frst term on the rghthand sde of equatons (13) and (14) represents the log real exchange rate for traded goods n steady state, q T. Ths term wll not equal zero and may exhbt nonstatonary behavor f the composton of a country s traded-goods basket dffers from that of the reference country. In the case of heterogeneous expendture shares, q T represents an addtonal channel through whch the terms of trade nfluence the real exchange rate, regardless of whether there s dversfcaton or specalzaton. 11 In our emprcal analyss based on panel data, 10Lettng E and I represent sets of country s export and mport goods, we defne p X θ Tj p Tj / θ X, θ X = θ Tj, j E, and p M k θtk p Tk /(1 θx ), k I j k. 11 Although q T = (θ j θj Tj m j= 1 1 )p 1 n equatons (13) and (14), we can also relate t to the terms of trade by usng equaton (12) to express: q T = s + p M p M1 +θx tt θ X 1 tt 1. j 394

REAL EXCHANGE RATES IN DEVELOPING COUNTRIES however, we do not lnk q T to the terms of trade; nstead, we use tme effects to control for varatons n ths varable. Next, the relatve prce of nontraded goods can be related to the productvty dfferental between domestcally produced traded and nontraded goods. We defne the log labor productvty n the two sectors as T m j lp y Tj l Tj j = 1 ω, ( 15) N N N lp y l, ( 16) where ω j s the weght for good j s labor productvty n the aggregate labor productvty ndex for traded goods. In the specalzaton case, ω j equals one for j = and zero otherwse. Let lp lp T lp N denote the labor productvty dfferental between traded and nontraded goods. In defnng the dversfcaton labor productvty ndex n steady state, we use the same weghts as those n the prce ndex for traded goods. Thus, let ω j =θ j under dversfcaton; and ω = 1 for j = and ω j = 0 for j under specalzaton. Usng equaton (8) and steady-state versons of equatons (4), (15), and (16), we can express the steady-state relatve prce as rp = ϑ + lp, ( 17) ( ) j where ϑ equals θ logβ β j j log = 1 logβ N n the case of specalzaton. m N n the case of dversfcaton and logβ II. Emprcal Implementaton Data We use a number of sources to put together a developng economes panel-data set that ncludes tme seres from 1976 to 1994 for 16 countres. 12 Traded goods are assumed to consst of manufacturng and agrculture sectors. Nontraded goods represent all other sectors. The Unted States s chosen as the reference country. The real exchange rate s based on consumer prce ndces and represents the real value of a currency n terms of U.S. dollars. Although our classfcaton of the traded- and nontraded-goods sectors s smlar to the one used for ndustral countres, one potental problem s that a substantal porton of the agrculture sector (and possbly of the manufacturng sector) n developng countres may consst of tradtonal actvtes producng nontraded goods. Another problem s that the qualty of labor s lkely to vary consderably across sectors n developng countres, and our labor productvty measure (based on employment fgures unadjusted for qualty changes) does not account for ths 12 Detals of the varables and data sources are provded n Appendx II. 395

Ehsan U. Choudhr and Mohsn S. Khan varaton. 13 We are unable to address these ssues because of data lmtatons. However, we explore below certan mplcatons of these measurement problems for the estmaton of the emprcal model. Emprcal Model To undertake panel-data tests of the Balassa-Samuelson relatons, we assume that long-run parameters are the same across our developng country set (D). 14 Thus, we set θ X =θ X and γ =γfor D. However, to allow for possble dfferences n expendture shares between developng and ndustral countres, we do not requre U.S. (country 1) parameters to be the same as those for our developng country sample. The followng two equatons are estmated to test for Balassa-Samuelson effects: q = µ + κ + πrpd + τ ttd + u, ( 18) t t t t t rpd = ψ + χ + λ lpd + v, D, ( 19) t t t t where rpd t = rp t rp 1t, ttd t = tt t tt 1t, and lpd t = lp t lp 1t are, respectvely, the log dfferences n the relatve prce of nontraded goods, the terms of trade, and the traded-nontraded productvty rato between developng country and the Unted States; µ and ψ are country-specfc fxed effects whle κ t and χ t are common tme effects; and u t and v t are error terms. Tme effects represent the nfluence of common tme-specfc (short- and long-run) factors, and error terms capture the effects of short-term devatons from steady state (that are not ncluded n tme effects). Equaton (18) s derved from equatons (13) and (14). Under our assumpton that θ j =θ j for D, tme effects n equaton (18) would control for movements n q T m t (= (θ j θ j 1 )p ) arsng from parametrc dfferences between developng j= 1 1Tj countres and the Unted States. In the presence of tme effects, equaton (18) nests the dversfcaton and specalzaton cases wth τ =0 under dversfcaton and τ =(1 θ X )(1 γ) > 0 under specalzaton. 15 In both cases, π=(1 γ) > 0. 13 If ntersector labor qualty dfferences are not taken nto account, the margnal productvty condton equaton (8) would not be satsfed and there would be departures from the relatve prce equaton (19) based on ths condton. Another lmtaton of the data on labor nputs s that employment measures for the manufacturng, agrculture, and other (nontraded-goods) sectors come from dfferent sources, and are not fully comparable. Also, note that labor productvty for traded goods s smply measured as the rato of total output to total employment n the traded-goods sector. For the dversfcaton case, ths ndex does not fully conform to the theoretcal ndex used n equaton (17), snce the mplct weghts for ndvdual traded goods n ths ndex could dffer from the weghts used n the traded-goods prce ndex. 14We later allow these parameters to vary between developng countres at dfferent ncome levels. Tt 15In the estmaton of equaton (18), f tme effects do not fully capture changes n q because of dfferences n expendture shares across countres, τ could also pck up the effect of the terms of trade va q Tt and could be postve even n the absence of specalzaton. 396

REAL EXCHANGE RATES IN DEVELOPING COUNTRIES Equaton (19) s based on equaton (17). In ths equaton, λ=1. The absence of Balassa-Samuelson effects would mply that π =τ=λ=0. 16 Although the long-run parameters n equatons (18) and (19) π, τ, and λ are constraned to be the same across developng countres, these relatons allow the short-run dynamcs (reflected n the tme-seres behavor of the error terms) to be dfferent across countres. The explanatory varables rpd t, ttd t, and lpd t can be statonary, trend-statonary, or nonstatonary. In the case of trend-statonary behavor, equatons (18) and (19) can be modfed to nclude a tme trend. Coeffcents of tme trends n the two relatons would be homogeneous across countres and depend on the long-run parameters. 17 Note that f the explanatory varables are ntegrated or trend-statonary, then q t would also be ntegrated or trend-statonary. In ths case, Balassa-Samuelson effects would cause permanent departures from the purchasng power party. As dscussed above, our measure for the traded-goods sector (.e., agrculture plus manufacturng) may be too broad for developng countres and could nclude nontraded goods. As dscussed n Appendx I, the measured relatve prce of nontraded goods n ths case would understate the true relatve prce and bas the relatve-prce coeffcent upward n equaton (18). Ths measurement problem would not lead to a systematc bas n the estmaton of equaton (19), snce the measured value of the traded-nontraded productvty dfferental would also understate ts true value. A more serous problem for estmatng equaton (19) s that the labor productvty measure s not adjusted for qualty varaton. Appendx I also shows that the estmated effect of the measured labor productvty dfferental would be based downward f there s a postve assocaton between the average labor qualty and the true labor productvty. III. Results Estmaton Before estmatng equatons (18) and (19), we examne whether the varables n these relatons contan a unt root or not. Table 1 shows the results of two tests of a unt root n panel data. In the frst test (LL), based on Levn and Ln (1993), the null hypothess of a unt root s tested aganst the alternatve of a homogeneous autoregressve coeffcent. The second test (IPS), based on Im, Pesaran, and Shn (2003), tests the unt root null aganst a more general alternatve of a heterogeneous autoregressve coeffcent. Both tests ndcate that q t contans a unt root (wth or 16 Tests of Balassa-Samuelson effects could also be based on alternatve versons of equatons (18) and (19) that exclude U.S. varables rp 1t, tt 1t, and lp 1t and are expressed as q t = µ * +κ * t +πrp t +τtt t + u * t, and rp t =ψ * +χ * t +λlp t + v * t. However, we estmate relatons n the form that ncludes U.S. varables because ths form allows us to explore whether U.S. varables exert an effect addtonal to ther effect va rpd t, ttd t,and lpd t. 17Lettng rpd t = g 1 t + rpd t, ttd t = g 2 t + ttd t, and lpd t = g 3 t + lpd t, we can restate equatons (18) and (19) as follows: q t = µ +κ t + (g 1 π+g 2 τ)t +πrpd t +τttd t + u t, and rpd t =ψ +χ t + g 3 λt +λlpd t + v t. 397

Ehsan U. Choudhr and Mohsn S. Khan Table 1. Unt Root Tests Levn-Ln Test Statstc Im-Pesaran-Shn Test Statstc Varable Wthout trend Wth trend Wthout trend Wth trend q t 0.478 1.008 1.513 1.480 rpd t 0.231 3.730** 0.358 6.615** ttd t 0.070 1.327 0.388 1.987* lpd t 0.604 3.297** 2.059* 6.169** Notes: q t s country s dollar real exchange rate n logs, whle rpd t, ttd t, and lpd t represent, respectvely, log dfferences n the relatve prce of nontraded goods, the terms of trade, and the traded-nontraded labor productvty rato between country and the Unted States. * ndcates sgnfcance at the 5 percent level, and ** at the 1 percent level. wthout a tme trend). 18 For the remanng varables, the tests are senstve to whether a tme trend s ncluded or not. In the absence of a trend, the unt root hypothess s not rejected for rpd t and ttd t by both the LL and IPS tests, and for lpd t by the LL test. However, f a trend s present, both tests ndcate that rpd t and lpd t are not ntegrated, and the IPS test ndcates that ttd t s also not ntegrated. We frst consder the basc form of equatons (18) and (19), whch does not nclude a tme trend. In ths case, snce there s ndcaton of nonstatonary behavor for varables n these relatons, we also undertake tests for co-ntegraton. We use two parametrc tests, the panel t-test and the group t-test, suggested by Pedron (1999). The panel t-test rejects the hypothess that there s no co-ntegraton for the vector (q t, rpd t ), but does not reject ths hypothess for vectors (rpd t, lpd t ) and (q t, rpd t, ttd t ). The group t-test rejects the no-co-ntegraton hypothess for all three vectors. 19 The group t-test (unlke the panel t-test) does not constran the frst-order correlaton n the resduals to be homogeneous under the alternatve hypothess and s more relevant for our model, whch allows the short-run dynamcs to vary across countres. The test s falure to reject the hypothess of no co-ntegraton for the above vectors supports the Balassa-Samuelson model s mplcaton that a long-run relaton exsts between the real exchange rate and relatve prces (and possbly the terms of trade) as well as between relatve prces and productvty ratos. We next estmate Balassa-Samuelson effects n these relatons. We estmate equatons (17) and (18) by Dynamc Ordnary Least Squares (DOLS), whch s an approprate framework for estmatng and testng hypotheses for homogeneous co-ntegratng vectors. 20 The relatons are estmated n the followng form: 18Because of the assumpton of homogeneous autoregressve coeffcents, the LL test s encompassed by the IPS test. The results of the IPS test, however, are not conclusve. Although the test does not reject the unt-root hypothess for q t at the 5 percent level, t does ndcate rejecton at slghtly hgher levels (p-value = 0.069 wth trend and p-value = 0.065 wthout trend). 19For vectors (q t, rpd t ), (rpd t, lpd t ), and (q t, rpd t, ttd t ), the panel-t test statstc s 1.730*, 1.093, and 0.278, respectvely. The correspondng statstc for the group-t test s 2.074*, 1.955*, and 1.959.* An astersk ndcates sgnfcance at the 5 percent level. 20See Kao and Chang (2000), and Mark and Sul (2002) for a dscusson of the propertes of panel DOLS. 398

REAL EXCHANGE RATES IN DEVELOPING COUNTRIES n qt = µ + κt + πrpdt + τttdt + ( ξr rpd,t + r + ζr ttd ) +,t r u r= n + t, ( 20) n t t t r = n r,t + r t rpd = ψ + χ + λlpd + ϕ lpd + v, ( 21) where n s the number of lags and leads used for the frst-dfference terms. Coeffcents of these terms capture the short-run dynamcs. We allow the short-run dynamcs to be heterogeneous (.e., let ξ r, ζ r, and ϕ r dffer across ). We test the null hypotheses that π =τ=0 n equaton (20) and λ =0 n equaton (21) aganst the alternatve hypotheses that these varables are postve. If a lnear trend s ncluded, unt root tests suggest that the explanatory varables n equatons (18) and (19) are not ntegrated. We, thus, also consder the trend-statonary settng for estmatng these relatons. DOLS s a useful estmatng procedure even n ths case. Snce frst-dfference terms are ncluded n ths procedure, the coeffcents of level terms represent long-run effects. Therefore, we estmate equatons (20) and (21) wth trend varables to dentfy long-run Balassa- Samuelson nfluences n the trend-statonary case. Basc Results Tables 2 and 3 present DOLS estmates of dfferent varants of the real exchange rate equaton wth one lag and one lead of the frst-dfference terms. 21 Table 2 shows the estmates of the equaton for the dversfcaton case excludng the terms of trade varable, and Table 3 for the specalzaton case ncludng ths varable. For both cases, we report the results for homogeneous as well as heterogeneous short-run dynamcs. Regressons 1 and 4 n these tables show estmates of the basc form of the equaton wthout a tme trend. In all of these cases, the effect of the relatve-prce varable s postve and sgnfcant. The predcted value of ths varable s coeffcent equals 1 γ(whch represents the share of the nontradedgoods sector). The estmated value, however, s greater than unty n most cases. The small sze of our sample (based on only 19 years of data for each country) s a concern; t could be a source of bas n DOLS estmates. As dscussed above, however, the dscrepancy between the predcted and estmated values could reflect an upward bas arsng from defnng the traded-goods sector too broadly. 22 The results also show that the terms of trade varable exerts a postve and sgnfcant 21 The short length of each tme seres makes t dffcult to explore the possblty that the short-run dynamcs nvolve hgher lags and leads. Indeed, there are not enough degrees of freedom to estmate equaton (20) wth addtonal lags and leads n the case of heterogeneous dynamcs. In the case of homogeneous dynamcs, however, we dd estmate equatons (20) and (21) wth two lags and leads, and found lttle dfference n the results. 22 The magntude of the bas depends on the extent to whch the share of the traded-goods sector s overestmated. For our sample, the average share of manufacturng and agrculture n GDP s 35 percent. It s nterestng to note that the true share of traded goods does not have to be much below ths value to mply that the estmated coeffcent of the relatve prce varable s greater than unty. For example, f about 30 percent of manufacturng plus agrculture sectors n fact consst of nontraded goods, so that the actual share of traded goods s 22.5 percent, then (as shown n Appendx I) the estmated coeffcent of rpd t would equal 1.12 (after settng φ =0.3 and π =0.775). 399

Table 2. The Exchange Rate Relaton Wthout the Terms of Trade Coeffcent Estmates Varable (1) (2) (3) (4) (5) (6) Homogeneous short-run dynamcs Heterogeneous short-run dynamcs rpd t 0.962** 0.962** 0.790** 1.066** 1.066** 0.846** (0.146) (0.146) (0.161) (0.156) (0.156) (0.173) Trend 0.057 0.071 (0.055) (0.060) rpd t *D 0.329* 0.401* (0.129) (0.156) Adjusted R 2 0.997 0.997 0.997 0.997 0.997 0.997 Standard error 0.154 0.154 0.152 0.160 0.160 0.158 of regresson Notes: The dependent varable s q t (see notes to Table 1 for the defntons of varables). All regressons nclude country-specfc and tme-specfc dummy varables as well as frst dfferences of each explanatory varable at tme t, t 1, and t + 1. Coeffcents of the frst-dfference terms are constraned to be the same across countres under homogeneous dynamcs, and unconstraned under heterogeneous dynamcs. Whte heteroskedastcty-consstent errors are shown n parentheses. D s a dummy varable, whch equals one for low-ncome developng countres and zero for others. The number of observatons equals 256. * ndcates sgnfcance at the 5 percent level, and ** at the 1 percent level (usng a one-sded test for rpd t and a two-sded test for other varables). Table 3. The Exchange Rate Relaton wth the Terms of Trade Coeffcent Estmates Varable (1) (2) (3) (4) (5) (6) Homogeneous short-run dynamcs Heterogeneous short-run dynamcs rpd t 1.111** 1.111** 0.851** 1.217** 1.217** 0.834** (0.143) (0.143) (0.163) (0.204) (0.204) (0.251) ttd t 0.300** 0.300** 0.477** 0.332** 0.332** 0.565** (0.091) (0.091) (0.103) (0.129) (0.129) (0.141) Trend 0.063 0.111 (0.054) (0.075) rpd t *D 0.407** 0.601* (0.143) (0.271) ttd t *D 0.348** 0.407 (0.123) (0.209) Adjusted R 2 0.997 0.997 0.998 0.997 0.997 0.997 Standard error 0.142 0.142 0.139 0.152 0.152 0.148 of regresson Notes: The dependent varable s q t (see notes to Table 1 for the defntons of varables). All regressons nclude country-specfc and tme-specfc dummy varables as well as frst dfferences of each explanatory varable at tme t, t 1, and t + 1. Coeffcents of the frst-dfference terms are constraned to be the same across countres under homogeneous dynamcs, and unconstraned under heterogeneous dynamcs. Whte heteroskedastcty-consstent errors are shown n parentheses. D s a dummy varable, whch equals one for low-ncome developng countres and zero for others. The number of observatons equals 246. * ndcates sgnfcance at the 5 percent level, and ** at the 1 percent level (usng a one-sded test for lpd t and ttd t, and a two-sded test for other varables). 400

REAL EXCHANGE RATES IN DEVELOPING COUNTRIES effect when ntroduced n the real exchange rate equaton (see Table 3). Ths fndng s consstent wth the specalzaton verson of the model, n whch each country produces a dfferent good. Table 4 shows the results for estmatng the relatve-prce relaton by DOLS. Regressons 1 and 4 n ths table estmate the basc form of the relaton wthout a tme trend. The effect of the labor productvty ndex n both regressons s postve and sgnfcant. But the estmated values of ts coeffcents n the two regressons are substantally below the predcted value of unty. One possble explanaton of ths result, suggested above, s that measurng employment wthout adjustment for qualty changes leads to a downward bas n the productvty coeffcent. 23 Other lmtatons of employment data and the small sample sze could also have contrbuted to a bas n the estmates of the productvty coeffcent. Tables 2 4 also report the results for the trend-statonary case, n whch a homogeneous lnear trend (wth the same coeffcent across countres) s ncluded n the two relatons. The tables show (see regressons 2 and 4 n each table) that the coeffcent of the trend varable s nsgnfcant n all cases, and the ntroducton of ths varable n the regressons makes no dfference to the estmates of Balassa- Samuelson parameters. We also ntroduced heterogeneous trends n the two relatons, but ths varaton made lttle dfference to the results. Further Analyss Our emprcal model ncludes tme effects to allow the effect of U.S. varables to be dfferent from that of developng countres varables because of parametrc dfferences. Tme effects are, n fact, sgnfcant n both relatons. Nevertheless, we also estmated the two relatons wthout tme effects but dd not fnd a substantal dfference n results. We further examned whether the results are senstve to varaton n ncome levels across countres. To explore ths queston, we dvded the developng country sample nto hgh- and low-ncome groups, and tested whether coeffcents of Balassa-Samuelson varables dffer between the two groups. 24 Regressons 3 and 6 n Tables 2 4 show the results of these tests. These regressons nclude nteractons between explanatory varables and a dummy varable for the low-ncome group. Thus, coeffcents of the varables show the effects for the hghncome group, and nteracton terms represent the addtonal effects for the lowncome group. Interestngly, the results show that the effect of the relatve-prce varable (n the real exchange rate regressons) s sgnfcantly hgher for the lowncome group, whle the effect of the labor productvty dfferental (n the relatveprce regressons) s sgnfcantly lower. The departures from predcted values are, 23 The downward bas arses because unobserved labor qualty s assumed to be postvely related to true labor productvty. It s not clear, however, how much bas would be produced by ths relaton. Accordng to Appendx I, the magntude of the bas would depend on the elastcty of labor qualty wth respect to true labor productvty (ρ). Ths elastcty would need to be 2.3 to generate, for example, an estmate of the productvty coeffcent equal to 0.3. 24 The classfcaton of countres n the two groups s based on average ncome per capta for the sample perod. Each group ncludes eght countres (see Appendx II for the lsts of countres). 401

Ehsan U. Choudhr and Mohsn S. Khan Table 4. The Relatve-Prce Relaton Coeffcent Estmates Varable (1) (2) (3) (4) (5) (6) Homogeneous short-run dynamcs Heterogeneous short-run dynamcs lpd t 0.287** 0.287** 0.345** 0.302** 0.302** 0.397** (0.042) (0.042) (0.051) (0.048) (0.480) (0.062) Trend 0.000 0.004 (0.028) (0.028) lpd t *D 0.152* 0.229** (0.076) (0.086) Adjusted R 2 0.833 0.833 0.835 0.832 0.832 0.838 Standard error 0.073 0.073 0.072 0.073 0.073 0.072 of regresson Notes: The dependent varable s rpd t (see notes to Table 1 for the defntons of varables). All regressons nclude country-specfc and tme-specfc dummy varables as well as frst dfferences of each explanatory varable at tme t, t 1, and t + 1. Coeffcents of the frst-dfference terms are constraned to be the same across countres under homogeneous dynamcs, and unconstraned under heterogeneous dynamcs. Whte heteroskedastcty-consstent errors are shown n parentheses. D s a dummy varable, whch equals one for low-ncome developng countres and zero for others. The number of observatons equals 256. * ndcates sgnfcance at the 5 percent level, and ** at the 1 percent level (usng a one-sded test for lpd t and a two-sded test for other varables). thus, more pronounced for low-ncome countres. Snce data problems are lkely to be more severe for the developng countres at the lower end of the ncome scale, ths fndng supports our suggested explanaton that the estmates of Balassa- Samuelson effects are based because of measurement errors. The results also ndcate that the terms of trade effect s smaller for the low-ncome group. 25 The conventonal tests of Balassa-Samuelson effects are based on a sngle relaton that lnks the real exchange rate drectly to the labor productvty ndex. To derve such a relaton, we combne equatons (18) and (19) to obtan q = µ + κ + πλlpd + τ ttd + u, ( 22) t t t t t where µ = µ +πψ, κ t =κ t +πχ t, and u t = u t +πv t. For the purpose of comparson wth the exstng lterature, we also present results for the sngle-equaton verson of our two relatons. Table 5 reports DOLS estmates of sx varants of equaton (22), whch are smlar to those shown n Tables 2 4. Note that the estmates of the coeffcents of the labor productvty and terms of trade varables n the DOLS verson of equaton (22) need not fully conform to the estmates of these 25 Thus, the support for the specalzaton verson seems to be weaker for the poorer developng countres. Ths result may seem paradoxcal, as producton and exports of low-ncome countres tend to be less dversfed. However, specalzaton could also mean producton of goods (e.g., sophstcated manufactured products) that are sgnfcantly dfferentated from goods produced elsewhere. Poor countres may be less specalzed n ths sense. 402

REAL EXCHANGE RATES IN DEVELOPING COUNTRIES Table 5. The Combned Exchange Rate Relaton Coeffcent Estmates Varable (1) (2) (3) (4) (5) (6) Homogeneous short-run dynamcs Heterogeneous short-run dynamcs lpd t 0.177* 0.177* 0.205** 0.212* 0.212* 0.302** (0.080) (0.080) (0.087) (0.109) (0.109) (0.124) ttd t 0.357** 0.357** 0.388** 0.432** 0.432** 0.203 (0.089) (0.089) (0.102) (0.135) (0.135) (0.184) Trend 0.007 0.014 (0.047) (0.078) lpd t *D 0.080 0.157 (0.169) (0.271) ttd t *D 0.085 0.347 (0.120) (0.224) Adjusted R 2 0.997 0.997 0.997 0.997 0.997 0.997 Standard error 0.154 0.154 0.155 0.155 0.155 0.154 of regresson Notes: The dependent varable s q t (see notes to Table 1 for the defntons of varables). All regressons nclude country-specfc and tme-specfc dummy varables as well as frst dfferences of each explanatory varable at tme t, t 1, and t + 1. Coeffcents of the frst-dfference terms are constraned to be the same across countres under homogeneous dynamcs, and unconstraned under heterogeneous dynamcs. Whte heteroskedastcty-consstent errors are shown n parentheses. D s a dummy varable, whch equals one for low-ncome developng countres and zero for others. The number of observatons equals 246. * ndcates sgnfcance at the 5 percent level, and ** at the 1 percent level (usng a one-sded test for lpd t and ttd t, and a two-sded test for other varables). varables n equatons (20) and (21) because of the use of dfferent varables to control for short-run dynamcs. 26 The results ndcate that the labor productvty coeffcent n the sngle-equaton verson s sgnfcant n all cases, but ts value tends to be smaller than the product of the estmates of π and λ (obtaned from regressons of equatons (20) and (21)). The terms of trade coeffcent also dffers somewhat from the estmate of τ based on equaton (20) and s sgnfcant n all cases except regresson (6) n the table. The effect of the two varables s no longer sgnfcantly dfferent between the hgh- and low-ncome groups. For the labor productvty varable, ths result (that ts coeffcent, πλ, does not dffer between the two ncome groups) s consstent wth the earler fndngs that π s hgher and λ s lower for the low-ncome group. Durng our sample perod, currency crses nvolvng large exchange rate deprecatons occurred n a number of countres. Adverse economc condtons durng crss tmes could have caused comovements n exchange rates, labor productvty, and relatve prces. Ths paper uses an estmaton procedure that attempts to dsentangle long-run Balassa-Samuelson effects from short-run correlatons produced 26 The DOLS verson of equaton (22) ncludes frst dfferences of ttd t (whch do not appear n equaton (21)) but does not nclude those of rpd t (whch enter equaton (20)). 403

Ehsan U. Choudhr and Mohsn S. Khan by temporary shocks (such as those leadng to currency crses). However, to address the concern that our method may not have adequately removed the nfluence of crss shocks, we explore the senstvty of our results to ncluson of crss perods. To dentfy crss perods, we follow Kamnsky, Renhart, and Vegh (2004), who defne a crss year as a year n whch there s a 25 percent or hgher monthly deprecaton that s at least 10 percent hgher than the prevous month s deprecaton. 27 Usng ther crss data, we reestmate our basc regressons, excludng the observatons for crss years. 28 Note that snce our regressons nclude one lag and one lead of each explanatory varable s frst dfferences (whch are not avalable for the year of the crss and the followng year), the excluson wndow for these regressons s generally four years for a sngle crss. 29 Longer perods are excluded for countres wth multple crses. In fact, for three countres Ecuador, Turkey, and Venezuela there were not enough observatons to estmate country-specfc dynamcs. These countres were, thus, excluded from regressons wth heterogeneous dynamcs. Table 6 presents the results of basc regressons based on data for crss-free perods for both the two- and one-equaton versons of the model (see columns 1 2 and 4 5 of the table for the two-equaton verson and columns 3 and 6 for the oneequaton verson). As the table shows, the effect of the basc Balassa-Samuelson varables the relatve-prce and labor productvty ndces remans robust even after excludng crss perods. The effect of the labor productvty varable, n fact, becomes stronger. The terms of trade effect, however, becomes weaker and s nsgnfcant n most cases. Thus, the results on the nfluence of the terms of trade on the real exchange rate are senstve to whether crss perods are ncluded or not. Although our regressons generally exclude four years for a crss, ths perod may not be consdered long enough to fully remove the effect of a crss shock. 30 To deal wth ths concern, we explored addtonal varatons that ntroduced longer excluson wndows or excluded all the data for countres that faced multple crses wthn the sample perod. 31 These varatons further reduced the sample sze but stll dd 27 See Frankel and Rose (1996) for a dscusson of the usefulness of ths measure of crss for emergng economes. For ndustral countres, Echengreen, Rose, and Wyplosz (1996) use an alternatve measure based on a weghted average of changes n the exchange rate, nternatonal reserves, and nterest rates. Ths measure s desgned to develop a crss ndex that would nclude unsuccessful speculatve attacks (whch do not change the exchange rate but lead to a loss of nternatonal reserves and/or a rse n the nterest rate). We need, however, to dentfy only successful attacks that could cause co-movements between the exchange rate and other varables and potentally bas our results. Thus, nternatonal reserves and nterest rates may not be useful ndcators for our purposes. For developng countres, moreover, nterest rate data are generally lackng and nternatonal reserve changes are often an nadequate measure of exchange market nterventon. 28 See Appendx II for a lst of crss years for our sample. 29 For example, f the crss year s 1982, the perod from 1981 to 1984 s excluded from the regresson. A shorter perod would need to be excluded f the crss occurs n the frst or last two years of the sample. 30 Estmates of half-lfe for shocks to the real exchange rate, for example, typcally range from three to fve years. 31 In the frst varaton, we also dropped the observatons for one year before and one year after the crss year, whch generally extended the regresson excluson wndow for a crss to sx years. Four countres Mexco, Ecuador, Turkey, and Venezuela experenced multple crses. These countres were excluded from the sample n the second varaton. 404

REAL EXCHANGE RATES IN DEVELOPING COUNTRIES Table 6. Basc Regressons, Excludng Crss Years Coeffcent Estmates Varable (1) (2) (3) (4) (5) (6) Homogeneous short-run dynamcs Heterogeneous short-run dynamcs lpd t 0.342** 0.247** 0.337** 0.240* (0.042) (0.093)* (0.044) (0.123) ttd t 0.152 0.222* 0.130 0.161 (0.098) (0.105) (0.196) (0.141) rpd t 1.153** 1.099** (0.135) (0.192) Adj. R 2 0.861 0.998 0.997 0.877 0.997 0.997 Standard error 0.069 0.132 0.150 0.065 0.144 0.140 of regresson No. Obs. 215 205 205 215 190 190 Notes: The dependent varable s rpd t for regressons n columns (1) and (4), and q t for other regressons (see notes to Table 1 for the defntons of varables). All regressons nclude countryspecfc and tme-specfc dummy varables as well as frst dfferences of each explanatory varable at tme t, t 1, and t + 1. Coeffcents of the frst-dfference terms are constraned to be the same across countres under homogeneous dynamcs, and unconstraned under heterogeneous dynamcs. Whte heteroskedastcty-consstent errors are shown n parentheses. * ndcates sgnfcance at the 5 percent level, and ** at the 1 percent level (usng a one-sded test). not much affect our results about the robustness of the effect of the labor productvty and relatve-prce varables. IV. Conclusons The Balassa-Samuelson hypothess would seem to be especally relevant for developng countres where relatve prces and productvtes are lkely to be more varable. Yet, there s lttle or no emprcal evdence on whether Balassa-Samuelson effects can successfully explan long-run movements of the real exchange rate n developng countres. Ths paper presents new tme-seres evdence for developng countres on the presence of Balassa-Samuelson effects. To test for these effects, we estmate two long-run relatons: relatve prces (of nontraded goods) affect the real exchange rate n one relaton, and labor productvty dfferentals (between traded and nontraded goods) affect relatve prces n the second relaton. Terms of trade also affect the real exchange rate (n the frst relaton) under certan condtons. A key fndng of ths paper s that the labor productvty dfferental exerts a sgnfcant effect on the real exchange rate va ts nfluence on the relatve prce of nontraded goods. 32 The paper also fnds that terms of trade are a sgnfcant determnant 32Prevous work (for example, Lane and Mles-Ferrett, 2004), usng GDP per capta as a proxy for the labor productvty dfferental, has not found a systematc effect of the productvty varable on real exchange rates n developng countres. We beleve that we are able to dentfy ths effect by usng a more approprate measure of labor productvty dfferental based on sectoral data. 405

Ehsan U. Choudhr and Mohsn S. Khan of the real exchange rate. Ths fndng, however, s senstve to whether the sample ncludes crss perods or not. Although the effect of relatve-prce and labor productvty varables operates n the drecton ndcated by the Balassa-Samuelson hypothess, the effect of relatve prces s stronger and that of productvty dfferentals weaker than the predcted value. The paper also fnds that the departures from predcted values are larger for developng countres wth lower ncome levels. We suggest an explanaton that attrbutes these results to bases caused by measurement problems. These problems are lkely to be more pronounced n countres wth lower ncomes and, thus, could account for dfferences n estmated Balassa-Samuelson effects between countres at low and hgh ncome levels. Our tests of the Balassa-Samuelson explanaton are based on two long-run relatons, whch are derved from theory under farly general condtons and can be mplemented emprcally for developng countres. One mportant caveat for our formulaton s that labor productvty s used to capture the effect of permanent technology shocks emphaszed by the Balassa-Samuelson theory. Ths measure could also pck up the nfluence of permanent demand shocks. Dsentanglng the nfluence of permanent demand and technology shocks on long-run labor productvty would be an nterestng topc for future research. Further theoretcal and emprcal analyss could also extend the framework consdered here and explore the role of addtonal factors. 33 Such analyss s beyond the scope of ths paper. The results of ths paper do suggest that the Balassa-Samuelson mechansm s an emprcally useful framework for nvestgatng the long-run behavor of the real exchange rate for developng countres. APPENDIX I Potental Bases Due to Measurement Problems Traded-Goods Sector Measure Includes Nontraded Goods Usng a hat over a varable to denote the measured value, let the measured traded-goods prce be pˆ Tt =φp N t + (1 φ)p T t, 1 > φ > 0, where φ s the weght for the nontraded goods that are mproperly ncluded n the traded-goods sector measure. The measured relatve prce of nontraded goods s then related to the true prce as rpˆ t = p N t pˆ Tt = (1 φ)rp t. Let the correspondng relaton for country 1 be rpˆ 1t = (1 φ 1 )rp 1t,wth 1 > φ 1 0. Usng these relatons and lettng rpˆd t = rpˆ t rpˆ 1t, we can express equaton (18) n the text as q = µ + κ + π rpd ˆ + τttd + u, t t t t t where κ t =κ t +π[1/(1 φ) 1/(1 φ 1 )]rpˆ 1t and π =π/(1 φ). Thus, f rpˆd t s used nstead of rpd t n equaton (18), ts coeffcent would be based upward. Note that ths problem need not ntroduce a systematc bas n equaton (19). For example, f we also have lpˆ Tt =φlp N t + (1 φ)lp T t, then lpˆ t = lpˆ Tt lp N t = (1 φ)lp t. Usng ths relaton 33For example, Lane and Mles-Ferrett (2004) explore the theoretcal lnk between the real exchange rate and net foregn assets, and provde evdence that the net foregn assets poston s an mportant determnant of the real exchange rate for developng (as well as developed) countres. 406