Asian Development Bank Institute. ADBI Working Paper Series GLOBAL VALUE CHAINS AND EFFECTIVE EXCHANGE RATES AT THE COUNTRY-SECTOR LEVEL

ADBI Working Paper Series GLOBAL VALUE CHAINS AND EFFECTIVE EXCHANGE RATES AT THE COUNTRY-SECTOR LEVEL Nikhil Patel, Zhi Wang, and Shang-Jin Wei No. 799 Deember 2017 Asian Development Bank Institute

Nikhil Patel is at Bank for International Settelements; Zhi Wang is at United States International Trade Commission; and Shang-Jin Wei is at Columbia University, NEBR, CEPR, and CIER. The views expressed in this paper are the views of the author and do not neessarily reflet the views or poliies of ADBI, ADB, its Board of Diretors, or the governments they represent. ADBI does not guarantee the auray of the data inluded in this paper and aepts no responsibility for any onsequenes of their use. Terminology used may not neessarily be onsistent with ADB offiial terms. Working papers are subjet to formal revision and orretion before they are finalized and onsidered published. The Working Paper series is a ontinuation of the formerly named Disussion Paper series; the numbering of the papers ontinued without interruption or hange. ADBI s working papers reflet initial ideas on a topi and are posted online for disussion. Some working papers may develop into other forms of publiation. The Asian Development Bank reognizes China as the People s Republi of China. Suggested itation: Patel, N., Z. Wang, and S.-J. Wei. 2017. Global Value Chains and Effetive Exhange Rates at the Country-Setor Level. ADBI Working Paper 799. Tokyo: Asian Development Bank Institute. Available: https://www.adb.org/publiations/global-value-hains-and-effetiveexhange-rates Please ontat the authors for information about this paper. Email: nikhil.patel@bis.org, Zhi.Wang@usit.gov, sw2446@gsb.olumbia.edu Asian Development Bank Institute Kasumigaseki Building, 8th Floor 3-2-5 Kasumigaseki, Chiyoda-ku Tokyo 100-6008, Japan Tel: +81-3-3593-5500 Fax: +81-3-3593-5571 URL: www.adbi.org E-mail: info@adbi.org 2017 Nikhil Patel, Zhi Wang, and Shang-Jin Wei

Global Value Chains and Effetive Exhange Rates at the Country-Setor Level Nikhil Patel Zhi Wang Shang-Jin Wei August 10, 2017 Abstrat The real effetive exhange rate (REER) is one of the most ited statistial onstruts in open-eonomy maroeonomis. We show that the models used to ompute these numbers are not rih enough to allow for the rising importane of global value hains. Moreover, beause different setors within a ountry partiipate in international prodution sharing in different ways, setor level variations are also important for determining ompetitiveness. Inorporating these features, we develop a framework to ompute REER at the setor, ountry, and bilateral level and apply it on inter-ountry input-output tables to study the properties of the new measures of REER for 35 setors in 40 ountries. JEL No. F1,F3,F4, F6 We are grateful to Pol Antras, Charles Engel, Enisse Kharroubi, Giovanni Lombardo, Stephanie Shmitt- Grohe, Hyun Song Shin, Christian Upper and Martin Uribe and our disussants Martin Berka, Beata Javorik and Giorgio Valente for helpful omments and disussions. We would also like to thank seminar partiipants at the Asian Development Bank, the ABFER annual onferene, the Bank for International Settlements, Columbia University, the Czeh National Bank and the University of International Business and Eonomis for useful omments and Joy Glazener for editorial assistane. All remaining errors are our own. The views expressed here are those of the authors and do not neessarily orrespond to those of the institutions they are affiliated with. Bank for International Settlements. E-mail: nikhil.patel@bis.org. United States International Trade Commission. E-mail: Zhi.Wang@usit.gov. Columbia University, NBER, CEPR, and CIER. E-mail: sw2446@gsb.olumbia.edu.

1 Introdution The Real Effetive Exhange Rate (REER) is one of the the most quoted indies in international eonomis. It measures ompetitiveness by quantifying the sensitivity of demand for output originating from a partiular ountry as a funtion of hanges in world pries. 1 Leading organizations like the International Monetary Fund (IMF), Bank of International Settlements (BIS), OECD as well as various entral banks around the world devote substantial time, effort and resoures into omputing and analyzing these REER indies. However, most of these standard REER measures make a number of simplifying assumptions whih are inreasingly beoming questionable in a world haraterized by global value hains. For instane, they assume that every ountry exports only final goods whih are produed without using imported intermediate goods, and work with single setor models, impliitly imposing that all setors within a ountry are idential in terms of their interation with eah other and the rest of the world. The pitfall assoiated with these assumptions an be illustrated in the ontext of a stylized world with three ountries involved in a global value hain the People's Republi of China (PRC), Japan and the US. Suppose Japan manufatures raw materials for the prodution of a mobile phone and ships it to the PRC whih ats as an assembly point. The PRC in turn exports the finished produt to the US, where it is onsumed by US onsumers. Not reognizing this global value hain struture, traditional models would assume that Japan exports final goods to the PRC, and hene a depreiation of the Japanese urreny hurts Chinese ompetitiveness. In reality however, a derease in the prie of Japanese omponents ould very well lead to an inrease in demand for the PRC s output and hene an improvement of its ompetitiveness, i.e a depreiation of its REER. This example shows that REER omputed using the standard frameworks is not only inaurate in terms of magnitude, but may also have the wrong sign. Aounting for suh influenes is beoming inreasingly more important given the rise in intermediate goods trade in the last two deades as shown by Wang et al. (2013). 2 Addressing these issues through the lens of a maroeonomi model designed to apture global value hains and setoral heterogeneity within and aross ountries, the paper makes four novel ontributions to the literature on REER. Firstly, we depart from the single setor framework and allow for multiple setors within eah ountry. Setors differ in the nature and extent of their interation with eah other and 1 See Chinn (2006) for a primer on the onept of REER and Rogoff (2005) for an appliation and disussion. 2 For OECD ountries Miroudot et al. (2009) find the share of trade in intermediate goods and servies to be 56% and 73% respetively. As emphasized in Baldwin and Lopez-Gonzalez (2012), intermediate goods trade and vertial speialization have grown many-fold in developing ountries starting in the 1980s (see also Wang et al., 2013) Also important is the import ontent of exports, epitomized by the prevalene of proessing trade involving Asian eonomies, espeially the People's Republi of China (PRC). Koopman et al. (2014) find that the import ontent of exports is as high as 90 perent for some setors in the PRC. 1

with setors in the rest of the world, both in terms of souring inputs as well as selling their output. We build on the literature (in partiular Bems and Johnson (2017), heneforth BJ) that has already shown the importane of distinguishing intermediate and final goods trade in measuring REER, and find that allowing for setoral heterogeneity provides an even bigger improvement in the quantifiation of REER as ompared to inorporating imported inputs in a single setor framework. Setoral heterogeneity affets both omponents of REER-weights as well as pries. The intuition omes from the fat that setors that are typially prominent exporters are also simultaneously large importers, and hene models whih aggregate them with setors that non-traded, overstate the domesti value added ontent in exports and hene the impat of hanges in foreign pries on ompetitiveness as measured by the REER. Seondly, aknowledging that value added and gross output (as well as exports) beome delinked in the presene of imported inputs, we develop separate REER measures for value added (GVC-REER) and gross output (Q-REER). While value added ompetitiveness is the primary objet of interest, gross output ompetitiveness may also be useful in ertain ontexts. For instane, produtivity gains from exports may be linked to gross exports rather than their value added ounterparts, due to positive spillovers from imported inputs and tehnology. Thirdly, apart from ountry-level REERs, we also develop REER measures at the setoral level. With inreasing speialization and trade in intermediate inputs, inter-setoral linkages between ountries differ substantially from aggregate ountry level relationships. Wang et al. (2013) have doumented and explored various dimensions of this heterogeneity and have found that different setors in a ountry tend to partiipate in ross-border prodution sharing by different extents and in different ways. For example, aording to Wang et al. (2013), some setors mostly engage in regional value hains (i.e., buying or selling intermediate inputs with neighboring ountries), whereas others engage in truly global value hains (i.e., souring and selling a signifiant amount of inputs to ountries on different ontinents). This implies substantial heterogeneity in hanges in ompetitiveness aross setors to a given hange in foreign prie vetor. An aggregate ountry level measure is inapable of apturing these. Indeed, in setion 6 we doument several instanes where the REERs move in opposite diretions for different setors within a ountry. This makes setoral REERs a useful addition to the information set of poliy makers. Fourthly, we apply the framework to a bilateral ontext and develop a new measure of bilateral real exhange rate (GVC-RER) that provides an improvement upon the urrent measures by aknowledging the presene of setoral heterogeneity and trade in inputs. We take the framework to the data by parametrizing the model using global input output tables from the world input-output database (WIOD), and reate a database of 2

REER weights and REER indies for 40 ountries and 1435 ountry-setor pairs for the period 1995-2009. The results highlight the importane of the novel features introdued in the modeling part. For instane, we find t hat w hile a llowing f or t he d istintion between intermediate and final goods flows does lead to differenes in REER weights (as shown by BJ) the differene is muh starker one we allow for setoral heterogeneity as well. With regard to the muh disussed ase of the PRC s REER, our results reveal two important findings over the period 1995-2009. Firstly, we find that the exhange rate appreiated more during this time when viewed in value added terms (GVC-REER) as opposed to gross output terms ( Q-REER), signaling that a depreiation in ountries from whih the PRC soured inputs lead to an inrease in the ompetitiveness of its exports whih was greater than that of its own domesti fators of prodution. Seondly, when viewed in a bilateral ontext against the US, the appreiation of the Chinese exhange rate from 1995-2009 was muh more pronouned (i.e the ase for the exhange rate being undervalued during this time is muh weaker) under our GVC-RER sheme that orretly aounts for the PRC s omplex partiipation in global value hains, ompared to the standard measures whih ignore these features. On the debate on imbalanes within the eurozone, our results based on the bilateral GVC-RER between Greee and Germany indiate that the fall in ompetitiveness for Greee (i.e an appreiation) vis-a-vis Germany from 1995-2009 was muh larger when measured through GVC-RER as opposed to the onventional real exhange rate measure, indiating that the standard bilateral REER measure underestimated the extent to whih lak of inflation in Germany was hurting ompetitiveness in Greee. It is worth emphasizing that our objetive is to model relatively short-term and small-sale movements in ompetitiveness. We therefore take the nature of GVC and trade patterns aross ountries and setors as given and do not onsider the issue of endogenous off-shoring and prodution sharing deisions. 3 The remainder of the paper is strutured as follows: We begin with a disussion of the literature on REER in setion 2, followed by a brief introdution to the onept of REER in setion 3. Setion 4 presents the main model whih is then used in setion 4.4 to develop new measures of REER at the setor level. Setion 4.5 uses the setor-level framework to develop measures of REER at the ountry level. Setion 5 provides a stylized example to illustrate the properties of the new REER measure. We then proeed to the empirial part of the paper in setion 6 whih fousses on highlighting properties of the new REER measures 3 There is a growing literature on organization of global value hains that looks into these questions. See for instane Antràs and Chor (2013), Antràs (2014), Costinot et al. (2013) and Johnson and Moxnes (2012). Moreover, due to the omplex nature of the model we solve it using log linearization tehniques. This further reinfores the view that our REER indies are best suited for short-term movements resulting from shoks that are not too large so as to affet organization of Global value hains (GVCs). 3

omputed from the data, both at the ountry and at the setor level, drawing omparisons with the existing literature in the proess. Setion 6.3 disusses the extension of the analysis to a bilateral setting, and setion 7 onludes. 2 Related Literature This paper is a ontribution to the literature on international trade and prie ompetitiveness. As mentioned above, the most prominent and ommonly ited REER measures today do not distinguish between trade in intermediate and final goods and onsider all trade flows to be in the latter ategory. A few reent papers have reognized this drawbak and have made attempts to address them. BJ allow for trade in intermediates and ompute the REER weighting matrix at the ountry level. They however do not allow for setoral heterogeneity whih we find to be a ritial feature in determining patterns in ompetitiveness, and do not onsider REERs at the setor level. Our attempt to inorporate setor level prie indies and build setor level exhange rates has a preedent in the work of Bennett and Zarni (2009), Sato et al. (2013) and Ito and Shimizu (2015). However, their work does not inorporate trade in intermediate goods and uses an IMF-like weighting matrix. In developing measures designed speifially to measure external (export) ompetitiveness, Lommatzsh et al. (2016) also onstrut REER indies in whih they adjust the prie index by putting weight on setors in aordane with their export shares. However, they do not allow for setoral heterogeneity in weights, whih in turn also influenes the relevant foreign prie index used in the REER omputation and hene biases the REER measure as we show in the paper. With regard to gross output ompetitiveness, Bayoumi et al. (2013) propose a measure in whih they borrow the weighting matrix from the IMF but adjust the prie indies to aknowledge the presene of imported inputs. As we show however, this only ends up being a partial adjustment as the original weighting matrix is not adjusted. More broadly, the paper is motivated by and is linked to the relatively new but rapidly expanding literature on global value hains and their impliations for maroeonomi variables (see Hummels et al., 2001, Baldwin and Lopez-Gonzalez, 2012 and Auer et al. (2016)) as well as the literature on trade statistis and export aounting in the presene of intermediate goods trade (Koopman et al., 2012 and Wang et al., 2013). 3 The Conept of REER as a Measure of Competitiveness The real effetive exhange rate measures hange in ompetitiveness by quantifying hanges in the demand for goods produed by a ountry as a funtion of hanges in relative 4

pries. 4 To be more preise, if V J is the demand for the goods produed (or alternatively, value added) by ountry J, then the effetive exhange rate of ountry J is defined as: REER J = V J = G J ({ p} n i=1 ) (3.1) where { p} n i=1 is a vetor of prie hanges in all ountries inluding the home ountry. Note that by assumption no other variables exept the pries expliitly enter the funtion G(.). Hene by onstrution REER is a partial equilibrium onstrut where the primitive shoks that lead to the observed prie hanges are not modeled. Moreover the demand side of the eonomy is assumed to be exogenous and the aggregate final demand is assumed to be onstant (although demand is allowed to swith between different goods in response to hanges in pries). The funtion G J (.) is homogenous of degree zero, so that the model satisfies neutrality in the sense that if all pries (inluding the home prie) double, then the relative demands remain unhanged, and sine by onstrution aggregate demand is held fixed, the absolute demand for eah good also remains unaffeted. It is important to note that suh REER models do not assume balaned trade or any restritions on the trade balane. In our empirial framework, trade balanes are allowed to be non-zero in the steady state and are alibrated to their observed ounterparts in the data. This is in line with the partial equilibrium setup ommon in the literature in whih the demand side is exogenous. 4 The Model Consider a world eonomy omprising n ountries. There are m setors within eah ountry. Eah ountry-setor is alled a prodution entity and there are a total number nm of these prodution entities in the world eonomy. Eah entity uses a prodution funtion with its own value added and a omposite intermediate input whih an ontain intermediate inputs from all mn entities inluding itself. The output of eah entity an be used either as a final good (onsumed in any of the n ountries) or as an input by another entity. Hene there are a total of nm produers and nm + n onsumers (nm entities plus n final goods onsumers) in the eonomy. Both the prodution funtion and final goods onsumption aggregators are nested CES (onstant elastiity of substitution) aggregators whih are desribed in detail next. 4 In this literature the use of the word ompetitiveness is appropriate only in the ontext of prie ompetitiveness, and does not neessarily extend to the notion of ompetitiveness measured in terms of profits, market shares et. 5

4.1 Prodution The prodution funtion for entity (, l) is given the expression: 5 [ Q l = (wl v ) 1/σ3 (V l ) σ 3 1 σ 3 + (w X l ) 1/σ3 (X l ) σ ] σ 3 3 1 σ 3 1 σ 3 (4.1) Here, Vl is the value added by the entity, Xl is an aggregate bundle of intermediate inputs, and σ 3 is the elastiity of substitution between the two inputs. Xl is in turn a CES aggregate, ombining inputs from eah entity (i, s), denoted by Xsl i, in a three stage nested CES aggregate with elastiities of substitution σ 2, σ 1h and σ 1 as follows: The intermediate input X l is and aggregate of m setoral omponents, X l = [ m s=1 (wsl) 1/σ2 (X sl) σ2 1 σ 2 ] σ 2 σ 2 1 (4.2) eah of whih is in turn a ombination of the setor s input from the domesti setor and an aggregate setor s input form foreign setors. The elastiity of substitution between these two inputs is σ 1h s. 6 X sl = [ (w sl ) 1/σ1h s (X sl ) σs 1h 1 σs 1h + (w(f) sl) 1/σ1h s (X(f) sl ) σs 1h 1 σs 1h ] σ1h s σs 1h 1 (4.3) For the setor s foreign input bundle, inputs from all foreign ountries from that setor are aggregated to form setoral intermediate inputs {X(f) sl }m s=1. In other words, X(f) sl is the aggregate setor s foreign intermediate input used in prodution by ountry setor l X(f) sl = [ n (wsl) i 1/σ1 s (X i i=1,i sl ) σ 1 s 1 σs 1 ] σ1 s σ 1 s 1, s = 1, 2,..m (4.4) Here X i sl denotes inputs from ountry i setor s used in prodution by ountry setor l, the w s are aggregation weights and σ 1 is the (onstant) elastiity of substitution between different foreign varieties of the setor s output in the prodution funtion of entity (, l) 5 Notation: We use supersripts to denote ountries and subsripts to denote setors. When 2 sripts are present, the first one denotes the soure ountry and the seond denotes the destination ountry. For example, Xsl i denotes output produed by (soure) ountry i setor s that is used by (destination) ountry setor l. 6 With this two step framework we are allowing for a distintion between maro (σ 1h ) and miro (σ 1 ) elastiities for eah setor, whih is a feature of the data doumented in the literature see Feenstra et al. (2014). 6

4.2 Preferenes A ountry speifi final good is obtained by aggregating goods from all nm prodution entities in two stages. F s (f) = [ n i=1,i (κ i s ) 1/θ1 s() (F i s ) θ 1 s () 1 θ 1 s () ] θ 1 s () θs 1() 1 (4.5) F s = [ (κ s ) 1/θ1h s () (F s ) θ 1 s () 1 θs 1() + (κ(f) s) 1/θ1h s () (F (f) s) ] θs 1h θ 1h s () () 1 θs 1h θs 1h() 1 () (4.6) [ m F = (κ s) 1/θ2 () (F s) θ s=1 2 () 1 θ 2 () ] θ 2 () θ 2 () 1 (4.7) 4.3 Market learing: Gross output from an entity is absorbed either as an intermediate input or a final good (we do not allow for inventory aumulation or any inter-temporal effets). Thus the following market learing ondition holds (, l) Q l = n i=1 F i l + m n j=1 k=1 X k lj (4.8) 4.4 Computation of Effetive Exhange Rate Weighting Matries In order to define the exhange rates we take pries and final demands in all ountries as exogenous and ompute the demand for value added and gross output of different entities as funtions of pries. Demand for value added as a funtion of prie of value added: (GVC-REER) The appendix shows that the demand for value added an be written as ve ( ) ( ˆV l = W V ve (ˆp(V ) l ) + W F V ve ˆF ) (4.9) ( ( )) Here ve ˆV l is the vetor of hanges in value added staked aross all ountries nmx1 and setors, and W V and W( F are ) nm by nm matries derived in the appendix. Assuming the hange in final demand ve ˆF to be zero, the nm by nm matrix premultiplying ve (ˆp(V ) l ) 7

an be interpreted as a matrix of weights for the real effetive exhange rate, as it measures how the demand for value added originating in a ountry-setor hanges when prie of value added hanges in any other entity. Interpretation in the ase with onstant elastiity Appendix C shows that under the onstant elastiity assumption the weight assignment by ountry setor (h, l) to ountry-setor (, s) where (h, l) (, s) an be written as follows: w h ls = [( ) ( )] n p(v ) h l Vl hk p(v ) s Vs k ( ) p(v ) h l Vl h (P K, (h, l) (, s) (4.10) F k ) k=1 where we use lower ase w to denote onstant elastiity weights. The weight assigned by ountry setor (h, l) to ountry-setor (, s) where (h, l) (, s) is a weighted sum of the value added reated by ountry-setor (, s) and absorbed by eah of the ountries k(= 1,.., n), where the weights are given by the value added reated by (h, l) that is absorbed in the same ountry k. This aptures both mutual and third ountry ompetition, beause the weight is high if both ( p(v ) h l V ) ( ) l hk and p(v ) s Vs k are high, whih happens when both (h, l) and (, s) have a high share of value added exports to ountry k. Relaxing the Uniform Elastiity Assumption In this paper, we fous primarily on the onstant elastiity ase in order to fous on our main ontribution, whih is to highlight the role of setoral heterogeneity in omputing REER indies. Here we provide a brief flavor of the results when the onstant elastiity assumption is relaxed, and further results, with examples are developed in the appendix. Proposition 4.1. Suppose all prodution and onsumption elastiities are onstant and equal to σ and θ respetively. 7 Then starting at the uniform elastiity equilibrium, the effet of a hange in elastiity on the weight assigned by entity (h, l) to entity (, s) is given by: w h ls θ n n m = wh ls vh l v s 1 =1 2 =1 k=1 bh 1 lk b 1 sk (p(q) 1 k F 1 2 p(v ) h l V l h k ), (h, l) (, s) (4.11) Proof(sketh): See appendix C. Here b is used to denote elements of the global Leontief inverse matrix and p(q) is used to denote prie of gross output.(4.11) shows that an inrease in elastiity of substitution 7 This is equivalent to assumption (A2) in setion D 8

of onsumption holding everything else onstant (inluding the prodution elastiity) has two opposing effets on the weight assigned by home entity (h, l) to the foreign entity (, s). The two terms orrespond to the expenditure swithing and omplementarity effet. In partiular, the first effet (expenditure swithing) is positive and is given by the onstant elastiity weight wls h, whih is always positive in the onstant elastiity ase. In addition, there is the ountervailing omplementarity effet whih omes from the seond term on the right hand side. This term is high when the produts b h 1 lk b 1 sk are high for various entities indexed by ( 1, k), whih in turn happens if the outputs of the two entities are used together in prodution (i, e entities suh as ( 1, k) whih use the output of (, s) as an input, also uses the output of (h, l) as an input). Intuitively, when the prie of (, s) dereases, its quantity demanded inreases. This effet is greater the greater is the elastiity of substitution between goods (θ). Moreover, an inrease in demand for (, s) will end up inreasing the output of (h, l) if it is highly omplementary with (, s). Gross Output Competitiveness We also derive the demand for aggregate output as a funtion of the prie of value added (this is analogous to the goods REER measure proposed in Bayoumi et al. (2013) (See appendix for steps of proof). ve ( ) ( ) ( ˆQ l = W Q ve p(v ˆ ) l + W F Q ve ˆF ) (4.12) Here W Q is an nm by nm ( weighting ) matrix derived in appendix B. Again putting the hange in final demand ve ˆF to be zero, the nm by nm matrix premultiplying ve (ˆp v l ) an be interpreted as a matrix of weights for the real effetive exhange rate with regard to gross ompetitiveness, i.e it measures how the demand for output of a ountry-setor hanges with hanges in pries of other ountry-setors. This is in ontrast to the first measure defined above, whih looks at hanges in demand for value added. (As is shown in D.2, the two are the same in the speial ase where gross output is the same as value added) 4.5 Building Country-level REER From Ground Up Value added weights at the ountry level This setion provides a method to aggregate the ountry-setor level weights derived above and defines ountry level weights analogous to the ones ommonly disussed in the literature. We show that the aggregated weights so derived in general do not orrespond to 9

any of the ones proposed in the literature exept in knife-edge ases. This is attributable to the fat that our measure exploits inter-setoral linkages between ountries to provide a more omprehensive measure of ompetitiveness than what an be obtained by using just ountry level data. To derive the expression for ountry-level value added weights, we start with the following deomposition of the nominal GDP of ountry into its different setoral omponents: p(v ) V = m l=1 p(v ) l V l (4.13) log linearizing this equation we get: ˆp(V ) + ˆV = m l=1 ( ) p(v ) l Vl [ˆp(V ) p(v ) V l + ˆV ] l Staking the n equations in (4.14) we an write the system in matrix notation as: (4.14) ( ( ) ] ve (ˆp(V ) ) nx1 + ve ˆV ) = R V [ve (ˆp(V ) l ) nmx1 + ve ˆV l nx1 nmx1 (4.15) where (R V ) nxnm = S1 V 0 m.. 0 m 0 m S2 V : :.. : (4.16) 0 m 0 m.. S V n and ( ( Si V )1Xm = p(v ) i 1 V1 i, p(v )i p(v ) i V i 2 V 2 i,.., p(v )i p(v ) i V i m V m i and 0 m is an m by 1 matrix of zeros. By definition the hange in the GDP deflator is the weighted sum of hange in its omponents and hene (4.15) redues to p(v ) i V i ) ( ( ) ] ve ˆV ) = R V [ve ˆV l nx1 nmx1 ( ) using (4.9) in (4.17) and imposing ve ˆF = 0 as before we get: ve (4.17) ( ) ˆV l = R V W V ve (ˆp(V ) l ) (4.18) 10

Defining the two measures of ountry level value added exhange rates: When setor level prie indies are available, (4.18) defines the hange in the ountry level GVC-REER, i.e log(gv C REER) = W V (C)ve (ˆp(V ) l ) (4.19) where the n by nm matrix W V = R V W V is the weighting matrix whih an be interpreted as follows: the weight assigned by ountry i to ountry j setor l is itself a weighted sum of the weights assigned by eah setor of ountry i to (j, l), with the weights being proportional to the ountry i setor s share of value added as a fration of total value added by ountry i W V ij l = m s=1 ( ) p(v ) i s Vs i (W p(v ) i V i V ) ij sl (4.20) If setor level pries are not available, a further approximation is needed. In partiular, we need to assume a mapping between setor level pries and GDP deflator, i.e between ˆp v and {ˆp v l } M l=1. We make the relatively uninformed assumption that all setoral level pries hange in the same proportion as the aggregate GDP deflator, i.e we make the following assumption 8. Assumption (AP): p(v ˆ ) j = ˆp(V ) j l l j (4.21) Using this assumption we an define our seond measure of ountry level value added exhange rate, GVC-REER(GDPdef) as follows: log(gv C REER(GDP def)) = W V (CG)ve (ˆp(V ) ) (4.22) where W V (CG) = R V W V R g is an n by n matrix of weights and R g = I n 1 m To summarize, both setor level pries (the more aurate and our preferred measure) and ountry level pries (as in the literature) an be used to ompute REER indies using the setor level weighting matries disussed above, yielding the following two expressions for ountry level GVC-REERs. 8 Note that in a world with prie rigidity and produer urreny priing this assumption is satisfied automatially. 11

log(gv C REER) = W V (C)ve (ˆp(V ) l ) (4.23) log(gv C REER(GDP def)) = W V (CG)ve (ˆp(V ) ) (4.24) Where W V (C) and W V (CG) are weighting matries of dimension nby nm and n by nrespetively. The two measures of Q-REER (for gross output ompetitiveness are defined analogously). 9 In general, weighting matries using setor level information (WV s ) as well as REER indies inorporating setor level prie variations provide a more aurate measure of ompetitiveness ompared to the measures whih use only ountry level aggregate trade flows and prie indies. 10 This is illustrated in the example that follows. Link to other measures in the literature Our seond measure of ountry level exhange rates whih uses only the GDP deflator (GVC-REER(GDPdef)) has an n by n weighting matrix as all other measures in the literature and we an hene make a omparison with them. Given the ountry-setor level weights (W V ), the ountry level weights (W V (CG)) have an intuitive interpretation. The weight assigned by ountry i to ountry j is a weighted sum of the weights assigned by eah setor of ountry i to eah setor of ountry j, with the weights being proportional to the home setor s share of value added as a fration of total home value added. W V (GDP def) ij = m s=1 ( ) ( p(v ) i s Vs i m ) (W p(v ) i V i V ) ij sk k=1 (4.25) These ountry level weights defined here are different from others proposed in the literature in several respets. The losest to our measure is the one by BJ who also take into aount the input-output linkages in their measure and define weights in terms of value added, but do not exploit setor level linkages aross ountries. Beause of the greater information used in our measure, it is in general different from their VAREER and IOREER, even under the assumption of all elastiities being the same. The following proposition shows that even under the uniform elastiity assumption, GVC-REER and VAREER differ from eah other exept in speial ases. 9 The detailed derivations are provided in appendix 10 Appendix D disusses the set of restritive onditions under whih the two approahes give idential expressions 12

Condition 7.1 v i n b i F j = =1 m n m vs i l=1 =1 s=1 b i lsf j s i, j (4.26) where vl i = p(v )i l V l i is the value added share for entity (i, l) and b denotes a generi element of p(q) i l Qi l the global inter-ountry Leontief inverse matrix. Proposition 4.2. Under the onstant elastiity assumption, the ountry level weights (W V (GDP def)) defined above redues to VAREER (and IOREER) weights defined in BJ if either of the two onditions below are satisfied. 1. 4.26 2. No trade in intermediates The proof is given in appendix D. The first part of the proposition shows that outside of the knife-edge ase in whih the above ondition is satisfied, the GVC-REER(GDPdef) weights whih exploit inter-setoral linkages between ountries will be different from the VAREER measure. Intuitively, ondition (4.26) is satisfied if different setors within a ountry are symmetri with regard to their input-output linkages with the rest of the world, for in that ase aggregation aross setors within a ountry will be a loser approximation to the behavior of eah individual setor. The next setion will provide an example to illustrate the role played by the ondition in aggregating weights at the ountry level. The seond part of the proposition shows that differenes between GVC-REER and VAREER vanish when there is no trade in intermediates. in this ase aggregating trade flows aross setors within a ountry does not lead to any loss of information as far as omputation of real effetive exhange rate is onerned. Intuitively, if all prodution by all entities involves only own value added and no intermediates, then there is no asymmetry between setors within a ountry and hene aggregation does not lead to any loss of relevant information. Links to other ommon REER measures in the literature, whih are even further removed from our framework than BJ, is disussed in a proposition in Appendix D. Gross output exhange rate at ountry level Following a similar proedure to the one used for GVC-REER, we an define weights and exhange rates for gross output at the ountry level: 13

log(qreer) = W Q (C)ve (ˆp(V ) l ) (4.27) log(qreer(gdp def)) = W Q (CG)ve (ˆp(V ) ) (4.28) 5 Illustrative Example: A three ountry global value hain Consider a world eonomy omprising three ountries (J, C and U) and two setors within eah ountry indexed by subsript i {1, 2}. The input-output linkages are given in table 1. The example mimis a stylized global value hain of the following form: J 1 C 2 (C, U) (5.1) Setor J 1 in ountry J exports raw materials to setor C 2 in ountry C, whih ombines them with its own value added input to produe final goods whih are then subsequently onsumed in C and exported to U. The rest of the setors only use their own value added input and sell domestially. Next, we illustrate how setoral heterogeneity affets the measurement of REER along two dimensions-the REER weights themselves and their interation with setoral prie hanges. Setoral heterogeneity and GVC-REER weights The key advantage in our REER weighting sheme ompared to the literature is that the framework is flexible enough to inorporate information from input output tables like Table 1a that are at the ountry-setor level, whereas the other REER shemes in the literature work with input-output linkages at the ountry level (analogous to table 1b). To see the onsequenes of the loss of information on setoral heterogeneity that this aggregation entails, table 2 shows the weight assigned by ountry U to ountry C and J under different REER weighting shemes. Consider first a omparison between GVC-REER and the VAREER measure of BJ. Both reognize that part of the trade between J and C omprises of intermediate goods, and hene assign a lower value to W UC than the IMF weight. However, GVC-REER has a lower value of W UC ompared to VAREER. This is attributable to the fat that unlike VAREER, the GVC-REER reognizes that the setor in C whih atually ompetes with U is C 2, and C 2 has a lower value added share than C 1. Hene, the VAREER weight, whih essentially treats U as ompeting with C as a whole (whih is an average of 14

Table 1 Input output table for example 5 (a) Setor level input-output table J C U JFinal CFinal Ufinal total output J 1 J 2 C 1 C 2 U 1 U 2 J J 1 0 0 0 2 0 0 1 0 0 3 J 2 0 0 0 0 0 0 1 0 0 1 C C 1 0 0 0 0 0 0 0 2 0 2 C 2 0 0 0 0 0 0 0 1 2.5 3.5 U U 1 0 0 0 0 0 0 0 0 2 2 U 2 0 0 0 0 0 0 0 0 1 1 VA 3 1 2 1.5 2 1 total output 3 1 2 3.5 2 1 (b) Country level input output table J C U J final C final U final Total output J 0 2 0 2 0 0 4 C 0 0 0 0.5 2.5 2.5 5.5 U 0 0 0 0 0 3 3 Value added 4 3.5 3 Total output 4 5.5 3 C 1 and C 2 ) puts a higher weight on C as it overestimates the value added originating in C that is ompeting with U in U s final goods market. Similarly, GVC-REER assigns a higher value to W UJ ompared to VAREER, reognizing the importane of J in determining the ompetitiveness of U through the input it supplies to C 2. The benhmark IMF measure not only fails to reognize this setoral heterogeneity, but also impliitly assumes that all trade is in final goods, and hene no part of prodution arried out in J is onsumed in U. This is evident from a value of zero assigned to W UJ under IMF framework. Note that sine neither setor in U uses intermediate inputs and onsequently there is no distintion between value added and gross output, and Q-REER and GVC-REER weights oinide. This equivalene breaks down only when a ountry imports intermediate inputs, as is the ase with C in this example. In this ase W CJ is higher in GVC-REER (W CJ =0.56) than it is under the Q-REER (W CJ =-1.33). In fat, in the latter ase W CJ is atually negative, implying that a fall in J s pries leads to an inrease in the demand for C s output (although not of its value added) as it embodies the output of J 1 whih beomes more ompetitive with the fall in its prie. 15

Table 2 REER weight assigned by J to C (W JC ) under different weighting shemes for example 5 GVC-REER VAREER (BJ) IMF Q-REER W UJ 0.57 0.36 0 0.57 W UC 0.43 0.67 1 0.43 Notes: GVC-REER and Q-REER are measures proposed in this paper. VAREER (BJ) stands for the value added exhange rate measure proposed in BJ and IMF stands for the IMF REER measure based on Bayoumi et al. (2005). Setoral heterogeneity and REER indies The seond dimension of setoral heterogeneity whih leads to an improvement in our REER measure ompared to others in the literature is the flexibility to inorporate heterogeneity in setoral pries. As an example, onsider the impliations for the REER of U when the prie of C 1 inreases, and all other pries remain unhanged (i.e pˆ 1 = 1, pˆ 2 = 0, pˆ J1 = pˆ J2 = pˆ U1 = pˆ U2 = 0). Sine the value added share of C 1 and C 2 in C are 0.57 and 0.43 respetively, the omputed hange in aggregate prie index in C is given by ˆp = 0.57. Given a value of W UC = 0.43, a measure like VAREER whih uses aggregate (ountry level) prie indies and weights would ompute the hange in REER for U that is different from GV C REER, whih reognizes that the entire weight of W UC is onentrated on C 2, and sine pˆ 2 = 0, the GV C ˆREER U = 0 as well. In partiular: ˆ V AREER U = W UC ˆp = 0.57 0.43 = 0.25 GV C ˆREER U = W UC1 pˆ 1 + W UC2 pˆ 2 = 0 1 + 0.43 0 = 0 Sine the only prie hange onerns the setor in C whih is entirely domestially oriented, ompetitiveness of U should not be affeted, as rightly onluded by the GVC-REER measure. Indeed, as evident in Table 3 whih shows the full setor level GVC-REER weighting matrix, the weight assigned by both setors on U on C 1 is zero. On the other hand, the aggregation impliit in VAREER and all other measures in the literature limits their flexibility in properly deiphering suh distintions. 6 Taking the model to the data Our main soure of data is the World Input-Output Database (WIOD), whih provides a time series of input-output tables overing 40 ountries and 35 setors from 1995-2011. The data is available in both urrent and previous year pries whih enables us to ompute prie 16

Table 3 Country-Setor level weighting matrix for 5 J C U J 1 J 2 C 1 C 2 U 1 U 2 J 1-1 0.25 0.19 0.18 0.26 0.13 J J 2 1-1 0 0 0 0 C C 1 0.57 0-1 0.43 0 0 C 2 0.29 0 0.23-1 0.32 0.16 U U 1 0.41 0 0 0.31-1 0.29 U 2 0.32 0 0 0.24 0.44-1 indies for different entries in the input-output table. A detailed desription of this database an be found in Timmer and Erumban (2012). In order to fous on the role of setoral heterogeneity, in this setion we fous exlusively on the ase with onstant elastiities. Appendix E provides a detailed disussion for the heterogenous elastiity ase, inluding the estimation of elastiities and their inorporation in GVC-REERs. 6.1 REER Weights Table 4 summarizes the different REER weighting matries that are generated by the framework. In addition to the ountry level weights whih have been studied in the literature, our framework also provides weights at various levels of disaggregation. Eah of these ould be of interest to poliy makers depending on the question at hand, and provide information whih annot be aptured in the aggregated ountry level weights. For instane, if a prie shok (through tariffs, produtivity or the nominal exhange rate) has a heterogenous impat aross different setors in the ountry of origin, then the ountry by ountry-setor weighting matrix (row 3) would provide a more aurate estimate of the impat on a foreign ountry as opposed to the ountry by ountry weighting matrix. As an example to illustrate the differene in REER weights in our measure ompared to others in the literature, Table 5 shows the ranking of 5 largest ompetitor ountries for Japan in the year 2007 based on the different ountry-level REER shemes disussed above. The GVC-REER sheme, whih aknowledges the prominene of supply hain trade between the PRC and Japan, assigns a lower weight to the PRC, reognizing that the final destination of exports from Japan to the PRC is not always the PRC itself, whereas the standard IMF weighting sheme whih fails to make this distintion assigns a higher weight to the PRC than the US, due to the high volume of gross trade between the PRC and Japan. 17

With the prominene of global value hains and the aompanying divergene between Table 4 Summary of REER weights Dimension Country by ountry Country by ountry-setor Country-setor by ountry Country-setor by ountry-setor n by n by T n by nm by T nm by n by T nm by nm by T Note: n= number of ountries, m = number of setors, T = number of time periods in the sample. Table 5 Ranking of Countries Aording to REER Weight Assigned by Japan Rank GVC-REER(CE) Goods-REER IMF 1 ROW ROW ROW 2 United States PRC PRC 3 PRC United States United States 4 Germany Rep. of Korea Rep. of Korea 5 Rep. of Korea Taipei,China Taipei,China Notes: ROW stands for the rest of the world region in WIOD. IMF and Goods-REER orrespond to weighting shemes proposed in Bayoumi et al. (2005) and Bayoumi et al. (2013) respetively. 18

Figure 6.1 Correlation between Value added and Gross Output REER Weights 1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 1995 2000 2005 2010 gross and value added exports that has been doumented in the literature, our analysis allows us to see how the relationship between gross output and value added ompetitiveness has evolved over time. Figure 6.1 plots the ross-setional orrelation between value added (GVC-REER) and gross output (Q-REER) REER weights for the 17 years in the sample (1995-2011). While no disernible pattern emerges when we look at the ountry level weights, a delining trend is visible at the setoral level, pointing towards a divergene between value added and gross output ompetitiveness. These results show that as far as REER weights are onerned, the effet of global value hains is more visible at the setor level than at the ountry level. 6.2 Multilateral Exhange rates Figure 6.2 illustrates a omparison between three different REER indies. The GVC-REER is our proposed measure of REER whih inorporates input-output linkages as well as setoral heterogeneity (in both REER weights as well as prie indies). The VAREER orresponds to the value-added REER measure proposed in BJ whih aounts for input-output linkages but not setoral heterogeneity. IMF-REER is a measure whih uses the IMF weighting sheme that ignores both input-output linkages as well as setoral heterogeneity. 11 As is evident in the figure, although the three measures move broadly in line with one another through the sample, differenes do emerge and are partiularly pronouned for ertain ountries in ertain time periods. It is also pertinent to note that the the IMR-REER 11 To make the omparison more transparent, we use the GDP deflator in onstruting the IMF-REER, instead of CPI or unit labor ost whih are the other ommonly used alternatives. 19

Figure 6.2 Comparison of three REER indies for selet ountries 0.4 0.35 0.3 0.25 People's Republi of China GVC REER IMF REER VAREER 0 0.05 0.1 Germany GVC REER IMF REER VAREER 0.2 0.15 0.15 0.1 0.2 0.05 0.25 0 1995 2000 2005 2009 Spain 0.15 0.1 0.05 0 0.05 0.25 GVC REER IMF REER VAREER 1995 2000 2005 2009 Ireland 0.2 1995 2000 2005 2009 Frane 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 GVC REER IMF REER VAREER 1995 2000 2005 2009 United States 0.2 0.15 0.1 0.15 0.1 0.05 0 0.05 0.05 GVC REER 0.1 GVC REER IMF REER 0.15 IMF REER VAREER VAREER 0 0.2 1995 2000 2005 2009 1995 2000 2005 2009 Comparison of three REER indies for selet ountries.the GVC-REER is our proposed measure of REER whih inorporates input-output linkages as well as setoral heterogeneity (in both REER weights as well as prie indies). The VAREER orresponds to the valueadded REER measure proposed in Bems and Johnson (2017) whih aounts for input-output linkages but not setoral heterogeneity. IMF-REER is a measure whih uses the IMF weighting sheme that ignores both input-output linkages as well as setoral heterogeneity. 20

Table 6 Comparison of orrelations aross three REER indies GVC-REER VAREER IMF-REER GVC-REER 1 VAREER 0.92 1 IMF-REER 0.92 0.99 1 The table displays the mean time series orrelations between the indiated pairs of REERs aross the sample of 41 ountries. GVC-REER is the measure in developed in this paper, whereas VAREER is the measure proposed by BJ. The IMF REER is onstruted using a method similar to that in BJ. and VAREER tend to have a higher omovement with one another ompared to that with the GVC-REER, an observation whih is onfirmed by looking more systematially at the orrelations in table 6. This suggests that aounting for setoral heterogeneity is even more important than merely aounting for the presene of input-output linkages at the aggregate ountry level as is done by BJ. As shown in the preeding setions, the GVC-REER measures improve upon VAREER by inorporating setoral heterogeneity, whih enters the former in two forms (i) REER weights and (ii) prie indies. To further investigate the nature and soure of differenes between the two measures, we deompose the differene into a term that aptures the ontribution of weights, and the remaining term whih aptures the ontribution of differenes in pries using the following framework. REER_GAP it = V AREER it (GV C REER it ) = n n m i,j,v AREER W ˆp j t W i,j,v AREER Here, Wt = j=n t n ( W j=1 i,j,v AREER t j=1 s=1 W i,j,gv C t }{{} + W i,j,gv C t ˆp j t T erm1 n j=1 m W s=1 ) i,j,gv C REER j s,t pˆ s,t ˆp j t i,j,gv C REER j s,t pˆ s,t } {{ } T erm2 i,j,gv C REER is the VAREER weighting matrix, Ws,t is the n by nm GVC-REER weighing matrix, and W i,j,gv C t is the n by n GVC-REER weighting matrix designed to measure the departure of weights from VAREER. ˆp j t is the ndimensional vetor of hanges in the GDP deflator and pˆ j s,t is the nm dimensional vetor of setoral prie hanges. 21

Table 7 Deomposing the differene between GVC-REER and VAREER Country REER GAP (%) Contributions (share in %) Weights Pries Australia 11.94 5.73 6.21 Brazil 1.79 7.64-5.84 PRC -6.64 3.72-10.35 Germany -0.41 6.29-6.7 Spain -0.85 4.93-5.79 Frane -10.48 5.81-16.29 Ireland -9.95 4.28-14.23 Taipei,China 8.49 5.72 2.77 United States -7.1 8.51-15.61 REER GAP denotes the umulative (from 1995-2009) differene between VAREER and GVC-REER in perentage points. Table 7 shows a deomposition of the umulative differene (between 1995 and 2009) between the VAREER and GVC-REER for selet ountries. For Australia for instane, the table shows that the differene between the VAREER and GVC-REER between 1995 and 2009 is 11.94%, implying that the Australian dollar has appreiated more by 11.9% aording to VAREER as opposed to GVC-REER. Of this differene of 11.9%, 5.73% is attributable to differenes in weighs between the two measures, and the remainder (6.2%) is attributable to differenes in pries. As is evident based on the numbers in the table, both the REER weights as well as prie indies make signifiant ontributions to the overall differenes attributable to setoral heterogeneity. An advantage of our framework is that it allows us to study the ompetitiveness of value added separately from that of gross output. Figure 6.3 shows a omparison of value added ompetitiveness (GVC-REER) and gross output ompetitiveness (Q-REER) for selet ountries. It is interesting to see that for the PRC, the GVC-REER has appreiated in a muh more pronouned fashion than the Q-REER. This reflets the fat that even as Chinese labor has beome more expensive over these years, the fall in imported input osts has been responsible for ushioning the impat of this rise in labor osts on output and gross output and exports. This patten also shows how ignoring value added omponents and looking at gross output ompetitiveness an lead to a false inferene of the Chinese urreny being undervalued. On the other hand, for the US, whih operates relatively upstream in the global value hain ompared to the PRC, the differenes between the two measures are more modest. 22

Figure 6.3 Comparison of GVC-REER and Q-REER for selet ountries 0.3 0.25 0.2 People's Republi of China GVC REER Q REER 0 0.05 0.1 Germany GVC REER Q REER 0.15 0.15 0.1 0.2 0.05 0 1995 2000 2005 2009 Spain 0.15 0.1 0.25 1995 2000 2005 2009 Frane 0 GVC REER 0.05 Q REER 0.05 0 0.05 0.1 0.15 0.2 0.1 GVC REER Q REER 1995 2000 2005 2009 Ireland 0.25 0.3 1995 2000 2005 2009 United States 0.2 0.15 0.1 GVC REER Q REER 0.15 0.1 0.05 0 0.05 0 0.05 0.1 0.15 GVC REER Q REER 0.05 1995 2000 2005 2009 0.2 1995 2000 2005 2009 Comparison of GVC-REER and Q-REER for selet ountries. GVC-REER measures value added ompetitiveness, whereas Q-REER measures ompetitiveness of gross output produed by the ountry. 23

6.3 Bilateral Real Exhange Rates The bilateral real exhange rate (RER) between ountries h and f is defined as follows: RER hf = ˆp(V ) f ˆp(V ) h (6.1) where ˆp f and ˆp h are hanges in aggregate (ountry wide) prie indies measured in a ommon urreny. Based on the the insights gained from the previous setions we argue that to measure ompetitiveness of one ountry against another in a bilateral ontext, a modified version of the GVC framework proposed in this paper provides an improvement over the standard RER measures omputed using an aggregate prie index (suh as those in Chinn, 2006) like the GDP deflator. One again, the key insight is that ignoring trade in intermediates and/or setoral heterogeneity an lead to inorret inferenes regarding movements in prie ompetitiveness. For instane, an overall inrease in GDP deflator in ountry A relative to ountry B ould indiate a depreiation or an inrease in ompetitiveness for A, even if the setors in B whih ompete more intensively with A experiene an inrease in relative pries. 12 We define our bilateral RER measure, the GVC-RER as follows Here,vi h = p(v )h i V i h m j=1 p(v )h j V h m i=1 vh i GV C RER hf = j m i=1 v h i [ m j=1 w hh ij ˆp(V ) h j + m j=1 w hf ij ˆp(V )f j ] (6.2) is the share of setor i in ountry h s total value added, so that = 1. 13 The ws are weights that are analogous to the GVC-REER weights. Figure 6.4 shows the omparison of the two RER measures for selet ountry pairs that highlight differenes between the two measures. The left panel shows that while China s real exhange rate vis-a vis the US depreiated substantially between 1998 and 2004 when measured using the standard RER measure, GVC-RER measure displays a more seular appreiation through the sample period. 14 The right panel shows that the loss in ompetitiveness for Greee (i.e an appreiation) vis a vis Germany is muh larger when measured through GVC-RER as opposed to the onventional real exhange rate measure, indiating that the standard 12 Appendix F provides a numerial example to illustrate this point 13 Bilateral gross output effetive exhange rates (Q-RER) an be defined analogously. 14 Eletrial and optial equipment (WIOD setor 14), a setor whih has seen a substantial deline in prie (over 100%) in the US through the sample period, provides a useful illustration of this divergene. While the standard RER measure gives a small weight to this setor in line with its value added share in the US eonomy, the GVC-RER measure gives a muh higher weight, reognizing the importane of this setor as far as ompetitiveness with the PRC is onerned. 24