Decomposition of Value-Added in Gross Exports:Unresolved Issues and Possible Solutions

Transcription

1 MPRA Munch Personal RePEc Archve Decomposton of Value-Added n ross Exports:Unresolved Issues and Possble Solutons Sébasten Mroudot and Mng Ye 12 December 2017 Onlne at MPRA Paper No , posted 24 Aprl :24 UTC

2 Decomposton of Value-Added n ross Exports: Unresolved Issues and Possble Solutons Sébasten Mroudot 1 and Mng Ye 2, OECD December 2017 Abstract: To better understand trade n the context of global value chans, t s mportant to have a full and explct decomposton of value-added n gross exports. Whle the decomposton proposed by Koopman, Wang and We (2014 s a frst step n ths drecton, there are stll three outstandng ssues that need to be further addressed: (1 the nature of double countng n gross exports; (2 the calculaton of the foregn value-added net of any double countng; and (3 the decomposton of gross exports at the ndustry level (the ndustry where exports take place. In ths paper, we propose a new accountng framework that addresses these dfferent ssues and clarfes the defnton of exports n nter-country nput-output (ICIO tables. It contrbutes to the lterature: ( by refnng the defnton of double-counted value-added n gross exports; ( by provdng new expressons for the foregn value-added and double-counted terms; and ( by ndcatng how the new framework can be used to decompose exports at the ndustry level. Keywords: Trade accountng, nput-output table, Value-added decomposton, lobal value chans JEL Codes: E01, E16, F14, F23, L14 1 Senor Trade Polcy Analyst, Trade n Servces Dvson, Trade and Agrculture Drectorate, Organsaton for Economc Co-operaton and Development, sebasten.mroudot@oecd.org 2 Consultant, Trade n Servces Dvson, Trade and Agrculture Drectorate, Organsaton for Economc Co-operaton and Development, mng.ye@oecd.org 1

3 The recent avalablty of nter-country nput-output (ICIO tables has created new opportuntes for analyzng the ntrcate flows of value-added that are embedded n nternatonal trade. A frst approach conssts n followng the Leontef model and lookng at the orgn of value-added n the fnal demand of countres (Johnson and Noguera, The resultng decomposton dentfes as exports of value-added the value-added contrbuted by a gven country and ndustry to fnal demand abroad. Such decomposton does not depart from the foundatons of nput-output analyss as t multples the Leontef nverse by a vector of fnal demand. It can provde results at the country level (exports of value-added to the world, blaterally (exports of value-added to a gven partner and by ndustry (but based on the ndustry of orgn of value-added n the exportng economy. A second approach, proposed by Koopman, Wang and We (KWW, 2014, ams at decomposng gross exports, whch s the basc aggregate used n trade economcs and reported by countres n ther natonal accounts and balance of payments. Ths approach has to deal wth the fact that gross exports are made both of fnal products and ntermedate goods and servces. The latter also end up n fnal products at the end of the producton process. It explans why the decomposton cannot smply be the multplcaton of the Leontef nverse by a vector of gross exports and why there s some double countng as some of the ntermedate goods and servces exported can also be part of the value of exports of fnal products n the case of vertcal specalzaton trade. However, t s also possble to use the Leontef model and nput-output relatonshps to derve mathematcal expressons for the value-added emboded n gross exports, as t s done by KWW. In a comment, Los, Tmmer and de Vres (LTV, 2016 provde an alternatve decomposton based on hypothetcal extracton where the domestc value-added n exports s expressed n a way fully consstent wth the Leontef model. But despte the sound theoretcal support provded to the concept of domestc value-added n exports, the comment by LTV has left unanswered the queston of the 2

4 calculaton of the foregn value-added n exports. 3 And beyond the domestc and foregn value-added consstent wth value-added measured n DP, gross exports are also made of value-added that has already been accounted for before n the domestc and foregn value-added and therefore corresponds to some double countng. The KWW framework ntroduces pure double counted terms (correspondng to term 6 and term 9 n ther decomposton. These terms multply by a coeffcent the gross exports of the exportng economy (domestc term and the exports of partner countres (foregn term. They are ndcated as not beng part of the DP of any country (KWW, p. 469 and related to two-way ntermedate trade from all blateral routes (KWW, p There s no consensus at ths stage on how to calculate the domestc and foregn double countng, leavng also unanswered the queston of the foregn value-added net of any double countng. Three recent papers n partcular queston the KWW result. Nagengast and Stehrer (2016 argue that there s some arbtrarness n the decomposton of ntermedate and fnal gross exports n KWW and that they do not correctly dentfy multple border crossngs. Nagengast and Stehrer propose an alternatve decomposton for the domestc value-added n exports (terms 1, 2 and 3 of KWW but do not explore further the mplcatons for double countng and the foregn value-added, as the focus of ther paper s on blateral gross exports and trade balances. However, they ntroduce the dstncton between the source-based and snk-based approaches that lead to a dfferent double-countng n blateral gross exports. Born and Mancn (2017 also look at the decomposton of blateral gross exports and are more explct about how a defnton of double-countng as any VA that crosses the same (domestc border more than once affects the calculaton of the foregn value-added. They propose a decomposton where the foregn value-added at the aggregate level (summng across partners s the same n the source-based and snk-based approach. Ther decomposton ponts to a dfferent foregn double counted 3 The authors ndcate that t s left for future research and requres a complete decomposton of world DP. 3

5 term as compared to KWW. Lastly, Johnson (2017 also notes that KWW and LTV have not fully solved the queston of the domestc and foregn content of exports and offers addtonal nsghts on the foregn value-added n a framework smlar to Los, Tmmer and de Vres (2016. The paper only ncludes a two-country decomposton of aggregate exports but wth results departng from KWW for the foregn value-added (and foregn double countng. In ths paper, we are also nterested n provdng a decomposton of value-added n a country s gross exports, leavng asde the blateral decomposton. As emphaszed by LTV, we also beleve that such decomposton should be consstent wth the foundatons of nput-output analyss. Moreover, from our pont of vew, the decomposton of the foregn value-added terms should be symmetrc wth the domestc ones, snce the foregn value-added n the exports of a gven country s domestc value-added n the exports of another. For nstance, n the decomposton framework, there should be terms to dentfy the foregn value-added that returns to the exportng country, smlar to the terms ndcatng the domestc value-added that returns home. In addton to ths dscusson on the measurement of the foregn value-added n aggregate exports, nether the KWW framework nor the hypothetcal extracton method can be easly extended to decompose the value-added n gross exports at the ndustry level. Here, t s mportant to specfy the ndustry from the pont of whch value-added s measured. There are (at least 3 ndustry dmensons n the gross exports decomposton: the source ndustry (.e. the ndustry of orgn of prmary nputs used to generate the value-added n exports, the gross exports ndustry (.e. the ndustry that has produced the gross exports whch are decomposed nto dfferent value-added terms and the fnal demand ndustry (.e. the last ndustry usng the value-added dentfed n exports before fnal consumpton. 4 4 More ndustres can be nvolved when the ntermedate nputs exported are further processed n dfferent ndustres across countres before beng ncorporated nto a fnal product. The ncorporaton n the fnal product can take place ether n the last exportng economy or n the mportng country 4

6 A decomposton of gross exports at the ndustry level means that the startng pont of the decomposton s the value of gross exports for a specfc ndustry (and country,.e. the exports ndustry. In an extenson of KWW to the ndustry level, Wang, We and Zhu (WWZ, 2013 pont out that there s an addtonal layer of complexty when decomposng ndustry-level gross exports. Instead of 9 terms, ther decomposton has to rely on 16 terms to cover all the complex nter-ndustry nteractons across countres n the ICIO. For the hypothetcal extracton method as well, whle t s possble to calculate an hypothetcal DP where only the exports of a sngle ndustry are removed, the dfferent terms of the LTV framework are also not easly obtaned at the ndustry level. Therefore, there s also a need to better explan how the results of the trade n value-added lterature can be derved for specfc ndustres. In ths paper, we explore some solutons to the ssues mentoned above. We frst clarfy the relatonshp between gross exports and fnal demand n the nter-country nput-output framework and how we can express the domestc and foregn value-added n exports n some new nput-output framework focusng on gross exports rather than gross output. Then, we use the hosh nsght to provde a more straghtforward decomposton of gross exports that gves the ntal domestc value-added, frst round foregn value-added and later rounds double counted value-added n a consstent nput-output framework. Ths decomposton s fully consstent wth the one that s derved from the Leontef model. It provdes a domestc value-added n exports equal to KWW and LTV but new foregn value-added terms whch are dfferent from KWW. Fnally, we show how ths framework can accommodate analyss at the ndustry level. The paper s organzed as follows. In secton I, we ntroduce an alternatve mathematcal framework to clarfy the relatonshp between gross exports and fnal demand n the ICIO model and explan how t can be used to express the domestc and foregn value-added n exports (consstent wth DP and net of any double countng. In secton II, we use the hosh nsght to defne value-added trade flows and ( transtng through dfferent domestc ndustres. 5

7 decompose gross exports nto domestc value-added, foregn value-added and double counted terms. In secton III, we explan how our decomposton dffers from KWW and how t can be extended to provde terms smlar to ther framework that dstngushes ntermedates from fnal products, as well as the country of absorpton of value-added. Secton IV deals wth the extenson of the framework to the ndustry level. Secton V concludes. I. Clarfyng the relatonshp between gross exports and fnal demand n nter-country nput-output tables The nput-output model comes from the work of Leontef (1936 who demonstrated that the amount and type of ntermedate nputs needed n the producton of one unt of output can be estmated based on the nput-output (IO structure across ndustres. The model allows tracng gross output n all stages of producton needed to produce one unt of fnal goods (or servces 5. When the gross output flows assocated wth a partcular level of fnal demand are known, the value-added generated and traded can smply be derved by multplyng these flows wth the value added to gross output rato n each ndustry. In the IO table, all gross output must be used ether as an ntermedate or a fnal good, X AX Y (1 where, X s the N 1 gross output vector, Y s the N 1 fnal demand vector, and A s the N N IO coeffcents matrx. A. The nput-output framework for exports If we splt the output n the ICIO table nto exports (E and domestc sales (H, the F F followng accountng equatons can be obtaned: E A ( E H Y and D D H A ( E H Y, where D A s a matrx of the domestc coeffcents n the global 5 We use the expresson goods n a generc way. Input-output tables cover all types of products or ndustres,.e. goods and servces. 6

8 ICIO table (.e. the block dagonal of the A matrx and F A s the export matrx (the elements of the A matrx off the block dagonal ncludng the IO coeffcents for the use of ntermedate nputs from one country nto another country, so that we have D F A A A. D Y s the domestc fnal demand and F Y s the foregn fnal demand, so that D F Y Y Y. After re-arrangement (see Appendx A, the accountng relatonshp between gross exports and the fnal demand n destnaton countres n the ICIO model can be expressed as: E AE Y (2 wth F D Y Y AY and A A I A F D 1 (. Equaton (2 s to gross exports what equaton (1 s to gross output. It suggests a dfferent type of nput-output table where gross exports have replaced gross output. 6 Conceptually, we have a new type of Leontef matrx A and a new fnal demand Y wth nterpretatons smlar to the orgnal A and F but n the context of gross exports. The elements of the A matrx descrbe the unts of ntermedate goods produced and exported that are used n the producton of one unt of exports n the destnaton country. For example, the element A j means that n order to produce one unt of exports n country j, country needs to produce A j unts of ntermedate goods that are shpped to j and emboded n exports of j. AE j j ndcates country s ntermedate nputs used n country j s exports. Therefore, we can call A the drect nputs requrement matrx for exports. The term AE j j also corresponds to the vertcal specalzaton (VS exports as defned n Hummels, Ish and Y ( Another way of ntroducng equaton (2 s to thnk about the elements extracted from gross output n the hypothetcal extracton method proposed by LTV. As such, the two frameworks are consstent and they provde the same results as llustrated n Appendx B. 7

9 1 Re-arrangng equaton (2, we can also obtan equaton E BY, and B ( I A, smlar to B I A 1 ( n the tradtonal IO model. Matrx B s the total nputs requrement matrx for exports. Y s the vector of fnal demand for exports. For country, the element Y n the vector Y s smply other countres fnal demand for exports of. But snce the perspectve s the destnaton country (.e. the fnal demand n the partner country, Y ncludes both ntermedate goods and fnal goods produced n country. It combnes the demand for fnal goods F Y manufactured n (and exported as fnal goods and the demand for ntermedate goods D AY that are used to produce fnal goods n the destnaton country that are consumed domestcally. In ths case, trade n ntermedate goods takes place between country and country j but n order to produce fnal goods n j. Therefore, A E s the ntermedate demand for gross exports that covers all trade n ntermedate nputs that are further emboded n exports, whle Y s a fnal demand for gross exports combnng all trade flows n fnal goods but also trade n ntermedates that are drectly used to produce fnal goods n the partner country. Intermedate and fnal are defned from the pont of vew of the partner country n exports. If we extend the expresson E exports of country can be decomposed as follows: BY to the countres and N ndustres case, (3 E B Y B Y B Y ( B I Y t tj j jj t t t jt, j t In ths equaton, each term clarfes what s the destnaton of country 's exports and whether exports are for ntermedate or fnal use. Subscrpt j ndcates n ths case country s ultmate export destnaton. Term 1 and term 2 correspond to country s exports of goods to country j that are fnally absorbed by country j. Term 1 descrbes 8

10 the goods exported by (ntermedate or fnal and absorbed by j as fnal goods. These goods can be frst exported as ntermedates to a thrd-country before comng as fnal goods n j. Term 2 ndcates the ntermedate goods from country that are exported and processed n country j nto fnal goods before beng absorbed by country j. Agan, they can transt through dfferent countres to be further processed before reachng j, whch s the ultmate destnaton. But they reach j as ntermedate goods. The next two terms are about exports of nputs that come back to country (after transtng through one or several other countres. Term 3 ndcates the exports from country that fnally return back to country as fnal goods (and drectly absorbed by country whle term 4 descrbes the exports from country that come back to country as ntermedate goods and are processed n country nto fnal goods before beng absorbed. B. How to measure the domestc value-added n exports In addton to the drect nputs requrement matrx for exports and total nputs requrement matrx for exports, we can also derve a concept smlar to the value-added rato n our IO framework for exports. We call t V, the exports value-added multpler. Theorem 1: For country s exports, the domestc value-added multpler coeffcent s V u( I A V ( I A 1 j. j Here, we defne V u[ I A A ] as a 1 N drect value-added coeffcent vector j j n the IO table and u s a 1 N unty vector. Each element of V gves the share of drect domestc value-added n total output. Accordngly, when workng wth the new matrx A, we can see that n country s exports E, all of ntermedate nputs are j AE. Therefore, country s value-added j 9

11 n exports s u VaE( u( E A E. The domestc value-added multpler j j coeffcent s V u( I A V ( I A j j 1. Ths s equal to one mnus the ntermedate nput share from all countres (ncludng domestcally produced ntermedates. The domestc value-added n country can be expressed as: uvae( V E V ( I A E. Ths expresson s consstent wth KWW and LTV 1 (more detals after and n Appendx A. To better understand the domestc value-added multpler, we can deduce the consstent expresson for the domestc value-added (or DP from the ntal ICIO model. In the ICIO model, country s gross output can be wrtten as: Rearrangng equaton (4, we get: X A X Y A X Y A X Y E j j j j j (4 X ( I A Y ( I A E (5 1 1 Matrx ( I s sometmes called the local Leontef nverse n the ICIO model. 1 A From there, country s value-added (or DP can be calculated as follows: VA ( DP V X V ( I A Y V ( I A E (6 1 1 Accordng to equaton (6, country s value-added (or DP s dvded nto two parts: one part s the value-added n country s fnal demand and the other part V ( I A E s the value-added n exports of country. From there, we can also get 1 the expresson of the domestc value-added n exports whch s consstent wth the dscusson before, and regard V ( I as the value-added multpler coeffcent 1 A for a country s exports. C. How to measure the foregn value-added n exports The next ssue s how to measure the foregn value-added n exports. From the above analyss, we already know that AE j are the ntermedate nputs exported from 10

12 country j to country and used n country s exports. Therefore, f we want to measure country j s value-added n country s exports, we can just multply ths expresson by the value-added multpler coeffcent: V ( I A A E. The same 1 j jj j expresson can also be derved from the ntal ICIO model. Smlarly, we can express country j s value-added (DP as: VA ( DP V X V ( I A Y V ( I A E. Meanwhle, we have country j s 1 1 j j j j j jj jj j jj j exports equal to: E E E. Therefore, country j s value-added (or DP j j js s, j exported nto country s V ( I A E 1 j jj j. We can then expand the blateral exports expresson from j to as follows: E A X Y A ( I ( I A A E A ( I A Y Y 1 1 j j j j j j A E A Y Y j j j (7 In ths expresson, country j s value-added exported to country, V ( I A E 1 j jj j, can be dvded nto 3 parts: V ( I A A E, 1 j jj j V ( I A A Y and 1 j jj j V ( I A Y. 7 1 j jj j And these parts can be descrbed as: country j s value-added (or DP n country s 1 exports ( V ( I A A E, country j s value-added entered nto country as part of j jj j 1 an ntermedate good, processed and absorbed by country ( V ( I A A Y, and j jj j country j s value-added entered nto country as part of a fnal good and then 1 absorbed by country drectly ( V ( I A Y j jj j. If we sum up the value-added from all countres, except country, n country s exports, we obtan the foregn 7 Ths decomposton s smlar to what Johnson (2017 develops for two countres n the supplemental appendx of hs paper. These terms lnk value-added n exports to an overall decomposton of DP along the lnes suggested by LTV but left for future research. Ths decomposton s also what dstngushes our results from other papers that unlke Johnson (2017 follow the orgnal KWW framework where the startng pont s exports rather than DP and where value-added n ntermedate or fnal exports s defned from the pont of vew of the exportng economy rather than the destnaton country. 11

13 value-added n country s exports, expressed as 1 Vj ( I Ajj AjE. j II. Tracng value-added and double countng n gross exports: the hosh nsght The prevous secton has already provded an expresson for the domestc and foregn value-added n gross exports. Now we need to gve a full decomposton of gross exports and deal wth the ssue of the double countng. Because ntermedate nputs can travel several tmes across countres before beng ncorporated nto fnal products and come back to ther source country before beng exported agan, the sum of the domestc and foregn value-added as defned above s dfferent from gross exports. ross exports nclude some double countng n the sense that the same value-added (already defned as domestc or foregn s counted twce or more. As a frst approach, the double countng s the dfference between gross exports and the domestc and foregn value-added consstent wth the DP of countres (where prmary factors of producton cannot contrbute two tmes to the same value. KWW refer to some pure double countng because any foregn value-added s n a way already double counted n gross exports statstcs. The foregn value-added of one country n the exports of another s also domestc value-added n the exports of ths country. Also, the domestc value-added that returns home (but wthout beng ncorporated n exports agan s part of the double countng n trade statstcs. But any concept of double countng s relatve to the aggregate to whch t s appled. Therefore, when workng wth the gross exports of a specfc country, t seems reasonable to dentfy a domestc and foregn value-added consstent wth DP (both n the domestc economy and n foregn countres and a resdual called double countng whch s splt nto a domestc and foregn part. But stll we need some explanaton and economc nterpretaton for ths resdual and why we regard t as double countng. 12

14 The objectve n ths secton s to provde explct expressons for the domestc, foregn and double counted value-added terms n gross exports, but also an nterpretaton based on the hosh nsght. hosh (1958 has ntroduced what s known as the supply drven nput-output model, where value-added s the exogenously specfed drvng force n the framework. As the hosh model descrbes the generaton of value-added n successve rounds, t seems more approprate to trace flows of value-added n exports. There are some debates n the nput-output lterature on the nterpretaton and plausblty of the hosh model (Oosterhaven, 1988; Detzenbacher, However, the way we use t n ths secton does not depend on these debates, as we are dscussng an accountng framework for the decomposton of gross exports and not an economc model where we have to dentfy exogenous and endogenous varables. In the hosh framework, output coeffcents are defned as l x / x. An output j j coeffcent gves the percentage of output of ndustry that s sold to ndustry j. The accountng equaton can be rewrtten as: T T T X VA X L VA (8 where I L 1 ( s the hosh nverse; meanwhle, n ˆ ˆ, ˆX s a 1 X BX N N dagonal matrx wth output on the dagonal. Transposng the model to the export ICIO table descrbed n Secton II, exports can be wrtten as T T T T E VaE E L VaE. Here ˆ ˆ 1 E BE, L ˆ ˆ 1 E AE and ˆ 1 L ˆ j E Aj E j. L j measures the share of country s output n country j s exports. To llustrate the relatonshp between exports and value-added, we can refer to the Taylor expanson: E VaE I L L L T T 2 3 ( (9 As before, we use the tradtonal concepts of nput-output analyss lnkng output and value-added, transposed to the relatonshp between gross exports and value-added. The export value T E can be decomposed nto dfferent rounds where value s added. 13

15 In partcular, we can dstngush three value-added nputs: an ntal nput T VaE, a drect nput T VaE L n the frst round and ndrect nputs n subsequent rounds amountng to T 2 3 VaE ( L L. We can gve the full expresson for the specfc exports of country as follows: T T T T E VaE( VaE( L VaE( j L j j T VaE( [ L] VaE( [ L] 2 T 3 2 T 3 j j j T VaE( j [ L] VaE( j [ L] j The above expresson provdes an explct nterpretaton of the decomposton of gross exports (ncludng the double countng n an nput-output context, followng the hosh nsght. The ntal effect s country s value-added n exports, whch s equal to T T VaE( u V ( I A E. Ths term s the domestc value-added n exports 1 (consstent wth DP and we call t ntal domestc value-added as a reference to the hosh framework but also to make t clear that t s the frst tme ths value s generated and that subsequently t can be double counted because t comes back n later rounds n the producton process. For smplcty (and to follow KWW and LTV, we wll just call t domestc value-added n the rest of the paper. 8 In the frst round, the drect effect can be dvded nto two parts, the effect from the (10 domestc country and from the foregn country j. Because L s equal to 0, we have VaE( T L 0. We are left only wth the effect from country j. Snce the foregn value-added s n the ntermedate goods mported from country j, ths term s equal to: 8 Whle we are not dealng wth the decomposton of blateral exports n ths paper, t should be noted that a blateral domestc value-added can be calculated by smply replacng E by blateral exports E j. It would be what Nagengast and Stehrer (2016 descrbe as a source-based approach. All the subsequent terms descrbed n ths secton can be derved at the blateral level the same way as they all nclude E. 14

16 T T 1 ˆ ˆ 1 1 VaE( j Lju Vj ( I Ajj E j E j AjE Vj ( I Ajj AjE j j j (11 whch s the foregn value-added n exports. We can therefore call t frst round foregn value-added (and wll refer to t smply as foregn value-added n exports. It should be noted that the ntal and frst rounds already provde the domestc and foregn value-added n exports, consstent wth DP and net of any double-countng. From equaton (10, we have derved the same equatons as n Secton I. They are not dependent on the hosh framework snce they were prevously derved from the Leontef model. But the hosh nsght offers an nterpretaton for the resdual or why we have further value-added n gross exports and why we can reasonably call t double countng. Snce the ntal and frst rounds have already exhausted the domestc and foregn value-added n country 's exports, what we measure as domestc value-added and foregn value-added n the later rounds of equaton (10, when contnung the Taylor expanson, s somethng that was already measured n the ntal and frst rounds and s comng back. In the second round, the addtonal value-added can also be dvded nto a domestc part and a foregn part. It ncludes the value-added passed over from country s exports to foregn countres whch has returned back home before beng exported agan. In ths domestc part, country s value-added s VaE( T T Lk Lku and k reflects country s value-added VaE( T L u T that has propagated to country k before k comng back home. Ths value-added has already been measured n the ntal round, so t s part of the domestc double countng. We have T 2 T T T ( [ ] ( k k k VaE L u VaE L L u 1 ˆ ˆ 1 ˆ ˆ 1 1 ( k k k k ( k k k k V I A E E A E E A E V I A A A E (12 For the foregn part of the second round, country j s value-added s 15

17 VaE( j T T LjkLku, correspondng to country j s value-added VaE( j T T jk k L u that has propagated to country k before comng back to country. Ths value-added has also already been counted n the frst round, so t s part of the foregn double counted term. We have: j T 2 T T T ( [ ] j ( jk k k VaE j L u VaE j L L u 1 ˆ ˆ 1 ˆ ˆ 1 1 j ( jj j j jk k k k j ( jj jk k k k V I A E E A E E A E V I A A A E (13 Therefore, n the second round, the foregn double counted value-added s: j 1 j ( jj jk k k V I A A A E. Summng up all the domestc double counted value-added (from the second and later rounds, we can obtan an expresson for the full domestc double countng n gross exports: VaE( [ L] u VaE( [ L] u T 2 T T 3 T 1 1 ( ( j j j jk k ( ( j k j V I A A A A A A E V I A B I E (14 Theorem 2: The domestc double counted value-added n ths framework s equal to the pure domestc double counted term n KWW (see proof n Appendx A. 1 1 ( ( j j ( j V I A B I E V B A I A E The dervaton we propose confrms the KWW result for the domestc double countng (the double counted ntermedate exports produced at home part of the pure double counted terms. However, the hosh nsght explans how ths double countng s bult through successve rounds of value-added nputs. Smlarly, the foregn double counted value-added n gross exports s (summng the second and later rounds: 16

18 j T 2 T T 3 j j T j VaE( j [ L] u VaE( j [ L] u 1 1 Vj ( I Ajj ( AjkAk AjkAktA t E V j ( I Ajj ( B j Aj E j k t k j We can also show that n ths decomposton of gross exports, the sum of the ntal domestc value added and later rounds double counted domestc value-added s equal to the domestc content of exports: 1 1 ( ( ( (15 V I A E V I A B I E V B E (16 Also, the sum of the frst round foregn value-added and later rounds double counted foregn value added n gross exports s equal to the foregn content of exports: 1 1 Vj ( I A jj AjE Vj ( I Ajj ( Bj Aj E VjBjE j j j (17 III. The value-added decomposton of gross exports: addtonal terms and comparson wth KWW In the KWW decomposton of gross exports, the domestc value-added and foregn value-added are decomposed nto further terms (a total of 9. Our decomposton can also provde smlar terms f one s nterested n dstngushng the domestc and foregn value-added mported va ntermedate or fnal goods, or the value-added that returns home. Mergng equatons (3, (16 and (17, we can obtan the terms detaled n the table below: Table 1. A 10-term decomposton of gross exports Terms Domestc value-added absorbed by foregn countres n fnal mports (T1 Domestc value-added absorbed by foregn countres n ntermedate mports (T2 Domestc value-added that returns home va fnal mports (T3 1 ( t tj t jt, V I A B Y 1 ( j jj j V I A B Y 1 ( j j j V I A B Y 17

19 Domestc value-added that returns home va ntermedate mports (T4 Domestc double counted value-added (T5 Foregn value-added absorbed by foregn countres n fnal mports (T6 Foregn value-added absorbed by foregn countres n ntermedate mports (T7 Foregn value-added that returns va fnal mports (T8 Foregn value-added that returns va ntermedate mports (T9 Foregn double counted value-added (T10 V I A B I Y 1 ( ( V I A B I E 1 ( ( 1 Vj ( I Ajj Aj BtYtk j t k t, j 1 j ( jj j k kk k j V I A A B Y 1 j ( jj j t t t j j V I A A B Y V I A A B I Y 1 j ( jj j ( V I A B A E 1 j ( jj ( j j As compared to the KWW decomposton, there are two dfferences n the above table. Frst, the domestc terms are defned slghtly dfferently because our perspectve s not the same when dentfyng ntermedate and fnal trade flows. The KWW decomposton s motvated by how often value-added crosses nternatonal borders. More specfcally, V B Y s the value-added n country 's fnal exports; j j V B Y s the value-added n country 's ntermedate exports used by the drect j jj j mporter to produce fnal goods consumed by the drect mporter; and V B Y j js j s, j s the value-added n country 's ntermedate exports used by the drect mporter to produce fnal goods for thrd countres. In contrast, the decomposton n our framework s based on the destnaton country. Fnal or ntermedate flows are defned relatve to the mportng economy. The two approaches reman nonetheless consstent 18

20 on the domestc sde. 9 We can show below that the formulas are the same f we consder the domestc value-added absorbed by other countres, the domestc value-added that returns home and the domestc double counted value-added (addtonal proof n Appendx A. 1 Domestc value-added absorbed by other countres: 1 ( t tj j j jk t jt, j j k, j V I A B Y V B Y V B Y When t=, we have 1 ( j j j j ; V I A B Y V B Y 1 ( j jj j jj j j V I A B Y V B Y 2 Domestc value-added that returns home: 1 ( j j j j j j V I A B Y V B Y 1 1 ( ( j j ( j V I A B I Y V B A I A Y 3 Domestc double counted value-added: 1 1 ( ( j j ( j V I A B I E V B A I A E When t comes to the foregn value-added n exports, two new terms emerge n our decomposton related to the foregn value-added that returns back to the exportng country I (where t s absorbed. These terms provde a full symmetry between the analyss of the domestc value-added and foregn value-added n our gross exports decomposton. In the KWW framework, we can assume that these terms are part of the foregn value added n fnal goods exports and the foregn value added n 9 Referrng to Fgure 1 n KWW, T1 n Table 1 s equal to (1 DV n drect fnal goods exports and (3 DV n ntermedates re-exported to thrd countres n KWW, whle T2 s equal to (2 DV n ntermedates absorbed by drect exporters. In our destnaton country framework, the thrd term of KWW corresponds to value added enterng the last country as a fnal product and s therefore smlar to the frst term. But we have the same sum for the three frst terms descrbng the value-added absorbed by other countres (see Appendx B for an emprcal llustraton. 19

21 ntermedate gross exports snce unlke what they do for the domestc value-added, the authors do not specfcally dentfy the foregn value added that returns to the exportng economy. Beyond dfferences n the defnton of the foregn value added terms, our framework does not provde the same foregn double countng (and therefore not the same foregn value added net of any double countng. It s a more fundamental dfference and not related to the hosh nsght and our 10-term decomposton. Already n Secton I, we have defned the domestc value-added n exports consstent wth DP and the foregn value-added n exports consstent wth DP. The dfference between these two terms and gross exports s by defnton the double countng. Summng the domestc and foregn double counted terms n KWW does not provde ths double countng as defned n Secton I. And snce we have exactly the same domestc double countng, the foregn double countng s the reason why t s not the case. An llustraton of these dfferences can be found n Appendx B where the gross exports of 6 countres n 2014 are decomposed accordng to the dfferent methodologes revewed. IV. From country-level to ndustry-level analyss: the source, gross export and fnal demand ndustry dmenson In order to extend the gross exports decomposton to the ndustry level, we need frst to clarfy what are the source ndustry, gross exports ndustry and fnal demand ndustry n the nput-output framework and ts gross exports verson. The source and gross exports ndustres are smlar to the concepts of forward lnkages and backward lnkages ntroduced by Wang, We and Zhu (2013 n the paper that transposes to the ndustry level the KWW method. The source ndustry decomposton s about measurng the value-added orgnatng n a specfc sector whle the gross exports ndustry decomposton ams at measurng the value-added (domestc or foregn n a specfc exportng ndustry. The exportng ndustry reles on value-added from all other (source ndustres n the domestc economy and foregn countres supplyng 20

22 nputs. As for the fnal demand ndustry decomposton, the objectve s to measure the value-added absorbed by a specfc sector (.e. the ndustry of the fnal product whch s mported or manufactured wth mported nputs. Ths later approach s not commonly used n the lterature but could also be nterestng from an analytcal pont of vew to analyze value-added trade flows related to specfc fnal products. The source ndustry approach s the one followed by Johnson and Noguera (2012 n the calculaton of the sectoral VAX rato 10, whle the gross exports ndustry decomposton s the purpose of the WWZ paper. In the gross exports ndustry decomposton, all terms sum to the sectoral exports of a specfc country. In ths secton, we frst show how we can decompose gross exports by ndustry n a smlar way to the approach we have suggested at the country level n Secton I. Then, we llustrate how the same can be done for possbly all terms presented n Table 1. The process s more tedous but there s no partcular dffculty once one has clearly dentfed the ndustry dmenson (source, exports or fnal demand n the equatons. From Secton I, we know that the (ntal domestc value-added n gross exports can be expressed as V ( I A E. For the convenence of wrtng, we denote the local 1 Leontef nverse matrx ( I as L. The subscrpt means country. To better 1 A explan the value-added generaton at the ndustry level, we ntroduce a sectoral superscrpt. At the ndustry level, country s value added n exports can be expressed wth the local Leontef nverse as follows: 10 VAX s defned by Johnson and Noguera as the rato of value-added to gross exports. 21

23 Vˆ L Eˆ n 1 v 0 0 l l l e n 2 0 v 0 0 l l l 0 e 0 0 n n1 n2 nn n 0 0 v l l l 0 0 e n n v l e v l e v l e n n v l e v l e v l e n n1 1 n n2 2 n nn n v l e v l e v l e (18 The matrx n equaton (18 provdes estmates of domestc value-added n exports by ndustry. Each element n the matrx accounts for the value-added from a source ndustry drectly or ndrectly emboded n the exports of a specfc ndustry. In ths matrx, the values along the rows ndcate the dstrbuton of value-added orgnatng from a specfc ndustry across all sectors. Therefore, summng up the sth row of the matrx, we can have total value-added orgnatng from country s sth sector n country s exports. In other words, we have the source ndustry value-added s s1 1 s2 2 sn n decomposton whch can be expressed mathematcally as v ( l e l e l e. In the same matrx but along the columns, we have the dstrbuton of value-added from all ndustres to the exports of a specfc ndustry. Summng up all the elements n the hth column, ( v h h n nh h l v l v l e, provdes the total domestc value-added n the gross exports ndustry. To put t n a nutshell, the sum of the Vˆ L E ˆ matrx across columns along a row 22 traces the forward lnkages across all downstream sectors from a supply-sde perspectve and provdes the source ndustry decomposton. And the sum of the Vˆ L E ˆ matrx across rows along a column traces backward lnkages across upstream sectors from a users perspectve and provdes the gross exports ndustry decomposton. If we apply smlar matrx arrangements nto the other terms n equatons (16 and (17, we can obtan an ndustry-level decomposton of gross exports smlar to the one descrbed at the country level. When consderng the destnaton of exports, the ndustry-level extenson s more

24 tedous but straghtforward. We can llustrate ths wth term 1 and term 6 n Table 1, as an example. Assumng that domestc value-added from country s gong to country t before beng fnally absorbed by country j, we can expand the elements n the expresson V ( I A B Y as Vˆ L B Y ˆ. For the elements n the matrx above, 1 t tj t tj we have the unversal expresson v l b s sh hf f t tj y where superscrpts s, h and f dentfy respectvely the source, gross exports and fnal demand ndustres. Therefore, f we extend the decomposton term n the source ndustry dmenson (country s sth ndustry, the other two dmensons have to be summed up. The equaton becomes h f v l b y s sh hf f t tj. In contrast, the extenson to the gross exports decomposton (country s hth ndustry s s sh hf f v l bt ytj and the extenson to the fnal demand s f decomposton s sh hf f v l bt ytj (country j s fth ndustry. s h Smlarly, we can also decompose country s frst round foregn value-added by ndustry. We ntroduce superscrpt m for the ndustry n country that mports from country j. The expresson s sm mh hf f v jl j a j bt y tk s the value-added flow from country j to country that goes through country t before beng fnally absorbed by country k. Country s foregn value-added (from country j n exports s m h f v l a b y s sm mh hf f j j j t tk n the source ndustry decomposton (the value-added from country j s sth ndustry. It becomes s sm mh hf f v jl j a j bt ytk n the gross exports ndustry dmenson (country s m f s hth ndustry and s sm mh hf f v jl j a j bt ytk n the fnal demand ndustry s m h decomposton (country k s fth ndustry. For the later rounds double counted terms, the ndustry expanson s a bt dfferent. In Secton II, we have derved these terms from the hosh nsght. If we wrte 23

25 V I A B I E as Vˆ L ( B I Eˆ, the elements n the matrx can be expressed 1 ( ( as: v s l sm ( b mh e h, Here, s equal to 1 when m h, and 0 otherwse. In ths ndustry level expresson, the element mh b ndcates how value-added has returned home (.e. been re-mported and been re-exported agan. Superscrpt m also defnes the mport sector of the returned domestc value-added. Therefore, for country s domestc later rounds double counted value added, the formula n the source ndustry (country s sth ndustry decomposton s v l ( b e m h s sm mh h ; and the formula n the gross exports ndustry (country s hth ndustry decomposton s s m v l ( b e s sm mh h. Also, we can obtan smlar ndustry-level expressons for the foregn later rounds double counted value added as v l ( b a e j m h s sm mh mh h j j j j (source ndustry or v s sm ( mh mh h jl j bj a j e (gross exports ndustry. j s m The KWW framework can also provde a source ndustry decomposton and a fnal demand ndustry decomposton n a consstent way by followng the same logc (the gross exports ndustry decomposton beng explaned n WWZ. As soon as the source, gross exports and fnal demand ndustres are clearly dentfed, t s straghtforward to derve ndustry-level formulas. But the more sophstcated and detaled the gross exports decomposton s, the more complcated t becomes to track the dfferent ndustry dmensons. As an llustraton, we provde below the full expanson of our 10-term decomposton n Table 1 at the gross exports ndustry level. Country s gross exports n ndustry h can be decomposed as: 24

26 e v l b y v l b y h s sh hf f s sh hf f t tj j jj t jt, s f j s f v l b y v l ( b y s sh hf f s sh hf f j j j s f s f s m v l ( b e s sm mh h j t k t, s m f v l a b y v l a b y s sm mh hf f s sm mh hf f j j j t tk j j j k kk j k s m f v l a b y v l a ( b y s sm mh hf f s sm mh hf f j j j t t j j j j t s m f j s m f j s m v l ( b a e s sm mh mh h j j j j (19 Here, s equal to 1 when h f and 0 otherwse. For sub-term s sm mh h v l ( b e, s equal to 1 when m h and 0 otherwse. s m V. Concludng remarks Ths paper has ntroduced a new framework for the decomposton of value-added n gross exports that has a frm foundaton n nput-output analyss and provdes terms wth a clear economc nterpretaton, ncludng for the double counted elements. It confrms the results of earler lterature for the decomposton of the domestc value-added n exports but brngs new results for the foregn value-added and the foregn double countng. The startng pont s a renterpretaton of the nput-output model n terms of a relatonshp between gross exports and ntermedate and fnal demand for exports n the destnaton country. Usng the hosh nsght, the framework allows to fully decompose gross exports nto an ntal domestc value-added consstent wth DP, a frst round foregn value-added also consstent wth DP and later rounds domestc and foregn double counted terms that account for some value-added comng back to the exportng economy and enterng agan nto exports. The generaton of ths multple countng n successve rounds of value addton s explct n the hosh framework but the ntal domestc value-added and frst round foregn value-added do not depend on the hosh nsght. 25

27 The domestc and foregn value-added can be further decomposed to dstngush, for example, the value-added that returns home (before beng absorbed n the domestc economy or whether value-added s enterng the destnaton country va a fnal or ntermedate product. Such dstnctons, as ntroduced by KWW, can be useful for trade economcs or polcymakng. But we beleve t s mportant to have some symmetry n the domestc and foregn terms. For example, the foregn value-added that returns to the country where t was frst emboded n exports s nterestng to dentfy some crcular trade. Also, t seems more practcal to use a destnaton country perspectve n the gross exports decomposton to avod some overlap n the terms. When the global Leontef nverse s ntroduced n a term, value-added can cross borders several tmes before beng absorbed abroad or returnng back, transtng through dfferent countres and leadng to ambguous nterpretatons wth respect to flows of fnal or ntermedate goods. Fnally, also havng n mnd the popularty of trade n value-added ndcators among economsts and polcymakers, t seems mportant to provde ndustry-level formulas for the decomposton of gross exports. It requres a careful analyss of the ndustry dmenson n nput-output relatonshps and n partcular to clearly dstngush the source ndustry, the gross exports ndustry and the fnal demand ndustry. We show that our framework can be extended to decompose the value-added n gross exports of a specfc ndustry but also to track the value-added orgnatng n a specfc ndustry or endng up n the fnal products of a specfc ndustry. But t s not a feature specfc to ths framework and can be done for other decompostons of gross exports proposed n the lterature. 26

28 References Born, Alessandro, and Mchele Mancn Follow the Value Added: Trackng Blateral Relatons n lobal Value Chans. MPRA Paper, No Detzenbacher, Erk In Vndcaton of the hosh Model: A Renterpretaton as a Prce Model. Journal of Regonal Scence 37 (4: hosh, Ambca Input-Output Approach to an Allocatve System. Economca 25 (1: Hummels, Davd, Jun Ish, and Ke-Mu Y The Nature and rowth of Vertcal Specalzaton n World Trade. Journal of Internatonal Economcs 54, Johnson, Robert C Measurng lobal Value Chans. Annual Revew of Economcs, forthcomng. Johnson, Robert C., and ullermo Noguera Accountng for Intermedates: Producton Sharng and Trade n Value-added. Journal of Internatonal Economcs 86 (2: Koopman, Robert, Zh Wang, and Shang-Jn We Tracng Value-added and Double Countng n ross Exports. Amercan Economc Revew 104 (2: Leontef, Wassly Quanttatve Input and Output Relatons n the Economc System of the Unted States. The Revew of Economc and Statstcs 18: Los, Bart, Marcel P. Tmmer, and aatzen J. de Vres Tracng value-added and double countng n gross exports: Comment. Amercan Economc Revew 107 (7: Nagengast, Arne J., and Robert Stehrer Accountng for the Dfferences Between ross and Value Added Trade Balances. The World Economy 39 (9: Oosterhaven, Jan On the Plausblty of the Supply-Drven Input-Output Model. Journal of Regonal Scence 28 (2: Tmmer, Marcel P., Erk Detzenbacher, Bart Los, Robert Stehrer, and aatzen J. de Vres An Illustrated User ude to the World Input Output Database: the Case of lobal Automotve Producton. Revew of Internatonal Economcs 23: Wang, Zh, Shang-Jn We and Kunfu Zhu Quantfyng Internatonal Producton Sharng at the Blateral and Sector Levels. NBER Workng paper No

29 Appendx A Proposton 1:The accountng relatonshp between gross exports E and fnal demand n destnaton n an Inter-Country Input-Output (ICIO model can be expressed as: E AE Y Here, A A I A F D 1 (, D A s the matrx of domestc coeffcents n the global ICIO table (.e. the block dagonal matrx of the A matrx. F A s the matrx of export coeffcents (.e. the elements of the A matrx off the block dagonal that ndcate the use of ntermedate nputs from one country nto another country. In addton, F D Y Y AY, wth D Y the domestc fnal demand and F Y the fnal demand n foregn countres. Proof: Accordng to the descrpton of the matrxes above, we can obtan the followng accountng equaltes: F E A ( E H Y D H A ( E H Y wth H the vector of gross domestc shpments (and E the vector of exports. Solvng for H, we obtan: H ( I A A E ( I A Y D 1 D D 1 D Mergng the expresson for H and the expresson for E, we have: F E A ( E H Y F A E I A A E I A Y Y F D 1 D D 1 D F [ ( ( ] A [ I ( I A A ] E A ( I A Y Y F D 1 D F D 1 D F A ( I A E A ( I A Y Y F D 1 F D 1 D F AE Y F D here, we defne A A I A F D 1 (, for the elements n the matrx A, 28

30 A j 0 j 1 Aj ( I Ajj j and D F Y AY Y. 1 Proposton 2:The total nputs requrement matrx for exports B ( I A, for the elements n matrx B, B ( I A B. Proof: We can express B as j j B ( I A [ I A ( I A ] [( I A ( I A A ( I A ] 1 F D 1 1 D D 1 F D 1 1 D F D [( I A A ( I A ] D ( I A B 1 1 So for the elements n the matrx, we have B ( I A B. j j Theorem 1: For country s exports, the domestc value-added multpler coeffcent s u( I A V ( I A j j 1 Proof: Based on the defnton of A, we already know that for country s exports E, all of ntermedate nputs are j AE. uvae( u( E A E u( I A E j j j j j Expandng the equaton u( I A, we have: j j, so country s value-added n exports s 1 ( j [ j ( ] j j u I A u I A I A 1 1 [( ( j ( ] j u I A I A A I A 1 1 j j j j u( I A A ( I A u( I A ( I A V ( I A 1 29

31 Here, f we want to extend the value-added multpler coeffcent at the ndustry level, we can just transform the value-added coeffcent vector V nto a dagonal matrx V ˆ. Theorem 2: The later rounds domestc double-countng value-added term n our framework s equal to the domestc pure double countng term n the KWW framework: 1 1 ( ( j j ( j V I A B I E V B A I A E Proof: Based on the defnton of the Leontef nverse matrx n the ICIO model, we have: I A11 A12 A1 B11 B12 B1 I 0 0 A21 I A22 A 2 B21 B22 B 2 0 I 0 A 1 A 2 I A B1 B 2 B 0 0 I B11 B12 B1 I A11 A12 A1 B21 B22 B 2 A21 I A22 A 2 B1 B 2 B A 1 A 2 I A Then, we can obtan the followng two equatons: B A B B B A I k k k k k k B A B 0, j j k kj k Therefore, we already have the equaton B B A I. Re-wrtng ths equaton, we can obtan: 30 k k k B B A B B A B A B ( I A B A I j j j j j j j j j Re-arrangng the equaton above, we have:

32 j B A I A B I A I A I A B I I A B I j j ( ( ( [( ] ( (. Proposton 3.1 The sum of the ntal domestc value-added and the later rounds domestc double counted value-added are equal to the domestc content n exports. V I A E V I A B I E V B E 1 1 ( ( ( Proof: Because V ( I A E V ( I A ( B I E V ( I A B E. Then accordng to the Proposton 2, we have B ( I A B. Therefore, V ( I A E V ( I A ( B I E V ( I A B E V B E Proposton proved. Proposton 3.2 The sum of the frst round foregn value-added and the later rounds foregn double counted value-added are equal to the foregn content n export. 1 1 Vj ( I A jj AjE Vj ( I Ajj ( Bj Aj E VjBjE j j j Proof: Smlar wth Proposton 3.1. Proposton 4.1 In the decomposton framework of ths paper, for the domestc value-added absorbed by other countres, we have 1 ( t tj j j jk t jt, j j k, j V I A B Y V B Y V B Y When t=, we have 1 ( j j j j ; and V I A B Y V B Y 1 ( j jj j jj j j V I A B Y V B Y Proof: Accordng to Proposton 2, we have B ( I A B. Therefore, t t 1 ( t tj t tj t jt, t jt, V I A B Y V B Y 31