Volume 31, Issue 3. Consistency of the proposed additive measures of revealed comparative advantage

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1 Volume 31, Issue 3 Consstency of the proposed addtve measures of revealed comparatve advantage Ufuk gunes Bebek Unversty of Kent Abstract The recently proposed addtve measures of revealed comparatve advantage (RCA) have been argued as better alternatves to the Balassa Index. Ths note bulds on those suggestons and provdes a framework to assess ther applcablty by means of ther consstency across the dmensons and nferences that the ndces' nformatonal content allow. A formal emprcal nvestgaton supports the presented arguments that the proposed addtve constructs of RCA possess certan nconsstences that may obscure comparatve analyses based on them, whereas alternatve addtve measures proposed here are shown to be more consstent over space and tme, and hence may serve as better nstruments n related quanttatve research. The author wshes to acknowledge, wthout mplcatng, the comments and suggestons by Roger Vckerman, Rodney Falvey, the anonymous referee and James Warren. All remanng errors are the author's. Ctaton: Ufuk gunes Bebek, (2011) ''Consstency of the proposed addtve measures of revealed comparatve advantage'', Economcs Bulletn, Vol. 31 no.3 pp Submtted: Jun Publshed: August 30, 2011.

2 1. Introducton The law of comparatve advantage stll stands as one of the core pllars of nternatonal trade theory. Yet as relatve autarkc prces are not observable and the avalable data s lkely be n post-trade equlbra, dentfcaton of the true comparatve advantage s not feasble. Nevertheless the use of actual trade flows and ther relatve shares to construct certan ndces that would reveal comparatve advantage has become an emprcal conventon, followng the semnal paper by Balassa (1965). Whle the vast amount of the assocated lterature employs the Balassa Index (BRCA) or ts normalzed varants 1, recent studes (Hoen & Oosterhaven, 2006; Yu et al., 2009) challenge the multplcatve nature and nformatonal content of the ndex n favour of an addtve construct. Ths note bulds on those suggestons and provdes a framework to nvestgate ther applcablty. By employng Kunmoto s (1977) probablstc framework, the recently proposed addtve constructs of revealed comparatve advantage (RCA) are expressed as normalzed forms of the level devatons n actual trade flows from ther expected levels. As RCA ndces provde nference as cardnal, ordnal and dchotomous measures 2, the employed normalzaton should not alter the ntal nferences based on those level devatons, hence provde a lnear monotonc transformaton 3. Furthermore, gven that those level devatons retan varaton across ndustres, countres and tme, ther normalzaton should not alter exstng varatons across those dmenson. On the other hand, napproprate normalzaton of those devatons that dstorts ther dstrbuton would result n a based transformaton 4 makng the ndces nconsstent wth the level devatons, whch would then prevent a robust comparatve analyss. Based on these arguments, n a frst step, proposed addtve constructs of RCA are evaluated based on ther consstency wth the level devatons across the three dmensons and the three nferences that ther nformatonal content allow. In a second step, the note provdes alternatve measures that comply wth the relevant consstency arguments. A formal emprcal nvestgaton supports the presented arguments that the prevously proposed addtve constructs of RCA possess certan nconsstences, whch may obscure comparatve analyses based on them, whle proposed alternatves possess the necessary propertes for a robust comparatve analyss. The rest of the note s organzed as follows. Secton 2 ntroduces the framework n whch RCA s defned as devatons from the comparatve neutral state (expected levels). Secton 3 presents the recently proposed addtve measures of RCA and dscusses the relevant consstency ssues. In secton 4, alternatve measures are presented. Secton 5, then emprcally 1 e.g. Vollrath (1991), Dalum et al. (1998) and Proudman & Reddng (2000) 2 for an extensve dscusson please refer to Ballance et al. (1987) 3 whle a monotonc transformaton would retan the order of the RCA scores, preservng ther ntal nferences as ordnal and dchotomous measures, t should also be lnear to retan the orgnal shape of the dstrbuton hence preserve ther ntal cardnal nference. 4 that s ether non-lnear but monotonc, whch retans consstency only as ordnal and dchotomous measures or non-monotonc, whch retans consstency only as a dchotomous measure assumng that the transformaton s sgn-preservng

3 nvestgates the consstency of the pervously and presently proposed addtve measures of RCA. Secton 6 concludes. 2. RCA as Devatons from the Comparatve Neutral State Kunmoto (1977) argues that wthn a hypotheszed post-autarkc world where countres do not possess a comparatve advantage, exports of a partcular ndustry would be dstrbuted among countres n proporton to ther shares n total world exports such that, each country s expected level of exports n that partcular ndustry would be the product of the share of that ndustry wthn world trade and the country s total exports. That s E ( X j) = X z (X w j /X w z ), (1a) where subscrpt j and z, respectvely, refer to the reference and the aggregate of all traded ndustres, whle superscrpts and w, respectvely, represent the examned country and the world and X stands for the export flows. Hence, n a dstorton free world, the equvalence of the expected level of exports wth the actual level of exports would ndcate a neutral comparatve advantage. That s E ( X j) = X z (X w j /X w z ) = X j. (1b) On the other hand, f the actual level of exports exceeds (falls behnd) the expected level, then the country would have a comparatve advantage (dsadvantage) n that partcular ndustry. Thus the devatons n the actual level of exports from ther expected levels would ndcate the comparatve state of the country n that partcular ndustry. If the extent of the devaton s represented as a fracton of the expected level of exports, then one would express BRCA as a rato of actual level of exports to ther expected levels. That s BRCA j = X j E(X j ) = ( X j /X z) ( X w j /X w z ). (1c) Such a formulaton of BRCA comples wth both Kunmoto s framework and Balassa s ratonale snce ndex values greater (smaller) than 1 would ndcate a comparatve advantage (dsadvantage), whereas at the comparatve neutral state as ndcated by the ndex value of 1, devatons from the expected export levels are zero. Alternatvely, devatons of actual level of exports from ther expected levels can be expressed n levels. That s E ( ) [ = E ( ) ]. (2) Once agan, f the actual level of exports exceeds (falls behnd) the expected level, then the country would have a comparatve advantage (dsadvantage) n that partcular ndustry. However unlke BRCA, although the comparatve neutral state corresponds to zero devatons from the expected level of exports, t wll be prevaled as 0. Although equaton (2) may be

4 employed n a smlar fashon as BRCA, t needs to be normalzed over a sensble range snce the sze of E ( X j) wll be n levels dependng on the sze of the ndustry, country and tme at hand. On the other hand, once approprately normalzed, one may use the transformed level devatons to reveal comparatve advantage. However, gven the fact that the nformatonal content of the devatons of actual exports from ther comparatve neutral (or expected) levels allow a comparson across ndustres, countres and tme, such normalzaton should not dstort the dstrbuton of those devatons across these dmensons. In addton, RCA measures permt nterpretaton as cardnal, ordnal and dchotomous measures, whch should also be taken nto consderaton for means of consstency. 3. Exstng Addtve Indces The proposton for an alternatve RCA ndex, that challenges the multplcatve nature and nformatonal content of BRCA 5 n favour of an addtve construct, was frst ntroduced by Hoen & Oosterhaven (2006). Instead of defnng RCA as a rato between the share of an ndustry wthn a country and that of the world, they defned RCA as the dfference between them, namely the numerator and the denomnator of (1c). That s ARCA j = ( X j/x z) ( X w j /X w z ), (3a) whch corresponds to the level devatons of country s exports n ndustry j from ts comparatve neutral level, scaled down by the total exports of country. That s ARCA j = [ E ( ) ]. (3b) Yet as the scalng factor wll change from country to country, the ndex wll be based, whch would partcularly affect cross-ndustry and cross-temporal comparsons. Furthermore, because the magntude of the scalng factor dffers for each country, cardnal and ordnal nterpretatons of the ndex values would not match n all three dmenson, least pronounced across countres 6. Yu et al. (2009), on the other hand, propose to scale the term n brackets wth the total level of world exports. That s 5 the asymmetry caused by the nequalty of the ntervals of BRCA, [0,1] sgnfyng a comparatve dsadvantage whle [1, ] sgnfes a comparatve advantage, ndcates that the demarcaton of the ndex s not symmetrc and the relatve weght attached to specalzed sectors compared to unspecalzed sectors would be unrestraned. Furthermore, BRCA has an nherent bas to sgnfy strong comparatve advantage for countres and ndustres that comprse a small market share. Such shortcomngs of BRCA are argued to be caused by ts multplcatve nature. For further dscusson, please refer to Yu et al. (2009). 6 that s, normalzng E ( ) wth X z results n a non-monotonc transformaton. X z

5 NRCA j = [ E ( ) ], (4) where the ndex measures the devatons of country s exports n ndustry j from ts comparatve neutral level, scaled down by the total world exports. Although Yu et al. s scalng of E ( X j) wth the total world trade s consstent across tme, t s based over ndustres and countres. Gven ths bas, cross-ndustry and cross-country comparson of NRCA j wll not be robust. But unlke ARCA j, because the scalng factor wll be constant wthn each year, the ndex s nterpretaton as a cardnal and an ordnal measure wll not be based across tme 7. Snce nether of the proposed addtve RCA measures allow an overall consstency nor a comprehensve comparson but rather permt lmted nference, comparatve analyses based on them would not be robust unless comparson across only those consstent dmensons are amed for. X w z 4. Approprately Normalzed Addtve Indces The approprate normalzaton of E ( X j) should not alter ts dstrbuton across ndustres, countres or tme as well as ntal nferences as cardnal, ordnal and dchotomous measures. The smplest method would be to apply lnear scalng transformaton. That s LSRCA j = where the ndex wll have ts crtcal value 8 at E ( ) [ ( )] mn E X j max [ E ( )] [ ( )], (5a) mn E X j [ ( )] [ max E mn E ( )] [ ( mn E )] and devatons from ths pont would ndcate the relatve comparatve state. The ndex has fxed upper and lower bounds at 1 and 0, respectvely. As the crtcal value s varable dependng on the data employed and wll unlkely be at 0.5, the ndex wll be asymmetrc. Although LSRCA j wll be consstent wth E ( X j), as t ntroduces no dstorton n the transformed values, ts nterpretaton s not straghtforward. A possble transformaton would be to calculate the rato of the devatons of each RCA score from the crtcal value of the ndex to the crtcal value tself. That s LSRCA = LSRCA j LSRCA LSRCA, (5b) where LSRCA s the crtcal value of LSRCA j. Usng LSRCA one can consstently compare the RCA scores of countres. The sgn of the ndex wll show whether the country 7 that s, normalzng E ( X j) wth X w z results n a non-monotonc transformaton across countres and ndustres whle s lnear monotonc across tme. 8 ndcatng the comparatve neutral state

6 has a comparatve advantage or a dsadvantage n that ndustry, whle the magntude would ndcate the relatve advantage or dsadvantage. Another possble normalzaton would be to transform the devatons of exports from ther comparatve neutral levels usng a logstc functon, whch would agan transform the values over the range of [0,1 ] wth crtcal value at 0.5. However as E ( X j) are n levels, the transformed values wll lkely be out-of-range and snce ths type of scalng gves lnear normalzaton over ts range, t must be transformed to nclude those out-of range values. Theoretcally, there wll be an arbtrary out-of-range value encountered at ether end of the range and to reduce that, one can apply a softmax scalng whch uses the logstc transformaton (Pyle, 1999). That s and SSRCA j = e s. (6a) s = E( ) µ E(X j ). (6b) λ σ E(X j ) 2π where s denotes the transformed value of E ( ) wth softmax scalng, µ and σ denote the mean and the standard devaton of E ( ) concernng the whole sample 9, respectvely, and the value of λ wll determne the extent of the lnear range. Although ths type of normalzaton would be monotonc, there wll be some dfferences n the normalzed values between any two nondentcal non-transformed values (Pyle, 1999), thus cardnal consstency may not be obtaned 10. Gven the dffculty n nterpretng the asymmetrc LSRCA j and the lkely loss of cardnal consstency usng SSRCA j, a thrd opton would be to normalze E ( ) by σ E(X j )11,whch would be consstent across ndustres, countres and tme. That s SNRCA j = E( X j σ E(X j ) ). (7) 5. Consstences of the Proposed Addtve Indces As mentoned, RCA ndces permt nterpretaton as cardnal, ordnal and dchotomous measures across ndustres, countres and tme; hence should be consstent vs-à-vs the level 9 as the use of µ and σ across ndustres, countres or tme would obscure the consstency of the transformed values across the dmensons unaccounted for. 10 by choosng the approprate λ one can alter ths by tral and error. Here the arbtrary value of λ = 8 s used, whch gves a relatvely hgh nterval for the lnearzed range. 11 whch s the standard devaton n E( ) concernng the whole sample n order to acheve consstency across all three dmensons

7 devatons from comparatve neutral levels n each dmenson for a robust comparson. Followng Ballance et al. (1987) Pearson, Spearman and Pearson correlaton coeffcents wll be calculated for evaluatng the extent 12 of consstency as cardnal, ordnal and dchotomous measures, respectvely 13. Concernng the three dmensons, the correlaton coeffcents wll frst be calculated for the whole sample and then for pars across ndustres, countres and tme to assess the overall consstency of the ndces and f they are nconsstent, to determne the ambguous dmenson creatng the nconsstency. Although the RCA ndces were shown to be calculated by takng the whole world as the group of reference countres, such an emprcal pursut may not yeld sound results, as the countres theren wll be qute heterogeneous regardng the market condtons that ther tradng partners face. Thus nstead of takng the world as a whole as the reference countres, EU15 countres wll be employed snce they are qute homogenous concernng the dstortons that ther exports face. For the export destnaton, EU15 countres exports to the whole world wll be consdered as choosng a partcular country may bas the results. For the export flows, only those of manufacturng ndustres wll be consdered. The data s obtaned from OECD s STAN Blateral Trade Database for 22 ndustres coverng the perod between 1989 and 2008, yeldng 6,248 observatons. Table 1 summarzes the extent of consstency of the addtve RCA ndces vs-à-vs the level devatons from comparatve neutral levels for the whole sample. Table 1 Consstency of the Addtve RCA Indces vs-à-vs E(X j ) Index Cardnal Measure Ordnal Measure Dchotomous Measure ARCA j NRCA j LSRCA j SSRCA j SNRCA j As the normalzaton methods do not alter the sgn of the devatons, consstency of all ndces as dchotomous measures can be presumed. Evdently all ndces are perfectly consstent n revealng the relatve comparatve state of the export flows. On the other hand nether of the prevously proposed ndces show consstency as cardnal nor ordnal measures for whch the former s more severe 14, whereas the three alternatve ndces proposed here obtan perfect ordnal consstency. Furthermore LSRCA j and SNRCA j are also perfectly consstent as cardnal measures. Gven these results, a dmensonal breakdown wll be pursued only for cardnal and ordnal consstences to verfy whether the problematc dmensons are ndeed the ones expressed before. Table 2 presents the dmensonal breakdown of the relevant consstences, the frst 3 rows ndcatng average cardnal consstences whle the last 2 rows ndcate average ordnal consstences. 12 a perfectly consstent ndex should yeld a perfect correlaton. 13 for testng the consstency as a dchotomous measure, ndces bnary transformatons are employed. 14 the lkelhood of a change n the cardnal value that also alters the ordnal value would be less than the overall lkelhood of a change n the cardnal value

8 Table 2 Dmensonal Breakdown for Inconsstent Indces Index Across Industres Across Countres Across Tme ARCA j NRCA j SSRCA j ARCA j NRCA j The correlatons presented n table 2 correspond to the prevously emphaszed ponts. As ARCA j coresponds to E(X j) scaled by the total trade of country at tme t, ts crosscountry consstency as a cardnal measure s much hgher than ts consstency across ndustres and tme. On the other hand scalng of E(X j) by the total world trade at tme t makes NRCA j perfectly consstent across tme whle nconsstent across ndustres and countres. As for SSRCA j, the cardnal outcomes depend on the chosen extent of lnear range used n the relevant softmax scalng and, as stated, a certan degree of nconsstency was expected. Consderng the dmensonal breakdown of ordnal consstences, NRCA j s found to be perfectly consstent only across tme whereas ARCA j obtans ts hghest rank correlaton across countres, whle shows hgher nconsstency across ndustres and tme. These results correspond to the prevously emphaszed ponts, as well as the fndngs n table 1. More explctly, cardnal nconsstency s further shown to be a much more problematc ssue compared to ordnal nconsstency. 6. Concluson Ths note shows that the applcablty of the recently proposed addtve RCA ndces as means of comparatve nstruments s rather questonable. Although these ndces fundamentally dffer from the Balassa Index due to ther addtve construct, they do comply wth the latter wthn Kunmoto s framework. Nevertheless they are shown to be nconsstent wth the level devatons from the comparatve neutral levels as cardnal and ordnal measures, and ths nconsstency s due to the napproprate normalzaton of those devatons. From a statstcal pont, such normalzaton should not alter the dstrbuton of those devatons across ndustres, countres and tme whle preservng the ntal nferences. Although Yu et al. s proposed ndex allows a more robust comparson than Hoen & Oosterhaven s addtve ndex, t s stll nconsstent across ndustres and countres, whch would obscure any comparson conducted across those dmensons. Whereas cross-temporal comparsons based on ther ndex would permt a robust comparson. On the other hand the three alternatve measures proposed here are shown to be more consstent over space and tme compared to the prevously proposed ndces and hence may serve as better nstruments n related quanttatve research

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