SWSS FOREGN TRADE NDCES USERS GUDE Ma 26 Federal Cusoms Admnsraon (FCA) Secon Dssemnaon and analyses The resen documen s he reference gude for Swss foregn rade ndces and s nended for all s users. Through examles, reveals and exlans se-by-se he mehodology used o calculae he ndces. ncludes n arcular: he avalable ndces, he mehod used o calculae hem and her ossble uses. The ueson of un values and he rocedures used o guaranee ha he resuls are reresenave and relable are analysed n deal. Fnally, he mos raccal asecs of he ndces (dssemnaon, erodcy) are ndcaed.
CONTENTS 1 FOREGN TRADE NDCES: OVERVEW... 3 2 UNT VALUES PROBLEM AND SOLUTONS APPLED... 3 2.1 Un value and rce... 3 2.2 Soluons chosen n relaon o he roblem of un values... 5 2.2.1 Mehod aled n relaon o arff headngs... 5 2.2.2 Mehods aled n relaon o mean values... 5 2.2.3 Connual chec of he relably of un values and ndces... 7 3 CALCULATNG THE NDCES... 8 3.1 Calculaons on a movng base for grous by naure of goods... 8 3.1.1 Un value ndex a he lowes level of subgrous by naure of goods... 8 3.1.2 Nomnal ndex a he lowes level of subgrous by naure of goods... 15 3.1.3 Real ndex for he lowes level of subgrous by naure of goods... 15 3.2 Calculaon on a movng base for he grous by broad economc caegores.... 17 3.3 Channg and year-on-year comarson... 17 3.3.1 Channg... 17 3.3.2 Year-on-year comarson... 19 4 WORKNG DAYS AND SEASONAL ADJUSTMENTS... 21 4.1 Why are hese adusmens necessary?... 21 4.2 Mehod... 21 4.3 Resuls... 21 5 PERODCTES... 24 6 DSSEMNATON... 24 7 POSSBLE USES FOR THE NDCES... 24 8 CONTACT... 26 2
1 FOREGN TRADE NDCES: OVERVEW Swss foregn rade sascs rovde he general ublc no only wh absolue rade fgures (value n Swss francs, uany n lograms) bu also ndces whch brea down he nomnal rend no wo elemens, namely rce and volume. Ths reveals he real rend n rade. The followng ndces are avalable o he ublc: nomnal ndex (or value ndex) un value ndex (or rce ndex) real ndex (or volume ndex) The nomnal ndex s calculaed from sascal values and ndcaes he varaon n value beween wo erods of me. The un value ndex measures he rend n rces on he bass of un values. The real ndex ndcaes he real rend (or removed from rce effecs) n foregn rade. Ths s a resdual value resulng from he nomnal ndex and he un value ndex. These ndces are comled for oal rade as well as for grous of goods accordng o her naure (breadown by branches) or her broad economcs caegores (breadown by basc caegores of he naonal accoun). n conras, no ndex by counry or by arff headng s avalable. 2 UNT VALUES PROBLEM AND SOLUTONS APPLED An undersandng of he basc characerscs of un values enables users o roerly nerre he esmaed varaon n rces usng foregn rade ndces. n hs secon we resen he conce of un value and he uesons ha arse from. Subseuenly, we descrbe he soluons aled o guaranee he ualy and relably of he ublshed nformaon. 2.1 Un value and rce The rce of mored and exored goods s no recorded by he cusoms auhores. The cusoms declaraon does, however, nclude he ye of merchandse, he uany and he value. Varaons n mor and exor rces are esmaed for each arff headng 1 on he bass of un values, whch are defned as he rao beween he value and he uany. The un value s herefore no a real rce, bu an average rce er logram for each arff headng. For a arff headng ha s ermed homogeneous, conanng for examle only one sngle roduc, un values vary n drec rooron o rces. n general, varaons n rces and un values are closely lned emrcally over he long erm. n he shor erm, here may be a degree of dvergence. 1 Caegory of merchandse 3
The use of un values n relaon o foregn rade offers he followng advanages n arcular: No addonal recordng The un values are calculaed from cusoms nformaon. Unle rces, hey do no have o be secfcally noed by dfferen comanes. The advanages are hus obvous for boh exorng and morng frms (no exra burden) and our sascs secon (n erms of cos). Comrehensve summary of rade The un values are calculaed for all cusoms ransacons ha are ncluded n foregn rade sascs. Usng un values as a bass can nvolve he followng dsadvanages: Hgher volaly Un values are generally much more volale han rces. Varaons arsng from facors oher han rce. The un value of a arff headng may change even f he rce of he arcle n ueson remans consan. Un values are n fac nfluenced by many facors aar from rce, rncally he followng: changes n he range of goods whn a heerogeneous arff headng,.e. ncludng dfferen roducs (see box below); mnaursaon: hans o echnologcal rogress roducs are beng manufacured n smaller and lgher versons whou he characerscs or he funcon of he roduc beng mroved. The rce er logram (mean value) of hese roducs ends herefore o gradually rse; acagng modfcaon: snce he un value deends on he wegh, s affeced by he acagng (o a greaer or lesser exen); ualy modfcaon: hs facor s a roblem n relaon no only o he relably of an un value ndex bu also o a classcal rce ndex. BOX Change n he range of roducs and un value Un values are more volale han rces and do no necessarly reflec he real varaon n rce. n exreme cases, un values may aear o vary whle rces reman sable over he erod n ueson. Le us consder a heorecal arff headng ha ncludes hree roducs (A, B and C) for whch we have nown uanes and values as well as, for our uroses, rces: PEROD 1 PEROD 2 g CHF/g CHF g CHF/g CHF Produc A 3 3 9, 1 3 3, Produc B 2 2 4, 2 2 4, Produc C 1 2 2, 1 2 2, Toal for he arff headng 6-15, 4-9, There aears o be no varaon n rce among he roducs. The mored uanes of roducs B and C have no changed. Only sales of roduc A have slumed. Now le us calculae he un values for he headng: - Over erod 1, he headng shows a value of CHF 15, for a uany of 6 g un value: CHF 25.-/g (= 15,.- / 6 g) - Over erod 2, he value of he headng s CHF 9, and he uany n ueson s 4 g un value: CHF 22.5/g 4
Beween erods 1 and 2 he un value of he arff headng has fallen from Fr. 25 o 22.5,.e. a dro of 1%. whou nowng he real rces one would assume ha hey had fallen by 1% whle n fac here has been no change n rce. n hs examle he un value has changed followng a modfcaon n he comoson of he arff headng. 2.2 Soluons chosen n relaon o he roblem of un values n order o omse he use of un values he chosen mehod s aled a hree comlemenary levels: selecon of reresenave ems, rocessng of un values and safey ne (connual chec of he relably of he un values and ndces). 2.2.1 Mehod aled n relaon o arff headngs To guaranee he ualy and relably of he ndces for un values he 8, or so arff headngs are sl no wo grous: reresenave ems: he un values for hese arff headngs are suffcenly sable and her varaon s lely o corresond o ha of rces. The un value ndex s based solely on hese ems. n Ocober 25 hs grou ncluded 69% of mored ems for 93% of he value; on he exor sde, hs grou reresened 49% of goods for 92% of value. non-reresenave ems: he un values of hese ems generally resen an exreme volaly and can be lned wh he evoluon of rces. Ths caegory can also nclude ems ha are raded very lle. n Ocober 25, whle hs grou comrsed 31% of mored ems, reresened only 7% of he oal value of mors. On he exor sde, ncluded 51% of ems mored and 8% of he value. The dvson of arff headngs no hese wo caegores s based rmarly on a dealed examnaon ha s generally carred ou once a year. Ths comrses an (auomaed) sysemac dscrmnan analyss amed a erodcally revsng he exen o whch un values are reresenave for each arff headng. Dfferen ualy ndcaors for each em are aen no accoun: he coeffcen of varaon before and afer oulers have been correced, he number of erods whou any flow, he relave morance (whn he merchandse grou) and absolue morance (n relaon o oal rade) of he em, ec. n concree erms, he mehod s used o assess he robably of an em belongng o one grou or he oher. Ths rae of robably s hen used o draw u roosed classfcaons. A fnal chec of he resuls, ogeher wh an n-deh sudy for ceran arff headngs, wll hen confrm or nvaldae he roosals resulng from he dscrmnan analyss. 2.2.2 Mehods aled n relaon o mean values n order o elmnae devan un values ha do no relae o he real rend n rces, he orgnal seres of un values are rocessed every monh before he ndces are calculaed. Ths rocedure may be carred ou n any of he followng ways: oulers correcon, exernal rces, medan, orgnal daa. 5
Oulers correcon Ths s he sandard mehod for rocessng seres of un values. n Ocober 25 hs mehod was used on 99.6% and 99.9% of reresenave mored and exored ems resecvely. The mehod for rocessng un values s fully auomaed and consss of denfyng oulers and relacng hem wh lausble values. The basc ool s he AUTOBOX rogramme 2 devsed by Davd P. Relly (USA) secfcally for analysng me seres. A verson has also been develoed ha s secally adaed o our reuremens. For each seres of un values (monhly seres coverng he revous 6 years and he curren year) he rogramme denfes he ARMA model whch bes descrbes he daa evoluon. Ths model aes no accoun n arcular any level shfs, seasonal facors, changes n he rend and changes n varance. The rogramme hen deecs any oulers defned as values ousde he confdence nerval se by he model. Once hey have been denfed, oulers are relaced by a lausble esmaon ha conforms o he model. Ths mehodology allows he varably of he un values o be consderably reduced, hus mang hem more reresenave, whch means ha a larger number of arff headngs can be used o calculae he un value ndex. Whle hs mehod rovdes relable resuls for he large maory of ems, may nvolve nadeuae correcons, deendng on he characerscs of he seres of orgnal daa. n such cases, oulers are no correced auomacally and one of he hree oher mehods s used. Exernal rces The oon of exernal rces allows un values for a arff headng o be relaced by values for an exernal seres of rces. Ths seres may be rovded by an exernal source no relaed o foregn rade sascs. For raccal reasons and n vew of he avalably of nformaon, an nernal soluon s generally referred. Ths mehod s secfcally for arff headngs wh a huge radng value bu for whch he un values are no arcularly sgnfcan and are so varable ha no model can be found and oulers canno be deeced. A resen, he oon of exernal rces s used only o rocess ems relang o arcraf. These arff headngs cover flucual rade n new arcraf (exremely hgh mean value) and second-hand arcraf and sare ars whose un values are very volale. Medan The un value of a arff headng can also be relaced by he medan, whch s defned as he cenral value (rce er g) of all he shmens relang o ha em over one monh. By defnon, he medan s he value whch dvdes all he shmens no wo grous of he same sze: 5% of he shmens are a a rce er g above he medan and 5% a a rce er g below he medan. Ths oon s suable for ems of morance wh exremely varable mean values, where exreme values gve oally ncorrec resuls. Ths oon s rarely used. 2 www.auobox.com 6
Orgnal seres may haen ha orgnal seres aear o be more realsc ha hose obaned usng sandard correcon. n such cases he sandard correcon s no carred ou. 2.2.3 Connual chec of he relably of un values and ndces Gven he rad changes n reresenavy and he delcae as of correcng oulers n ceran cases, decsons regardng annual classfcaon may ucly become nvald. s for hs reason ha, as well as beng revsed annually, arff headngs are subeced o a monhly ualy chec whch consss of searchng ou unrealsc un values (defned by a varaon n rce beween wo erods eual o or over 1) before he erodcal ublcaon of new daa. f necessary, roblemac headngs are elmnaed mmedaely from he reresenave ems and he ndex s recalculaed ang no accoun he modfcaons. The nroducon of hs monhly safey ne means ha an acve (as oosed o a reacve) olcy can be followed wh regard o he ualy and he relably of he ndces. 7
3 CALCULATNG THE NDCES The nomnal and real ndces are based on all he arff headngs, whereas only he reresenave ems are used o calculae he un value ndex. ndces are avalable down o he lowes level of subgrous accordng o he naure of goods (breadown by branches) or he broad economcs caegores (breadown by basc caegores of he naonal accoun). They are frs calculaed for hese grous. The resuls obaned are hen aggregaed o gve daa for subgrous a hgher levels, hen for he man grous and fnally for oal rade. The ndces are calculaed on he bass of orgnal values or of oulers correced daa. n any case, only he second are ublshed. Snce rade n recous meals, recous sones, gemsones, wors of ar and anues s unceran and unredcable, such goods are no ncluded n he calculaons for he ndces (.e. accordng o oal 1). 3.1 Calculaons on a movng base for grous by naure of goods The mehodology and formulae used for calculang nomnal, real and un value ndces are ndcaed se-by-se. To mae hs more comrehensble, he varous rocedures and calculaons are llusraed wh a smle examle. For he un value ndex he basc elemens are frs ndcaed for he deal case,.e. for a grou accordng o he naure of goods made u solely of reresenave ems. We shall hen focus on he general case of a grou ha also ncludes non-reresenave ems. BOX Advanages of a movng base as oosed o a fxed base The comoson of oal mors and exors s consanly changng and from one erod of me o anoher and varaons can be consderable. f he ndex s calculaed on a movng base he weghng s deermned by he curren base of goods exchanged. s herefore no necessary o revse he conens of he base a regular nervals snce wll auomacally change from one erod o he nex. Ths mehod serves o mnmse he recurren roblems of rce ndces when he ualy of he roducs changes. f a fxed base s used he conens of he base reman he same over me and changes n ualy beween he nal erod and he curren erod may gve a false dea of rces. 3.1.1 Un value ndex a he lowes level of subgrous by naure of goods 3.1.1.1 Grous by naure of goods made u solely of ndex ems Foregn rade ndces are calculaed on he bass of nformaon obaned from cusoms declaraons. n arcular, he uany and he value consue he man daa for he calculaons. Based on rovsonal fgures for he monh of June 25, he subgrou Socs, socngs, ghs (3.2.2.2), whch s ar of he man grou exles, clohng, foowear (3) s used as an examle. BOX The examle n bref The subgrou socs, socngs, ghs ncludes 1 arff headngs ha can be dsngushed by he ualy of he fbre used (such as synhec fbre, coon or vegeable fbre). Ths grou ncludes only reresenave ems. 8
Naure Tarff headng 3.2.2.2 6115.11 2131258 4931 27477 53145 curren erod (e.g. June 25) value a uany (orgnal or correced) a un value a 6115.12 389367 662 2386 5481 6115.191 32465 841 282112 744 6115.199 16543 329 175676 3265 6115.2 97926 224 142814 2111 6115.91 28958 8466 647759 1498 6115.92 515338 21111 4882938 195683 6115.931 95334 14947 155251 16867 6115.932 47963 1244 8243 27 6115.99 95366 285 146291 338 Toal 1454858 11991997 s no he value a he same erod he revous year, bu he value for an average erod durng he revous year (erod ). uany (orgnal or correced) a un value a f Q (1) where Q = oal uany for he revous year f P Q (2) where P Q = oal value for he revous year where f 1 12 1 4 x 12 for he monhly daa for heuarerly daa for hecumulaed daa (e.g. x 8 for he erod January oaugus) BOX Orgnal and oulers correced uanes The correcon of exreme values s aen no accoun when he ndex s calculaed by usng and. For each reresenave arff headng he uanes are adaed o oban a oseror he adused un value ndcaed by he model. Ths mehod guaranees ha each em s correced n a neural way, based on he defnon uany mes rce. The correced ndex s based on correced uanes, whle he orgnal ndex s calculaed from orgnal uanes. The Laseyres ndex Snce foregn rade ndces are calculaed from a movng base, and relae o he recedng year as a whole. The frs sage s o oban un values for and for roduc ( and ). n order o do hs he value for he curren erod and ha for he recedng year (e.g. average monhly value for 24) are dvded by her 9
resecve uany e (e.g. he average monhly uany for 24). By defnon, he value/uany uoens reresen he un values. For he frs arff headng of he grou (6115.11), he followng s hus obaned: 2131258 (3) = 27477 5. 9 (4) 53145 = 52. 1 4931 Naure Tarff headng 3.2.2.2 6115.11 2131258 4931 52.1 27477 53145 5.9 6115.12 389367 662 64.2 2386 5481 42. 6115.191 32465 841 38.6 282112 744 37.9 6115.199 16543 329 5.3 175676 3265 53.8 6115.2 97926 224 48.9 142814 2111 49.4 6115.91 28958 8466 33.2 647759 1498 43.2 6115.92 515338 21111 24.2 4882938 195683 25. 6115.931 95334 14947 63.8 155251 16867 62.6 6115.932 47963 1244 37.9 8243 27 41.2 6115.99 95366 285 33.5 146291 338 44.2 Toal 1454858 11991997 Usng esmaed rces and uanes s ossble o reconsruc he values for he desred erods. n arcular, he (hyohecal) value of he nal base a curren rces can be exressed. Ths value s necessary for he Laseyres ndex o be calculaed. Naure Tarff headng Laseyres 3.2.2.2 6115.11 2131258 4931 52.1 27477 53145 5.9 2768855 6115.12 389367 662 64.2 2386 5481 42 35188 6115.191 32465 841 38.6 282112 744 37.9 287184 6115.199 16543 329 5.3 175676 3265 53.8 16423 6115.2 97926 224 48.9 142814 2111 49.4 132279 6115.91 28958 8466 33.2 647759 1498 43.2 497336 6115.92 515338 21111 24.2 4882938 195683 25 4735529 6115.931 95334 14947 63.8 155251 16867 62.6 176115 6115.932 47963 1244 37.9 8243 27 41.2 758265 6115.99 95366 285 33.5 146291 338 44.2 11818 Toal 1454858 11991997 11782491 98.25 The Laseyres ndex can be calculaed usng he followng formula: where P Q P Q Laseyres 1 1 11782491 1 98. 25 (5) P Q 11991997 = he value of base a erod 1
P Q = he hyohecal value of he base a erod exressed n curren rces (erod ). BOX The Laseyres ndex The formula for he Laseyres ndex was devsed over 13 years ago by Erns Lous Eenne Laseyres (1834-1913). He used frs hs formula for he rce of goods n he or of Hamburg. The hnng behnd hs formula s easly undersood hrough he followng smlfed examle: ae a counry ha mors only wne and bananas. Over a gven year hs counry has mored 2 lres of wne a Fr. 4 er lre and 3 g of bananas a Fr. 2 er g. A year laer he wne coss Fr. 5 er lre and he bananas Fr. 3 er g. Wha s he average ercenage ncrease n he rce of he mored goods? Laseyres 5 2 33 19 1 1 1 126.74 4 2 2 3 86 The Laseyres rce ndex shows he rae of varaon n rces f he base for he reference erod remans he same unl he resen erod. n our examle he rce of he mored goods rose on average by 27%. The Laseyres ndex s a weghed arhmec mean of rce raos. The weghng s defned here by he rao of he value of em o he oal value for he reference erod (erod ) : where g Relacng m 1 Laseyres m g 1 he weghng of em based on erod g by s exresson n he ndex formula, we ge he shorened Laseyres formula: Laseyres m g 1 m 1 1 m Ths s hus he exresson (5) of he calculaon of he un value ndex. should be noed ha he shor formula for he ndex mlcly uses he weghng of he basc formula. The ndex The ndex s calculaed alongsde he Laseyres ndex. For he former, he (hyohecal) value of curren base a rces for erod s calculaed frs, noed as. Ths value s obaned smly by mullyng he rce by he uany as defned revously. g m 1 m 1 11
Naure Tarff headng 3.2.2.2 6115.11 2131258 4931 52.1 27477 53145 5.9 283388 6115.12 389367 662 64.2 2386 5481 42 25464 6115.191 32465 841 38.6 282112 744 37.9 31874 6115.199 16543 329 5.3 175676 3265 53.8 177 6115.2 97926 224 48.9 142814 2111 49.4 989186 6115.91 28958 8466 33.2 647759 1498 43.2 365731 6115.92 515338 21111 24.2 4882938 195683 25 527775 6115.931 95334 14947 63.8 155251 16867 62.6 935682 6115.932 47963 1244 37.9 8243 27 41.2 512528 6115.99 95366 285 33.5 146291 338 44.2 12597 Toal 1454858 11991997 1594413 98.68 The ndex s obaned for each naure-based grou usng he followng formula: P Q 1 1 1454858 1 98. 68 (6) P Q 1594413 BOX The ndex The ndex, as devsed by Hermann (1851-1925), shows he relave rce of a base for he curren erod comared wh wha he same base coss for he reference erod. n he case of hs ndex he weghng vares from one erod o he nex. f, n our smlfed examle, we noe ha no only has he rce of he goods ncreased, bu ha he uanes of wne and bananas mored have rsen o 3 lres and 15 g resecvely, he ndex can be calculaed as follows: 53 315 1 1 4 3 2 15 195 1 15 13. The rce ndex accordng o hus shows he varaon n rces f he base for he curren erod were also vald for he reference erod. n our examle he rce of he mored goods has rsen on average by 3%. The ndex s a harmonc weghed mean of rce raos. The weghng s defned here as he rao of he value of em o he oal value for he curren erod (erod ): where g m 1 m 1 weghng of em based on erod f g s relaced by s exresson n he ndex formula, one obans he shorened formula: g 1 12
m 1 g 1 m m 1 1 g 1 Ths s hus he exresson (6) of he formula for calculang he un value ndex. should be noed ha he shor formula for he ndex mlcly uses he weghng of he basc formula. m 1 m 1 The Fsher ndex The ublshed un value ndex s calculaed usng Fsher s formula, defned as he geomercal means of he Laseyres and ndces. s based on he followng formula: Fsher Laseyres = 98.25 98.68 98. 46 (7) BOX The Fsher ndex The Fsher ndex was devsed by rvng Fsher (1867-1947) as a comromse soluon beween he Laseyres and he ndces. s generally referred o he wo ohers for he followng reasons: - s an deal ndex: f, on average rces double and uanes rle whn a gven erod of me he number obaned mus be mulled by sx. Ou of he hree ndces consdered here, only he Fsher ndex resecs hs axom; - s an nermedae alernave beween he Laseyres and he ndces: from a raccal on of vew: he Fsher ndex comensaes for he endency of he Laseyres ndex o overesmae he varaon of rces and ha of he ndex o underesmae. from a heorecal on of vew: as neher he Laseyres nor he ndex has he favour, seems reasonable o loo a an nermedae soluon; - unle he oher wo ndces, he Fsher ndex resecs he desred roery of reversbly. Accordng o hs rncle he ndex for he erod n relaon o s he nverse of he ndex for he erod n relaon o. 3.1.1.2 Grous by naure of goods wh non-ndex ems A he lowes level of classfcaon by naure, mos of he subgrous nclude ems ha are no reresenave. Gven ha such ems do no rovde any vald nformaon abou rce, he varaon n rce of he grou o whch hey belong s aled o hem oo (on condon ha he grou ncludes a leas one ndex em). Ths measure guaranees ha he non-reresenave ems do no have any effec on he un value ndex for her grou. To llusrae hs on, he calculaons are aled o he grou Tes (3.2.3.3), whch ncludes 5 ems of whch one s non-reresenave (P = no). 13
Naure P Tarff headng Laseyres 3.2.3.3 yes 6117.29 1278 65 158.1 2328 15 193.6 1661 12584 yes 6215.1 443393 14813 299.3 329883 13919 237. 4165957 351681 yes 6215.2 179925 2944 61.1 132977 1679 79.2 1587 233165 yes 6215.9 2779 11 268.1 2917 152 19.9 4751 19281 Fsher Toal 4651212 3481125 4233896 3775711 121.62 123.19 122.4 no 6117.21 96 2846 16 177.9 3461 78 Toal 96 2846 3461 78 Toal grou 465138 3483971 4237357 3775789 121.62 123.19 122.4 As before he Laseyres, and Fsher ndces are calculaed solely from reresenave ems (P = yes). Tang he grou whch s made u of n ndex ems and m non-ndex ems : Grou ndex ems 1 2 Non-ndex ems 1 2 m n P Q Laseyres 1 1 4233896 1 121. 62 (8) P Q 3481125 P Q 1 1 4651212 1 123. 19 (9) P Q 3775711 Fsher Laseyres 121.62 123.19 122.4 (1) These ndces are hen used o calculae ems : e for he non-reresenave Laseyres 2846 121.62 3461 (11) 1 1 14
96 78 (12) 1 123.19 1 Once and are nown for he non-ndex ems oo, s ossble o deermne he value of hese hyohecal bases for he whole of he naure grou: P Q 4233896 3461 4237357 (13) P Q 3775711 78 3775789 (14) The ndces can fnally be recalculaed for he grou, hs me ncluded he non-ndex ems. P Q Laseyres 1 4237357 1 121. 62 (15) P Q 3483971 P Q 1 465138 1 123. 19 (16) P Q 3775789 One can chec ha he Laseyres and ndces wh and whou non-ndex ems are srcly dencal, snce hese ems are nally alloed he values of he ndces for her grou. 3.1.2 Nomnal ndex a he lowes level of subgrous by naure of goods The nomnal ndex (or value ndex) of he grou, nom, ndcaes he varaon n value beween wo erods. s calculaed usng he formula: P Q nom 1 1 1454858 1 87. 18 (17) P Q 11991997 Once he ndces are avalable for he 271 grous accordng o he naure of goods he daa are aggregaed o calculae he nomnal ndex for oal mors or exors. 3.1.3 Real ndex for he lowes level of subgrous by naure of goods The real ndex (or volume ndex) for grou, real, shows he real or removed from nflaon rend for foregn rade. Ths s a resdual value ha s obaned from he rao of he value ndex o he un value ndex. 15
nom real 1 87.18 1 88. 54 (18) 98.46 Fsher 3.1.3.1 Aggregaon The ndces for he uer levels are calculaed by aggregang he daa for all her resecve subgrous. From he aggregaed values, he Laseyres, and Fsher ndces can be calculaed usng he same formulae as before. Ths rocedure s hen reeaed for each level of he herarchy u o he oal ndex. Le us ae he grou Underwear (3.2.2), whch s made u of 4 subgrous: Grdles, corses, braces, ec. (3.2.2.1) Socs, socngs, ghs (3.2.2.2) Oher ems of hosery underwear such as yamas, T-shrs, brefs (3.2.2.3) Oher ems of fabrc underwear such as yamas, bah-robes, brefs (3.2.2.4) Naure P P Q P Q PQ P Q Laseyres Fsher nom real 3.2.2.1 yes 8492318 931478 828989 922115 3.2.2.2 yes 11991997 1594413 11782491 1454858 3.2.2.3 yes 39817227 3981927 37921146 37916961 3.2.2.4 yes 2453261 1729518 2513566 178773 3.2.2 6275483 61447548 6498192 591277 96.4 96.2 96.3 94.2 97.8 Snce all he subgrous of hs grou comrse a leas one reresenave em (P = yes), he dfferen ndces can be obaned drecly as follows: P Q P Q Laseyres 1 1 6498192 1 96. 4 (19) P Q P Q 6275483 P Q P Q 1 1 591277 1 96. 2 (2) P Q P Q 61447548 Fsher Laseyres 96.4 96.2 96. 3 (21) P Q P Q nom 1 1 591277 1 94. 2 (22) P Q P Q 6275483 16
nom real 1 94.2 1 97. 8 (23) 96.3 Fsher f a subgrou ncludes no reresenave ems, s omed when he un value ndces (Laseyres, e Fsher) for he grou are calculaed. Ths subgrou s hen alloed he values of he un value ndces for he uer grou o whch belongs, so ha hey are comlee: P Q P Q 1 Laseyres (24) P Q P Q 1 (25) The resuls are obaned for he uer levels of aggregaon usng he same rncle. 3.2 Calculaon on a movng base for he grous by broad economc caegores Whle here s a slgh dfference n how he daa s rocessed for he ndex by broad economc caegores and he ndex by naure of goods, he way he ndex er se s calculaed s absoluely dencal o ha for he grous by naure. Accordngly, we shall no exlan he mehod n deal (see Secon 3.1). Wh resec o he calculaon of he grous by broad economc caegores a he lowes level here s a sngle dfference ha should be noed: he rocessng of nonreresenave ems. To reca, hese ems are alloed he Laseyres and ndces for her resecve naure-based grou n order o calculae he hyohecal values of he corresondng bases (see formulae 11 and 12). When he broad economc caegores-based grous are calculaed hese ems manan her hyohecal values, so ha all he arff headngs can hen be consdered as ndex ems n he broad economc caegores-based grous. Ths rc guaranees ha he resuls are eual afer aggregaon accordng o he wo nomenclaures. 3.3 Channg and year-on-year comarson All he ndces for he dfferen caegores of goods and for he oal are calculaed on a movng base. On he bass of hese resuls he ndces are hen ransformed no bases ha are easer o use and nerre (chan ndex and revous year=1 ndex). 3.3.1 Channg Foregn rade ndces are ublshed n he form of chan ndces. The movng base resuls are hus lned n a mullcave fashon wh he revous year resul, whch 17
s lned o ha for he year before, ec. 1997 has been aen as he bass for he ndex. n order o allow comarsons o be made beween he varous erods, he dfferen movng base ndces movng base 97 movng base, 98, 99 movng base are hen made no a chan,.e. exressed n relaon o a common bass (1997), usng he followng formula:,... chan movng base 1 chan revous year (26) chan chan chan movng base where un value) ( value) ( volume) 1 ( 1997 1997 1997 1997 ( un value) chan ( un value) movng base ( un value) 1 chan revous year (27) ( value) ( volume) chan chan ( value) ( volume) movng base ( value) 1 movng base ( volume) 1 chan revous year chan revous year (28) (29) Ths oeraon s called channg and allows varaons over wo dsnc erods of me o be lned o gve he varaon for he oal erod. Channg for annual daa The channg rocess s llusraed usng oal exors as an examle: Movng base ndex Chan ndex: 1997=1 Year Perod Nomnal Un value Real Nomnal Un value Real 23 1.2 1.1 1.1 124.3 13.3 12.4 24 18.5 12. 16.4 134.8 15.3 128.1 ( value) chan 24 movng base chan ( value) 24 ( value) 23 18.5124.3 134. 8 (3) 1 1 The chan ndex s nerreed as follows: exors have rsen n value by 34.8% n relaon o 1997. 18
( un value) ( volume) chan 24 chan 24 movng base chan ( un value) 24 ( un value) 23 12 13.3 15. 3 (31) 1 1 movng base chan ( volume) 24 ( volume) 23 16.4 12.4 128. 1 (32) 1 1 should be noed ha, by defnon, he laer can also be deduced from he wo formulae above: chan chan ( value) 24 ( volume) 24 1 134.8 chan 128. 1 (33) ( un value) 15.3 24 Channg for oher erods The monhly and uarerly seres are no chaned wh he chan ndex for he same erod n he recedng year bu wh ha for he recedng year (annual resul). Ths rocedure s usfed from a echncal on of vew. By defnon, he movng base corresonds o he average erod for he revous year (see formulae 1 and 2). Ths rao mus hen be lned wh he comarson of he mean erod for he revous year n relaon o 1997, n oher words he chan ndex of he revous year. Here s an examle for he monhly resuls regardng exors: Movng base Chan ndex: 1997=1 Year Perod Nomnal Un value Real Nomnal Un value Real 25 Augus 94.7 12.6 92.3 127.6 18. 118.2 ( value) chan Augus 25 movng base chan ( value) Augus 25 ( value) 24 94.7 134.8 127. 6 1 1 (34) The chan ndex for 24 (134.8) s gven n he recedng examle. 3.3.2 Year-on-year comarson The year-on-year comarson s calculaed from he chan ndces for he wo erods. Snce he chan ndex for each erod shows he varaon beween ha erod and he mean erod of 1997, he varaon beween erod of year and erod of year -1 s nohng oher han he rao beween he wo chan ndces: yearon year comarson chan chan 1 1 (35) 19
To undersand hs, le us reurn o our revous examle: Movng base Chan ndex: 1997=1 Year Perod Nomnal Un value Real Nomnal Un value Real 24 Augus 115.9 14.5 11.9 119.4 1.1 119.3 25 Augus 127.6 18. 118.2 11.1 13.3 16.5 ( value) chan yearon year comarson Augus 25 Augus 25 chan Augus 24 1 127. 6 1 11. 1 (36) 115. 9 The nerreaon s as follows: n Augus 25 nomnal exors were 1.1% hgher han n Augus 24. 2
4 WORKNG DAYS AND SEASONAL ADJUSTMENTS 4.1 Why are hese adusmens necessary? n general economc acvy vares wh me. Over a year acvy ends o be concenraed n ceran erods, wh monhs of low acvy n beween. Vacaon erods and holdays also lay an moran role. Seres of daa for economc acvy are smlar and reflec hese seasonal comonens among oher hngs. s herefore no easy o nerre hese seres n he shor erm: does a dro n exors n Augus comared wh July ndcae an economc slum or s merely a seasonal flucuaon? The am of seasonal adusmen s o elmnae hs mechancal and regular seasonal varaon. Subseuenly, seres can be roerly comared over me and resuls can be duly nerreed, arcularly wh regard o shor-erm rends. Snce mors and exors are he core of economc exchange beween dfferen counres hey are auomacally subec o seasonal varaon. For hs reason seasonally adused ndces are ublshed n addon o he ndces menoned above. 4.2 Mehod The seasonally adused ndces for Swss foregn rade are drawn u n collaboraon wh he Cenre for Economc Research (KOF) 3 a he Zurch Federal nsue of Technology (ETHZ). The aled mehod s he mos common one, whch was develoed n he Uned Saes by he US Bureau of Census (verson X12-ARMA) 4. The X12-ARMA mehod s based on he same hlosohy as he X11-ARMA and X11 versons. The dfferen comonens of a seres, such as he rend-cycle and he seasonal and rregular comonens, are successvely esmaed usng an algorhm based on arorae movng averages. These movng averages allow he seres o be smoohed and he dfferen comonens o be denfed. n order o reduce he nsably of he revson of seasonally adused daa for recen erods, he nal seres s exended by forecass esmaed by an ARMA model. The algorhm menoned above uses he exended seres o esmae he comonens. 4.3 Resuls The nomnal and real ndces and he un value ndces are avalable from 1997 n he form of monhly or uarerly seres. As he basc ndex, he seasonally adused ndex s based on classfcaon of goods by naure and broad economc caegores. Ths rocedure s aled only o he mos moran grous of merchandse. Three seres are drawn u from he foregn rade ndces (oulers correced chan ndex): he worng days adused ndex, by whch he resuls refer o a consan number of worng days. Such an ndex means ha one monh (or one uarer) can be comared wh anoher monh (or uarer) whn he same year or he same erod of he revous year; 3 www.of.ch 4 www.census.gov/srd/www/x12a/ 21
he seasonally adused ndex, where varaons due o he dfference n he number of worng days and recurrng seasonal varaons have been elmnaed; he rend comonen, whch shows he rend afer he elmnaon of he seasonal, rregular (all he random elemens ha canno be nerreed) and cyclcal comonens. BOX Varaon n seasonally adused daa and rend n oal exors NOMNAL NDEX : SEASONAL ADJUSTMENT (chan ndex 1997=1) 165 155 145 135 125 115 15 95 85 75 oulers correced seasonally adused rend comonen JFMAMJ JASONDJFMAMJJASONDJFMAMJ JASONDJFMAMJJASONDJFMAMJ JASONDJFMAMJ JASONDJFMAMJJASONDJFMAMJ JASONDJFMAMJ JA 1997 1998 1999 2 21 22 23 24 25 The seasonally adused ndex shows he rend-cycle of a me seres afer elmnaon of he shorerm and seasonal varaons. The correced seres can herefore be used for analysng hsorcal values as well as for forecasng. The rend comonen reflecs he long-erm evoluon (rend) and reveals he defned busness cycle effecs as movemens around hs general rend. BOX Worng days adusmen s dffcul o nerre he resuls regardng foregn rade owng o calendar effecs. n general economc acvy reacs osvely o he number of worng days and negavely o he number of holdays. The worng days adused ndex (WDA) shows he resuls for foregn rade based on he mean number of days n a gven monh of he year. Thans o hs correcon, he comarson and nerreaon of he daa s much more ernen. Conrary o wha one mgh hn, he correcon of he dfference n he number of worng days does no nvolve a drec comarson of he number of worng days durng a gven erod wh ha for he same erod n he recedng year, bu wh ha for he mean erod n he curren year. For examle, he mean number of worng days er monh n 25 s 21.17, snce 25 has a oal of 254 worng days ( 21.17 254 12 ). The worng days adused chan ndex can be calculaed as follows: WDA nowda n N f J 22
where n = number of worng days durng erod, N J = number of worng days n year J (of whch s a ar), f = 12 f he erod aen s one monh, 4 f he erod aen s a uarer. Ths ndex s he chan ndex ha would aly for he erod f he number of worng days corresonded o he monhly mean for he year. Examle: he monh of Augus 25 had 22 worng days, whch was.8 worng days more han he monhly mean for 25 ( 21.17). For hs reason, he resuls for Augus need o be correced downwards so ha hey can be comared wh he oher monhs n 25 or wh he same monh of he recedng year. Nomnal chan ndex for Augus 25 = 127.6 127.6 254 22 12 127.6 22 Nomnal chan ndex WDA: 21.17 122. 8 The year-on-year comarson can be calculaed agan as he rao beween wo chan ndces: ( year on year comarson) WDA nowda nowda 1 n n 1 N N f J J 1 f nowda nowda 1 n 1 n N N J J 1 Ths formula shows ha he year-on-year comarson s nohng else ha o adus he no worng days adused comarson wh a coeffcen relang o he number of worng days n he monhs n ueson as well as wh a coeffcen relang o he number of worng days n he years n ueson. Conrary o wha one mgh hn a ror, he ndces for he number of worng days, uncorreced and correced are no necessarly eual f he monhs have he same number of worng days. n order for hem o be eual, he years n ueson mus have he same number of worng days. The worng days adusmens should correc erods of less han a full year bu have no effec on annual resuls. A he end of he year he correced daa are hus adused so ha he sum of he monhly chan ndces are euvalen wh and whou he number of worng days beng correced: ( defnve ) 12 WDA WDA 1 12 Below s he examle for oal mors for 24 (nomnal ndex) : 1 nowda WDA No WDA WDA CWD and correced January 115 122.7 122.6 February 119.4 127.4 127.3 March 143.7 133.3 133.2 Arl 131.6 14.4 14.3 May 115.7 129.9 129.8 June 136.2 132.1 132 July 129.1 125.2 125.1 Augus 117 113.5 113.4 Seember 136.2 132.1 132 Ocober 133.6 135.7 135.6 November 137.1 132.9 132.8 December 126.9 117.7 117.6 Toal 1541.5 1542.8 1541.5 23
12 WDA WDA 1 ( defnve ) March March 12 1 nowda WDA 1541.5 133.3 133.2 1542.8 5 PERODCTES ndces are avalable for he followng erods (number of erods) : year (1) semeser (2) rmeser (4) monh (12) cumulaed monhs: for examle January o Arl (8) n all, here s a choce of 27 dfferen erods durng he year. 6 DSSEMNATON Foregn rade ndces are comled for oal rade as well as for grous of goods by naure or by broad economc caegores. n conras, no ndces are avalable by counry or by arff headng. The foregn rade ndces are avalable o he ublc n he followng forms: he ables wh he man grous of goods can be consuled on our webse under foregn rade ndces, all he resuls concernng he ndex from 1997 on can also be consuled n SWSS-mex (daabase for Swss foregn rade) on he nerne (more nformaon under our headng roducs), he ndex CD-ROM conans he ndces for value, un value and volume for all erods from 1997 on. should be oned ou ha only he oulers correced ndces are ublshed. These resuls are rovsonal for he curren year and he revous year (unl he fnal closure n May of he followng year) and are revsed every monh. Resuls for earler years are defnve. Please noe ha seasonally adused ndces are never defnve, neher for he curren year nor for earler years. 7 POSSBLE USES FOR THE NDCES Foregn rade ndces are an essenal ool for any economc analyses of exors and mors and allow growh n rade for a gven secor or roduc grou or for all rade 24
o be roerly nerreed, be n nomnal or real erms. The ndces can also be used as a bass for esmang rends n rces of mored or exored goods. For a gven secor or roduc grou, foregn rade ndces can be used noably o: measure rce ncreases; deflae seres: foregn rade sascs always corresond o curren rces (nomnal ndex). Daa a consan rces (real ndex) are ofen more arorae for a long-erm analyss, however. Un value ndces can be used o deflae seres,.e. o elmnae rce varaons; analyse real rends n nernaonal mares; analyse comevy n nernaonal mares; analyse rce elascy of mors or exors,.e. deermne how urchases or sales abroad reac o a varaon n rce. The greaer he reacon, he more sensve urchases or sales are o varaons n rce. For he economy n general, foregn rade ndces can be used n arcular o: measure nflaon: he rce of mored goods may lay an moran role n relaon o he level of rces whn a counry. A rse n he rce of mored goods generally leads o a rse n domesc rces, albe wh a slgh delay; ancae nflaon: he delay beween he movemen of rces of mors and domesc rces means ha he laer can be foreseen on he bass of he former; deflae seres: foregn rade sascs always corresond o curren rces (nomnal ndex). Daa for consan rces (real ndex) are ofen more arorae for a long-erm analyss, however. Mean value ndces can be used o deflae seres,.e. o elmnae rce varaons; analyse real develomen of a counry on nernaonal mares; analyse he economc rend n foregn rade; analyse he comevy of a counry on he nernaonal mares; analyse rce elascy of mors or exors,.e. o deermne how urchases or sales abroad reac o a varaon n rce. The greaer he reacon, he more sensve urchases or sales are o varaons n rce; analyse he erms of rade. BOX Calculaon and nerreaon of erms of rade Terms of rade ndcae varaons n condons of comevy beween he domesc and he foregn mare. They consue an ndex of relave rces and ndcae he rce of exors n relaon o he rce of mors. Terms of rade are sad o deerorae f he rao falls, wh he conseuence ha a counry mus exor more o manan he same level of mors. The oose s an mrovemen n erms of rade. The un value ndex s he ey ool for calculang erms of rade usng he formula: erms of rade ( un value ( un value for ex ors) for mors) yearon year comarson yearon year comarson 1 Examle : 25
SWSS TERMS OF TRADE, from 1997 o Augus 25 11 18 16 14 12 1 98 96 JFMAMJ JASONDJFMAMJJASONDJFMAMJ JASONDJFMAMJJASONDJFMAMJ JASONDJFMAMJ JASONDJFMAMJJASONDJFMAMJ JASONDJFMAMJ JA 1997 1998 1999 2 21 22 23 24 25 nerreaon of erms of rade The erceon of erms of rade s more easly undersood usng he followng smlfed examle. A counry mors only a raw maeral and exors only a fnshed roduc. f he rce of he raw maeral rses by 5% on he world mare (over one year) and he rce of he exored fnshed roduc remans unchanged, he erms of rade deerorae by around 5% ( 1 15). Ths means ha he counry mus exor more o be able o connue morng he same uany of he raw maeral. 8 CONTACT f you have any uesons or commens you can conac us easly va our webse ( message o accreded exer, heme ndex ). You can also conac us by e-mal a he followng address: ozd.ahs.dffuson@ezv.admn.ch. 26