FINAL REPORT TASK FORCE CHAIN-LINKING IN STS

Transcription

1 EUROPEAN COMMSSON EUROSTAT Drecorae G: Global Busness Sascs Un G3: Shor-er Sascs; Tours Doc. Eurosa/G3 STS TF Chan-Lnkng SEP 202 EN FNAL REPORT TASK FORCE CHAN-LNKNG N STS MEETNGS OF THE SHORT-TERM STATSTCS TF LUXEMBOURG 0- NOVEMBER 200 LUXEMBOURG JUNE 202

2 Conens. Execuve Suary Glossary and sandard echnues for chan-lnkng n STS Chan-lnked ndex Fxed base year ndex Annual chan-lnked ndex Technues for annual chan-lnkng of onhly/uarerly daa Channg erod Base erod Weghng reference erod Reference erod Bencharkng he chaned seres o he annual chaned seres Level for erforng chan-lnkng Calculaon of eleenary ndces Calculaon of hgher level ndces Source of weghs Year of weghs Oher sources used o udae weghs o For volue ndces: a whch sage o erfor seasonal adjusen Praccal exales fro counres on annual chan-lnkng of rce ndces Norway PP Mehod aled Channg erod Wegh erod s he chaned seres bencharked o he annual chaned seres A wha level s chan-lnkng erfored Calculaon of eleenary ndces Calculaon of hgher level ndces Source of weghs Year of weghs Are oher sources used o udae weghs o T Oulne of he workflow: whch se s done when French coens on he Norwegan case of nconssency n aggregaon and on he correcon o aly o weghs n case of channg France PP SPP and or rces Calendar: no ye leened (wa unl nex Ocober) Mehod aled: one-onh overla (PP and or rces) or one-uarer overla (SPP).e. arge ehodology Channg erod Wegh erod Levels of chan-lnkng: all Are oher sources used o udae weghs o T-? Turkey PP Mehod aled Channg erod Wegh erod s he chaned seres bencharked o he annual chaned seres A wha level s chan-lnkng erfored Calculaon of eleenary ndces Calculaon of hgher level ndces... 2

3 Source of weghs Year of weghs Are oher sources used o udae weghs o T Oulne of he workflow: whch se s done when Croaa PP Mehod aled Channg erod Wegh erod s he chaned seres bencharked o he annual chaned seres A wha level s chan-lnkng erfored Calculaon of eleenary ndces Calculaon of hgher level ndces Source of weghs Year of weghs Are oher sources used o udae weghs o T Oulne of he workflow: whch se s done when Ausra PP Mehod aled Channg erod Wegh erod s he chaned seres bencharked o he annual chaned seres A wha level s chan-lnkng erfored Calculaon of eleenary ndces Source of weghs and year of weghs Are oher sources used of udae weghs o T Oulne of he workflow Lhuana PP Mehod aled Channg erod Wegh erod s he chaned seres bencharked o he annual chaned seres A wha level s chan-lnkng erfored Calculaon of eleenary ndces Calculaon of hgher level ndces Source of weghs Year of weghs Are oher sources used o udae weghs o T Oulne of he workflow: whch se s done when Lhuana SPP Mehod aled Channg erod Wegh erod s he chaned seres bencharked o he annual chaned seres A wha level s chan-lnkng erfored Calculaon of eleenary ndces Calculaon of hgher level ndces Source of weghs Year of weghs Are oher sources used o udae weghs o T Oulne of he workflow: whch se s done when

4 3.9. Lhuana or rce ndex Mehod aled Channg erod Wegh erod s he chaned seres bencharked o he annual chaned seres A wha level s chan-lnkng erfored Calculaon of eleenary ndces Calculaon of hgher level ndces Source of weghs Year of weghs Are oher sources used o udae weghs o T Oulne of he workflow: whch se s done when Praccal exales fro counres on annual chan-lnkng of volue ndces Fnland P Mehod aled Channg erod Wegh erod s he chaned seres bencharked o he annual chaned seres A wha level s chan-lnkng erfored Calculaon of eleenary ndces Calculaon of hgher-level ndces Source of weghs Year of weghs For volue ndces: a wha level s seasonal adjusen erfored Oulne of he workflow Croaa P Mehod aled Channg erod Wegh erod s he chaned seres bencharked o he annual chaned seres A wha level s chan-lnkng erfored Calculaon of eleenary ndces Calculaon of hgher level ndces Source of weghs Year of weghs Are oher sources used o udae weghs o T For volue ndces: a wha level s seasonal adjusen erfored Oulne of he workflow: whch se s done when Slovena P Calculaon Weghs Oulne of he workflow Uned Kngdo P Overvew Coarson of uarerly and annual overla echnues Uned Kngdo Real Sales ndex Overvew The chan-lnkng ehod Sofware Dssenaon

5 User reureens/engageen Oher relaed chan-lnkng research Basc RS workflow Nonal ndces Buldng u a chaned ndex on a revous fxed one (exale fro alan PP) Chaned ndex forulas Nesng chan-lnkng on a fxed base rce ndex TC and BC concden TC laer BC Chan-lnkng drf adjusen ndex dynacs n chan-lnkng: aled ocs The Rbe s rae of change decooson Soe algebrac ocs of he above forulas Cos-benef analyss Tes calculaons France reland Czech Reublc Croaa Norway Turkey Uned Kngdo Task Force conclusons on heorecal asecs and coss Theorecal asecs ros and cons Coss Task Force recoendaons regardng he leenaon of chan-lnkng n STS Task Force conclusons regardng he coon arge ehodology for chan-lnkng n STS Mebers of he Task Force

6 . EXECUTVE SUMMARY The curren STS regulaon allows o udae he weghs used for calculaon of ndces n STS every fve years or ore freuenly eanng yearly n cobnaon wh annual chanlnkng. Fro a ehodologcal on of vew annually chaned ndces are ofen consdered as a sueror aroach for shor-er sascs because of he use of ore recen weghng nforaon. However here s also soe concern abou he aoun of resources reured for he leenaon of such an aroach on he one hand and also for he regular annual work of udang he weghs. The STS Task Force on chan-lnkng was creaed o collec exerences on boh ehodologcal and raccal asecs fro counres ha have already leened he annual udae of weghs and chan-lnkng n STS naonally (see Chaer 3 for rce ndces and 4 for volue ndces) and o ssue recoendaons o hose counres nendng o leen such an aroach. The Task Force ebers' reors on osve asecs and robles encounered as well as on he nal and roune coss faced are subjec of Chaer 7. The recoendaons of he Task Force are resened n Chaer 8. n bref: he Task Force recoends o leen he annual udae of weghs and chanlnkng for rce and volue ndces n STS n suaons where he econoc srucure s develong fas; recognsng however ha no all Meber Saes wll be able o leen such an aroach n he shor er he Task Force found ha s ore relevan o have one coon arge ehod for he chan-lnkng of a gven STS ndcaor raher han havng all Meber Saes changng fro he fve-yearly rebasng o he annual udae of weghs and chan-lnkng; he coon arge ehodology for he chan-lnkng of STS rce ndces recoended by he Task Force s he one-onh overla for onhly ndces and he one-uarer overla n he case of uarerly ndces usng Deceber and he fourh uarer resecvely as lnk erods; for he chan-lnkng of STS volue ndces he recoended coon arge ehodology s he annual overla echnue; n order o acheve coarably of daa across counres and faclae he calculaon of Euroean aggregaes counres wllng o leen he annual udae of weghs n STS n cobnaon wh chan-lnkng are srongly advsed o follow he recoendaons regardng hese coon arge ehodologes. A glossary and sandard echnues for annual chan-lnkng n STS are resened n Chaer 2. Chaer 5 s a bref excurson on nonal ndces for whch chan-lnkng s no relevan. Buldng u a chaned ndex on an ndex wh a revously fxed base year s he subjec of Chaer 6. Chaer 9 conans he Task Force conclusons regardng he ehodology of chan-lnkng n STS. Fnally he Mebers of he Task Force are lsed under Chaer 0.

7 2 All docuens fro he Task Force are avalable on CRCABC: hs://crcabc.euroa.eu/w/browse/5bacd0b8-7a6e-498c-b4fa-d68f86e3d22 2. GLOSSARY AND STANDARD TECHNQUES FOR CHAN-LNKNG N STS 2.. Chan-lnked ndex Chan-lnkng eans consrucng long-run rce or volue easures by cuulang oveens n shor-er ndces wh dfferen base erods. For exale a erod-o-erod chan-lnked ndex easurng he changes fro erod 0 o C 0.e. can be consruced by ullyng a seres of shor-er ndces easurng he change fro one erod o he nex as follows: C where reresens a rce or volue ndex easurng he change fro erod o wh erod as base and reference erod. Chan-lnked ndces do no have a arcular base or wegh erod. Each lnk of he chan-lnked ndex has a base erod and wegh erod and he base and wegh erod are changng fro lnk o lnk. The chan-lnked ndex wll consue a erod-o-erod chan-lnked Laseyres volue ndex seres f for each lnk he shor-er ndces are consruced as Laseyres volue ndces wh he revous erod as base and reference erod. Tha s f V w LQ where LQ reresens a Laseyres volue ndex easurng he volue change fro erod o wh erod as base and reference erod; s he rce of e n erod (he rce weghs ); s he uany of e n erod ;

8 w s he base erod share wegh ha s he e s share n he oal value of erod ; and V s he oal value a curren rces n erod. Slarly he chan-lnked ndex wll consue a erod-o-erod chan-lnked Laseyres rce ndex seres f for each lnk he shor-er ndces are consruced as Laseyres rce ndces wh he revous erod as base and reference erod. Tha s f LP w V where LP reresens a Laseyres rce ndex easurng he rce change fro erod o wh erod as base and reference erod; Growh raes and ndex nubers coued for seres ha conan negaves or zeroes generally are sleadng and eanngless. Chan-lnkng should no be done ore freuenly han annually. Ths s anly because shor-er volaly n relave rces (e.g. caused by salng errors and seasonal effecs) can cause volue easures ha are chan-lnked ore freuenly han annually o show subsanal drf arcularly so for nonsuerlave ndex forulas lke Laseyres and Paasche. Slarly shor-er volaly n relave uanes can cause rce easures ha are chanlnked ore freuenly han annually o show subsanal drf. The urose of chan-lnkng s o ake no accoun long-er rends n changes n relave rces no eorary shor-er varaons Fxed base year ndex Fxed wegh ndces have her wegh srucure fxed a a arcular on n e. These weghs are used o coue ndces over an exended erod. Consan rce/volue esaes use he average rces/uanes of a arcular erod he base erod o wegh ogeher he corresondng uanes/rces. Consan rce/uany daa have he advanage for he users of he coonen seres beng addve unlke alernave volue/rce easures. The aern of relave rces/uanes n he base year however gh be less reresenave of he econoc condons for erods farher away fro he base year. Therefore fro e o e s necessary o udae he base erod o ado weghs ha beer reflec he curren condons and changes n he econoc srucure. 3

9 n STS n general he change of base erods s currenly every 5 years. Dfferen base erods and hus dfferen ses of rce/uany weghs gve dfferen ersecves. One he one hand when he weghs are udaed every 5 years he enre e seres can be recalculaed based on he new se of weghs. On he oher hand f he base erod s changed and daa for he dsan as s no recalculaed (rebased) a conssen e seres can be obaned by lnkng ffe year chunks of daa each of hese havng been calculaed on s own base year and weghng syse. Ths laer aroach wll lead a fve-yearly chan of Laseyres or Paasche ndces. ndeed hs rocess can be acceleraed o yeld annual channg whch s he rncle subjec of hs glossary. Noe he lnkng should be done for each seres aggregaes as well as subcoonens of he aggregaes ndeendenly of any aggregaon or accounng relaonsh beween he seres. n general fve-yearly chan-lnkng les ha he ndex e seres s no revsed for s enre hsory when he base year and ndex weghs are changed. s herefore necessary ha he dscree nervals (5 years) of he coonen ndexes are aggregaed by usng weghs fro hese nervals. n hs case he ndex s coled for a successon of dfferen segens whle keeng he orgnal weghs for each as segen fxed Annual chan-lnked ndex Annual chan-lnkng of onhly/uarerly daa les ha each lnk n he chan s consruced usng he chosen ndex nuber forula wh he average of he revous year ( ) as base and reference erod. The resulng shor-er onhly/uarerly ndces us subseuenly be lnked o for long conssen e seres exressed on a fxed reference erod. The chan-lnked Laseyres ye volue easures should be derved by colng onhly/uarerly esaes a he average rces of he revous year. The Laseyres and Paasche annually chan-lnked onhly/uarerly volue ndex forulas for each shor-er lnk n he chan are gven as Shor-er lnk n annually chan-lnked Laseyres: LQ Shor-er lnk n annually chan-lnked Paasche: PQ where s he uany-weghed annual arhec average of he rce of e n each onh/uarer of year -; 4

10 s he rce of e n onh/uarer of year -; and s he average uany of e n year -. Slarly he chan-lnked Laseyres ye rce easures should be derved by colng onhly/uarerly esaes a he average uanes of he revous year. The Laseyres and Paasche annually chan-lnked onhly/uarerly rce ndex forulas for each shor-er lnk n he chan are gven as follows Shor-er lnk n annually chan-lnked Laseyres: LP Shor-er lnk n annually chan-lnked Paasche: PP The weghs of an annual chan-lnked ndex are ycally udaed once a year. Techncally an annual chan-lnked ndex can l he annual udae o he weghs whou nroducng or reovng new or old roducs (a he eleenary aggregae level) reorng uns and reresenave roducs. On he oher hand he annual re-weghng can also nvolve drawng a new sale of roducs and a new ls of reorng uns Technues for annual chan-lnkng of onhly/uarerly daa As he chan-lnked Laseyres ye volue easures are derved by colng onhly/uarerly esaes a he average rces of he revous year he rce bass changes also each year. The resulng breaks do no lead o a connuous volue seres. By chanlnkng he onhly/uarerly daa he break resulng fro he annual change n he rce bass s elnaed. For onhly/uarerly daa here are hree dfferen echnues annual overla (AO) one-onh overla (MO)/one-uarer overla (QO) and over-he-year (OTY). The echnue of usng annual overlas (AO) for volue easures les colng esaes for each onh/uarer a he weghed annual average rces of he revous year wh subseuen lnkng usng he corresondng annual daa o rovde lnkng facors o scale he onhly/uarerly daa uward or downward. A foral resenaon of he annually chan-lnked onhly/uarerly Laseyres volue ndex for easurng he overall change fro he average of year 0 (he reference year) o onh/uarer of year : 5

11 6 0 s s s s s L AO CLQ Usng he annual overla echnue he annually chan-lnked onhly/uarerly Laseyres ndex aggregaes o he corresondng drec annual ndex. The annual overla echnue ay nroduce a se beween each lnk. Ths eans ha he develoen of he onhly ndex fro Deceber o January gh be nfluenced by changes n he weghng. The echnue of one-onh overlas (MO) for volue easures reures colng esaes for he overla onh (Deceber) a he weghed annual average rces of he curren year n addon o esaes a he average rces of he revous year. The rao beween he esaes for he lnkng onh a he average rces of he curren year and a he average rces of he revous year hen rovdes he lnkng facor o scale he onhly daa u or down. A foral resenaon of he one-onh chan-lnked onhly Laseyres volue ndex for easurng he overall change fro he average of year 0 (he reference year) o onh of year : s s s s s L MO CLQ The las facor s he lnk fro onh of year o Deceber of he revous year boh exressed a rces of -. The frs facor naes he chan by coarng Deceber of year no o Deceber of year 0 bu o he average of year 0 (akng year 0 he reference year 00). The one-onh overla echnue does no resul n daa ha aggregae exacly o he corresondng drec annual ndex. The one-onh overla rovdes he soohes ranson beween each lnk. The echnue of one-uarer overlas (QO) for volue easures reures colng esaes for he overla uarer (fourh uarer) a he weghed annual average rces of he curren year n addon o esaes a he average rces of he revous year. The rao beween he esaes for he lnkng uarer a he average rces of he curren year and a he average rces of he revous year hen rovdes he lnkng facor o scale he uarerly daa u or down. A foral resenaon of he one-uarer chan-lnked uarerly Laseyres volue ndex for easurng he overall change fro he average of year 0 (he reference year) o uarer of year : s s s s s L QO CLQ The las facor s he lnk fro uarer of year o he fourh uarer of he revous year boh exressed a rces of -. The frs facor naes he chan by coarng he fourh

12 uarer of year no o he fourh uarer of year 0 bu o he average of year 0 (akng year 0 he reference year 00). The one-uarer overla echnue does no resul n daa ha aggregae exacly o he corresondng drec annual ndex. The one-uarer overla rovdes he soohes ranson beween each lnk for uarerly daa. The over-he-year echnue (OTY) for volue easures reures colng esaes for each onh/uarer a he weghed annual average rces of he curren year n addon o esaes a he average rces of he revous year. The year-on-year changes n hese consan rce daa are hen used o exraolae he onhly/uarerly consan rce daa of he chosen reference erod. A foral resenaon of he over-he-year chan-lnked onhly Laseyres volue ndex for easurng he overall change fro he average of year 0 (he reference year) o onh/uarer of year : CLQ OTY L s2 s s s s The las facor s he lnk fro onh/uarer of year o onh/uarer of he revous year boh exressed a rces of -. The chan roduc s dfferen for every. The frs facor naes he chan by coarng onh/uarer of year no o onh/uarer of year 0 bu o he average of year 0 (akng year 0 he reference year 00). The over-he-year echnue does no resul n daa ha aggregae exacly o he corresondng drec annual ndex. All growh raes wh resec o he revous erod gh be nfluenced by changes n he weghng. n suaons wh srong changes n relave rces he over-he-year echnue can resul n dsored seasonal aerns n he lnked seres. Slarly chan-lnked Laseyres ye rce easures are derved by colng onhly/uarerly esaes a he average uanes of he revous year he uany bass also changes each year. The resulng breaks do no lead o a connuous rce seres. By chan-lnkng he onhly/uarerly daa he break resulng fro he annual change n he uany bass s elnaed. The echnue of usng annual overlas (AO) for rce easures les colng esaes for each onh/uarer a he weghed annual average uanes of he revous year wh subseuen lnkng usng he corresondng annual daa o rovde lnkng facors o scale he onhly/uarerly daa uward or downward. A foral resenaon of he annually chanlnked onhly/uarerly Laseyres rce ndex for easurng he overall change fro he average of year 0 (he reference year) o onh/uarer of year : CLP AO L 0 s s s s s The echnue of one-onh overlas (MO) for rce easures reures colng esaes for he overla onh (Deceber) a he weghed annual average uanes of he curren 7

13 8 year n addon o esaes a he average uanes of he revous year. The rao beween he esaes for he lnkng onh a he average uanes of he curren year and a he average uanes of he revous year hen rovdes he lnkng facor o scale he onhly daa u or down. A foral resenaon of he one-onh chan-lnked onhly Laseyres rce ndex for easurng he overall change fro he average of year 0 (he reference year) o onh of year : s s s s s L MO CLP The las facor s he lnk fro onh of year o Deceber of he revous year boh exressed a uanes of -. The frs facor naes he chan by coarng Deceber of year no o Deceber of year 0 bu o he average of year 0 (akng year 0 he reference year 00). The echnue of one-uarer overlas (QO) for rce easures reures colng esaes for he overla uarer (fourh uarer) a he weghed annual average uanes of he curren year n addon o esaes a he average uanes of he revous year. The rao beween he esaes for he lnkng uarer a he average uanes of he curren year and a he average uanes of he revous year hen rovdes he lnkng facor o scale he uarerly daa u or down. A foral resenaon of he one-uarer chan-lnked uarerly Laseyres rce ndex for easurng he overall change fro he average of year 0 (he reference year) o uarer of year : s s s s s L QO CLP The las facor s he lnk fro uarer of year o he fourh uarer of he revous year boh exressed a uanes of -. The frs facor naes he chan by coarng he fourh uarer of year no o he fourh uarer of year 0 bu o he average of year 0 (akng year 0 he reference year 00). The over-he-year echnue (OTY) for rce easures reures colng esaes for each onh/uarer a he weghed annual average uanes of he curren year n addon o esaes a he average uanes of he revous year. The year-on-year changes n hese consan uany daa are hen used o exraolae he onhly/uarerly consan uany daa of he chosen reference erod. A foral resenaon of he over-he-year chan-lnked onhly Laseyres volue ndex for easurng he overall change fro he average of year 0 (he reference year) o onh/uarer of year : s s s s s L OTY CLP

14 The chan roduc s dfferen for every. n suaons wh srong changes n relave uanes he over-he-year echnue can resul n dsored seasonal aerns n he lnked seres. To conclude whle sandard rce sascs colaon exclusvely uses he one-onh/oneuarer overla echnue he annual overla echnue ay be ore raccal for Laseyres ye volue easures. The over-he-year echnue should be avoded Channg erod For he one-onh overla (MO) Deceber of he revous year s he onh chosen as he lnk of he chan. n Deceber of he year Y- he new calculaon base for he year Y s se u. Such a work les he udang of he selecon of roducs (a he eleenary aggregae level) he ls of reorng uns and he se of reresenave roducs. For rce ndces sarng fro January n year Y he denonaor of he raos wll be gven by he rce uoaon a e Deceber of year Y- (such a denonaor for he es enered n he new calculaon base s eual o 00). For he one-uarer overla (QO) he las uarer of he revous year s he uarer chosen as he lnk of he chan. The average onh/uarer of he revous year s chosen as he lnk n he chan for he annual overla echnue (AO). The corresondng erod (onh/uarer) n he revous year s chosen as he lnk for he over-he-year echnue (OTY) Base erod The base erod s he base of he rce or uany raos beng weghed ogeher a he eleenary level of aggregaon (e.g. erod 0 s he base for he uany rao ) Weghng reference erod The weghng reference erod s he erod fro whch he weghs are aken. The weghng reference erod s eual o he base erod for a fxed-base Laseyres ndex and o he curren erod for a fxed-base Paasche ndex. An ndex s sad o be annually chan-lnked f s weghs syse s annually udaed. The chan aroach does no re-calculae he enre hsorcal seres whenever he weghs are udaed bu raher lnks ogeher he wo ndex seres o roduce a coheren e seres. The chan-lnked ndex s coled for a successon of dfferen segens whle keeng he orgnal weghs for each as segen fxed. For an annual chan-lnked volue ndex he base-erod for he rce weghs s he annual average of he revous year. The rces of one arcular onh/uarer are no suable as rce weghs for volue easures because of seasonal flucuaons and oher shor-er volales n relave rces. Use of weghed annual average rces reduces hese effecs. Therefore weghed annual average rces are ore reresenave for he oher onhs/uarers of he year. The rces of he corresondng onh/uarer of he revous year or he corresondng uarer of a fxed base year are no suable as rce weghs for 9 0

15 volue easures because he derved volue easures only allow he curren onh/uarer o be coared wh he sae onh/uarer of he revous year or years. Seres of year-oyear changes do no consue e seres ha allow dfferen erods o be coared and canno be lnked ogeher o for such e seres. n arcular because hey nvolve usng dfferen rces for each onh/uarer of he year hey do no allow dfferen onhs/uarers whn he sae year o be coared. The rces of he revous onh/uarer are also no suable as rce weghs for Laseyres-ye volue easures for he followng wo reasons. Frs he use of dfferen rce weghs for each onh/uarer of he year does no allow he onhs/uarers whn he sae year o be aggregaed and coared wh her corresondng drec annual esaes. Second f he onh-oonh/uarer-o-uarer changes are lnked ogeher o for a e seres shor-er volaly n relave rces ay cause he onhly/uarerly chan-lnked easures o show subsanal drf coared o corresondng drec easures Reference erod n he reference erod he ndex seres s exressed as eual o 00. The reference erod can be changed by sly dvdng he ndex seres wh s level n any erod chosen as he new reference erod. For uroses of resenaon he reference erod of he annual chan-lnked ndex s se o eual 00. Changng he reference erod sly consss n a rescalng racce and can be done a any e. The rescalng coeffcen s sly he arhec ean of he 2-onhly/4-uarerly ndces n he year of he new reference erod. The rescalng does no affec eher he onh-o-onh/uarer-o-uarer ndex rae of change or he 2-onh/4- uarer ndex rae of change Bencharkng he chaned seres o he annual chaned seres When conssency beween onhly/uarerly and annual daa s an ssue he conssency can be forced on he onhly/uarerly daa usng bencharkng echnues. Bencharkng echnues can be necessary even f he basc reureen ha onhly/uarerly and he annual easures are based on he sae ehods of colaon and resenaon (.e. sae ndex forula and reference erod) s e. f bencharkng echnues are used he erods afer he las base year gh be consraned and hs should no lead o a break n he seres Level for erforng chan-lnkng The aggregaon of he lower-level ndces o oban he hgher levels ones u o he overall ndex should gran (aar fro roundng ssues) he sae resul as f he oal ndex had been coled n one se. There gh be a sgnfcan growh dfference f chan-lnkng s leened a a ore dealed level e.g. 4-dg level agans ore broadly 2 dg level. How are ndces below he level of chan-lnkng calculaed? f 4 dg seres are coled fro lower level seres lower level aggregaon gh ake lace usng he fxed based ehod. 2.. Calculaon of eleenary ndces For rce ndces he frs se n colng concerns rce relaves. Each rce relave s he uoen of he rao beween he curren onhly rce (nueraor) and he base rce (denonaor). The denonaor s eual o he base onhly/uarerly rce used for he annual chan lnkng. 0

16 For he one-onh overla he base erod rce s Deceber of he revous year. The rce relave forula s 00 2 n a second se rce relaves are aggregaed o oban he eleenary rce ndex. The ndex s also known as he eleenary roduc ndex Calculaon of hgher level ndces The eleenary roduc ndces are aggregaed as weghed averages (ycally as a Laseyres-ye ndex) o rovde a se of synhec ndces u o he overall ndex. The weghs are udaed annually. The e seres usng yearly udaed weghs are chan-lnked Source of weghs Srucural busness sascs (SBS) he Prodco survey naonal accouns daa he foregn rade sascs and sales daa are ofen used as he bass for he annual weghs udae. However a nuber of counres are no sasfed wh he elness of hese weghs referrng freuenly o wo years before he reorng erod (-2). For he PP concernng he lowes level of ndex deal or roduc ndces he os wdely used source for weghs s he Prodco survey alhough naonal accouns daa are also used; soe counres also have weghs resened usng he CPA. For hgher level ndces he source of weghs for he PP norally concerns he value of urnover fro SBS or fro naonal accouns and n soe cases Prodco daa. For STS he referred source of weghs s SBS. Ths s he only source wh he necessary deal avalable for all Meber Saes. For he sake of coarably across counres s furherore desrable ha all Meber Saes are usng he sae source of weghs Year of weghs The use of annual chan-lnkng les he annual udae of weghs. However he ueson s f for he calculaon of January or he frs uarer of he curren year he weghs are already avalable for he revous year Oher sources used o udae weghs o - The use of recen weghs leads o a rade-off beween elness and accuracy. f weghs refer o year -2 hey are udaed n order o ake he reresenave for year -. Dfferen esaon ehods based on naonal accouns onhly urnover sascs or rce udang are used n dfferen counres o udae he weghs o year - e.g. n Norway SBS daa s avalable for -2 and hus no consdered as beng suffcenly ely for calculang he P SBS daa s rojeced o - usng naonal accouns For volue ndces: a whch sage o erfor seasonal adjusen n racce he os sragh-forward aroach s o aly seasonal adjusen o chan-lnked ndces raher han o seres of values a revous year s rces. The reason s ha such seres do no consue a rue e seres and hus dsors he seasonal adjused resuls because he

17 change of base fro Deceber o January or uarer four o uarer one wll be seen as a seasonal aern. The annual-overla echnue gh lead o a break fro Deceber o January or fro he fourh uarer of a year o he frs uarer of he followng year. f changes n relave rces across dealed coonens go no he sae drecon and have a slar ac n soe consecuve years here s a rsk ha he annual overla chan-lnkng echnues ay creae an arfcal seasonaly o he volue seres. Therefore s generally recoended and os coon n racce ha seasonal adjusen s carred ou afer chan-lnkng. However he use of dfferen rce bases n he channg rocess ay have an ac on he seasonal facors and he seasonal adjusen ay conseuenly no be able o erfecly correc for seasonaly n he volues. The over-he-year echnue acs he nfra-annual rofle of a seres. Therefore fro he ersecve of seasonal adjusen he use of he over-he-year echnue s no recoended. 3. PRACTCAL EXAMPLES FROM COUNTRES ON ANNUAL CHAN-LNKNG OF PRCE NDCES n he followng counry exales are resened. The ex conrbuons cover he ons fro he glossary and sandard echnues of he revous chaer. 3.. Norway PP 3... Mehod aled The Norwegan PP s calculaed usng a chaned Laseyres forula n whch he weghs are udaed annually. Ths ehodology was leened n 200. However snce he weghs and base erod are no exacly he sae s ore correc o descrbe as chaned Young ndex. Pror o he year 200 he Norwegan PP was calculaed usng a fxed base year forula. The ehod of chan-lnkng and udang he weghs was rarly leened because of he flexbly n ers of ncludng new reresenave goods and also o rove he elness of he weghs Channg erod The chaned ndex s obaned usng a onhly overla (MO). The channg erod s always Deceber year -. Thus he chaned ndex s a seres of chaned Laseyres ndces Wegh erod The source of he weghs s -3 bu hey are udaed o refer o year - he sae year as he base year s he chaned seres bencharked o he annual chaned seres The chaned seres are no bencharked o he annual seres. 2

18 3..5. A wha level s chan-lnkng erfored The chan lnkng s erfored a every level n he aggregaon whch s sx fro-dg CPA hrd and second level of he sandard ndusral classfcaon (SC 2007) as well as on aggregaes corsng several SC seres (such as PP oal). Because he PP s corsed of ndces for he doesc and exors arke eans here are hree ses of chan lnkng facors; doesc exors and PP oal Calculaon of eleenary ndces The eleenary level n he Norwegan PP s he HS he Haronzed Syse. An ndex s calculaed for every HS ha s ncluded n he se of weghs as he geoerc average of he rce changes for he roducs classfed whn he resecve HS. The rce changes are adjused for ualy changes based on varous echnues as well as checked hrough varous error checkng rocedures before ncluded n he calculaon of he eleenary ndex. Mssng rce observaons are esaed n he eleenary level based on he rce changes of roducs classfed whn he sae HS as he ssng observaon rovded here are a leas he fve acual rce (no ued) n he resecve HS. f hs condon s broken he ssng rce s esaed based on he lowes ossble level of he aggregaon caalogue n whch here a leas fve acual rce observaons: Frs he resecve CPA hen accordng o he herarchcal srucure of SC or ulaely esaed as no rce change Calculaon of hgher level ndces The eleenary ndces are hen lnked o her resecve CPA accordng o annual corresondence ables. The CPA ndex s calculaed as he weghed average of he se of lnked eleenary ndces he HS. Fro he CPA accordng o he herarchcal srucure of SC and also o he an ndusral groungs. Ths s erfored searaely n boh arkes n whch he goods are sold; doesc and/or exor arke. Fnally he PP aggregaes are calculaed he sae way usng he weghs n he eleenary level calculaed as he relave orance of he eleenary level across he doesc and/or he exor arke hus he wegh of any PP eleenary level consue he relave orance of he eleenary level across boh arkes corsng he PP Source of weghs The source of he weghs s he laes avalable fnal calculaon of he Naonal Accouns. The sascal un of he naonal accouns used n he wegh s roducer values base values n curren rce n he naonal verson of CPA. To calculae dsrbuon keys fro CPA o he eleenary level he sources used are he annual PRODCOM survey as well as exor and or values fro foregn rade sascs Year of weghs The fnal NA usually refers o year -3 bu hey are udaed o reresen -. 3

19 3..0. Are oher sources used o udae weghs o T- The weghs are udaed o year - usng he uarerly naonal accouns. Ths s erfored for roducon value and exor value. The doesc arke weghs are hen defned as he udaed roducon values nus he udaed exor values. n addon he sources nvolved n calculang dsrbuon forulas enoned n A Oulne of he workflow: whch se s done when. Calculae dsrbuon keys fro CPA o HS 2. Udang o - and dsrbue accordng o dsrbuon keys 3. Esablsh base erod - Resar shor er ndces ( 0 =00) - Long er ndces for base erod 5. Calculae weghs for every level n he aggregaon caalogue 3.2. French coens on he Norwegan case of nconssency n aggregaon and on he correcon o aly o weghs n case of channg Durng he frs eeng of he ask force chan lnkng n STS? 0- Noveber 200 Cahrne BERJORDET of Norway showed us a srange henoenon on roducs 06 - crude eroleu and naural gas (aggregae) crude eroleu and naural gas (coonens) n July 2009 due o chan-lnkng: 4

20 s well known ha a chan-lnked Laseyres ndex does no kee he neresng roery of conssency n aggregaon bu he fac ha coonens ndces 06.0 and were boh eual o 50 or abou n July 2009 whle aggregaed ndex 06 overassed 200 was a serous arguen agans he relevance of chan-lnked ndces. Durng he eeng exressed he dea ha he henoenon was due o he drec use of weghs year n- (~ average year n- ) cobned wh an overla on Deceber n- rce ndex whou correcon. The absence of correcon s confred by he Norwegan June 202 resenaon on chanlnkng n PP: Wegh erod does no exacly ach he base erod: Wegh erod: - Base erod: Dec year - Srcly seakng hnk ha he Norwegans should have wren: base erod: (average year) - reference erod: Dec year - n he Lavan resenaon of he sae frs eeng of he TF we could read ha a correcon was aled (beween average year n-2 and Deceber n-): n order o ensure he syery of weghs and rce base erods he weghs aled for he calculaon of he PP are rceudaed o base rces (Deceber of he revous year). The rncle of hs correcon s ue sle o undersand. The hyohess of fxed uanes cobned wh absolue rces s euvalen wh rce-udaed values cobned wh onhly changes. Le us consder he onhly change of rce of an aggregae accordng o he Laseyres forula: / b b ( ( ) * b b b b b ( ) * ) * b Monhly changes Fxed uanes of base erod b nal weghs Prce-udang of weghs When fxed base Laseyres ndces (values) gve lace o chan-lnked (values) Laseyres ndces he udae of values beween erod b and year n-2 or n- eans lcly udae of uanes and udae of rces beween erod b and year n-2 or n- bu udae of rces beween (average) year n-2 or n- and Deceber n- (n he case of exlc one-onh-overla on Deceber n- ) s sll ssng (he Laseyres ndex beween Deceber n- and onh akes lcly 5

21 no accoun he udae of rces snce Deceber n-) and he dfference beween average year 2008 and Deceber 2008 was ue large for crude eroleu! Wh an exlc one-onh-overla on Deceber n- he revous forula becoes: / Dec _ n b Dec _ n b ( ( ) * b b b Dec _ n ( ) * b ) * b Dec _ n b Dec _ n Correcon o aly o he weghs of year n-2 or n- unl Deceber n- n case of exlc one-onh Wh an lc one-onh-overla on Deceber n- as n he French case where all eleenary ndces rean n a fxed reference (bu no n a fxed base) he revous forula suggess: / ref ref b b ( ( ) * b b b b ref b ( ) * ) * ref b ref General correcon o aly o he weghs n case of udae of he base erod Bu hs absolue ndex would be rue only f he change of base erod had occurred snce he begnnng ( would hen be a Löwe ndex). n fac he syse of chan-lnkng ransfors / ref / ref no hs rue forula (dvson of by ): / ref ( ( ) * ) * ( ) / ) * ref b / ref / ref b b b b b / ref ref / ref * * b / ref / ref ref ( ( bb ) / ) * ( ( b b ) * ) * b ref ndeed he French PP s coled wh a onhly channg and has seeed us easer o ove oward a onhly chaned ndex n whch he weghs are udaed annually accordng o hs forula we can read n he resenaon of Ber M. BALK n he frs eeng of he TF: A chaned ndex: For onh of year relave o soe base year 0 a rce ndex can be defned as: ( Correcon o aly o he French weghs (lc one-onh overla) P 0 P Lo P Lo ( 2 ; x ) P Lo ( Lo ( ; x ) P ( ; x ) Ths can be wren as a onhly chaned ndex wh he weghs are udaed annually. ; x 6 2 ) P Lo ( ; x 3 )

22 n hs case he weghs udae needs a correcon for he asyery beween he base erod (year n-2 or n-) and he reference erod (can be Deceber n- or he reference of he chanlnked ndces). The dvson of he new weghs by he rce ndex of he new base year n he reference erod s a general rule (rue for Deceber n- n case of exlc one-onh overla or for he reference year of he chan-lnked ndces n case of lc one-onh overla). For hs syse of drec forulas n reference year (lc one-onh overla) hs correcon can be nerreed lke hs: he onhly channg s euvalen o a eranen udae of he rces snce he reference erod; he udae of weghs s euvalen o an udae of uanes and of rces beween he reference erod and he new base erod (base = erod of he new uanes / weghs aken no accoun); hence he udae of rces beween he reference erod and he new base erod has been couned wce! A correcon us be aled for once. Afer he frs eeng of he Task Force Sascs Norway sen e all he fgures: weghs shor er ndces and long er ndces of roducs 06.0 and n July 20 was n conac wh Esen KRSTANSEN. was hen able o re-cole he chaned ndces n he Norwegan way ( long er ndces whou correcon on he weghs of year n-) n he Norwegan way wh he correcon had roosed and n he French way (chaned ndces whou neredae n Deceber n-.e. lc one-onh overla) was lannng. The las wo seres were very close (and canno be dsngushed on he grah below) and uch beer for he conssency n aggregaon even f no erfec (see soe onhs n 2007): CPA0600 CPA06200 NACE06 FR2DNACE06 FR2CNACE n he French rojec Paaye we have decded ha f we dscover an aggregae (lke 06 n hs exale) ou of he nerval fored by s coonens we wll relace by an absolue average for he concerned onh: 7

23 / ref ( ( ( b ) / b ( b b b / ref ) / ) * b / ref / ref ) Noe: a he occason of a recen sson n Ukrane noced ha he Ukranan PP had been chan-lnked for ore han weny years (n hree ses: reference onh - reference Deceber n- fxed reference year) hanks o an orgnal Swedsh echncal asssance. Snce he begnnng sees ha hs correcon udae of he weghs: Dec _ n * b (coeffcen) was aled for he annual Tes calculaons were erfored n he Ukranan way wh he Norwegan fgures and resuled no he sae fgures as n he Norwegan aggregaon when no correcon was aled and as n he French roosals when he usual Ukranan correcon was aled France PP SPP and or rces Calendar: no ye leened (wa unl nex Ocober) French PP (ncludng SPP and or rces) has no ye been convered no chaned ndcaors. The rojec Paaye whch sounds lke PP n French nends o nroduce chan-lnkng ogeher wh oher roveens or changes n Auun 202 ( s of Ocober 202 exacly) n reference 200. Tha s for roducon and for each level of classfcaon. For dssenaon of aggregaes (CPA 4 dgs and above) unl February 203 French PP wll rean n fxed base Laseyres base and reference year 2005 hanks o a arallel rogra of colaon under Excel. On February 203 he new seres n reference chan-lnked - wll be dssenaed nsead of he forer seres n reference fxed base Laseyres Mehod aled: one-onh overla (PP and or rces) or one-uarer overla (SPP).e. arge ehodology Annual weghs wll be refreshed every onh of May corresondng o defnve ndces for onh of January (PP and or rces) and rovsonal ndces for frs uarer (SPP). Maheacally forulas wll be euvalen wh a one-onh overla n Deceber (PP and or rces) or a one-uarer overla n fourh uarer (SPP) bu we wll no use an ndex reference 00 n las Deceber or n las fourh uarer as an neredae for colaon neher an ndex reference 00 for las onh or las uarer: raher we wll change he annual weghs n order ha our chan-lnked ndces - whch have always been coled by onhly 8

24 chan-lnkng n reference 2000 now 2005 soon ake no accoun new annual urnovers and new annual aouns for all erods of he sae year based on daa of year n-2 correced on rce changes snce ha year. f daa of year n- becoe avalable on May we wll of course use he bu we wll only udae annual weghs once a year on May. Our curren syse of colaon / aggregaon reles already on a onhly channg n reference 2005 (wh fxed weghs): SVAL j SVAL j x SVAL x SPOND x ( S) SVAL x SPOND x ( S ) x ( S) Hence he dea of chan-lnkng s only o change he weghs (SPOND) conssenly once a year Channg erod Srcly seakng channg s (always) ade wh onh - or uarer - bu forulas wll be euvalen o chan-lnkng wh Deceber or las uarer of year n- exce ha he conen n eleenary rces or roducs ndces can Wegh erod We exec year n-2 and we hoe n edu er year n- avalable on May of year n for ndces snce January or frs uarer of year n. For hgher levels NA should rovde weghs on year n Levels of chan-lnkng: all The dea of rojec Paaye s ha chan-lnkng would be oeraed a each level.e. for eleenary ndces (fro SBS-ProdCo or cusos daa for each fr) for edu level ndces (fro SBS-ProdCo or cusos daa for each sub-class of roducs) and for aggregaes (fro Naonal Accouns and SBS or cusos daa). 9

25 Secondary aggregaon ree (oher seres) Man aggregaon ree (colaon of CPA4 level and P seres) Man aggregaon rees and secondary aggregaon rees for fuure PP Colaon of weghs n a o-down aroach For each ndcaor (oal ouu sold on doesc arke on foregn arkes ors) Noe : he or rees can be dfferen fro ouu rees. Aggregaes (CPA4 or sura) weghs fro NA Class of roducs (CPA4) Weghs fro SBS wedged on NA Grou of ProdCo es Weghs fro ProdCo = SBS (EAP) (wedged on NA) Grou 2 Grou 3 Grou 4 These grous of ProdCo es coose a aron of he class of roducs desgned for P needs. Enerrse * Grou Weghs fro ProdCo = SBS (EAP) Enerrse j * Grou Weghs fro ProdCo = SBS (EAP) SR SR2 SR3 SR4 SR5 SR6 SR7 f oher seres-ndces han n he an aggregaon ree are o be coled hey are descrbed n a secondary aggregaon ree (norally fro SR bu could be fro oher levels). Sere-ndex 00 Sere-ndex 200 Sere-ndex 200 Sere-ndex 2200 Sere-ndex 000 Sere-ndex 2000 The arrows reresen he way he weghs are osed fro a level o anoher Are oher sources used o udae weghs o T-? A hghes levels Naonal Accouns should rovde weghs on year n-. For eleenary and edu level ndces sources (SBS-ProdCo and cusos) should only concern year n-2 n near fuure bu could haen n edu er ha hese sources would be avalable on year n- n e for he udae occurrng n May. Even f weghs concern only year n-2 a correcon s aled o hese sources n order o rovde relevan weghs as f he rce changes beween year n-2 and Deceber (or fourh uarer) n- were aled n order o exraolae sources on Deceber n-; bu as we rean n chan-lnked ndces reference 200 we have only o dvde by annual average rce ndces of year n-2 n reference 200 whch s euvalen. f a hghes levels new weghs rely on aouns of year n- he correcon wll conss on a dvson by annual average rce ndces of year n- n reference 200. Weghs are ade addve n a o-down logc. 20

26 3.4. Turkey PP Mehod aled PP s calculaed usng a chaned Laseyres forula n whch he weghs are udaed annually. Ths ehodology was leened n 2003 nsred by CP/ HCP works of Turkey whch s also chaned Laseyres and was udaed a he sae e wh PP. Econoc crss ror o 2003 (n he years 998 and 2002) ade dffcul o defne an arorae base year for Turkey Channg erod Deceber of he revous year (Deceber year -) s he channg erod. The one-onhoverla echnue s used for annual chan-lnkng Wegh erod The source of he weghs s -2 bu hey are udaed o refer o year - he sae year as he base year s he chaned seres bencharked o he annual chaned seres The chaned seres are no bencharked o he annual seres A wha level s chan-lnkng erfored The chan lnkng s erfored a os dealed level n he aggregaon whch s fro 0 dg naonal Prodco (ProdTR) o NACE secons Calculaon of eleenary ndces Weghed arhec average of rces s used o cobne basc rce observaon o he frs level Calculaon of hgher level ndces Fro he ProdCo accordng o he herarchcal srucure of CPA/NACE: Aggregaon of lower level ndces accordng o CPA ( and an secons) JAN 202 JAN 202( Dec 20) 00 = w ( dec20) DEC base erod: Deceber 20 JAN 202 = DEC 20 x JAN 202 reference year: 2003 ( Dec 20) 00 The channg erod s Deceber Source of weghs The source of he weghs s he Naonal Accouns. Prncally os dealed level fro he Naonal Accouns should be used as source currenly 3 dg grous of CPA. The sascal un of he naonal accouns used n he wegh s roducer sales. ndusral roducon daa (4 2

27 dg and lower deals local uns and enerrses ) and Prodco sascs (now only for cross-check -2 daa are no avalable for PP) used for lower level weghs Year of weghs The weghs refer o year -2 bu hey are udaed o Deceber of year Are oher sources used o udae weghs o T- Weghs are rce udaed o Oulne of he workflow: whch se s done when. Annual udae of baske of goods (fro Ocober o Deceber): Selecon of new o-sellng roducs and local uns fro he ndusral Producon daa (-2 for calculaon and lus las udaed daa for decson of coverage) as well as elnaon of roducs and local uns fro he sale. PP uesonnares are sen. 2. Annual udae of weghs (n January): cobne he weghng nforaon fro he naonal accouns and he roducon survey wh he udaed baske of goods (aoun of work s arox. onh). Calculae weghs for every level n he aggregaon. 3. Make new ables wh new weghs and new baske (n January). 4. Colaon of chan-lnkng PP (every onh) 3.5. Croaa PP Mehod aled The Croaan PP s annually chan-lnked Laseyres ye ndex. PP weghs are beng udang annually usng PRODCOM daa (.e. naonal ore dealed verson) snce 998. The base erod s Deceber of revous year. However snce he weghs for PP relae o a whole year bu he corresondng base erod s a sngle onh he PP s acually an annually chan-lnked Young ndex. The sae ehods for calculaon of PP on doesc arke have beng aled fro 962 when acually calculaon of he PP on doesc arke sared n Croaa (long radon). Snce January 20 calculaon of boh searae PP on non-doesc arke and coose PP oal are beng sared besdes PP on doesc arke usng he sae ehod of calculaon Channg erod The PP s annually chan-lnked usng a onhly overla. The channg erod s Deceber of revous year (-). The base erod s also he Deceber of revous year. Because he weghs relae o a whole year bu he corresondng base erod s a sngle onh (Deceber) he PP s ore recsely an annually chan-lnked Young ndex hen Laseyres. 22

28 Wegh erod The weghs erod s -2 bu hey are udaed regularly o refer o year - he sae year as he base year s he chaned seres bencharked o he annual chaned seres The chaned seres s no bencharked A wha level s chan-lnkng erfored The chan lnkng s erfored a each level of aggregaon sarng fro en-dg roduc level of PRODCOM based naonal noenclaure o herarchcal level of NKD 2007 (=NACE Rev.2) classes grous and dvsons as well as on aggregae sub-ndces levels (PP on doesc and non-doesc arke) and PP oal Calculaon of eleenary ndces Croaan eleenary rce ndces for each (eleenary) reresenave roduc/e of naonal based PRODCOM noenclaure are beng calculaed fro daa on ndvdual rces by dvdng ndvdual rces of a curren onh by ndvdual rces of a base erod (Deceber of a revous year) Calculaon of hgher level ndces Croaan hgher level ndces ha s aggregae rce ndces of a classes grous dvsons and secons of he NKD (= NACE Rev.2) as well as for MGs are beng calculaed by a weghed arhec ean fro eleenary ndces accordng o he odfed Laseyres forula (.e. Young forula): Whereby: s an ndex of a class grou dvson or secon and he oal ndex Pn Po s a rce n a curren erod (onh) s a rce n a base erod (Deceber revous year) Wo s a relave sale srucure n a base erod Source of weghs The source of he weghs for NACE Rev.2/CPA 2008 hgher heracal levels (4-dgs 3 dgs 2 dgs MGs ) s roducon sold volues and values of annual PRODCOM based survey for boh doesc and non-doesc arke (so cold relave base srucure). 23

29 The source of he weghs for eleenary roduc/e rce ndces on 0-dg levels are based on roducon enerrses nforaon on roducon sold (enerrse-roduc cobnaon) Year of weghs Weghs refer o year -2 bu hey are arally udaed o reresen year Are oher sources used o udae weghs o T- The weghs are udaed o year - for eleenary roduc/e rces usng enerrses nforaon Oulne of he workflow: whch se s done when PRODCOM s used as a salng frae for Croaan PP. The PRODCOM survey s a near census of relevan enerrses; all hose wh an eloyen of a leas 0 are saled accounng for 95% of roducon sold on doesc and non-doesc arke The PP sale survey consss of all enerrse-roduc cobnaons coverng hose roducs whch accoun for 80% of hose NACE classes wh a sold roducon value on doesc arke of a leas 3000 and on non-doesc arke of a leas The selecon of enerrses has beng done accordng o her share n he roducon of seleced roducs searaely for doesc and non-doesc arke. For each such enerrse-roduc cobnaon he rce of one e s colleced er onh. The workflow ses are: Udang of sale frae accordng o selecon crera fro PRODCOM based survey resuls. Udang sale ncludes refreshng he sale wh new roduc-es/enerrses as well as elnang hose roduc-es below he selecon crera (Noveber o Deceber) Defnng he new roduc-e secfcaon by conacng enerrses drecly by hone or e- al (second half of Deceber o frs half of January) Udang he weghs by cobnng nforaon fro PRODCOM resuls wh udaed roduc-es (baske of goods). Dsrbuon of weghs o all heracal levels concerns n PP calculaon (Deceber/January). Uloadng he udaed PP daabases wh new weghs and new roduc-es secfcaons akng fnal sofware sengs for regular daa collecon (PP survey s CAW based) rocessng valdaon coung and dssenaon (January) Oenng dedcaed web-se for new PP daa collecon (6 h of January each year) Daa collecon (CAW) valdaon rocessng and coung he chan-lnkng PP (second half of January o 8 h of February) Analysng he chan-lnkng PPs (ossble correcon go back o ndvdual daa) rearaon for ublcaons and fnally dssenaon o naonal users and Eurosa (+5 a laes) 24

30 Noe: The PP onhly survey for 202 covers for PP daa collecon on he doesc arke he sale for 555 e rces whn he seleced PRODCOM roducs n 65 enerrses whle for he PP on he non-doesc arke covers 83 e rces whn he seleced PRODCOM roducs n 509 enerrses Ausra PP Mehod aled n Ausra a chan-lnked Laseyres rce ndex s used for PP. The PP should ee he followng reureens: - Colaon of ndces for all NACE levels (4- dg 3-dg 2-dg oal ndusry) regardless of wheher roducon was characersc or non-characersc - Colaon of ndces for all NACE levels and all CPA levels - Colaon of ndces for he doesc and non-doesc arke (exor arke) Therefore he ake-arx (-3) fro he Naonal Accouns (NA) was chosen as source of weghs on hgher levels. The ake-arx rovdes nforaon of weghs for all NACE levels (4-dg level uwards) as well as for all CPA levels (6-dg level uwards) for he doesc and he non-doesc arke (Foregn Trade daa). Below he value of sold roducon fro he Prodco survey (-) s used as a source of weghs. The an reason for he alcaon of chan-lnkng was o absorb he e lag of 3 years for he avalably of he ake-arx. Chan-lnkng allows he udae of weghs annually. n addon chan-lnkng has he advanage ha he baske of goods can be udaed on an annual bass Channg erod The channg erod s Deceber las year (one-onh overla echnue) Wegh erod Las avalable sources of weghs: PRODCOM survey (-) for ndces on CPA 6-dg level; Make-Marx fro Naonal Accouns (NA) (-3) for ndces on NACE 4-dg level and for ndces on hgher NACE levels (3-dg 2-dg MGS oal ndusry) s he chaned seres bencharked o he annual chaned seres The chaned seres s no bencharked. 25

31 A wha level s chan-lnkng erfored Fro CPA 6-dg level o NACE 2-dg level MGS and oal ndusry chan-lnkng s erfored for he oal doesc and non-doesc arke Calculaon of eleenary ndces Frs se: Each rce relave s he uoen of he rao beween he curren onhly rce and he base rce Second se: he rce relaves are aggregaed (usng he geoerc ean) o an eleenary roduc ndex (PRODCOM level). Geoerc ean s aled because s assued ha all roducs have aroxaely he sae develoen n all sraa Source of weghs and year of weghs Las avalable sources of weghs: PRODCOM survey (-) for ndces on CPA 6-dg level; Make-Marx fro Naonal Accouns (NA) (-3) for ndces on NACE 4-dg level and for ndces on hgher NACE levels (3-dg 2-dg MGS oal ndusry) Are oher sources used of udae weghs o T- A rce-udae o Deceber of he revous year s erfored Oulne of he workflow. Se (Noveber o Deceber) Annual udae of baske of goods: Selecon of new o-sellng roducs and local uns fro he Prodco survey (-) as well as elnaon of roducs and local uns fro he sale 2. Se (January) Annual udae of weghs (n January): cobne he weghng nforaon fro he akearx and he ProdCo survey wh he udaed baske of goods (aoun of work s arox. onh) 3. Se (every onh) Colaon of chan-lnkng PP (every onh) 3.7. Lhuana PP Producer rce ndex (PP) s calculaed fro 995 usng Laseyres forula n Sascs Lhuana Mehod aled The annual chan-lnkng ehod s aled. Ths ehod was leened because: 26

32 ) gves a ossbly o udae a baske of reresenave roducs and reove non-exsng roducs annually. 2) Annually revsed weghs are ore accurae and u o dae because he arke s changng radly Channg erod Deceber s he lnkng erod of year - ( reorng year) Wegh erod The wegh erod s calendar year s he chaned seres bencharked o he annual chaned seres The chaned seres s no bencharked A wha level s chan-lnkng erfored A he 4-dg level by NACE Rev.2 chan-lnkng s erfored Calculaon of eleenary ndces The lowes level rce ndces are he raos of he ndvdual rces of ndvdual reresenave roducs of he curren onh o he rces for Deceber of he revous year (rce reference erod) Calculaon of hgher level ndces ndvdual roduc rce ndces are aggregaed usng Laseyres forula and reference erod weghs o calculae hgher level ndces for roduc headngs as well as for NACE Rev. 2 classes (4 dg level) grous (3 dg level) dvsons (2 dg level) secons ( leer level) and he overall ndex (for ndusry) Source of weghs Weghs by NACE Rev. 2 are based on sascal daa of ndusral roducon sales volue n value esaon when VAT and excses are excluded. ndusry Sascs s used as an nforaon source. Weghs for ndvdual roduc rce ndces are based on roducon sales volue obaned fro enerrses Year of weghs The weghs refer o he sales volue n he year -2 whle he reference erod of rces refers o Deceber of he -. The annual weghs are rce adjused o algn wh he rce reference erod Are oher sources used o udae weghs o T- No oher sources are used o udae weghs o -. 27

33 3.7.. Oulne of he workflow: whch se s done when. Salng of enerrses (~ n Seeber); 2. Sendng of annual sascal uesonnare for he selecon of reresenave ndusral roducs (~ n Ocober); 3. Generaon of weghngs (~ n Noveber); 4. Daa collecon enry valdaon and rocessng; 5. Calculaon of rce ndces; 6. Publcaon. Ses -3 are carred ou ones a year ses 4-6 every onh Lhuana SPP Servce roducer rce ndex (SPP) s ublshed fro 2007 n Sascs Lhuana. Sascs Lhuana does no calculae oal SPP bu ndvdual ndexes of followng acves: H49_H492 Transor va ralways H494 Fregh ransor by road H495 Transor va elne H50_H502 Sea and coasal waer ransor H5 Ar ransor H52 Warehousng and sorage H5224 Cargo handlng H53 Posal acves under unversal servce oblgaon H532 Oher osal and courer acves J6 Telecouncaons J62 Couer rograng consulancy and relaed acves J63 Daa rocessng hosng and relaed acves; web orals M69 Legal acves M692 Accounng bookkeeng and audng acves; ax consulancy M702 Manageen consulancy acves M7 Archecural and engneerng acves; echncal esng and analyss M73 Adversng and arke research N78 Eloyen acves 28

34 N80 Secury and nvesgaon acves N82 Cleanng acves Mehod aled The annual chan-lnkng ehod s aled. Ths ehod was leened because: ) gves a ossbly o udae a baske of reresenave roducs and reove non-exsng roducs annually. 2) Annually revsed weghs are ore accurae and u o dae because he arke s changng radly Channg erod The fourh uarer s he lnkng erod of year - (year s he reorng year) Wegh erod The wegh erod s calendar year s he chaned seres bencharked o he annual chaned seres The chaned seres s no bencharked A wha level s chan-lnkng erfored A 4 dg-level by NACE Rev. 2 s cha-lnkng erfored Calculaon of eleenary ndces The lowes level rce ndces are he raos of he ndvdual rces of ndvdual reresenave servces of he curren uarer o he rces for V uarer of he revous year (rce reference erod) Calculaon of hgher level ndces ndvdual servces rce ndces are aggregaed usng Laseyres forula and reference erod weghs o calculae hgher level ndces for servces headngs CPA (6- and 5-dg level) and NACE Rev.2 (4-dg level) for each resonden. These ndces are aggregaed no he rce ndces for servces headng as well as for NACE Rev.2 classes (4-dg level) grous (3-dg level) and dvsons (2-dg level) Source of weghs Weghs for hgher level ndces are based on daabase of urnover by NACE Rev.2 rovded by he Transor and Servces Sascs Dvson. Weghs for he reresenave servces are based on sales values receved fro enerrses. 29

35 Year of weghs The weghs refer o he sales volue n he year - whle he reference erod of rces refers o V uarer of he -. The annual weghs are rce adjused o algn wh he rce reference erod Are oher sources used o udae weghs o T- No oher sources are used o udae weghs o Oulne of he workflow: whch se s done when. Salng of enerrses (~ n Ocober); 2. Sendng of annual sascal uesonnares for selecon of reresenave servces and weghs reured o calculae lower level ndces (~ end of January); 3. Generaon of weghngs (~ n March); 4. Daa collecon enry valdaon and rocessng; 5. Calculaon of rce ndces; 6. Publcaon. Ses -3 are carred ou ones a year ses every uarer Lhuana or rce ndex or roducer rce ndex s ublshed fro 2007 n Sascs Lhuana Mehod aled The annual chan-lnkng ehod s aled. Ths ehod was leened because: ) gves a ossbly o udae a baske of reresenave roducs and reove non-exsng roducs annually. 2) Annually revsed weghs are ore accurae and u o dae because he arke s changng radly Channg erod The revous year - s he lnkng erod (year s he reorng year) Wegh erod The calendar year - s he wegh erod s he chaned seres bencharked o he annual chaned seres The chaned seres s no bencharked. 30

36 A wha level s chan-lnkng erfored A 4 dg-level by CPA chan-lnkng s erfored Calculaon of eleenary ndces The lowes level rce ndces are he raos of he rces of ndvdual reresenave goods of he curren onh o he average rces of he revous year (rce reference erod) Calculaon of hgher level ndces ndvdual goods rce ndces are aggregaed usng he Laseyres forula and reference erod weghs o calculae hgher level ndces for goods subcaegores (6-dg level) of he CPA as well as for caegores (5-dg level) classes (4-dg level) grous (3-dg level) dvsons (2-dg level) secons (-leer level) and he overall P Source of weghs Weghs for he or rce ndex calculaon are based on Foregn Trade Sascs daa for ors n value ers accordng o all levels of he CPA. Weghs for ndvdual goods rce ndces are based on ors n value ers obaned fro enerrses Year of weghs The weghs refer o he ors volue n he year Are oher sources used o udae weghs o T- No oher sources are used o udae weghs o Oulne of he workflow: whch se s done when. Salng of enerrses; 2. Sendng of annual sascal uesonnares for selecon of reresenave servces and weghs reured o calculae lower level ndces; 3. Generaon of weghngs; 4. Daa collecon enry valdaon and rocessng; 5. Calculaon of rce ndces; 6. Publcaon. Ses -3 are carred ou ones a year (~Augus-Ocober) ses 4-6 every onh. 4. PRACTCAL EXAMPLES FROM COUNTRES ON ANNUAL CHAN-LNKNG OF VOLUME NDCES n he followng counry exales rofound descrons are rovded on he ehods aled n he calculaon of he onhly volue ndces. 3

37 4.. Fnland P 4... Mehod aled n Fnland he leenaon of he Laseyres chan ndex ehod n he calculaon of he onhly ndex of ndusral roducon began n Fnland leened he chan ndex ehod arly because of soe user feedback sayng ha he base year ndex dd no reflec he srucural change of econoy uckly enough. For exale he ndex undervalued elecrcal and elecroncs ndusry and overvalued consrucon secor n he lae 990s Channg erod Each Deceber s he channg erod Wegh erod The weghs are changed annually. Produc and esablshen weghs are changed n he auun - fro Seeber 202 onwards 20 weghs are used. ndusry weghs are changed a he end of he year - fro Deceber 202 onwards value added and gross value weghs fro 20 are used s he chaned seres bencharked o he annual chaned seres Yes e.g. a he end of he year 202 Fnland calculaes he annual ndex. Fro Deceber onwards he annual ndex fro year 20 s ublshed A wha level s chan-lnkng erfored A 3-dg level chan-lnkng s erfored Calculaon of eleenary ndces A esablshen level: The esablshens reor her onhly roducon volues/values by roduc and he lowes-level eleenary ndex (esablshen level) s calculaed based on hs nforaon. Value-for nforaon s deflaed before calculaons. Frs he reored curren onhly roducon level of each roduc s coared agans he revous year s average onhly roducon level of he roduc. Esablshen s ared coarsons are hen cobned by sung her weghed value. The roduc-level weghs are based on each roduc s roducon values fro he revous year. The esablshenlevel volue ndex s fored by dvdng he su of he weghed ared coarsons by he oal of he roduc weghs and ullyng by 00. The calculaon forula can be found below. 32

38 sascal year *. = volue ndex for esablshen j on year onh and = roduc wegh for roduc = roducon of roduc n year and on onh = average of onhly roducon of roduc n year - n = oal nuber of roducs of esablshen j * = sascal year.e. he year of ndex calculaon A srau level: The ndusry ndex s frs calculaed searaely for each srau. Srau consss of esablshens eloyng 50 or ore eloyees srau 2 of esablshens wh eloyees and srau 3 of esablshens wh less han 50 eloyees. To for he srau-level ndusry ndex a su of weghed esablshen-level ndces s frs calculaed. Eher esablshen weghs (su of esablshen s roduc weghs) or weghs based on salng desgn are used n weghng. Then he su of weghed esablshen-level ndces s dvded by he oal su of esablshen and salng desgn weghs o ge he srau-level ndusry ndex. The srau-level ndusry ndex s calculaed boh for he sascal year and for he coarson year -. The calculaon forula can be found below. Noe: VAT daa s ulzed o calculae he ndusry ndex for Srau 3. = volue ndex for Srau k ndusry aaa year and onh calculaed n sascal year * n sascal year * = volue ndex for esablshen j year and onh calculaed = esablshen wegh for esablshen n = oal nuber of esablshens belongng o Srau k on ndusry aaa A ndusry-level: A hs sage of he ndex calculaon rocess he srau-level ndces are cobned o an ndusry-level ndex. Srau ndces are weghed usng nforaon on he gross value of coanes corresondng o each srau s sze. The gross value nforaon s colleced fro he Srucural Busness Sascs nforaon. The ndusry-level ndex s calculaed for boh year and year -. The calculaon forula can be found below. 33

39 sascal year *. sascal year *. = new volue ndex for ndusry aaa year and onh calculaed n = volue ndex for Srau k year and onh calculaed n = wegh for srau k.e. gross wegh = oal nuber of sraa on ndusry aaa ( 3). A fnal ndusry-level: The fnal ndusry-level ndex s acheved by calculang he relave change beween he new ndex for year and -. The coarson year s ndex s ulled by hs change and hus he fnal ndusral roducon ndex for sascal year * s fored. sascal year *. sascal year *. = fnal ndusry-level ndex for ndusry aaa n year onh and = new volue ndex for ndusry aaa year and onh calculaed n = relave change of he new volue ndex on ndusry aaa for year and onh o he new ndex of he corresondng onh n year - calculaed n sascal year * n sascal year -* = fnal ndusry-level ndex for year - and onh calculaed Calculaon of hgher-level ndces The fnal ndusry-level ndces can be used o calculae varyng aggregae ndces. The aggregae ndces are calculaed for boh he sascal (curren) and he coarson year. n aggregaon he ndusry s weghed based on s value added n he Srucural Busness Sascs nforaon. Corresondngly o he calculaon of he fnal ndusry-level ndex he relave change beween he sascal and coarson year s new aggregae ndex s 34

40 calculaed. The fnal corresondng aggregae ndex fro he revous year s ulled by hs change o for he fnal aggregae ndex for he sascal year Source of weghs Survey daa: Produc weghs (value of esablshen s revous year s roducon of he roduc) and esablshen-level weghs (su of roduc weghs or weghs based on salng desgn). Srucural Busness Sascs: Srau s gross-value weghs and he ndusry s value added Year of weghs Produc and esablshen weghs fro year - are nroduced yearly n Seeber. For exale n 202 fro January ll Ocober ndusry weghs are fro 200 (-2) and fro Noveber ll Deceber P uses value added and gross weghs based on year 20 (-) For volue ndces: a wha level s seasonal adjusen erfored Seasonal adjusen s erfored a 3-dg level Oulne of he workflow 35

41 4.2. Croaa P Mehod aled The Croaan P s arally annually chan-lnked Laseyres ye ndex. P weghs on aggregaes (acvy) level are beng udang annually usng value added nforaon (shares). However udang weghng coeffcen for eleenary ndces on roduc level has beng done every fve years (fx base) snce Pror o 2005 he annually chan-lnked ehods for calculaon of P have been aled on aggregae and eleenary ndces level. n Croaa acually calculaon of he P sared n 952 when (long radon) Channg erod The P hgher level ndces are annually chan-lnked usng an annual overla (annual average of year -) Wegh erod The weghs erod for calculaon of hgher level ndces (.e. shares of value added) s -2 bu hey are udaed regularly o refer o year -. The weghs erod for calculaon of eleenary ndces on roduc level refers o he fx base erod (currenly 2005 base year) s he chaned seres bencharked o he annual chaned seres The chaned seres s no bencharked A wha level s chan-lnkng erfored The chan lnkng s erfored o heracal level of NKD 2007 (=NACE Rev.2) classes grous dvsons and secons as well as on aggregae sub-ndces levels (MGs) and P oal. Seres adjused for workng days are also chaned accordng o he ehod for channg he unadjused seres Calculaon of eleenary ndces ndusral roducon volue ndces for varous levels of he NKD 2007 (= NACE Rev.2) are calculaed n wo ses accordng o he Laseyres forula. n he frs se eleenary ndces are calculaed fro uany daa on roducon of ndvdual roducs (sung he u across roducers) accordng o he PRODCOM based naonal noenclaure (NPUM) ulled by adeuae weghng coeffcen o reach he so cold ass of values for each roduc whch are hen sued u o he 4-dg level of NKD 2007 (=NACE Rev.2). Eleenary ndces are calculang usng Laseyres forula. Weghng coeffcens are calculaed on he bass of un values of he annual PRODCOM survey on ndusral roducon for 2005 and are revsed every fve years. Producon s easured n hyscal ers by wo easureen uns eher hyscal uanes uns (roducs) or effecve hours worked (servces). 36

42 Calculaon of hgher level ndces Croaan hgher level ndces are calculang n he second se n he way ha all ndces of grous and hgher levels of NKD 2007 (= NACE Rev.2) are weghed (ulled) wh shares of value added (so cold acvy srucure). n hs way he relave orance of ndvdual levels s defned and a he sae e dfferen levels of coverage are levelled. The weghs (dvson srucure) was calculaed for year -2 on he bass of he gross value added of facor coss of he Croaan SBS survey resuls hen furher correced wh P for -. The weghs (dvson srucure) are udaed a he begnnng of every year for he calculaon of P n a curren year Source of weghs The source of he weghs for NACE Rev.2 heracal levels (3-dgs 2-dgs Secon MGs) s he annual SBS survey ha are calculang as share of value added a facor cos n he -2 year hen correced wh P for - year. Source for P s Monhly survey for ndusral roducon. The source for calculang weghng coeffcens for aggregang uanes of roducs o eleenary ndces on 4-dg class level s annual PRODCOM survey on ndusral roducon (currenly for year 2005) Year of weghs Weghs for hgher level ndces refer o year -2 bu hey are udaed o reresen year - usng he ndusral sascs nforaon (P for year -). Weghs for calculang eleenary ndces ha are weghng coeffcens refer o year -5 (fx base year) Are oher sources used o udae weghs o T- ndusral sascs are used o udae weghs o For volue ndces: a wha level s seasonal adjusen erfored Croaan P s coled as unadjused workng-day adjused seasonally adjused and rendcycle ndces. P adjusens are ade for he ndusry oal MGs and Dvsons of NKD 2007 (=NACE Rev.2). TRAMO-SEATS ehod (regresson ehod) based on ARMA odels s used for he adjusen on a e seres fro January 998. Drec ehod s used for he seasonal adjusen of e seres. n he seasonal adjusen he ac of he nuber of workdays Easer and oher naonal holdays was aken no accoun n hose e seres for whch he enoned nfluences were sascally sgnfcan Oulne of he workflow: whch se s done when n general SBR and PRODCOM are usng as a frae for Croaan Monhly survey on ndusral roducon (cu off survey). The selecon of enerrses has beng done accordng 37

43 o nuber of ersons eloyed and share n value added on 4-dg level. The workflow ses are:. Udang of sale frae accordng o selecon crera. Udang sale ncludes refreshng he sale wh new enerrses/local uns as well as elnang hose below he selecon crera (Deceber/January) 2. Selecon of he new born enerrse and enerrse above selecon crera o be conacng by hone or e-al (January) 3. Udang he weghs by cobnng nforaon fro SBS resuls and P. Dsrbuon of weghs o all heracal levels concerns n P calculaon (Deceber/January). 4. Uloadng he udaed P daabases wh new weghs hen akng fnal sofware sengs for regular daa collecon (P survey s CAW based) rocessng valdaon coung and dssenaon (January/frs half of February) 5. Oenng dedcaed web-se for new P daa collecon (0 h of February each year) 6. Daa collecon (CAW) valdaon rocessng and coung he chan-lnkng PP (second half of January o 20 h of February) 7. Analysng he Ps (ossble correcon go back o ndvdual daa) rearaon for ublcaons and fnally dssenaon o naonal users and Eurosa (+35 a laes) 4.3. Slovena P Calculaon Slovena calculaes and ublshes ndces on ndusral roducon as follows:. Curren onh on las year bass e.g. February 202/20 based on reored daa (ncludng ued and deflaed daa); 2. Curren onh on revous onh e.g. February 202/January 202 = (Feb202/20) / (Jan202/20) usng he one-onh overla ehod; 3. Curren onh of he curren year on curren onh of he revous year e.g. February 202/February 20 = (Feb202/20) / (Feb20/20) usng he over-he-year ehod; 4. Curren erod of he curren year on curren erod of he revous year e.g. (January - February 202)/(January - February 20) usng he over-he-year ehod. ndces of curren onh on las year bass are calculaed drecly fro reored daa and all oher ndces are calculaed fro hese basc ndces. 38

44 Weghs Fro 952 o 2004 Slovena was collecng uany daa on he roducon of ndvdual ndusral roducs and servces and Slovena was usng weghs (whch were shares of value added) when aggregang daa (calculaon of P for he hgher levels of classfcaon). Shares were based on he daa on value added fro he year 2000 and were correced every year wh growh of he P. Fro 2005 (2004) o 2008 Slovena sared collecng value daa and for he urose of calculang weghs shares of value added were based on he daa on value added fro he year 2005 and were also correced every year wh growh of he P. Fro 2008 on Slovena s sll collecng value daa bu we adjus weghs as soon as he value added daa s avalable (ublshed). Once a year weghs are adjused due o rovsonal value added daa and once a year due o fnal value added daa for a secfc year. ndusral daa fro January 20 on s currenly sll rovsonal. Snce Slovena has only avalable value added daa for 200 Slovena uses on daa (ndces) for 20 and 202 because unl Slovena ublshes fnal ndusral daa for 20 ha s ossble. Ths s he reason we use - and also eorarly -2 weghs. As soon as he value added daa becoe avalable for 20 Slovena wll use he nsead of ha for Oulne of he workflow January: salng (a new ls of reorng uns) udang docuenaon. February: Sendng uesonnares o reorng uns and udang rograes. March: adjusng weghs (and n Ocober) conrollng daa on new reorng uns adjusng odels for seasonal adjusen. Each onh: When daa on urnover (doesc non-doesc euro area non-euro area) new orders (doesc non-doesc euro area non-euro area) and socks n ndusry s receved Slovena ues ssng values (for new orders here s uaon of»0«) and deflaes all daa. Then Slovena calculaes value of roducon for each reorng un. Slovena has defned so called ndusral grous (for he urose of weghed P) and n he nex se Slovena calculaes value of roducon for each ndusral grou. Then Slovena calculaes he aggregaed non-weghed P for each ndusral grou. n he end weghs are used for calculang aggregaed levels. Fro reored daa (ued deflaed) Slovena calculaes ndces for curren onh on las year bass and hen chan-lnkng s used for he calculaon of all oher ndces. Afer ha seasonal adjusen s erfored only on daa seres 2005=00. Slovena sared chan-lnkng n 2003 wh a cuso ade sofware. The revson of weghs s done very uckly n jus a few nues because of he auoaed syse (Enerrse Gude 4). Enerrse brhs and deahs are deal on a onhly bass. f a new enerrse arse s ncluded n he survey and f an enerrse des s excluded fro he survey (enerrse s gven a saus whch exlans wha haened wh ) enerrse s no longer nvolved n calculang ndces. 39

45 4.4. Uned Kngdo P Overvew The Uned Kngdo P s an annually chaned Laseyres-ye volue ndex whch uses he uarerly overla ehod and bencharkng o he annual seres. Ths ensures ha he uarerly seres s conssen wh he annual seres whle sll ananng he uarerly ah. Accordng o he UN SNA 2008 hs gves he bes resuls. Followng user engageen hs ehod was consdered he os cos effecve way o leen chan-lnkng and ee users needs. A conssen aroach s aken for all of he shor er ndcaors (P os RS) whn he Uned Kngdo Naonal Accouns. A coarson of he uarerly and he annual overla echnues can be found n he followng sub-chaer. Channg s done va a sngle uarer overla wh he lnk erod beng Q4 of he revous year u o he laes base year. Daa for 2008 and onwards s lnked ono he 2007Q4 value and he ndex s referenced o 2008 = 00. For he os ar of he es seres he weghs erod s he revous year. However for recen years (currenly 2009 and onwards) weghs are aken fro he base year Ths ensures ha he seres are addve n he os recen years; whch was denfed as advanageous for our users. The base year udaes by one each year as new weghs daa becoe avalable. The weghs are based on Gross Value Added and are obaned fro he Suly Use Tables. n a ycal year 2 years worh of daa are oen for revsons and so he fnal weghng daa are no confred unl 3 years afer he year (.e weghs wll be nroduced n 202). The uarerly seres s bencharked o he annual chaned seres o ensure ha he annual growh aern s ananed and he 4 uarers n a year average o he annual level. Chan-lnkng s erfored a he Suly Use Table level. A hs level he econoy s dvded no 4 ndusres and ycally corresonds o he 2 or 3 dg level of NACE Rev2. Ths level was decded uon based on coss daa avalably and user reureens; ensures colance wh ESA 202 ranssson rograe whch reures daa a he A64 level. The curren rce seres are calculaed fro daa colleced n a onhly busness survey. Daa s colleced a a dealed level and sued o SUT-4 level. A hs sage eleenary ndces are calculaed as fxed base ndces by deflang he CP seres by an arorae rce ndex (whch could be a PP SPP or HCP ec). Quanes are hen exressed n ers of revous year rces and curren year rces and unchaned ndces calculaed. Hgher level seres are calculaed by un-lnkng he ndces aggregang he ogeher and hen channg he ogeher by ullyng by a scalng facor. Seasonal adjusen s erfored a he sae level ha he ndces are chan-lnked a SUT

46 Coarson of uarerly and annual overla echnues As enoned before he UK ndex of Producon (P) ndex of Sevces (os) and Real Sales ndex (RS) are all annually chan-lnked ndces usng he uarerly overla echnue wh bencharkng. Ths sae chan-lnkng ehodology s used conssenly hroughou he UK naonal accouns. The UK shor er volue ndcaors (P OS RS) are fully negraed wh he uarerly and annual naonal accouns; ha s onhly esaes are consraned o su o annual esaes boh n ers of curren and consan rces. s herefore an oran reureen for he UK ha hese basc accounng convenons are reserved whn a chan-lnked syse. A furher reureen s ha he uarerly syse of accouns should rovde good easures of growh wh no dsconnues and should allow for growh o be esaed over varyng erod lenghs. The choce of an annually-chaned Laseyres ndex as he forula for coung annual growh raes s sraghforward and unabguous. However he secfc lnkng ehodology has o ake no accoun a nuber of facors ncludng conssency wh oher seres onhly ah and annual growh raes. Consulaon wh key users of hese sascs revealed ha here was a srong reureen for he bes easure of growh for all uarers and coheren daa where onhs su o years. A conssen aroach o chan-lnkng has o be aken for he uarerly naonal accouns and shor er volue ndcaors n order o ensure conssency beween he dfferen seres. The uarerly ah s bes calculaed usng he uarerly overla echnue (wh Q4 beng he lnk erod) as usng an annual overla can nroduce a ju beween Q4 of one year and Q of he nex. Alyng he uarerly overla o a onhly seres ensures conssency wh he uarerly seres whle ananng a sooh onhly ah. However on s own uarerly overla can lead o dvergence beween he onhly / uarerly seres and he annual seres. Thus he onhly seres s bencharked o he annual seres n order o ensure conssency wh he annual seres and reove any dvergence. Conseuenly uarerly overla wh bencharkng cobnes he rncal advanages of boh uarerly overla (bes nra-year ah) and annual overla (conssency wh annual daa) and ees he reureens of key users of he daa. The annual overla and uarerly overla lnkng ehodologes have been coared usng daa fro he UK ndex of servces (Fgure ). Absolue dfferences are sall oallng less han 0.5 ndex ons over a 5 year erod. As execed whn-year oveens are nvaran of he chan-lnkng ehodology used bu he Deceber January oveens do deend on he secfc ehodology used. The growh beween Deceber of one year and January of he followng year s on average 0.04 ercenage ons lower when he annual overla ehod s used (Table ). Ths s a easure of how uch he annual overla ehod dsors he Deceber January oveen and also a easure of he dscreancy nroduced by he uarerly overla ehod f no bencharkng s carred ou. 4

47 Fgure : Coarson of he non-seasonally adjused UK ndex of Servces coled usng he annual overla and uarerly overla whou bencharkng ehodologes. The wo ehodologes gve alos dencal e seres wh dfferences of less han 0.5 ndex ons n 996 and less han 0. n 202. Annual overla Q4 overla dfference Dec-97 Jan % -.2% -0.03% Dec-98 Jan % -2.57% -0.04% Dec-99 Jan % -2.42% -0.08% Dec-00 Jan % 0.98% -0.3% Dec-0 Jan-02.06%.08% -0.02% Dec-02 Jan % 0.9% 0.00% Dec-03 Jan % -2.3% -0.07% Dec-04 Jan % -2.97% -0.06% Dec-05 Jan % -.35% -0.05% Dec-06 Jan % 0.98% -0.03% Dec-07 Jan-08.57%.64% -0.07% Dec-08 Jan % -3.28% 0.05% Dec-09 Jan % -3.34% 0.05% average -.6% -.2% -0.04% Table : Deceber January oveens as calculaed fro he UK os usng annual overla and Q4-overla chan-lnkng ehodologes. 42

48 For UK he key advanages of he uarerly overla and bencharkng o he annual seres ehod are ha here s no arfcal ju n he onhly seres and daa are conssen wh he annual and uarerly naonal accouns Uned Kngdo Real Sales ndex Overvew The real sales ndex (RS) s an annually chaned Laseyres volue ye ndex. Prce deflaors used are Consuer Prce ndces (CP s {HCP s}). Coody rce ndces are creaed fro aggregang low level CP s usng CP weghs. CP s are chan-lnked Laseyres ndces referenced o 2005=00 and are collaed onhly. CP weghs are udaed annually usng Naonal Accouns Household Exendure daa RS s are roduced onhly wh he ajory of volue easures creaed by deflang urnover daa. Currenly he ndex s referenced o 2008=00 wh 2008 beng he las base year. Chan-lnkng s erfored a he 4 dg level searaely for large and sall/edu busnesses. The lnk erod s he fourh uarer of each year The chan-lnkng ehod The RS s annually chan-lnked usng he sae ehods as he UK Naonal Accouns. The basc ses aken n our syse o calculae chaned volue easures are as follows:. ndces below he level of chan-lnkng are calculaed as Laseyres volue fxed base ndces. 2. These ndces are ulled by her resecve weghs. (Weghs based on value of sales roorons calculaed fro RS daa.) 3. The resulan seres are ulled by her resecve wegh n he revous year (-) and hen dvded by he su of all seres creaed n se 2 for year -. Ths creaes a onhly seres n Prevous Year s Prces (PYP). 4. Followng he sae rocess as 3 we creae a onhly seres n Curren Year s Prces (CYP) by ullyng by curren years () weghs and dvdng by he su of all seres creaed n se 2 for year. 5. PYP s and CYP s are hen aggregaed o he level of chan-lnkng (4-dg level searaely for Large and Sall/Medu busnesses). 6. Frs he syse calculaes nernal scalng facors. nally hese are se o for all e erods afer he las base year (.e. afer Deceber of las base year so f 2006 s he las base year all scalng facors fro January 2007 are se o ). 7. The syse hen works backwards o calculae all oher scalng facors. 8. For he onh of Deceber scalng facors are calculaed as January s scalng facor ulled by CYP for he lnk erod dvded by he PYP for lnk erod. 43

49 E.g. Deceber 2004 SF = January 2005 SF x (Q CYP/Q PYP). 9. These scalng facors are hen used for all onhs back o he nex Deceber when he above calculaon s reeaed. 0. When here are no ore revous years rces he las (frs) scalng facor s carred backwards o he sar of he seres.. The unconsraned chaned volue easure (CVM) s hen calculaed as: he CYP seres for he e erod ulled by he scalng facor f no PYP s avalable (usually a he sar of he seres); or he PYP seres for he e erod ulled by he scalng facor. 2. These unconsraned chaned volue easures are hen bencharked o he annual chaned volue easures. 3. Perods afer he las base year are se o he unconsraned seres. 4. Annual chaned volue easures are calculaed by alyng he sae ses bu o annual ndces Sofware Chan-lnkng was nroduced usng sandard UK Offce for Naonal Sascs (ONS) sofware. Fro Seeber 200 he RS has been swched o a newly develoed syse called CORD whch s an Oracle based syse. Oher Naonal accouns ouus op (P) and os (Servces) all use he sae ehod Dssenaon Daa s dssenaed onhly hrough a Sascal Bullen h:// Tables ublshed nclude value and volue ndces onh on a year ago onh on onh 3 onh on 3 onh and 3 onhs on a year ago growh raes User reureens/engageen Followng user engageen annual chan-lnkng was denfed as one of he ajor user reureens for he RS. As a key nu no he GDP(O) calculaon boh nernal (anly Naonal Accouns) and exernal users beleved he RS should ado ehods o brng he n-lne wh Naonal Accouns. The ehod used was consdered he os cos effecve way for he UK o leen chanlnkng as he sofware develoed s used for he RS ndex of Producon and ndex of Servces. Provded conssency for users across he Naonal Accouns 44

50 Chan-lnkng was nroduced alongsde a nuber of oher ehodologcal roveens. The arcle Changes o he real sales ehodology descrbes all he changes ade ncludng chan-lnkng and he overall ac on he all realng aggregae. h:// As here were nuerous ehods changes ade o he RS a hs on n e he ac fro chan-lnkng alone could no be solaed. Key users ncludng he Bank of England Her Majesy s Treasury and he Dearen for Busness nnovaon and Sklls were fully consuled on he changes and acceed he as a ajor roveen o ehods Oher relaed chan-lnkng research As enoned above he UK has also nroduced chan-lnkng usng he sae ehods as RS for he ndex of Producon and ndex of Servces. Soe key ons for he aroach used for hese wo ndcaors are:. Weghs are based on Gross Value Added and obaned fro Suly Use Tables. 2. Chan-lnkng s erfored a he Suly Use Table level (Tycally 2-3 dg level of NACE Rev2 for Producon and 2-dg level of NACE Rev2 for Servces). Ths ensures we are colan wh he ESA 200 ranssson rograe whch reures daa a he A64 level. 3. Level of chan-lnkng was decded based on coss avalably of daa user needs (arcularly Naonal Accouns and he Bank of England). 4. Mehods ensure colance wh he ESA95 (and ESA0) regulaons Basc RS workflow. Calculae urnover seres (roaon sale) 2. Deflae urnover (usng aggregaed CP s) 3. Seasonally adjus 4. Aggregae and Chan Lnk 5. NOMNAL NDCES Annual chan-lnkng s relevan for rce and volue easures. However for nonal ndces e.g. urnover a curren rces or nuber of ersons eloyed annual chan-lnkng s no relevan. The relaonsh beween nonal ndex volue ndex and rce ndex s as follows: he nonal ndex dvded by he volue ndex euals he rce ndex. f for exale he reorng erod s January 202 and he reference year s 200. follows for he nonal ndex chan-lnkng s no relevan he annual chan-lnked volue ndex uses 45

51 he annual overla echnue and he resulng annual chan-lnked rce ndex s a Paasche ndex. 6. BULDNG UP A CHANED NDEX ON A PREVOUS FXED ONE (EXAMPLE FROM TALAN PP) Ths Task Force conrbuon deals wh he oc of nesng a chaned rce ndex on a fxed base one. A bref noe has also added and focuses he rae of change ndex decooson n chan-lnkng on he bass of he resuls nroduced by M. Rbe. 6.. Chaned ndex forulas Le us suose he overall ndex be ade u of k sub-aggregaes; a e calculaon base (CB) ndex s Y y he [ ] y y y 0 k w k k y 0 ( ) y 0 ( ) and he reference (RB) base or chaned ndex s [ 2] y C y y 0 y j 2 j 0 j B ndeed he forula [2] s go by develong recursvely he euaon [ 3 ] y C y y 2 C y0 wh resec o he second er on he rgh sde. n fac [ 4 ] y C 2 y 2 y 22 C y 0 Subsung [4] n [3] we ge [ 5 ] y y y 2 y 22 C C y0 y 0 The las er on he rgh sde of he euaon [5] can be develoed as n [3] and hen subsued n [5]. Afer y ses hs recursvely aroach leads o he chan roduc n euaon [2] (he second facor on he rgh hand sde) so ha [ 6 ] y j 2 j 0 j B B 2 2 y 2 2 y 2 B 0... y 2 0 y 0 Therefore he euaon [2] can be re-wren as y 2 j 2 y 2 j 0 y 0 j B 46

52 [ 7 ] y C y y 2 y 2 j 2 y 0 y 0 j 0 j B [ 8 ] so ha he euaons [3] and [7] are euvalen.e. y 2 y 2 y 2 j 2 C y 0 j 0 j B Gven he euaons [3] [7] and he euvalence [8] s sraghforward o noe ha [ 9 ] y y0 y C y 2 C y y0 y C y 2 y 0 y 2 j 2 j 0 j B The forula [9] sly shows ha once he chaned ndex s aroraely coled we can ge he CB ndex by reversng he forula [3] or euvalenly he forula [7]. n hs sense forulas [3] and [7] are srcly coheren. Trvally all hese forulas as shown below refer he overall ndex; he corresondng forulas for he sub-aggregae can be derved by secfyng for each sub-aggregae he subscr k Nesng chan-lnkng on a fxed base rce ndex n he resen conex he ndex ye changeover (TC) concerns he ranson fro a fxed base ndex o a chaned one. Deendng uon he e when he ranson occurs he chaned ndex can be or no affeced by a drf. n arcular f he TC concdes wh he ndex base changeover (BC) no drf n he level wll affec he chaned ndex. Dfferenly f he TC akes lace and he ndex base s sll unchanged he chaned ndex could lye for any gven sub-aggregae k and he overall ndex as well u or down s rue ah TC and BC concden Ths case s raher heorecal. The ndex s fxed base ye u o he e Y y and snce he e Y y he ndex s chaned. Besdes u o unl Y y he (fxed) ndex base s B 0 ( B 0 y) and snce Y y onwards B ( B y hen B 0 ror B.e. B0 B ). To ge he ndex e seres exressed n he sae base he lnkng coeffcen fro B 0 o B s coled. s worh nong ha n Y y CB and RB concde by consrucon; snce Y y RB = (y2). A varan of he sae case occurs when B y. n oher words he erod chosen as new ndex base s ror he e when he BC and TC ake lace. As hs suaon generaes a drf n he ndex level wll be analysed n TC laer BC Le us suose o be a e Y y carryng ou he CT. We also ake he hyohess he ndex base reans unchanged. So dong he e Y y searaes he ndex e seres n wo nervals: on he lef he nerval Y y where he (fxed) base B holds; on he rgh he nerval Y y where he (reference) base s sll B bu he ndex s annually udaed. 47

53 n Y y he sles way of aroachng he chan-lnkng s o use he shor forula [3]. n racce beng years laer B hs choce s very aracve because he chaned ndex s sraghforwardly coled. On he oher hand owng o he CB lag hrough hs way he coherence (n he sense defned above) of he chaned ndex coes less: euvalenly he ndex s affeced by a drf. To see hs s suffcen o ay our aenon on he euaons [2] or [7]. Usng drecly he forula [3] years laer B we are acually song he recursvely roduc o s nex o he las er. Conseuenly we are no usng [3] bu s runcaed verson [ 0 ] y y C C T y0 y T 2 where [ ] [ 3 ] y 2 C y T y 0 Therefore he euaon [9] s subsued by y y y 2 C C y0 T Truncang he euaon [6] eans o ge y 2 j 2 j 0 j B Ths oson does no hold n racce (esecally when s far fro B ) because he above roduc wll be less or greaer han. n arcular we ge he uer drf f [ 4 ] y 2 j 2 j 0 j B y C T y C Y y and he lower drf f [ 5 ] y 2 j 2 j 0 j B y C T y C Y y Chan-lnkng drf adjusen We have seen ha he drf n he ndex level orgnaes when usng he shor (see runcaed) chan-lnkng forula. Furher as he drf can dfferenly affec he sub-aggregaes soe of hese could lye u and oher down her heorecal ah (where he drf s null). The resul s ha he RB srucure s ncoheren n he sense defned above and no hoogeneous Really he roduc could also be eual o one for soe sub-aggregae. Anyway hs s raher unlkely esecally when s far fro B. 48

54 aong he sub-aggregaes. To byass he drf we need o subsue he unknown roduc n [6] by an esaon [ 6 ] y 2 2 ˆY j 0 Y B y 2 2 ˆY j 0 Y B As shown n [6] alhough he ndex s suosed o be (onhly and) fxed base ye unl Y y s no necessary o re-buld u onh by onh for he whole backwards erod. Moreover we need only o reconsruc he ndex for each onh of Deceber.e. o ake an esaon of he ndex as f were chaned. s worh focusng ha he aral ndex re-colaon s really an esaon because we are suosng ha boh he weghs and he enerrses rean unchanged. The annual ndex udang should concern rces weghs and reorng uns bu for our uroses s suffcen o udae only rces. The sulaon s such n hs sense. n deal he esaon n (Y 2) s carred ou a rce relaves level: each rao s rebul u by subsung he old denonaor ( 0 ) 2 wh he new one gven by he rce surveyed a he e ( Y 2). Therefore wll hol for es he followng subsuon Y 2 ˆY 2 [ 7 ] FB j0 Y B... y where he ndex on he lef s he old fxed base one ha s gong o be relaced by he esaed-chaned ndex. So dong fnally we ge he euaon [0] s relaced by he followng [ 8 ] ˆy C y ˆ y 2 y0 C where [ 9 ] ˆ y 2 C y 2 y 0 y 2 ˆ j j0 j B Conseuenly he resuls n [9] are now subsued by [ 20 ] y y0 ˆ y C ˆ y C 2 ˆ y C y 2 y 0 y 2 ˆ j 2 j 0 j B 2 Usually n he onhly fxed based ndex he denonaor of rce relaves s gven by he onhly ean of rces surveyed n he year base. 49

55 Therefore n he followng euaon [ 2] ˆ y C y y 0 y 2 ˆ j j 0 j B we fnd agan he conssency of [2]; he esaon of calculaon bases leads o he resul execed: he drf has been reoved. U o unl now n re-buldng u he ndex we have lcly suosed anagng rce relaves ha relacng he old rce wh he new one were sraghforward. ndeed rces and hen rce relaves of each onh of Deceber have o be checked and n case adjused. As knew analysng a rce relave he ualy change consss n udang s denonaor. Esang he CB he relaceen of he fxed base rce n Deceber ( 0 ) wh ha of he revous year ( Y 2) could be affeced by an error f we wouldn ake no accoun he changng n he rce relave denonaor. To see hs le he e nerval beween he onhs of Deceber of wo adjacen years be [( Y 2)( Y2)] Y y; suosng ha a ualy change ook lace n [( Y 2)( Y2)] he above nerval s sl no wo ars: [( Y 2)( Y )] [ Y ]. Unl.e. for any onh before he rce relave of k (beng k any rce e seres) s Y Y ( k) [ 22 ] P ( k) 0 ( k) Snce onwards.e. u o [Y 2] he sae rao s Y Y ( k) [ 23 ] P ( k) ( k) where ( k ) s he rce relave base ebodyng he ualy change. To esae he CB a e Y Y y 0 ( k ) has o be relaced wh 2 Y ( k ). f n he eanwhle.e. n he onh he rce relave denonaor changed (because of a ualy change) hs subsuon should rovde a based rce relave beng no ore coarable he rces a he nueraor and denonaor. The adjusens works as follows [ 24 ] Pˆ Y 2 ( k) Y 2 ( k) f noqcook lase Y 2 ( k) Y 2 Y ( k) ( k) f aqcook Y 2 Y ( k) ( k) lace n concluson he euaons [8] and [9] have been defned by re-buldng u he ndex a rce relaves level by alyng he resuls n [24]. 50

56 6.3. ndex dynacs n chan-lnkng: aled ocs The Rbe s rae of change decooson Decoosng he (welve-onh) ndex rae of change. Le us sar fro he followng euaon y 2 y y y 0 y [ 25 ] D y 0 0 y y y 0 y 2 Addng and subracng y 0 on he rgh sde of [25] we ge y 2 y 2 0 y y y 0 [ 26 ] y 0 0 y D y y y y y 0 0 y where y y D y 0 ( ) and y y D y 0 ( ) denoe resecvely he coonen rovded by he curren year and ha of he revous year deernng he 2-onh rae of change. Suosng he overall ndex be coosed by k eleenary aggregaes he 2-onh rae of change can be decoosed n k addve sub-coonens y y [ 27 ] D y 0 k Posng y Cy ; k k yy D ( ) 0 yy y Dy 0 ( ) y 2 y 0; k y y 0; k y y 0; k y y y 0 y0; k wy0; k k [ 28. ] y 2 y 2 [ 28.2 ] y 0 y 0; k wy 0; k k y y [ 28.3 ] y 0 y 0; k wy 0; k k and usng he resul n [26] we have 5

57 [ 29 ] y 2 y 2 y y y 0 y y 0 D y 0 y y 0 y k k y 0 y 0 Posng [ 30. ] y 2 y y 0 C y ( ) y y 0 y y 0 [ 30.2 ] y 2 y y 0 C y ( ) y y 0 we can wre he colee forula y 2 y y 0 y [ 3 ] C y ; k w y 0; k y y0; k y 0 w y 0 y y 0 y 2 y y 0; k y 0; k Therefore reeberng he osons [28.]-[28.3] we ge [ 32 ] y 2 y y 0 y C y ; k ( ) w y 0; k y y0; k y 0 [ 33 ] y w y 0 y 2 y C y ; k ( ) y y0; k y 0; k y Soe algebrac ocs of he above forulas Le us consder he euaons [32] and [33]. Analysng her araeers we noe ha y y [ 34. ] C y ( ) 0 y 0 y 2 y y 0 [ 34.2 ] C y ( ) 0 y y 0 follows ha y y 0 y [ 34.3 ] C y 0 and y 2 y y 0 y 0 52

58 Furher =2 s a suffcen condon for y [ 34.4 ] C y ( ) 0 and holds. y y [ 34.5 ] C y ( ) y 0 Noe ha: y 2 y 0 y y y 0 [ 35 ] C y ( ) 0 y 2 y 0 y y 0 Fnally f f 2 y 2 y 2 y 0 y 0 y y 0 hen y y [ 36 ] C y C y ( ) 7. COST-BENEFT ANALYSS 7.. Tes calculaons 7... France The es calculaons have been erfored on or rces only. The ehods of PP S-PP and or rces are srcly coon exce ha S-PP s uarerly. or rces va PP-lke surveys and PP T ools have begun only a he end of year As he coon racce n France s o begn he seres wh value 00 a sarng on when s laer han he reference erod (here January 2005) os or rces seres are n fac n reference Ocober 2005 raher han year The or rces seres ransed o Eurosa slghly dffer fro he French seres dssenaed n France as UV have been cobned wh or rces n order o buld an average year 2005 reference. ors aouns have been re-coled for years 2005 o 200 n curren condons. Tha eans ha year n-2 s avalable on e for weghs of year n on May bu no ye aouns of year n-. Also new aouns for year 2005 dffer fro our old esaes whch were relyng on a cross-able wh CPA rev.. The old esaes of year 2005 have been used for weghs of years 2005 and 2006 ; he new esaes of year 2005 for weghs of year 2007; esaes of year 2006 for weghs of year 2008 esaes of year 2007 for weghs of year 2009 ec. Hence he chan-lnked seres wll dffer fro he fxed base seres (dervng fro old esaes for year 2005) fro January 2007 only (because of new esaes) and fro January 2008 for rue chan-lnkng causes. 53

59 0/0/2005 0/2/2005 0/02/2006 0/04/2006 0/06/2006 0/08/2006 0/0/2006 0/2/2006 0/02/2007 0/04/2007 0/06/2007 0/08/2007 0/0/2007 0/2/2007 0/02/2008 0/04/2008 0/06/2008 0/08/2008 0/0/2008 0/2/2008 0/02/2009 0/04/2009 0/06/2009 0/08/2009 0/0/2009 0/2/2009 0/02/200 0/04/200 0/06/200 0/08/200 0/0/200 0/2/200 0/02/20 0/04/20 0/06/20 0/08/20 0/0/20 0/2/20 0/02/202 0/04/202 As has always been descrbed on he shor noe on French ehodology he weghs of year n-2 are correced by he dvson by he annual average of or rces of year n-2 n he gven roduc n reference The arguen s ha he curren forula of onhly channg n reference 2005 already akes no accoun he change n rces snce reference erod f he udae of weghs akes no accoun he change of uany and he change of rces beween reference erod and year n-2 he change of rces beween reference erod and year n-2 s couned wce. f he reference erod was Deceber n- as n os counres (arge racce) he correcon would be he ullcaon by ndex (Deceber n- ) / ndex (average year n-2) as he Ukranans do for nsance. Ths es calculaon has concerned only aggregaon fro CPA 4 dgs uwards: CPA 4 dgs -> CPA 3 dgs -> CPA 2 dgs -> oal ndusry and anufacurng and MGS. Excel fles conen all esaes bu he followng chars only descrbe he conseuences on oals and MGS ue sall n fac and usually colan wh heory (fxed-base Laseyres ndces are suosed o over-esae rce changes and chan-lnked Laseyres ndces o correc hs henoenon arly) BE_chan-lnked BE_fxed base CZ_chan-lnked CZ_fxed base Toal ndusry (BE) and oal anufacured goods (CZ)

60 0/0/2005 0/2/2005 0/02/2006 0/04/2006 0/06/2006 0/08/2006 0/0/2006 0/2/2006 0/02/2007 0/04/2007 0/06/2007 0/08/2007 0/0/2007 0/2/2007 0/02/2008 0/04/2008 0/06/2008 0/08/2008 0/0/2008 0/2/2008 0/02/2009 0/04/2009 0/06/2009 0/08/2009 0/0/2009 0/2/2009 0/02/200 0/04/200 0/06/200 0/08/200 0/0/200 0/2/200 0/02/20 0/04/20 0/06/20 0/08/20 0/0/20 0/2/20 0/02/202 0/04/202 0/0/2005 0/2/2005 0/02/2006 0/04/2006 0/06/2006 0/08/2006 0/0/2006 0/2/2006 0/02/2007 0/04/2007 0/06/2007 0/08/2007 0/0/2007 0/2/2007 0/02/2008 0/04/2008 0/06/2008 0/08/2008 0/0/2008 0/2/2008 0/02/2009 0/04/2009 0/06/2009 0/08/2009 0/0/2009 0/2/2009 0/02/200 0/04/200 0/06/200 0/08/200 0/0/200 0/2/200 0/02/20 0/04/20 0/06/20 0/08/20 0/0/20 0/2/20 0/02/202 0/04/ MG_NG_chan-lnked MG_NG_fxed base MG_CAG_chan-lnked MG_CAG_fxed base MG_COG_chan-lnked MG_COG_fxed base MGS MG_NRG_chan-lnked MG_NRG_fxed base 06_chan-lnked 06_fxed base Energy France has added dvson 06 o hs las grah as he rce changes have been secacular n coodes 06.0: crude eroleu and 06.20: naural gas bu he resul of chan-lnkng s only aaren durng soe onhs a he end of 2008 and a he begnnng of reland reland nvesgaed he ac of varous chan lnkng ehods on he colaon of onhly roducon sub-ndces of he MP. The ndces san fro January 2005 o May 20 (2005 =00). 4 dg NACE ndces (base 2005 =00) are he coonen seres used o calculae he chan lnked cobned ndces. NACE Rev 2 base-weghs are currenly only avalable for and n hs analyss we aled; 2005 weghs o and

61 2008 weghs o 2008 and 2009; 2009 weghs o 200 and 20 The base-weghs are rovded n he for of he GVA values for each 4 dg NACE secor and he weghs are suled by CP ( ). The base-weghs are used o for cobned grous where he conrbuon of any one 4 dg NACE secors s sly: Fve ehods were used o cole he hgh level NACE Rev 2 ndces. The frs ehod resened s sly he curren fxed base year (base 2005 = 00). Ths ehod s resened sly as a benchark for he oher ehods. The second ehod s slar o he curren base year ehod bu n he second ehod he calculaons are usng wo ore fxed base year ndces.e. (base 2008 = 00) and (base 2009 = 00). n he second ehod he ndces are joned by slcng he ndces a arorae overlang onhs. The hrd ehod eloyed s a onhly change lnkng ehod The fourh ehod uses annual weghs -Change on Deceber - wh annual weghs. -Change on Deceber - wh weghs relave o Deceber. -Fnally change on year - (average of he onhly roducon ndces). ) Fxed base year ehod (currenly used ehod base year = 2005) n hs ehod an ndex s creaed by alyng roducon ndces for every secor of NACE 0 usng he 2005 weghs of hs secor and sung he o oban a onhly ndex for NACE 0. An ndex s obaned ha refers o he roducon for a onh o base year y X 05 y X y X y X * W 05 X Where YY reresens he ndex of roducon for he secor X a year y and onh calculaed a year YY weghs. y X reresens he fnal ndex for roducon for secor X a year y and onh. y X reresens he ndex of roducon for he -ee subsecor of secor X a year y and onh W reresens he wegh of he -ee subsecor on secor X n year YY. YY X An ssue assocaed wh hs ehod s ha he weghs of he econoy change over e. The assuon s ha weghs becoe less accurae he furher fro he base year. 56

62 2) Acualsed weghs fxed base year ehod. n hs ehod an ndex s creaed by alyng o he base ndces he ore u o dae weghs. So for he and 2007 onhly ndces 2005 weghs are aled for 2008 and 2009 ndces 2008 weghs are aled and for 200 and 20 ndces 2009 weghs are used. YY y y X X * W YY The roble encounered wh hs ehod s he lnk beween 2 onhs wh dfferen weghs so for exale he lnk beween Dec07 and Jan08 as hese 2 ndces are creaed wh dfferen weghs There wll be a oor reresenave of he change beween hese 2 onhs (f calculae Dec07 and Jan08 wh he sae weghs weghs or 2008 weghs- a coarable change beween hs 2 onhs can be seen bu by usng hs ehod he coarson beween 2 ndces relave o 2 dfferen base years). To oban a e seres reresenave of he change he ndex s slced.e. rescale he ndex afer 2008 (ncluded) o he ndex before and hs for every lnk beween 2 dfferen weghs ndces ake Dec - as a lnk onh (here Dec07 add or reove o afer Jan08 he dfference beween Dec07 a 2005 weghs and Dec07 a 2008 weghs). y y y2 y2 X y X y2 X y X y- s he wegh we would aly on year y f we had all weghs avalable n our exale year y- s no used bu he year whose wegh was decded o aly. X y y 05 X f y n y y X 08 X 05 X 08 X f y n

63 y y X 08 X 05 X 08X 08 X 09 X f y >= 200 The oucoe s an overvew of he change n he roducon bu he easures wll be false due o he slcng. Therefore dfferen ehods are used o chan he ndex below and coared. 3) Monhly change chan lnkng ehod n hs ehod a eorary ndex s creaed ha refers for each onh o he change snce he revous one ( he base ndex ully he ndex of onh by he ndex of onh - and dvde by 00). y y y y y y2 T hen T ( )* 00 and ( )* X X X X = reresens he eorary ndex for -ee subsecor n year y onh. X T f Then he ore accurae weghs (as descrbed earler) are aled o hs eorary ndex o each ndex: y y YY T X TX * WX (f y n : YY=2005 f y n : YY=2008 and f y>2009: YY = 2009). Nex he eorary ndex s rebased o he revous onh o oban he fnal one (kee he frs value Jan05 unchanged hen ully eorary Feb05 value by he fnal Jan05 value ec..) and hs s carred ou fro he begnnng o he end for every onh and leads o he fnal ndex. X X X 05 X T hen y ( y * y y y y2 T ) 00 or ( T * ) 00 f =. 05 X X X X X X X X 58

64 An alernave ehod was carred ou for secor NACE 08 as here s only a GVA only on 2005 base weghs. An ssue wh hs s annual weghs are used for calculang onhly changes and can lead (robably due o exree values esecally here for NACE 08 and aybe o he hgh nuber of changed calculaons) o an abnoral augenaon of he ndces. 4) Change on Deceber - chan lnkng ehod So we wll chan annually he frs way dd s wh he change on Deceber - chan lnkng ehod Calculae he change snce one onh on he revous year nsead of calculang he change he revous onh for every onh. Deceber was chosen as s he closes onh o he acual year. For dong ha he ndex of one onh of a year (year ) was ulled by he ndex of Dec - and dvded by 00. A eorary ndex s obaned ha conans for each year ndces referrng o he change snce revous Deceber (we kee base year 2005 unchanged): y y y2 T X X hen ( )* 00 T reresens he eorary ndex for -ee X subsecor n year y onh. X X Weghs of he revous year for each year are aled (or he ore accurae weghs as n hs case) o hs eorary ndex and a eorary ndex for NACE 0 s obaned: y y YY T X TX * WX (f y n : YY=2005 f y n : YY=2008 and f y>2009: YY = 2009) 59

65 s rebased o he year reference: here ke 2005 unchanged and for each year he onhly ndces are ulled by he fnal ndex of revous Deceber and dvded by X y y y2 T hen ( T * ) X X X X X The ssue ha could have an ac on ceran cases s ha annual weghs are used o coare a change snce Deceber; nsead weghs relave o Deceber should be used. Ths s he nex ehod. 5) Change on Deceber - wh aended weghs chan lnkng ehod For hs ehod he exac sae calculaon s used as for he revous one (4) exce ha here s adjusen o he annual weghs o gve an aroxaon of Deceber weghs. The curren GVA s ulled for one secor by he roducon of hs secor n Deceber n year -/Average of roducon of hs secor n year -. Wc W X X Wc ZZ X W YY X *( ZZ2 X ean ( ZZ X )) Year ZZ should be eualled o year YY bu weghs are no avalable for each year so ake for ZZ n : YY=2005; for ZZ n : YY = 2008; for ZZ>2009 YY =200. n exales fro oher counres has lead o good resuls n our case sees o be a good correcon of he revous Deceber change ehod. 60

66 6) The ean change ehod Where here are annual weghs s ossble o coare ndces o he whole revous year.e. he average of he onhly ndces n he revous year. A eorary ndex where we kee 2005 unchanged s creaed. Then he base ndces are dvded by he average of he revous year ndces for every secor: y y y X hen TX ( X ean ( X ))* 00 T X The weghs are hen aled and so a eorary ndex for NACE 0 s obaned: y y YY T X TX * WX (f y n : YY=2005 f y n : YY=2008 and f y>2009: YY = 2009) Ths s rebased o 2005 and he fnal ndex s obaned: keeng year 2005 unchanged. The eorary onhly ndces of a year are ulled by he average of he fnal ndces of he revous year and dvded by 00 (fro Jan2006 o May20). 05 X y y y T hen ( T * ean ( )) X X X X X 6

67 7) Coarson of dfferen ehods. The fxed base year wh acualsed weghs gve us a reresenaon of he change n he econoy. The onhly change ehod sn adaed o our conex and looks dsored. The change on Deceber - s also good bu afer correcon oherwse could lead o a wrong e seres. The ean change ehod sees o lead o good resuls also. Below s a grahc coarson. The resuls for NACE 0 are ue slar wh hese ehods. 62

68 The resuls for NACE 2 NACE 26 NACE 27 and Modern Secor can be vewed n grahcal for below. NACE 2 s neresng o see because here are only 2 subsecors n and we can see also he evoluon of hese subsecors and look a her weghs o arecae he effcency of each ehod; he calculaon for NACE 2 s done n Excel can also be a ore raccal vew of he calculaon. n reland here was a large change a he enerrse level n NACE 26 snce he weghs were calculaed n The wegh for hs secor s now oo hgh bu neher ehod sees o correc for hs. 63

69 64

70 7..3. Czech Reublc SPP - coarson of curren fxed-base onhly ndex wh heorecal chan-lnked ndex. The echnue used s one-uarer overla sarng n 2008 chan lnkng s erfored on he level of 2-dg NACE. PP - coarson of curren fxed-base onhly ndex wh heorecal chan-lnked ndex. The echnue used s one-onh overla sarng n 2007 chan lnkng s erfored on he level of MG grous. (As wh SPP s execed ha he dfferences would be sgnfcanly greaer were he channg erfored on lower levels.) 65

71 Volue of real sales for food non-food roducs (exce fuel) and oal. Coarson of curren fxed-base onhly ndex wh heorecal chan-lnked ndex. The echnue used s annual overla sarng n There s no ye a concree lan for channg hs ndcaor so hs s only a relnary calculaon wh rovsonal weghs. 66

72 7..4. Croaa The grahc shows he coarson beween he annual chan-lnked and fxe base year Croaan P. 67

73 2005M0 2005M M M0 2006M0 2006M M M0 2007M0 2007M M M0 2008M0 2008M M M0 2009M0 2009M M M0 200M0 200M04 200M07 200M0 20M0 20M04 20M07 20M0 202M0 202M Norway The grahc shows he coarson beween he annual chan-lnked and fxe base year Norwegan PP PP Fxed wegs 2005 PP Udaed weghs The coarson beween he annual chan-lnked and fxe base year Norwegan P s resened n he followng grah P Fxed weghs P Udaed weghs

74 7..6. Turkey The grahc shows he coarson beween he annual chan-lnked and fxe base year Turksh P Uned Kngdo The coarson beween he annual chan-lnked and fxe base year P s resened n he followng grah. 69