Weights in CPI/HICP and in seasonally adjusted series
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- Milo Hodges
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1 eghts n CI/HIC nd n sesonlly djusted seres Jn lschots Ottw Group Meetng Copenhgen 2 My 2013
2 Subject of the pper lterntve wys to wrte the Lspeyres ndex formul nd to clculte weghts. nnul bskets nd monthly ndces. The mpct of sesonl djustment on the weghts Theoretcl results ppled to ECB seres of the HIC CI/HIC - eghts n sesonlly djusted seres 1
3 LSEYRES ndex Bsc formul: 1 U b b Index wrtten s elementry ggregtes nd weghts: b b / 2 b Ub b CI/HIC - eghts n sesonlly djusted seres 2
4 Fxed bsket wrtten s chn ndex CI/HIC - eghts n sesonlly djusted seres b b b b U Π Π + + x x x b x x x b x b U x x x x x
5 Rel chn ndex wth chngng bsket CI/HIC - eghts n sesonlly djusted seres 4 7 eghts n HIC re ecember weghts 10 nd re bsed on n nnul bsket 12 Π + x x x b x b U 1 1
6 nnul bskets nd monthly ndces. Monthly fgures my led to sesonl ptterns n consumpton nd n prces Sesonl pttern n consumpton s ruled out of HIC by tkng nnul bskets nd by the Regulton on sesonl products In HIC seres usng Lspeyres type ndex there s only sesonl pttern n prces. CI/HIC - eghts n sesonlly djusted seres 5
7 How to del wth sesonl pttern of prce ndces Focus on nnul rtes Sesonl djustment of ndex seres Not performed by CBS Eurostt nd mny Sttstcl nsttutes Often performed by Ntonl Bnks reserch nsttutes nd Europen Centrl Bnk ECB CI/HIC - eghts n sesonlly djusted seres 6
8 rect nd ndrect sesonl djustment rect pproch: S ppled to hedlne seres. outsde scope of ths pper Indrect pproch: S ppled to components of HIC nd ggregted to totl S seres Components my hve stble nd dentfble ptterns where totl pttern chnges due to chngng weghts CI/HIC - eghts n sesonlly djusted seres 7
9 Orgnl nd S weghts n fxed bse Lspeyres ndex Orgnl seres 15 Sesonlly djusted seres 17 CI/HIC - eghts n sesonlly djusted seres 8
10 Orgnl nd S weghts n fxed bse Lspeyres ndex Consderng tht combnng 15 nd 17 leds to: 19 CI/HIC - eghts n sesonlly djusted seres 9
11 Orgnl nd S weghts n chn-lnked Lspeyres ndex HIC CI/HIC - eghts n sesonlly djusted seres 10
12 Orgnl nd S weghts n chn-lnked Lspeyres ndex HIC The lst term of 23 s constnt nd the qunttes re not sesonlly djusted. Therefore: 24 wth 25 1 CI/HIC - eghts n sesonlly djusted seres 11
13 Incomplete vlblty of dt ecember ndces from orgnl nd S seres re publshed nd computed from the weghts of yer -1 nnul weghts for yer re usully not publshed Formuls 24/25 re bsed on expendtures n yer nd cn not be clculted exctly. CI/HIC - eghts n sesonlly djusted seres 12
14 Current prctce of ECB ECB clcultes S seres for: Food Industrl goods excludng energy Servces nd ggregtes wth orgnl seres for Energy to derve S hedlne seres CI/HIC - eghts n sesonlly djusted seres 13
15 ggregton of ECB S seres usng djusted weghts - S seres for euro re. Source ECB - ecember eghts. Source Eurostt - ecember ndces. Source Eurostt - S ecember ndces. Source ECB gve djusted weghts for ggregton of S seres s n 24 CI/HIC - eghts n sesonlly djusted seres 14
16 Results S HIC ggregted seres euro re Impct of djusted weghts depends on: stnce of ecember prces from trend Importnce of sesonl pttern for product groups tht hve trends tht dffer from hedlne HIC Level of ggregton of ndex components Impct for ndvdul countres mybe bgger thn for euro re. CI/HIC - eghts n sesonlly djusted seres 15
17 fference between S seres wth djusted weghts nd publshed S seres HIC euro re ec 2004Mr 2004Jun 2004Sep 2004ec 2005Mr 2005Jun 2005Sep 2005ec 2006Mr 2006Jun 2006Sep 2006ec 2007Mr 2007Jun 2007Sep 2007ec 2008Mr 2008Jun 2008Sep 2008ec 2009Mr 2009Jun 2009Sep 2009ec 2010Mr 2010Jun 2010Sep 2010ec 2011Mr 2011Jun 2011Sep 2011ec 2012Mr 2012Jun 2012Sep 2012ec CI/HIC - eghts n sesonlly djusted seres 16
18 Conclusons On theoretcl consdertons weghts for S seres should be djusted n the cse of chn-lnked Lspeyres ndex In prctce the mpcts my be very smll Not ll dt for djusted weghts re publshed by Eurostt nd NSIs CI/HIC - eghts n sesonlly djusted seres 17
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