Linking factors for gross and seasonally adjusted series

Transcription

1 Lkg facors for gross ad seasoally adjused seres The purpose of hs oe s o expla problems wh he curre lkg mehodologes used he EI ad propose chages o solve dscrepaces recely defed bewee gross ad seasoally adjused dces whch are provded by coures bu for whch usg lks s ecessary o have eough hsorcal daa. uch dscrepaces are foud for sace from 99 o 997 for a Hugara seres: IIP Toal Idusry excludg cosruco afer usg he Frs Commo Perod lkg mehod. Dscrepacy bewee Gross ad easoally adjused IIP for Hugary Ja-9 ay-9 ep-9 Ja-93 ay-93 ep-93 HUN.PPEIN0.IXNB.4 Ja-94 ay-94 ep-94 Ja-95 ay-95 ep-95 Ja-96 ay-96 ep-96 Ja-97 HUN.PPEIN0.IXNBA.4 ay-97 ep-97 As oe ca oce, he seasoally adjused IIP s clearly above s aural poso vs à vs he gross seres (see graph below represeg verso 3 of he gross ad seasoally adjused IIP for Hugary, from 99 o 997).

2 Gross ad easoally adjused IIP for Hugary (prevous verso, before lkg) Ja-9 ay-9 ep-9 Ja-93 ay-93 ep-93 HUN.PPEIN0.IXNB.3 Ja-94 ay-94 ep-94 Ja-95 ay-95 ep-95 Ja-96 ay-96 ep-96 Ja-97 HUN.PPEIN0.IXNBA.3 ay-97 ep-97 I addo, as a resul of he work of Guseppe Parg, f oe cosders he IIP Toal dusry excludg cosruco, hs ype of dscrepacy appears sgfcaly o oly for Hugary bu also for Belgum, Demark, Germay, Ialy, Neherlads, Norway, wede, he Ued Kgdom ad o a lesser exe for Frace. Ths oe s orgased 5 pars. I Par I, we exame he mpac of lkg mehods o growh raes, wheher aual or mohly. I Par II, we aalyse he codos uder whch lkg mehods wll be able o solve he dscrepaces oced for he Hugara IIP as well as for he oher coures quoed above. I Par III, we gve he codos uder whch he aual value for he IXOBA seres for he OECD sadard base year (.e. 995) wll be equal o 00. Fally, Par 4 we gve a summary of he ma resuls from he prevous pars followg by a comme o recommedaos ad fuure work Par 5.

3 I Impac of lkg mehods o aual ad mohly growh raes Frsly, we gve below he oaos used hroughou he ex: Noaos: b before commo perod c commo perod me perod ew seres verso o old seres verso (o -) aw seres easoally adjused seres Fcp Frs Commo Perod lkg mehod Fcy Frs Commo Year lkg mehod I he followg, we suppose ha before applyg he lkg facor, he ew seres sars 0/9N ad ha s mohly (he resuls would be he same f we cosdered a quarerly seres). We defe as he lkg facor bewee he ew seres ad he old oe: f (, ) - Before 0/9N, he mohly growh raes are as follows: c oc Therefore, whaever he value of he lkg facor, he mohly growh raes (as well he aual growh raes) wll be preserved before 0/9N for he ew seres. - The oly mohly growh rae whch wll deped o he lkg facor s he oe bewee /9N- ad 0/9N ad s formula s gve by: c,0 / 9 N b, / 9 N c,0 / 9 N ob, / 9 N If we use he Frs Commo Perod mehod, ha s fcp 0/9N 0/9N, he above formula becomes: 0/9N /9 N fcp 0/9N /9N 0/9N 0/9N 0/9N /9N 0/9N /9 N 3

4 - Therefore, he Frs Commo Perod esures he mohly rae of chage bewee /9N- ad 0/9N for he ew seres verso s equal o ha of he old seres verso. I addo, s sraghforward o show ha he frs commo perod ad frs commo year lks wll gve he same lkg facors f he ew seres has o bee revsed compared wh he old seres, over he frs mohs of he commo perod (.e. f mohly growh raes of he ew seres are srcly equal o hose of he old seres, over he frs mohs of he commo perod). I hs case, we would have, for s o h moh: + /9N + /9N /9N ad, as a resul, he followg formula: /9N /9N 0/9N 0 /9N /9N /9N fcp K L fcy 0/9N 0 /9N /9 N /9N /9N Obvously, f he above codo does o hold meas here have bee revsos o he old seres over he frs mohs of he commo perod, ad hus he use of he frs commo perod lkg mehod (.e. he curre mehod) becomes quesoable. Tha s, why preserve he hsorcal mohly growh rae a he frs commo perod f we kow he ew seres has bee revsed? I hs case usg a frs commo year lkg mehod s lkely o lead o a more robus lkg facor. Aual growh raes We ow compue he aual growh raes for he ew seres a he mohs of he commo perod. If we oe s o h moh, we have: /9N /9N /9N /9N - We fd ha he aual growh raes for he ew seres a he frs mohs of he commo perod wll deped o he lkg facor used. Ths s mpora as aual growh raes are ofe used o aalyse mohly seres ad hese are publshed he EI. Furhermore, f we deoe as ad he lkg facors obaed wh wo dffere lkg mehods ad as ad he aual growh raes for he ew seres a he frs mohs of he commo perod, we oba he followg formula: Therefore, he average aual growh raes over he perod before ad afer he lk wll dffer by a facor equal o, whch explas he dvergece of levels seres expeced o show smlar pahs o average (e.g. seasoally adjused ad gross seres) caused by he use of dffere lkg mehods. 4

5 II Cosseces of he lkg facors for gross ad seasoally adjused dces provded by he coures The prevous formulas hold f we replace by s seasoally adjused couerpar. As a resul, f we oe he lkg facor appled o ad he lkg facor appled o, we have he followg formulas before 0/9N: Therefore, whaever he values of he lkg facors ad, he mohly growh raes (as well he aual growh raes) for he raw seres as well as for he seasoally adjused seres wll be preserved before 0/9N. BUT he followg formulas mus hold before 0/9N order o avod cosseces bewee he level (whch ca be vsually see o he graph) of he raw seres ad ha of he seasoally adjused seres: Bu we kow ha: Thus we eed: Therefore, order o avod cosseces bewee he level of he raw seres ad ha of he seasoally adjused seres before 0/9N (see for example he IIP Toal for Hugary), he value of he lkg facor mus be he same for he raw seres ad for he seasoally adjused seres: wh f (, ) ad f (, ) c oc hp:// c oc O p.7 of he above arcle from Davd F. Fdley e al (998) New Capables ad ehods of he X- AIA easoal Adjusme Program, "The oly calculaos [of he seasoal facors] whose role may o be clear are hose of sep (v) ages ad. Ther effec s usually o make welve-moh oals of he adjused seres be close o he correspodg oals of he uadjused seres." 5

6 Therefore, f daa are avalable for he commo year (ofe he case) for boh he gross seres ad he seasoally adjused seres, we have he approxmaed formulas: The relao below wll hold approxmaely: If we deoe fcy as he Frs Commo Year lkg mehod, we wll eveually have: fcy, fcy, fcy NB: f we chage he lkg facor opo from Frs Commo Perod o Frs Commo Year case of Gross ad easoally adjused dces provded by he coures, we wll be close o equaly bewee he lkg facors bu he equaly wll ever be perfec. I addo, we have o oe ha he seasoally adjused values are usable a he begg ad a he ed of a me seres. However, we ca force he equaly as chard ckeze ad Jes Dossé sugges, by usg he lkg facor of he raw seres ad applyg o he seasoally adjused seres. Noe ha f we use he Frs Commo Perod lkg mehod, we wll always ge a dscrepacy bewee ad f he coures seasoally adjused seres has bee revsed wh he rebase whch s almos always he case (hece he problem we have defed). 6

7 III Cosseces of he value of he IXOBA seres a he OECD sadard base year (.e ), whe he IXNB ad IXNBA seres are provded by he coures afer 995 oly The formula below gves he aual value of he IXOBA seres (derved from he IXNBA seres), deoed as A, whe he IXNB ad IXNBA seres are uavalable for he OECD sadard base year (.e ); whe lks have hus bee appled o boh seres (currely Frs Commo Perod ) o have daa avalable for he OECD sadard base year; whe he aual segme of he IXNBA seres s a proxy of he correspodg IXNB seres (as s currely he recommedao for EI seres). A Average * Average ( o ) ( ) o *00 Ths formula shows ha A ca be decomposed o a lkg facor effec: effec: Average Average ( o ) ( ) o. We ca see ha A wll exacly be equal o 00 f ad oly f: ad o, /995 o, /995 ad a seasoal facor We already kow from Par I ha f we ca force he frs equaly, s o he case for he secod equaly. If o, /995 s almos decal o o, /995 he we ca use a aual segme for he IXNBA seres whch would be a proxy of he correspodg IXNB seres. If o, usg a aual proxy segme could creae a sgfca dfferece f a user waed o comple he average of he year. He or she would fd a dffere value from wha we dcae he EI daabase for he year. For he Hugara IIP, he curre average value for he year 995 for he IXOBA seres s 06.9 whereas we should fd a value close o 00. Ths dscrepacy s maly explaed by he use of he Frs Commo Perod mehod for boh he Gross ad easoally adjused seres. As a resul, for he Hugara IIP parcular, he lkg effec measured by s oo large (.065 > ). 7

8 Chagg he aual segme of he IXNBA seres from proxy o frequecy wll esure ha he IXOBA value for he OECD sadard base year be equal o 00 accordg o he evde formula: ' A Average * Average ( o ) ( ) o *00 00 NB: he case of Hugary, he cosseces of he Gross ad easoally adjused dces wll rema f we chage he aual segme of he IXNBA seres from proxy o frequecy whou chagg he lkg mehod (.e. Frs Commo Perod ) a he same me. The above ex esseally summarses he coe of Appedx, whch descrbes more dealed he mpac assocaed wh he use of proxy or frequecy for defg aual seres. IV Cocludg remarks Before he Frs Commo Perod (geerally 0/9N), he mohly (ad aual) growh raes of he ew seres are decal o hose of he old seres, whaever he value of he lkg facor; From Frs Commo Perod +, he mohly growh raes of chage wll be based o he ew daa (o problem!); The value of he lkg facor has oly a mpac o he mohly growh rae bewee Frs Commo Perod ad Frs Commo Perod because we compare wo seres comg from dffere sources. The Frs Commo Perod lkg mehod esures hs growh rae s he same for he old ad ew seres, whch s quesoable f he ew seres has bee revsed from he sar of he frs commo perod; Aual growh raes from Frs Commo Perod o Frs Commo Perod + wll also deped o he value of he lkg facor whch s sgfca due o he mporace of aual growh raes for aalysg mohly seres. Where he ew seres has bee revsed, use of he Frs Commo Year lkg mehod s a more robus mehod for measurg hese aual growh raes ha he frs commo perod; Whe coures provde EI wh Gross ad easoally adjused dces, he Frs Commo Perod mehod geerally leads o a dscrepacy bewee he levels of he Gross ad easoally adjused seres: possble soluos explored would be eher o chage he Frs Commo Perod mehod o he Frs Commo Year mehod for all versos of boh he gross ad seasoal adjused seres or o apply he Frs Commo Year lkg facor obaed wh he gross seres, o he seasoally adjused seres; Chagg lkg mehods mples a chage of he aual growh raes a he mohs of he year coag he commo perod, ad for he level of he hsorcal seres; The use of aual proxy segmes for our seasoally adjused seres (excep for Balace of Paymes seres) combao wh he curre lkg mehod resuls value of he IXOBA seres for he OECD base year o beg equal o 00. 8

9 IV ecommedaos ad fuure work. Immedaely chage our lkg procedures o he Frs Commo Year mehod. I cojuco wh hs chage, gudeles wll be gve o wha eeds o be assessed whe lks are performed for boh gross ad seasoally adjused seres a he same me (e.g. eed o esure commo perods are he same, eed o esure he resula lkg facors are very close ec.);. The operaoal ssues of usg a lk derved from he Frs Commo Year mehod from he gross seres for he seasoally adjused seres should be dscussed (e.g. sysem ad goverace ssues); 3. All rece lks pu place assocaed wh coures chage o year 000 base year (or oher rece chages o base year) eed o be defed ad fxed as soo as possble (work program ssue); 4. All hsorcal seres wh hs problem (.e. cosderg lks performed may years he pas) eed o be defed ad opos for revsg hese seres cosdered, parcular for hose wh very large dscrepaces log me seres (r Parg has developed a program o defy hese seres); 5. The curre polcy of usg aual proxy segmes for seasoally adjused seres should be revewed, bu probably afer errors seres caused by he lkg problem have bee resolved. Frederck Parro & chard ckeze hor Term Ecoomc ascs Dvso 3 December 003 Appedx Usg a FCY mehod wll resul a revso o he mohly growh rae for he frs commo perod bewee he old ad ew seres equal o he perceage dfferece he lkg facors derved from he FCP ad FCY mehods (easy o show algebracally). If hs s large could cause a exreme value he mohly growh rae seres a hs po. However, hs s o cosdered a major problem for a umber of reasos: If here s a large dfferece bewee lkg facors derved from he FCP ad FCY mehods, geerally meas he ew seres has bee subsaally revsed over he frs commo year. I hs case, revsos o mohly growh raes for he frs commo year (bewee he old ad ew seres) are lkely o be sgfca. For example, for he Hugara IIP seres show above, 4 of revsos o he mohly growh raes for he frs commo year bewee verso 3 ad 4 of he seres were greaer ha he revso he growh rae for he frs commo moh caused by usg he FCY mehod. easoally adjused seres are lkely o be more sable ha gross seres ad herefore you may o expec as large a dfferece bewee he lkg facors derved from FCP ad FCY mehods, mplyg ha hs could be less of a ssue for he seasoally adjused seres. 9

10 If here are large dffereces bewee he FCP ad FCY lkg facors, s very lkely ha here would also be a large dfferece bewee FCP lkg facors for he s.a. ad gross seres. Thus oe mus cosder whch s worse, a large revso o he mohly growh rae for he frs commo perod (from usg FCY mehod) or he roduco of a large dscrepacy bewee he gross ad s.a. seres (from usg FCP mehod). The laer problem s judged o be more serous. Despe hese ssues, careful aeo should be pad f he lkg facors derved from FCP ad FCY mehod are cosderably dffere (say greaer ha 5% bu hs should deped o he volaly of he seres as well) by brgg o he aeo of he Admsraor ad havg a broader dscusso o he case cocered. Appedx : Impac of usg aual proxy or frequecy segmes for seasoally adjused seres The purpose of hs appedx s o aalyse he mpac of defg he aual segme of seasoally adjused dces as eher Frequecy or Proxy (of he correspodg gross seres). I Par, we exame he case whe TD/TE rus s ow seasoal adjusmes ad Par, he case whe coures provde TD/TE wh seasoally adjused dces. ) Case : TD/TE seasoally adjuss dces by self The value of he IXOBA seres wll ever perfecly be equal o 00 for he OECD sadard base year (currely 99500) bu wll be close eough o 00; The queso s: shall we defe he aual segmes of hese seasoally adjused dces as proxy of he raw dces order o ge a exac 00 for he OECD base year? However, so dog, he followg formula would o perfecly hold whereas we assume ha holds he subjec ables Idusral Produco Idces ad eal Trade (we clearly sae sa he EI publcao): / There s o dfferece bewee usg proxy or frequecy for he aual segmes of he seasoally adjused dces f: /995 /995 (I) Aga, he dfferece s geerally small a he OECD sadard base year (currely 99500) bewee 00 ad he mohly (or quarerly) average of a dex seasoally adjused by TD/TE; The seasoal adjusme sofware X-Arma makes relaoshp (I) close o equaly so ha usg segmes such as proxy or frequecy case s o a bg ssue. 0

11 ) Case : The coures provde TD/TE wh gross ad seasoally adjused dces.- We use he same assumpos as above paper o he lkg mehods (maly ha here are o eough hsorcal daa back o he OECD sadard base year,.e ) ad we exame he cosequeces o a IXOBA seres of defg he aual segme of a IXNBA seres as frequecy : I he followg, we deoe as Ω 995 ad Φ 995 he respecve values of he IXNB ad IXNBA seres for 995, whch s he OECD sadard base year. If he aual segme of he IXNB ad IXNBA seres s frequecy (evde for he IXNB seres), we wll have: Ω 995 / 995, b ad Φ995. /995, b The rasformao used o oba he IXOBA seres from he IXNBA seres wll he be equal o: 00. / 9N, IXOBA * /9 N, IXNBA Φ995 Noaos: deoes a mohly daa po, s he raw seres, he ew seres, o he old seres ad a gve moh. - I ha case, he average value of he IXOB ad IXOBA seres for he OECD sadard base year (.e ) wll exacly be equal o Furhermore, he values of he IXOBA seres over he year 003 say, wll deped o he values of he IXNB, IXOB, IXNBA seres as well as o he lkg facors ad (f coures do o provde hsorcal daa for he gross ad seasoally adjused dces back o 995), as follows: / 003, IXOBA, * /995, IXNB, o /995, IXNBA, o * / 003, IXNBA, * / 003, IXNB, / 003, IXOB,. Therefore, s mpora o oe ha he Idusral Produco dces publshed he EI paper publcao or CD-om (IXOBA measure as Par I) wll be revsed over he ere perod f we chage our lkg procedures for boh he IXNB ad he IXNBA seres..- We use he same assumpos as. ad we exame he cosequeces o a IXOBA seres of defg he aual segme of a IXNBA seres as proxy : - If we defe he aual segme of he IXNBA seres as proxy of he IXNB seres, he we oba: Φ 995 Ω 995. /995, b

12 - The rasformao used o oba he IXOBA seres from he IXNBA seres wll he be equal o: 00. / 9N, IXOBA * /9N, IXNBA Ω995 - The average value of he IXOB seres for he OECD sadard base year (.e ) wll exacly be equal o However, as he aual segme of he IXNBA seres s defed as a proxy of he IXNB seres, we wll o ge a perfec 00 whe complg he rue aual average (based o he mohly daa) for he OECD sadard base year (.e ). The dfferece bewee 00 ad he compled aual average s measured by a facor equal o: * /995, b /995, b. - I addo, he values of he IXOBA seres over 003 say, wll deped o he values of he IXNB, IXOB ad IXNBA seres ad also o he lkg facors (as he values of he IXOB seres wll deped o how he IXNB seres s lked), as follows: / 003, IXOBA, / 003, IXNBA, * / 003, IXOB,. / 003, IXNB, Therefore, he cocluso s he same as.: he Idusral Produco dces publshed he EI paper publcao or CD-om (IXOBA measure as Par I) wll be revsed over he ere perod f we chage our lkg procedures for boh he IXNB ad he IXNBA seres. - We have hus show ha he values of a IXOBA seres over he ere perod deped o: The choce of he lkg procedure for he IXNB ad he IXNBA seres ad; The defo of he aual segme of he IXNBA seres as proxy or frequecy of he IXNB seres. - We oe ha here s a posve correlao of he effecs o he values of he IXOBA seres of he lkg mehod ad he defo of he aual segme of he IXNBA seres. - I oher words, choosg he rgh lkg procedure,.e. he oe whch esures ha he lkg facor for he IXNBA seres s close o he lkg facor of he IXNB seres, sgfcaly reduces he effec of defg he aual segme of he IXNBA seres as proxy or frequecy (cf. graphs below represeg he Idusral Produco Idex of Hugary base year 99500; frs commo perod: Jauary 998; frs commo year: 998).

13 - Furhermore, as also show o he graphs, f he OECD sadard base year (currely 99500) s before he lkg po, he mpac o he IXOBA seres of he opos frequecy or proxy s as follows: Frequecy : IXOBA seres exhbs a dscrepacy wh he IXNB seres afer he lk po (he dscrepacy wll be small f a good lkg mehod s chose); Proxy : IXOBA seres exhbs dscrepacy wh he IXNB seres before he lk po,.e. a he OECD sadard base year. Case of Hugary: Hugary - Idusral Produco Idex: Frs Commo Perod (Jauary 998), mpac of aual segme of IXNBA seres - "proxy" or "frequecy" IIP - Hugary (base 99500) Proxy FCP (Frs Commo Perod) IIP IXOB Proxy FCP IIP IXOBA Frequecy FCP IIP IXOB Frequecy FCP IIP IXOBA 3

14 Hugary - Idusral Produco Idex: Frs Commo Year (998), mpac of aual segme of IXNBA seres - "proxy" or "frequecy" IIP - Hugary (99500) Proxy FCY (Frs Commo Year) IIP IXOBA Frequecy FCY IIP IXOB Frequecy FCY IIP IXOBA - Oce a proper lkg mehod s used, here remas o exame he mpac o he values of he IXOBA seres of defg he aual segme of he IXNBA seres as proxy of he correspodg IXNB seres. The followg able summarzes he ma fdgs: Aual segme of he IXNBA seres proxy. The value for he OECD base year (currely 99500) for he IXOB seres wll exacly be equal o 00. The compled aual average for he OECD base year for he IXOBA seres wll dffer from 00 by a small amou. However, he EI daabase wll dsplay 00 for 995 because of he proxy segme. No dscrepacy bewee he paer of he IXNB/IXNBA seres ad ha of he IXOB/IXOBA seres. Aual segme of he IXNBA seres frequecy The value for he OECD base year for he IXOB seres wll exacly be equal o 00. The value for he OECD base year for he IXOBA seres wll exacly be equal o 00. A small dscrepacy bewee he paer of he IXNB/IXNBA seres ad ha of he IXOB/IXOBA seres. However, f hs dscrepacy s small eough could be oleraed gve ha he aual values of he IXNBA ed o oscllae aroud he aual values of he IXNB seres ayway. 4

15 Lasly, defg he aual segme of he IXNBA seres as proxy wll gve he same resuls as defg as frequecy ff: The lkg facors of he gross ad seasoally adjused dces are decal; The average of he IXNB seres over he OECD sadard base year (.e ) s exacly equal o he average of he IXNBA seres over he OECD sadard base year. 5