Comparison of Alternative Labour Force Survey Estimators

Transcription

1 Surve Mehodolog, June Vol. 27, No. 1, pp Sascs Canada, Caalogue No Comparson of Alernave Labour Force Surve Esmaors Phlp ell 1 Absrac Ths paper loos a a range of esmaors applcable o a regularl repeaed household surve wh conrolled overlap beween successve surves. The paper shows how he es Lnear Unbased Esmaor (UE) based on a fxed wndow of me pons can be mproved b applng he echnque of generalzed regresson. Ths mproved esmaor s compared o he esmaor of urne and Dal (1965) and he modfed regresson esmaor of Sngh, Kenned, Wu and rsebos (1997), usng daa from he Ausralan Labour Force Surve. Ke Words: Compose esmaor; es lnear unbased esmaor; Modfed regresson; Repeaed Surves. 1. Inroducon Ths paper loos a a range of esmaors applcable o a regularl repeaed household surve wh conrolled overlap beween successve surves. The common heme of he esmaors s o use daa from prevous mes o mprove curren esmaes, b ang advanage of correlaons n he overlappng sample. I refer o all such esmaors as compose esmaors. The esmaors are evaluaed for use n he Ausralan Labour Force Surve (LFS). In he LFS, overlap s conrolled b dvdng he frs sage sample of geographc areas no egh roaon groups from whch dwellngs are seleced. In each monh he same dwellngs are seleced from seven of he roaon groups, whle new dwellngs are seleced n he remanng group. The sample consss of cvlan persons aged 15 ears old and over resdng n he seleced dwellngs. Ths sample desgn leads o hgh overlap of sample beween wo successve monhs whn he seven mached roaon groups. Usng onl daa from hese roaon groups raher han he whole sample can decrease he samplng error on an esmae of monh o monh movemen. Compose esmaon echnques see o explo hs o gve esmaes wh lower samplng error. Secon 2 of he paper nroduces he Ausralan LFS and s curren generalsed regresson esmaor. The ssue of me n surve bas (called roaon group bas b alar 1975) s also dscussed. Secon 3 presens he compose esmaor proposed b Gurne and Dal (1965). Ths mehod has been used n he US Curren Populaon Surve for man ears. An exenson nown as compose weghng has been used for he las few ears; hs was proposed b Fuller (1990) and suded b Len, Mller and Canwell (1994, 1996). Secon 4 presens he modfed regresson mehod of compose esmaon (Sngh and Merours 1995, Sngh 1996). Here I focus on he esmaor of Sngh, e al. (1997), whch provdes he larges reducons n samplng error. I also presen a varan of hs mehod suggesed b Fuller (1999) for use n he Canadan Labour Force Surve. Secon 5 presens a es Lnear Unbased Esmaor (UE) based on daa from a wndow conanng a fxed number of successve monhs. Ths esmaor was orgnall gven b Jessen (1942) n he case of 2 occasons. A UE based on all occasons n a long seres appears mpraccal, hough a recursve approxmaon o hs was developed b Yansaneh and Fuller (1998). Ths paper mproves he fxed wndow UE descrbed n ell (1998) usng he echnque of generalsed regresson. Secon 6 gves he resuls of applng he dfferen mehods o he esmaon of emploed persons and unemploed persons n he LFS. Sandard errors are esmaed for longer erm ndcaors such as rend and rend movemen, as well as for esmaes of monhl level and s movemen. Possble bases are explored, as well as evdence of change o seasonal paerns. I conclude b comparng he advanages and dsadvanages of he dfferen pes of esmaor for applcaon n he LFS. The mproved UE esmaor s found o be effcen, and when appled o he LFS s no subjec o an large bas. 2. Curren Esmaes for he Labour Force Surve 2.1 Overvew of he LFS The LFS has a mulsage sample desgn, he frs sage beng a sample of small geographc areas nown as Census collecor s dsrcs (CDs). A new sample of CDs s seleced ever fve ears, and he CDs are classfed o egh roaon groups. The dwellngs seleced from a CD reman n he sample for egh surves, and hen are replaced b oher dwellngs from he same CD. Ths replacemen of dwellngs s nown as roaon, wh all he dwellngs n a roaon group beng replaced a he same 1. Phlp ell, Ausralan ureau of Sascs. E mal: Phlp.bell@abs.gov.au.

2 54 ell: Comparson of Alernave Labour Force Surve Esmaors me. Inervewers see o collec daa for all n scope persons n he seleced dwellngs. Of parcular neres n he LFS s he person s labour force saus wheher he are emploed, unemploed or no n he labour force. The number of persons n each labour force saus, for varous caegores of person, are e ems o be esmaed n he surve. Even more mporan o man users of he surve daa han hese level esmaes are he esmaes of movemen n he fgures beween successve me pons. I can be argued ha longer erm ndcaons of he drecon of he seres are even more mporan e.g., he movemen of he X11 rend or of a smlar smooher (ell 1999). The sample desgn ensures ha he uncondonal probabl of selecon π, s nown for each sampled person a me. Ths allows a smple esmaor for a populaon oal due o Horvz and Thompson (1952). If Y s he populaon em o be esmaed a me, and h s he same em as repored b he un a me, he Horvz Thompson esmaor s for w π, H π ˆ w = (1) = π nown as he selecon weghs. 2.2 The Generalsed Regresson (GR) Esmaor Generalsed regresson s a mehod for adjusng or calbrang a se of un weghs o add o a se of populaon arbues nown as benchmars. For a suable choce of benchmars he resulng weghs gve an mproved esmae b ang accoun of exernall avalable nformaon. In he LFS we sar wh he Horvz Thompson weghs and calbrae hem o add o demographc benchmars ha gve numbers of people n he populaon for 5 possraa (14 geographc regons classfed b sex and 20 age groups). The weghs from a gven pos sraum are proraed o add o he sraum benchmar. Ths pos srafed rao esmaor s a parcular case of he generalsed regresson or GR esmaor. Le x be a row vecor of auxlar varables for un a me, and xˆ = b x be esmaes for he correspondng row vecor of benchmar values X, based on some nal weghs b. The GR esmaor based on hese nal weghs s hen gven b G ˆ = ˆ + ( X x ˆ ) β ˆ (2) for ˆ β = b x x b x..e., ˆ G = w G for (3) G w = b 1 + ( X xˆ ) b x x x. (4) In pos srafed rao esmaon he row vecors x conan zeroes excep n he column correspondng o he un s pos sraum, and b are he selecon weghs w π. In hs case he regresson parameers are jus he pos sraum means, esmaed usng he selecon weghs. 2.3 Roaon Group Esmaes Each roaon group consss of a represenave sample of dwellngs, and so can provde a separae esmae. Number he roaon groups a a me pon accordng o he number of mes he dwellngs n he roaon group have been sampled. Wre R (, ) = r f h un s n he roaon group sampled for he r me a me. The Horvz Thompson esmae of Y based on roaon group r s H ˆ r = 8 w π. (5) : R (, ) = r Generalsed regresson can be used o mprove hese esmaors, b calbrang he weghs o add o a se of benchmars. Unforunael he lower sample sze n a sngle roaon group ma requre usng a smaller number of benchmars han n he overall case. In he LFS suaon I used a sngle generalsed regresson sep on he whole sample so ha across he whole sample he weghs add o he benchmars for he curren 5 possraa, whle n each roaon group he weghs add o an eghh of he benchmars for 71 collapsed possraa. The resulng weghs, when appled o a gven roaon group r and mulpled b R egh, gve he roaon group esmaes ˆ r. 2.4 Tme n Surve as Ideall roaon group esmaes should have he same expecaon Y, bu n pracce he have slghl dfferen expecaons, and hence dfferen bases. Some of he dfference s due o collecon pracces for example, dwellngs sampled for he frs me are nervewed usng a personal vs, whle oher roaon groups are mosl nervewed b elephone. I s no clear whch roaon group s leas affeced b hs sor of me n surve bas. The overall esmae wll have a me n surve bas ha s some mx of he bases from each roaon group. We rel on good surve mehods o eep hs bas small. Noe ha all he compose esmaors wll have dfferen conrbuons from he roaon groups, and herefore dfferen me n surve bases. 3. Compose Esmaon 3.1 Compose Esmaor The compose esmaor (Gurne and Dal 1965) s desgned o pu exra emphass on he movemen from he mached roaon groups (hose roaon groups n whch he same dwellngs were seleced n he curren and prevous monhs). The esmaor has hree componens. The frs s a mean of he roaon group esmaes for he curren monh Sascs Canada, Caalogue No

3 Surve Mehodolog, June daa (me ). The second s las monh s compose plus a movemen esmae based onl on he mached roaon groups. The hrd componen s he dfference beween esmaes from he unmached roaon group and from he mached ones. How much of each componen o use s gven b wo parameers A and K, as follows: ˆ 1 = (1 K) 8 8 r = 1 ˆ R r K ˆ + ˆ ˆ Rr R r 1 7 r= 2 7 r = 1 1 (6) 8 R1 R r A ˆ ˆ. 7 r = Choosng Parameer Values The e parameer s K, whch gves how much of he new esmae s based on he mached roaon group movemen. The opmal A and K o use wll depend on he varable beng esmaed. Hgher K values are approprae for emplomen han for unemplomen, snce emplomen has a hgher correlaon beween monhs. compose esmaes of persons emploed, unemploed and no n he labour force wll no add correcl o he oal populaon unless he same parameers are used for all he esmaes. Ths leads o usng a compromse choce of A and K. The resuls n hs repor are based on A = 0.06 and K = 0.7. These values were found b rng a range of values of A and K, and choosng hose ha gave opmal emploed esmaes. In hs sud no values of A and K gave unemploed esmaes apprecabl beer han hese values. Our emprcal sud dd no show parcularl good samplng errors for he esmaor. The fne calbraon ha was used n obanng he roaon group esmaes ma be o blame s possble ha usng broader caegores would mprove he samplng errors. 3.3 Properes of he Esmaor The esmaor pus exra emphass on he movemen n he mached roaon groups. Thus he roaon group conanng dwellngs n sample for he frs me conrbues less han n he GR esmaor. The esmaor hus has a dfferen me n surve bas o he GR esmaor. The esmaor s recursve, n ha las monh s esmaor s requred n order o produce hs monh s. Ths s nconvenen for producng esmaes for a new em or caegor. Also, he need o use he same values of A and K for all ems can gve sub opmal esmaes for an gven em. These concerns have led o he US Curren Populaon Surve changng o a varan nown as compose weghng (Len, Mller and Canwell 1994). In compose weghng, separae emploed and unemploed esmaes are produced for a number of mporan publshed caegores, usng he compose wh opmal parameers for he esmae n queson. The curren daa s hen calbraed so ha he un weghs add o hese esmaes as well as demographc benchmars. esmaes are hen produced from he curren daase usng hese new compose weghs. The convenence of producng all esmaes as a weghed sum of a sngle monh s daa s a major advanage of he compose weghng approach. Anoher s ha he mos mporan esmaes are compose esmaes wh near opmal choce of. A dsadvanage s ha onl he mos mporan esmaes are rue compose esmaes. An oher esmaes (ncludng esmaes of persons no n he labour force) are pcall no much mproved over he sandard GR esmaes (Len, Mller and Canwell 1996). 4. Modfed Regresson Esmaon 4.1 Overvew of Modfed Regresson The modfed regresson mehod s anoher wa o provde compose esmaes ha can be obaned as weghed aggregaes of he curren surve daase. The mehod arges a predeermned se of e ems, for whch acheves parcularl low samplng errors. The modfed regresson echnque uses generalsed regresson on he curren monh s daase afer aachng new auxlar varables z o each un a me. Here z s a row vecor wh an elemen for each of he e ems. Correspondng o hese we have pseudo benchmars Z based on he prevous monh s esmaes for he e ems. The modfed regresson esmaor s hen gven b a generalsed regresson sep applng boh he demographc benchmars and he pseudo benchmars. M H H H M ((, ) (, )) ˆ = ˆ + X Z xˆ z ˆ β (7) M π π for β = w ( x, z ) ( x, z ) w ( x, z ).e., (8) M M ˆ w H H 1 + (( X, Z ) ( xˆ, z ˆ )) M π w w π w x z x z x z = for = (, ) (, ) (, ) The e o he mehod s he defnon of he auxlar varables. Le D be he se of uns n he mached roaon groups (hose wh dwellngs seleced a boh me pons) a me. Le be he vecor of e ems for un a me and Y he correspondng populaon oals. For D, le 1, be he prevous monh s value for he vecor of e ems, or f no value was repored le, be mpued I used 1, = as suggesed b Sngh (1996). (9) Sascs Canada, Caalogue No

4 56 ell: Comparson of Alernave Labour Force Surve Esmaors I loo a modfed regresson esmaes for z of he followng form, for a [0,1]: 8 8 z = (1 a) 1, + a (, ) for D 7 7 = a for D. (10), Gven hs defnon we have H + HD H HD + HD zˆ a ˆ 1 a ˆ ˆ ˆ = (1 ) + ( ( )), (11) +HD π HD where ˆ 1 = 8 7 D w, 1, and ˆ = 8 7 D π w,, are esmaes of Y and Y respecvel based on uns n D onl and usng hs monh s selecon weghs. H HD For a = 0, z ˆ s jus he esmae ˆ + H. For a = 1, z ˆ s hs monh s Horvz Thompson esmae mnus an esmae of movemen based on he mached roaon groups HD + HD ˆ ˆ. Values a = 0 and a = 1 gve he mehods MR1 and respecvel of Sngh e al. (1997). Use of an nermedae a was suggesed b Fuller (1999). An approprae pseudo benchmar Z would be an esmae of Y adjused o agree wh hs monh s weghs. Followng Sngh e al. (1997) I used a sep of generalsed regresson o adjus las monh s modfed regresson esmaor o add o hs monh s benchmars: M M adj ˆ 1 ( ˆ 1 ) Z = + X x β (12) 1, 1, 1, 1, 1, 1,. adj M M for β = w x x w x (13) M Noe ha Z ˆ M snce xˆ 1 = X X. Ths complees he defnon of he modfed regresson esmaors. 4.2 Properes of Modfed Regresson Esmaors HD HD The movemen ˆ ˆ + a (11) s acuall based on he mached sample onl (.e., uns reporng a boh mes), snce oher uns n he mached roaon groups D conrbue zero o he movemen (for he mpuaon used here). Ths ma lead o he modfed regresson esmaors havng a lower samplng error han an esmaor, as hs mached sample movemen s no affeced b uns no presen n boh monhs. Unforunael, hs also gves he possbl of a bas f persons no represened n he mached sample have dfferen behavour o hose n he mached sample. Ths ma well be he case he mached sample excludes persons ha changed dwellng beween he wo monhs, and s possble ha changes of dwellng are relaed o changes of emplomen. Ths mached sample bas wll be n addon o an me n surve bas. Anoher problem arses wh he esmaor (.e., h a = 1). If he e varable, has hgh monh omonh correlaon hen wll also have a hgh correlaon h wh he new auxlar varable z,. For such a M varable he elemen of β correspondng o z, wll ae M some value close o one. Usng (7), (11), and Z ˆ, he esmaor aes he form M H M HD + HD,, + 1, +,, ˆ (1 ) ˆ ( ˆ ( ˆ ˆ )) + oher erms. (14) In hs case s possble ha he mached sample movemen a a gven me wll have a srong nfluence on esmaes for man me pons hereafer. In addon, an small bas n he movemen wll end o accumulae over me. Ths danger was recognsed b Fuller (1999), and referred o as he drf problem. Ths was a movaon for hs suggeson of he form of esmaor gven here, wh a value of a less han 1. In summar, modfed regresson has smlar advanages o he compose weghng approach, bu wh possbl lower samplng error. The mehod s no dffcul o appl, and avods he need o separael calbrae he roaon groups o he benchmars. 5. es Lnear Unbased Esmaon (UE) 5.1 Fxed Wndow UE The fxed wndow UE esmaor (denoed b ˆ ) s obaned b choosng an opmal lnear combnaon of he R roaon group esmaes ˆ r (as defned n 2.3) from a wndow of l + 1 monhs, as follows: 8 R r sr ˆ s s= l r = 1 ˆ a = (15) where he parameers a sr are chosen o mnmze var ( ˆ ) 8 8 under he consrans r = 1 a sr = 1 for s = and r = 1 a sr = 0 for s = l,...,. These consrans ensure ha ˆ wll be unbased for Y provded ha he roaon group G esmaes are unbased,.e., E( ˆ r s ) = Y s for s = l,...,. The mnmsaon requres nowng he varances and covarances of he roaon group esmaes. In pracce hese are esmaed based on hsorcal daa. The problem can hen be wren n a marx form: we am o choose he column vecor a (wh elemens a sr for s = l,..., and r = 1,..., 8) so as o mnmse a quadrac form a V a subjec o consrans C a = c. The relevan sandard resul (Rao 1973 page 65) s ha he mnmum occurs for a = V Cq where q s a soluon of ( C V C) q = c. In hs sud he marx V was replaced b a correlaon marx, under he assumpon ha all he roaon group esmaes n he wndow had he same varance. 5.2 Correlaon Srucure of Roaon Group Esmaes Snce dfferen correlaon paerns gve dfferen UE esmaes, choosng a correlaon paern has smlar ssues Sascs Canada, Caalogue No

5 Surve Mehodolog, June assocaed wh as choosng parameers A and K n he compose. I s desrable o use he same lnear combnaon for all esmaes o assure addv of he esmaes. I assumed a four parameer model for he correlaon paern: Gr Gr W corr ( ˆ, ˆ ) = ρ for r r = s s s = ρ for r r = s + 8 m s for neger m 0 = 0 oherwse. (16) Thus he correlaon beween esmaes a lag from he W same roaon group s ρ f he roaon group conans he same dwellngs a he wo mes, and ρ oherwse. Esmaes from dfferen roaon groups are uncorrelaed. A four parameer model s used: and W ru P rp r P ρ = (1 ) ( θ + θ (1 )) (17) 2 2 ru r P ρ = (1 ) θ (1 ). (18) ell and Carolan (1998) dscusses hs model. The parameer values used n hs paper were θ P = , θ = 0.94, r U = and r P = These values resul from fng he model o esmaed auocorrelaons for roaon group esmaes of proporon emploed. I s mporan o noe ha he UE esmaes are unbased regardless of he correcness of he assumed correlaon model. The model used here ams o be opmal for esmaes of emploed persons, bu urns ou o perform well for unemploed persons as well. Trng oher values for he model parameers dd no gve an mared mprovemen n sandard errors for unemploed persons. 5.3 Improved UE Esmaes A problem wh he UE esmaes above s ha GR esmaes are requred a roaon group level. The lower sample sze a roaon group level ma lm he benchmars ha can be used, as dscussed for he. For he UE, however, an alernave approach s avalable. The esmaor s defned b formng a UE esmaor based on he Horvz Thompson esmaors a roaon group level, and hen applng he generalsed regresson echnque o mprove hs esmaor. Ths proceeds as # # follows. Defne = ar(, ) and x = ar(, ) x, where a R (, ) s he UE mulpler applcable o he roaon group un s n a me. Then he UE esmaor based on he Horvz Thompson esmaors can be wren H π # s s. s= l ˆ w = (19) Calbrang o he benchmars we ge he mproved UE esmaor : H H ( )β ˆ ˆ = ˆ + X x ˆ (20) π # # π # # ws xs xs ws xs s s= l s= l for β ˆ =. for w s π s sr( s, ) w a = (21) s s s= l. e., ˆ w = (22) H 1 + ( X x ˆ ) s. π wuj aur( uj) x uj xuj as R( s, ) x s u = s l j Properes of he lue and Esmaors 2 (23) The UE and esmaes are sums of weghed un daa from a wndow of monhs. Each esmae needs onl daa from hs wndow, and can be produced ndependenl from he esmaes for prevous monhs so he mehod s no recursve. The same monh of daa wll conrbue wh dfferen weghs o he esmae for dfferen mes. A un wll conrbue a szeable wegh o s curren monh esmae, and a wegh near zero, ofen negave, o esmaes for oher monhs. The wor requred n producng a able s he same as for GR mulpled b he sze of he wndow. There s also a possbl of negave esmaes for n cells conanng no curren uns. Noe ha n he esmaor he weghs appled o monhs oher han he curren one are no forced o sum o zero. Under he model assumpons he esmae ˆ H H remans uncondonall unbased, snce ˆ and x ˆ are unbased for Y and X respecvel. In pracce he curren monh conrbues around 99.5 percen of he oal wegh. I consder he resulng bas o be small and no dangerous (leadng as does o some slgh smoohng of he esmaes over me). For an esmae n whch daa from monh o monh s apprecabl correlaed, he UE and esmaes should have lower samplng error han he GR esmae. Ths s a heorecal advanage over a mehod ha s desgned for mprovng a predeermned se of esmaes (le modfed regresson or he wh compose weghng). In pracce hs advanage ma no be oo mporan, as for he LFS much of our neres s n a small number of well defned esmaes. The user mus also deermne he me perod or wndow from whch esmaes wll be used. Usng oo man me pons wll be expensve compuaonall, whle oo few wll lm he gans avalable. The seven monh wndow used here was suffcen o oban nearl all he avalable gans, whle smaller wndows gve noceabl hgher sandard errors. Sascs Canada, Caalogue No

6 58 ell: Comparson of Alernave Labour Force Surve Esmaors 6. Comparng he Mehods 6.1 Mehod of Comparson Esmaes for Jul 1993 o Januar 1999 were produced based on daa from Januar 1993 o Januar Esmaes were obaned classfed b monh, sae, sex, maral saus and emplomen saus. Esmaes were also obaned for lag one movemen, quarerl average and movemen beween successve quarerl averages. Sandard errors for hese esmaes were calculaed usng he delee a group jacnfe echnque (Ko 1998). The geographc uns ha form he frs sage of sample selecon were dvded ssemacall no G = 30 groups, and replcae groups were formed conssng of he whole sample excludng he uns from one of hese groups. Each esmae suded was also produced for each of he G replcae groups. Wrng e for he esmae and e ( g ) he esmae from replcae g, he delee a group jacnfe esmae of sandard error s gven b G = (24) G SE ( e) G 2 ( e ( g ) e ). g = 1 Esmaes and sandard errors were obaned for each of he followng esmaors (lsed wh shor mnemoncs for laer reference): GR: Generalsed regresson esmae as currenl used n he LFS : esmae wh K = 0.7, A = 0.06 : UE based on 7 monh wndow : Improved UE based on 7 monh wndow : esmaor (modfed regresson wh a = 1) : Fuller s varan of modfed regresson ( a = 0.7) The modfed regresson esmaors requre a choce of he e varables o be opmsed for. In producng he modfed regresson esmaes n hs repor, z varables were produced for esmaes of emploed and unemploed for each sae and sex. Ths gves a oal of 32 exra auxlar 100 varables, n addon o he usual 5 pos sraum benchmars used n generalsed regresson. 6.2 Dfferences from GR Esmae The curren GR esmaor can be used as a bass of comparson for he oher esmaors. Raher han presen graphs of level esmaes, I presen he dfferences of he alernave esmaes from he curren GR esmaes. Graphs 1 and 2 show hese dfferences for esmaes of emploed persons and unemploed persons respecvel. To pu he sze of hese dfferences n perspecve, noe ha he publshed sandard errors for he curren esmae were 25,200 for emploed persons and 7,900 for unemploed persons n Januar 1999 (and smlar for oher monhs). The, and esmaes are que smlar, snce n all hree mehods he conrbuon of a un depends on s roaon group. In boh graphs he, and esmaors appear o gve lower values on average han he GR esmaes. Ths ndcaes a change n he me n surve bas, resulng from pung less wegh on he roaon group beng sampled for he frs me. The esmaes var up and down from her average dfference for shor perods. The and esmaes end o be dfferen o he oher esmaes snce he emphasse he conrbuon of uns from he mached sample. For emploed persons, he and esmaors are consderabl larger on average han he GR esmaes, up unl Sepember There s hen a drop n he dfferences correspondng o he phase n of a new sample from Sepember For reasons ha are no clear, over hs perod he mached sample behaved dfferenl o he overall sample. Ths affecs he dfference beween hese modfed regresson seres and he GR seres. Wha ma be of some concern s ha he level change nfluences he level of he seres for a consderable perod hereafer, possbl a manfesaon of he so called drf problem. Dfference ('000) Jul Tme Graph 1. Dfference of alernave esmaes from GR esmae, emploed persons ( 000s), Jul 1993 o Januar Jan Sascs Canada, Caalogue No

7 Surve Mehodolog, June For unemploed persons he M2 and esmaes end o be lower han he GR esmaes. There s no evdence of a drf problem for unemploed persons, whch s no surprsng gven he lower correlaons nvolved. 6.3 Average Dfferences b Calendar Monh To quanf he lel change n bas from movng o a new esmaor, he average dfference over he perod of each esmae from he GR esmae was calculaed. I s possble ha hs dfference s seasonal, so averages were obaned separael for each monh of he calendar ear, as well as overall. Average dfferences over he perod Jul 1993 o Januar 1999 are gven for emploed persons n graph 3. The graph shows ha esmaes of emploed persons would have been hgher on average usng he or esmaor. Ths upward dfference for he modfed regresson esmaors ma acuall be a feaure of he parcular perod, snce he dfference has apparenl dsspaed snce Sepember The oher feaure of he and esmaes s ha he dfference for emploed s hghl seasonal. For example, he movemen from December o Januar of he esmaes s abou 40,000 hgher han he movemen n he GR esmaes. Ths suggess ha he mached sample ends o mss people who were emploed n December bu no n Januar. The same seasonal shows up n loong a esmaes from he mached sample drecl. The mached roaon group movemen does no show hs large seasonal bas. For he, and esmaes here s some seasonal n he dfferences, bu he dfferences are much smaller. Graph 4 shows he average dfferences of he varous esmaes from he GR esmae for unemploed persons over he same perod. Here here appears o be a negave dfference for all he esmaors, hough less pronounced for he, and esmaes han for he and. The change n seasonal from changng from he GR o he and esmaors s agan more exreme han for movng o he oher esmaors 20 Dfference ('000) Jul Tme Graph 2. Dfference of alernave esmaes from GR esmae, unemploed persons ( 000s), Jul 1993 o Januar Jan Average dfference ('000) all J F M A M J J A S O N D Calendar Monh Graph 3. Average dfference from GR esmae, overall and b calendar monh, emploed ( 000). Sascs Canada, Caalogue No

8 ell: Comparson of Alernave Labour Force Surve Esmaors 6.4 Sandard Errors Sandard errors (SEs) of esmaes overall, b maral saus and b sex are presened n he followng graphs. The SE esmaes are obaned as a percenage of he SE esmae for he same esmae usng he GR mehod (.e., he curren LFS SEs), and hese percenages are hen averaged over he perod for whch he were produced (June 1993 o Januar 1999 for level esmaes). Graphs 5, 6, 7 and 8 show SEs of boh emploed and unemploed persons for level, movemen, quarerl average and movemen of quarerl average respecvel. For all hese esmaes he UE class esmaor has lower samplng error han he or esmaors. Gven ha he esmae appears o have smlar bas and seasonal of bas appears ha he and esmaors used n hs sud are no compeve wh he esmaor. The modfed regresson esmaors and, on he oher hand, gve much lower samplng errors han he esmaor for emploed persons for overall esmaes and esmaes b sex. These are e esmaes used n he modfed regresson oher e esmaes such as sae esmaes also gave smlarl mproved sandard errors. Esmaes b maral saus are no e esmaes, and hese have hgher sandard errors for and han for he esmaor. For unemploed persons he mprovemen n SEs from usng and are less conssen, dsappearng alogeher for esmaes of quarerl average. The esmaor s more conssen n lowerng he sandard error, alhough he gans avalable for unemploed are lower han for emploed. 5 Average dfference ('000) all J F M A M J J A S O N D Calendar Monh Graph 4. Average dfference from GR esmae, overall and b calendar monh, unemploed ( 000). SE as % of curren SE Oher Oher Emploed persons Unemploed persons Graph 5. Sandard Error of Level (% of curren SE). Sascs Canada, Caalogue No

9 Surve Mehodolog, June SE as % of curren SE Oher Emploed persons Oher Unemploed persons Graph 6. Sandard error of movemen (% of curren SE). SE as % of curren SE Oher Emploed persons Oher Unemploed persons Graph 7. Sandard error of quarerl average (% of curren SE). SE as % of curren SE Oher Emploed persons Oher Unemploed persons Graph 8. Sandard error of movemen of quarerl average (% of curren SE). 6.5 Seasonall Adjused and Trend Seres The AS uses he X11 pacage (Shsn, Young and Musgrave 1967) o produce seasonall adjused esmaes ha am o remove varous calendar effecs from he seres. The pacage also produces a rend, whch s an ndcaor of he underlng behavour of he seres. The rend value for a me pon s revsed as daa for laer mes becomes avalable. I esmaed he sandard error of rend esmaes a he end of he seres (end rend) and for he same pons when welve furher monhs of daa are avalable (md rend). Revsons of he rend (or rend movemen) were defned as he dfference beween he md and end values of he rend (or rend movemen). The sze of he revson depends on he shape of he rue seres and on he samplng error n he esmaed seres. The mean squared rend revson for a seres of unbased esmaes s he sum of wo componens: he mean squared rend revson ha would have occurred even wh no samplng error, and he varance of he esmae of revson. Thus he sandard error of he revson s a measure of he samplng error componen of he mean squared rend revson (see ell 1999). Seasonall adjused fgures are smlarl subjec o revsons. I presen sandard errors for level and movemen of seasonall adjused esmaes a he end of he seres. Sandard errors for laer revsons of hese esmaes were ver smlar. Sascs Canada, Caalogue No

10 62 ell: Comparson of Alernave Labour Force Surve Esmaors The delee a group jacnfe echnque was used o produce esmaes of sandard error for he varous rend and seasonall adjused esmaes. Ths echnque requres producng replcae versons of he esmaes. Unforunael, he sud provded replcae values for he me seres onl for me pons from Jul 1993 o Januar Each of hese replcae me seres were supplemened b he prevous 9 ears of hsorcal daa so as o have suffcen daa o appl he X11 pacage. ecause he replcae seasonall adjused and rend seres are based on he same values before Jul 1993 he jacnfe esmae of SE wll end o underesmae he rue SE slghl, especall for mes earl n he seres. To mnmse hs effec he measures of change n samplng error were averaged over monhs from Januar 1995 on onl (and onl up o Januar 1998, so ha he 12 monhs o Januar 1999 can be used for esmang revsons). Table 1 Sandard error as percenage of sandard error of curren GR esmaor Emploed persons: level movemen quarerl average movemen of quarerl average seasonall adjused movemen of seasonall adjused rend a end movemen of rend a end revson of rend revson of movemen of rend Unemploed persons: level movemen quarerl average movemen of quarerl average seasonall adjused movemen of seasonall adjused rend a end movemen of rend a end revson of rend revson of movemen of rend Table 1 gves hese average sandard errors for varous seasonall adjused and rend measures, relave o hose avalable from he curren GR esmaor, for boh emploed and unemploed persons. Also n he able are correspondng fgures for level, movemen, quarerl average and movemen of quarerl average, as presened n graphs 5 o 8. I would argue ha for man purposes he mos mporan ndcaors are hose ha gve he underlng drecon of he seres a he curren end,.e., movemen of quarerl average, and movemen of rend. A reduced sandard error for hese ems maes he underlng drecon of he seres a he end clearer, even for users who rel on vsual nspecon or on some smoohng process oher han he X11 rend. Ths n urn mproves he abl o deec urnng pons n he underlng seres. For movemen of rend he esmaor acheves an 18% reducon n sandard error for emploed persons and an 8% reducon for unemploed persons. For he hese reducons are 35% and 7% respecvel. The compose esmaors also reduce he conrbuon of samplng error o revsons n he rend seres. 6.6 Summar Ths paper presens a varan of he UE esmaor, he esmaor, whch apples he generalsed regresson echnque o a compose esmae based on a wndow of seven monhs of daa. On Ausralan daa, he has lower samplng error han he radonal UE or esmaors for a vare of measures ncludng seasonall adjused and rend esmaes. The paper also evaluaed a modfed regresson compose esmaor proposed b A.C. Sngh and a varan of hs proposed b W. Fuller. These esmaors gave consderabl lower samplng errors han he esmaor for a number of measures, especall hose based on emploed persons. The evaluaon of a compose esmaor wll depend on man facors oher han he samplng errors. The esmaor has he dsadvanage ha abulaons requre weghed aggregaon of seven monhs of daa, whereas he modfed regresson esmaors provde weghs for a sngle monh s daa. On he oher hand, he modfed regresson esmaors ma be based f persons reporng n wo successve monhs (he mached sample) are no represenave of oher persons (such as people movng house). Inroducng he modfed regresson esmaors would also nduce a larger change n esmae and n seasonal han nroducng he esmaor. Acnowledgemens The auhor wshes o han he referees for her ver helpful npu. Ths wor was suppored b he Ausralan ureau of Sascs. Vews expressed n hs paper are hose of he auhor and do no necessarl represen hose of he Ausralan ureau of Sascs. Where quoed are used, he should be arbued clearl o he auhor. References alar,.a. (1975). The effec of roaon group bas on esmaes from panel surves. Journal of Amercan Sascal Assocaon, 70, ell, P.A. (1998). Usng sae space models and compose esmaon o measure he effecs of elephone nervewng on labour force esmaes. Worng Papers n Economercs and Appled Sascs, Caalogue no , no. 98/2, AS, Canberra. Sascs Canada, Caalogue No

11 Surve Mehodolog, June ell, P.A. (1999). The mpac of sample roaon paerns and compose esmaon on surve oucomes. Worng Papers n Economercs and Appled Sascs, Caalogue no , no. 99/1, AS, Canberra. ell, P.A., and Carolan, A. (1998). Trend esmaon for small areas from a connung surve wh conrolled sample overlap. Worng Papers n Economercs and Appled Sascs, Caalogue no , no. 98/1, AS, Canberra. Fuller, W.A. (1990). Analss of repeaed surves. Surve Mehodolog, 16, Fuller, W.A. (1999). Canadan Regresson Compose Esmaon. Unpublshed manuscrp. Gurne, M., and Dal, J.F. (1965). A mulvarae approach o esmaon n perodc sample surves. Proceedngs of he Surve Research Mehods Secon, Amercan Sascal Assocaon, Jessen, R.J. (1942). Sascal nvesgaon of a farm surve for obanng farm facs. Iowa Agrculural saon research ullen, 304. Ko, P.S. (1998). Usng he delee a group jacnfe varance esmaor n pracce. Proceedngs of he Surve Research Mehods Secon, Amercan Sascal Assocaon, Len, J., Mller, S. and Canwell, P. (1996). Effec of compose weghs on some esmaes from he Curren Populaon Surve. Proceedngs of he Surve Research Mehods Secon, Amercan Sascal Assocaon, Rao, C.R. (1973). Lnear Sascal Inference and s Applcaons. Second edon, New Yor: John Wle & Sons, Inc. Sngh, A.C., and Merours, P. (1995). Compose esmaon b modfed regresson for repeaed surves. Proceedngs of he Surve Research Mehods Secon, Amercan Sascal Assocaon, Sngh, A.C. (1996). Combnng nformaon n surve samplng b modfed regresson. Proceedngs of he Surve Research Mehods Secon, Amercan Sascal Assocaon, Sngh, A.C., Kenned., Wu S. and rsebos F. (1997). Compose esmaon for he Canadan Labour Force Surve. Proceedngs of he Surve Research Mehods Secon, Amercan Sascal Assocaon, Shsn, J., Young, A. and Musgrave, J. (1967). The X 11 varan of Census Mehod II Seasonal Adjusmen, ureau of he Census, U.S. Deparmen of Commerce, Techncal Paper 15. Yansaneh, I.S., and Fuller, W.A. (1998). Opmal recursve esmaon for repeaed surves. Surve Mehodolog, 24, Len, J., Mller, S. and Canwell, P. (1994). Compose weghs for he Curren Populaon Surves. Proceedngs of he Surve Research Mehods Secon, Amercan Sascal Assocaon, Sascs Canada, Caalogue No