Statistics Norway Department of Economic Statistics

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1 2004/3 Mach 2004 Documents Statstcs Noway Depatment of Economc Statstcs Jan Henk Wang Non-esponse n the Nowegan Busness Tendency Suvey

2 Peface Ths pape descbes methods fo adjustng fo non-esponse set n the empcal famewok of the Nowegan Busness Tendency Suvey fo manufactung, mnng and quayng. The pape has pevously been publshed n Nowegan n Statstcs Noway's publcaton Notate, no. 2003/81. In the analyss we use some well-known technques fo adjustng fo non-esponse n sample suveys. Dffeent models fo weghtng fo non-esponse and methods of mputaton ae nvestgated and compaed. 1

3 Contents 1. Intoducton About the suvey Unt, scope and sample Calculaton of statstcs and weghtng of answes On statum level On aggegated levels Vaable of nteest Peod of analyss Non-esponse n the Busness Tendency Suvey Adjustng fo non-esponse Weghtng fo unt non-esponse Dect weghtng Estmaton wth a non-nfomatve RHG-model Estmaton wth a smple nfomatve RHG-model Calbaton of dect weghtng by use of a ato estmato Imputaton of tem non-esponse Neaest-neghbou mputaton Stochastc mputaton wth a non-nfomatve RHG-model (hot-deck) Calbaton of estmates fom mputaton models by usng a ato estmato The effect of calbaton Summay Refeences Recent publcatons n the sees Documents

4 1. Intoducton Ths pape povdes an empcal analyss of dffeent methods fo adjustng fo non-esponse n the Nowegan Busness Tendency Suvey fo manufactung, quayng and mnng (BTS). The suvey maps out manufactung leades' judgement of the busness stuaton and the outlook fo a fxed set of ndcatos such as level of poducton, capacty utlsaton, employment and judgement of the geneal outlook. The suvey was developed n 1973 and put nto opeaton on a egula bass fom the fst quate of Chapte 2 descbes the suvey's analytcal famewok and defnes the vaable of nteest and the peod of analyss. Futhe, chapte 3 we pefom an analyss of non-esponse n the Busness Tendency Suvey by the use of dffeent technques fo adjustng fo non-esponse. A summay of the esults wll be pesented n chapte About the suvey 2.1 Unt, scope and sample The epotng unt s defned as a knd of actvty unt (KAU). The KAU s deved by combnng all establshments n an entepse cayng out the same ndustal actvty, egadless of the locaton of the actvty. The ndustal actvty s defned as 3-dgt ndusty goup (SIC94) n the followng efeed to as the ndusty. In the data collecton pocess the esponse unt s defned as the lagest establshment n the KAU,.e. hghest numbe of employees, but othe esponse unts may also be used, such as the entepse head offce. These adjustments ae usually adapted n accodance wth the wshes of the entepse, but may also occu fo othe easons. In analyss and n the calculaton of the statstcs the unt s defned as the KAU. The populaton coves all KAUs wthn Mnng and quayng (10, 13-14) and Manufactung (15-37), see the Standad of Industal Classfcaton 1994 (SIC94). The Busness and Entepse Regste defnes the populaton. The samplng populaton does not nomally nclude unts wth 10 employees o less. The sample fame s defned by a status fle n the second quate of evey yea, and the sample s updated once a yea. The new samplng plan ntoduced n the fst quate of 1996 was desgned wth the pupose of achevng a holstc ovevew of the busness tendency stuaton and outlook fo each ndusty 1. The KAU's employment s used as a measue of sze n the statfcaton pocess n connecton wth the samplng of unts, whee each ndusty populaton s dvded nto fou stata. Statum 1 Statum 2 Statum 3 Statum 4 Unts wth 300 employees and ove Unts wth employees Unts wth employees Unts wth less than 100 employees Unts wth moe than 300 employees ae ncluded as a panel (statum 1). Unts ae dawn wth a pobablty popotonal to ts sze n the emanng stata (popotonal allocaton). Ths pocess of dawng the sample s caed out fo each statum n each ndusty. 1 The samplng plan was adjusted n the second quate of Some adjustments wee made to the statum classfcaton and a pat of the ognal sample was emoved and eplaced by new unts. The sample was also supplemented and the sze of the goss sample became appox. 700 unts. 3

5 In the analytcal pat of ths pape we have smplfed somewhat by assumng that the pobablty of beng dawn s the same wthn each statum, and that the pobablty depends on the coveage of employees dawn n each statum. Ths s done to smulate the fact that thee s an ove-epesentaton of the lage unts n each statum. The goss sample coves appoxmately 54 pe cent of total employment n the populaton and some 62 pe cent of total tunove. The coveage, howeve, vaes between ndustes. On 2-dgt ndusty goup level the coveage vaes fom 30 to 90 pe cent. Howeve, n some ndustes the coveage could be hghe and lowe than ths. 2.2 Calculaton of statstcs and weghtng of answes On statum level Results on statum level ae calculated by assgnng each actve unt's answe a weght equal to ts employment. Moe pecsely, the calculaton of the shae of answes n pe cent, SY n,,j,b, fo queston n, esponse altenatve, n statum j and ndusty B may be expessed by the followng thee steps: The numbe of employees coded to esponse altenatve s: (1) Y n,,j,b = Σ b (α b,j * β b, * S b,j,b ) whee α b,j β b, S b,j,b states f a unt s ncluded n the sample n statum j, and f t s actve,.e. has answeed the questonnae n the elevant quate. α b,j may adopt the values 0 / 1. An actve unt s gven a value equal to 1 - othewse 0. A unt that s not epesented n the sample s gven the value 0 n the calculaton of the statum level. may take the values 0/1, dependng on whch esponse altenatve the ndvdual espondent n the statum has chosen fo the elevant queston. Fo nstance, f a espondent has chosen «ncease», t s gven a facto equal to 1 when the shae of answes fo ths esponse altenatve s calculated. Othewse the value 0 s used. expesses the employment fo the ndvdual KAU, b, n the statum populaton, j, n ndusty B. The total numbe of employees fo all actve KAUs n statum j s: (2) SS n,,j,b = Σ Σ b (α b,j * β b, * S b,j,b ) The shae of answes n pe cent fo altenatve, n statum j s then expessed by: (3) SY n,,j,b = Y n,,j,b * 100 / SS n,,j,b (1) - (3) show that the bass fo the calculaton of the popoton of answes fo a vald esponse altenatve fo queston n s all KAUs whch ae coded to the same ndusty n the populaton. A unt whch s not pat of the sample o whch s not actve (non-esponse) n a quate s emoved fom the calculaton by the use of the α-facto. The β-facto s used to goup the esponse altenatves that the actve unts have chosen, and s gven a weght equal to the KAU's level of employment. It follows fom (1) - (3) that the sum of shae of answes n pe cent fo a queston s equal to 100,.e.: (4) Σ SY n,,j,b = 100 4

6 2.2.2 On aggegated levels Calculatons of the popoton of answes on ndusty level ae based on the popoton of answes on the statum level. In the tanston fom statum to ndusty, the statum esults ae, howeve, weghted wth the populaton employment to coect fo elatve dffeences between the stata n a patcula ndusty. Moe pecsely, the calculaton of the shae of answes n pe cent, SY n,,b, fo queston n, esponse altenatve, n ndusty B may be expessed by the followng equatons: (5) SY n,,b = ( Σ j Y n,,j,b * a j,b ) * 100 / SS B whee SS B s the sum of employment fo all unts n the ndvdual statum populaton n ndusty B and (6) a j,b = 1 / (SS n,,j,b / SS j,b ) Equaton (6) expesses the nvese of the sum of the pobablty to be dawn fo actve unts n statum j, ndusty B. The shae of answes n pe cent fo altenatve on the ndusty level emege by addng up the poduct of the numbe of employees allocated to each esponse altenatve n statum j wth the nvese sum of the pobablty to be dawn fo actve unts n the statum. The same pncples apply to futhe aggegaton. As ths explanaton of the calculaton of the popoton of answes and the weghtng of eples n the BTS shows, the shae of answes fo the net sample s calculated n each statum befoe the populaton shae s calculated by weghtng the nvese sum of the pobablty to be dawn fo unts n the net sample n statum j, ndusty B. To be able to conduct the analyss of non-esponse, we must use the nvese pobablty to be dawn as desgn weght fo each unt, and then aggegate. The calculaton pocedues used n ths pape wll theefoe devate somewhat fom the pocedues used n the quately poducton of the statstcs. 2.3 Vaable of nteest The questonnae fo the Nowegan Busness Tendency Suvey contans 28 questons on dffeent aspects of the obsevaton unt's maket stuaton. To smplfy the analyss we have only used one of the questons n the suvey: Geneal judgement of the outlook fo the establshment n the next quate 2. Ths queston has thee esponse altenatves: Bette Unchanged Wose We have futhe defned the esponse altenatve as 1 f the unt has answeed 'bette' and 0 f one of the othe altenatves has been chosen. Because the answes ae weghted wth the KAU's employment, the vaable of nteest used n the analyss of non-esponse s defned as the esponse altenatve multpled wth the unt's level of employment. In the calculaton pocedues used n the quately poducton of the statstcs a shae of answes s calculated fo each of the thee esponse altenatves. In addton, a shae of the net sample that has not 2 Ths s queston 18 n the questonnae and the complete text fo the queston s: How do you judge - geneally fo the establshment's busness stuaton n ths ndusty - the outlook fo the fothcomng quate compaed wth the stuaton n the pesent quate? 5

7 answeed the queston (Item non-esponse 3 ) s computed. Fom these esults balances and dffuson ndces ae computed fo the vaous questons and ndustes. Balance = Postve - negatve Dffuson ndex = Postve + (0,5*neutal) 2.4 Peod of analyss We use data fom the suvey caed out n the second quate of The table below shows the numbe of unts n the populaton and sample n the dffeent employment stata. Thee wee a total of unts n the populaton and a goss sample of 701 KAUs. Table 1 Populaton and sample Employment Goss Populaton statum sample 300 o moe Sum See Chapte 3 fo moe nfomaton on tem non-esponse. 4 As the table shows, not all unts n the statum '300 o moe employees' ae ncluded n the goss sample even though the pobablty to be dawn s 1 (see chapte 2.1). Ths s because some unts have epoted that they do not wsh to patcpate n the suvey and consequently have been emoved fom the sample. 6

8 3. Non-esponse n the Busness Tendency Suvey Patcpaton n the Busness Tendency Suvey s voluntay and we theefoe expeence a somewhat hghe shae of non-esponse than n compulsoy suveys. If we look at othe suveys amed at the same populaton (manufactung, quayng and mnng), fo nstance the Nowegan quately nvestment statstcs o the statstcs on new odes, whch both ae compulsoy, the esponse ate s close to 98 pe cent. Unt non-esponse n the Busness Tendency Suvey.e. unts n the sample that have not etuned the questonnae s qute stable at aound 15 pe cent. Ths coesponds to an aveage esponse ate of 85 pe cent n ecent quates. Item non-esponse.e. mssng values fo some, but not all of the questons on a questonnae vaes between the dffeent questons. A summay of tem non-esponse n the second quate of 2003 shows that t vaes between 9.7 and 0.1 pe cent. The eason fo the huge vaaton between dffeent questons s that some questons ae not elevant fo all ndustes and ae not answeed. Howeve, the questons of focus n the pess elease have a low level of tem non-esponse. Thee may be dffeent souces and causes fo non-esponse n the Busness Tendency Suvey. As mentoned eale the suvey s voluntay and some espondents choose not to patcpate n the suvey. The sample s based on a panel whee unts that have gone bankupt o have shut down ae eplaced wth new unts annually. In addton, unts that have not epled n the pevous two quates ae emoved and eplaced by new unts dawn fom the populaton usng popotonal allocaton. The suvey s based on postal questonnaes. The followng causes may be dentfed as easons fo nonesponse: Unt non-esponse: Does not want to patcpate. Most espondents n the sample based on the populaton of unts n manufactung, quayng and mnng also patcpate n compulsoy suveys. Some unts theefoe choose not to eply because the suvey s voluntay and the esponse buden s consdeed too hgh. Questonnae does not each the contact. In some cases the contact peson has ethe left the company o s not pesent, and theefoe the questonnae does not each the ght peson. The questonnae has not been pnted fo all unts. The questonnae s not egsteed n the data collecton pocess. Eo n the calculaton pocess. Regsteed questonnaes ae not ncluded n the calculaton of the aggegates. Expeence shows that eluctance to patcpate s the bggest eason fo non-esponse. To contol whethe the questonnae s sent to the ght place and peson, coss compasons ae caed out between unts n the sample of the Busness Tendency Suvey and samples of othe suveys wth the same populaton. In most cases of non-esponse we eceve the questonnae fo the compulsoy suveys, but not the one fo the Busness Tendency Suvey, even f the espondent s the same. Item non-esponse: Ielevant queston. The same questonnae s sent to all espondents, espectve of whch ndusty they ae n. Ths may lead to poblems n answeng all the questons n the questonnae fo espondents n some ndustes. Intoducng the esponse altenatve 'Not elevant' has educed ths poblem. But because t s beleved to be temptng to use ths altenatve too often, t s not ncluded fo all questons. Wong contact. The questons n the Busness Tendency Suvey eque that the espondent has thoough knowledge of a numbe of economc vaables connected to the establshment's actvty. Ths s not always the case, and thus we may expeence tem non-esponse. 7

9 The queston s not undestood. The espondents may not undestand all the questons and so do not answe them. Eo n the egstaton pocess. In most cases the questonnaes ae optcally ead and tansfeed to an electonc medum. In such cases eos ae not common. Howeve, questonnaes that cannot be vefed optcally (fax, copy) ae manually egsteed. In ths pocess t may occu that some questons ae not egsteed. Fo the queston used n ths analyss, Geneal judgement of the outlook fo the establshment n the next quate, the choce of answes and non-esponse n the second quate of 2003 ae dstbuted as shown n table 2. Table 2 Choce of esponse altenatve and non-esponse n the vaous employment stata Employment statum Bette Unchanged Wose Net sample Item nonesponse Unt nonesponse Goss sample 300 and ove Sum Table 2 shows that tem non-esponse s evenly dstbuted wth one unt n each stata, and amounts to a non-esponse ate of 0.6 pe cent n elaton to the goss sample. In the futhe analyss we consde the tem non-esponse togethe wth the unt non-esponse. Ths means that the total non-esponse s 92 unts. Ths level of non-esponse poduces a esponse ate of 86.9 pe cent. A close look at the non-esponse n each employment statum eveals the followng esponse ates: Table 3 Response ates Employment statum Response ate 300 and ove Total Adjustng fo non-esponse Thee s no lage vaaton n the employment statum non-esponse ate (Table 3). In the cuent estmaton of the Nowegan Busness Tendency Suvey, t s assumed that the non-esponse s mssng-completely-at-andom (MCAR). Non-esponse s mputed mplctly by teatng the net sample estmates as the goss sample estmates. In the followng analyss we wll take a close look at ths assumpton to see f t holds, o f t s bette to use a moe complex modellng of the nonesponse. The fst pat of the analyss uses dffeent non-esponse models (weghtng) to adjust fo nonesponse. In the second pat we test dffeent methods of mputaton of the non-esponse unts. The followng notaton wll be used: U = {1,...,N} => Populaton & = unt ndex s = (goss-)sample & s = net sample (eply sample) & s m = unt non-esponse s the esponse vaable => =1 f s & =0 f sm 8

10 π s the pobablty to be dawn & p s the esponse pobablty & φ a = p = 1 => Desgn weght π 1 => Non-esponse weght w 1 = a φ = ( π p ) => Non-esponse-adjusted weght fo s y s the vaable of nteest & Y = U y => total of y n the populaton The fgue below llustates the dffeence between weghtng and mputaton Fg 1 Weghtng and mputaton Weghtng fo nonesponse Imputaton of nonesponse a = 1 π Populaton a = 1 π Goss sample Reconstucted goss sample φ = 1 p Net sample Imputaton As the fgue shows, the dffeence between weghtng and mputaton s that wth weghtng we nflate (analogous to the step fom goss sample to populaton level) the sample fom net to goss befoe we calculate the populaton level, whle n mputaton mssng answes ae eplaced wth estmated values befoe calculatng the populaton level. When weghtng, the poduct of desgn weght and non-esponse weght defne the non-esponse-adjusted weght: 1 w = aφ = ( π p ) In the analyss that follows, we look at the popoton who espond that the geneal outlook s bette. We smplfy by only calculatng aggegated esults fo manufactung, quayng and mnng and not fo each ndusty. To undetake a stuctued mplementaton of the dffeent models and methods of mputaton, data at unt level have been adapted n SAS softwae, and all calculatons ae caed out n SAS. The vaable of nteest n the analyss s defned as 9

11 (1) y = β * S Whee β 1 = 0 If unt has chosen 'bette' If unt has chosen a dffeent esponse altenatve S s the unt's numbe of employees We want to estmate the popoton of employees that consde the geneal outlook to be bette fo the fothcomng quate, Y, descbed by equaton (2) (2) Y = ( )/ U y S U Fom the populaton fle we fnd that the total level of employment s S = U Weghtng fo unt non-esponse S = Dect weghtng In ths secton we assume that the non-esponse s MCAR and use the method of dect weghtng. We consde the non-esponse as an addtonal phase n dawng a pobablty based sample. The nvese esponse pobablty s used as a non-esponse weght. Thus, the non-esponse-adjusted weght s the poduct of the desgn and non-esponse weghts. An estmate fo Y, as the popoton of the employment-weghted answes fo the unts who have answeed 'bette' on the queston of the geneal outlook, may then be expessed as (3) Y = ( w y )/( S ) s U To fnd w we have to estmate the esponse pobabltes, p, and the non-esponse weghts, φ, n such a way that we can estmate the non-esponse-adjusted weght defned by (4): (4) w 1 = a φ = ( π p ) whee φ = ( 1 p ) n = n + m 1 and n s the numbe of unts n s, and m the numbe of unts n s m. By usng dect weghtng wth MCAR non-esponse φ wll be constant,.e. that the esponse pobablty s the same egadless of whch unt we look at. Wth these assumptons we get the followng estmate (3) Y = ( w y )/( S ) = = s U Whch means that wthn manufactung, quayng and mnng 23.3 pe cent consde the geneal outlook fo the fothcomng quate to be bette. 10

12 Estmaton wth a non-nfomatve RHG-model We wll now ty to estmate the shae of answes usng a non-nfomatve RHG 5 -model. Wth ths type of model we ty to dvde the sample nto goups that ae beleved to have the same mechansms fo geneatng non-esponse. Ths model s desgned to adjust fo vaaton that ases because the nonesponse s consdeably hghe wthn cetan goups of the sample. These goups may be defned as unts wthn the same employment stata o wthn the same ndusty o othe constellatons whee you expect that the non-esponse may be coelated wth the composton of the goups. The am of dvdng nto these esponse homogenety goups s to geneate a esponse pobablty p that s as equal as possble wthn each goup, and at the same tme as unequal as possble between the dffeent goups. In geneal the model may be expessed n the followng way: We assume that the sample s dvded nto G RHGs, defned by s g fo g = 1,...,G. Let sg nclude esponse unts n s g, and let smg nclude non-esponse unts n s g n such a way that sg = sg smg We let ng be the numbe of unts n s g, and mg the numbe of unts n s mg. We can then estmate the esponse pobablty, p, fo sg as descbed by equaton (5) (5) p = ng /( ng + mg ) By usng (5) n (4) we can calculate the non-esponse-adjusted weght to each unt dependent on whch RHG the unt s classfed unde. Futhe aggegaton s caed out as descbed n (3). Wthn ths famewok we have chosen to exploe two possble classfcatons of the esponse homogenety goups. In a) we have gouped unts wthn the same employment stata, and n b) we have dvded the sample nto goups dependng on whch ndusty the unts ae classfed unde. The assumpton unde a) mples that thee s a hghe pobablty of non-esponse among the smalle unts than among the lage. Howeve, fom table 3 above, thee s no ndcaton of a consdeable dffeence n the ate of non-esponse among the smalle and lage unts, whee sze s defned by numbe of employees. The assumpton unde b) mples that the ate of non-esponse may be hghe wthn some ndustes, and because of ths thee s a systematc vaaton n the ate of non-esponse. a) Goupng by employment stata By settng an RHG-ndex equal to the vaable fo employment stata n the pogam used fo estmaton of the dect weghted estmate wth MCAR non-esponse, we obtan the estmate based on the non-nfomatve RHG-model. The model wll contan fou esponse homogenety goups that coespond to the employment stata shown n table 4 (g=1,2,3,4). Table 4 RHG = Employment stata RHG Employment stata and ove RHG = Response homogenety goup 11

13 Ths model poduces the followng estmate (3) Y = ( w y )/( S ) = = s U Fom the estmate we see that t s appoxmately equal to the assumpton of MCAR non-esponse. Ths s no supse when the esponse ate n the dffeent employment stata was appoxmately the same (see table 3). b) Goupng by ndusty In ths case we chose to goup the esponse homogenety goups accodng to whch ndusty the unt s classfed unde. To avod too many goups the unts ae gouped accodng to publcaton level. Table 5 shows the coheence between NACE 2-dgt level and statum. The table also ncludes the esponse ate n each statum. Table 5 RHG = Industy RHG Industy 6 Response ate 1 10, , , , , , , , , , , , , , , ,5 Table 5 shows that the esponse ate vaes between the dffeent RHGs and especally that g=3 (NACE 17-19; Textles, weang appael and leathe) and g=12 (NACE 29; Machney and equpment) have lowe esponse ates than the othe RHGs. Wth ths model we get the same estmate as unde the model wth RHG = Employment stata: (3) Y = ( w y )/( S ) = = s U The pogam used n the calculaton s the same as unde a) except that we have changed the RHGndex fom g=x wth g=x2 (g defnng the RHG-ndex, x s employment stata and x2 s the ndexaton of the ndusty goups). Fom these calculatons thee does not appea to be a clea coelaton between the RHGs we have defned and the non-esponse, at least not n such a way that t affects the estmate. 6 The numbes n the column coespond to 2-dgt NACE (SIC94) 12

14 As shown n table 5, some ndustes have a lowe esponse ate than othes, but the popoton of employment vaes sgnfcantly between the dffeent ndusty goups. If we look at the goup Textles, weang appael and leathe; g=3, ths goup wll have a hghe numecal value on the nonesponse weght than the othe goups. Howeve, ths wll be of lttle sgnfcance on the total employment-weghted estmate because ths goup has a vey small popoton of the oveall employment n Nowegan manufactung ndusty Estmaton wth a smple nfomatve RHG-model Ths model assumes that the non-esponse s coelated wth the vaable of nteest. I.e. that t s assumed that the non-esponse s hghe o lowe among unts choosng one esponse altenatve above anothe. we defne RHGs s g fo g = 1,...,G that, among othe thngs, depend on the vaable of nteest futhe, auxlay goups s h fo h=1,...,h ae geneated based on vaables that ae known n the ente sample suppose futhe that the esponse pobablty to unt s ndependent of sh gven that sg On these assumptons we suppose that the non-esponse s homogeneous among espondents who answe bette, unchanged o wose and that the esponse altenatves defne s g fo g=1,..,3. Because the vaable of nteest s unknown fo the non-esponse unts, s mg, we have to estmate whch goup they belong to. To do that, auxlay goups based on vaables known n the ente sample ae used. We theefoe assume that we have the auxlay goups s h fo h=1,..,4, defned by the fou employment stata whch ae known fo the ente sample, s = s + sm. Fnally, we assume that the non-esponse s ndependent of the employment stata gven the esponse altenatve. To estmate the esponse pobabltes we also have to estmate whch goup the non-esponse unts belong to. We let sgh denote the pat of the sample sg sh,.e. esponse unts whch belong to both sg and s h. Futhe, we let smgh denote the pat of the sample smg smh,.e. non-esponse unts whch belong to both sg and s h. We denote the sze of s gh, whch s known n the ente sample, wth n gh. Futhe, we let m gh be the sze of s mgh, whch s unknown except fom m h = g = m 1 Gven an estmate fo m gh, denoted gh G gh snce sh s known. m, we can estmate the esponse pobablty wth (6) (6) H n n g h = 1 gh p = = fo s H H g ng + m g n + h = gh m 1 h = 1 gh We use an teatve algothm to estmate m gh : 13

15 1. Intal values fo m gh s chosen, denoted by (0) m gh, as fo nstance m m n m n (0) h gh h gh gh = = G nh g = n 1 gh 2. Fo k=1,2,... the followng expesson s calculated )( ( k 1) ( k 1) w ( ngh + mgh m ( k ) h gh gh = ( k 1 n + h bh m ) h gh ) and m ( k ) mhw ( k ) gh gh = G ( k ) g = w 1 gh 3. The algothm s stopped afte 40 teatons (k=40), and we use ( k ) m gh = m gh as an estmate fo m gh. To ty to estmate the esponse pobabltes unde the nfomatve RHG-model, ths algothm was pogammed n SAS and the RHGs and auxlay goups descbed above wee used n the estmaton pocess. Wth the descbed RHGs and auxlay goups we got no convegence fo the algothm. We ted to defne h and g fo dffeent vaables to get the algothm to convege, but wth no luck. To cay out ths analyss we have nevetheless used the esults fom the algothm afte 40 teatons. The esults fom ths analyss must theefoe be ntepeted wth an eye to the fact that the esponse pobabltes may not be coect. The followng esponse pobabltes, Table 6 Estmated esponse pobabltes n pe cent Bette Unchanged Wose p p, wee estmated fo the thee esponse altenatves: Fom the table wth the estmated esponse pobabltes fo the thee RHGs, we see that the estmates ae about the same fo those who answe bette o unchanged, whle t s somewhat hghe fo those who answe wose. By usng the estmated esponse pobabltes n equaton (6), we ae able to calculate the nonesponse-adjusted weght fo each unt, whch wll depend on the esponse altenatve chosen by the unt. (7) w = a φ = ( π p ) 1 By usng the estmated non-esponse-adjusted weghts fom (7) n equaton (3), we obtan an estmate of the popoton who say that the outlook s bette. (8) Y = ( w y )/( S ) = = s U As the estmate n (8) shows, ths model esults n a magnally hghe estmate on the popoton who consde the outlook to be bette. Ths follows fom the estmated esponse pobabltes. The estmated non-esponse weght, φ 1 =, wll be hghe fo unts espondng bette than fo those p espondng wose. Ths way the popoton bette nceases n elaton to the othe altenatves because the non-esponse s expected to be hghe n ths goup. It s mpotant to take nto 14

16 consdeaton that the estmated esponse pobabltes may be wong because the algothm, based on ou assumptons, dd not convege. It s dffcult to povde a good eason why the non-esponse should be lowe fo unts who answe wose than unts who answe bette. One possble eason may be that dung an economc ecesson n the ndusty thee s a geate need to complan (though offcal statstcs) than when the economy s ecoveng. To substantate ths hypothess one could cay out an analyss of the unt non-esponse ove a peod of tme, to fnd out whethe the esponse ate s coelated wth the busness cycle. Ths would, howeve, extend the scope of ths analyss Calbaton of dect weghtng by use of a ato estmato The models tested untl now only use nfomaton fom the sample. By usng addtonal nfomaton fom the populaton one may mpove the qualty of the dect weghted estmate. Seveal methods can be used to calbate the smple estmates; post statfcaton, ato model, egesson model. In ths analyss we wll use a ato model. We defne employment, S, as an addtonal vaable. Wth espect to educton n vaance and adjustng fo non-esponse, t s desable to use an addtonal vaable that s hghly coelated wth the vaable of nteest. We cannot be cetan of any coelaton between the choce of answe and the level of employment, but n lack of anothe egste vaable, employment s used. The ato estmato s then defned by: (9) ( Sw ) w, at = w ( S / S) = whee S = S and Ŝ = w S w S s U s Total numbe of employees, S, n the populaton s known: and we know S fo unts who have etuned the questonnae. S = = We use ths method of calbaton on the thee models of weghtng fo unt non-esponse that we have analysed: a) Dect weghtng (MCAR non-esponse) b) Non-nfomatve RHG-model c) Infomatve RHG-model a) Dect weghtng (MCAR non-esponse) By usng the calbated non-esponse-adjusted weght, w, at, fom (9) n equaton (3) we get the followng calbated ato estmate fo the popoton who answe 'bette' (10) Yat = ( w, at y )/( S ) = ( w ( S / S) y )/( S ) = = s U s In the estmaton pocess we fnd that the ato S / S s 1,065. Ths way the employment-calbated estmate s adjusted somewhat up, n elaton to the dect weghtng, because of too low coveage of employment n the sample on account of the non-esponse. Wthout calbaton the non-esponse unts 1 1 wll have dentcal weghts φ = p = ( n /( n + m)). When we wsh that unts wth a hgh level of employment should have a geate mpact than unts wth a low level of employment, the ato model wll compensate fo ths. U U S 15

17 b) Non-nfomatve RHG-model We calculate the calbated non-esponse-adjusted weght, w, at, n the same way as unde the assumpton of MCAR non-esponse wth equaton (9). Howeve, ths tme one ate s calculated fo each RHG. In ths example we wll calculate fo both a) and b) a) RHG equal to employment statum b) RHG equal to ndusty By usng equaton (9) and (3) we obtan the followng calbated ato estmate of the popoton who answe 'bette' (10a) Yat = ( w, at y )/( S ) = ( w ( S / S) y )/( S ) = = s U s (10b) Yat = ( w, at y )/( S ) = ( w ( S / S) y )/( S ) = = s U s Also n elaton to the non-nfomatve RHG-model, the non-esponse-adjusted weghts ae calbated wth the ato S / S = Ths way the employment-calbated estmates ae somewhat hghe than s the case of the non-nfomatve RHG-model wthout calbaton. c) Infomatve RHG-model As was the case n the non-nfomatve RHG-model we wll estmate the calbated non-esponseadjusted weght, but n ths case we use the estmated esponse pobablty whee the non-esponse s coelated wth the vaable of nteest. The calbated non-esponse-adjusted weght s denoted as 1 w = aφ = ( π p ). By usng ths estmate n equaton (9) and (3) the followng expesson s obtaned fo the calbated estmate of the nfomatve RHG-model (11) Yat = ( w, at y )/( S ) = ( w ( S / S) y )/( S ) = = s U s As was the case wth dect weghtng wth MCAR non-esponse and the non-nfomatve RHGmodel, the employment-calbated answe s calbated wth the ato S / S = 1.065, whch esults n an ncease n the estmate compaed to the estmate wthout calbaton Imputaton of tem non-esponse In ths secton we wll nvestgate methods fo mputaton of non-esponse. Instead of weghtng, we now ty to geneate answes fo the non-esponse unts and n ths way constuct a complete dataset fo the goss sample (see fg 1). Two types of mputaton: Detemnstc: The same values ae mputed when the mputaton pocess s epeated Stochastc: Dffeent values may be mputed when the pocess s epeated, and consequently the esult may be dffeent each tme the mputaton pocess s caed out. U U U 16

18 Neaest-neghbou mputaton Ths s a detemnstc method that estmates esponse altenatves based on a metc functon that uses addtonal vaables to measue the 'dstance' between a non-esponse unt and a dono 7. Employment s used as an addtonal vaable, S. We then get the dstance between the non-esponse unt and the dono by estmatng: (12) δ j = S S j Ths way the esponse altenatve s mputed fom the unt that geneates the smallest possble δ j between a non-esponse unt and a potental dono. I.e. the dono wth a numbe of employees closest to the numbe of employees n the non-esponse unt. We theefoe assume that thee s a coelaton between whch esponse altenatve s selected and numbe of employees. Fom (1) we have the vaable of nteest y = β * S Whee β 1 = 0 If unt has chosen 'bette' If unt has chosen a dffeent esponse and S s the numbe of employees fo unt Wth mputed values * β = β whee δ = S S s mnmzed we get the followng expesson j j j ~ β β = β * s s m Fom ths expesson we get (13) ~ y = β ~ * S We now have, ncludng the mputed values, a value fo all unts n the goss sample. Ths mples that n the calculaton of the estmate, the non-esponse-adjusted weght s equal to the desgn weght and the esponse pobablty, p s equal to (14) w = aφ = ( π p ) = ( π ) = a To estmate the employment-weghted popoton, Y mp, we use (13), (14) and (3) and get (15) ~ Y mp = ( a y ) /( S ) = = s U Fom (15) we see that the non-esponse adjusted estmate based on neaest-neghbou mputaton esults n a somewhat lowe estmate than what we obtaned wth models based on weghtng fo nonesponse. The popoton of mputed values that was assgned the value β * = 1 was 0.239, but because the esponse altenatves ae weghted wth the level of employment the employment-weghted 7 The unt fom whch the mputaton value s deved fom. 17

19 estmate s lowe. Among those that wee mputed wth the value β * = 0 thee was an oveepesentaton of lage unts (unts wth a hgh level of employment). Table 7 llustates ths. Table 7 Dstbuton of mputed values Imputed value Unts Sum employment * β Sum Popoton Fom the table we can see that the popoton that was mputed wth the value 1 was 0.239, but f we look at the popoton of the employment-weghted mputed esponse altenatve whch was assgned the value 1, the fgue was only Stochastc mputaton wth a non-nfomatve RHG-model (hot-deck) In contast to mputaton wth 'neaest-neghbou' ths method of mputaton s stochastc. Ths means that epeated smulatons of the mputaton pocess geneate dffeent estmates. In hot-deck mputaton the pupose s to goup togethe unts that n some way esemble each othe. To goup the unts we have chosen RHG = Industy (defned by table 5), as we assume that unts belongng to the same ndusty goup have a hghe pobablty of havng the same busness cycle than unts belongng to dffeent ndustes. In ths way we wll daw a dono fom the same ndusty goup => Non-esponse n the ndusty: Textles, weang appael and leathe, s coveed by mputaton fom a dono n the same ndusty. * The method of mputaton s based on mputng the value β fom a dono dawn andomly wthn the same RHG. In the same way as fo 'neaest-neghbou' we have the expesson ~ β β = β * s s m To estmate the employment-weghted popoton, Y mp get (15) Y = ( a ~ y ) /( S ) mp s U, we use (13), (14) and (3) and once agan we Because ths method of mputaton s stochastc, the estmates wll vay when the mputaton pocess s epeated. As an estmate fo the stochastc estmate we have chosen to un the smulaton 20 tmes and then compute the expected value, gven by the aveage of the stochastc estmates. (16) Ε, Y N mp ( Y mp ) =0.233 N=(1,...,20) N Fom (16) we see that the aveage of the 20 smulatons esults n the same estmate as when we used dect weghtng wth the assumpton of MCAR non-esponse, but the uncetanty n the estmate has nceased because of the stochastc pocess. The esults fom the 20 smulatons ae shown n table 8. 18

20 As ths table shows, the estmates adjusted fo non-esponse by the use of hot-deck mputaton vaes fom to The eason fo ths s that we daw at andom wthn each RHG, thus we get dffeent donos evey tme the smulaton s caed out. Table 8 Results fom hot-deck mputaton Smulaton Y mp , ,230 Aveage 0,233 St. dv 0, Calbaton of estmates fom mputaton models by usng a ato estmato As was seen n the case of calbaton of the dect weghted estmaton usng a ato estmato, we can also n the case of mputaton cay out a calbaton based on addtonal nfomaton fom the populaton. In ths case, t s not the non-esponse-adjusted weghts, w, that ae calbated, but the desgn weghts, a. Fom (14) we have w = a n the case of mputaton By usng (9) we can defne the calbated desgn weght as (17) Sa a at = a S S ~ ( ), ( / ) = whee S = S and = a S S~ a S s U s The total numbe of employees, S, n the populaton s known: and we know S fo all unts n the goss sample. S = = U S 19

21 Fom (17) and (15) we can then defne the calbated employment-weghted estmate based on mputaton as ~ (18) Y = ( a ~ y ) /( S ) = ( a ( S / S ) ~ y ) /( S ) mp, at, at s U s U We use ths calbaton method on the two methods of mputaton descbed above: a) Neaest-neghbou b) Hot-deck a) Neaest-neghbou When calbatng the employment-weghted estmate wth ths method of mputaton we get the followng esult ~ (18) Y = ( a ( S / S ) ~ y ) /( S ) = mp, at s U The estmaton shows that the ato S / S ~ s In ths case too, the employment-weghted estmate s calbated to be hghe, but by a smalle facto than wth dect weghtng ( S / S =1.065). Ths gves the expesson (19) S~ = a S > w S = S s s Ths means that the sum of the poducts of the desgn weghts and employment fo all unts n the goss sample s hghe than the sum of the poducts of the non-esponse-adjusted weghts and employment fo all unts n the net sample. b) Hot-deck We can also cay out calbaton of the employment-weghted estmate based on the ato estmato when usng stochastc mputaton wth a non-nfomatve RHG-model (hot-deck). As n the example wth hot-deck mputaton wthout calbaton, we use RHG = Industy (defned by table 5). By usng (18) and (16) we can estmate an aveage of the calbated stochastc estmates by unnng 20 smulatons, and then compute the aveage of the stochastc estmates. ~ (18) Y = ( a ( S / S ) ~ y ) /( S ) mp, at s U (20) Ε, Y N mp, at ( Y mp, at ) =0.244 N=(1,...,20) N As shown by (20), the aveage of the 20 smulatons esults n a somewhat hghe estmate than wth hot-deck mputaton wthout calbaton by the use of a ato estmato. Ths s because the ato, S / S ~, s Ths ato wll be constant (not stochastc) because the ato does not depend on the esponse altenatves, β ~, and the ato wll be the same as n the case of mputaton based on 'neaestneghbou'. 20

22 The eason why the ato s the same n the two cases s that the goss sample, the desgn weghts and the level of employment ae the same n the two cases, and ndependent of β ~ (see equaton (17)). The dffeence n the estmates les n the values whch ae mputed fo the non-esponse unts. The esults fom the 20 smulatons ae shown n table 9. As the table shows the estmates, adjusted fo non-esponse by the use of hot-deck mputaton calbated wth a ato estmato, vay fom to 0,258. As was the case fo hot-deck mputaton wthout calbaton we get a stochastc pocess because the donos ae dawn at andom wthn each RHG evey tme we un the smulaton. Table 9 Results fom the ato calbated hot-deck mputaton Smulaton Y mp, at Aveage St. dv The effect of calbaton To nvestgate the obtaned effect of calbaton by the use of the ato estmato, we can analyse the vaance of the employment-weghted estmate wth and wthout calbaton. To obtan educton n the vaance of the estmate calbated wth the use of the ato estmato the addtonal vaable, employment, should be coelated wth the vaable of nteest. Ths s not an uneasonable assumpton as the vaable of nteest y s the poduct of the employment level of the unt and the answe to the queston (1 o 0). To nvestgate f the ato estmato we have used n the calbaton poduces any educton n vaance, we measue the effect of addtonal nfomaton condtoned on the adjustment of non-esponse,.e. the non-esponse weghts. Fom Zhang (2003) we have a defnton of the estmate of vaance fo the dect weghted estmato Y, whee we assume constant vaance: (21) v 1 = (1 + c w) s y n 21

23 whee 2 c w s the coeffcent of vaance to w ove s, and va( y ), denoted 2 s y, may be wtten as (22) s 2 y 1 = ( y n 1 s y) 2 whee y s the employment-weghted answe defned as n equaton (1), and the aveage y s 1 (23) y = n s y Ths wll hold egadless of the non-esponse model beng nfomatve o not. A smple vaance estmate fo the calbated estmato, unde smla assumptons, has the followng geneal expesson (24) 1 *2 2 v 2 = (1 + c w ) s e n *2 w 2 se s the vaance of the whee c s the coeffcent of vaance to the calbated weghts, and calbaton esduals. The defnton of the calbaton esduals gven ato estmaton s (25) e = y x β = y x Y X = y x s s w y w x In equaton (25) the addtonal vaable employment, whch s used n the ato, s denoted x. The vaance of the calbaton esduals can then be calculated by the followng fomula 2 1 (26) s e = y x n 1 s s s 2 w y w x Wth these coheences we can measue the effect of addtonal nfomaton by the ato: *2 v2 1 + cw se (27) η = =. 2 2 v 1 + c s 1 w 2 y Assumng that non-esponse s MCAR, and that the coeffcent of vaance fo the calbated weghts s appoxmately equal to the coeffcent of vaance fo the non-esponse-adjusted weghts wthout * 2 calbaton, cw cw, we can educe the ato to η s 2 e / s y. We have calculated ths ato fo the model wth dect weghtng and MCAR non-esponse, wth and wthout calbaton. The esult fom ths calculaton s expessed n (28). 2 se (28) η = = s y In othe wods, we educe the vaance n the employment-weghted estmate by 26 pe cent by usng calbaton wth the ato estmato. 22

24 4. Summay In ths pape we have nvestgated the non-esponse n the Nowegan Busness Tendency Suvey fo manufactung, mnng and quayng, and n patcula queston 18; Geneal judgement of the outlook fo the establshment n the next quate. Chapte 3 pesented a geneal descpton of possble easons fo unt and tem non-esponse. Aggegated esponse ates fo the fou employment stata ae also calculated (see table 3). In chapte 3.1, Adjustment fo non-esponse, we have adjusted the employment-weghted estmate, fo the popoton who beleve that the geneal outlook s bette, by usng dffeent models fo weghtng fo non-esponse and two dffeent methods of mputaton. In addton to ths we have used a ato estmato to calbate these estmates. In chapte we have nvestgated the effect of calbaton wth the use of the ato estmato, and n patcula f t geneates any educton n vaance. The estmate usng dect weghtng wth the assumpton of MCAR non-esponse, calbated wth a ato estmato, s appoxmately the same as the one geneated by the cuent quately poducton of the statstcs. In the cuent poducton of the statstcs we assume MCAR non-esponse and n the ato estmato only the net sample s ncluded. One dstncton s that n the quately poducton pocess the tem non-esponse s calculated as a sepaate esponse altenatve (denoted popoton 'Non-esponse'). Anothe dstncton s that we calbate wth the ato fo each employment stata n each ndusty. If we look at the estmates fom the non-nfomatve RHG-model, the esults ae appoxmately the same as unde the assumpton of MCAR non-esponse. Ths apples both fo the estmates wth and wthout calbaton wth the use of the ato estmato. Ths ndcates that the defnton of the esponse homogenety goups (employment stata and goupng by ndusty) does not poduce goups wth dffeent pattens of non-esponse between the goups, and theefoe no adjustment of the estmates s ecoded. Thee may be othe ways of goupng the RHGs, n such a way that the esponse pobablty s dffeent between the dffeent goups, and as equal as possble wthn the goup. Howeve, we have not been able to fnd such a classfcaton. The esults fom the nfomatve RHG-model ae somewhat hghe than fo the est of the estmates, whch ndcate that the level of non-esponse s hghe among the unts that expect a bette development n the next quate. Because the algothm dd not convege, ths has an effect on the estmates and makes t dffcult to daw any conclusons. In chapte 3.1.2, Imputaton of tem non-esponse, we use two dffeent methods of mputaton; one detemnstc (neaest neghbou) and one stochastc (hot-deck). The esult usng 'neaest neghbou' mputaton shows that ths estmate s somewhat lowe than the esults fom the models of weghtng fo non-esponse. Ths ndcates that thee was an oveepesentaton of lage unts who got the mputed value 0 (esponse altenatve 'unchanged' o 'wose'). Ths way the employment-weghted estmate fo the popoton who beleve that the geneal outlook s 'bette', s somewhat educed. When t comes to the stochastc mputaton wth a non-nfomatve RHG-model (hot-deck), we see that the aveage estmate, based on 20 smulatons, s the same as unde the assumpton of MCAR nonesponse. When RHG equal to ndusty goup poved to have lttle mpact when used n the nonesponse model, ths method of mputaton wll poduce an estmate coespondng to mputaton usng andom donos wthn the whole net sample (no RHG-ndex). Gven that these esults ae equal, the non-esponse model wth MCAR non-esponse would be pefeed, because ths estmaton pocess wll geneate a lowe level of vaance than s the case of the stochastc mputaton pocedue. Futhe we note that n the case of calbaton wth ato estmaton, we get a lowe estmate wth the methods of mputaton than s the case fo non-esponse models. Table 10 sums up the dffeent estmates we have calculated. 23

25 Table 10 Results fom adjustng fo non-esponse wth the use of non-esponse models and methods of mputaton Non-esponse model Method of mputaton MCAR Non-nfomatve RHG non-esponse Empl. stata Industy goup Infomatve RHG Neaest Hot-deck neghbou (RHG=Industy) Calbaton wth No ato estmato Yes Fom the calculatons that have been caed out t s dffcult to conclude that thee s vaaton n the dstbuton of non-esponse n the Nowegan Busness Tendency Suvey, but we cannot ule out the possblty that mechansms of non-esponse causes systematc vaaton. Calbaton of the estmates wth the ato estmato esults n a hghe popoton who consde the geneal outlook to be bette. Ths holds fo all the nvestgated cases. The calculaton of the effect of calbaton wth the use of ato estmaton shows that ths pocedue geneates estmates wth a lowe level of vaance than estmates wthout calbaton, and that t s easonable to calbate the estmates n ths way. We have made a numbe of smplfcatons n ths analyss. Fo nstance, we only look at one esponse altenatve and one queston. A numbe of the questons n the Busness Tendency Suvey ae coelated wth each othe, and ths has an mpact on whch methods should be used to adjust fo nonesponse. The advantage of the estmaton pocedue used n the quately poducton of the statstcs, wth the assumpton of MCAR non-esponse, s that t povdes a smple and staghtfowad method fo geneatng esults fo all questons as a whole. If futhe analyss should be caed out n elaton to the non-esponse n the Busness Tendency Suvey, t would be nteestng to take a close look at dffeent methods of mputaton. Fo multpupose estmaton, a method of mputaton s ease to be ntegated nto the exstng poducton pocess than the weghtng adjustments. 24

26 Refeences Zhang (2003): SM05 - Intoducton to adjustng fo non-esponse, unpublshed pape fo the couse SM05 at Statstcs Noway August 2003, L-Chun Zhang, (n Nowegan only) 25

27 Recent publcatons n the sees Documents 2001/12 B. Hoem: Envonmental Pessue Infomaton System (EPIS) fo the household secto n Noway 2001/13 H. Bunbog, I. Bowle, A.Y. Choudhuy and M. Naseen: Appasal of the Bth and Death Regstaton Poject n Bangladesh 2001/14 K. Rypdal: CO 2 Emsson Estmates fo Noway. Methodologcal Dffcultes 2001/15 E. Røed Lasen: Bdgng the Gap between Mco and Maco: Intedependence, Contagous Belefs and Consume Confdence 2001/16 L. Rogstad: GIS-pojects n Statstcs Noway 2000/ /1 B. Hoem, K. Elandsen og T. Smth: Compasons between two Calculaton Methods: LCA usng EPIS-data and Input- Output Analyss usng Noway' s NAMEA-A Data 2002/2 R. Bjønstad: The Majo Debates n Macoeconomc Thought - a Hstocal Outlne 2002/3 J. L. Hass and T. Smth: Methodology Wok fo Envonmental Potecton Investment and Cuent Expendtues n the Manufactung Industy. Fnal Repot to Euostat. 2002/4 R. Bjønstad, Å. Cappelen, I. Holm and T. Skjepen: Past and Futue Changes n the Stuctue of Wages and Sklls 2002/5 P. Boug, Å. Cappelen and A. Rygh Swensen: Expectatons and Regme Robustness n Pce Fomaton: Evdence fom VAR Models and Recusve Methods 2002/6 B.J. Eksson, A.B. Dahle, R. Haugan, L. E. Legenes, J. Myklebust and E. Skauen: Pce Indces fo Captal Goods. Pat 2 - A Status Repot 2002/7 R. Kjeldstad and M. Rønsen: Welfae, Rules, Busness Cycles and the Employment of Sngle Paents 2002/8 B.K. Wold, I.T. Olsen and S. Opdahl: Basc Socal Polcy Data. Basc Data to Monto Status & Intended Polcy Effects wth Focus on Socal Sectos ncopoatng Mllennum Development Goals and Indcatos 2002/9 T.A. Bye: Clmate Change and Enegy Consequenses. 2002/10 B. Halvosen: Phlosophcal Issues Concenng Appled Cost-Beneft Analyss 2002/11 E. Røed Lasen: An Intoductoy Gude to the Economcs of Sustanable Tousm 2002/12 B. Halvosen and R. Nesbakken: Dstbutonal Effects of Household Electcty Taxaton 2002/13 H. Hungnes: Pvate Investments n Noway and the Use Cost of Captal 2002/14 H. Hungnes: Causalty of Macoeconomcs: Identfyng Causal Relatonshps fom Polcy Instuments to Taget Vaables 2002/15 J.L. Hass, K.Ø. Søensen and K. Elandsen: Nowegan Economc and Envonment Accounts (NOREEA) Poject Repot /16 E.H. Nymoen: Influence of Mgants on Regonal Vaatons of Ceebovascula Dsease Motalty n Noway /17 H.V. Sæbø, R. Gløsen and D. Sve: Electonc Data Collecton n Statstcs Noway 2002/18 T. Lappegåd: Educaton attanment and fetlty patten among Nowegan women. 2003/1 A. Andesen, T.M. Nomann og E. Ugennov: EU - SILC. Plot Suvey. Qualty Repot fom Stastcs Noway. 2003/2 O. Ljones: Implementaton of a Cetfcate n Offcal Statstcs - A tool fo Human Resouce Management n a Natonal Statstcal Insttute 2003/3 J. Aasness, E. Bøn and t. Skjepen: Supplement to <<Dstbuton of Pefeences and Measuement Eos n a Dsaggegated Expendtue System>> 2003/4 H. Bunbog, S. Gåsemy, G. Rygh and J.K. Tønde: Development of Regstes of People, Companes and Popetes n Uganda Repot fom a Nowegan Msson 2003/5 J. Ramm, E.Wedde and H. Bæve: Wold health suvey. Suvey epot. 2003/6 B. Mølle and L. Belsby: Use of HBS-data fo estmatng Household Fnal Consupton Fnal pape fom the poject. Pape buldng on the wok done n the Euostat Task Foce /7 B.A. Holth, T. Rsbeg, E. Wedde og H. Degedal: Contnung Vocatonal Tanng Suvey (CVTS2). Qualty Repot fo Noway. 2003/8 P.M. Begh and A.S. Abahamsen: Enegy consumpton n the sevces secto /9 K-G. Lndqust and T. Skjepen: Explong the Change n Skll Stuctue of Labou Demand n Nowegan Manufactung 2004/1 S. Longva: Indcatos fo Democatc Debate - Infomng the Publc at Geneal Electons. 26