Scanner Data Price Indexes: The Dutch Method versus Rolling Year GEKS

Transcription

1 Scnner Dt rice Indexes: The Dutch Method versus Rolling Yer GEKS Heymerik A. vn der Grient nd Jn de Hn b Mrch 2011 Abstrct: In 2010, Sttistics Netherlnds expnded the use of scnner dt in the CI to six supermrket chins. At the sme time new method ws introduced to construct the scnner dt indexes. Monthly chined Jevons price indexes re now computed t the lowest ggregtion level. This pproch ws chosen to mximize the number of mtches in the dt through chining while circumventing the problem of chin drift. However, the lck of weighting t the item level is n obvious wekness. The solution proposed by Ivncic, Diewert nd Fox (2009) is to pply ( rolling version of) the GEKS method, known from sptil price index mesurement, to intertemporl price mesurement. To mke n informed decision bout possible implementtion, Sttistics Netherlnds hs shdow system running which computes rolling yer GEKS indexes for ech COICO ctegory nd ech supermrket chin nd ggregtes the indexes up. This pper briefly outlines both methods nd presents monthly index numbers for 2009 nd At the ll items, ll chins level the two methods yield similr results. At lower ggregtion levels there pper to be some mrked differences. Key words: chin index, consumer price index, GEKS method, scnner dt. Division of Mcroeconomic Sttistics, Sttistics Netherlnds; h.vndergrient@cbs.nl. b Corresponding uthor; Division of Mcroeconomic Sttistics, Sttistics Netherlnds,.O. Box 24500, 2490 HA the Hgue, The Netherlnds; j.dehn@cbs.nl. per prepred for the twelfth meeting of the Ottw Group, 4-6 My 2011, Wellington, New Zelnd. The views expressed in this pper re those of the uthors nd do not necessrily reflect the views of Sttistics Netherlnds. The uthors re grteful to Wim Kiewiet for developing the system tht computes index numbers.

2 1. Introduction The interntionl CI Mnul (ILO et l., 2004) notes tht Scnner dt constitute rpidly expnding source of dt with considerble potentil for CI purposes (p. 54); Scnner dt obtined from electronic points of sle include quntities sold nd the corresponding vlue ggregtes on very detiled level (p. 92); Scnner dt re up to dte nd comprehensive (p. 478). In spite of the potentil dvntges, s fr s we know only three countries, i.e., Switzerlnd, Norwy nd the Netherlnds, re ctully using scnner dt in the compiltion of the CI; see lso Ivncic (2010). 1 Scnner dt cn be exploited in different wys. The simplest wy would be to use scnner dt s n lterntive source for price collection, which replces collection in the stores, without chnging the trditionl principles of computing the price indexes. More specificll the smples of items observed nd the expenditure weights would be left unchnged. This method is currently pplied by the Swiss Federl Sttisticl Office (Becker-Vermeulen, 2006). In the Netherlnds nd Norwy more rigorous pproch hs been followed, though the computtion methods differ. The sub-index for food nd non-lcoholic beverges in the Norwegin CI, introduced in August 2005, is bsed on chined Törnqvist indexes t the lowest level of ggregtion (Rodriguez nd Hrldsen, 2006). The Dutch scnner dt indexes for supermrkets were introduced into the CI lredy by June They relied on nnully chined Lspeyres indexes t the lowest level (Schut, 2002). In Norwy nd the Netherlnds, both prices nd weights for lrge smple of items from product ctegory re derived from the scnner dt. In Jnury 2010 Sttistics Netherlnds expnded the use of scnner dt (vn der Grient nd de Hn, 2010). Seven more supermrket chins hve been found willing to co-operte nd regulrly supply scnner dt but two of them were not yet implemented in Jnury The six chins for which scnner dt were included in Jnury 2010 hve n ggregte mrket shre of some 50% nd weight of slightly over 5% in the CI. 1 A number of sttisticl gencies re investigting the use of scnner dt t the moment, in prticulr the Austrlin Bureu of Sttistics, the U.S. Bureu of Lbor Sttistics nd Sttistics New Zelnd. In the pst, severl sttisticl gencies round the world hve been looking into the issue. There is lso lrge cdemic literture on scnner dt, both on price index construction, including qulity djustment, nd on broder economic mesurement issues. 2 Scnner dt from one of those two chins ws introduced in Jnury It is nticipted tht the dt from the other chin will be introduced in the ner future. 1

3 Aprt from incresing the ccurcy of the CI (nd the Europen Hrmonized Index of Consumer rices, HIC), there re two more resons behind the wider use of scnner dt in the Netherlnds: to rise cost efficiency nd to lower response burden. Visiting supermrkets to collect shelf prices is mjor cost component of producing CI in the trditionl wy. A totl reduction of round 15,000 price quotes ech month hs been ttined for the six supermrket chins. 3 The use of scnner dt is beneficil to the dt providers s well. They will no longer be bothered by price collectors who wlk round in the stores collecting prices or sking stff for help. Lowering response burden is key issue for Sttistics Netherlnds. The expnsion of the use of scnner dt in Jnury 2010 ws ccompnied by new index construction method t the lowest ggregtion level. While expenditure dt is vilble for individul items, this informtion is only indirectly used, i.e., to select smple of items for prticulr product ctegory through cut-off smpling. No explicit weighting is pplied in the index computtion; monthly chined unweighted geometric, or Jevons, price index numbers re clculted. This method ws chosen to mximize the number of mtches in the dt through chining which ws deemed necessry given the high ttrition rte of items in scnner dt without running the risk of introducing chin drift. As ws demonstrted in number of empiricl studies (see e.g. Feenstr nd Shpiro, 2003; Ivncic, Diewert nd Fox, 2009; nd de Hn nd vn der Grient, 2009), high-frequency chining of weighted price indexes, including superltive indexes such s the Fisher nd Törnqvist, cn led to huge chin drift. Yet the lck of weighting t the item level is wekness of the nd hs been criticized on vrious occsions. Ivncic, Diewert nd Fox (2009) proposed n ppeling solution to the problem of chin drift in superltive indexes. They dpted the (G)EKS pproch from interntionl price comprisons to price comprisons cross time. To ddress the problem of revisions, they suggested rolling yer (RY) version. During 2010, the method ws extensively nlysed t Sttistics Netherlnds. In order to mke n informed decision bout possible implementtion, shdow system ws developed tht computes indexes on monthly bsis. This enbled us to mke full-scle comprison with the currently computed index numbers. The present pper presents selection of the results. 3 It should be noted tht the initil number of price quotes for supermrkets ws reltively lrge given their weight in the CI. 2

4 The pper is structured s follows. Section 2 gives n overview of the Dutch method for treting supermrket scnner dt. Section 3 briefly outlines the method. Section 4 describes the scnner dt used nd number of ctivities, like dt clening, which re crried out before ctully computing the indexes. Section 5 then compres the index numbers bsed on the two methods. Section 6 discusses issues tht rise in prctice when working with scnner dt. Some of these issues pply in generl, regrdless of the computtion method, wheres others re method dependent. Section 7 concludes by describing the dvntges (nd few potentil prcticl drwbcks) of the pproch over the currently used method. 2. The Dutch Method 2.1 An Overview Scnner dt revels tht purchses in supermrkets re highly dynmic. For exmple, for some product ctegories the ttrition rte is huge: mny old items dispper nd mny new ones pper. A fixed-bsket index would ignore these dynmics. This effect cn be mitigted by keeping the smple up to dte when items leve but, depending on the smple size, this might men lot of work for the price sttisticins. This ws one of the resons for Sttistics Netherlnds to seek for n lterntive method. It lso hppens tht items temporrily dispper from the dt sets, either becuse they re out of stock or becuse purchses re zero. Scnner dt lso revel the distribution of the item expenditures in ech month. There re two importnt spects. First, Dutch consumers seem to rect instntneously to promotionl sles. De Hn (2008) presented n exmple on detergents showing tht the quntities purchsed increse enormously when the price is reduced. 4 The fct tht prices of supermrket products re not sticky t ll hs been observed nd nlyzed in mny cdemic studies. This hs the impliction tht, t low ggregtion levels, scnner dt price indexes could be rther voltile. Second, even without sles, the distribution of expenditures within product ctegory is usully highly skewed. Tht is, reltively 4 Triplett (2003) rgued tht this could be prtly due to consumers who minly purchse the goods when they re on sle. If this is the cse, then the popultion of consumers tht buy t prticulr store or t prticulr supermrket chin will continuously chnge over time. 3

5 smll number of items ccount for the mjority of expenditures. To put it differently: in mny cses, 50-60% of the items ccount for less thn 10% of the totl expenditures. Thus, the use of n unweighted index number formul would overstte the importnce of the mny low-expenditure items. Given the high number of exits nd entries observed in scnner dt, the choice mde by Sttistics Netherlnds for chin index t the lowest ggregtion level seems quite nturl. As mentioned in the introduction, chining of weighted indexes cn led to substntil chin drift, so the unweighted Jevons index formul ws chosen. To tke the skewed expenditure distribution into ccount, crude type of implicit weighting ws introduced through cut-off smpling: the most importnt items in terms of expenditures re included in the smple with certinty wheres less importnt items re excluded. More specificll n item is used in the computtion of the price index between two djcent months if its verge expenditure shre in the current nd preceding month with respect to the set of mtched items those items tht re purchsed in both months is bove certin threshold vlue. The threshold ws chosen such tht roughly 50% of the items is selected, representing 80-85% of ggregte expenditure. This ws done t the elementry ggregtion level, i.e., for ech product ctegory t the most detiled level within ech supermrket chin. 5 Our price concept is the unit vlue (expenditures divided by the quntities sold) for n item within supermrket chin. So we ggregte cross stores belonging to the sme chin but not cross different chins. 6 A drwbck of n djcent-period mtched-items pproch is tht temporrily unobserved items re excluded from the computtion. This mens tht the price chnges of those items occurring between the lst month they were in the smple nd the month they re-enter the smple would be ignored. The missing prices re therefore imputed by multiplying the lst observed price by the (Jevons) price index of the mtched items within the sme elementry ggregte, s usul. In wy pnel element is forced onto the mtched-items pproch so tht price chnges occurring during period of bsence re included in the index. 5 We use the term elementry level for the ggregtion level below which expenditure informtion is not used in the Dutch pproch, which coincides with the lowest level t which price indexes re constructed (though not published). 6 Ivncic nd Fox (2010), using Austrlin scnner dt, found tht items cn be deemed homogeneous cross stores belonging to the sme chin. This mens tht ggregting cross those stores mkes sense to compute unit vlues. We ssume tht their results lso pply to the Netherlnds. 4

6 Like in ny mtched-items method, qulity chnges re not explicitly tken into ccount. Implicit qulity-djustment methods hve been most prominent in the Dutch CI in the pst, nd in this respect the new method is comprble to former prctices. The computer system does llow for mking explicit qulity djustments, in prticulr djustments for chnges in pckge nd pck size, but we expect this feture to be used infrequently. 7 The ggregtion of elementry price indexes computed from the scnner dt is similr to the ggregtion of price indexes computed from other sources. This is bsed on nnul chining of fixed-weight ( Lspeyres-type ) indexes, where the weights refer to the previous yer nd where short-term index series re chined in December. The elementry ggregtion level cn be seen s sub-division of the 5-digit COICO level, referred to s 6-digit COICO. It is constructed using product clssifictions provided by the supermrket chins, which mkes it chin specific. The dvntge of using these clssifictions is tht Sttistics Netherlnds does not need to clssify items into product ctegories, n ctivity which previously proved to be very lbor intensive. 8 Becuse the elementry ( 6-digit COICO ) level is chin-specific, the first step of the ggregtion procedure is to ggregte the elementry price indexes for ech chin to the officil 5-digit COICO level nd to higher levels. At ech of these COICO levels the price index numbers re subsequently ggregted cross the different chins. The weights re derived from the scnner dt. This detiled weighting informtion ws unvilble prior to the use of scnner dt. Not only do the ggregte mrket shres of the supermrket chins differ substntill which we lredy knew, they lso pper to differ significntly cross product ctegories. The computtion nd ggregtion of scnner dt indexes is seprte module in the utomted CI process. The finl ggregtion step is to combine the scnner dt indexes t ll COICO levels with the corresponding indexes estimted from mnul price collection in other store types. To this end so-clled mtrix of expenditures ws developed, which is updted every yer. 9 7 Fox nd Melser (2011) ddress the issue of djustments for chnges in pck nd pckge size. 8 A limited number of items my not be clssified properly nd need to be re-clssified. 9 Although the vilbility of expenditure dt tht cn be used s weights is big dvntge, t the sme time it my revel inconsistencies with dt obtined from other sources used to construct CI weights such s the ntionl ccounts, the household expenditure surve etc. Adjustments re then necessry to construct consistent overll weighting scheme. 5

7 2.2 The Actul Clcultion In this section we describe the computtion of the scnner dt indexes for prticulr supermrket chin in greter detil. Dt clening procedures, which precede the ctul computtion, will be ddressed in section 4. The following nottion is used. The price (unit vlue) nd expenditure shre of item i for elementry ggregte in month m of yer y re denoted by y m p, i, nd y m s, i, ; 10 ( m N 1),( m) denotes the number of mtched items between months m nd m-1 of yer y (where m-1 is equl to y-1,12 for m= 1). To introduce crude type of weighting, every item i is given probbility y m w, i, to be included in the smple used to compute the price chnge between month m-1 to month m. These inclusion probbilities or implicit weights re given by m s w 1 if i, = + s m w 0 otherwise. i, = m 1 m i, i, 1 > ( m 1),( m) 2 N ; χ This mens tht if the item s verge expenditure shre in months m-1 nd m exceeds N ( m 1),( m) the threshold 1/( χ), the item will be included in the smple. Notice tht the sum of ll implicit weights determines the smple size of elementry ggregte, tht (, 1),(, ) N, (, 1),(, ) is, y m y m y m y m y m w i 1 i, = n =. The prmeter χ must be set in dvnce. It cn be given ny positive vlue, but in prctice there is lower boundry becuse if the vlue is too low, the smple will be empty. We decided to use χ = for ll elementry ggregtes, i.e., for ll product ctegories t the pseudo 6-digit COICO level nd ll supermrket chins. A simultion study did not indicte n urgent need to differentite between elementry ggregtes. 11 ( m 1),( m) The choice for χ = mens tht if, for exmple, N = 80, then items with n verge expenditure shre greter thn 1% will be selected. computed s The price chnge between m-1 nd m for elementry ggregte is now 1/ n ( y, m 1),( y, m) ( y, m 1),( y, m) n m m / m 1 pi, π =. m 1 (1) i= 1 pi, 10 Becuse the elementry ggregtes re chin specific, n item cn pper in more thn one elementry ggregte with chin-specific prices nd expenditure shres. 11 There is lso prcticl spect to it: differentiting would imply determining χ vlues for severl hundreds of elementry ggregtes. 6

8 Expression (1) is smple-bsed month-to-month Jevons index. These monthly indexes re subsequently multiplied (chined) to obtin long-term time series with n rbitrry reference or strting month y,m : 0 0 = π, (2) m / y0, m0 m 1/ y0, m0 m / m 1 m 1/ 0, m0 where y is the chined mtched-items price index going from the strting month to month m-1 of yer y. For items tht re not vilble in month m but which were purchsed in previous periods, price is imputed s follows: 12 pˆ = p π. (3) m i, m 1 i, m / m 1 For higher ggregtes A short-term price indexes re clculted ccording to fixed-weight ( Lspeyres-type ) formul with index reference period y-1: w y 1 m / y 1 m / y 1 A A = y 1 w A where m / y 0, m0 m / y 1 = 12 1 y 1, s / y0, m0 12 s= 1. (4). (5) y 1 The weights w in (4) re bsed on the nnul expenditures of ll items belonging to elementry ggregte, regrdless whether items were included in the smple or not. 13 Next, the short-term series re chined in December, which is the link month, to construct long-term series with index reference period m / y 1 y 1,12 / 1 m / 0 = A A 0,12 / 0 ch, A y 1,12 / y 1 1,12 / 1 A τ τ τ τ A τ = 1 A Short-term indexes nd chined indexes m / y 1 A. (6) re computed t ll COICO m / 0 ch, A levels, both for ech supermrket chin seprtely nd cross ll chins, using formule (4) nd (6). 12 The previous price (in month m-1) cn lso be n imputed price. 13 At the 5-digit COICO level, monthly vrying weights re used for sesonl items, such s fresh fruit nd fresh vegetbles. At the 4-digit COICO level, fixed nnul weights re used. 14 Currently the index reference period of the Dutch CI is

9 3. A Brief Overview of the Method The method described in section 2 ws chosen by Sttistics Netherlnds to circumvent the problem of drift in chined weighted (preferbly superltive) indexes. An lterntive solution, which does mke use of superltive index number formul, ws put forwrd by Ivncic, Diewert nd Fox (2009). They dpted the GEKS procedure, known from the interntionl (sptil) price comprisons literture, to price comprisons cross time. In this section we will briefly outline their method. The GEKS method tkes the geometric men of the rtios of ll bilterl indexes (clculted using the sme index number formul) between number of entities, such s countries, where ech entity serves s the bse. Let jl nd kl be the bilterl indexes between pir of entities j nd l ( l = 1,..., M ) nd between entities k nd l, respectively. The GEKS index between j nd k cn be written s jk GEKS = M M jl kl 1/ M jl lk [ ] = [ ] l= 1 l= 1 1/ M /. (7) The second expression of (7) holds when the bilterl price indexes stisfy the entity reversl test, so tht jk GEKS jl GEKS kl GEKS / kl lk = 1. It cn esily be shown tht = /. (8) Expression (8) sys tht the GEKS price index stisfies the circulrity or trnsitivity requirement: the sme result is obtined if entities re compred with ech other directly or vi their reltionships with other entities. For price comprisons cross time, the entities in (7) re time periods, for CI purposes usully months. Consider rnge [0,T] of T + 1 months, where T is the current (most recent) month. The GEKS index for month t ( t T ) with reference period 0 then is 0, t GEKS = T T 0, τ t, τ 1/( T + 1) 0, τ τ, t [ / ] = [ ] τ = 0 τ = 0 1/( T + 1). (9) One month lter T+1 is the current month nd the time series is clculted for [0,T+1]. The GEKS index for month t ( t T +1) with reference period 0 now becomes: 0, t GEKS = T + 1 T + 1 0, τ t, τ 1/( T + 2) 0, τ τ, t [ / ] = [ ] τ = 0 τ = 0 1/( T + 2). (10) 8

10 A problem with this pproch is tht the results for ll months 1,..., T clculted using (10) will differ from those clculted using (9). So when the observtion period is extended nd new dt is dded, the GEKS index numbers will be subject to continuous revision, something which is uncceptble for CI. A solution to this problem would be to use the index chnge between T nd T+1, clculted using (10), to updte the time series (9) through chin linking. By construction, this monthly GEKS price chnge is ffected by the prices nd quntities of ll months 0,..., T + 1, hence including months 0,..., T 1. If we would continue to extend the time series in this w the index chnge between the lst two months will be influenced by the prices nd quntities pertining to more nd more months in the pst. This involves loss of chrcteristicity. Ivncic, Diewert nd Fox (2009) therefore suggested rolling yer pproch. The rolling yer pproch uses 13 month moving window to compute GEKS indexes. A 13 month window ws chosen becuse it is the shortest window tht llows comprison of strongly sesonl items. The GEKS index (9) for periods [0,12] remins the strting point. As bove, the next month-to-month index chnge is chin linked to the GEKS time series. This index chnge is computed s the rtio of the GEKS indexes, bsed on dt of [1,13], for months 13 nd 12 with reference period 1, which re given by 13 1, τ 13, τ [ / ] 1,13 GEKS = ; (11) τ = , τ 12, τ [ / ] τ = 1 1/13 1/13 1,12 GEKS =. (12) Becuse GEKS indexes re trnsitive, the following reltions hold: = =. (13) 12,13 GEKS 12,1 13,1 1,13 1,12 GEKS / GEKS GEKS / GEKS This mens tht, insted of tking the rtio of (11) nd (12), the GEKS index between months 12 nd 13, i.e , τ 13, τ 1/13 τ,13 τ,12 [ / ] = [ / ] 12,13 GEKS = (14) τ = 1 τ = 1 1/13 cn be used to updte the existing time series. The expression for the rolling yer GEKS () index pertining to month 13 then becomes 9

11 0,13 = 0,12 GEKS , τ 13, τ 1/13 0, τ 12, τ 1/13 12, τ 13, τ [ / ] = [ / ] [ / ] τ = 1 τ = 0 τ = 1 1/13. (15) The generl expression for the index pertining to the current month T ( T > 12) with reference month 0 is 15 0, T = 12 T t 0, τ 12, τ 1/13 t 1, τ t, τ [ / ] [ / ] τ = 0 t = 13 τ = t 12 1/13, (16) nd the generl expression for the monthly index chnge is t t 12, t t 11, t t 3, t t 2, t t 1, τ t, τ 1/13 t 1, t [ / ] =... ( ) t 12, t 1 t 11, t 1 t 3, t 1 t 2, t 1 τ = t /13. (17) Formul (17) provides useful insight into the ctul clcultion procedure. The monthly chnge of the index simply equls the (geometric) men of the direct index between t-1 nd t, months. t t 1,, which is counted twice, nd 11 indirect indexes between these As mentioned before, the price indexes tht re inputs in the (RY)GEKS method should preferbly be superltive indexes. These indexes re symmetric, re grounded in microeconomic theory nd hve good xiomtic properties, including the time reversl requirement. Ivncic, Diewert nd Fox (2009) used Fisher price indexes. In follow-up stud de Hn nd vn der Grient (2009) used Törnqvist indexes insted. The recently built shdow scnner dt system t Sttistics Netherlnds is lso bsed on Törnqvisttype indexes. 4. Scnner Dt nd Dt Clening 4.1 Dt Description At present, eight supermrket chins send dt files to Sttistics Netherlnds every week contining scnner dt on ll individul items sold, seven of which re currently used in the CI. Items re identified by the Europen Article Number (EAN). Ech record of dt file reltes to single EAN nd contins weekly expenditures nd quntities sold. It lso contins short product description, often including pck size nd pckge size. Records tht hve identicl EANs re considered to refer to the exct sme (physicl) 15 In our empiricl illustrtion, formul (16) will be pplied t the 5-digit-COICO level. 10

12 item. Items with different EANs re treted s different products. The consequences of these choices re ddressed in section 6. Ech chin dds its own clssifiction code indicting to which product ctegory the EANs belong. Hving clssifiction code ttched to the dt is indispensble for n efficient CI process given the overll huge ttrition rte of EANs. Once the reltion between the chin-specific clssifiction nd COICO hs been estblished, EANs re utomticlly ssigned to the pproprite 5-digit COICO ctegory. To prevent regulr recoding, prerequisite is tht the chin-specific clssifictions re stble through time. Of course they should lso be more detiled thn the 5-digit COICO level. Supermrket chins sometimes group together items relted to specil occsions like children s birthdys. roducts tht serve prticulr im, such s met, chrcol nd suces bought when orgnising brbecue, my lso be grouped together. In these cses the EANs cnnot utomticlly be ssigned to one of the COICO ctegories. For efficiency resons it ws decided not to ssign the items to the pproprite ctegory but to simply exclude them. Supermrkets considerbly expnded the rnge of products sold during the pst decdes. The ssortment presently includes, for instnce, clothing, glsswre, tblewre nd household utensils. For the time being Sttistics Netherlnds decided to restrict the clcultion of scnner dt indexes to the more trditionl product ctegories. Tble 1 lists the COICO ctegories for which scnner dt indexes re now clculted. Tble 1. COICO ctegories for which scnner dt indexes re clculted Code Description 01 Food nd non-lcoholic beverges Wine Beer 05.5 Tools nd equipment for house nd grden 05.6 Goods nd services for routine household mintennce 06.1 Not reimbursble medicl nd phrmceuticl products ets, pet foods nd products for pets Applinces, rticles nd products for personl cre 4.2 Dt Clening nd Dt reprtion Timeliness is n importnt spect of CI. The Dutch CI for month t is published in the first week of month t+1. A consequence is tht dt referring to the lst week of 11

13 month t cnnot be used. rice collection in the field is therefore restricted to the first three full weeks of ech month. A similr procedure is pplied to scnner dt. Tht is, the unit vlue of n item is bsed on the expenditures nd quntities sold pertining to the first three full weeks of clendr month from ll stores within chin for which scnner dt is received. The sme goes for the verge expenditure shres used in the (cut-off) smpling procedure. The prices (unit vlues) re subject to two utomtic dt clening procedures. First, month-to-month price reltives greter thn 4 or smller thn ¼ re considered implusible nd declred invlid. Thus, items for which the current price is more thn 300% higher or more thn 75% lower thn the previous price re utomticlly deleted. Second, n lgorithm ws developed, referred to s dumping filter, tht excludes items from the computtion which exhibit strong price decreses in combintion with strong decreses in expenditures. Dumping occsionlly occurs in cse of stock clernces when n item is sold t n extrordinry low price. Since the item will not be vilble ny longer, it does not return to regulr price. The resulting price decreses, without offsetting price increses, cn hve n undesirble downwrd effect on the index of the product ctegory in question. In prctice this dumping filter my lso delete some items tht re not relted to stock clernces. This should not be viewed s serious problem s missing prices re imputed. While it cn be rgued tht the dumping filter should be ugmented for the computtion of indexes, or tht it should not be used t ll, we implemented it in the shdow scnner dt system without mking ny chnges. This mkes it possible in section 5 below, where we compre the results of the two methods, to focus solely on the impct of the choice of index number formul. 5. A Comprison of the Two Methods 5.1 The 5-digit COICO Level The shdow system computes indexes for 58 different product ctegories t the 5-digit COICO level, being the lowest publiction level in the Dutch CI (though the scnner dt indexes re not published seprtely). At this level, price indexes re computed for ech of the six supermrket chins tht re in the Dutch CI since Jnury However, some of the chins do not sell products of ll 58 ctegories, so tht

14 cross clssifictions of product groups nd supermrket chins remin, lso referred to s strt. Note gin tht 5-digit COICO is one level higher thn the elementry 6- digit COICO level for which Jevons indexes in the re compiled. We hve chosen the 5-digit level to increse the number of observtions. Since indexes re bsed on (bilterl) superltive index numbers, there seems to be no need to compute them t the lower ggregtion level. In the present study we compre monthly nd officil price index numbers, covering the period Jnury 2009, which serves s the index reference period, to October The price index numbers for the 343 different strt using the Dutch method were extrcted from the officil CI dtbse nd re-scled to mke them equl to in Jnury For ech of the 343 strt we computed the verge difference between the nd the officil index numbers during the 22-month period. Tble 2 provides summry of the findings. For 81% of the strt (278 out of 343) the verge difference is less thn 2 index points, for 62% even less thn 1 index point. If we tke s the benchmrk, we my be tempted to conclude tht the Dutch method performs resonbly well. Tble 2. Averge difference between officil nd indexes t the 5-digit COICO level Averge difference Number of strt bsolute % (-14, -4) 14 4 [-4, -3) 5 2 [-3, -2) 14 4 [-2, -1) 21 6 [-1, 1] (1, 2] (2, 3] 15 4 (3, 4] 11 3 (4, 12] 6 2 On the other hnd, there re 20 strt where the verge difference of the index numbers ccording to the two methods exceeds 4 index points. Differences tht lrge cnnot be ignored. Tble 3 indictes tht 9 out of these 20 strt pertin to the 4-digit COICO ctegories fruit nd vegetbles nd pottoes, product ctegories which re dominted by fresh produce. In few instnces the verge bsolute differences even exceed 10 index points. 13

15 Tble 3. COICO (4-digit) ctegories where officil nd strtum indexes differ more thn 4 index points on verge COICO Description Number of strt Met Fish Fruit Vegetbles nd pottoes Minerl wters, soft drinks, fruit nd vegetble juices Alcoholic beverges Non-durble household goods Articles nd products for personl cre Higher Aggregtes The indexes for the 343 (product ctegory x supermrket chin) strt hve been ggregted to higher COICO levels using fixed weights tht relte to the yer The sme procedure ws used to ggregte the officil indexes. It should be noted tht this upper-level weighting procedure differs from the procedure pplied in the Dutch CI where, s ws described in section 2, nnul chining is used. We pplied this ggregtion method to the officil strtum indexes lso, so tht the ggregtion method does not ffect the comprisons. 16 Figure 1 shows the ll items, ll supermrket chins scnner dt price indexes, i.e. the price indexes ggregted cross ll strt, ccording to both methods. There is no cler sign of persistent difference. The index is on verge 0.08 points bove the index bsed on the (pproximte). Apprently the differences t the strtum level cncel out. Thus if the pproch is considered idel, the performs stisfctorily t the highest level of ggregtion. As cn be seen from Figure 1, supermrket prices in the Netherlnds slightly went down during Although the observtion period is too short to drw ny definitive conclusions, there seems to be sesonl pttern with prices being reltively high in spring nd reltively low in utumn. The most striking feture of Figure 1 is the 16 We chose this ggregtion procedure for simplicity. It gives rise to Young-type index, which cn be problemtic. A better choice would hve been to price bckdte the expenditure shres to Jnury 2009, leding to Lowe-type index. 14

16 shrp drop in prices in Jnury As we found in erlier yers s well, Jnury is populr month for promotionl sles. Figure 1. Aggregte price chnge (58 product ctegories, 6 supermrket chins) The impct of sle prices in Jnury 2010 cn lso be observed for mny product ctegories t the 4-digit COICO level; see Figure 2. Not surprisingl mesured price chnges t this level re more voltile thn the price chnge t the most ggregte level. For some COICO clsses, for exmple met nd food products n.e.c., the monthto-month fluctutions re substntil. In most cses the impct of the method used on the 4-digit results is limited to few index points but there re some notble exceptions. For fruit the index numbers using the differ up to 4 points from those using. Yet, the trends re similr nd the differences seem to be incidentl rther thn structurl. In severl other cses, e.g., for lcoholic beverges nd nondurble household goods, the differences re persistent nd the clerly understtes the price development. As will be discussed lter on, while those differences re persistent, they do not lwys grow over time but my be cused by oneoff incidents. Figure 2. Scnner dt price indexes indexes; COICO 4-digit level 102 Bred nd cerels (Coicop ) 102 Met (Coicop )

17 106 Fish (Coicop ) 102 Milk, cheese nd eggs (Coicop ) Oils nd fts (Coicop ) Fruit (Coicop ) Vegetbles nd pottoes (Coicop ) Sugr, jm, chocolte nd confectionry (Coicop ) Food products n.e.c. (Coicop ) Coffee, te nd coco (Coicop ) Minerl wters, soft drinks, fruit nd vegetble juices (Coicop ) Alcoholic beverges (Coicop 02.1) Non-durble household goods (Coicop ) Articles nd products for personl cre (Coicop )

18 The indexes in Figures 1 nd 2 hve been clculted s weighted verges of (5-digit COICO) indexes, using fixed-weight index number formul. Tht is, the price indexes t ll levels bove 5-digit COICO re in fct hybrid indexes. The dvntge of this two-stge procedure is tht, t the upper level, the price indexes re consistent in ggregtion. 17 However, the methodology cn be pplied directly to ny ggregtion level. As mtter of fct, from theoreticl point of view it would be better to compute indexes t ll levels becuse this would not only ccount for substitution within product ctegories but lso cross ctegories. To get n ide of wht the impct might be of keeping upper level weights fixed, we computed for ech supermrket chin indexes for COICO division 01 ( food nd non-lcoholic beverges ), using the pproch directly s well s using the hybrid versions where ws pplied t the 5-, 4- nd 3-digit level. All items, ll chins indexes were clculted using the fixed-weight formul. Figure 3 shows the differences between these hybrid versions nd the true index. Figure 3. The effect of using t different levels of ggregtion 0.5 Food nd non-lcoholic beverges (Coicop 01): distnce to direct vi on 3-digit level vi on 4-digit level vi on 5-digit level Keeping weights fixed t the 3-digit level only hs negligible effect. But when the weights re kept fixed t lower levels lso, sesonl pttern emerges tht is minly due to fruit nd vegetbles. Expenditures on these sesonl goods re much greter in summer thn in winter, nd the prices of fresh produce re lower in summer, which hs downwrd effect on the true index. 17 This is true becuse we re using fixed weights. If we hd used nnul chining, s in the officil Dutch method, then the long-term (chined) indexes would not hve been consistent in ggregtion. 17

19 6. Issues When Deling with Scnner Dt (Lck of) Weighting Although the nd the method differ in other respects s well, by fr the most importnt reson why they generte different results, especilly t lower ggregtion levels, is the tretment of the reltive importnce of the items. The lck of expenditure weights in the for the items included in the cut-off smples t the lowest (elementry) ggregtion level is of course the biggest issue. This becomes most pprent for elementry ggregtes where price chnges differ substntilly mong items nd where the expenditure distribution is highly skewed. Fresh fruit is typicl exmple. A lrge proportion of the expenditures on fresh fruit in the Netherlnds is spent on bnns; hence the impct of bnns will be too low in the. During the first hlf of 2009 nd the first hlf of 2010, the price of bnns incresed lot less thn the price of other fresh fruit. This explins to lrge extent the difference in price development ccording to both methods shown in Figure 4, which reltes to single supermrket chin ( C ). The index bsed on the clerly hs n upwrd bis. Figure 4. Fresh fruit (COICO ), supermrket chin C The Use of rice Filters As ws mentioned in section 4, two dt clening procedures, or price filters, re used in the nd hve lso been implemented in the shdow system, dumping filter nd filter tht excludes items with implusibly lrge price chnges. The usefulness of the filters is illustrted in Figures 5 nd 6. These figures show the ll 18

20 items indexes (pertining to 58 5-digit COICO ctegories) for two supermrket chins E nd B, respectivel bsed on the (including the two price filters) nd bsed on the method, both with nd without using filters. The rw dt for chin E registered huge price rise for prticulr item between April nd My Not pplying price filters would hve cused increse of 3% t the ll items level, s cn be seen in Figure 5. The dt entry error which we think it ws ws one-off incident s in June 2009 the index returns to norml level. The price filters effectively remove the implusible spike. Figure 5. All items price indexes; supermrket chin E with price filters without price filters While the dt entry error in the exmple of Figure 5 would not hve ffected the trend, unnoticed chnges in the wy the dt is registered cn lso cuse structurl breks. An exmple is given in Figure 6. In My 2010, supermrket chin B suddenly chnged the unit of mesurement for mny items from price per (hlf) kilo to price per grm. Most of these items were given new EAN but for limited number of items the EAN ws left unchnged. Since the EAN is the item identifier, the ltter items were mtched nd showed n incorrect price decrese by fctor of 500 or 0. Without the use of the price filters, the method would hve mesured price decrese of 15% t the ll items level for chin B, s shown in Figure 6. Agin, the filters effectively remove the implusible price chnge Obviousl it would hve been better if we hd repired the error by re-computing the prices in constnt units of mesurement becuse the number of mtched items now is much lower thn the true number. However, tht would hve been lot of work. See lso section

21 Figure 6. All items price indexes; supermrket chin B with price filters without price filters Imputtions for Temporrily Missing rices A feture of the is tht the missing prices for temporrily unvilble items re imputed. When n item hs disppered nd re-ppers fter while, the new price is compred with n imputed previous price, ensuring tht in the longer term the true price chnge is cptured. Without imputtions the price chnge during the period of bsence would be missed. Since the method tkes into ccount price chnges of mtched items during whole yer to compute the most recent monthly price chnge, it my not be necessry to impute prices explicitly. 19 The EAN s Item Identifier Records identified by the sme EAN re considered to refer to the exct sme (physicl) item. EANs re ssigned to specific products by the mnufctures, nd for the mjority of the items sold in supermrkets we cn be confident tht prticulr EAN in different stores nd in different time periods reltes to single homogeneous product, t lest during couple of yers. For some products, such s fresh fruit, supermrkets ssign unofficil EANs themselves, either t the store level or t the chin level. A specific set of EANs is vilble for this purpose; shorthnd codes re sometimes used t the checkout. The use of these store-specific or chin-specific EANs does not pose ny problems for price index construction s long s they refer to the sme items over time. However, identicl store-specific codes re irregulrly ssigned to different products in 19 This is bit specultive though. We re currently estimting indexes in which the missing prices re ctully imputed to investigte if the effect of imputtions is indeed negligible. 20

22 different months, in which cse we would not be compring like with like. Fortuntel this phenomenon hppens so rrel nd the impct on the results ppers to be so smll, tht we cn sfely ignore the problem. Moreover, if the resulting price chnges were substntil, they would most likely be eliminted by the price filters in the dt clening procedures or during the monthly routine of checking nd nlysing the results of the index computtion. 20 In some instnces the EAN level could be too detiled for CI purposes. Items with different EANs, but which re identicl from the consumers point of view, should in principle be treted s the sme product. If n item (identified by its EAN) disppers nd completely comprble item with different EAN ppers, then the prices should be directly compred. An exmple would be pck of coffee tht is normlly wrpped in red pper but, for promotionl resons, hs suddenly been wrpped in blck pper. Neither the nor the method would utomticlly compre the prices. As mentioned before, the possibility to mke explicit djustments is built into the current computer system. So if the CI sttisticins were to know those situtions, they could in principle mke direct comprisons. 21 The problem shown in Figure 6 is n exmple where new EANs were suddenly ssigned to existing items, in this cse becuse the unit of mesurement ws chnged. The best option would obviously be to compre the prices directly fter djusting for the chnge in the unit of mesurement. In relit the Dutch index ws completely bsed on the (mtched) items whose EANs hd not chnged. romotionl Sles nd Discounts Supermrkets frequently sell items t prices fr below the regulr price; discounts cn be up to 50%. Consumers typiclly rect to the reltive price chnges by purchsing the items tht re on sle in lrge quntities, in prticulr when the items cn be stored t home. The method ws in fct designed to cope with this sitution. Becuse the increse in expenditures nd the decrese in lter period re explicitly tken into ccount, the elementry indexes often turn out to be more voltile thn the 20 For some supermrkets we know which EANs re used for store- or chin-specific coding, nd we might decide to exclude them from the index clcultion in the future. 21 The computer system provides the user with indictors pointing to mjor chnges in the ssortment of the supermrket chin in question, which might be helpful in this respect. 21

23 corresponding indexes ccording to the unweighted. Figure 7 provides nice illustrtion. Supermrket chin C offered prticulr brnd of rice t discount prices in Jnur April nd September As result the index behves in n errtic wy. This voltility is not necessrily undesirble. If the im is to estimte n cquisitions index (like in Austrli, for exmple), s opposed to cost-of-use or costof-living index, it cn be rgued tht we ought to mesure the instntneous impct of the purchses mde. Figure 7. Voltility of the index; Rice (COICO ), supermrket chin C romotionl prices cn cuse strting problem, s we cll it, in the index. This phenomenon occurs when the month of introduction of supermrket chin into the index clcultion includes sles period (which in the Netherlnds usully endures full clendr week). During the month fter the introduction, the prices tend to return to regulr levels, nd the index will show strong increse. Obviousl n unweighted index will be much less ffected. This is clerly demonstrted in Figure 8 for the price chnge of wine in supermrket chin A. Becuse the price decrese between December 2008 nd Jnury 2009 is unobserved, the index hs n upwrd bis during the whole observtion period. Of course the problem cn simply be voided by incorporting the chin, or the elementry ggregte(s) in question, one month lter, but prcticl considertions my hmper this. The strting problem is generl problem with linking in voltile index series. The reson we hve discussed it is tht one should be wre of the problem when interpreting the results nd compring the two methods. 22

24 Figure 8. The strting problem; Wine (COICO ), supermrket chin A Lrge price cuts do not only hppen in cse of temporry promotionl discounts, they cn lso be structurl. Figure 9 shows n exmple for milk sold in supermrket chin F. In My nd June 2009 chin F lowered the prices of severl items. This generted lrge increse in turnover, presumbly by ttrcting mny new customers s milk is not storble product. The price cuts nd the resulting increse in expenditures hd downwrd effect on the index of lmost 10%. The (unweighted) Dutch method mesures much smller price decrese. The difference between both indexes remins more or less constnt over time becuse prices did not return to their originl levels. Figure 9 once gin illustrtes the problem of using n unweighted index number formul. Figure 9. The effect of structurl price cuts; Milk (COICO ), supermrket chin F

25 Strongly Sesonl Items Strongly sesonl items re items which re only vilble during certin periods of the yer. Fresh fruit like strwberries nd vegetbles re typiclly mentioned, but there re more items tht hve strong sesonl pttern. rior to Ester, Christms nd specific Dutch December event ( Sinterkls ) consumers purchse lrge quntities of chocolte deliccies. These products re on the mrket for two or three consecutive months only. After the events, i.e., in the second or third month, the lst remins re sold t clernce prices. A yer lter the items my re-pper on the mrket, nd most of them pper to hve the sme EAN s lst yer so tht prices cn be directly compred. Figure 10 shows the price chnge of the pseudo 6-digit COICO product group Chocolte sold by supermrket chin F. In the relevnt months, like November nd December, the sesonl deliccies dominte the expenditures. The product ctegory lso contins items tht re vilble throughout the yer. Given tht the method explicitly compres current prices with those of the previous yer, we would expect the method to work fine. 22 In ny cse, the indexes re very stble through time, which is ressuring since t the item level we did not observe mjor price chnges during twelve-month periods, neither for the sesonl items nor for the stndrd ones. The compres the prices of the sesonl items implicitly by mens of imputtions. While mesured price chnges re similr for both methods during subperiods, by the end of the period the index is 10 points higher. Figure 10. Strongly sesonl items; Chocolte (COICO ), supermrket chin F Törnqvist (direct) Törnqvist (chined) 22 Blk (1981) proposed the use of the GEKS method for sesonl goods in producer price index context lredy thirty yers go, though he did not propose rolling yer pproch. 24

26 For this exmple we lso computed direct nd monthly chined Törnqvist price indexes (without imputtions). As cn be seen from Figure 10, the chined Törnqvist hs severe downwrd bis. Tht chining cn led to drift when there is sesonlity in the prices is well known. In this cse the prices of the sesonl deliccies systemticlly fll during djcent months nd these price decreses re hevily weighted. Actull this exmple illustrtes tht, without imputtions, monthly mtching nd chining does not cpture the implicit (but unobserved) offsetting price increses. The direct Törnqvist index compres the prices of items purchsed in the current month nd in the strting period, which is Jnury Thus, this index does not tke the Ester deliccies into ccount. The strong increse during the lst months of 2009 stems from the fct tht the regulr prices of Christms 2009 deliccies re compred with the low clernce prices in Jnury Assessment of the Two Methods Our empiricl comprison of the for treting supermrket scnner dt with the lterntive method ws ment in the first plce to provide input to Sttistics Netherlnds mngement to mke n informed decision bout implementtion of the method. Unfortuntely the shdow system tht currently computes price indexes does not meet officil IT requirements. Implementtion would therefore men (re-)strting costly IT project. Bsed on our findings, below we ssess the two methods by looking t three spects: ccurcy of the method, techniclities nd consequences for the CI production process. Accurcy From theoreticl point of view the method is undoubtedly better thn the. The method produces weighted indexes, is bsed on bilterl superltive indexes (which re grounded in economic theory nd hve good xiomtic properties), nd mkes optiml use of ll the vilble price nd quntity informtion without suffering from chin drift. Our empiricl evidence supports this view. While t the ll items, ll supermrket chins level, the Dutch scnner dt index is very similr to the, t lower ggregtion levels we found some exmples where the Dutch 25

27 method produced rther implusible results. For some product ctegories, such s fresh fruit, the differences with the corresponding indexes re persistent nd grow over time. The method, s it is mtched-model pproch, does not explicitly djust for qulity chnges. Whether this gives rise to qulity chnge bis is difficult to sy. A mtched-model pproch does not necessrily led to bis; much depends on the mrket circumstnces. Given the degree of competition in the Dutch mrket, it my well be tht explicit djustments would be superfluous. Furthermore, we do not believe tht qulity improvements for goods purchsed in supermrkets re substntil (t lest not compred with high-tech goods). Sttistics Netherlnds decided not to explicitly djust for qulity chnges when implementing the current method. We would dvice to do the sme if the method is to be implemented. Techniclities An rtificil 6-digit COICO ggregtion level ws introduced in the to llow for weighting below the 5-digit COICO level. This rtificil ggregtion level is differs cross supermrket chins, which is bit imprcticl for further ggregtion steps. Also, the weighting scheme t the 6-digit level hs to be updted every yer since nnul chining is used. The method cn be pplied directly to the 5- digit COICO level there is no need for further disggregtion unless users would like to hve more detiled figures in the future, which is unlikely nd the resulting price index numbers cn be trnsferred directly to the CI ggregtion module. In ddition, the method cn nd probbly should be pplied to ll items belonging to 5- digit COICO ctegory (s we hve done) insted of smple thereof. Thus, the cut-off smpling procedure cn be dropped. This, nd dropping the rtificil 6-digit COICO level, would mke the system simpler thn the current one. A drwbck of using the method might be the incresed voltility of the time series nd the strting problem this could cuse. On the other hnd, s ws mentioned erlier, n increse in voltility is not undesirble if this describes the rel world. The strting problem, though bigger for thn for the, is generl problem rising from the use of voltile index series for which remedy cn esily be found. 26