Measuring inflation through different sampling designs implemented on scanner data

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1 Measuring inflation through different sampling designs implemented on sanner data A. Bernardini 1, C. De Vitiis 2, A. Guandalini 3, F. Inglese 4, M. D. Terribili 5, Abstrat The Italian National Institute of Statistis (ISTAT) is planning a redesign of Consumer Prie Survey (CPS). Register of loal units and availability of sanner data (SD) from retail modern distribution, provided through an agreement ith Nielsen, are the starting point of this transformation. Espeially SD represents a big opportunity for introduing improvements in terms of both data olletion and sampling perspetive. This ork aims to ompare the properties of eighted and uneighted higher level elementary prie indies hen different sample shemes are implemented on SD (modern distribution for food and groery data). Probabilisti and non-probabilisti samples of series have been dran ith different shemes. Furthermore, different riteria of sample alloation both for outlets and elementary items ere also onsidered. The omparison among different sampling strategies (alloation, seletion) has been arried out through a Montearlo simulation evaluating bias and effiieny of the Consumer Prie Index (CPI) derived using three lassi aggregation formulas (suh as Jevons, Fisher and Loe). The simulation has been onduted on permanent series of some onsumption segments (Italian COICOP6) for the Turin provine. Keyords: Consumer Prie index, sanner data, sampling 1. Introdution The Italian National Institute of Statistis (ISTAT) is planning a redesign of Consumer Prie Survey (CPS). Sanner data (SD) represent a big opportunity for introduing improvements in the CPS in terms of both data olletion and sampling perspetive. Statistial sampling theory strongly reommends the use of probability sampling for all types of statistial surveys inluding the eonomi ones. Nevertheless several ountries arry out CPS on the basis of a non-probability sampling sheme. Other national statistial offies, as ell as the Italian National Institute of Statistis (ISTAT), produe estimates for CPS using a purposive multistage sampling seletion sheme, in hih the seletion riterion at eah stage is based on the onept of most representative units Researher (Istat), bernardini@istat.it. Senior researher (Istat), deviitis@istat.it. Junior researher (Istat), alessio.guandalini@istat.it. Senior researher (Istat), fringles@istat.it. Junior researher (Istat), terribili@istat.it. 1

2 The CPS has reently undergone a revie aiming to redesign different aspets of the data olletion proedures and sampling methods. The goal of the projet is introduing progressively in the CPS more rigorous sampling proedures (that is probabilisti) starting from the seletion of outlets and elementary items for the setors here this is feasible. The register of loal units and the availability of sanner data (SD) from the retail modern distribution are the starting point for the implementation of this transformation. Furthermore, the use of eb-sraping for olleting pries referred to online market (tourism, mobile phone, et.) is involved in the revie of the survey. Sine 2014, ISTAT is olleting, thanks of a ontrat ith Nielsen, SD referred to food and groery market from the six main retail hains operating in Italy. Atually, SD are used for experimenting the omputation of Consumer Prie Index (CPI). Therefore, Italy plaes among ountries using or testing the use of this soure of data for ompiling CPI. SD from retail stores, ontaining both pries and quantities, and allos the use of different aggregation formulas at the elementary level, involving or not the use of quantities (eighted or uneighted formulas). In this paper different methods for seleting referenes are ompared. The values of different elementary index formulas have been ompared ith the value of the orresponding prie indies obtained from the hole set of referenes for the same elementary aggregate. In the paper the projet of redesigning the CPI based on use of sanner data are presented (par. 2) and the former proedure for treating these data (par. 3) are outlined; paragraph 4 fouses on the sampling sheme tested for the seletion of referenes, hile the results of these sampling experiments are illustrates in paragraphs 5 and 6. Finally, some onlusions and open issues are disussed in paragraph The use of sanner data in CPI and ISTAT redesign projet 2.1 Use of sanner data for CPI Sanner data files ontain generally elementary information referred to single EAN odes (GTIN) for speifi outlets onsisting in turnover and quantities sold during a eek. This information does not provide the shelf prie of the produt individuated by the EAN ode (European Artile Number) and outlet (referenes or series), but it allos to define a unit value or average eekly prie. This feature introdues a ruial issue in the disussion among eonomists, hih goes beyond the fous of this paper. Furthermore, usually SD do not inlude information about disounts or speial sales. This is not a problem beause the harmonized CPI onsiders the prie atually paid, inluding disount. Atually Sitzerland, Noray, Netherlands and Seden, are using SD in the ompilation of the CPI, hile Belgium and Denmark are going to use them from Sanner data an be exploited in different ays. The simplest ay ould be to use SD as an alternative soure for prie olletion, hih replaes olletion in the stores, ithout hanging the traditional priniples of omputing the prie indies. This method is urrently applied by the Siss Federal Statistial Offie (Vermeulen and Herren, 2006). Alternatively, as in Noray and Seden, SD an be used as universe from hih samples of referenes an be seleted folloing different methods (Nygaard, 2010; Norberg, 2014). Finally, all (or almost all) SD an be used to ompile prie indies, ithout a strit seletion 2

3 but ith onsequenes on the theoretial definition of the index. In the Netherlands, the omputation methods differ and data are used in a more extensive ay to alulate prie indies (Van der Grient and De Haan, 2010). In a study perspetive, moreover, SD from retail stores allos to evaluate ho different aggregation formulas at the elementary level perform. In fat, offiial CPI are usually onstruted in to broad steps. First, for narroly defined, relatively homogeneous produts, also knon as elementary aggregates, elementary prie indies are alulated. In a seond step, these elementary indies are aggregated into a single onsumer prie index using expenditure eights. Elementary indies, named also higher level elementary indies, are therefore the building bloks of prie index numbers. Their development over time measures the inflation of narro produt ategories. While the aggregation at higher level is arried out using generally Laspeyres type formulas ith eights deriving from national aount or expenditure survey data, offiial praties in elementary prie index onstrution are still not uniform aross ountries, deserving further investigation in the onsequenes of different hoies (Gábor and Vermeulen, 2014). On the basis of SD reently obtained, ISTAT is planning an experimental phase of prie index evaluation, starting from the omparison among different formulas for the elementary indies ombined ith different ays of using those data through sampling seletion shemes. The hoie, in fat, is beteen using all or the most of data or a sample of them. The first option is very appealing and seems to exploit all the potentialities of sanner data but leaves open relevant issues both theoretial, regarding the definition of the prie index and operational, the managing of a huge quantity of elementary items (EAN odes) eah month for the prodution of the CPI. In the former it is needed to fae the hoie of the more effiient sampling design. Moreover, it presents some risks due to the need of managing the shrinking during the year of a fixed representative sample of elementary items seleted on the basis of the previous year universe of items. 2.2 ISTAT projet Sampling redesign The urrent strategy atually adopted in CPS arried out at territorial level is based on three purposive sampling stages. The sampling units are respetively the muniipalities, the outlets and the elementary items for hih the pries are olleted. The biggest muniipalities are fored by la to partiipate to the survey. The Muniipal Offies of Statistis selet the outlets sample, here the pries of a fixed basket of produts (inluding roughly 1,500 produts) are olleted. The outlets sample is hosen to be representative of onsumer behavior in the muniipality. For eah produt of the basket the most sold item is seleted and the prie of this item is olleted throughout the year. At the end of eah year, besides the sample of outlets and the elementary items, ISTAT refreshes the fixed basket of produts. The elementary prie indies are urrently omputed at muniipality level by uneighted geometri mean. The general prie index is alulated by subsequent aggregation of elementary indies, using eights at different levels based on population and national aount data on onsumer expenditure. A orking group established at ISTAT is developing and testing different sampling 3

4 strategies (alloation, seletion ith respet to different aggregation formulas) to evaluate hih ombination leads to best results in terms of CPI estimates effiieny. The first step to make the sampling seletion feasible, is the preparation of the sampling frame. The basis for this operation is the availability of an exhaustive list of outlets ontaining data for the unit identifiation (suh as address, telephone, et.) and data referring to the eonomi ativity, number of employees, produts sold. The Loal Unit Arhive of ative enterprise in Italy (ASIA), yearly updated ith administrative soures, represents a good starting list for the onstrution of the outlets list. In order to produe a suitable sampling frame, the information urrently olleted in this arhive are appropriately enrihed. Furthermore, the information available only referred to the total enterprise and not for eah single loal unit, suh as turnover, has to be subdivided among its loal units aording to some rule or model. For the elementary item level different approahes ill oexist at the beginning. SD for food and groery in the modern distribution allos the use of sampling methods and prie index ompilation using eights from quantities (or expenditures). For the traditional distribution (small shops) and the other retail setors, data olletion and prie index ompilation ill ontinue unhanged at first. The outlets sample ill be defined for all the eonomi ativities for hih the arhive is available, independently on the availability of sanner data. In fat, also for the modern distribution ith SD it is useful to follo an outlets sample in order to have the possibility to deal eah month ith a manageable quantity of data. The seletion of elementary items from SD allos to implement a suffiiently feasible field proedure and to overome the potential soure of bias of the proedure adopted in the urrent survey, based on subjetive hoies. Further, the seletion proedure an be based on Permanent Random Number (PRN) tehniques and assuring a good overlap of the samples of different years Sanner data struture and uses at ISTAT At the moment Nielsen provides to ISTAT eekly data of turnover and quantities at EAN ode (elementary item) and outlet level for six modern retail distribution hains (Conad, Coop, Esselunga, Auhan, Carrefour, Selex) operating in the food and groery market in 35 Italian provines. In the experimental stage Nielsen provides bakard data for at least one full year and the preeding month of Deember, starting from Deember 2013 or 2014 (depending on the starting point of delivery of eah provine). The overage of the six hains ith respet the entire modern distribution is quite high in all provines, ith some variability in the geographial areas of the ountry. Furthermore, Nielsen provided the ditionary for the lassifiation of EAN odes to GS1-ECR-Indiod produt lassifiation. ISTAT ensures internally the translation from ECR to COICOP, the lassifiation of produts used for the CPI. Consumption segments, not foreseen by the EU-COICOP, are the most detailed domain of estimate for Italian CPI, onstitute groupings of homogeneous produts; those defined for the food and groery are 121 out of a total of 324. For the aim of CPI omputation, the referene for hih the prie are observed during a ertain period are defined as series, individuated by an outlet and an EAN ode. Furthermore, only the relevant eeks, defined as the first three full eeks (omposed of seven days) in eah month are onsidered. Also in the reommendation drafted by 4

5 EUROSTAT, the use of data referred to the first to full eek for eah month is advised. 3. The treatment of data The use of SD for the prodution of the CPI in modern retail distribution implies a very important data proessing stage. The main goal of the definition and implementation of quality heks is to ahieve a leaned data set. The SD quality heks aims to ensure the ompleteness and orretness of the ontinuous flo of information eekly uploaded by Nielsen. First, formal heks have been defined to ensure the ompleteness of the data olleted at provinial level, distribution hains, outlets and eeks. Then, others quality heks on loaded data are made in the treatment stage introduing editing rules. At this stage missing or inadmissible values on the variables of interest (eekly turnover, quantities sold and unit pries per EAN ode) are identified. The quality hek implemented to identify and eliminate the problemati series are: quantity<1 not motivated by unit of measurement; deimal values on quantities>1 not motivated by unit of measurement; unit pries <= 0,01 ; missing turnover. In this ase the heks on the presene of the inadmissible values ere arried out onsidering the data aquired for the relevant eeks in eah month at provinial level. To identify inadmissible unit pries several methods have been tested. For the sake of simpliity, also in terms of omputational burden, the hoie has been redued beteen to methods. Both methods are based on the omputation of the median unit pries onsidering the quantities sold for eah single ourrene (EAN ode, eek, outlet) at provinial level. The first method onsists in a fixed trimming method and the identified tolerane interval of pries is: Median, K2 * Median, K1 hile the other it an be named mobile trimming and the related tolerane interval is Median K1 1 K log 1 10 Median Median 10, Median K2 1 log 10 Median Median. 10 Trimming depends on the values assigned to K 1 and K 2. Assign values to K 1 and K 2 implies assumptions on maximum disount and maximum rise of pries ith respet to the provinial median prie of the produt alloed. For food and groery K 1 =5 (it means that 80% of disount ith respet to the median prie of the produt at most is alloed) and K 2 =3 (it means that 3 times of rise ith respet to the median prie of the produt at most is alloed) seem to be plausible values. Hoever, hile in fixed trimming the relative length of the tolerane intervals remain unhanged, ith mobile trimming it beomes narros as the median prie of the produt inreases (see Figure 1). The mobile trimming is preferable 5

6 ith respet to the fixed one beause it narros don, thanks to the log funtion, the extremes as the median prie of the produt inreases. Figure 1 Tollerane interval limits of (pries/median) ith fixed and mobile trimming. Prie/Median_ Median in of EAN at provinial level (Median_) 4. Sampling from Sanner Data 4.1 Outline The first experiments on the SD have been aimed at the study of the performane of the eighted and uneighted higher level elementary prie indies in different seletion shemes of series. In this stage of the experiments, series life-yle, seasonality problems and missing data substitutions haven t been taken into aount. For the first experiments reported here data leaning is applied and a simplifiation is used: only permanent series are onsidered as universe for sampling and prie index evaluation, so as not to have the neessity to deal ith disontinued items. Permanent series are referred to those referenes ith not-null turnover for at least one relevant eek in eah month of the onsidered year, starting from the Deember of previous year. The experimental study has been developed in to phases. In the first phase probabilisti and non-probabilisti seletion shemes of series are ompared; seletion shemes ere analyzed separately for three onsumption segments (offee, pasta and mineral ater) in Turin provine (121 outlets). Several designs haraterized by the use of different riteria of sample alloation, both for outlets and elementary items, and different seletion methods of the sampling units have been onsidered. Herein, the market as assumed as a domain of interest and the sampling designs are referred to all markets (ECR groups) belonging to the six onsumption segments (offee, pasta, mineral ater, olive oil, spumante and ie ream) in Turin provine. For eah seletion sheme onsidering, starting from the monthly prie ratios ith fixed base (Deember 2013) available for 2014, the higher level elementary indies ere alulated using three lassi aggregation formulas: Jevons (uneighted), Fisher (ideal) and Loe (eights from quantities of previous year). The hoie of the prie indies as made on the basis of theoretial and empirial onsiderations: Fisher ideal index is thus preferred by eonomi theory, it uses quantities in different times and allos for substitution effets; Loe index is a modified Laspeyres in hih a base month for the prie (Deember 2013) and a base year (2013) for the quantities 6

7 are taken into aount for the eight omputation; Jevons index is, in the set of indies using only prie information (as Carli and Dutot indies), the one that as found to sho a more stable bias (measured ith respet to the ideal Fisher index) among produt ategories (this result ourred from some empirial studies arried out on several onsumption segments taken from the universe panel series SD). Finally, in addition to Fisher index onsidered for its properties, Loe and Jevons indies as ditated by attentions onneted to the referene urrent ontext of CPI ompilation. Comparison beteen alternative seletion shemes are made for eah prie index taking the orresponding universe (panel series SD) index value as benhmark. Indies performane ere evaluated in terms of bias for all seletion shemes of series. For probability seletion shemes, auray (relative bias and sampling variane) of the prie indies have been studied in a Montearlo simulation senario. In this ontext 500 samples have been seleted, aording to different sampling designs. Indies variability is measured onsidering the estimate of the relative sampling error, omputed on the estimated indies in the repliated samples. For the sample seletion and eighting of prie indies the total annual turnover as taken as referene. 4.2 Elementary index aggregation The parameters of interest taken into aount in this experimental stage are monthly Jevons, Fisher and Loe indies defined at the onsumption segment level. Jevons index is an uneighted CPI that uses prie information only (it assumes that expenditure shares remain onstant), hile Fisher and Loe use also quantity information. These last indies onsider expenditure shares at different times (urrent and referene period) as eights (Gábor and Vermeulen, 2014). Indiating by the subsript t the urrent month (12 months in year 2014), t 0 the referene month (Deember 2013), m (m=1,,m i ) the series and (=1,2,3) the onsumption segment, Jevons, Fisher and Loe formulas an be expressed as follos: Jevons index - geometri average of the prie ratios M 1 M pmt JEVONS t p m mt0 ; (4.1) Fisher ideal index - geometri mean of the Laspeyres and Paashe FISH t LASP PAAS (4.2) in hih: Laspeyres index - arithmeti eighted average of the prie ratios t M p p mt q mt 0 mt0 LASP t (4.3) M p m mt0 p m mt q 0 mt0 t 7

8 Paashe index - harmoni eighted average of the prie ratios M pmt 0 p mt qmt PAAS t M ; (4.4) p m mt p m mt qmt Loe index - arithmeti eighted average of the prie ratios here Mi z p p mt q mt 0 ml LOWE t (4.5) M p z m mt0 p m mt q 0 ml z ml 11 q qmt a. a0 z The q measure refers to the m-th quantity series of the -th onsumption segment in ml the previous year (2013). 4.3 Auray of prie index estimates The prie indies (Loe, Fisher and Jevons) are estimated in the sample using a plug-in estimator. Montearlo simulations ith 500 repliated samples have been performed for eah sampling design. Bias, ith respet to the related index omputed in the universe of SD and relative sampling error formulas shon belo, are expressed for a generi parameter (prie index) and ith referene to simulation ontext. For a generi estimated index in the -th onsumption segment (=1,2,3), ˆ, the bias an be expressed as in hih ˆ RB E ˆ ˆ ˆ (4.6) E is the expeted value of the estimated index 0 ˆ in the onsumption segment, obtained from 500 samples, and is the orresponding index value omputed on the referene universe (panel series SD). The relative sampling error of a generi estimated index ˆ in the onsumption segment an be expressed by Var ˆ RE ˆ (4.7) ˆ 8

9 ˆ and in hih ˆ are is the mean of Var ˆ variane of are alulated on the estimates generated from the seletion of 500 samples in the onsumption segment. 5. First experimental studies In the first experimental stage probabilisti and non-probabilisti seletion shemes of series in eah onsumption segment are onsidered: probability proportional to size samples in the first approah; ut-off and representative elementary item samples in the seond approah. Probability sampling design onsidered in the experiments is a to-stages sampling ith stratifiation of the first stage units. The primary stage units (PSU) are the outlets hile the seondary stage units (SSU) are the EAN. The outlets sample size has been fixed at a number of 30 out of 121 outlets available in SD. The sample size for the seond stage is given by a sampling rate of 5 perent of the overed turnover by the elementary items in eah sampled outlet to the first stage. The outlets are stratified in the universe by hains (Conad, Coop, Esselunga, Auhan, Carrefour, Selex) and outlet types (hypermarket and supermarket). In eah stratum, outlets sample has been alloated proportionally to the turnover of the strata. The outlets seletion is arried out on eah stratum ith a simple random sampling (SRS), hile the elementary items seletion is done ith probability proportional to size (PPS) sampling. In the latest ase, the inlusion probability of sampling unit is proportional to its turnover during the previous year, The elementary items seletion as arried out by adopting to different methods for draing PPS samples: Sampford (Sampford, 1967) and Pareto (Rosén, 1997a and 1997b) sampling. As regards to non-probabilisti seletion approah the seletion of series is obtained on ut-off samples based on thresholds of overed turnover in previous year, 2013: to samples are formed ith all elementary items overing respetively the 60 and 80 perent of all turnover in eah seleted outlet. Moreover, onsidering the urrent fixed basket approah, a seond seletion sheme as defined; in this ase most sold elementary items for eah representative produt (of the fixed basket) in the seleted outlets are onsidered. Irrespetive of the onsumption segment, probability sampling alays brings more effiient estimates than non-probability seletion shemes. The ut-off at 80% is alays better than the ut-off at 60% and both are loser to the real value of the index loer is the variability of the segments in terms of pries and turnovers of series (see De Vitiis et al., 2015 for further results). 6. Further experimental studies 6.1 Operational frameork In this stage of experiment, three different sampling designs have been onsidered: stratified sample of EAN, stratified one-stage sample of the outlets and to-stages sampling (outlets and EAN) ith stratifiation of PSU and SSU. In eah sampling design the size of EAN has been fixed in average at 7,400 to ompare the different sampling strategies on 9

10 equal omputational effort. Moreover, different riteria of sample alloation both for outlets and elementary items and different seletion methods of the sampling units have been onsidered. The stratified sampling design has been arried out stratifying the EAN by markets (ECR groups) in eah six onsumption segments (offee, pasta, mineral ater, olive oil, spumante and ie ream). In eah market, sample size is defined through a Neyman 6 formula. Neyman alloation takes into aount the pries relative variability of the elementary items in the markets observed in the referene year To seletion sheme for the seletion of units have been onsidered: simple random sampling (SRS) and probability proportional to size sampling (PPS). In the former ase, all the EAN in the same market have the same inlusion probability. In the latter ase, they have inlusion probability proportional to the markets turnover during the previous year, In Stratified one-stage sampling design a sample of outlets (14 out of 121 outlets) have been seleted. The outlets have been stratified as desribed in paragraph 5.2 (by hains and types). In eah stratum, to different alloation of outlets have been tested: proportionally to the strata turnover and optimal alloation by Neyman (based on the pries relative variability of the EAN observed in the strata during the previous year, 2013). Also in stratified one-stage sampling the units (in this ase outlets) have been seleted both ith a simple random sampling (SRS) and ith probability proportional to size sampling (PPS) ith size equal to turnover (2013). All EAN in the seleted outlets are inluded in the sample. To-stages sampling design is haraterized by a stratifiation of both primary and seondary units. The adopted stratifiation of the PSU (outlets) and the SSU (EAN) are the same already desribed above. The outlets sample size has been fixed at a number of 30 out of 121 outlets present in the Turin provine. For both outlets and elementary items, sample alloation in the strata is defined through the probability proportional to size sampling (PPS). The primary (outlets) and seondary (elementary items) sampling units are seleted ith a simple random sampling (SRS) and a probability proportional to size sampling (PPS). In both seletion methods some sampling units are seleted ith ertainty. 6.2 Indies evaluation under alternative sampling designs The omparison among behaviors in a sampling perspetive of the three index aggregation formulas has been onduted ith the aim of underline the differenes among them under the different sampling strategies onsidered. The same sampling estimator (i.e. a plug-in estimator) has been onsidered for all the index aggregation formulas and the same overall sample size have been dran under eah sampling strategy. The CPI have been omputed at market and onsumption segment level for 13 months (from Deember 2013 to Deember 2014) for the provine of Turin in the 88 markets related to the 6 onsumption segments already listed above. 6 See Neyman (1934) and Tshupro (1923). 10

11 6.2.1 Stratified sampling Under stratified sampling to different seletion shemes in the strata (markets) have been implemented. The estimates, for all the aggregation formulas, are in both ases unbiased (RB approximately equal to 0). With respet to the variability, it possible to see a slight differene among the indies. Looking at Figure 2 the point loud related to Jevons is usually belo those related to Loe and Fisher, that are almost at the same level. Figure 2 Relative perentage error (RE%) of estimates for Jevons, Loe and Fisher indies in markets onsumption under stratified sampling hen simple random sampling (SRS) or probability proportional to size (PPS) seletion methods are used. Turin, markets in offee, pasta, olive oil, spumante, mineral ater, ie ream. Deember 2013 Deember In the figure belo, it is possible to notie also a different behavior of the estimators of the indies ith respet to the onsumption segments. In partiular for offee segment the estimator of Jevons index is more effiient hen EAN are seleted under SRS, hilst those for Loe and Fisher are more effiient hen seletion of units is based on PPS. For the other segments there is no signifiant differenes beteen the seletion methods Stratified one stage sampling In stratified sampling to different alloation methods for outlets in the strata defined as hain and type (ipermarket and supermarket) - have been onsidered: optimal Neyman alloation based on the pries relative variability of the EAN observed in the strata during 2013 and proportional alloation based on the turnover of the strata in For eah alloation method to seletion shemes of outlets, SRS and PPS methods, have been onsidered. To keep in average around 7,400 EAN the outlets sample has been fixed at 14. In all the senarios, also in this ase, the estimator of the indies are unbiased. Hoever, hen the outlets are seleted through a PPS the estimates are more effiient, under both the alloation methods. Instead, beteen them the optimal Neyman alloation seems to be less effiient for the outlets. Then the proportional alloation based on turnover of previous year is preferable. This advantage is more remarkable hen the interest parameter are eighted 11

12 prie indies, suh as Loe and Fisher (see Figure 3). In this ase there are no signifiant differene among onsumption segments and among the level of RE% of the estimator of the indies. Figure 3 Relative perentage error (RE%) of estimates for Jevons, Loe and Fisher indies in market onsumption under stratified one stage sampling hen proportional alloation for the outlets is based on the turnover of the previous year is adopted. Comparison beteen simple random sampling (SRS) and probability proportional to size (PPS) seletion of outlets. Turin, Deember 2013 Deember Stratified to stages sampling In this ase to stages of seletion, outlets (PSU) and EAN (SSU) has been onsidered. The PSU have been stratified by hain and type, alloated through a proportional alloation and seleted ith PPS based on the turnover of previous year. The SSU in the seleted outlets have been alloated proportionally ith the Neyman alloation defined for the stratified sampling and seleted ith SRS and PPS. To keep in average around 7,400 EAN in this ase the sample of outlets has been fixed at 30. No signifiant differenes arise using SRS or PPS, probably beause the most of the variability is at outlet level. This result points the attention on the importane on the alloation and seletion method to be used at PSU level and on the size of the PSU sample. In some markets this ould bring an advantage in terms of RE% even if usually to stages sampling implies a higher design effet. Looking at Figure 4 is possible to notie the differene among the indies estimated under the to different sampling strategies. The to sampling strategies ompared are stratified one stage, proportional alloation of outlets and PPS seletion versus stratified to stages, proportional alloation and PPS seletion of outlets and furthermore riproportionated Neyman alloation of EAN in the seleted outlets in hih EAN have been seleted ith SRS. The results of estimates on a single sample for the indies in offee segment in Turin obtained under the to sampling strategies has ompared ith the real value (omputed on the universe of SD of offee segment in Turin). All the estimates seems to ath properly the level and the trend of the related real index. The estimator of Jevons index has in both ases more narro onfidene intervals (CI) ith respet to the other to, it means that its RE% is loer. In general the length of CIs are ider under to stages 12

13 sampling than under stratified one stage, even if the differene does not seem so large. In terms of bias ith respet to stratified sampling, in one stage and to stages sampling designs the RB inreases slightly, but the estimators an be still onsidered unbiased. Figure 4 Jevons, Loe and Fisher indies for offee segment estimated on one sample, onfidene interval (CI) of estimates at 95% and real value (omputed on the universe of SD). Turin, Deember 2013 Deember Open issues and onlusions This ork is an overvie of the first analyses onduted in ISTAT for testing the sampling strategies for omputing CPI from SD. The results presented sho the advantages in using probability sampling designs ith respet to the non-probability ones. Among the probability sampling designs several sampling strategies have been tested for estimating Jevons, Loe and Fisher indies. The estimator of the indies are alays unbiased and in terms of sampling variability the Jevons index has a slightly advantage ith respets to the other to that are more similar beteen eah other. Besides the stratified sampling that represents an ideal but hard to realize benhmark, due to the huge quantity of data to manage for the monthly estimates for all the Italian territory, the sampling effiieny of the estimators in stratified one stage and the stratified to stages are not so different. The hoie beteen these to strategies is not simple and it is not only a deision from a sampling perspetive, that is onsidering just the effiieny of estimates, but also the omputational burden has to be taken into aount. Moreover also impat of attrition and possible substitution of elementary items during the yearly data olletion in these sampling design must be onsidered and evaluated. 13

14 For this reason the studies onduted ill be extended to all onsumption segments and other provines. The experiments should also be expand by introduing alternative prie index formulas (as monthly hained mathed-item index), here not onsidered and evaluating the robustness of prie index formula. Moreover an open issue to deal ith is the integration beteen sanner data and traditional data for CPI ompilation, as SD do not over all outlet typology. A further problem to be addressed onerns the ombination of prie indies obtained ith different approahes. Referenes Anderberg M. R. (1973). Cluster Analysis for Appliations, Aademi Press In., Ne York. De Vitiis C., Casiano M. C., Guandalini A., Inglese F., Seri G., Terribili M.D., Tiero F. (2015). Sampling design issues in the first Italian experiene on sanner data. Under revie on Rivista di Statistia Uffiiale ISTAT. Feldmann B. (2015). Sanner-data-urrent-pratie, WS-Sanner-data-Rome-1-2-Ot_Feldmann-Sanner-data-urrent-pratie.pdf. Gábor E. and P. Vermeulen (2014). Ne evidene in elementary index bias. ILO, IMF, OECD, Eurostat, United Nations, World Bank (2004). Consumer Prie Index Manual: Theory and Pratie, Geneva: ILO Publiations. Nygaard R. (2010). Chain drift in a monthly hained superlative prie index. Workshop on sanner data, Geneva, 10 may Norberg A. (2014). Sampling of sanner data produts offers in the Sedish CPI. Draft version 8 Statisti Seden. Neyman, J. (1934). On the To Different Aspets of the Representative Method: The Method of Stratified Sampling and the Method of Purposive Seletion, Journal of the Royal Statistial Soiety, 97: Rosén B. (1997a). Asymptoti theory for order sampling. Journal of Statistial Planning and Inferene. 62(2): Rosén B. 1997b. On sampling ith probability proportional to size. Journal of Statistial Planning and Inferene. 62(2): Sampford M.R On sampling ithout replaement ith unequal probabilities of seletion. Biometrika. 54(3-4): Tshupro, A. A. (1923). On the Mathematial Expetation of the Moments of Frequeny Distributions in the Case of Correlated Observations, Metron, 2: SAS Institute (1988). SAS ISTAT User's Guide. Release 6.03 Edition. SAS Inst. Cary, NC. Van der Grient, H. A. and J. de Haan (2010). The Use of Supermarket Sanner Data in the Duth CPI, Paper presented at the Joint ECE/ILO Workshop on Sanner Data, Eurostat (2015). Vermeulen B. C. and H. M. Herren (2006). Rents in Sitzerland: sampling and quality adjustment. 11th Meeting - Ottaa Group - Neuhâtel May. 14