Quality in Italian consumer price survey: optimal allocation of resources and indicators to monitor the data collection process Federico Polidoro, Rosabel Ricci, Anna Maria Sgamba ( Istat - Italy )

introduction quality in Consumer Price Survey two research topics 1. the optimal allocation of the available resources (minimizing sample error + burden and cost) 2. the definition of a system of indicators to monitor data collection process (minimizing non sample error)

the calculation of a consumer price index (CPI) requires a large amount of resources the optimal allocation of the available resources introduction allocating these resources in the most efficient way (quality: burden and cost) the aim the issue

indicators to monitor data collection process introduction improving data quality (quality: accuracy) the definition of a system of indicators to monitor data collection process the issue the aim

1. the optimal allocation of the available resources

Approach description Italian background Approach to variance estimation Cost function Case study and results 1. the optimal allocation of the available resources

identifying the optimal sample sizes either in terms of outlets or in terms of elementary items observed in order to minimize sample error measured by sample variance the objective of this research 1. the optimal allocation of the available resources

the optimal allocation approach 1. the optimal allocation of the available resources derive optimal sample sizes minimizing variance of the estimates for a given cost  a variance function  a cost function 2 pillars in order to

Italian background consumer price index sampling structure Sampling of geographical areas Sampling of outlets Sampling of products Sampling of elementary items in each outlet 1. the optimal allocation of the available resources

consumer price index sampling design non-probability sampling consumer price index sampling methods Italian background 1. the optimal allocation of the available resources

Italian background consumer price index sampling methods Sampling of geographical areas the selection of geographical areas is established by Italian laws (No 222/1927 and 621/1975) in 2007 prices were collected in 85 county chief towns (Municipal Offices of Statistics, MOS) all over the national territory 1. the optimal allocation of the available resources

Italian background Sampling of outlets within each county chief towns, the selection of outlets is carried out by MOS sample is drawn by outlet list of the Chamber of commerce, statistical business register (ASIA), census data and other local sources the outlets with the highest total sales are chosen (mix of cut-off and quota sampling) in 2007 prices are collected in about outlets all over the national territory consumer price index sampling methods 1. the optimal allocation of the available resources

Sampling of products in 2007, 540 products are included in the CPI’s consumer price index sampling methods the selection of products is carried out by National Institute of Statistics (Istat) the selection of the products - a list (basket) of products types with product type specifications - is based on sales data (cut-off sampling) Italian background 1. the optimal allocation of the available resources

Sampling of elementary items in each outlet within each outlet, the selection of elementary items is carried out by MOS’s price collector the most sold elementary items is chosen (the representative item method) in the 2007 about price quotations are collected all over the national territory consumer price index sampling methods Italian background 1. the optimal allocation of the available resources

sample update yearly base revision consumer price index sampling methods optimum sample allocation current sizes of samples for elementary items are not optimal Italian background 1. the optimal allocation of the available resources

the approach to variance estimation 1. the optimal allocation of the available resources The Swedish approach has been used to estimate the variance of CPI (Dalén, Ohlsson, 1995) the sample is considered drawn from a two- dimensional population of products and outlets a cross-classified sample (CCS)

the approach to variance estimation 1. the optimal allocation of the available resources  representative products – as rows (i)  outlets – as columns (j)  stratification into categories of products – stratum (g)  stratification into outlet groups – stratum (h)  the crossing of strata - cell (g,h)  the parameter (index) = I  parameter estimator (index) = Î

the approach to variance estimation 1. the optimal allocation of the available resources the general index (target parameter) V gh = weight for cell turnover for the category of products g traded in the outlets of group h where the cell index is I gh = index cell

the approach to variance estimation 1. the optimal allocation of the available resources w i = weight for representative product i w h = weight for outlet j l ij = 1 if representative product i is traded in outlet j l ij = 0 otherwise the cell index where

the approach to variance estimation 1. the optimal allocation of the available resources the estimated general index the estimated cell index

1. the optimal allocation of the available resources in CCS assumption the variance estimator can be decomposed into: V PRO = variance between representative products V OUT = variance between outlets V INT = outlet and representative product interaction variance V(Î) tot ~ V PRO + V OUT + V INT where the approach to variance estimation

1. the optimal allocation of the available resources formulas for variance estimation the approach to variance estimation

1. the optimal allocation of the available resources with the following formula for variance estimation the approach to variance estimation where

Case study 1. the optimal allocation of the available resources one geographical area Udine county chief town (Resident population: ) one COICOP division (two-digit level) “Food and non alcoholic beverages” reference period December 2007

Case study 1. the optimal allocation of the available resources Outlets are divided into 12 strata according a commercial distribution type (reduced to 5 types for Food and non alcoholic beverages) Representative products are divided into 52 strata according to the national nomenclature (categories of products) Currently for outlets and products purposive sampling is used but a probability sampling has been postulated for both the approach to variance estimation

Case study 1. the optimal allocation of the available resources Inclusion probabilities for representative products (π gi ) Inclusion probabilities for outlets (π hj ) Imputation by brands information in each strata Imputation by the amount of representative products collected in each outlet the approach to variance estimation

Case study 1. the optimal allocation of the available resources main numerical results the approach to variance estimation Sample size = Î (index) = Food and non alcoholic beverages Division V PRO = V OUT = V INT = V TOT = % confidence interval

1. the optimal allocation of the available resources the cost function one data collection method Thus the following function cost is used interviewers collect prices each month by visiting each outlet

1. the optimal allocation of the available resources the approach to cost function estimation C 0 = fixed cost (i.e. for administration and other) n h = the number of outlets into stratum h m g = the number of products into stratum g a h = fixed cost per outlet into stratum h (i.e. for travel time) b h = cost to measuring one product in the outlets of stratum h r gh = average relative frequency of products in stratum g sold in outlets of stratum h where

1. the optimal allocation of the available resources the allocation problem County chief town: Udine Resident population: Reference time: December 2007 Food and non alcoholic beverages price quotes: Food and non alcoholic beverages outlets: 43 C 0 = not considered a h = we consider the average travel time  h b h = we consider the average collecting time  h Estimate C TOT = 182 h. Case study

Conclusion 1. the optimal allocation of the available resources Developing the contents of the paper solving the problem of nonlinear optimization deriving from the Cost and Variance formula Important news: preliminary attempt to estimate Italian CPI variance Enhancing effort to move towards a probability approach to CPI sampling

2. indicators to monitor data collection process

Data collection: the net design Istat CPI Office Data server DB Oracle server FTP server Web server Firewall intranet Data collector PSTN or UMTS Data collector PSTN or UMTS Data collector

2. indicators to monitor data collection process 8 Different steps of data check and data quality indicators 1.Data collection software 2.UMTS data transmission for each outlet or data collection tour: first check and first data quality set of indicators on the web server (possible real time data in the outlet)

2. indicators to monitor data collection process 8 3.Second check on the total amount of monthly elementary data and second data quality set of indicators (MOS) 4.Final check (the third one) on total amount of elementary data coming from all the chief towns (Istat) and third set of data quality indicators 5.Quarterly check concerning sampling Different steps of data check and data quality indicators

2. indicators to monitor data collection process 8 A completely integrated data production process where each event that will be stressed by the system of indicators will produce consequences in order to remove mistakes or their possible causes Different steps of data check and data quality indicators

Thank you for your attention Federico Polidoro (Istat - Italy, Rosabel Ricci (Istat - Italy, Anna Maria Sgamba (Istat - Italy,