A Geostatistical Fuzzy Index to Measure Geographical and Population Coverage of Consumer Prices Collection : The Case of Groceries Webscraping in Italy

Prices collection for consumer price indices (CPI) compilation has come a long way in the past 20 years. While ideally, the index should include expenditure made by all households, urban and rural, throughout the country, usually CPIs in various countries had limited geographic coverage both for price collection and consumption expenditures. The introduction of new data sources, such as webscraping and scanner data, have contributed to reduce price collection costs and increase the reach across national territories, thus allowing to enhance the accuracy and quality of the CPI. The geographical dimension, which is related to the scope of the index, becomes more important the smaller the region to which the index relates. While classifications of CPI geographical coverage usually refer to administrative areas (regional, capital city, urban-rural) a finer measurement would provide price statisticians with better insights on the actual reach of data collection. This would be particularly useful in cases where prices vary substantially across space, as it is proven that consumers only travel within limited extents for their purchases and a sparse network of outlets may lead to biased measurements. We propose a geostatistical fuzzy index to measure the reach of data collection in terms of geographical and population coverage of outlets where prices are collected. This index uses a fuzzy membership function to calculate the coverage value for each municipality, inversely proportional the driving distance in minutes from the closest outlet where prices have been collected. Total coverage value for a given territory is calculated as mean of each municipality coverage value, either simple or weighted by each municipality population. Using a dataset deriving from geo-localized groceries webscraping in Italy, we provide a practical application calculating coverage at a regional level and comparing results from two different functional forms - linear and non-linear - as well as a set of different parameters for spatial decay of coverage. Our findings corroborate the robustness of the index, as rank correlations amongst different parameters or functional values are close to 1 and statistically significant. We believe this index may be used to evaluate the degree of coverage for price data collection, both in the context of probabilistic and non-probabilistic outlet selection