CONTROLLING FREQUENCY-INDUCED IMPLICIT WEIGHTS IN MULTI-SOURCE CONSUMER PRICE DATA

Abstract

This study examines implicit statistical weights induced by unequal observation frequencies when fieldcollected prices, electronic cash-register records, web-scraped prices, and administrative data are combined in consumer price statistics. The geometric mean of all individual price records is compared algebraically with a hierarchical procedure that first aggregates prices within outlets and data sources and then combines source-specific means using the shares of validated outlets (Kⱼ/K). The latter procedure is mathematically equivalent to an equally weighted geometric mean across outlets, thereby preventing repeated records from mechanically increasing an outlet’s final weight. As an empirical illustration, the author’s summary calculations for loose rice sold by weight in Tashkent in August 2026 report 1,818 price records from 64 outlets. Electronic cash-register data accounted for 84.7% of the records but only 14.1% of the outlets. The two reported mean prices are UZS 22,354.86 and UZS 22,439.10, a difference of UZS 84.24 (+0.38%), which can be verified arithmetically. Because the underlying record-level observations were unavailable for independent replication, the reported figures are treated as an illustrative case rather than independently validated evidence of improved CPI accuracy. Equal-outlet weighting controls frequency-driven mechanical weighting; however, it does not, by itself, establish representativeness in terms of sales or consumer expenditure.