Estimating Components of Variance of Price Change from a Scanner-Based Sample

Opinions expressed in this paper are those of the authors and do not constitute policy of the Bureau of Labor Statistics. In this paper we present estimates of components of variance of price change for cereal for several publication areas. Components of variance for 1-, 6-, and 12-month lags were computed using a weighted restricted maximum likelihood estimation method. Estimates are contrasted among publication areas using two different random effects models, and findings are discussed with respect to approaches to sample design. In section one the official CPI and scanner-based geometric price index estimators are described. Section two presents the random effects model fitted to our data and the construction of components of variance estimators for the scanner index series. Section three presents computational results and compares estimates of the components over time and across cities. Sources of price change variability are identified and discussed. Conclusions are given in section four. The CPI is calculated monthly for the total US metropolitan and urban non-metropolitan population for all consumer items, and it is also estimated at other levels defined by geographic area and item groups such as cereal, women's suits, and tobacco products. The CPI is estimated for items grouped into 211 strata for each index area, although not all such indexes are published every month. It is constructed in two stages. In the first or elementary level stage, the price index for an item-area is updated every 1 or 2 months via a function of sample price changes called a price relative. Let t ia X denote the index at time t, in item stratum i, area a, relative to time period 0. Then t ia X = 1 1 , − − t ia t t ia X R where 1 , − t t ia R denotes the price relative between times t and t-1. Since 1999, elementary indexes for most commodities and services, including cereal, have been computed using a weighted geometric average (BLS, 1997): 1 , − t t ia R ∏         ∈ − ′ = ia iaj S j P P t iaj t iaj w 1 , , = ∑ ∈ −         ′ ia S j t iaj t iaj iaj P P w e 1 , , ln ; Here S ia represents the sample for item …