### U.S. Bureau of Labor Statistics

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Office of Survey Methods Research

# Abstract

**Owen Shoemaker and William Johnson** (1999)
"Estimation of Variance Components for the U.S. CONSUMER PRICE INDEX," Proceedings of the Section on Business and Economic Statistics, American Statistical Association.

For every new sample for the commodities and services (C&S) component of the U.S. Consumer Price Index (CPI), the Bureau of Labor Statistics attempts to produce a C&S sample design that allocates outlets and quotes in an optimal fashion. This item-outlet optimization C&S sample design requires the estimation of components of variance for the three factors in the design: non-certainty primary sampling units (PSUs), item-strata and outlets. The fourth component of variance is the error term. The total variance of these unit components of variance, divided by their respective number of PSUs, item-strata, outlets and quotes, is then minimized by the optimal number of respective outlets and unique quotes. To produce these components of variance a Random Effects Model was chosen, with the independent random variable for the model an individual price change. Weighted Restricted Maximum Likelihood (REML) estimates were used to calculate the variance components. This paper explicates the methology for and the results from these estimates.

**Last Modified Date: **July 19, 2008