Sampling Schemes for Price Index Construction: A performance comparison across the COICOP Food Groups

Five sampling schemes for price index construction one cut-off sampling technique and four probability proportional to size (pps) methods are evaluated by comparing their performance on a homescan market research data set across 21 months for each of the 13 COICOP food groups. Classifications are derived for each of the food groups and the population index value is used as a reference to derive performance error measures such as RMSE, bias and standard deviation for each food type. Repeated samples are taken for each of the pps schemes and the resulting performance error measures analyzed using regression of three of the pps schemes to assess the overall effect of sampling scheme and COICOP group whilst controlling for sample size, month and population index value. Cut-off sampling appears to perform less well than pps methods and multistage pps seems to have no advantage over its single stage counterpart. The jackknife resampling technique is also explored as a means of estimating the standard error of the index and compared with the actual results from repeated sampling. Acknowledgements This paper arises out of work with the U.K. Office for National Statistics (ONS) and we are most grateful for their permission to publish this work and to thank Jo Woods, Mat Berger, Lewis Conn, Kat Pegler, Matthew Powell and Richard Campbell from ONS and John Doyle from Cardiff Business School for many helpful discussions. The opinions expressed here are ours and, of course, not necessarily those of the ONS. We also thank Mick Silver for his most helpful advice. Data supplied by TNS UK Limited. The use of TNS UK Ltd data in this work does not imply the endorsement of TNS UK Ltd. in relation to the interpretation or analysis of the data. All errors and omissions remain the responsibility of the authors.