Jacek Białek https://orcid.org/000-0002- 0952-5327

© Jacek Białek. Article available under the CC BY-SA 4.0 licence


(English) PDF


A wide variety of retailers (supermarkets, home electronics, Internet shops, etc.) provide scanner data containing information at the level of the barcode, e.g. the Global Trade Item Number (GTIN). As scanner data provide complete transaction information, we may use the expenditure shares of items as weightsfor calculating price indices at the lowest (elementary) level of data aggregation. The challenge here is the choice of the index formula which should be able to reduce chain drift bias and substitution bias. Multilateral index methods seem to be the best choice due to the dynamic character of scanner data. These indices work on a wholetime window and are transitive, which is key to the elimination of the chain drift effect. Following what is called an identity test, however, it may be expected that even when only prices return to their original values, the index becomes one. Unfortunately, the commonly used multilateral indices (GEKS, CCDI, GK, TPD, TDH) do not meet the identity test. The paper discusses the proposal of two multilateral indices and their weighted versions. On the one hand, the design of the proposed indices is based on the idea of the GEKS index. On the other hand, similarly to the Geary-Khamis method, it requires quality adjusting. It is shown that the proposed indices meet the identity test and most other tests. In an empirical and simulation study, these indices are compared with the SPQ index, which is relatively new and also meets the identity test. The analytical considerations as well as empirical studies confirm the high usefulness of the proposed indices.


scanner data, product classification, product matching, Consumer P rice Index, multilateral indices, GEKS index.


Australian Bureau of Statistics (2016), Making Greater Use of Transactions Data to Compile the Consumer Price Index, Information Paper 6401.0.60.003, Canberra.

Białek, J. (2021), ‘Priceindices – a new R package for bilateral and multilateral price index calculations’, Statistika – Statistics and Economy Journal 36(2), 122–141.

Białek, J. and Ber˛esewicz, M. (2021), ‘Scanner data in inflation measurement: from raw data to price indices’, The Statistical Journal of the IAOS 37, 1315–1336.

Białek, J. (2022), ‘Improving quality of the scanner CPI: proposition of new multilateral methods’, Quality and Quantity In press, online at: https://doi.org/10.1007/s11135- 022-01506-6.

Caves, D. W., Christensen, L. R. and Diewert, W. E. (1982), ‘Multilateral comparisons of output, input, and productivity using superlative index numbers’, Economic Journal 92(365), 73–86.

Chessa, A. (2015), Towards a generic price index method for scanner data in the dutch cpi, in ‘14th meeting of the Ottawa Group, Tokyo’, pp. 20–22.

Chessa, A. (2016), ‘A new methodology for processing scanner data in the Dutch CPI’, Eurostat review of National Accounts and Macroeconomic Indicators 1, 49–69.

Chessa, A. (2019), A comparison of index extension methods for multilateral methods, in ‘Paper presented at the 16th Meeting of the Ottawa Group on Price Indices, Rio de Janeiro, Brazil’.

Chessa, A. G., Verburg, J. andWillenborg, L. (2017), A comparison of price index methods for scanner data, in ‘15th meeting of the Ottawa Group, Eltville’, pp. 10–12.

de Haan, J., Hendriks, R. and Scholz, M. (2021), ‘Price measurement using scanner data: Time-product dummy versus time dummy hedonic indexes’, Review of Income and Wealth 67(2), 394–417.

de Haan, J. and Krsinich, F. (2018), ‘Time dummy hedonic and quality-adjusted unit value indexes: Do they really differ?’, Review of Income and Wealth 64(4), 757–776.

de Haan, J. and van der Grient, H. A. (2011), ‘Eliminating chain drift in price indexes based on scanner data’, Journal of Econometrics 161(1), 36–46.

Diewert, W. E. (2020), The chain drift problem and multilateral indexes, Technical report, Discussion Paper 20-07, Vancouver School of Economics.

Diewert, W. E. and Fox, K. J. (2018), ‘Substitution bias in multilateral methods for CPI construction using scanner data’, UNSW Business School Research Paper (2018-13).

Eltetö, O. and Köves, P. (1964), ‘On a problem of index number computation relating to international comparison’, Statisztikai Szemle 42(10), 507–518.

Fisher, I. (1922), The making of index numbers: a study of their varieties, tests, and reliability, Vol. xxxi, Houghton Mifflin.

Geary, R. C. (1958), ‘A note on the comparison of exchange rates and purchasing power between countries’, Journal of the Royal Statistical Society. Series A (General) 121(1), 97– 99.

Gini, C. (1931), ‘On the circular test of index numbers’, Metron 9(9), 3–24.

Inklaar, R. and Diewert, W. E. (2016), ‘Measuring industry productivity and cross-country convergence’, Journal of Econometrics 191(2), 426–433.

International Labour Office (2004), ‘Consumer Price Index Manual: Theory and Practice’, Geneva.

Ivancic, L., Diewert, W. E. and Fox, K. J. (2011), ‘Scanner data, time aggregation and the construction of price indexes’, Journal of Econometrics 161(1), 24–35.

Jaro, M. (1989), ‘Advances in record-linkage methodology as applied to matching the 1985 census of Tampa, Florida’, Journal of the American Statistical Association 84(406), 414– 420.

Jevons, W. S. (1865), ‘On the variation of prices and the value of the currency since 1782’, Journal of the Statistical Society of London 28(2), 294–320.

Khamis, S. H. (1972), ‘A new system of index numbers for national and international purposes’, Journal of the Royal Statistical Society: Series A (General) 135(1), 96–121.

Krsinich, F. (2014), The FEWS Index: Fixed Effects with a Window Splice–Non-Revisable Quality-Adjusted Price Indexes with No Characteristic Information, in ‘Meeting of the group of experts on consumer price indices’, pp. 26–28.

Lamboray, C. (2017), The Geary-Khamis index and the Lehr index: how much do they differ, in ‘Paper to be presented at the 15th meeting of the Ottawa Group’, pp. 10–12.

Melser, D. (2018), ‘Scanner data price indexes: Addressing some unresolved issues’, Journal of Business and Economic Statistics 36(03), 516–522.

Tianqi, C. and Carlo, G. (2016), Xgboost: A scalable tree boosting system, in ‘Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA, August 13-17, 2016. ACM’, p. 785–794.

Törnqvist, L. (1936), ‘The bank of Finland’s consumption price index’, Bank of Finland Monthly Bulletin pp. 1–8.

van Loon, K. V. and Roels, D. (2018), Integrating big data in the Belgian CPI, in ‘Paper presented at the meeting of the group of experts on consumer price indices, 8-9 May 2018, Geneva, Switzerland’.

von Auer, L. (2019), The nature of chain drift, in ‘Paper presented at the 17th Meeting of the Ottawa Group on Price Indices, 8–10 May 2019, Rio de Janerio, Brasil’.

von der Lippe, P. (2007), Index Theory and Price Statistics, Peter Lang, Berlin, Germany. Zhang, L.-C., Johansen, I. and Nyagaard, R. (2019), ‘Tests for price indices in a dynamic item universe’, Journal of Official Statistics 35(3), 683–697.

Back to top
© 2019–2024 Copyright by Statistics Poland, some rights reserved. Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0) Creative Commons — Attribution-ShareAlike 4.0 International — CC BY-SA 4.0