© Jacek Białek. Article available under the CC BY-SA 4.0 licence
ARTICLE
ABSTRACT
Although modern price index theory is based on comparisons of ratios of prices, quantities and expenditures, we may be more interested in the magnitude of differences in these characteristics in many business applications. The benefit of using these differences is that there is no problem associated with the occurrence of zero prices and quantities, a problem that arises when we work with ratios. In practice, we most often care about decomposing value difference into indicators of contributions from price and quantity differences. The best-known price and quantity indicators are the Bennet indicators, which are not transitive. Although there have been papers in the literature that propose a transitive version of the Bennet indicators, they deal with comparisons across firms in cross-section or panel contexts.
This paper revises the price and quantity Bennet indicators and their multilateral versions for the analysis of scanner data. Specifically, i nstead o f c onsidering c omparisons across firms, c ountries or r egions, the t ransitive versions of t he Bennet i ndicators a re a dapted to work on scanner data sets observed over a fixed time w indow. Since the scanner data sets have a high turnover of products, which can make it difficult to interpret the difference in sales values over the compared time periods, the paper also considers a matched sample approach. One of the objectives of the study is to compare bilateral and multilateral Bennet indicator results across all available products or strictly matched products over time. It also examines the impact of data filters used and the level of data aggregation on the price and quantity Bennet indicators. According to the best author’s knowledge, this study is a pioneer in the field of implementing the multilateral Bennet indicators in scanner data analysis.
KEYWORDS
scanner data, the Bennet indicator, transitivity, multilateral indicators.
REFERENCES
Balk, B. M., (2008). Price and Quantity Index Numbers: Models for Measuring Aggregate Change and Difference. Cambridge University Press.
Balk, B. M., (2016). A Review of Index Number Theory, pp. 1–24. John Wiley and Sons, Ltd.
Balk, B. M., Färe, R., and Grosskopf, S., (2004). The theory of economic price and quantity indicators. Economic Theory, 23(1), pp. 149–164.
Bennet, T. L., (1920). The theory of measurement of changes in cost of living. Journal of the Royal Statistical Society, 83(3), pp. 455–462.
Białek, J., (2021). Priceindices – a new R package for bilateral and multilateral price index calculations. Statistika – Statistics and Economy Journal, 36(2), pp. 122–141.
Białek, J., (2023). Improving quality of the scanner CPI: proposition of new multilateral methods. Quality and Quantity, 57, pp. 2893–2921. 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), pp. 73–86.
Chambers, R. G., (1998). Input and Output Indicators. Springer Netherlands, Dordrecht, pp. 241–271.
Chambers, R. G., (2001). Consumers’ surplus as an exact and superlative cardinal welfare indicator. International Economic Review, 42(1), pp. 105–119.
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, pp. 1:49–69.
Cross, R. M., Färe, R., (2009). Value data and the Bennet price and quantity indicators. Economics Letters, 102(1), pp. 9–21.
de Boer, P. and Rodrigues, J. F. D., (2020). Decomposition analysis: when to use which method? Economic Systems Research, 32(1), pp. 1–28.
de Haan, J., Krsinich, F., (2018). Time dummy hedonic and quality-adjusted unit value indexes: Do they really differ? Review of Income and Wealth, 64(4), pp. 757–776.
Diewert, W., (2005). Index number theory using differences rather than ratios. American Journal of Economics and Sociology, 64, pp. 311–360.
Diewert, W. E., (1976). Exact and superlative index numbers. Journal of econometrics, 4(2), pp. 115–145.
Diewert,W. E., (2020). The chain drift problem and multilateral indexes. Technical report, Discussion Paper 20-07, Vancouver School of Economics.
Eltetö, O., Köves, P., (1964). On a problem of index number computation relating to international comparison. Statisztikai Szemle, 42(10), pp. 507–518.
Eurostat, (2022). Guide on Multilateral Methods in the Harmonised Index of Consumer Prices. Luxembourg: Publications Office of the European Union.
Fisher, I., (1922). The making of index numbers: a study of their varieties, tests, and reliability, volume xxxi. Houghton Mifflin.
Fox, K. J., (2006). A method for transitive and additive multilateral comparisons: A transitive bennet indicator. Journal of Economics, 87(1), pp. 73–87.
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), pp. 97–99.
Gini, C., (1931). On the circular test of index numbers. Metron, 9(9), pp. 3–24.
International Labour Office, (2004). Consumer Price Index manual: Theory and practice. Geneva.
International Monetary Fund, (2020). Consumer Price Index manual: Concepts and methods. Washington, D.C.
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), pp. 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), pp. 414–420.
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), pp. 96–121.
Konü¸s, A., (1939). The problem of the true index of the cost of living. Econometrica, 7, pp. 10.
Szulc, B., (1964). Indices for multiregional comparisons. Przeglad statystyczny, 3, pp. 239–254.
Tianqi, C., 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, pp. 785–794.
van Loon, K. V., 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 der Lippe, P., (2007). Index Theory and Price Statistics. Peter Lang, Berlin, Germany