Proposition of a hybrid price index formula for the Consumer Price Index measurement
DOI:
https://doi.org/10.24136/eq.2020.030Keywords:
price index, Consumer Price Index, Lowe index, Young index, hybrid price indexAbstract
Research background: The Consumer Price Index (CPI) is a basic, commonly accepted and used measure of inflation. The index is a proxy for changes in the costs of household consumption and it assumes constant consumer utility. In practice, most statistical agencies use the Laspeyres price index to measure the CPI. The Laspeyres index does not take into account movements in the structure of consumption which may be consumers' response to price changes during a given time interval. As a consequence, the Laspeyres index can suffer from commodity substitution bias. The Fisher index is perceived as the best proxy for the COLI but it needs data on consumption from both the base and research period. As a consequence, there is a practical need to look for a proxy of the Fisher price index which does not use current expenditure shares as weights.
Purpose of the article: The general purpose of the article is to present a hybrid price index, the idea of which is based on the Young and Lowe indices. The particular aim of the paper is to discuss the usefulness of its special case with weights based on correlations between prices and quantities.
Methods: A theoretical background for the hybrid price index (and its geometric version) is constructed with the Lowe and Young price indices used as a starting point. In the empirical study, scanner data on milk, sugar, coffee and rice are utilized to show that the hybrid index can be a good proxy for the Fisher index, although it does not use the expenditures from the research period.
Findings & Value added: The empirical and theoretical considerations con-firm the hybrid nature of the proposed index, i.e. in a special case it forms the convex combination of the Young and Lowe indices. This study points out the usefulness of the proposed price index in the CPI measurement, especially when the target index is the Fisher formula. The proposed general hybrid price index formula is a new one in the price index theory. The proposed system of weights, which is based on the correlations between prices and quantities, is a novel idea in the price index methodology.
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Abe, N., & Prasada Rao, D. S. (2019). Multilateral Sato-Vartia index for international comparison of prices and real expenditures. Economic Letters, 183(C), 1-4. doi: 10.1016/j.econlet.2019.108535. DOI: https://doi.org/10.1016/j.econlet.2019.108535
View in Google Scholar
Armknecht, P., & Silver, M. (2012). Post-Laspeyres: the case for a new formula for compiling Consumer Price Indexes. International Monetary Fund (IMF) Working Paper, 12/105. DOI: https://doi.org/10.5089/9781475502954.001
View in Google Scholar
Balk, M. (1995). Axiomatic price index theory: a survey. International Statistical Review, 63, 69-95. doi: 10.2307/1403778. DOI: https://doi.org/10.2307/1403778
View in Google Scholar
Białek, J. (2012). Proposition of the general formula for price indices. Communications in Statistics: Theory and Methods, 41(5), 943-952. doi: 10.1080/0361092 6.2010.533238. DOI: https://doi.org/10.1080/03610926.2010.533238
View in Google Scholar
Białek, J. (2014a). Simulation study of an original price index formula. Communications in Statistics - Simulation and Computation, 43(2), 285-297. doi: 10.108 0/03610918.2012.700367. DOI: https://doi.org/10.1080/03610918.2012.700367
View in Google Scholar
Białek, J. (2015). Generalization of the Divisia price and quantity indices in a stochastic model with continuous time. Communications in Statistics: Theory and Methods, 44(2), 309-328. doi: 10.1080/03610926.2014.968738. DOI: https://doi.org/10.1080/03610926.2014.968738
View in Google Scholar
Białek, J. (2017a). Approximation of the Fisher price index by using the Lloyd?Moulton index: simulation study. Communications in Statistics - Simulation and Computation, 46(5), 3588-3598. doi: 10.1080/03610918.2015.1100737. DOI: https://doi.org/10.1080/03610918.2015.1100737
View in Google Scholar
Białek, J. (2017b). Approximation of the Fisher price index by using Lowe, Young and AG Mean indices. Communications in Statistics - Simulation and Computation, 46(8), 6454-6467. doi: 10.1080/03610918.2016.1205608. DOI: https://doi.org/10.1080/03610918.2016.1205608
View in Google Scholar
Białek, J. (2019a). Remarks on geo-logarithmic price indices. Journal of Official Statistics, 35(2), 287-317. doi: 10.2478/JOS-2019-0014. DOI: https://doi.org/10.2478/jos-2019-0014
View in Google Scholar
Białek, J. (2020a). Remarks on price index methods for the CPI measurement using scanner data. Statistika ? Statistics and Economy Journal, 100(1), 54-69.
View in Google Scholar
Białek, J. (2020b). Comparison of elementary price indices. Communications in Statistics - Theory and Methods, 49(19), 4787-4803, doi: 10.1080/03610926. 2019.1609035. DOI: https://doi.org/10.1080/03610926.2019.1609035
View in Google Scholar
Białek, J., & Bobel, A. (2019). Comparison of price index methods for CPI measurement using scanner data. Paper presented at the 16th Meeting of the Ottawa Group on Price Indices, Rio de Janeiro, Brazil.
View in Google Scholar
Biggeri, G., & Ferrari (eds.) (2010). Price indexes in time and space. Berlin Heidelberg: Springer-Verlag. doi: 10.1007/978-3-7908-2140-6. DOI: https://doi.org/10.1007/978-3-7908-2140-6
View in Google Scholar
Boskin, M. J., Dulberger, E. R., Gordon, R. J., Griliches, Z., & Jorgenson, D. (1996). Toward a more accurate measure of the cost of living. Final Report to the Senate Finance Committee from the Advisory Commission to Study the Consumer Price Index.
View in Google Scholar
Carli, G. (1804). Del valore e della proporzione de?metalli monetati. Scrittori Classici Italiani di Economia Politica, 13, 297-336.
View in Google Scholar
Chessa, A. G. (2017). Comparisons of QU-GK indices for different lengths of the time window and updating methods. Paper prepared for the second meeting on multilateral methods organized by Eurostat, Luxembourg, 14-15 March 2017. Statistics Netherlands.
View in Google Scholar
Clements, K. W., & Izan, H. Y.(1987). The measurement of inflation: a stochastic approach. Journal of Business and Economic Statistics, 5, 339-350. doi: 10.108 0/07350015.1987.10509598. DOI: https://doi.org/10.1080/07350015.1987.10509598
View in Google Scholar
Consumer Price Index Manual. Theory and practice (2004). ILO/IMF/OECD /UNECE/Eurostat/The World Bank. International Labour Office (ILO), Genev.
View in Google Scholar
Crawford, A. (1998). Measurement biases in the Canadian CPI: an update. Bank of Canada Review, Spring, 38?56.
View in Google Scholar
de Haan, J., & Krsinich, F. (2017). Time dummy hedonic and quality-adjusted unit value indices: do they really differ? Review of Income and Wealth, 64(4), 757-776. doi: 10.1111/roiw.12304. DOI: https://doi.org/10.1111/roiw.12304
View in Google Scholar
de Haan, J., Willenborg, L., & Chessa, A. G. (2016). An overview of price index methods for scanner data. Paper presented at the Meeting of the Group of Experts on Consumer Price Indices, 2-4 May 2016, Geneva, Switzerland.
View in Google Scholar
Diewert, W. E. (1976). Exact and superlative index numbers. Journal of Econometrics, 4, 114-145. doi: 10.1016/0304-4076(76)90009-9. DOI: https://doi.org/10.1016/0304-4076(76)90009-9
View in Google Scholar
Diewert W. E. (1993). The economic theory of index numbers: a survey. In W. E. Diewert and A. O. Nakamura (Eds.). Essays in index number theory, vol. 1. Amsterdam, 177-221.
View in Google Scholar
Diewert, W. E., (2005). Weighted country product dummy variable regressions and index number formulae. Review of Income and Wealth, 51, 561-570. doi: 10.1111/j.1475-4991.2005.00168.x. DOI: https://doi.org/10.1111/j.1475-4991.2005.00168.x
View in Google Scholar
Diewert, W. E., & Fox, K. J. (2017). Substitution bias in multilateral methods for CPI construction using scanner data. School of Economics, University of British Columbia, Discussion Paper, 17-02. DOI: https://doi.org/10.2139/ssrn.3276457
View in Google Scholar
Dutot, C. F., (1738). Reflexions politiques sur les finances et le commerce. In The Hague: Les Freres Vaillant et Nicolas Prevost, Vol. 1.
View in Google Scholar
Eichhorn, W., & Voeller J. (1976). Theory of the price index. Fisher?s test approach and generalizations. Berlin, Heidelberg, New York: Springer-Verlag. DOI: https://doi.org/10.1007/978-3-642-45492-9
View in Google Scholar
Eltetö, Ö., & Köves, P. (1964). On a problem of index number computation relating to international comparisons. Statisztikai Szemle, 42, 507-518.
View in Google Scholar
Feenstra, R. C., & Reinsdorf, M. B. (2007). Should exact index numbers have standard errors? Theory and application to Asian growth. In E. R. Berndt and C. R. Hulten (Eds.). Hard-to-measure goods and services: essays in honor of Zvi Griliches. National Bureau of Economic Research. DOI: https://doi.org/10.7208/chicago/9780226044507.003.0017
View in Google Scholar
Fisher, I. (1922). The making of index numbers. Boston: Houghton Mifflin.
View in Google Scholar
Geary, R. G. (1958). A note on comparisons of exchange rates and purchasing power between countries. Journal of the Royal Statistical Society Series A, 121, 97-99. doi: 10.2307/2342991. DOI: https://doi.org/10.2307/2342991
View in Google Scholar
Gini, C. (1931). On the circular test of index numbers. Metron, 9(9), 3-24.
View in Google Scholar
Greenlees, (2011). Improving the preliminary values of the chained CPI-U. Journal of Economic and Social Measurement, 36, 1?18. doi: 10.3233/jem-2011-0341. DOI: https://doi.org/10.3233/JEM-2011-0341
View in Google Scholar
Hałka, A., & Leszczyńska, A. (2011). The strengths and weaknesses of the Consumer Price Index: estimates of the measurement pias for Poland. Gospodarka Narodowa, 9, 51-75. doi: 10.33119/gn/101086. DOI: https://doi.org/10.33119/GN/101086
View in Google Scholar
Jevons, W. S. (1865). The variation of prices and the value of the currency since 1782. Journal of the Statistical Society of London, 28, 294-320. DOI: https://doi.org/10.2307/2338419
View in Google Scholar
Jorgenson, D. W., & Slesnick D. T. (1983). Individual and social cost of living indexes. In W. E. Diewert and C. Montmarquette (Eds.). Price level measurement: proceedings of a conference sponsored by Statistics Canada. Ottawa: Statistics Canada, 241-336.
View in Google Scholar
Juszczak, A. (2020). Estimation of the optimal parameter of Delay in Young and Lowe indices in the Fisher index approximation. Statistika ? Statistics and Economy Journal, 1, 32-53.
View in Google Scholar
Khamis, S. H. (1972). A new system of index numbers for national and international purposes. Journal of the Royal Statistical Society Series A, 135, 96-121. doi: 10.2307/2345041. DOI: https://doi.org/10.2307/2345041
View in Google Scholar
Krsinich, F. (2014). The FEWS index: fixed effects with a window splice ? non-revisable quality-adjusted price indices with no characteristic information. Paper presented at the meeting of the group of experts on consumer price indices, 26-28 May 2014, Geneva, Switzerland.
View in Google Scholar
Laspeyres, E. (1871). Die Berechnung einer mittleren Waarenpreissteigerung. Jahrbücher für Nationalökonomie und Statistik, 16, 296-314. DOI: https://doi.org/10.1515/jbnst-1871-0124
View in Google Scholar
Lent, J., & Dorfman, A. H. (2009). Using a weighted average of base period price indexes to approximate a superlative index. Journal of Official Statistics, 25(1), 139-149.
View in Google Scholar
Lloyd, P. J. (1975). Substitution effects and biases in non true price indices. American Economic Review, 65, 301-313.
View in Google Scholar
Martini, M. (1992). A general function of axiomatic index numbers. Journal of the Italian Statistics Society, 1(3), 359-376. doi: 10.1007/bf02589086. DOI: https://doi.org/10.1007/BF02589086
View in Google Scholar
Mehrhoff, J. (2019). Towards a new paradigm for scanner data price indices: applying big data techniques to big data. Paper presented at the 16th Meeting of the Ottawa Group on Price Indices, Rio de Janeiro, Brazil.
View in Google Scholar
Moulton, B. R. (1996). Constant elasticity cost-of-living index in share-relative form. Washington DC: U. S. Bureau of Labour Statistics, Mimeograph.
View in Google Scholar
Olt, B. (1996). Axiom und Struktur in der statistischen Preisindex theorie. Frankfurt: Peter Lang.
View in Google Scholar
Pollak, R. A. (1989). The theory of the cost-of-living index. Oxford: Oxford University Press.
View in Google Scholar
Santosa, F., & Symes, W. W. (1986). Linear inversion of band-limited re?ection seismograms. Journal on Scienti?c and Statistical Computing, 7(4), 1307?1330. doi: 10.1137/0907087. DOI: https://doi.org/10.1137/0907087
View in Google Scholar
Selvanathan, E. A., & Prasada Rao, D. S. (1994). Index numbers: a stochastic approach. Ann Arbor: The University of Michigan Press. DOI: https://doi.org/10.3998/mpub.13784
View in Google Scholar
Shapiro, M. D., & Wilcox, D. W. (1997). Alternative strategies for aggregating prices in the CPI. Federal Reserve Bank of St. Louis Review, 79(3), 113?125. DOI: https://doi.org/10.20955/r.79.113-126
View in Google Scholar
Szulc, B. (1964). Indices for multiregional comparisons. Przegląd Statystyczny, 3, 239-254.
View in Google Scholar
Tibshirani, R., Bien, J., Friedman, J., Hastie, T., Simon, N., Taylor, J., & Tibshirani, R. J. (2012). Strong rules for discarding predictors in lasso-type problems. Journal of the Royal Statistical Society: Series B, 74(2), 245?266. doi: 10.1111/ j.1467-9868.2011.01004.x. DOI: https://doi.org/10.1111/j.1467-9868.2011.01004.x
View in Google Scholar
White, A. G. (1999). Measurement biases in Consumer Price Indexes. International Statistical Review, 67(3), 301-325. doi: 10.1111/j.1751-5823.1999.tb00 451.x. DOI: https://doi.org/10.1111/j.1751-5823.1999.tb00451.x
View in Google Scholar
Van Loon, K. V., & Roels, D. (2018). Integrating big data in the Belgian CPI. Paper presented at the meeting of the group of experts on consumer price indices, 8-9 May 2018, Geneva, Switzerland.
View in Google Scholar
Von Auer L. (2019). The nature of chain drift. Paper presented at the 17th Meeting of the Ottawa Group on Price Indices, 8 ? 10 May 2019, Rio de Janerio, Brasil.
View in Google Scholar
Von der Lippe, P. (2007). Index theory and price statistics. Peter Lang, Frankfurt, Germany. doi: 10.3726/978-3-653-01120-3. DOI: https://doi.org/10.3726/978-3-653-01120-3
View in Google Scholar
Zhang, L., Johansen, I., & Nyagaard, R. (2019). Tests for price indices in a dynamic item universe. Journal of Official Statistics, 35(3), 683-697. doi: 10.2478/jos-2019-0028. DOI: https://doi.org/10.2478/jos-2019-0028
View in Google Scholar
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