Proposition of a Hybrid Price Index Formula for the Consumer Price Index Measurement

• Autorzy: Jacek Białek
• Języki publikacji: EN

Abstrakty

EN

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. (original abstract)

Słowa kluczowe

EN

Price index; Consumer price index (CPI)

PL

Indeks cen; Indeks cen konsumpcyjnych

• Czasopismo: Equilibrium
• Rocznik: 2020
• Tom: 15
• Numer: nr 4
• Strony: 697--716

Twórcy

autor

Jacek Białek

• University of Lodz, Poland; Statistics Poland, Poland

Bibliografia

• 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.
• 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.
• Balk, M. (1995). Axiomatic price index theory: a survey. International Statistical Review, 63, 69-95. doi: 10.2307/1403778.
• Białek, J. (2012). Proposition of the general formula for price indices. Communications in Statistics: Theory and Methods, 41(5), 943-952. doi: 10.1080/03610926.2010.533238.
• Białek, J. (2014a). Simulation study of an original price index formula. Communications in Statistics - Simulation and Computation, 43(2), 285-297. doi: 10.1080/03610918.2012.700367.
• 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.
• 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.
• 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.
• Białek, J. (2019a). Remarks on geo-logarithmic price indices. Journal of Official Statistics, 35(2), 287-317. doi: 10.2478/JOS-2019-0014.
• Białek, J. (2020a). Remarks on price index methods for the CPI measurement using scanner data. Statistika - Statistics and Economy Journal, 100(1), 54-69.
• Białek, J. (2020b). Comparison of elementary price indices. Communications in Statistics - Theory and Methods, 49(19), 4787-4803, doi: 10.1080/03610926.2019.1609035.
• 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.
• Biggeri, G., & Ferrari (Eds.) (2010). Price indexes in time and space. Berlin Heidelberg: Springer-Verlag. doi: 10.1007/978-3-7908-2140-6.
• 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.
• Carli, G. (1804). Del valore e della proporzione de'metalli monetati. Scrittori Classici Italiani di Economia Politica, 13, 297-336.
• 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.
• Clements, K. W., & Izan, H. Y.(1987). The measurement of inflation: a stochastic approach. Journal of Business and Economic Statistics, 5, 339-350. doi: 10.1080/07350015.1987.10509598.
• Consumer Price Index Manual. Theory and practice (2004). ILO/IMF/OECD/UNECE/Eurostat/The World Bank. International Labour Office (ILO), Genev.
• Crawford, A. (1998). Measurement biases in the Canadian CPI: an update. Bank of Canada Review, Spring, 38-56.
• 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.
• 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.
• Diewert, W. E. (1976). Exact and superlative index numbers. Journal of Econometrics, 4, 114-145. doi: 10.1016/0304-4076(76)90009-9.
• Diewert W. E. (1993). The economic theory of index numbers: a survey. In W. E. Diewert & A. O. Nakamura (Eds.). Essays in index number theory, vol. 1. Amsterdam, 177-221.
• 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.
• 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.
• Dutot, C. F., (1738). Reflexions politiques sur les finances et le commerce. In The Hague: Les Freres Vaillant et Nicolas Prevost, Vol. 1.
• Eichhorn, W., & Voeller J. (1976). Theory of the price index. Fisher's test approach and generalizations. Berlin, Heidelberg, New York: Springer-Verlag.
• Eltetö, Ö., & Köves, P. (1964). On a problem of index number computation relating to international comparisons. Statisztikai Szemle, 42, 507-518.
• Feenstra, R. C., & Reinsdorf, M. B. (2007). Should exact index numbers have standard errors? Theory and application to Asian growth. In E. R. Berndt & C. R. Hulten (Eds.). Hard-to-measure goods and services: essays in honor of Zvi Griliches. National Bureau of Economic Research.
• Fisher, I. (1922). The making of index numbers. Boston: Houghton Mifflin.
• 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.
• Gini, C. (1931). On the circular test of index numbers. Metron, 9(9), 3-24.
• Greenlees, J. S. (2011). Improving the preliminary values of the chained CPI-U. Journal of Economic and Social Measurement, 36, 1-8. doi: 10.3233/jem-2011-0341.
• 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.
• 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.
• Jorgenson, D. W., & Slesnick D. T. (1983). Individual and social cost of living indexes. In W. E. Diewert & C. Montmarquette (Eds.). Price level measurement: proceedings of a conference sponsored by Statistics Canada. Ottawa: Statistics Canada, 241-336.
• 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.
• 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.
• Krsinich, F. (2014). The FEWS index: fixed effects with a window splice - nonrevisable 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.
• Laspeyres, E. (1871). Die Berechnung einer mittleren Waarenpreissteigerung. Jahrbücher für Nationalökonomie und Statistik, 16, 296-314.
• 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.
• Lloyd, P. J. (1975). Substitution effects and biases in non true price indices. American Economic Review, 65, 301-313.
• Martini, M. (1992). A general function of axiomatic index numbers. Journal of the Italian Statistics Society, 1(3), 359-376. doi: 10.1007/bf02589086.
• 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.
• Moulton, B. R. (1996). Constant elasticity cost-of-living index in share-relative form. Washington DC: U. S. Bureau of Labour Statistics, Mimeograph.
• Olt, B. (1996). Axiom und Struktur in der statistischen Preisindex theorie. Frankfurt: Peter Lang.
• Pollak, R. A. (1989). The theory of the cost-of-living index. Oxford: Oxford University Press.
• Santosa, F., & Symes, W. W. (1986). Linear inversion of band-limited reflection seismograms. Journal on Scientific and Statistical Computing, 7(4), 1307-1330. doi: 10.1137/0907087.
• Selvanathan, E. A., & Prasada Rao, D. S. (1994). Index numbers: a stochastic approach. Ann Arbor: University of Michigan Press.
• 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.
• Szulc, B. (1964). Indices for multiregional comparisons. Przegląd Statystyczny, 3, 239-254.
• 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.
• White, A. G. (1999). Measurement biases in Consumer Price Indexes. International Statistical Review, 67(3), 301-325. doi: 10.1111/j.1751-5823.1999.tb00451.x.
• 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.
• 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.
• Von der Lippe, P. (2007). Index theory and price statistics. Peter Lang, Frankfurt, Germany. doi: 10.3726/978-3-653-01120-3.
• 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.

Identyfikatory

DOI

10.24136/eq.2020.030