Abstract
Index numbers are used to aggregate detailed information on prices and quantities into scalar measures of price and quantity levels or their growth. The article reviews four main approaches to bilateral index number theory where two price and quantity vectors are to be aggregated: fixed basket and average of fixed baskets, stochastic, test or axiomatic and economic approaches. The article also considers multilateral index number theory where it is necessary to construct price and quantity aggregates for more than two value aggregates. A final section notes some of the recent literature on related aspects of index number theory.
This chapter was originally published in The New Palgrave Dictionary of Economics, 2nd edition, 2008. Edited by Steven N. Durlauf and Lawrence E. Blume
Bibliography
Afriat, S.N. 1972. The theory of international comparisons of real income and prices. In International comparisons of prices and outputs, ed. D.J. Daley. New York: Columbia University Press.
Allen, R.G.D. 1949. The economic theory of index numbers. Economica NS 16: 197–203.
Alterman, W.F., W.E. Diewert, and R.C. Feenstra. 1999. International trade price indexes and seasonal commodities. Washington, DC: Bureau of Labor Statistics.
Armknecht, P.A., and W.E. Diewert. 2004. Treatment of seasonal products. In Producer price index manual: Theory and practice. Washington, DC: International Monetary Fund.
Balk, B.M. 1980. A method for constructing price indices for seasonal commodities. Journal of the Royal Statistical Society, Series A 143: 68–75.
Balk, B.M. 1985. A simple characterization of Fisher’s price index. Statistische Hefte 26: 59–63.
Balk, B.M. 1995. Axiomatic price index theory: A survey. International Statistical Review 63: 69–93.
Balk, B.M. 1996. A comparison of ten methods for multilateral international price and volume comparisons. Journal of Official Statistics 12: 199–222.
Balk, B.M. 1998. Industrial price, quantity and productivity indices. Boston: Kluwer.
Balk, B.M. 2003. The residual: On monitoring and benchmarking firms, industries, and economies with respect to productivity. Journal of Productivity Analysis 20: 5–47.
Balk, B.M. 2005. Annual and quarterly productivity measures. Paper presented at the Economic Measurement Group Workshop, Coogee, 12–13 Dec.
Balk, B.M., and W.E. Diewert. 2001. A characterization of the Törnqvist priceindex. Economics Letters 73: 279–281.
Balk, B.M., and W.E. Diewert. 2004. The Lowe consumer price index and its substitution bias. Discussion Paper No. 04–07. Department of Economics, University of British Columbia.
Bennet, T.L. 1920. The theory of measurement of changes in cost of living. Journal of Royal Statistical Society 83: 455–462.
Boskin, M.J. (chair), E.R. Dullberger, R.J. Gordon, Z. Griliches, and D.W. Jorgenson. 1996. Final report of the commission to study the consumer price index. US Senate, Committee on Finance. Washington, DC: US Government Printing Office.
Bowley, A.L. 1899. Wages, nominal and real. In Dictionary of Political Economy, ed. R.H.L. Palgrave, vol. vol. 3. London: Macmillan.
Bowley, A.L. 1901. Elements of statistics. Westminster: P.S. King and Son.
Bowley, A.L. 1919. The measurement of changes in the cost of living. Journal of the Royal Statistical Society 82: 343–372.
Bowley, A.L. 1928. Notes on index numbers. Economic Journal 38: 216–237.
Cage, R., J.S. Greenlees, and P. Jackman. 2003. Introducing the chained CPI. Paper presented at the Seventh Meeting of the International Working Group on Price Indices, (Ottawa Group), Paris.
Carli, G.-R. 1764. Del valore e dellaproporzione de’ metallimonetati. In Scrittoriclassiciitaliani di economiapolitica, vol. 13. Milano: G.G. Destefanis, 1804.
Caves, D.W., L.R. Christensen, and W.E. Diewert. 1982a. Multilateral comparisons of output, input and productivity using superlative index numbers. Economic Journal 92: 73–86.
Caves, D.W., L.R. Christensen, and W.E. Diewert. 1982b. The economic theory of index numbers and the measurement of input, output and productivity. Econometrica 50: 1393–1414.
Christensen, L.R., D.W. Jorgenson, and L.J. Lau. 1971. Conjugate duality and the transcendental logarithmic production function. Econometrica 39: 255–256.
Clements, K.W., H.Y. Izan, and E.A. Selvanathan. 2006. Stochastic index numbers: A review. International Statistical Review 74: 235–270.
Dalén, J. 1992. Computing elementary aggregates in the Swedish consumer price index. Journal of Official Statistics 8: 129–147.
de Haan, J. 2004a. Direct and indirect time dummy approaches to hedonic price measurement. Journal of Economic and Social Measurement 29: 427–443.
de Haan, J. 2004b. Hedonic regression: The time dummy index as a special case of the imputation Törnqvist index. Paper presented at the 8th Ottawa Group Meeting, Helsinki.
Diewert, W.E. 1974. Applications of duality theory. In Frontiers of quantitative economics, ed. M.D. Intriligator and D.A. Kendrick, vol. 2. Amsterdam: North-Holland.
Diewert, W.E. 1976. Exact and superlative index numbers. Journal of Econometrics 4: 114–145.
Diewert, W.E. 1978. Superlative index numbers and consistency in aggregation. Econometrica 46: 883–900.
Diewert, W.E. 1981. The economic theory of index numbers: A survey. In Essays in the theory and measurement of consumer behaviour in honour of Sir Richard Stone, ed. A. Deaton. London: Cambridge University Press.
Diewert, W.E. 1983a. The theory of the cost of living index and the measurement of welfare change. In Price level measurement, ed. W.E. Diewert and C. Montmarquette. Ottawa: Statistics Canada.
Diewert, W.E. 1983b. The theory of the output price index and the measurement of real output change. In Price level measurement, ed. W.E. Diewert and C. Montmarquette. Ottawa: Statistics Canada.
Diewert, W.E. 1983c. The treatment of seasonality in a cost of living index. In Price level measurement, ed. W.E. Diewert and C. Montmarquette. Ottawa: Statistics Canada.
Diewert, W.E. 1986. Microeconomic approaches to the theory of international comparisons. Technical Working Paper No. 53. Cambridge, MA: NBER.
Diewert, W.E. 1987. Index numbers. In The New Palgrave: A dictionary of economics, ed. J. Eatwell, M. Milgate, and P. Newman, vol. 2. London: Macmillan.
Diewert, W.E. 1988. Test approaches to international comparisons. In Measurement in economics, ed. W. Eichhorn. Heidelberg: Physica-Verlag.
Diewert, W.E. 1992a. Fisher ideal output, input and productivity indexes revisited. Journal of Productivity Analysis 3: 211–248.
Diewert, W.E. 1992b. Exact and superlative welfare change indicators. Economic Inquiry 30: 565–582.
Diewert, W.E. 1993a. The early history of price index research. In Essays in index number theory, ed. W.E. Diewert and A.O. Nakamura. Amsterdam: North-Holland.
Diewert, W.E. 1993b. Symmetric means and choice under uncertainty. In Essays in index number theory, ed. W.E. Diewert and A.O. Nakamura. Amsterdam: North- Holland.
Diewert, W.E. 1995a. Axiomatic and economic approaches to elementary price indexes. Discussion Paper No. 95-01. Department of Economics, University of British Columbia.
Diewert, W.E. 1995b. On the stochastic approach to index numbers. Discussion Paper No. 95-31. Department of Economics, University of British Columbia.
Diewert, W.E. 1997. Commentary on Mathew D. Shapiro and David W. Wilcox: Alternative strategies for aggregating price in the CPI. Federal Reserve Bank of St. Louis Review 79: 127–137.
Diewert, W.E. 1998a. Index number issues in the consumer price index. Journal of Economic Perspectives 12 (1): 47–58.
Diewert, W.E. 1998b. High inflation, seasonal commodities and annual index numbers. Macroeconomic Dynamics 2: 456–471.
Diewert, W.E. 1999a. Index number approaches to seasonal adjustment. Macroeconomic Dynamics 3: 48–68.
Diewert, W.E. 1999b. Axiomatic and economic approaches to multilateral comparisons. In International and interarea comparisons of income, output and prices, ed. A. Heston and R.E. Lipsey. Chicago: University of Chicago Press.
Diewert, W.E. 2001. The consumer price index and index number purpose. Journal of Economic and Social Measurement 27: 167–248.
Diewert, W.E. 2002a. The quadratic approximation lemma and decompositions of superlative indexes. Journal of Economic and Social Measurement 28: 63–88.
Diewert, W.E. 2002b. Harmonized indexes of consumer prices: Their conceptual foundations. Swiss Journal of Economics and Statistics 138: 547–637.
Diewert, W.E. 2003. Hedonic regressions: a review of some unresolved issues. Paper presented at the 7th Meeting of the Ottawa Group, Paris.
Diewert, W.E. 2004. A new axiomatic approach to index number theory. Discussion Paper No. 04-05. Department of Economics, University of British Columbia.
Diewert, W.E. 2005a. Index number theory using differences instead of ratios. American Journal of Economics and Sociology 64: 311–360.
Diewert, W.E. 2005b. Weighted country product dummy variable regressions and index number formulae. Review of Income and Wealth 51: 561–571.
Diewert, W.E. 2005c. Adjacent period dummy variable hedonic regressions and bilateral index number theory. Discussion Paper No. 05-11. Department of Economics, University of British Columbia.
Diewert, W.E. 2007a. Similarity indexes and criteria for spatial linking. In Purchasing power parities of currencies: Recent advances in methods and applications, ed. D.S. Prasada Rao. Cheltenham: Edward Elgar.
Diewert, W.E. 2007b. On the stochastic approach to linking the regions in the ICP. In Price and productivity measurement, ed. W.E. Diewert et al. Vancouver: Trafford Press.
Diewert, W.E., and K.J. Fox. 2004. On the estimation of returns to scale, technical progress and monopolistic markups. Discussion Paper No. 04-09. Department of Economics, University of British Columbia.
Diewert, W.E., and D. Lawrence. 2006. Measuring the contributions of productivity and terms of trade to Australia’s economic welfare. Report by Meyrick and Associates to the Australian Government. Canberra: Productivity Commission.
Diewert, W.E., and C.J. Morrison. 1986. Adjusting output and productivity indexes for changes in the terms of trade. Economic Journal 96: 659–679.
Diewert, W.E., and A.O. Nakamura. 2003. Index number concepts, measures and decompositions of productivity growth. Journal of Productivity Analysis 19: 127–159.
Edgeworth, F.Y. 1888. Some new methods of measuring variation in general prices. Journal of the Royal Statistical Society 51: 346–368.
Edgeworth, F.Y. 1923. The doctrine of index numbers according to Mr. Correa Walsh. Economic Journal 33: 343–351.
Edgeworth, F.Y. 1925. Papers relating to political economy. Vol. 1. New York: Burt Franklin.
Eichhorn, W. 1978. Functional equations in economics. London: Addison-Wesley.
Eichhorn, W., and J. Voeller. 1976. Theory of the price index. Berlin: Springer.
Eltetö, O., and P. Köves. 1964. On a problem of index number computation relating to international comparison. Statisztikai Szemle 42: 507–518.
Fisher, I. 1911. The purchasing power of money. London: Macmillan.
Fisher, W.C. 1913. The tabular standard in Massachusetts history. Quarterly Journal of Economics 27: 417–451.
Fisher, I. 1921. The best form of index number. Journal of the American Statistical Association 17: 535–537.
Fisher, I. 1922. The making of index numbers. Boston: Houghton Mifflin.
Fox, K.J., and U. Kohli. 1998. GDP growth, terms of trade effects and total factor productivity. The Journal of International Trade and Economic Development 7: 87–110.
Frisch, R. 1936. Annual survey of economic theory: The problem of index numbers. Econometrica 4: 1–39.
Funke, H., and J. Voeller. 1978. A note on the characterization of Fisher’s ideal index. In Theory and applications of economic indices, ed. W. Eichhorn et al. Würzburg: Physica-Verlag.
Funke, H., G. Hacker, and J. Voeller. 1979. Fisher’s circular test reconsidered. Schweizerische Zeitschrift für Volkswirtshaft und Statistik 115: 677–687.
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.
Gini, C. 1924. Quelques considérations au sujet de la construction des nombres indices des prix et des questions analogues. Metron 4: 3–162.
Gini, C. 1931. On the circular test of index numbers. Metron 9: 3–24.
Hicks, J.R. 1941–42. Consumers’ surplus and index numbers. Review of Economic Studies 9, 126–137.
Hill, T.P. 1988. Recent developments in index number theory and practice. OECD Economic Studies 10: 123–148.
Hill, T.P. 1993. Price and volume measures. In System of national accounts 1993. Luxembourg/Paris/New York/Washington, DC: Eurostat/IMF/OECD/UN/World Bank.
Hill, T.P. 1996. Inflation accounting. Paris: OECD.
Hill, R.J. 1997. A taxonomy of multilateral methods for making international comparisons of prices and quantities. Review of Income and Wealth 43: 49–69.
Hill, R.J. 1999a. Comparing price levels across countries using minimum spanning trees. The Review of Economics and Statistics 81: 135–142.
Hill, R.J. 1999b. International comparisons using spanning trees. In International and interarea comparisons of income, output and prices, Studies in income and wealth, NBER, ed. A. Heston and R.E. Lipsey, vol. 61. Chicago: University of Chicago Press.
Hill, R.J. 2001. Measuring inflation and growth using spanning trees. International Economic Review 42: 167–185.
Hill, R.J. 2004. Constructing price indexes across space and time: The case of the European Union. American Economic Review 94: 1379–1410.
Hill, R.J. 2006a. Superlative index numbers: Not all of them are super. Journal of Econometrics 130: 25–43.
Hill, R.J. 2006b. When does chaining reduce the Paasche-Laspeyres spread? An application to scanner data. Review of Income and Wealth 52: 309–329.
Hill, R.J. 2007. Comparing per capita income levels across countries using spanning trees: Robustness, prior restrictions, hybrids and hierarchies. In Purchasing power parities of currencies: Recent advances in methods and applications, ed. D.S. Prasada Rao. Cheltenham: Edward Elgar.
ILO/IMF/OECD/UNECE/Eurostat/World Bank. 2004. In Consumer price index manual: Theory and practice, ed. P. Hill. Geneva: International Labour Office.
IMF/ILO/OECD/UNECE/Eurostat/World Bank. 2004. In Producer price index manual: Theory and practice, ed. P. Armknecht. Washington, DC: International Monetary Fund.
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. Reprinted in Investigations in currency and finance. London: Macmillan and Co, 1884.
Jevons, W.S. 1884. A serious fall in the value of gold ascertained and its social effects set forth (1863). In Investigations in Currency and Finance. London: Macmillan and Co.
Jorgenson, D.W., and Z. Griliches. 1967. The explanation of productivity change. Review of Economic Studies 34: 249–283.
Jorgenson, D.W., and Z. Griliches. 1972. Issues in growth accounting: A reply to Edward F. Denison. Survey of Current Business 52: 65–94.
Keynes, J.M. 1930. Treatise on money. Vol. 1. London: Macmillan.
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.
Kohli, U. 1990. Growth accounting in the open economy: Parametric and nonparametric estimates. Journal of Economic and Social Measurement 16: 125–136.
Kohli, U. 2003. Growth accounting in the open economy: International comparisons. International Review of Economics and Finance 12: 417–435.
Kohli, U. 2004. Real GDP, real domestic income and terms of tradechanges. Journal of International Economics 62: 83–106.
Kohli, U. 2007. Terms of trade, real exchange rates, and trading gains. In Price and productivity measurement, ed. W.E. Diewert et al. Vancouver: Trafford Press.
Konüs, A.A. 1924. The problem of the true index of the cost of living. Trans. in Econometrica 7 (1939), 10–29.
Konüs, A.A., and S.S. Byushgens. 1926. K probleme pokupatelnoi cili deneg. Voprosi konyunkturi 2: 151–172.
Kravis, I.B. 1984. Comparative studies of national incomes and prices. Journal of Economic Literature 22: 1–39.
Kravis, I.B., Z. Kenessey, A. Heston, and R. Summers. 1975. A system of international comparisons of gross product and purchasing power. Baltimore: Johns Hopkins University Press.
Laspeyres, E. 1871. Die berechnung einer mittleren waarenpreissteigerung. Jahrbücher für Nationalökonomie und Statistik 16: 296–314.
Lebow, D.E., and J.B. Rudd. 2003. Measurement error in the consumer price index: Where do we stand? Journal of Economic Literature 41: 159–201.
Lehr, J. 1885. Beitrage zur Statistik der Preise. Frankfurt: J.D. Sauerlander.
Lowe, J. 1823. The present State of England in regard to agriculture, trade and finance. 2nd ed. London: Longman, Hurst, Rees, Orme and Brown.
Malmquist, S. 1953. Index numbers and indifference surfaces. Trabajos de Estadística 4: 209–242.
Marshall, A. 1887. Remedies for fluctuations of general prices. Contemporary Review 51: 355–375.
Montgomery, J.K. 1929. Is there a theoretically correct price index of a group of commodities? Rome: Roma L’Universale Tipogr. Poliglotta (privately printed).
Montgomery, J.K. 1937. The mathematical problem of the price index. Orchard House: P.S. King & Son.
Morrison, C.J., and W.E. Diewert. 1990. Productivity growth and changes in the terms of trade in Japan and the United States. In Productivity growth in Japan and the United States, ed. C.R. Hulten. Chicago: University of Chicago Press.
Moulton, B.R., and E.P. Seskin. 1999. A preview of the 1999 comprehensive revision of the national income and product accounts. Survey of Current Business 79: 6–17.
Paasche, H. 1874. Über die preisentwicklung der letzten Jahre nach den hamburger borsennotirungen. Jahrbücher für Nationalökonomie und Statistik 12: 168–178.
Pierson, N.G. 1895. Index numbers and appreciation of gold. Economic Journal 5: 329–335.
Pierson, N.G. 1896. Further considerations on index-numbers. Economic Journal 6: 127–131.
Pollak, R.A. 1980. Group cost-of-living indexes. American Economic Review 70: 273–278.
Pollak, R.A. 1981. The social cost-of-living index. Journal of Public Economics 15: 311–336.
Pollak, R.A. 1983. The theory of the cost-of-living index. In Price level measurement, ed. W.E. Diewert and C. Montmarquette. Ottawa: Statistics Canada.
Rao, D.S.P. 1990. A system of log-change index numbers for multilateral comparisons. In Comparisons of prices and real products in Latin America, ed. J. Salazar-Carillo and D.S. PrasadaRao. New York: Elsevier.
Reinsdorf, M. 1993. The effect of outlet price differentials on the U.S. consumer price index. In Price measurement and their uses, ed. M.F. Foss, M.E. Manser, and A.H. Young. Chicago: University of Chicago Press.
Reinsdorf, M. 2007. Axiomatic price index theory. In Measurement in economics: A handbook, ed. M.J. Boumans. Amsterdam: Elsevier.
Reinsdorf, M., and A. Dorfman. 1999. The monotonicity axiom and the Sato-Vartia index. Journal of Econometrics 90: 45–61.
Reinsdorf, M.B., W.E. Diewert, and C. Ehemann. 2002. Additive decompositions for the fisher, Törnqvist and geometric mean indexes. Journal of Economic and Social Measurement 28: 51–61.
Ruggles, R. 1967. Price indexes and international price comparisons. In Ten economic studies in the tradition of Irving Fisher, ed. W. Fellner. New York: Wiley.
Samuelson, P.A. 1947. Foundations of economic analysis. Cambridge, MA: Harvard University Press.
Samuelson, P.A., and S. Swamy. 1974. Invariant economic index numbers and canonical duality: Survey and synthesis. American Economic Review 64: 566–593.
Schreyer, P. 2001. OECD productivity manual: A guide to the measurement of industry-level and aggregate productivity growth. Paris: OECD.
Schultze, C.L., and C. Mackie. 2002. At what price? Conceptualizing and measuring cost-of living and price indices. Washington, DC: National Academy Press.
Scrope, G.P. 1833. Principles of political economy. London: Longman, Rees, Orme, Brown, Green and Longman.
Selvanathan, E.A., and D.S. PrasadaRao. 1994. Index numbers: A stochastic approach. Ann Arbor: University of Michigan Press.
Shephard, R.W. 1953. Cost and production functions. Princeton: Princeton University Press.
Sidgwick, H. 1883. The principles of political economy. London: Macmillan.
Silver, M. 2003. The use of weights in hedonic regressions: The measurement of quality adjusted price changes. Room document for the 7th meeting of the Ottawa Group, Paris.
Silver, M., and S. Heravi. 2005. A failure in the measurement of inflation: Results from a hedonic and matched experiment using scanner data. Journal of Business and Economic Statistics 23: 269–281.
Summers, R. 1973. International comparisons with incomplete data. Review of Income and Wealth 29: 1–16.
Szulc, B. 1964. Indices for multiregional comparisons. Przeglad Statystyczny 3: 239–254.
Szulc, B.J. 1983. Linking price index numbers. In Price level measurement, ed. W.E. Diewert and C. Montmarquette. Ottawa: Statistics Canada.
Theil, H. 1967. Economics and information theory. Amsterdam: North-Holland.
Törnqvist, L. 1936. The bank of Finland’s consumption price index. Bank of Finland Monthly Bulletin 10: 1–8.
Törnqvist, L., and E. Törnqvist. 1937.Vilket är förhällandet mellan finska markens och svenska kronans köpkraft? Ekonomiska Samfundets Tidskrift 39, 1–39. Repr. In Collected Scientific Papers of Leo Törnqvist. Helsinki: Research Institute of the Finnish Economy, 1981.
Triplett, J.E. 2004. Handbook on hedonic indexes and quality adjustments in price indexes: Special application to information technology products. Working Paper 2004/9. Paris: Directorate for Science, Technology and Industry, OECD.
Triplett, J.E., and R.J. McDonald. 1977. Assessing the quality error in output measures: the case of refrigerators. Review of Income and Wealth 23: 137–156.
Turvey, R. 1979. The treatment of seasonal items in consumer price indices, Bulletin of labour statistics, fourth quarter, 13–33. Geneva: International Labour Office.
US Bureau of Labor Statistics. 1983. Trends in multifactor productivity, 1948–81, Bulletin 2178. Washington, DC: U.S. Government Printing Office.
van IJzeren, J. 1957. Three methods of comparing the purchasing power of currencies, Statistical studies. Vol. 7. The Hague: Central Bureau of Statistics.
van IJzeren, J. 1983. Index numbers for binary and multilateral comparisons. Statistical studies no. 34. The Hague: Central Bureau of Statistics.
van IJzeren, J. 1987. Bias in international index numbers: A mathematical elucidation. Dissertation for the Hungarian Academy of Sciences. The Hague: Koninklijke Bibliotheek.
Vartia, Y.O. 1976. Relative changes and index numbers. Helsinki: Research Institute of the Finnish Economy.
Vogt, A. 1980. Der Zeit und der Faktorumkehrtestals ‘Finders of Tests’. StatistischeHefte 21: 66–71.
Vogt, A., and J. Barta. 1997. The making of tests for index numbers. Heidelberg: Physica-Verlag.
von der Lippe, P. 2001. Chain indices: A study in price index theory, spectrum of federal statistics. Vol. 16. Wiesbaden: Statistisches Bundesamt.
Walsh, C.M. 1901. The measurement of general exchange value. New York: Macmillan and Co..
Walsh, C.M. 1921a. The problem of estimation. London: P.S. King &Son.
Walsh, C.M. 1921b. Discussion. Journal of the American Statistical Association 17: 537–544.
Westergaard, H. 1890. Die Grundzüge der Theorie der Statistik. Jena: Fischer.
Wynne, M.A. 1997. Commentary on measuring short run inflation for central bankers. Federal Reserve Bank of St. Louis Review 79: 161–167.
Young, A. 1812. An inquiry into the progressive value of money in England as marked by the price of agricultural products. London: Macmillan.
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Diewert, W.E. (2008). Index Numbers. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95121-5_940-2
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