The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Index Numbers

  • W. Erwin Diewert
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_940

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.

Keywords

Allen quantity index Bowley, A.L. Carli price index Chain indexes Consumer price index Edgeworth, F. Y. Fisher ideal index Fisher, I. Fixed base indexes Frisch, R. A. K. Ideal indexes Index number theory Index numbers Jevons price index Jevons, W. S. Konüs price index Konüs-Pollak quantity index Laspeyres price index Laspeyres-Konüs quantity index Logarithmic price ratios Lowe index Malmquist quantity index Marshall, A. Marshall-Edgeworth index Paasche price index Pierson, N. G. Producer price index Productivity indexes Scrope, G. P. Sidgwick, H. Sidgwick-Bowley index Superlative indexes Theil, H. Törnqvist-Theil price index Walsh index Walsh, C. M. Young index 

JEL Classifications

C43 
This is a preview of subscription content, log in to check access.

Bibliography

  1. 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.Google Scholar
  2. Allen, R.G.D. 1949. The economic theory of index numbers. Economica NS 16: 197–203.CrossRefGoogle Scholar
  3. Alterman, W.F., W.E. Diewert, and R.C. Feenstra. 1999. International trade price indexes and seasonal commodities. Washington, DC: Bureau of Labor Statistics.Google Scholar
  4. 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.Google Scholar
  5. Balk, B.M. 1980. A method for constructing price indices for seasonal commodities. Journal of the Royal Statistical Society, Series A 143: 68–75.CrossRefGoogle Scholar
  6. Balk, B.M. 1985. A simple characterization of Fisher’s price index. Statistische Hefte 26: 59–63.CrossRefGoogle Scholar
  7. Balk, B.M. 1995. Axiomatic price index theory: A survey. International Statistical Review 63: 69–93.CrossRefGoogle Scholar
  8. Balk, B.M. 1996. A comparison of ten methods for multilateral international price and volume comparisons. Journal of Official Statistics 12: 199–222.Google Scholar
  9. Balk, B.M. 1998. Industrial price, quantity and productivity indices. Boston: Kluwer.CrossRefGoogle Scholar
  10. 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.CrossRefGoogle Scholar
  11. Balk, B.M. 2005. Annual and quarterly productivity measures. Paper presented at the Economic Measurement Group Workshop, Coogee, 12–13 Dec.Google Scholar
  12. Balk, B.M., and W.E. Diewert. 2001. A characterization of the Törnqvist priceindex. Economics Letters 73: 279–281.CrossRefGoogle Scholar
  13. 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.Google Scholar
  14. Bennet, T.L. 1920. The theory of measurement of changes in cost of living. Journal of Royal Statistical Society 83: 455–462.CrossRefGoogle Scholar
  15. 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.Google Scholar
  16. Bowley, A.L. 1899. Wages, nominal and real. In Dictionary of Political Economy, ed. R.H.L. Palgrave, vol. vol. 3. London: Macmillan.Google Scholar
  17. Bowley, A.L. 1901. Elements of statistics. Westminster: P.S. King and Son.Google Scholar
  18. Bowley, A.L. 1919. The measurement of changes in the cost of living. Journal of the Royal Statistical Society 82: 343–372.CrossRefGoogle Scholar
  19. Bowley, A.L. 1928. Notes on index numbers. Economic Journal 38: 216–237.CrossRefGoogle Scholar
  20. 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.Google Scholar
  21. Carli, G.-R. 1764. Del valore e dellaproporzione de’ metallimonetati. In Scrittoriclassiciitaliani di economiapolitica, vol. 13. Milano: G.G. Destefanis, 1804.Google Scholar
  22. 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.CrossRefGoogle Scholar
  23. 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.CrossRefGoogle Scholar
  24. Christensen, L.R., D.W. Jorgenson, and L.J. Lau. 1971. Conjugate duality and the transcendental logarithmic production function. Econometrica 39: 255–256.Google Scholar
  25. Clements, K.W., H.Y. Izan, and E.A. Selvanathan. 2006. Stochastic index numbers: A review. International Statistical Review 74: 235–270.CrossRefGoogle Scholar
  26. Dalén, J. 1992. Computing elementary aggregates in the Swedish consumer price index. Journal of Official Statistics 8: 129–147.Google Scholar
  27. de Haan, J. 2004a. Direct and indirect time dummy approaches to hedonic price measurement. Journal of Economic and Social Measurement 29: 427–443.Google Scholar
  28. 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.Google Scholar
  29. 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.Google Scholar
  30. Diewert, W.E. 1976. Exact and superlative index numbers. Journal of Econometrics 4: 114–145.CrossRefGoogle Scholar
  31. Diewert, W.E. 1978. Superlative index numbers and consistency in aggregation. Econometrica 46: 883–900.CrossRefGoogle Scholar
  32. 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.Google Scholar
  33. 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.Google Scholar
  34. 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.Google Scholar
  35. 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.Google Scholar
  36. Diewert, W.E. 1986. Microeconomic approaches to the theory of international comparisons. Technical Working Paper No. 53. Cambridge, MA: NBER.Google Scholar
  37. 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.Google Scholar
  38. Diewert, W.E. 1988. Test approaches to international comparisons. In Measurement in economics, ed. W. Eichhorn. Heidelberg: Physica-Verlag.Google Scholar
  39. Diewert, W.E. 1992a. Fisher ideal output, input and productivity indexes revisited. Journal of Productivity Analysis 3: 211–248.CrossRefGoogle Scholar
  40. Diewert, W.E. 1992b. Exact and superlative welfare change indicators. Economic Inquiry 30: 565–582.CrossRefGoogle Scholar
  41. 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.Google Scholar
  42. 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.Google Scholar
  43. Diewert, W.E. 1995a. Axiomatic and economic approaches to elementary price indexes. Discussion Paper No. 95-01. Department of Economics, University of British Columbia.Google Scholar
  44. Diewert, W.E. 1995b. On the stochastic approach to index numbers. Discussion Paper No. 95-31. Department of Economics, University of British Columbia.Google Scholar
  45. 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.Google Scholar
  46. Diewert, W.E. 1998a. Index number issues in the consumer price index. Journal of Economic Perspectives 12 (1): 47–58.CrossRefGoogle Scholar
  47. Diewert, W.E. 1998b. High inflation, seasonal commodities and annual index numbers. Macroeconomic Dynamics 2: 456–471.CrossRefGoogle Scholar
  48. Diewert, W.E. 1999a. Index number approaches to seasonal adjustment. Macroeconomic Dynamics 3: 48–68.CrossRefGoogle Scholar
  49. 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.Google Scholar
  50. Diewert, W.E. 2001. The consumer price index and index number purpose. Journal of Economic and Social Measurement 27: 167–248.Google Scholar
  51. Diewert, W.E. 2002a. The quadratic approximation lemma and decompositions of superlative indexes. Journal of Economic and Social Measurement 28: 63–88.Google Scholar
  52. Diewert, W.E. 2002b. Harmonized indexes of consumer prices: Their conceptual foundations. Swiss Journal of Economics and Statistics 138: 547–637.Google Scholar
  53. Diewert, W.E. 2003. Hedonic regressions: a review of some unresolved issues. Paper presented at the 7th Meeting of the Ottawa Group, Paris.Google Scholar
  54. Diewert, W.E. 2004. A new axiomatic approach to index number theory. Discussion Paper No. 04-05. Department of Economics, University of British Columbia.Google Scholar
  55. Diewert, W.E. 2005a. Index number theory using differences instead of ratios. American Journal of Economics and Sociology 64: 311–360.CrossRefGoogle Scholar
  56. Diewert, W.E. 2005b. Weighted country product dummy variable regressions and index number formulae. Review of Income and Wealth 51: 561–571.CrossRefGoogle Scholar
  57. 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.Google Scholar
  58. 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.Google Scholar
  59. 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.Google Scholar
  60. 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.Google Scholar
  61. 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.Google Scholar
  62. 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.CrossRefGoogle Scholar
  63. Diewert, W.E., and A.O. Nakamura. 2003. Index number concepts, measures and decompositions of productivity growth. Journal of Productivity Analysis 19: 127–159.CrossRefGoogle Scholar
  64. Edgeworth, F.Y. 1888. Some new methods of measuring variation in general prices. Journal of the Royal Statistical Society 51: 346–368.Google Scholar
  65. Edgeworth, F.Y. 1923. The doctrine of index numbers according to Mr. Correa Walsh. Economic Journal 33: 343–351.CrossRefGoogle Scholar
  66. Edgeworth, F.Y. 1925. Papers relating to political economy. Vol. 1. New York: Burt Franklin.Google Scholar
  67. Eichhorn, W. 1978. Functional equations in economics. London: Addison-Wesley.Google Scholar
  68. Eichhorn, W., and J. Voeller. 1976. Theory of the price index. Berlin: Springer.CrossRefGoogle Scholar
  69. Eltetö, O., and P. Köves. 1964. On a problem of index number computation relating to international comparison. Statisztikai Szemle 42: 507–518.Google Scholar
  70. Fisher, I. 1911. The purchasing power of money. London: Macmillan.Google Scholar
  71. Fisher, W.C. 1913. The tabular standard in Massachusetts history. Quarterly Journal of Economics 27: 417–451.CrossRefGoogle Scholar
  72. Fisher, I. 1921. The best form of index number. Journal of the American Statistical Association 17: 535–537.Google Scholar
  73. Fisher, I. 1922. The making of index numbers. Boston: Houghton Mifflin.Google Scholar
  74. 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.CrossRefGoogle Scholar
  75. Frisch, R. 1936. Annual survey of economic theory: The problem of index numbers. Econometrica 4: 1–39.CrossRefGoogle Scholar
  76. 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.Google Scholar
  77. Funke, H., G. Hacker, and J. Voeller. 1979. Fisher’s circular test reconsidered. Schweizerische Zeitschrift für Volkswirtshaft und Statistik 115: 677–687.Google Scholar
  78. 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.CrossRefGoogle Scholar
  79. Gini, C. 1924. Quelques considérations au sujet de la construction des nombres indices des prix et des questions analogues. Metron 4: 3–162.Google Scholar
  80. Gini, C. 1931. On the circular test of index numbers. Metron 9: 3–24.Google Scholar
  81. Hicks, J.R. 1941–42. Consumers’ surplus and index numbers. Review of Economic Studies 9, 126–137.Google Scholar
  82. Hill, T.P. 1988. Recent developments in index number theory and practice. OECD Economic Studies 10: 123–148.Google Scholar
  83. 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.Google Scholar
  84. Hill, T.P. 1996. Inflation accounting. Paris: OECD.Google Scholar
  85. 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.CrossRefGoogle Scholar
  86. Hill, R.J. 1999a. Comparing price levels across countries using minimum spanning trees. The Review of Economics and Statistics 81: 135–142.CrossRefGoogle Scholar
  87. 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.Google Scholar
  88. Hill, R.J. 2001. Measuring inflation and growth using spanning trees. International Economic Review 42: 167–185.CrossRefGoogle Scholar
  89. Hill, R.J. 2004. Constructing price indexes across space and time: The case of the European Union. American Economic Review 94: 1379–1410.CrossRefGoogle Scholar
  90. Hill, R.J. 2006a. Superlative index numbers: Not all of them are super. Journal of Econometrics 130: 25–43.CrossRefGoogle Scholar
  91. 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.CrossRefGoogle Scholar
  92. 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.Google Scholar
  93. ILO/IMF/OECD/UNECE/Eurostat/World Bank. 2004. In Consumer price index manual: Theory and practice, ed. P. Hill. Geneva: International Labour Office.Google Scholar
  94. IMF/ILO/OECD/UNECE/Eurostat/World Bank. 2004. In Producer price index manual: Theory and practice, ed. P. Armknecht. Washington, DC: International Monetary Fund.Google Scholar
  95. 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.CrossRefGoogle Scholar
  96. 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.Google Scholar
  97. Jorgenson, D.W., and Z. Griliches. 1967. The explanation of productivity change. Review of Economic Studies 34: 249–283.CrossRefGoogle Scholar
  98. Jorgenson, D.W., and Z. Griliches. 1972. Issues in growth accounting: A reply to Edward F. Denison. Survey of Current Business 52: 65–94.Google Scholar
  99. Keynes, J.M. 1930. Treatise on money. Vol. 1. London: Macmillan.Google Scholar
  100. 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.CrossRefGoogle Scholar
  101. Kohli, U. 1990. Growth accounting in the open economy: Parametric and nonparametric estimates. Journal of Economic and Social Measurement 16: 125–136.Google Scholar
  102. Kohli, U. 2003. Growth accounting in the open economy: International comparisons. International Review of Economics and Finance 12: 417–435.CrossRefGoogle Scholar
  103. Kohli, U. 2004. Real GDP, real domestic income and terms of tradechanges. Journal of International Economics 62: 83–106.CrossRefGoogle Scholar
  104. 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.Google Scholar
  105. Konüs, A.A. 1924. The problem of the true index of the cost of living. Trans. in Econometrica 7 (1939), 10–29.Google Scholar
  106. Konüs, A.A., and S.S. Byushgens. 1926. K probleme pokupatelnoi cili deneg. Voprosi konyunkturi 2: 151–172.Google Scholar
  107. Kravis, I.B. 1984. Comparative studies of national incomes and prices. Journal of Economic Literature 22: 1–39.Google Scholar
  108. 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.Google Scholar
  109. Laspeyres, E. 1871. Die berechnung einer mittleren waarenpreissteigerung. Jahrbücher für Nationalökonomie und Statistik 16: 296–314.CrossRefGoogle Scholar
  110. 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.CrossRefGoogle Scholar
  111. Lehr, J. 1885. Beitrage zur Statistik der Preise. Frankfurt: J.D. Sauerlander.Google Scholar
  112. Lowe, J. 1823. The present State of England in regard to agriculture, trade and finance. 2nd ed. London: Longman, Hurst, Rees, Orme and Brown.Google Scholar
  113. Malmquist, S. 1953. Index numbers and indifference surfaces. Trabajos de Estadística 4: 209–242.CrossRefGoogle Scholar
  114. Marshall, A. 1887. Remedies for fluctuations of general prices. Contemporary Review 51: 355–375.Google Scholar
  115. Montgomery, J.K. 1929. Is there a theoretically correct price index of a group of commodities? Rome: Roma L’Universale Tipogr. Poliglotta (privately printed).Google Scholar
  116. Montgomery, J.K. 1937. The mathematical problem of the price index. Orchard House: P.S. King & Son.Google Scholar
  117. 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.Google Scholar
  118. 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.Google Scholar
  119. Paasche, H. 1874. Über die preisentwicklung der letzten Jahre nach den hamburger borsennotirungen. Jahrbücher für Nationalökonomie und Statistik 12: 168–178.Google Scholar
  120. Pierson, N.G. 1895. Index numbers and appreciation of gold. Economic Journal 5: 329–335.CrossRefGoogle Scholar
  121. Pierson, N.G. 1896. Further considerations on index-numbers. Economic Journal 6: 127–131.CrossRefGoogle Scholar
  122. Pollak, R.A. 1980. Group cost-of-living indexes. American Economic Review 70: 273–278.Google Scholar
  123. Pollak, R.A. 1981. The social cost-of-living index. Journal of Public Economics 15: 311–336.CrossRefGoogle Scholar
  124. 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.Google Scholar
  125. 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.Google Scholar
  126. 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.Google Scholar
  127. Reinsdorf, M. 2007. Axiomatic price index theory. In Measurement in economics: A handbook, ed. M.J. Boumans. Amsterdam: Elsevier.Google Scholar
  128. Reinsdorf, M., and A. Dorfman. 1999. The monotonicity axiom and the Sato-Vartia index. Journal of Econometrics 90: 45–61.CrossRefGoogle Scholar
  129. 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.Google Scholar
  130. 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.Google Scholar
  131. Samuelson, P.A. 1947. Foundations of economic analysis. Cambridge, MA: Harvard University Press.Google Scholar
  132. Samuelson, P.A., and S. Swamy. 1974. Invariant economic index numbers and canonical duality: Survey and synthesis. American Economic Review 64: 566–593.Google Scholar
  133. Schreyer, P. 2001. OECD productivity manual: A guide to the measurement of industry-level and aggregate productivity growth. Paris: OECD.Google Scholar
  134. Schultze, C.L., and C. Mackie. 2002. At what price? Conceptualizing and measuring cost-of living and price indices. Washington, DC: National Academy Press.Google Scholar
  135. Scrope, G.P. 1833. Principles of political economy. London: Longman, Rees, Orme, Brown, Green and Longman.Google Scholar
  136. Selvanathan, E.A., and D.S. PrasadaRao. 1994. Index numbers: A stochastic approach. Ann Arbor: University of Michigan Press.CrossRefGoogle Scholar
  137. Shephard, R.W. 1953. Cost and production functions. Princeton: Princeton University Press.Google Scholar
  138. Sidgwick, H. 1883. The principles of political economy. London: Macmillan.Google Scholar
  139. 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.Google Scholar
  140. 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.CrossRefGoogle Scholar
  141. Summers, R. 1973. International comparisons with incomplete data. Review of Income and Wealth 29: 1–16.CrossRefGoogle Scholar
  142. Szulc, B. 1964. Indices for multiregional comparisons. Przeglad Statystyczny 3: 239–254.Google Scholar
  143. Szulc, B.J. 1983. Linking price index numbers. In Price level measurement, ed. W.E. Diewert and C. Montmarquette. Ottawa: Statistics Canada.Google Scholar
  144. Theil, H. 1967. Economics and information theory. Amsterdam: North-Holland.Google Scholar
  145. Törnqvist, L. 1936. The bank of Finland’s consumption price index. Bank of Finland Monthly Bulletin 10: 1–8.Google Scholar
  146. 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.Google Scholar
  147. 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.Google Scholar
  148. 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.CrossRefGoogle Scholar
  149. Turvey, R. 1979. The treatment of seasonal items in consumer price indices, Bulletin of labour statistics, fourth quarter, 13–33. Geneva: International Labour Office.Google Scholar
  150. US Bureau of Labor Statistics. 1983. Trends in multifactor productivity, 1948–81, Bulletin 2178. Washington, DC: U.S. Government Printing Office.Google Scholar
  151. van IJzeren, J. 1957. Three methods of comparing the purchasing power of currencies, Statistical studies. Vol. 7. The Hague: Central Bureau of Statistics.Google Scholar
  152. van IJzeren, J. 1983. Index numbers for binary and multilateral comparisons. Statistical studies no. 34. The Hague: Central Bureau of Statistics.Google Scholar
  153. van IJzeren, J. 1987. Bias in international index numbers: A mathematical elucidation. Dissertation for the Hungarian Academy of Sciences. The Hague: Koninklijke Bibliotheek.Google Scholar
  154. Vartia, Y.O. 1976. Relative changes and index numbers. Helsinki: Research Institute of the Finnish Economy.Google Scholar
  155. Vogt, A. 1980. Der Zeit und der Faktorumkehrtestals ‘Finders of Tests’. StatistischeHefte 21: 66–71.Google Scholar
  156. Vogt, A., and J. Barta. 1997. The making of tests for index numbers. Heidelberg: Physica-Verlag.CrossRefGoogle Scholar
  157. von der Lippe, P. 2001. Chain indices: A study in price index theory, spectrum of federal statistics. Vol. 16. Wiesbaden: Statistisches Bundesamt.Google Scholar
  158. Walsh, C.M. 1901. The measurement of general exchange value. New York: Macmillan and Co..Google Scholar
  159. Walsh, C.M. 1921a. The problem of estimation. London: P.S. King &Son.Google Scholar
  160. Walsh, C.M. 1921b. Discussion. Journal of the American Statistical Association 17: 537–544.Google Scholar
  161. Westergaard, H. 1890. Die Grundzüge der Theorie der Statistik. Jena: Fischer.Google Scholar
  162. Wynne, M.A. 1997. Commentary on measuring short run inflation for central bankers. Federal Reserve Bank of St. Louis Review 79: 161–167.Google Scholar
  163. Young, A. 1812. An inquiry into the progressive value of money in England as marked by the price of agricultural products. London: Macmillan.Google Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • W. Erwin Diewert
    • 1
  1. 1.