Hostname: page-component-848d4c4894-xfwgj Total loading time: 0 Render date: 2024-06-27T18:07:18.692Z Has data issue: false hasContentIssue false
  • English
  • Français

IRVING FISHER AND INDEX NUMBER THEORY

Published online by Cambridge University Press:  10 May 2013

ERWIN DIEWERT
Get access Rights & Permissions [Opens in a new window]

Abstract

There are four main approaches to bilateral index number theory: the fixed basket, stochastic, test, and economic approaches. The paper reviews the contributions of Irving Fisher to these approaches to index number theory, which are still in use today. The paper also reviews Fisher’s contributions to multilateral index number theory. The main themes of the paper are developed in the context of a review of the early history of index number theory: a history that conveys a wealth of information and insight into the making and use of index numbers today.

Type
Articles
Information
Journal of the History of Economic Thought , Volume 35 , Issue 2 , June 2013 , pp. 199 - 232
Copyright
Copyright © The History of Economics Society 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Aldrich, J. 1992. “Probability and Depreciation: A History of the Stochastic Approach to Index Numbers.” History of Political Economy 24: 657–687.CrossRefGoogle Scholar
Allen, R.G.D. 1949. “The Economic Theory of Index Numbers.” Economica 16: 197–203.Google Scholar
Alterman, W.F., Diewert, W.E., and Feenstra, R.C.. 1999. International Trade Price Indexes and Seasonal Commodities. Bureau of Labor Statistics, Washington, DC.Google Scholar
Balk, B.M. 1985. “A Simple Characterization of Fisher’s Price Index.” Statistische Hefte 26: 59–63.Google Scholar
Balk, B.M. 1995. “Axiomatic Price Index Theory: A Survey.” International Statistical Review 63: 69–93.CrossRefGoogle Scholar
Balk, B.M. 2005. “Divisia Price and Quantity Indices: 80 Years After.” Statistica Neerlandica 59: 119–158.Google Scholar
Balk, B.M. 2008. Price and Quantity Index Numbers. New York: Cambridge University Press.Google Scholar
Barber, W.J. 1997. “Fisher: Career Highlights and Formative Influences, 1867–1947.” In Barber, W. J., assisted by Dimand, R.W. and Foster, K., eds., The Works of Irving Fisher. Volume 1: The Early Professional Works. London: Pickering & Chatto, pp. 3–21.Google Scholar
Bowley, A.L. 1899. “Wages, Nominal and Real.” In Dictionary of Political Economy. Volume 3. London: MacMillan, pp. 640–651.Google Scholar
Bowley, A.L. 1901. Elements of Statistics. Westminster: P.S. King and Son.Google Scholar
Carli, Gian-Rinaldo. [1746] 1804. “Del valore e della proporzione de’ metalli monetati.” In Scrittori classici italiani di economia politica, Volume 13. Milano: G.G. Destefanis, pp. 297–366.Google Scholar
Christensen, L.R., Jorgenson, D.W., and Lau, L.J.. 1975. “Transcendental Logarithmic Utility Functions.” American Economic Review 65: 367–383.Google Scholar
Clements, K.W., Izan, H.Y., and Selvanathan, E.A.. 2006. “Stochastic Index Numbers: A Review.” International Statistical Review 74: 235–270.Google Scholar
Cobb, C., and Douglas, P.H. 1928. “A Theory of Production.” American Economic Review 18: 139–165.Google Scholar
Davies, G.R. 1924. “The Problem of a Standard Index Number Formula.” Journal of the American Statistical Association 19: 180–188.Google Scholar
Diewert, W.E. 1974. “Applications of Duality Theory.” In Intriligator, M.D. and Kendrick, D.A., eds., Frontiers of Quantitative Economics. Volume II. Amsterdam: North-Holland, pp. 106–171.Google Scholar
Diewert, W.E. 1976. “Exact and Superlative Index Numbers.” Journal of Econometrics 4: 114–145.CrossRefGoogle Scholar
Diewert, W.E. 1978. “Superlative Index Numbers and Consistency in Aggregation.” Econometrica 46: 883–900.Google Scholar
Diewert, W.E. 1980. “Aggregation Problems in the Measurement of Capital.” In Usher, Dan, ed., The Measurement of Capital. Studies in Income and Wealth. Volume 45. National Bureau of Economics Research, Chicago: University of Chicago Press, pp. 433–528 .Google Scholar
Diewert, W.E. 1992. “Fisher Ideal Output, Input and Productivity Indexes Revisited.” Journal of Productivity Analysis 3: 211–248.CrossRefGoogle Scholar
Diewert, W.E. 1993a. “The Early History of Price Index Research.” In Diewert, W. E. and Nakamura, A.O., eds., Essays in Index Number Theory. Volume 1. Amsterdam: North-Holland, pp. 33–65.Google Scholar
Diewert, W.E. 1993b. “Symmetric Means and Choice under Uncertainty.” In Diewert, W. E. and Nakamura, A.O., eds., Essays in Index Number Theory. Volume 1. Amsterdam: North-Holland, pp. 355–433.Google Scholar
Diewert, W.E. 1995. “On the Stochastic Approach to Index Numbers.” Discussion Paper 95–31, Department of Economics, University of British Columbia, Vancouver, Canada.Google Scholar
Diewert, W.E. 1997. “Commentary on Mathew D. Shapiro and David W. Wilcox: Alternative Strategies for Aggregating Prices in the CPI.” The Federal Reserve Bank of St. Louis Review 79 (3): 127–137.Google Scholar
Diewert, W.E. 1999. “Axiomatic and Economic Approaches to International Comparisons.” In Heston, A. and Lipsey, R.E., eds., International and Interarea Comparisons of Income, Output and Prices. Studies in Income and Wealth. Volume 61. Chicago: The University of Chicago Press, pp. 13–87.Google Scholar
Diewert, W.E. 2001. “The Consumer Price Index and Index Number Purpose.” Journal of Economic and Social Measurement 27: 167–248.CrossRefGoogle Scholar
Diewert, W.E. 2002. “The Quadratic Approximation Lemma and Decompositions of Superlative Indexes.” Journal of Economic and Social Measurement 28: 63–88.Google Scholar
Diewert, W.E. 2009a. “Cost of Living Indexes and Exact Index Numbers.” In Slottje, D., ed., Quantifying Consumer Preferences. Contributions to Economic Analysis Series. United Kingdom: Emerald Group Publishing, pp. 207–246.Google Scholar
Diewert, W.E. 2009b. “Similarity Indexes and Criteria for Spatial Linking.” In Prasada Rao, D.S., ed., Purchasing Power Parities of Currencies: Recent Advances in Methods and Applications. Cheltenham, UK: Edward Elgar, pp. 183–216.Google Scholar
Diewert, W.E. 2011. “The Axiomatic Approach to Bilateral Index Number Theory.” Chapter 3, Lecture Notes for Index Number Theory and Measurement Economics, Department of Economics, University of British Columbia, Canada. http://faculty.arts.ubc.ca/ediewert/580ch3.pdf.Google Scholar
Divisia, F. 1926. L’indice monetaire et la theorie de la monnaie. Paris: Societe anonyme du Recueil Sirey.Google Scholar
Drobisch, M.W. 1871. “Űber die Berechnung der Veränderungen der Waarenpreise und des Geldwerths.” Jahrbücher für Nationalökonomie und Statistik 16: 143–156.Google Scholar
Dutot, Charles. 1738. Réflexions politiques sur les finances et le commerce. Volume 1. La Haye: Les frères Vaillant et N. Prevost.Google Scholar
Edgeworth, F.Y. 1888. “Some New Methods of Measuring Variation in General Prices.” Journal of the Royal Statistical Society 51: 346–368.Google Scholar
Edgeworth, F.Y. 1896. “A Defense of Index Numbers.” Economic Journal 6: 132–142.Google Scholar
Edgeworth, F.Y. 1901. “Mr. Walsh on the Measurement of General Exchange Value.” Economic Journal 11: 404–416.Google Scholar
Edgeworth, F.Y. 1925. Papers Relating to Political Economy. Volume 1. New York: Burt Franklin.Google Scholar
Eichhorn, W. 1978. Functional Equations in Economics. London: Addison-Wesley.Google Scholar
Eichhorn, W., and Voeller, J.. 1976. Theory of the Price Index. Lecture Notes in Economics and Mathematical Systems. Volume 140. Berlin: Springer-Verlag.Google Scholar
Ferger, W.F. 1946. “Historical Note on the Purchasing Power Concept and Index Numbers.” Journal of the American Statistical Association 41: 53–57.Google Scholar
Fisher, I. 1911. The Purchasing Power of Money. London: Macmillan.Google Scholar
Fisher, I. 1921. “The Best Form of Index Number.” Quarterly Publication of the American Statistical Association 17: 533–537.Google Scholar
Fisher, I. 1922. The Making of Index Numbers. Boston: Houghton-Mifflin.Google Scholar
Fisher, I. 1997. “An Address on the Irving Fisher Foundation, 11 September 1946.” In Barber, W. J., assisted by Dimand, R.W. and Foster, K., eds., The Works of Irving Fisher. Volume 1: The Early Professional Works. London: Pickering & Chatto, pp. 22–37.Google Scholar
Fisher, W.C. 1913. “The Tabular Standard in Massachusetts History.” Quarterly Journal of Economics 27: 417–451.Google Scholar
Frisch, R. 1930. “Necessary and Sufficient Conditions Regarding the Form of an Index Number which Shall Meet Certain of Fisher’s Tests.” American Statistical Association Journal 25: 397–406.Google Scholar
Frisch, R. 1936. “Annual Survey of General Economic Theory: The Problem of Index Numbers.” Econometrica 4: 1–39.Google Scholar
Funke, H., and Voeller, J.. 1978. “A Note on the Characterization of Fisher’s Ideal Index.” In Eichhorn, W., Henn, R., Opitz, O., and Shephard, R.W., eds., Theory and Applications of Economic Indices. Würzburg: Physica-Verlag, pp. 177–181.Google Scholar
Gini, C. 1931. “On the Circular Test of Index Numbers.” Metron 9 (9): 3–24.Google Scholar
Hicks, J.R. 1946. Value and Capital. Second edition. Oxford: Claredon Press.Google Scholar
Hill, R. J. 1999a. “Comparing Price Levels across Countries Using Minimum Spanning Trees.” The Review of Economics and Statistics 81: 135–142.Google Scholar
Hill, R.J. 1999b. “International Comparisons using Spanning Trees.” In Heston, A. and Lipsey, R.E., eds., International and Interarea Comparisons of Income, Output and Prices. Studies in Income and Wealth. Volume 61. NBER, Chicago: The University of Chicago Press, pp. 109–120.Google Scholar
Hill, R.J. 2001. “Measuring Inflation and Growth Using Spanning Trees.” International Economic Review 42: 167–185.Google Scholar
Hill, R.J. 2004. “Constructing Price Indexes Across Space and Time: The Case of the European Union.” American Economic Review 94: 1379–1410.Google Scholar
Hill, R.J. 2009. “Comparing Per Capita Income Levels Across Countries Using Spanning Trees: Robustness, Prior Restrictions, Hybrids and Hierarchies.” In Prasada Rao, D.S., ed., Purchasing Power Parities of Currencies: Recent Advances in Methods and Applications. Cheltenham, UK: Edward Elgar, pp. 217–244.Google Scholar
Hill, T.P. 1988. “Recent Developments in Index Number Theory and Practice.” OECD Economic Studies 10: 123–148.Google Scholar
ILO/IMF/OECD/UNECE/Eurostat/The World Bank. 2004. Consumer Price Index Manual: Theory and Practice, edited by Hill, PeterGeneva: International Labour Office.Google Scholar
Ivancic, L., Diewert, W.E., and Fox, K.J.. 2011. “Scanner Data, Time Aggregation and the Construction of Prices Indexes.” Journal of Econometrics 161: 24–35.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. Reprinted in Investigations in Currency and Finance. London: Macmillan and Co., 1884, pp. 119–150.Google Scholar
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, pp. 13–118.Google Scholar
Keynes, J.M. 1930. Treatise on Money. Volume 1. London: Macmillan.Google Scholar
Knibbs, Sir G.H. 1924. “The Nature of an Unequivocal Price Index and Quantity Index.” Journal of the American Statistical Association 19: 42–60 and 196–205.CrossRefGoogle Scholar
Konüs, A.A. 1924. “The Problem of the True Index of the Cost of Living.” Translated in Econometrica 7 (1939): 10–29.Google Scholar
Konüs, A.A, and Byushgens, S.S.. 1926. “K probleme pokupatelnoi cili deneg.” Voprosi Konyunkturi 2: 151–172.Google Scholar
Laspeyres, E. 1871. “Die Berechnung einer mittleren Waarenpreissteigerung.” Jahrbücher für Nationalökonomie und Statistik 16: 296–314.Google Scholar
Lehr, J. 1885. Beitrage zur Statistik der Preise. Frankfurt: J.D. Sauerlander.Google Scholar
Lowe, J. 1823. The Present State of England in Regard to Agriculture, Trade and Finance. Second edition. London: Longman, Hurst, Rees, Orme and Brown.Google Scholar
Malmquist, S. 1953. “Index Numbers and Indifference Surfaces.” Trabajos de Estatistica 4: 209–242.Google Scholar
Paasche, H. 1874. “Über die Preisentwicklung der letzten Jahre nach den Hamburger Borsennotirungen.” Jahrbücher für Nationalökonomie und Statistik 12: 168–178.Google Scholar
Persons, W.M. 1928. The Construction of Index Numbers. Cambridge, MA: The Riverside Press.Google Scholar
Samuelson, P.A., and Swamy, S.. 1974. “Invariant Economic Index Numbers and Canonical Duality: Survey and Synthesis.” American Economic Review 64: 566–593.Google Scholar
Scrope, G.P. 1833. Principles of Political Economy. London: Longman, Rees, Orme, Brown, Green and Longman.Google Scholar
Selvanathan, E.A., and Prasada Rao, D.S.. 1994. Index Numbers: A Stochastic Approach. Ann Arbor: The University of Michigan Press.Google Scholar
Shephard, R.W. 1953. Cost and Production Functions. Princeton: Princeton University Press.Google Scholar
Sidgwick, H. 1883. The Principles of Political Economy. London: Macmillan.Google Scholar
Szulc, B.J. 1983. “Linking Price Index Numbers.” In Diewert, W.E. and Montmarquette, C., eds., Price Level Measurement. Ottawa: Statistics Canada, pp. 537–566.Google Scholar
Theil, H. 1967. Economics and Information Theory. Amsterdam: North-Holland Publishing.Google Scholar
Törnqvist, L. 1936. “The Bank of Finland’s Consumption Price Index.” Bank of Finland Monthly Bulletin 10: 1–8.Google Scholar
Törnqvist, L, and Törnqvist, E.. 1937. “Vilket är förhällandet mellan finska markens och svenska kronans köpkraft?” Ekonomiska Samfundets Tidskrift 39: 1–39. Reprinted in Collected Scientific Papers of Leo Törnqvist. Helsinki: The Research Institute of the Finnish Economy, 1981, pp. 121–160.Google Scholar
Vogt, A. 1978. “Divisia Indices on Different Paths.” In Eichhorn, W., Henn, R., Opitz, O., and Shephard, R. W., eds., Theory and Applications of Economic Indices. Würzburg: Physica-Verlag, pp. 297–305.Google Scholar
Vogt, A. 1980. “Der Zeit und der Faktorumkehrtest als ‘Finders of Tests.’” Statistische Hefte 21: 66–71.Google Scholar
Walsh, C.M. 1901. The Measurement of General Exchange Value. New York: Macmillan and Co.Google Scholar
Walsh, C.M. 1921a. The Problem of Estimation. London: P. S. King & Son.Google Scholar
Walsh, C.M. 1921b. “The Best Form of Index Number: Discussion.” Quarterly Publication of the American Statistical Association 17: 537–544.Google Scholar
Walsh, C.M. 1924. “Professor Edgeworth’s Views on Index Numbers.” Quarterly Journal of Economics 38: 500–519.Google Scholar
Wynne, M.A. 1997. “Commentary on Measuring Short Run Inflation for Central Bankers.” Federal Reserve Bank of St. Louis Review 79 (3): 161–167.Google Scholar