Chapter 04, LASPEYRES, ERNST LOUIS ETIENNE

68 Essays in Index Number Theory Selected Works Konu¨s, A.A., 1924. English translation, titled “The Problem of the True Index of the Cost of Living,” published in 1939 in Econometrica 7, 10–29. Konu¨s, A.A., and S.S. Byushgens [Buscheguennce], 1926. “K probleme poku- patelnoi cili deneg” (English translation of Russian title: “On the Problem of the Purchasing Power of Money”), Voprosi Konyunkturi II(1) (supple- ment to the Economic Bulletin of the Conjucture Institute), 151–172. Konu¨s, A.A., 1968. “The Theory of the Consumer Price Indexes and the Problem of the Comparison of the Cost of Living in Time and Space.” In The Social Sciences: Problems and Orientations, Paris: UNESCO, 93–107. References for Chapter 3 Court, L.M. and H.E. Lewis, 1942–43. “Production Cost Indices,” The Review of Economic Studies 10, 28–42. Manser, M.E. and R.J. McDonald, 1988. “An Analysis of Substitution Bias in Measuring Inflation, 1959–85,” Econometrica 56, 909–930. Chapter 4 LASPEYRES, ERNST LOUIS ETIENNE* W.E. Diewert Laspeyres, Ernst Louis Etienne (1834–1913). Laspeyres was born at Halle, Germany, on 28 November 1834 and died on 4 August 1913 at Giessen, Ger- many. From 1853 to 1857, he studied at the universities of Tu¨bingen, Berlin, Go¨ttingen and Halle. He received a law degree from the University of Halle in 1857. He studied at the University of Heidelberg from 1857 to 1859, and in 1860 he obtained his PhD from Heidelberg for the thesis, ‘The Correlation between Population Growth and Wages’. From 1860 until 1864 he worked as a lecturer at Heidelberg, where he wrote a history of the economic views of the Dutch (Laspeyres [1863]). In the following ten years, he taught at four different universities: 1864 – Basel; 1866 – the Polytechnic at Riga; 1869 – Dorpat; 1873 – Karlsruhe. Finally, from 1874 to 1900, he taught at the Justus-Liebig University at Giessen. Laspeyres’ main contribution to economics was his development of the index number formula that bears his name. Let the price and quantity of commod- ity n in period t be ptn and qtn respectively for n = 1, . . . , N and t = 0, 1, . . . , T . Then the Laspeyres price index of the N commodities for period t (relative to the base period 0) is defined as PL ≡ ∑N n=1 ptnq0n /∑N n=1 p0nq0n. Laspeyres wrote his classic paper [1871] which suggested the above formula partly as an outgrowth of his empirical work on measuring price movements in Germany and partly to criticize the index number formula of Drobisch [1871]. Using the notation defined above, the Drobisch price index for period t is defined as PD ≡ (∑N n=1 ptnqtn /∑n n=1 qtn ) / (∑N n=1 p0nq0n /∑N n=1 q0n ) . *First published in The New Palgrave: A Dictionary of Economics, Vol. 3, J. Eatwell, M. Milgate and P. Newman (eds.), The Macmillan Press, 1987, pp. 133–134. 70 Essays in Index Number Theory Laspeyres criticized this formula by showing that the index generally changed even if all prices remained constant (i.e. PD does not satisfy an identity test to use modern terminology). An even more effective criticism of PD is that it is not invariant to changes in the units of measurement (whereas PL is invariant). Laspeyres did not write any further papers on index number theory. He wrote papers on economic history, the history of economic thought and on topical economic issues of his time; see Rinne [1981]. Selected Works Laspeyres, E., 1863. Geschichte der Volkswirtschaftlichen Anschauungen der Niederla¨nder und ihrer Literatur zur Zeit der Republik, Leipzig. Laspeyres, E., 1871. “Die Berechnung einer mittleren Waarenpreissteigerung,” Jahrbu¨cher fu¨r Nationalo¨konomie und Statistik 16, 296-315. References for Chapter 4 Drobisch, M.W., 1871. “Uber die Berechnung der Veranderungen der Waaren- preise und des Geldswerths,” Jahrbucher fu¨r Nationalo¨konomie und Statis- tik 16, 143–156. Rinne, H., 1981. “Ernst Louis Etienne Laspeyres 1834–1913,” Jahrbucher fu¨r Nationalo¨konomie und Statistik 198, 194–216. Chapter 5 INDEX NUMBERS* W.E. Diewert The index number problem may be phrased as follows. Suppose we have price data pi ≡ (pi1, . . . , piN ) and quantity data xi ≡ (xi1, . . . , xiN ) on N com- modities that pertain to economic unit i or that pertain to the same economic unit at time period i for i = 1, 2, . . . , I . The index number problem is to find I numbers P i and I numbers X i such that (1) P iX i = pi · xi ≡ ∑N n=1 pinxin for i = 1, . . . , I. P i is the price index for period i (or unit i) andX i is the corresponding quantity index. P i is supposed to be representative of all of the prices pin, n = 1, . . . , N in some sense, while X i is to be similarly representative of the quantities xin, n = 1, . . . , N . In what precise sense P i and X i represent the individual prices and quantities is not immediately evident and it is this ambiguity which leads to different approaches to index number theory. Note that we require that the product of the price and quantity indexes, P iX i, equals the actual period (or unit) i net expenditures on the N commodities, pi · xi. Thus if the P i are determined, then the X i may be implicitly determined using equations (1), or vice versa. Each individual consumes the services of thousands of commodities over a year and most producers utilize and/or produce thousands of individual prod- ucts and services. Index numbers are used to reduce and summarize this over- whelming abundance of microeconomic information. Hence index numbers in- trude themselves on virtually every empirical investigation in economics. Index number theory splits naturally into two divisions, depending on the size of I . If I = 2, so that there are data for only two time periods or two economic units, then we are in the realm of bilateral index number theory while if I > 2, then we are in the realm of multilateral indexes. Bilateral approaches are considered in Sections 1–5 below and multilateral approaches are considered in Sections 6–10. *First published in The New Palgrave: A Dictionary of Economics, Vol. 2, J. Eatwell, M. Milgate and P. Newman (eds.), The Macmillan Press, 1987, pp. 767–780.