von der Lippe, Peter (2015): Generalized Statistical Means and New Price Index Formulas, Notes on some unexplored index formulas, their interpretations and generalizations.

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Abstract
The theory of (increasingly more generalized types of) statistical means can be used to create a plethora of index formulas. Some of them are new and some were indeed discussed in the past but fallen into oblivion, because their rationale was not well understood. Surprisingly many possess interesting interpretations and attractive properties that deserve being unveiled. We begin with unweighted indices with implications to what now is called "low level aggregation" and proceed to weighted index formulas that lend themselves to productive generalizations and thereby to some new formulas. It turns out that contrary to popular belief the Laspeyres and Paasche formula are not equally well justified and that some indices from the more comprehensive system of statistical means are attractive regarding their economic interpretation and how they are related to indices of "quantity" and purchasing power of money.
Item Type:  MPRA Paper 

Original Title:  Generalized Statistical Means and New Price Index Formulas, Notes on some unexplored index formulas, their interpretations and generalizations 
Language:  English 
Keywords:  Index Numbers, Generalized means, antiharmonic mean, index of purchasing power, unit value indices 
Subjects:  C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C43  Index Numbers and Aggregation C  Mathematical and Quantitative Methods > C8  Data Collection and Data Estimation Methodology ; Computer Programs > C82  Methodology for Collecting, Estimating, and Organizing Macroeconomic Data ; Data Access E  Macroeconomics and Monetary Economics > E0  General E  Macroeconomics and Monetary Economics > E0  General > E01  Measurement and Data on National Income and Product Accounts and Wealth ; Environmental Accounts E  Macroeconomics and Monetary Economics > E3  Prices, Business Fluctuations, and Cycles > E31  Price Level ; Inflation ; Deflation 
Item ID:  64952 
Depositing User:  Peter von der Lippe 
Date Deposited:  10 Jun 2015 11:45 
Last Modified:  28 Sep 2019 16:30 
References:  Ferger Wirth H, 1936, Distinctive Concepts of Price and Purchasing Power Index Numbers, Journal of the American Statistical Association, Vol. 31, No. 194, pp. 259 – 272 Fisher, Irving 1922, The Making of Index Numbers, Boston Vogt, Arthur 1979, Das statistische Indexproblem im ZweiSituationenFall, Diss. ETH Zürich von der Lippe, Peter 2000, Preisindizes mit konstanten Wertgewichten, Jahrbücher für Nationalökonomie und Statistik 220/6, 2000, S. 742  758. von der Lippe, Peter 2007, Index Theory and Price Statistics, Frankfurt, 2007 von der Lippe, Peter 2013, Recurrent Price Index Problems and Some Early German Papers on Index Numbers. Notes on Laspeyres, Paasche, Drobisch, and Lehr, Jahrbücher für Nationalökonomie und Statistik Vol. 233/3, pp 336 – 366 Young, Allyn A. 1921, The Measurement of Changes of the General Price Level, Quarterly Journal of Economics, Vol. 35, No. 4, pp. 557  573 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/64952 