Abstract
A price index formula is derived from a least-squares principle. The approach is closely related to Theil’s construction of best linear index numbers. The restriction on a base period and a current period yields an explicit representation of the index number and does not require more data than Laspeyres’ index. This least-squares index number will be compared with Laspeyres’ index. The consideration of both indices could prevent from overestimating the accuracy of the Laspeyres index number and from jumping to irrelevant conclusions of price trends.
Zusammenfassung
Eine Preisindexformel wird unter Verwendung des Kleinst-Quadrate-Prinzips hergeleitet und dabei analog zur Theilschen Konstruktion des besten linearen Index vorgegangen. Im Gegensatz zu den symmetrischen besten linearen Indizes oder den besten linearen unverfälschten Indizes (Kloek/De Wit) stellt der explizit angegebene Kleinst-Quadrate-Index keine höheren Datenanforderungen als der Laspeyres-Index. Eine gleichzeitige Betrachtung beider Indizes könnte beispielsweise dazu dienen, die Nachkommastellen des Laspeyres-Index sowie die aus dem zeitlichen Indexverlauf herausinterpretierten Trendaussagen geeignet zu relativieren.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Eichhorn, W.; Voeller, J. (1976): Theory of the Price Index, Berlin-Heidelberg-New York
Hasenkamp, G. (1978): Economic and Atomistic Index Numbers: Contrasts and Similarities, 207–243 in: Eichhorn, W.; Henn, R.; Opitz, O.; Shephard, R.W. (Hrsg.): Theory and Applications of Economic Indices, Würzburg
Hild, C.; Hacker, G. (1978): A Note on Criteria for Price Index Systems, 245–255 in: Eichhorn, W.; Henn, R.; Opitz, O.; Shephard, R.W. (Hrsg.): Theory and Applications of Economic Indices, Würzburg
Kloek, T.; De Wit, G.M. (1961): Best Linear and Best Linear Unbiased Index Numbers, Econometrica 29, 602–616
Menges, G. (1978): Semantics and “Object Logic” of Price Indices, 43–54 in: Eichhorn, W.; Henn, R.; Opitz, O.; Shephard, R.W. (Hrsg.): Theory and Applications of Economic Indices, Würzburg
Opitz, O. (1978): Numerische Taxonomie in der Marktforschung, München
Pfouts, R.W. (1966): An Axiomatic Approach to Index Numbers, Review of the International Statistical Institute 34, 174–185
Pfouts, R.W. (1972): Index Number Systems, Econometrica 40, 931–934
Samuelson, P.A.; Swamy, S. (1974): Invariant Economic Index Numbers and Canonical Duality: Survey and Synthesis, American Economic Review 64, 566–593
Theil, H. (1960): Best Linear Index Numbers of Prices and Quantities, Econometrica 28, 464–480
Wald, A. (1937): Zur Theorie der Preisindexziffern, Zeitschrift für Nationalökonomie 8, 179–219
Wald, A. (1939): A New Formula for the Index of Cost of Living, Econometrica 7, 319–331.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1985 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bamberg, G., Spremann, K. (1985). Least-Squares Index Numbers. In: Schneeweiss, H., Strecker, H. (eds) Contributions to Econometrics and Statistics Today. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-70189-4_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-70189-4_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-70191-7
Online ISBN: 978-3-642-70189-4
eBook Packages: Springer Book Archive