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A New Index Number Formula

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Part of the Advanced Studies in Theoretical and Applied Econometrics book series (ASTA, volume 25)

Abstract

Several years ago (1965, 1967) I started working with price and quantity index numbers, advocated particularly by the Finnish econometrician Törnqvist (1936), whose log-changes are defined as
$$ \sum\limits_{{i = 1}}^n {{{\bar{w}}_{{it}}}\;\log \frac{{{p_{{it}}}}}{{{p_{{i,t - 1}}}}}\;and\;\sum\limits_{{i = 1}}^n {{{\bar{w}}_{{it}}}} \;\log } \frac{{{q_{{it}}}}}{{{q_{{i,t - 1}}}}} $$
(1.1)
where p 1 ,…,p n are prices of the n commodities, the q’s are quantities, \( m = \sum\nolimits_i \; {p_i}{q_i} \) is total expenditure, w i , = p i q i /m is total expenditure share of the i th commodity, while the subscripts t − 1 and t refer to two successive periods and
$$ {\bar{w}_{{it}}} = \frac{1}{2}\left( {{w_{{it}}} + {w_{{i + t - 1}}}} \right) $$
(1.2)
is the arithmetic average expenditure share of the i th commodity in the two successive periods. All logarithms are natural logarithms.

Keywords

Price Index Index Number House Rent Successive Period Expenditure Share 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Christensen, L.R., and D.W. Jorgenson: 1970, “U.S. Real Product and Real Factor Input, 1929–1967,” The Review of Income and Wealth, Series 16, 19–50.CrossRefGoogle Scholar
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Copyright information

© Springer Science+Business Media Dordrecht 1992

Authors and Affiliations

  1. 1.University of ChicagoChicagoUSA

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