# A New Index Number Formula

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## 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
where
is the arithmetic average expenditure share of the

$$ \sum\limits_{{i = 1}}^n {{{\bar{w}}_{{it}}}\;\log \frac{{{p_{{it}}}}}{{{p_{{i,t - 1}}}}}\;and\;\sum\limits_{{i = 1}}^n {{{\bar{w}}_{{it}}}} \;\log } \frac{{{q_{{it}}}}}{{{q_{{i,t - 1}}}}} $$

(1.1)

*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)

*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

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© Springer Science+Business Media Dordrecht 1992