A New Index Number Formula

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


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
$$ \sum\limits_{{i = 1}}^n {{{\bar{w}}_{{it}}}\;\log \frac{{{p_{{it}}}}}{{{p_{{i,t - 1}}}}}\;and\;\sum\limits_{{i = 1}}^n {{{\bar{w}}_{{it}}}} \;\log } \frac{{{q_{{it}}}}}{{{q_{{i,t - 1}}}}} $$
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
$$ {\bar{w}_{{it}}} = \frac{1}{2}\left( {{w_{{it}}} + {w_{{i + t - 1}}}} \right) $$
is the arithmetic average expenditure share of the i th commodity in the two successive periods. All logarithms are natural logarithms.


Price Index Index Number House Rent Successive Period Expenditure Share 
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Copyright information

© Springer Science+Business Media Dordrecht 1992

Authors and Affiliations

  1. 1.University of ChicagoChicagoUSA

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