# The Canadian Consumer Price Index Reference Paper Appendix A – Common Price Index Formulae

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Appendix A – Common Price Index Formulae
Table summary
This table displays the results of Appendix A – Common Price Index Formulae. The information is grouped by Common index formulae for elementary price indices (lower level) (appearing as row headers), (appearing as column headers).
Common index formulae for elementary price indices (lower level)
Name Index formulae Description
Dutot ${I}_{D,a}^{t-1:t}=\frac{\sum _{i=1}^{n}\frac{1}{n}{p}_{i}^{t}}{\sum _{i=1}^{n}\frac{1}{n}{p}_{i}^{t-1}}$ A price index defined as the ratio of the unweighted arithmetic average of the prices in the current period t to the unweighted arithmetic average of the prices in period t-1. See chapter 6, formula 6.3.
Jevons ${I}_{J,a}^{t-1:t}=\frac{\prod _{i=1}^{n}{\left({p}_{i}^{t}\right)}^{1}{n}}}{\prod _{i=1}^{n}{\left({p}_{i}^{t-1}\right)}^{1}{n}}}$ A price index defined as the ratio of the unweighted geometric average of the prices in the current period t to the unweighted geometric average of the prices in period t-1. See chapter 6, formula 6.2.
Weighted Jevons ${I}_{WJ,a}^{t-1:t}=\frac{\prod _{i=1}^{n}{\left({p}_{i}^{t}\right)}^{{w}_{i}/\sum _{i=1}^{n}{w}_{i}}}{\prod _{i=1}^{n}{\left({p}_{i}^{t-1}\right)}^{{w}_{i}/\sum _{i=1}^{n}{w}_{i}}}$ A price index defined as the ratio of the explicitly weighted geometric average of the prices in the current period t to the explicitly weighted geometric average of the prices in period t-1. See chapter 6, formula 6.4.
Common index formulae for aggregate price indices (upper level)
Name Index formulae Description
Fisher ${I}_{F,A}^{0:t}={\left({I}_{L,A}^{0:t}×{I}_{P,A}^{0:t}\right)}^{\frac{1}{2}}$ A price index defined as a geometric average of the Laspeyres price index and the Paasche price index. It is a symmetrically weighted index using quantities of goods and services from both periods 0 and t.
Laspeyres ${I}_{L,A}^{0:t}=\frac{\sum _{i=1}^{n}{p}_{i}^{t}{q}_{i}^{0}}{\sum _{i=1}^{n}{p}_{i}^{0}{q}_{i}^{0}}$ A price index defined as an asymmetrically weighted fixed-basket index that uses the quantities of goods and services from the base period 0. See chapter 6, formula 6.5.
Lowe ${I}_{Lo,A}^{0:t}=\frac{\sum _{i=1}^{n}{p}_{i}^{t}{q}_{i}^{b}}{\sum _{i=1}^{n}{p}_{i}^{0}{q}_{i}^{b}}$ A price index defined as an asymmetrically weighted fixed-basket index that uses the quantities of goods and services from the chosen weight reference period b. See chapter 6, formula 6.6.
Marshall-Edgeworth ${I}_{ME,A}^{0:t}=\frac{\sum _{i=1}^{n}{p}_{i}^{t}×\left[\frac{\left({q}_{i}^{0}+{q}_{i}^{t}\right)}{2}\right]}{\sum _{i=1}^{n}{p}_{i}^{0}×\left[\frac{\left({q}_{i}^{0}+{q}_{i}^{t}\right)}{2}\right]}$ A price index defined as the ratio of average weighted prices between period 0 and t with weights as the arithmetic average of quantities from both periods 0 and t. It is a symmetrically weighted fixed-basket index.
Paasche ${I}_{P,A}^{0:t}=\frac{\sum _{i=1}^{n}{p}_{i}^{t}{q}_{i}^{t}}{\sum _{i=1}^{n}{p}_{i}^{0}{q}_{i}^{t}}$ A price index defined as an asymmetrically weighted fixed-basket index that uses the quantities of goods and services from the current period t.
Törnqvist-Theil ${I}_{T,A}^{0:t}=\prod _{i=1}^{n}{\left(\frac{{p}_{i}^{t}}{{p}_{i}^{0}}\right)}^{\frac{1}{2}\left({s}_{i}^{0}+{s}_{i}^{t}\right)}$

Where

${s}_{i}^{0}\equiv \frac{{p}_{i}^{0}{q}_{i}^{0}}{\sum _{i=1}^{n}{p}_{i}^{0}{q}_{i}^{0}}$

${s}_{i}^{t}\equiv \frac{{p}_{i}^{t}{q}_{i}^{t}}{\sum _{i=1}^{n}{p}_{i}^{t}{q}_{i}^{t}}$
A price index defined as a geometric average of price relatives weighted by the average expenditure shares in both periods 0 and t. It is a symmetrically weighted index.
Walsh ${I}_{W,A}^{0:t}=\frac{\sum _{i=1}^{n}{p}_{i}^{t}\sqrt{{q}_{i}^{t}{q}_{i}^{0}}}{\sum _{i=1}^{n}{p}_{i}^{0}\sqrt{{q}_{i}^{t}{q}_{i}^{0}}}$ A price index defined as the ratio of average weighted prices between period 0 and t with weights as the geometric average of quantities from both periods 0 and t. It is a symmetrically weighted fixed-basket index.
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