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Different ways of measuring
the Consumer Price Index (CPI)
Economics, Economic / Financial Data The consumer price index ( The percentage change in the The following sections describe some of the different methods for calculating Laspeyres Index
Where: is
the price of item
i at
time 0 (the base period)
is the price of item i at time t is the quantity consumed of item i at time 0 An alternative formula for the Laspeyres index is as follows: Where is the level of expenditure of item i at time 0. An advantage of the Laspeyres index is that it is relatively easy to get timely figures. If you already have the prices and weights for the base period, you would only need prices for the period you want to investigate. For most other indices, you would need both prices and weights to be up-to-date for that period. A disadvantage of the Laspeyres index, is that it can suffer from item substitution bias (explained later). Paasche Index
Where: is
the price of item
i at
time 0 (the base period)
is the price of item i at time t is the quantity consumed of item i at time t An alternative formula for the Paasche index is as follows: Where is the level of expenditure of item i at time t. Fisher Index
The Fisher index helps overcome the problem of item substitution bias. Item Substitution
Bias
Let’s say the price increases for a good with a high weighting and the price remains the same for a good with a low weighting. If consumers respond to the price increase of the first good, by substituting it with the second, the overall inflation estimate would be overstated if a Laspeyres index is used. This is an example of item substitution bias. The Laspeyres method tends to over-estimate the general price level, while the Paasche method tends to under-estimate it. The above table and graph are from: OECD Seminar 2005, Inflation Measures: too high – too low – internationally comparable? Measurement Issues in the http://www.oecd.org/dataoecd/4/32/35081389.pdf Lowe Index
Where: is
the price of item
i at
time 0 (the base period)
is the price of item i at time t is the quantity consumed of item i at time r An alternative formula for the Lowe index is as follows: Where is the level of expenditure of item i at time r. Törnqvist Index
OR Walsh Index
See
also:
Elementary Indices Axiomatic Analysis of Elementary Indices |
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