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A chain price index is a specific method of measuring changes in prices over time. It does not use a fixed reference point to express each figure as a percentage. Instead each period is expressed as a comparison to the previous period. A chain price index for easier at-a-glance reference and also allows for changes to the method used to calculate the prices.
A standard price index is a way of measuring changes in prices over time. This could be the price of a specific item, a specific type of item, or an attempt to measure all items for sale in a country. In the latter case, the usual technique is to pick a "basket" of goods, which is a selection of items designed to fairly represent all types of product available.
This standard price index uses an initial figure as a base period. In future periods, the relevant figure is expressed as a percentage of that used in the base period. For example, if for the first three years the price being tracked rose from $200 US Dollars (USD) to $250 USD to $320 USD, the index would start at 100, then rise to 125 and then to 160.
There are two main limitations to this method. Firstly, once the system has been running for a long time, it becomes harder to see right away how big a rise has taken place between two periods. For example, most people would need to perform calculations to work out if a rise in the index from 800 to 885 was more significant than one from 3300 to 3600.
The second problem is that the index can only work if the research into the pricing was always directly comparable to the base period. In practice, this is usually not the case. Economists and statisticians tend to change the contents in the "basket" of goods and services to reflect changing tastes. For example, in 2011 UK statisticians stopped including the cost of pork shoulder, but began including the cost of online dating sites. This means that a direct comparison to the base year is no longer fair.
The solution is a chain price index. Under this system, the price figure for each period is expressed as a percentage of the price figure from the previous period. In the $200/250/320 USD example, the first two year's index figures would remain as 100 and 125 but the third year would now be based on the second year, changing the index to 128. This makes it easy to see that the change from the second to third year is proportionally only very slightly above the change from the first to second year. The name chain price index comes from the fact that each comparison between consecutive periods can be chained together to make a consistent and comparable series of index figures.