Price Index - Formal Calculation - Chained Vs Non-chained Calculations

Chained Vs Non-chained Calculations

So far, in our discussion, we have always had our price indices relative to some fixed base period. An alternative is to take the base period for each time period to be the immediately preceding time period. This can be done with any of the above indices. Here's an example with the Laspeyres index, where is the period for which we wish to calculate the index and is a reference period that anchors the value of the series:

P_{t_n}= \frac{\sum (p_{c,t_1}\cdot q_{c,t_0})}{\sum (p_{c,t_0}\cdot q_{c,t_0})} \times \frac{\sum (p_{c,t_2}\cdot q_{c,t_1})}{\sum (p_{c,t_1}\cdot q_{c,t_1})} \times \cdots \times \frac{\sum (p_{c,t_n}\cdot q_{c,t_{n-1}})}{\sum (p_{c,t_{n-1}}\cdot q_{c,t_{n-1}})}

Each term

answers the question "by what factor have prices increased between period and period ". When you multiply these all together, you get the answer to the question "by what factor have prices increased since period ".

Nonetheless, note that, when chain indices are in use, the numbers cannot be said to be "in period " prices.

Read more about this topic:  Price Index, Formal Calculation

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