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Chain Fisher volume index - Methodology
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Example 4: In the real world: the deflation method
In the real world, national accountants typically don't have prices and quantities as shown in the previous examples. Instead, they have series in nominal terms (in current dollars) and their corresponding prices, as shown in the table below:
| Q1 | Q2 | Q3 | Q4 | ||
|---|---|---|---|---|---|
| Cheese (kilos) | v | 1,500 | 1,680 | 1,944 | 2,240 |
| p | 15 | 16 | 18 | 20 | |
| Wine (litres) | v | 550 | 600 | 608 | 600 |
| p | 22 | 20 | 16 | 12 | |
| Total GDP | 2,050 | 2,280 | 2,552 | 2,840 |
In this example, real GDP will be calculated by the aggregation of the nominal series "deflated" by their prices series. We call this the "deflation method". The aggregation can be done by one or the other indexes presented in the text and expressed in terms of current dollars and prices. For example, the calculation of the Laspeyres index from equation (8) between periods Q2 and Q3 will give us:
The calculation of the Fisher index for the same period will give:
| Q1 | Q2 | Q3 | Q4 | ||
|---|---|---|---|---|---|
| Unchained Laspeyres index | 1.000 | 1.090 | 1.091 | 1.103 | |
| Chained Laspeyres index | 1.000 | 1.090 | 1.190 | 1.313 | |
| Unchained Fisher index | 1.000 | 1.088 | 1.084 | 1.095 | |
| Chained Fisher index | 1.000 | 1.088 | 1.179 | 1.291 |
We can see that the chained Fisher index gives us a growth of 17.9% between Q1 and Q3, compared to 19.0% for a chained Laspeyres.
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