 # Chain Fisher volume index - Methodology View the most recent version.

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## Example 3: Another way to remove the price effect

In example 2, the growth in GDP between Q3 and Q4 was evaluated using Q1 prices. However, with time a change in the price structure of our island economy is becoming evident: a litre of wine which was more expensive than a kilo of cheese in Q1, becomes less expensive than the latter by Q3. Thus, this time, we will measure the growth between Q3 and Q4 using Q3 prices as the base.

Q1 Q2 Q3 Q4
Cheese (kilos) q 100 105 108 112
p 15 16 18 20
1,500 1,680 1,944 2,240
Wine (litres) q 25 30 38 50
p 22 20 16 12
550 600 608 600
Total GDP   2,050 2,280 2,552 2,840

Applying Equation (3) gives us: The growth in real GDP is now evaluated at 10.3% between Q3 and Q4, rather than 13.2% with the fixed-based Laspeyres index. What happened? The change in quantities in the example 2 were evaluated using a different price structure: the change in production from 38 to 50 litres of wine was evaluated at \$22/litre, while now this increase in production is evaluated at \$16/litre. The increase in "quantity" thus carries less weight when the aggregation is done.

What would be the growth between Q1 and Q3? Since equation (3) measures only the relationship between the current and the previous period, we cannot deduct this directly from this equation. However, we can multiply the successive growth of each period between Q1 and Q3. For example, if the growth is 2.3% between Q1 and Q2 and 3.4% between Q2 and Q3, the growth between Q1 and Q3 will be 1.023 X 1.043 = 1.067, or 6.7%. This calculation (similar to the calculation of compound interest) illustrates the principle of chaining. Applied to our economy, equations (3) and (4) gives us:

Q1 Q2 Q3 Q4
Unchained Laspeyres index
i
1.000 1.090 1.091 1.103
Chained Laspeyres index
i
1.000 1.090 1.190 1.313

The growth between Q1 and Q3 will therefore be 19.0%: 