Statistics Canada
Symbol of the Government of Canada

Chain Fisher volume index - Methodology

Warning View the most recent version.

Archived Content

Information identified as archived is provided for reference, research or recordkeeping purposes. It is not subject to the Government of Canada Web Standards and has not been altered or updated since it was archived. Please "contact us" to request a format other than those available.

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:

Laspeyres unchained volume, Q3/Q2

The calculation of the Fisher index for the same period will give:

Fisher unchained volume, Q3/Q2

    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.

Table of contents