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## Sources of bias between the national and provincial systems

The national and provincial systems are additively consistent when expressed
in nominal value. However, in real terms, the properties of the chain
Fisher index are such that this consistency can no longer be guaranteed.

First, real series based on a chain Fisher calculation are not additive.
This means that for each province and for Canada as a whole, the sum of
the aggregates will not equal the main aggregate. Another consequence
of this non-additive problem is that for each aggregate, the sum of the
provinces will not equal the national level (for example, the sum of expenditure
on consumer goods and services in all of the provinces will not equal
the national expenditure on consumer goods and services).

Second, real series are calculated differently at the national and provincial
levels. While the national annual series represent an average of the quarters,
the provincial annual series represent a chain Fisher index calculated
on the year. These two different methodologies produce different results.

Third, theoretically there are two ways to calculate real series at the
national level. Fisher indexes can be calculated with the national series
(these being the sum of the provincial series), or calculated directly
with the provincial series. Since Fisher is an index sensitive to the
number of series involved in the calculation, the two calculations do
not produce exactly the same result.

Lastly, the level of detail is different between the national and provincial
calculations (respectively 435 and 502 series). Since Fisher is an index
sensitive to the number of series involved in the calculation, the difference
in level of detail produces an inevitable bias between the national and
provincial calculation.

For these reasons, it is unlikely that the provincial real GDP series
will be additively consistent with the national series.