Introduction of the Chain Fisher Measure of Real GDP

Introduction of the Chain Fisher
Measure of Real GDP
As of May 31 2001, the quarterly
Income and Expenditure Accounts
will adopt the chain Fisher index
formula as the official measure of real
expenditure-based Gross Domestic
Product.

Why Change?
• The new calculation produces the most
accurate measure of quarter to quarter
growth in GDP and its components;
• The change brings the Canadian measure in
line with the US quarterly Income and
Product Accounts which also use the chain
Fisher formula to measure real GDP.

What is different?
• The weights used to add up real GDP will
be based on the Fisher formula instead of
the Laspeyres formula
• Chaining is done quarterly instead of
periodically

The Old Measure
• Laspeyres formula
LV
=
∑
∑
p
p
0
0
q
q
t
0
• chained periodically

Strengths and Weaknesses of the Old Measure
• Strengths
– easy to use statistically and analytically
– additive in periods following the most recent
base year
• Weaknesses
– biased because weights are from the past
– tends to « drift » due to bias
– non-additive prior to the base year

The New Measure
• The Fisher formula
FV
=
∑
∑
p
p
t−1
t−1
q
q
t
t−1
×
∑
∑
p q
t
t
p q
t
t−1
• chained each quarter

The Fisher Formula
FV
=
∑
p
t−
1
q
t
×
∑
p
t
q
t
∑
p
t−
1
q
t−
1
∑
p
t
q
t−
1

Level of Detail
• 379 components of seasonally adjusted data
– 130 Personal Expenditure
– 25 Government Expenditure
– 30 Capital Formation
– 56 Inventories
– 68 Imports
– 69 Exports

Strengths and Weaknesses of the New Measure
• Strengths
– substitution bias is minimized
– « drift » is minimized
• Weaknesses
– computationally difficult
– not additive for any time period due to chaining

What is the Economic
Significance of the Change?
• The Laspeyres measure overstates
economic growth when:
– some prices are declining monotonically
relative to other prices in the economy (ICT)
– there is an abrupt shift in relative prices (Crude
petroleum)

Impact on GDP & Selected Components

Impact on GDP & Selected Components

Investment Growth Comparison
8
6
4
Canada vs US
%
2
0
-2
-4
-6
92q2
92q4
93q2
93q4
94q2
94q4
95q2
95q4
96q2
96q4
97q2
97q4
98q2
98q4
99q2
99q4
Gross Private Domestic Invest., US
Gross Private Domestic Invest., Canada, Laspeyres

Investment Growth Comparison - Fisher
Canada vs US
%
8
6
4
2
0
-2
-4
-6
92q2
92q4
93q2
93q4
94q2
94q4
95q2
95q4
96q2
96q4
97q2
97q4
98q2
98q4
99q2
99q4
Gross Private Domestic Invest., US
Gross Private Domestic Invest., Canada, Fisher

Impact on Overall GDP Growth
2
1.5
Laspeyres (base year 1992) vs Chain Fisher
%change
1
0.5
0
-0.5
92q2
92q4
93q2
93q4
94q2
94q4
95q2
95q4
96q2
96q4
97q2
97q4
98q2
98q4
99q2
99q4
00q2
Laspeyres
Chain Fisher

Cumulative Effect on GDP
% drift of GDP
ie. cumulative difference between Laspeyres growth and chain Fisher growth
1.4
1.2
1
0.8
0.6
%
0.4
0.2
0
-0.2
-0.4
92q2
92q4
93q2
93q4
94q2
94q4
95q2
95q4
96q2
96q4
97q2
97q4
98q2
98q4
99q2
99q4
00q2

Decomposition into Effect of Formula Change and
Frequency of Chaining
"drift" components
1.2
1
0.8
0.6
%
0.4
0.2
0
-0.2
-0.4
92q2
92q4
93q2
93q4
94q2
94q4
95q2
95q4
96q2
96q4
97q2
97q4
98q2
98q4
99q2
99q4
00q2
Laspeyres (base year 1992) minus quarterly chain Laspeyres
quarterly chain Laspeyres minus quarterly chain Fisher

Supplementary Information
• To facilitate analysis, STC will publish
« contribution to change » tables for each
set of chained estimates published (personal
expenditure, capital formation, international
trade, investment in inventories)
• 1997 constant price data will be published
as overlap for 2 years

Contribution to Change
∑
−
−
−
−
×
+
−
×
+
×
=
∆
j
j
t
j
t
t
j
t
i
t
i
t
i
t
t
i
t
t
i
q
p
FP
p
q
q
p
FP
p
C
1
1
1
1
,
)
)
/
((
)
(
)
)
/
((
100
%

Conclusions
• This change is important to make Canada ’s
official estimate of economic growth more
accurate and comparable to that of the US
• Statistics Canada will do its best to help
users in the transition to the Fisher measure