Rebasing and Linking of National
Accounts
Workshop on the Methodological Review of Benchmarking,
Rebasing and Chain-Linking of Economic Indicators
24-26 August 2011, Vientiane, Lao People’s Democratic
Republic
Benson Sim
UN STATISTICS DIVISION
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Nominal vs Volume measures of GDP
What is rebasing?
Why is rebasing needed?
How is rebasing done?
• Periodic rebasing
• With no linking
• With linking
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• Annual rebasing (annual chain-linking)
What are the main effects of rebasing and linking?
Conclusion
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GDP data are expressed at current prices, i.e., prices of
the prevailing accounting period
• Also known as nominal GDP
Changes in nominal GDP over time arise from two effects
• Price effect (inflation)
• Volume effect (quantity of goods and services)
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Proper assessment of economic growth requires removal
of price effect
This is done by calculating GDP for each year at the
prices of a particular year (base year)
Base year is the year to which the weights relate in the
construction of a volume or price index
GDP measures with the price effect removed are known
as volume measures of GDP
Changes in volume measures of GDP are referred to as
real GDP growth
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Volume measures of GDP can be obtained through
various methods
• Deflation
• Divide nominal value of the transaction (output,
intermediate consumption, final consumption, etc)
by an appropriate price index
• Quantity revaluation
• Multiply base period prices by actual quantity data
• Volume extrapolation
• Extrapolate base period value by appropriate
quantity indicator
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Deflation is preferred because
• Prices usually show less variation than quantities
• Sampling errors associated with price indexes tend to
be smaller
• Price indexes can capture quality changes better than
quantity revaluation and volume extrapolation
methods
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In principle, deflation is carried out by deflating
• Nominal value of transaction by
• Paasche price index
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Laspeyres volume index
• Prices of previous period are used as weights
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Problem
• Not easy to construct Paasche price index because of
detailed data requirements
• Available price indexes are usually Laspeyres price
indexes
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Solution?
• Compile nominal data at most detailed level possible
• Example: oranges, apples, rather than fruits
• Deflate nominal data at most possible detailed level by
• Laspeyres price index
• Approximate Laspeyres volume index
Aggregate to obtain volume measures of GDP
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Prices used to calculate volume measures of GDP need
to be frequently updated
Process of replacing present price structure (base year)
to compile volume measures of GDP with a new or more
recent base year is known as rebasing
• Changing price and quantity base for individual price
and quantity relatives
• Updating weights used in aggregating individual
quantity relatives into sub-indexes and aggregating
these sub-indexes into more aggregated indexes (for
example, GDP)
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Continually changing economic environment
• Production side
• Structural changes in production patterns over time
• Continuous developments and innovations
• Obsoleteness of many products
• Demand side
• Structural changes in consumption patterns
• Structural changes in acquisition of capital goods
• Changes in openness of economy to rest of the
world
Implies relative prices change over time
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Price structure less representative of base year structure
as time progresses
Products with relatively higher volume growth tend to
have relatively weaker price increases – substitution
effect
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But, they tend to comprise larger share of GDP at
present base year (prices of distant past)
Volume measures of GDP will become misstated because
of substitution bias
• Less useful for economic analysis
Need to update base year to more recent one to ensure
weights used to calculate volume measures of GDP are
more representative of economic reality
• Correct substitution bias
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Rebasing (update of base year) can be carried out as
follows:
• Periodic rebasing
• With no linking
• With linking
• Annual rebasing (annual chain-linking)
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Rebasing is often carried out in conjunction with the
incorporation of data for a new benchmark year
Nominal data between benchmark years will need to be
revised before rebasing is carried out
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Update base year every 5 years
Need to select appropriate new base year which should
be normal year without dramatic economic changes
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For volume measures of transactions which are obtained
by deflation
• Change reference year of deflator at most detailed
level possible to new base year (i.e., divide value of
deflators in old base year by value of deflator for new
base year)
• Deflate nominal value using the new deflators
• Alternatively, extrapolate most detailed nominal value
of transaction at new base year using real growth
rates of previous base year
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For volume measures of transactions which are obtained
by quantity revaluation
• Replace prices for revaluation with those for new base
year
For volume measures of transactions which are obtained
by volume extrapolation
• Change the year from which level is being
extrapolated to new base year
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Periodic rebasing with no linking can be carried out in
two ways
• Rebasing of entire time series of GDP and its
components
• Rebasing of GDP and its components from new base
year onwards
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Rebasing of entire time series with no linking
• Perform deflation, quantity revaluation, and/or volume
extrapolation for entire time series of transactions at
most detailed level
• Aggregate resultant entire time series of volume
measures of transactions to calculate volume measures
of GDP with price structure of new base year
• Volume measures of GDP from new base year are
Laspeyres volume measures
• Volume measures of GDP before new base year are
Paasche volume measures
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Result
• Entire time series of volume measures of GDP is additive
(i.e., components of GDP sum up to GDP)
• But, economic history is rewritten and real GDP growth
rates are revised throughout (tend to be lower)
• Price structure of new base year may not be appropriate
for earlier years of time series which may be far away
• May cause loss of confidence in estimates due to
revisions to historical growth rates
• Not recommended
• Can we improve things? Yes, we can
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Rebasing from new base year onwards with no
linking
• Perform deflation, quantity revaluation, and/or volume
extrapolation from new base year onwards at most
detailed level of transaction
• Aggregate resultant volume measures of transactions to
calculate volume measures of GDP from new base year
onwards using price structure of new base year
• Volume measures of GDP before new base year are
calculated using price structure of previous base years
• These volume measures are Laspeyres volume measures
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Result
• Volume measures of GDP are expressed at prices of
previous and new base years and are additive
• Real GDP growth rates will only be revised from new
base year onwards (tend to be lower)
• Real GDP growth rates of previous base years will not be
revised
• Thus, there is no entire historical revision of growth rates
• Real GDP growth rates are calculated using weights
which are more representative of each base year
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Result
• But, we have inconsistent time series of volume
measures of GDP due to use of different base years
• Example: If we have three base years, we will have
three time series of volume measures expressed at
the prices of three different base years
• Need to insert break (|) in series between ending year of
one base year and starting year of next base year
• Common practice in Asia and Pacific region
• Some examples: Bhutan, Cambodia, Fiji Islands,
Indonesia, Malaysia, Myanmar
• Can we improve things? Yes, we can
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Aggregate volume measures of transactions to calculate
volume measures of GDP from new base year onwards
using price structure of new base year
Volume measures of GDP before new base year are
calculated using price structure of previous base years
Join volume measures of GDP at new and previous base
years so that they are expressed in terms of the prices of
a specific year (i.e., reference year)
This process is known as linking
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Reference year is usually the same as new base year in
practice so that the GDP volume measures for recent
years are close to corresponding nominal measures
At the reference year, nominal and volume measures of
GDP and its components are the same
Linking is done by extrapolating backward separately the
volume measures of GDP and its components at the
most detailed level possible at the reference year using
the real growth rates of GDP and its components which
are calculated at the previous base years
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Result
• Consistent time series of volume measures of GDP
expressed at prices of a specific (reference) year
• Volume measures of GDP are chained at the reference
year
• Real GDP growth rates will only be revised from new
base year onwards (tend to be lower)
• Real GDP growth rates of previous base years will not be
revised
• Thus, there is no entire historical revision of growth rates
• Real GDP growth rates are calculated using weights
which are more representative of each base year
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Result
• But, volume measures of GDP before reference year will
not be additive due to linking of GDP and its components
separately
• Statistical agency will need to explain clearly in its
methodology notes and metadata why volume measures
of GDP are not additive
• Practiced in a few economies in Asia and Pacific region
• Example: Singapore
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Update base year (weights) every year (2008 SNA
recommendation)
For volume measures of transactions which are obtained
by deflation
• Change reference year of deflators annually
For volume measures of transactions which are obtained
by quantity revaluation
• Change prices for revaluation annually
For volume measures of transactions which are obtained
by volume extrapolation
• Change the year from which level is being
extrapolated annually
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Aggregate volume measures of transactions to calculate
annually-chained volume indexes of GDP and
components using index number formula
• Annually-chained Laspeyres volume indexes
Q
•
t
t 1
 

p
q

 ... 

2
t
t 

  p q 
3
Annually-chained Paasche volume indexes
Q
•
L
0
1
1
2
2



p
q
p
q
p
q






0
0
1
1
2



  p q   p q   p q
P
1
1
2
2
3



p
q
p
q
p
q






1
0
2
1
3



  p q   p q   p q
t 1
t 1
 

p
q

 ... 

2
t 1
t 

  p q 
3
Annually-chained Fisher volume indexes
Q
F

Q L Q P 
1
2
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Use annually-chained volume indexes to derive chained
volume measures of GDP and its components at the
prices of a specific reference year
Linking is done by extrapolating forward and backward
separately the volume measures of GDP and its
components at the reference year using the real growth
rates of GDP and its components which are calculated
from the annually-chained volume indexes
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Result
• Real GDP growth rates are calculated using weights of
previous year (Laspeyres), current year (Paasche), or
both (Fisher)
• Thus, real GDP growth rates are calculated using weights
which are more representative than those under periodic
rebasing (tend to be lower)
• Volume measures of GDP are chained at the reference
year
• Consistent time series of volume measures of GDP
expressed at prices of a specific (reference) year
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Result
• But, volume measures of GDP are mostly not additive
• More calculations needed, especially for Fisher
• More demanding data requirements
• Common in advanced economies in Asia and Pacific
region
• Examples: Australia; Hong Kong, China; Japan;
Republic of Korea; New Zealand – all use annuallychained Laspeyres index number formula
• Canada and the United States use annually-chained
Fisher index number formula
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Periodic rebasing
• Products with relatively higher volume growth and
relatively weaker price increases will tend to have lower
weight in new base year
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Periodic rebasing
• If new base year is used for entire GDP series
• Volume measures of GDP are additive
• Consistent time series of volume measures of GDP
• Economic history is rewritten
• If new base year is used for GDP series from new base
year onwards with no linking
• Volume measures of GDP are additive
• Real GDP growth rates will be revised from new base
year onwards (tend to be lower)
• Inconsistent time series for volume measures of GDP
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Periodic rebasing
• If new base year is used for GDP series from new base
year onwards with linking
• Consistent time series for volume measures of GDP
• Real GDP growth rates will be revised from new base
year onwards (tend to be lower)
• Volume measures of GDP are not additive
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Annual rebasing (annual chain-linking)
• Price structure to calculate volume measures of GDP is
updated annually
• Products with relatively higher volume growth and
relatively weaker price increases will have lower weight
• Growth rates calculated will tend to be lower than the
corresponding growth rates calculated using periodic
rebasing with different base years for different time
periods
• Loss of additivity for almost entire series
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Components of GDP do not add up to GDP
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2008 SNA recommends calculation of annually-chained
volume estimates of GDP
But, this is a resource-intensive and computationallydemanding exercise with many steps
Countries which are not in a position now to compile
annually-chained GDP may consider periodic rebasing in
the interim
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Base year should be updated every 5 years
Volume measures of GDP calculated using different base
years should be linked so that they are expressed at the
prices of a particular reference year
Countries should explain clearly to users why the linked
volume measures of GDP are not additive
At the earliest convenience, countries should switch to
computing annually-chained volume measures of GDP
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Thank You
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