Download Demonstration - United Nations Statistics Division

Demonstration on 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
•
•
•
Rebasing of national accounts using hypothetical
dataset
• Calculate volume measures of GDP and Laspeyres
volume indexes using a specific base year (Table 2)
• Rebase entire GDP series using new base year
(Table 3)
• Rebase GDP series from new base year onwards
with no linking (Table 4)
• Rebase GDP series from new base year onwards
with linking (Table 5)
• Calculate annually-chained volume indexes and
measures of GDP (Tables 6 to 8)
Conclusion
Extensive reference will be made to Excel tables
2
Assumptions
• 2 single (homogenous) products, X and Y, in an economy
• X and Y are most detailed products available (i.e., no
further breakdown possible)
• Real growth rates of X and Y will be the same in all
situations
• Statistical agency has available information on price
indexes and value at current prices of X and Y
• X shows rising prices and Y shows falling prices
• Example of X: service
• Example of Y: information technology good
3
•
•
Currently, statistical agency calculates volume measures of
entire GDP series using Year 1 as base year
For each product (X and Y), calculate volume measure by
deflating nominal value by price index for each year
• Example: Volume measure of X for Year 3 is
Nominal value for Year 3 from Table 1
×100
Price index for Year 3 from Table 1
233.1

 100  224.1
104.0
4
•
•
•
Sum up deflated values of X and Y to obtain volume
measures of GDP
Calculate real growth rates of X, Y, and GDP
Calculate Laspeyres volume index for GDP with Year 1 as
reference year (i.e., volume index for Year 1 will have value
of 100.0)
• Example: Laspeyres volume index for GDP for Year 3 is
Volume measure for Year 3 from Table 2
×100
Volume measure for Year 1 from Table 2
429.2

 100  122.6
350.0
5
•
•
•
Statistical agency realises that present base year (Year 1)
has become outdated and decides to rebase GDP
Statistical agency calculates volume measures of entire GDP
series using Year 6 as new base year as it finds that Year 6
is a normal year with no dramatic changes
For each product (X and Y), compute price indexes with
Year 6 as reference period (i.e., price indexes for Year 6 will
have value of 100.0)
• Example: Price index for X for Year 9 is
Price index for Year 9 from Table 1
×100
Price index for Year 6 from Table 1
116.0

 100  105.4
110.1
6
•
For each product (X and Y), calculate volume measure
by deflating nominal value by price index for each year
• Example: Volume measure of X for Year 9 is
Nominal value for Year 9 from Table 1
×100
Price index for Year 9 from Table 3
318.0

 100  301.8
105.4
7
•
•
•
Sum up volume measures of X and Y to obtain volume
measures of GDP
Calculate real growth rates of X, Y, and GDP
Compute Laspeyres volume index for GDP with Year 6 as
reference year (i.e., volume index for Year 6 will have
value of 100.0)
• Example: Laspeyres volume index for GDP for Year 9 is
Volume measure for Year 9 from Table 3
×100
Volume measure for Year 6 from Table 3
486.8

 100  125.7
387.2
8
•
•
•
•
•
Consistent time series for volume measures of GDP
Real growth rates of X and Y are same as those in Table 2
because X and Y are most detailed products available
Volume measures of GDP are additive, but real GDP growth
rates have been revised throughout and are much lower
Economic history has been rewritten
As mentioned earlier, this method of doing rebasing is not
recommended
9
•
•
•
•
Statistical agency realises that the rebasing method in Table
3 is not appropriate as economic history has been rewritten
Statistical agency decides to calculate volume measures of
GDP from Year 6 using Year 6 as base year and volume
measures of GDP from Years 1 to 6 using Year 1 as base
year
Volume measures of X, Y, and GDP from Years 1 to 6 will be
same as those in Table 2
Volume measures of X, Y, and GDP from Years 6 to 10 will
be same as those in Table 3
10
•
•
Combine the two sub-series to get entire time series (see
bottom of table)
Insert break (|) between volume measures for Years 5 and
6 to indicate they are calculated using different base years
11
•
•
Question
• Which real GDP growth rate for Year 6 do we use?
• Real GDP growth rate calculated using Year 1 as base
year (11.6%)?
• Real GDP growth rate calculated using Year 6 as base
year (7.4%)?
Answer
• Real GDP growth rate calculated using Year 1 as base
year (11.6%)
12
•
Why?
• Volume measures of GDP calculated using Year 6 as
base year only start from Year 6, not Year 5
• Volume measures of GDP from Years 1 to 6
calculated using Year 1 as base year are available
13
•
•
•
•
•
•
Real growth rates of X and Y are same as those in Table 2
because X and Y are most detailed products available
Volume measures of GDP are additive
Real GDP growth rates from Years 2 to 6 are the same as
those in Table 2
Real GDP growth rates from Year 7 are lower than those in
Table 2
Periodic rebasing ensures real GDP growth rates in recent
years are calculated with weights more representative of
new base year
But, inconsistent time series for volume measures of GDP
14
•
•
•
To solve problem with inconsistent volume measures of
GDP, statistical agency decides to link the two sub-series
in Table 4 using Year 6 as reference year
Volume measures of X, Y, and GDP from Years 6 to 10
will be same as those in Table 4
Calculate volume measures of X, Y, and GDP and volume
indexes of GDP separately before Year 6 by using their
real growth rates at prices of Year 1 to extrapolate
backwards their levels for Year 6
15
•
Example: Volume measure of X for Year 5 is
Volume measure for Year 6 from Table 5
 Real growth rate for Year 6 from Table 5 
1+

100


×100
271.1

 262.6
3.2 

 1  100 


16
•
Example: Volume measure of X for Year 4 is
Volume measure for Year 5 from Table 5
 Real growth rate for Year 5 from Table 5 
1+

100


×100
262.6

 254.0
3.4 

 1  100 


17
•
Example: Volume measure of GDP for Year 5 is
Volume measure for Year 6 from Table 5
 Real growth rate for Year 6 from Table 5 
1+

100


×100
387.2

 346.9
11.6 

1  100 


18
•
Example: Volume measure of GDP for Year 4 is
Volume measure for Year 5 from Table 5
 Real growth rate for Year 5 from Table 5 
1+

100


×100
346.9

 310.5
11.7 

1  100 


19
•
Example: Laspeyres volume index for GDP for Year 5
is
Laspeyres volume index for Year 6 from Table 5
 Real growth rate for Year 6 from Table 5 
1+

100



×100
100.0
 100  89.6
11.6 

1  100 


20
•
Example: Laspeyres volume index for GDP for Year 4
is
Laspeyres volume index for Year 5 from Table 5
 Real growth rate for Year 5 from Table 5 
1+

100


×100
89.6

 100  80.2
11.7 

1  100 


21
•
•
•
•
•
Real growth rates of X and Y are same as those in Table 2
because X and Y are most detailed products available
Real GDP growth rates from Years 2 to 6 are the same as
those in Table 2
Real GDP growth rates from Year 7 are lower than those in
Table 2
Laspeyres volume indexes for GDP are periodically chained
But, volume measures of GDP are non-additive from Years
1-5 (i.e., X and Y do not add up to GDP) due to the linking
of components and GDP independently
22
•
•
Nevertheless, it is preferable to rebase GDP and then link
the volume series so as not to create breaks
Explain in methodological notes and metadata why volume
measures of GDP are non-additive after rebasing and linking
23
•
•
•
•
Statistical agency decides to calculate experimental
annually-chained volume indexes and measures of GDP to
see how real growth rates would look like
Statistical agency decides to do this using the Fisher index
number formula
Statistical agency also decides to express the volume
measures using Year 6 as reference year
Statistical agency will need to calculate annually-chained
Laspeyres and Paasche volume indexes as the annuallychained Fisher volume indexes are the geometric mean
(i.e., square root) of the product of these two volume
indexes
24
•
•
Compute annually-chained Laspeyres volume indexes and
measures as follows
For each product (X and Y), calculate volume measure for
Year t at prices of previous year (t-1) separately by using
their real growth rates to extrapolate their nominal levels
for Year t
• Example: Volume measure of X for Year 2 at price of
Year 1 is
 Real growth rate for Year 2 from Table 2 
Nominal value for Year 1 from Table 1  1+

100


3.2 

 210.0  1 
 216.7

100 

25
•
Example: Volume measure of X for Year 3 at price of
Year 2 is
 Real growth rate for Year 3 from Table 2 
Nominal value for Year 2 from Table 1  1+

100


3.5 

 221.2  1 
 228.8

100 

26
•
•
Sum up resultant volume measures of X and Y to obtain
volume measures of GDP at prices of previous year (t-1)
Compute Laspeyres volume index for GDP at prices of
previous year (t-1)
• Example: Laspeyres volume index for GDP for Year 2 is
Volume measure for Year 2 from Table 6
×100
Nominal value for Year 1 from Table 1

386.0
 100  110.3
350.0
27
•
Example: Laspeyres volume index for GDP for Year 3 is
Volume measure for Year 3 from Table 6
×100
Nominal value for Year 2 from Table 1
393.3

 100  110.2
357.0
28
•
Compute annually-chained Laspeyres volume index for
GDP using Year 6 as reference year
• Example: Annually-chained Laspeyres volume index for
GDP for Year 7 is
Index for Year 6 from Table 6 
Laspeyres volume index for Year 7 from Table 6
100
107.9
 100.0 
 107.9
100
29
•
Example: Annually-chained Laspeyres volume index for
GDP for Year 8 is
Index for Year 7 from Table 6 
Laspeyres volume index for Year 8 from Table 6
100
 107.9 
107.3
 115.8
100
30
•
•
Compute annually-chained Laspeyres volume measures for
X, Y, and GDP using Year 6 as reference year
Thus, annually-chained Laspeyres volume measures for X,
Y and GDP for Year 6 will be same as corresponding
nominal values in Table 1
• Example: Annually-chained Laspeyres volume measure
for GDP for Year 7 is
Value for Year 6 from Table 6 
Laspeyres volume index for Year 7 from Table 6
100
 387.2 
107.9
 417.9
100
31
•
Example: Annually-chained Laspeyres volume measure
for GDP for Year 8 is
Chained value for Year 7 from Table 6 
 417.9 
•
Laspeyres volume index for Year 8 from Table 6
100
107.3
 448.4
100
Compute real growth rates of annually-chained Laspeyres
volume measures for X, Y, and GDP
32
•
•
•
Real growth rates of X and Y are same as those in Table 2
because X and Y are most detailed products available
Real GDP growth rates from Year 3 onwards are lower than
those in Table 2
Annually-chained Laspeyres volume measures of GDP are
non-additive (i.e., X and Y do not add up to GDP) for all
years except Years 6 and 7
33
•
•
Compute annually-chained Paasche volume indexes and
measures as follows
For each product (X and Y), calculate volume measure for
Year t at prices of following year (t+1) separately by using
the reciprocal of their real growth rates to extrapolate their
nominal levels for Year t+1
• Example: Volume measure of X for Year 1 at the price of
Year 2 is
Nominal value for Year 2 from Table 1  


1

Real
growth
rate
for
Year
2
from
Table
2


1+

100


 1

 221.2  
 214.4

3.2
1 

100 

34
•
Example: Volume measure of X for Year 2 at price of
Year 3 is
Nominal value for Year 3 from Table 1  


1

 Real growth rate for Year 3 from Table 2  
1+

100


 1

 233.1  
 225.3

3.5
1 

100 

35
•
•
Sum up resultant volume measures of X and Y to obtain
volume measures of GDP at prices of following year (t+1)
Compute Paasche volume index for GDP at prices of
following year (t+1)
• Example: Paasche volume index for GDP for Year 2 is
Nominal value for Year 2 from Table 1
×100
Volume measure for Year 1 from Table 7

357.0
 100  109.3
326.7
36
•
Example: Paasche volume index for GDP for Year 3 is
Nominal value for Year 3 from Table 1
×100
Volume measure for Year 2 from Table 7

364.4
 100  109.2
333.7
37
•
Compute annually-chained Paasche volume index for GDP
using Year 6 as reference year
• Example: Annually-chained Paasche volume index for
GDP for Year 7 is
Index for Year 6 from Table 7 
Paasche volume index for Year 7 from Table 7
100
107.3
 100.0 
 107.3
100
38
•
Example: Annually-chained Paasche volume index for
GDP for Year 8 is
Index for Year 7 from Table 7 
Paasche volume index for Year 8 from Table 7
100
 107.3 
106.8
 114.6
100
39
•
•
Compute annually-chained Paasche volume measures for
X, Y, and GDP using Year 6 as reference year
Thus, annually-chained Paasche volume measures for X, Y
and GDP for Year 6 will be same as corresponding nominal
values in Table 1
• Example: Annually-chained Paasche volume measure
for GDP for Year 7 is
Value for Year 6 from Table 7 
Paasche volume index for Year 7 from Table 7
100
 387.2 
107.3
 415.4
100
40
•
Example: Annually-chained Paasche volume measure
for GDP for Year 8 is
Chained value for Year 7 from Table 7 
 415.4 
•
Paasche volume index for Year 8 from Table 7
100
106.8
 443.7
100
Compute real growth rates of annually-chained Paasche
volume measures for X, Y, and GDP
41
•
•
•
Real growth rates of X and Y are same as those in Table 2
because X and Y are most detailed products available
Real GDP growth rates are lower than those in Table 2 and
Table 6
Annually-chained Paasche volume measures of GDP are
non-additive (i.e., X and Y do not add up to GDP) for all
years except Years 5 and 6
42
•
•
Compute annually-chained Fisher volume indexes and
measures as follows
Compute Fisher volume indexes for GDP as geometric mean
(square root) of corresponding Laspeyres and Paasche
volume indexes
• Example: Fisher volume index for GDP for Year 2 is
Laspeyres volume index from Table 6  Paasche volume index from Table 7
1
2
 110.3109.3   109.8
43
1
2
•
Example: Fisher volume index for GDP for Year 3 is
Laspeyres volume index from Table 6  Paasche volume index from Table 7
1
2
 110.2109.2   109.7
44
1
2
•
Compute annually-chained Fisher volume index for GDP
using Year 6 as reference year
• Example: Annually-chained Fisher volume index for GDP
for Year 7 is
Index for Year 6 from Table 7 
Fisher volume index for Year 7 from Table 8
100
107.6
 100.0 
 107.6
100
45
•
Example: Annually-chained Fisher volume index for GDP
for Year 8 is
Index for Year 7 from Table 7 
Fisher volume index for Year 8 from Table 8
100
 107.6 
•
107.0
 115.2
100
Annually-chained Fisher volume index for GDP can also be
computed as the geometric mean (square root) of
corresponding annually-chained Laspeyres and Paasche
volume indexes
46
•
•
Compute annually-chained Fisher volume measures for X,
Y, and GDP using Year 6 as reference year
Thus, annually-chained Fisher volume measures for X, Y
and GDP for Year 6 will be same as corresponding nominal
values in Table 1
• Example: Annually-chained Fisher volume measure for
GDP for Year 7 is
Value for Year 6 from Table 8 
Fisher volume index for Year 7 from Table 8
100
 387.2 
107.6
 416.7
100
47
•
Example: Annually-chained Fisher volume measure for
GDP for Year 8 is
Chained value for Year 7 from Table 8 
 416.7 
•
Fisher volume index for Year 8 from Table 8
100
107.0
 446.0
100
Compute real growth rates of annually-chained Fisher
volume measures for X, Y, and GDP
48
•
•
•
•
•
Real growth rates of X and Y are same as those in Table 2
because X and Y are most detailed products available
Real GDP growth rates are lower than those in Table 2 and
between those in Table 6 and Table 7
Real GDP growth rates computed using annually-chained
Fisher index number formula provide most appropriate
picture of economic growth as it uses weights from two
consecutive years
Annually-chained Fisher volume measures of GDP are nonadditive (i.e., X and Y do not add up to GDP) for all years
except Year 6
Calculation of annually-chained Fisher volume indexes is
demanding exercise as it involves many steps
49
•
•
•
Real growth rates of X and Y are same in all situations
because X and Y are most detailed products available
Periodic rebasing helps to ensure real GDP growth rates in
recent years are calculated with weights which are more
representative of new base year
Calculating annually-chained GDP volume measures (as
recommended by 2008 SNA) helps to ensure real GDP
growth rates are calculated with even more representative
weights
50
•
•
•
However, computation of annually-chained GDP volume
indexes and measures (especially, Fisher) is resourceintensive and computationally-demanding exercise
Also, additivity of GDP is not preserved
If statistical agencies are currently not in a position to
calculate annually-chained GDP volume measures, they
should consider periodic rebasing with linking so that
consistent time-series volume measures of GDP can be
produced
51
•
•
•
Base year should not be more than 5 years old
Statistical agencies should explain clearly in methodological
notes and metadata why periodic rebasing with linking will
result in volume measures of GDP becoming non-additive
At the earliest convenience, statistical agencies should
switch to computing annually-chained volume measures of
GDP
52
Thank You
53