benson sim un statistics division demonstration on rebasing and linking of national accounts...
TRANSCRIPT
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Benson Sim
UN STATISTICS DIVISION
Demonstration on Rebasing and Linking of National AccountsWorkshop on the Methodological Review of
Benchmarking, Rebasing and Chain-Linking of Economic Indicators
24-26 August 2011, Vientiane, Lao People’s Democratic Republic
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Outline of Demonstration• 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
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Demonstration of RebasingTable 1
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
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DemonstrationTable 2
• 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
233.1100 224.1
104.0
Nominal value for Year 3 from Table 1×100
Price index for Year 3 from Table 1
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DemonstrationTable 2
• 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
429.2100 122.6
350.0
Volume measure for Year 3 from Table 2×100
Volume measure for Year 1 from Table 2
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DemonstrationTable 3
• 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
116.0100 105.4
110.1
Price index for Year 9 from Table 1×100
Price index for Year 6 from Table 1
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DemonstrationTable 3
• 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
318.0100 301.8
105.4
Nominal value for Year 9 from Table 1×100
Price index for Year 9 from Table 3
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DemonstrationTable 3
• 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
486.8100 125.7
387.2
Volume measure for Year 9 from Table 3×100
Volume measure for Year 6 from Table 3
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DemonstrationTable 3
• 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
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DemonstrationTable 4
• 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
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DemonstrationTable 4
• 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
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DemonstrationTable 4
• 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%)
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DemonstrationTable 4
• 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
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DemonstrationTable 4
• 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
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DemonstrationTable 5
• 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
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DemonstrationTable 5
• Example: Volume measure of X for Year 5 is
271.1262.6
3.21
100
Real growth rate for Year 6 from Table 51+
100
Volume measure for Year 6 from Table 5×100
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DemonstrationTable 5
• Example: Volume measure of X for Year 4 is
262.6254.0
3.41
100
Real growth rate for Year 5 from Table 51+
100
Volume measure for Year 5 from Table 5×100
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DemonstrationTable 5
• Example: Volume measure of GDP for Year 5 is
387.2346.9
11.61
100
Real growth rate for Year 6 from Table 51+
100
Volume measure for Year 6 from Table 5×100
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DemonstrationTable 5
• Example: Volume measure of GDP for Year 4 is
346.9310.5
11.71
100
Real growth rate for Year 5 from Table 51+
100
Volume measure for Year 5 from Table 5×100
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DemonstrationTable 5
• Example: Laspeyres volume index for GDP for Year 5 is
100.0100 89.6
11.61
100
Real growth rate for Year 6 from Table 51+
100
Laspeyres volume index for Year 6 from Table 5×100
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DemonstrationTable 5
• Example: Laspeyres volume index for GDP for Year 4 is
89.6100 80.2
11.71
100
Real growth rate for Year 5 from Table 51+
100
Laspeyres volume index for Year 5 from Table 5×100
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DemonstrationTable 5
• 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
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DemonstrationTable 5
• 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
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Demonstration
• 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 annually-chained Fisher volume indexes are the geometric mean (i.e., square root) of the product of these two volume indexes
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DemonstrationTable 6
• 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
3.2210.0 1 216.7
100
Real growth rate for Year 2 from Table 2Nominal value for Year 1 from Table 1 1+
100
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DemonstrationTable 6
• Example: Volume measure of X for Year 3 at price of Year 2 is
3.5221.2 1 228.8
100
Real growth rate for Year 3 from Table 2Nominal value for Year 2 from Table 1 1+
100
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DemonstrationTable 6
• 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
386.0100 110.3
350.0
Volume measure for Year 2 from Table 6×100
Nominal value for Year 1 from Table 1
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DemonstrationTable 6
• Example: Laspeyres volume index for GDP for Year 3 is
393.3100 110.2
357.0
Volume measure for Year 3 from Table 6×100
Nominal value for Year 2 from Table 1
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DemonstrationTable 6
• 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
107.9100.0 107.9
100
Index for Year 6 from Table 6Laspeyres volume index for Year 7 from Table 6
100
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DemonstrationTable 6
• Example: Annually-chained Laspeyres volume index for GDP for Year 8 is
107.3107.9 115.8
100
Index for Year 7 from Table 6Laspeyres volume index for Year 8 from Table 6
100
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DemonstrationTable 6
• 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
107.9387.2 417.9
100
Value for Year 6 from Table 6Laspeyres volume index for Year 7 from Table 6
100
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DemonstrationTable 6
• Example: Annually-chained Laspeyres volume measure for GDP for Year 8 is
• Compute real growth rates of annually-chained Laspeyres volume measures for X, Y, and GDP
107.3417.9 448.4
100
Chained value for Year 7 from Table 6Laspeyres volume index for Year 8 from Table 6
100
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DemonstrationTable 6
• 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
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DemonstrationTable 7
• 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
1221.2 214.4
3.21
100
1Nominal value for Year 2 from Table 1Real growth rate for Year 2 from Table 2
1+100
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DemonstrationTable 7
• Example: Volume measure of X for Year 2 at price of Year 3 is
1233.1 225.3
3.51
100
1Nominal value for Year 3 from Table 1Real growth rate for Year 3 from Table 2
1+100
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DemonstrationTable 7
• 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
357.0100 109.3
326.7
Nominal value for Year 2 from Table 1×100
Volume measure for Year 1 from Table 7
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DemonstrationTable 7
• Example: Paasche volume index for GDP for Year 3 is
364.4100 109.2
333.7
Nominal value for Year 3 from Table 1×100
Volume measure for Year 2 from Table 7
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DemonstrationTable 7
• 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
107.3100.0 107.3
100
Index for Year 6 from Table 7Paasche volume index for Year 7 from Table 7
100
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DemonstrationTable 7
• Example: Annually-chained Paasche volume index for GDP for Year 8 is
106.8107.3 114.6
100
Index for Year 7 from Table 7Paasche volume index for Year 8 from Table 7
100
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DemonstrationTable 7
• 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
107.3387.2 415.4
100
Value for Year 6 from Table 7Paasche volume index for Year 7 from Table 7
100
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DemonstrationTable 6
• Example: Annually-chained Paasche volume measure for GDP for Year 8 is
• Compute real growth rates of annually-chained Paasche volume measures for X, Y, and GDP
106.8415.4 443.7
100
Chained value for Year 7 from Table 7Paasche volume index for Year 8 from Table 7
100
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DemonstrationTable 7
• 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
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DemonstrationTable 8
• 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
12 109.8110.3 109.3
1
2Laspeyres volume index from Table 6 Paasche volume index from Table 7
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DemonstrationTable 8
• Example: Fisher volume index for GDP for Year 3 is
12 109.7110.2 109.2
1
2Laspeyres volume index from Table 6 Paasche volume index from Table 7
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DemonstrationTable 8
• 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
107.6100.0 107.6
100
Index for Year 6 from Table 7Fisher volume index for Year 7 from Table 8
100
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DemonstrationTable 8
• Example: Annually-chained Fisher volume index for GDP for Year 8 is
• 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
107.0107.6 115.2
100
Index for Year 7 from Table 7Fisher volume index for Year 8 from Table 8
100
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DemonstrationTable 8
• 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
107.6387.2 416.7
100
Value for Year 6 from Table 8Fisher volume index for Year 7 from Table 8
100
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DemonstrationTable 8
• Example: Annually-chained Fisher volume measure for GDP for Year 8 is
• Compute real growth rates of annually-chained Fisher volume measures for X, Y, and GDP
107.0416.7 446.0
100
Chained value for Year 7 from Table 8Fisher volume index for Year 8 from Table 8
100
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DemonstrationTable 8
• 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 non-additive (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
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DemonstrationConclusion
• 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
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DemonstrationConclusion
• However, computation of annually-chained GDP volume indexes and measures (especially, Fisher) is resource-intensive 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
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DemonstrationConclusion
• 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
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Thank You