Benson Sim UN STATISTICS DIVISION Demonstration on Rebasing and Linking of National Accounts Workshop on the Methodological Review of Benchmarking, Rebasing and Chain-linking of Economic Indicators August 2011, Vientiane, Lao People’s Democratic Republic

2 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 non 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) Conclusions Extensive reference will be made to Excel tables

3 Demonstration of Rebasing Table 1 Assumptions 2 single products, X and Y, in an economy X and Y are most detailed products available (i.e., no further breakdown possible) 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

4 Demonstration Table 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

5 Demonstration Table 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

6 Demonstration Table 3 Statistical agency realises that present base year (Year 1) has become outdated and decides to rebase GDP Statistical agency calculates volume measures of entire GDP series using Year 7 as new base year as it finds that Year 7 is a normal year with no dramatic changes For each product (X and Y), compute price indexes with Year 7 as reference period (i.e., price indexes for Year 7 will have value of 100.0) Example: Price index for X for Year 9 is

7 Demonstration Table 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

8 Demonstration Table 3 Sum up deflated values 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 7 as reference year (i.e., volume index for Year 7 will have value of 100.0) Example: Laspeyres volume index for GDP for Year 9 is

9 Demonstration Table 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 written As mentioned earlier, this method of doing rebasing is not recommended

10 Demonstration Table 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 7 using Year 7 as base year and volume measures of GDP from Years 1 to 6 using Year 1 as the 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 7 to 10 will be same as those in Table 3

11 Demonstration Table 4 Combine the two sub-series to get entire time series (see bottom of table) Insert break (|) between volume measures for Years 6 and 7 to indicate they are calculated using different base years

12 Demonstration Table 4 Question Which real GDP growth rate for Year 7 do we use? Real GDP growth rate calculated using Year 1 as base year (12.0%)? Real GDP growth rate calculated using Year 7 as base year (7.3%)? Answer Real GDP growth rate calculated using Year 1 as base year (12.0%) Why? Volume measures of GDP calculated using Year 7 as base year only start from Year 7, not Year 6 Volume measures of GDP from Years 1 to 7 calculated using Year 1 as base year are available

13 Demonstration Table 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 7 are the same as those in Table 2 Real GDP growth rates from Year 8 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 Demonstration Table 5 To solve problem with inconsistent volume measures of GDP, statistical agency decides to link the two sub-series in Table 4 using Year 7 as reference year Volume measures of X, Y, and GDP from Years 7 to 10 will be same as those in Table 4 Calculate volume measures of X, Y, and GDP separately by using their real growth rates at prices of Year 1 to extrapolate backwards their levels for Year 7

15 Demonstration Table 5 Example: Volume measure of X for Year 6 is

16 Demonstration Table 5 Example: Volume measure of X for Year 5 is

17 Demonstration Table 5 Example: Volume measure of GDP for Year 6 is

18 Demonstration Table 5 Example: Volume measure of GDP for year 5 is

19 Demonstration Table 5 Example: Laspeyres volume measure of GDP for Year 6 is

20 Demonstration Table 5 Example: Laspeyres volume measure of GDP for Year 5 is

21 Demonstration Table 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 7 are the same as those in Table 2 Real GDP growth rates from Year 8 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 1-6 (i.e., X and Y do not add up to GDP) due to the linking of components and GDP independently

22 Demonstration Table 5 Nevertheless, it is preferable to rebase GDP and then link the volume series so as not to create breaks Explain in methodological notes why volume measures of GDP are non-additive after rebasing and linking

23 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 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

24 Demonstration Table 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

25 Demonstration Table 6 Example: Volume measure of X for Year 3 at price of Year 2 is

26 Demonstration Table 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

27 Demonstration Table 6 Example: Laspeyres volume index for GDP for Year 3 is

28 Demonstration Table 6 Compute annually-chained Laspeyres volume index for GDP using Year 1 as reference year Example: Annually-chained Laspeyres volume index for GDP for Year 2 is

29 Demonstration Table 6 Example: Annually-chained Laspeyres volume index for GDP for Year 3 is

30 Demonstration Table 6 Compute annually-chained Laspeyres volume measures for X, Y, and GDP using Year 1 as reference year Thus, annually-chained Laspeyres volume measures for X, Y and GDP for Year 1 will be same as corresponding nominal values in Table 1 Example: Annually-chained Laspeyres volume measure for GDP for Year 2 is

31 Demonstration Table 6 Example: Annually-chained Laspeyres volume measure for GDP for Year 3 is Compute real growth rates of annually-chained Laspeyres volume measures for X, Y, and GDP

32 Demonstration Table 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 from Year 3 onwards (i.e., X and Y do not add up to GDP)

33 Demonstration Table 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

34 Demonstration Table 7 Example: Volume measure of X for Year 2 at price of Year 3 is

35 Demonstration Table 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

36 Demonstration Table 7 Example: Paasche volume index for GDP for Year 3 is

37 Demonstration Table 7 Compute annually-chained Paasche volume index for GDP using Year 1 as reference year Example: Annually-chained Paasche volume index for GDP for Year 2 is

38 Demonstration Table 7 Example: Annually-chained Paasche volume index for GDP for Year 3 is

39 Demonstration Table 7 Compute annually-chained Paasche volume measures for X, Y, and GDP using Year 1 as reference year Thus, annually-chained Paasche volume measures for X, Y and GDP for Year 1 will be same as corresponding nominal values in Table 1 Example: Annually-chained Paasche volume measure for GDP for Year 2 is

40 Demonstration Table 6 Example: Annually-chained Paasche volume measure for GDP for Year 3 is Compute real growth rates of annually-chained Paasche volume measures for X, Y, and GDP

41 Demonstration Table 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 from Year 2 onwards (i.e., X and Y do not add up to GDP)

42 Demonstration Table 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

43 Demonstration Table 8 Example: Fisher volume index for GDP for Year 3 is

44 Demonstration Table 8 Compute annually-chained Fisher volume index for GDP using Year 1 as reference year Example: Annually-chained Fisher volume index for GDP for Year 2 is

45 Demonstration Table 8 Example: Annually-chained Fisher volume index for GDP for Year 3 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

46 Demonstration Table 8 Compute annually-chained Fisher volume measures for X, Y, and GDP using Year 1 as reference year Thus, annually-chained Fisher volume measures for X, Y and GDP for Year 1 will be same as corresponding nominal values in Table 1 Example: Annually-chained Fisher volume measure for GDP for Year 2 is

47 Demonstration Table 8 Example: Annually-chained Fisher volume measure for GDP for Year 3 is Compute real growth rates of annually-chained Fisher volume measures for X, Y, and GDP

48 Demonstration Table 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 from Year 2 onwards (i.e., X and Y do not add up to GDP) Calculation of annually-chained Fisher volume indexes is demanding exercise as it involves many steps

49 Demonstration Conclusion 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 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 Demonstration Conclusion However, computation of annually-chained GDP volume measures (especially, Fisher) is resource-intensive exercise Also, additivity of GDP is not preserved If statistical agencies decided not to calculate annually- chained GDP volumes, they should consider periodic rebasing Base year should not be more than 5 years old

51 Thank You