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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 24-26 August 2011, Vientiane, Lao People’s Democratic Republic. Benson Sim UN STATISTICS DIVISION. Outline of Demonstration.

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Benson Sim UN STATISTICS DIVISION

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  1. 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

  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 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

  3. 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

  4. 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

  5. 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

  6. DemonstrationTable 3 Statistical agency realises that present base year (Year 1) has become outdated and decides to rebase GDP Statistical agency calculates volume measures of entire GDP series using Year 6 as new base year as it finds that Year 6 is a normal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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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%)

  13. 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

  14. 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

  15. 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

  16. DemonstrationTable 5 Example: Volume measure of X for Year 5 is

  17. DemonstrationTable 5 Example: Volume measure of X for Year 4 is

  18. DemonstrationTable 5 Example: Volume measure of GDP for Year 5 is

  19. DemonstrationTable 5 Example: Volume measure of GDP for Year 4 is

  20. DemonstrationTable 5 Example: Laspeyres volume index for GDP for Year 5 is

  21. DemonstrationTable 5 Example: Laspeyres volume index for GDP for Year 4 is

  22. 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

  23. 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

  24. 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

  25. 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

  26. DemonstrationTable 6 Example: Volume measure of X for Year 3 at price of Year 2 is

  27. 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

  28. DemonstrationTable 6 Example: Laspeyres volume index for GDP for Year 3 is

  29. 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

  30. DemonstrationTable 6 Example: Annually-chained Laspeyres volume index for GDP for Year 8 is

  31. 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

  32. 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

  33. 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

  34. 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

  35. DemonstrationTable 7 Example: Volume measure of X for Year 2 at price of Year 3 is

  36. 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

  37. DemonstrationTable 7 Example: Paasche volume index for GDP for Year 3 is

  38. 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

  39. DemonstrationTable 7 Example: Annually-chained Paasche volume index for GDP for Year 8 is

  40. 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

  41. 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

  42. 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

  43. 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

  44. DemonstrationTable 8 Example: Fisher volume index for GDP for Year 3 is

  45. 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

  46. 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

  47. 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

  48. 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

  49. 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

  50. 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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