1. METAC Workshop March 14-17, 2016 Beirut, Lebanon National Accounts Compilation Issues Session 12 : Price and volume measures

2. Topics Purpose Main definitions Laspeyres and Paasche indexes Rebasing/Chaining Double deflation Single extrapolation/deflation GDP components in volume terms

3. Purpose To interpret changes in nominal values when relative prices and/or the general price level are changing – to explain changes in values in terms of changes in volumes and changes in prices – to measure in real terms the flows of money associated with transactions by deflating nominal values by price indices or By extrapolating base year values using volume indices

4. Purpose The scope of price and volumes: – goods and services – taxes and subsidies – trade margins – balancing items (value added, GDP) – compensation of employees – consumption of fixed capital – stocks of produced assets (inventories, fixed assets)

5. Main issues what is meant by price and volume measurement ? what is the relationship between the current price value and the price and volume measures ? how to aggregate them ? how to obtain price and volume measures in practice ?

6. Definitions quantity: unit for measuring amount of a good or service – cannot sum quantities of different products price: value of one unit of a good or service – cannot sum or average prices for different products value: price*quantity for individual products – can sum values of different products value at “constant prices”: value of one or more product for the current period using own price(s) from an earlier period – the use of “volume” not the same as “quantity”

7. Example Values in column (6) are in current prices showing a 140 percent increase over year 0 (index = 240). Values in column (7) are at constant prices of year 0. They reflect changes in quantity and/or quality. Values at constant prices are an aggregated volume measure, expressed in money terms and are additive.

8. Laspeyers volume index The ratio of the current year volume at prices of the base year to the base year value – as example from table 1: LQ 0  t = 540/450*100= 120.0 LQ 0  t = Q 0,t /Q 0,0 = Q 0,t /V 0 =  i p i,0 q i,t /  i p i,0 q i,0 (1) or LQ 0  t =  i (q i,t /q i,0 ).w i,o (2) where: w i,o is the base period weight, i.e. the share of item i in the total value in the base period: p i,0 q i,0 /  i p i,0 q i,0

9. Laspeyers volume index Formula (2), LQ 0  t derived using the data from the data in table 1:

10. Paasche price index the ratio of the value of output in current prices in year (1) to the value of output in year (1) measured in constant prices of year (0): – as example from table 1: PQ 0  t = 1080/540*100 = 200.0 PP 0  t =V t / Q 0,t =  i p i,t q i,t /  i p i,0 q i,t (1) or PP 0  t =1 /  i (p i,0 /p i,t ).w i,t (2) where w i,t is the current period weight, i.e. each item’s share in the total value in the current period

11. Paasche price index PP 0  t is derived as follows from the data in table 1: the ratio of any aggregate in current prices to the aggregate in constant prices yields an implicit Paasche price deflator price measures for the main national accounts aggregates are (always) derived implicitly

12. Relationship between value, volume and price indices, Price deflation The change in the current price value of car production from year 0 to year 1 can be expressed as: V t / V 0 =  i p i,t q i,t /  i p i,0 q i,0 Multiplying and dividing by  i p i,0 q i,t gives: = (  i p i,0 q i,t /  i p i,0 q i,0 ) * (  i p i,t q i,t /  i p i,0 q i,t ) = {Laspeyres Volume index} * {Paasche Price index} or… V t / V 0 = LQ 0  t * PP 0  t 240 = 120 * 200/100 When V t, V 0 are known and PP 0  t is available, the Laspeyres volume index can be derived indirectly from the above formula – a process called price deflation

13. Relationship between value, volume and price indices, Price deflation Multiplying and dividing the nominal change (in current price value) of car production, V t / V 0 =  i p i,t q i,t /  i p i,0 q i,0 by  i p i,t q i,0 gives: = (  i p i,t q i,0 /  i p i,0 q i,0 ) * (  i p i,t q i,t /  i p i,t q i,0 ) = {Laspeyres Price index} * {Paashe Volume index} or V t / V 0 = LP 0  t * PQ 0  t / 100 240 = 120 * 200 / 100 PQ 0  t can be obtained by inflating the base period values using the often available LP 0  t and then dividing the current price value by this amount

14. Laspeyres and Paasche indices Price or Volume Laspeyres is base-weighted Paasche is current-weighted Paasche price index * Laspeyres volume index gives a value index Laspeyres price index * Paasche volume index also gives a value index

15. Reference, base, and weight periods reference period: the period in an index number time series that is taken as =100 price base period (price reference period): the period for which prices are used as denominators in calculating price relatives p t /p 0 quantity base period (quantity reference period): the period for which quantities are used as denominators in calculating quantity relatives q t /q 0 weight period: the period from which the weights are taken – for example the period in which a survey is conducted

16. Changes to base and reference periods referencing shifts the focus to a new reference year (values in other periods are compared to the reference year) – rate of change remains the same rebasing occurs when new weights are introduced – different rates of change

17. Change the base year: reasons structural changes in: – production – consumption – relative prices appearance of new products/disappearance of old products goods and services are not comparable between periods which are too far apart need to derive a continuous, meaningful time series of index numbers from series of index numbers with fixed bases update frequently

18. Re-referencing, example Notes: – Growth rate remains the same – Re-referencing shifts focus to new reference year – Values of the other periods are now compared with the value in this year

19. Change of base year, example

20. Price index numbers and their coverage Consumer Price Index (CPI) – All consumption expenditures (including housing and rent) – Reflects changes in purchasers’ prices – Coverage: total population vs. urban only – Frequency of weight updates

21. Price index numbers and their coverage Producer Price Index (PPI) – Domestic industrial production (manufacturing and public utilities) – To include also mining, agriculture and transport (although could include total economy) – Reflects changes in basic prices (output index) – System of input and output indices by stage of processing – Domestic market sales vs. exports – Input index reflects changes in purchasers’ prices

22. Price index numbers and their coverage Wholesale Price Index (WPI) – Sales of primary, intermediate and finished goods by wholesalers – Reflects changes in producers’ prices, wholesalers trade margins and taxes on products levied on sales between producers and wholesalers – May reflect purchasers’ prices for products sold to final users – Based on price indices for commodities sold rather than industry of output – Includes imports – Not recommended

23. Price index numbers and their coverage Import and Export Price Indices (MXPI) – Data source can be customs for unit value indices and/or establishment surveys – Customs data good for weights and sampling frame Unit value indices from customs data (UVI) – Based on average price (value/quantity = unit value) of a group of somewhat heterogeneous goods and services: – Affected by changes in product mix as well as price changes – often volatile – Coverage problems for services and customs unions – Valuation issues – Limited quality adjustments

24. Price index numbers and their coverage Construction Price Indices – Usually measures price changes for construction materials – Some countries have capital construction indices – Reflects change in cost of construction for a representative number of building types

25. Chaining of indexes The standard Laspeyres and Paasche indexes compare directly base period 0 and current period t Period t and period 0 can be compared indirectly by comparing period 1 with period 0, then period 2 with period 1, and so on… the resulting indices between pairs of periods can be multiplied to form a chain index

26. Chaining of indexes, reasons When a fixed base Laspeyres index is used over a long period, the weights become increasingly out-of-date and irrelevant. – The base period has to be updated and the new index linked to the old Chaining is the case when the weights are updated each period

27. Chaining of indexes, warning A chain index between periods 0 and t is “path dependent”- it depends not just on the prices and quantities in 0 and t, but also on the prices and quantities in all the intervening places. – When the path is fairly smooth then the additional price and quantity information will tend to lead to a better measure of the overall change, but … – … if there are fluctuations in price and quantities, the use of additional price and quantity information may lead to drift, e.g. if the prices in 0 are the same as those in t, a chain Laspeyres index may exceed 100 if the path is not smooth.

28. Chaining of indexes, warning Additivity – When chain volume indices are converted into time series of values by using the indices to extrapolate the values of the base period, the index components may fail to add to aggregates in later periods. – To consider reference year closer to the end of the chain – Whether published in monetary terms or indices, it is advisable to inform users via a footnote or other meta-data that chain volume series are not additive

29. Price and volume measures for GDP Production approach value added by industry plus taxes less subsidies on products Expenditure approach government FCE plus households’ FCE plus NPISH’s FCE plus capital formation plus exports minus imports

30. Price and volume measures for Value added double deflation/double extrapolation gross value added is derived as the difference between output at constant prices and intermediate consumption at constant prices output and intermediate consumption can be: – deflated using an appropriate (Paasche-type) price index; or – extrapolated from base year values by an appropriate (Laspeyres-type) volume index note: sensitive to estimation error – when input data are not accurate – when value added is a small proportion of output

31. Double deflation, example GO: Gross Output IC: Intermediate Consumption GVA: Gross Value Added PPI: Producer Price Index ICI: Intermediate Consumption Indices

32. Price and volume measures for Value added single extrapolation base period gross value added is extrapolated using an appropriate indicator – output data – employment data single deflation ? gross value added is deflated directly using – output deflator – wage index ? – a general measure of inflation like the CPI ?

33. Single extrapolation/deflation … an approximation to double deflation: (1) use Laspeyres-type volume index for gross output to extrapolate base year gross value added used when: – index for intermediate inputs is not available; or – input data are not accurate underlying assumption: – input/output coefficients are fixed (2) use Paasche-type price deflator for output to deflate current price value added directly underlying assumption: – output and input prices do not diverge significantly

34. Intermediate inputs as indicators volume index for output is preferred, an index based on inputs has greater bias: number and variety of outputs is smaller than the variety of intermediate goods and services (and labor) consumed in the production process commodity composition of inputs is more variable over time however, a volume index for inputs may be used as a single indicator for value added in exceptional cases: examples are construction and capital goods- producing industries, where it is difficult to measure output in constant prices usually covers indexes for intermediate consumption and employment indicators

35. Employment as an indicator volume index for inputs of labor services may be used hours worked, weighted according to hourly wages paid to different kinds of workers, which accounts for: – changes in hours worked – changes in the composition of the labor force Number of employees is more common in practice, in particular for: – government services – financial, business, entertainment services

36. GDP by expenditure categories at constant prices Final expenditure components can be factored into prices and quantities thus, in theory, better constant price measures can be obtained from the expenditure approach usual approach is a deflation of current values, although extrapolation by volume index may also be used inventories are a special case

37. References 2008 SNA, Chapter 15 Eurostat manual on price and volume measures

38. Thank you