1. Gross Domestic Product Estimates at Constant Prices
Notes on SNA_GDP Estimates at ConstantPrice
3/31/2017
Module-I: PP5
Gross Domestic Product Estimates at Constant Prices
Welcome etc.
Training Course Material for e-Library on
System of National Accounts
March 2009
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2. Outline Concepts and principles Value, price, quantity and volume
Estimate of GO at constant prices
Index numbers for price and volume measures in a National Accounts System
Techniques for obtaining estimates at constant prices
Base, reference, and weighting periods of index
Choice of base year in the national accounts and chaining
II. Price and volume measures for Gross Value Added/ GDP

3. Value, Price and Quantity
Notes on SNA_GDP Estimates at ConstantPrice
3/31/2017
Value, Price and Quantity
Value = Price multiplied by Quantity
V = p * q
Quantity: Unit for measuring amount of a good or service
Price : Value per unit of quantity (of same quality)
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4. Value, Price and Quantity (Contd.)
Notes on SNA_GDP Estimates at ConstantPrice
3/31/2017
Value, Price and Quantity (Contd.)
Values are expressed in common unit (currency) and are additive across products
Quantities are additive only at the narrowly defined single product level
Value at a single product level vs at an aggregated (over several items, say, n ) level
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5. Value, Price and Quantity (Contd.)
Notes on SNA_GDP Estimates at ConstantPrice
3/31/2017
Value, Price and Quantity (Contd.)
For n items, denote,
: price of item i in period t ; i= 1,2,......,n
: quantity of item i in period t
: value of item i at current prices in period t
Thus at item level,
: total value at current prices in period t for all items
At aggregate level,
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6. Notes on SNA_GDP Estimates at ConstantPrice
3/31/2017
Quantity, Quality and Volume Prices and values in 000’units of currency No change in prices
Car production
High priced model
Low priced model
Total
Price per unit 20 15
Production in Year 1 10 30
Production in Year 2
Total value of production in Year 1
200
300
500
Total value of production in Year 2
400
150
550
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7. Quantity, Quality and Volume (Contd.)
Unit value in year 1 = 500/30 =
Unit value in year 2 = 550/30 =
Change in volume = 550/ percent
Change in quantity = 30/ percent
Change in prices = 0 percent;
because prices remain unchanged
Change in unit values = / percent

8. Quantity, Quality and Volume (Contd.)
Conclusions:
Unit values are affected by the change in the product mix
Change in product mix = change in average quality
The term “VOLUME” is preferred to “QUANTITY”
Change in “QUALITY” is regarded as change in “VOLUME”, not as change in “PRICE”

9. What Are the Ways to Value an Aggregate?
Aggregate at current price - the value of the items of the aggregate (e.g., goods and services) using prices of the period
Aggregate constant price - the value of items of the aggregate using fixed prices of a fixed period (called base period)

10. How to distinguish the two aggregates?
Notes on SNA_GDP Estimates at ConstantPrice
3/31/2017
How to distinguish the two aggregates?
For example Gross output (GO) at current price is represented as
i Pit Qit
Pit : price of ith item at the period t
Qit : volume or quantity of ith item at period t
t : reference period of the estimates
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11. How to distinguish..? GO at constant price is represented as i Pi0Qit
Pi0 : price of ith item at the base period 0
Qit : volume or quantity of ith item at period t

12. How to estimate GO at constant prices?
GO at current price
GOt = PtQt
Qt : quantity or volume at time t
Pt : price at time t
GO of period t at constant price of period 0
GO0,t = P0Qt
Qt : quantity or volume at time t
P0 : price at time 0

13. How to Estimate GO at Constant Prices? (Contd.)
Revaluation : Multiply the quantity or volume at time t by price at time 0
Deflation : Divide the GO at current price by price relative or price index with base 0
Extrapolation : Multiply the value at time 0 with volume relative or volume index

14. How to Estimate GO at Constant Prices? (Contd.)
Revaluation : Multiply quantity at time t by price at time 0
GO0,t = QtP0

15. How to Estimate GO at Constant Prices (Contd.)
Price deflation : Divide current price estimate by price relative/price index
GO0,t = QtPt / (Pt / P0 )

16. How to Estimate GO at Constant Prices (Contd.)
Volume extrapolation : Multiply base year value by volume relative or volume index
GO0,t = Q0P0 * Qt/Q0

17. Index Numbers of Prices and Volume
Denoting:
a (fixed-base) Laspeyres volume index with period 0 as the base period
a (fixed-base) Laspeyres price index with period 0 as the base period
wi0 the base period weight, that is, item i's share in the total value in the base period
What follows is popular Price and Volume Index ,

18. The Laspeyres Volume Index
Arithmetic average of quantity relatives with base period weights

19. The Laspeyres Price Index
Arithmetic average of price relatives with base period weights

20. The Paasche Volume Index
Further denoting:
a (fixed-base) Paasche volume index with period 0 as base period
Harmonic average of quantity relatives with current period weights

21. The Paasche price index
Further denoting:
a (fixed-base) Paasche price index with period 0 as base period
Harmonic average of price relatives with current period weights

22. The Fisher Price Index
The Fisher Volume Index
Geometric average of
Laspeyres and Paasche indices

23. What is Meant by Estimates at Constant Prices?
The value of a product or group of products, valued for the current period using its own prices from an earlier period (which are kept constant)
At the micro level:
At the aggregate level:
the total value of a group of products in period t where each item is revaluated at its own prices of period 0 (period 0 is kept constant for a period of time)
Where: is the price of item i in period 0
is the quantity of item i in period t
is the total value in period t measured at the prices of period 0

24. What is Meant by Estimates at Constant Prices?
Changes over time in a constant price time series reflects only changes on quantities (and quality)
Thus it is an aggregated volume measure
expressed in money terms
which thus is additive
It is not value of a product or group of products adjusted for changes in the general price level

25. What is the relationship between measures at Constant prices and Volume Index formulas?
Denoting:
Q0,t the total value in period t measured at the prices of period 0
a (fixed-base)
Laspeyres volume index with period 0 as the base period
wi0 the base period weight, that is, item i's share in the total value in the base period.
The measure of change from the base year in the constant price time series is:
the Laspeyres (fixed-base) Volume Index
Which is one of the several volume index formulas

26. What is the relationship between measures at Constant prices and Volume Index formulas?
The Laspeyres (fixed-base) Volume Index
Measures at constant prices, one of several alternative volume measures
Alternative volume measures based on:
the Fisher index formula
the Tornqvist superlative index formula
the Paasche index formula
chain-linked indices

27. The Implicit Price “Deflator”
For an aggregate, the relationship between a measure at constant prices and a measure at current prices is
an implicit price ‘deflator’
Price measures for the main national accounts aggregates are (always) derived implicitly
a (fixed base) Paasche Price Index implicitly derived
One of several alternative formulas for aggregated price measures in general
The proper index formula for constructing deflators to derive constant price estimates for (detailed) national accounts items

28. Two main requirements for volume and price measures in an accounting system
Volume measures for multiplicity of goods and services within an accounting framework should for each period be additive
Required for compilation reasons (Use of the accounting framework as an estimation tool + consistency in aggregation)
Analytical convenience
The aggregate price measure times the aggregate volume measure should be equal to the current price value-
The (weak) Factor Reversal Criteria (test)
Required for: Compilation reasons
Integrated analysis of movements in current price values and the related price and volume components

29. Two main requirements for volume and price measures in an accounting system
Volume measures should for each period be additive
The (weak) Factor Reversal Criteria (test)
Constant price Laspeyres (fixed-base) Volume measures combined with Paasche Price indices fulfill these requirements
But are not the only ones

30. How to Obtain Constant Price Estimates for Detailed National Accounts Items?
The three main techniques for deriving constant price estimates at the detailed compilation level
Revaluation
Volume extrapolation
Deflation

31. Revaluation
That is to revalue current quantities by multiplying with prices of base year
Require complete count of quantities produced or used
limited use, mainly in agriculture

32. Volume extrapolation
That is to update the base year's value according to the movement in an appropriate volume index (volume indicator)
difficult to incorporate new products properly when constructing volume indices directly
difficult to properly adjust for changes in quality
for many products it is difficult to define the unit of quantity
in general not the preferred technique (except under hyper inflation)

33. Deflation That is to deflate by a suitable price indicator
easy to incorporate new products and new activities when collected current price data
easier to properly adjust for changes in quality when constructing price indices
prices for related products may show similar movements: the idea of representative prices
in general the preferred technique

34. Base and Reference Periods
The period which is equal to 100
Base period:
(1)The pricing year (the base year) for the constant price data in the national accounts
(2) Price base period: The period (or data) whose prices are used as denominators in calculating the price relatives pt / p0
(3)Quantity base period: The period (or data) whose quantities are used as denominators in calculating the quantity relatives qt /q0

35. Weight Period The period (s) from which the weights are taken
Equal to the base period for a (fixed-base) Laspeyres index (w0) and to the current period for a (fixed-base) Paasche index (wt) Fisher, Tornqvist, and other (fixed-base) symmetric indices have weight from two periods. Chain-linked indices have as many weight periods as links
The base period is equal to the weight period for a Laspeyres index and other base year weighted indices, but not for current weighted indices such as Paasche, symmetric indices such as Fisher and Tornqvist, or for chain-linked indices

36. Why change base year? Structural changes in production structure
Structural changes in consumption patterns
Structural changes in relative prices
Appearance of new products
Disappearance of old products
Larger quality changes
Goods and services are not comparable between periods that are to far apart
How to derive continuous time series by chain-linking?
When to chain-link and when not to?

37. Choice of Base Periods in the National Accounts and Chaining
Main Recommendations
Do frequent change of base year and chain-linking
Do not change the base period more frequently than annually
(Years - not quarters as base period)
Do not chain link over periods with substantial price/ volume oscillation
Base years should be as normal as possible

38. How to Obtain Price and Volume Measurements for GDP?
Through the price and volume measures for its components
From the production approach
for Value added by industry
Plus for taxes less subsidies on products
From the expenditure approach
for Government final consumption expenditures
Plus for Households final consumption expenditures
Plus for NPISH’s final consumption expenditures
Plus for capital formation (including changes in inventories)
Plus for exports minus for imports
Integrated current supply and use tables, the optimal framework for price and volume measurements in the national accounts

39. Gross Value Added A residual item
No observable flows of goods and services as counterpart
Cannot be factored directly into its own quantity and price components
Value added at constant prices can only be defined and measured indirectly using the accounting relation as:
Where:
xij,t is the “quantity” of output of product i produced by industry j in period t
mij,t is the “quantity” of product i used as intermediate consumption by industry j in period t
is the (average) basic price of product i in period t, produced by domestic producers
is the (average) purchasers price of product i used by domestic producers (covers domestic produced and imported products, and includes trade and transport margins, subsidies, and non- deductible product taxes

40. Gross Value Added (contd.)
Laspeyres "volume" index for value added
Paasche "price" index for value added

41. Double Deflation
The derivation of value added at constant prices as a difference between output at constant prices and intermediate consumption (IC) at constant prices
is called “double deflation”, although output and IC at constant prices could be derived either by deflation or by extrapolation
Double deflation requires reliable volume and price measurements of both output and intermediate consumption
requires a breakdown of output and intermediate consumption by product
 Double deflation is not recommended when value added accounts for only a small proportion of output

42. Volume Measures for Value Added Alternative Methods
Double deflation - double extrapolation
Separate estimates for output and intermediate consumption at constant prices, value added as the difference
Requires current information regarding:
intermediate consumption shares
the structure of intermediate consumption

43. Volume Measures for Value Added Alternative Methods (Contd.)
Single extrapolation of value added
Extrapolation with output
Assumes fixed input output coefficients
Price measures for intermediate consumption implicitly given
Extrapolation with employment data
Adjustments for normal increases in labor productivity?

44. Volume Measures for Value Added Alternative Methods (Contd.)
Single deflation of value added
Deflation with the output deflator
Assumes parallel price movements for output and intermediate consumption
Changes in input output coefficients implicitly given
Deflation with a wage index
Deflation with a general measure of inflation such as the total CPI
Do not result in a volume measure
Provides a measure of a different concept, real income

45. Volume Measures for Value Added
Work explicitly with all elements of the production account for each kind of activity
Produce and publish price and volume measures for Gross output and intermediate consumption in addition to value added
Gross value added is a complex concept. Some economists even questions the economic meaning of volume measures for net concepts like value added
Jumping to value added, and not focusing on gross output and intermediate consumption with value added as a derived balancing item, may lead to use of inferior methods
In particular to deflation with the output deflator, when alternative and better methods exist. e.g., single extrapolation of value added with output as extrapolator

46. Volume Measures for Value Added...more
Other Approximate Measures of Value Added at Constant Prices
Intermediate inputs based estimates
Employment based estimates
Total inputs based estimates
Estimation of output at constant prices: some specific activities (Unique products):
Construction
Financial intermediation services indirectly measured
Trade margins
Non-market services

47. Volume Measures for Value Added...more
Input based measures for output and Value Added at Constant Prices to be used when no direct price or volume information for output is available
Volume indicators for output based on compound volume indices for total observable inputs
Price deflators for output based on compound price indices for total observable inputs
Adjustments for normal increases in total factor productivity
Adjustments for observed changes in mark-ups

48. Price and Volume Measures for GDP by Expenditure Categories
GDP at constant prices from the expenditure approach is derived as the sum of expenditure components at constant prices
The expenditure components of GDP are aggregates of transactions that can be compiled by observing and recording actual transactions
The value of these transactions can be factored into their own prices and quantities
Therefore, more accurate measure of price and volume for GDP conceptually could be obtained through expenditure approach
Commonly, the deflation of current values is used to derive data at constant prices for most of expenditure items, although extrapolation by volume index could also be used

49. Data requirements and compilation issues
Common problems:
Price indices usually are Laspeyres indices
Base year for volume and price indices differ from the base year for national accounts
Not all volume and price indices have similar base period
Coverage of activity in the national accounts and in the volume and price indices might (or usually) differ
Coverage of volume and price indices might also change over time
For many activities, no volume and price indices are available
Data on value and/or quantity and/or price are incomplete

50. Data requirements and compilation issues
Practical guidance
Compile estimates at more disaggregate level
Use all the possible methods, make comparative analysis of results, and choose the best
Make thorough analysis of coverage and compilation methods for source statistics, and adjust them to yield estimates consistent with SNA coverage and definitions
There is no single recommendation, much depends on compiler’s capability to tackle intelligently different situations

51. Steps Involved in Changing the Base Year
In principle:
Price and volume measurement in an integrated accounting framework (particularly constant price measures) requires access to large amount of detailed
Paasche price indices (deflators) and/or
Laspeyres volume indices
tailor made to the national accounts needs and covering all GDP by activity and expenditure items; all using the same price and quantity base
Change of base year implies a change of the price and quantity base for all these indices

52. Steps Involved in Changing the Base Year (Contd.)
In practice: National accountants are forced to use whatever information available
Compiles approximate implicit Paasche price deflators and approximate Laspeyres volume indices by deflating with Laspeyres price indices and extrapolating with whatever volume indicators available
Compilations should be conducted at a sufficient detailed level
Conduct the aggregation from this detailed level to the main national accounts aggregates in accordance with main principles

53. Steps Involved in Changing the Base Year (Contd.)
At the detailed compilation level:
Changing the reference period for the individual price and volume indices used from being equal to the old base year to being equal to the new base year
Conducting the aggregation from this detailed compilation level and up to the national accounts aggregates accordingly

54. Steps Involved in Changing the Base Year (Contd.)
Steps in Practice: When changing from 1990 to 2000 as base year:
Revaluation: Replace
With
Deflation: A change of base year by Changing the reference period from 1990 to 2000 for the deflators used at the most detailed level
Volume extrapolation: Changing the period from which the level are being extrapolated
Replace Q90,t = V2000 * I90,t
With Q2000,t = V2000 *(I90,t / I90,2000)

55. Chain Indices and Linking
Chain linking means to construct a volume index series by multiplying together the indices with different base and reference periods. For example, let I2,3 be a Laspeyres volume index measuring the volume change from period 2 to period 3 with weights from period 2, then an annual chain-linked Laspeyres index series from period 0 to period t can be constructed as
Furthermore, observe that if the index formulas constituting each link in the index series satisfy the factor reversal test (that V=P*Q), then the chain-linked index series will also satisfy the factor reversal test

56. Chain Indices and Linking (Contd.)
The above can easily be seen from the following formulas:

57. Notes on SNA_GDP Estimates at ConstantPrice
3/31/2017
Thank You
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