Gross Domestic Product Estimates at Constant Prices

Training Course Material for e-Library on System of National Accounts

March 2009

Module-I: PP5

2

Outline

I. Concepts and principlesi. Value, price, quantity and volumeii. Estimate of GO at constant pricesiii. Index numbers for price and volume measures in a

National Accounts Systemiv. Techniques for obtaining estimates at constant pricesv. Base, reference, and weighting periods of indexvi. Choice of base year in the national accounts and

chainingII. Price and volume measures for Gross Value Added/ GDP

3

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)

4

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

5

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,

ititit qpv

iti

iti

itt qpvV

itp

itq

itv

tV

6

Quantity, Quality and VolumePrices 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 20 30

Production in Year 2 20 10 30

Total value of production in Year 1

200 300 500

Total value of production in Year 2

400 150 550

7

Quantity, Quality and Volume (Contd.)

• Unit value in year 1 = 500/30 = 16.67• Unit value in year 2 = 550/30 = 18.33• Change in volume = 550/500 10 percent• Change in quantity = 30/30 0 percent• Change in prices = 0 percent; because prices remain unchanged• Change in unit values = 18.33 / 16.67 10 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?

• 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

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 tPt : price at time t

GO of period t at constant price of period 0GO0,t = P0Qt

Qt : quantity or volume at time tP0 : 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

2000 2001 2002 2003

Qt 100 120 126 145

Pt 5 6 6 9

P2000 Qt 500 600 630 725

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 )

2000 2001 2002 2003

Qt Pt 500 720 756 1305 Pt 5 6 6 9 Pt/P0 5 / 5 6 / 5 6 / 5 9 / 5

Qt Pt/ (Pt/P2000)

500 600 630 725

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

2000 2001 2002 2003

Qt Pt 500 720 756 1305 Qt 100 120 126 145 Qt/Q0 100 /

100 120 / 100

126 / 100

145 / 100

Q2000 P2000* (Qt/Q2000)

500 600 630 725

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 periodwi0 the base period weight, that is, item i's share in

the total value in the base periodWhat follows is popular Price and Volume Index ,

LQ t0

LP t0

18

The Laspeyres Volume Index

Arithmetic average of quantity relatives with base period weights

qp

qp=LQ

i,0i,0i

ti,i,0it0

wq

q=

qp

qp

q

q=LQ i,0

i,0

ti,i

i,0i,0i

i,0i,0

i,0

ti,it0

19

The Laspeyres Price Index

Arithmetic average of price relatives with base period weights

qp

qp=LP

i,0i,0i

i,0ti,it0

wp

p=

qp

qp

p

p=LP i,0

i,0

ti,i

i,0i,0i

i,0i,0

i,0

ti,it0

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

PQ t0

qp

qp= PQ

i,0ti,i

ti,ti,it0

wq

q / 1=

qp

qp

q

q / 1PQ ti,

ti,

i,0i

ti,ti,i

ti,ti,

ti,

i,0it0

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

PP t0

qp

qp= PP

ti,i,0i

ti,ti,it0

wp

p / 1=

qp

qp

p

p / 1PP ti,

ti,

i,0i

ti,ti,i

ti,ti,

ti,

i,0it0

22

The Fisher Price Index

The Fisher Volume Index

Geometric average of Laspeyres and Paasche indices

PPLP=FP t0t0t0

QPLQ=FQ t0t0t0

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

qp ti,i,0

qp=Q ti,i,0it0,

tQ ,0

0,iptiq ,

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

qp=Q ti,i,0it0,

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 periodwi0 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:

LQ t0

qp

qp=

V

Q=

Q

Q=LQ

i,0i,0i

ti,i,0i

0

t0,

0,0

t0,t0

the Laspeyres (fixed-base) Volume IndexWhich 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 IndexMeasures at constant prices, one of several alternative volume measuresAlternative volume measures based on:

• the Fisher index formula• the Tornqvist superlative index formula• the Paasche index formula• chain-linked indices

qp

qp=

V

Q=

Q

Q=LQ

i,0i,0i

ti,i,0i

0

t0,

0,0

t0,t0

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

qp

qp=

prices Constant

prices Current =

QV =PP

ti,i,0i

ti,ti,i

t0,

tt0

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 requirementsBut 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 usedlimited use, mainly in agriculture

qp=Q ti,i,0it0,

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 quantityin general not the preferred technique (except under hyper inflation)

LQ V=Q t00t0,

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

PP / V=Q t0tt0,

34

Base and Reference Periods Reference period:Reference period:The period which is equal to 100The period which is equal to 100

Base period:Base period:(1)The pricing year (the base year) for the constant price (1)The pricing year (the base year) for the constant price

data in the national accounts data in the national accounts (2)(2) Price base period:Price base period: The period (or data) whose prices The period (or data) whose prices

are used as denominators in calculating the price are used as denominators in calculating the price relatives prelatives ptt / p / p00

(3)Quantity base period:(3)Quantity base period: The period (or data) whose The period (or data) whose quantities are used as denominators in calculating the quantities are used as denominators in calculating the quantity relatives quantity relatives qqtt /q /q00

35

Weight Period

The period (s) from which the weights are taken The period (s) from which the weights are taken Equal to the base period for a Equal to the base period for a (fixed-base)(fixed-base) Laspeyres index (w Laspeyres index (w00) ) and to the current period for a and to the current period for a (fixed-base)(fixed-base) Paasche index (w Paasche index (wtt) ) Fisher, Tornqvist, and other Fisher, Tornqvist, and other (fixed-base)(fixed-base) symmetric indices have symmetric indices have weight from two periods. Chain-linked indices have as many weight from two periods. Chain-linked indices have as many weight periods as linksweight periods as links

The base period is equal to the weight period for a Laspeyres index and 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 other base year weighted indices, but not for current weighted indices such as Paasche, symmetric indices such as Fisher and Tornqvist, or such as Paasche, symmetric indices such as Fisher and Tornqvist, or for chain-linkedfor 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 apartHow 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 componentsFrom the production approach

for Value added by industry Plus for taxes less subsidies on products

From the expenditure approachfor Government final consumption expendituresPlus for Households final consumption expendituresPlus for NPISH’s final consumption expendituresPlus 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 AddedA residual itemNo observable flows of goods and services as counterpartCannot be factored directly into its own quantity and price componentsValue added at constant prices can only be defined and measured indirectly using the accounting relation as:

mp-xp tij,pi,0itij,

bi,0i

Where:xij,t is the “quantity” of output of product i produced by industry j in period tmij,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

producersis 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

pbti,

p pti,

40

Gross Value Added (contd.)

Laspeyres "volume" index for value added

Paasche "price" index for value added

mp-xp

mp-xp=LQVA

ij,0pi,0iij,0

bi,0i

tij,pi,0itij,

bi,0i

tj,0

mp-xp

mp-xp=PPVA

tij,pi,0itij,

bi,0i

tij,pti,itij,

bti,i

tj,0

41

Double Deflation The derivation of value added at constant prices as a difference The derivation of value added at constant prices as a difference

between between output at constant pricesoutput at constant prices and and intermediate consumption intermediate consumption (IC) at constant prices(IC) at constant prices

is called “is called “doubledouble deflation”, although output and IC at constant deflation”, although output and IC at constant prices could be derived either by deflation or by extrapolationprices could be derived either by deflation or by extrapolation

Double deflation requires reliable volume and price measurements Double deflation requires reliable volume and price measurements of both output and intermediate consumptionof both output and intermediate consumption

requires a breakdown of output and intermediate consumption requires a breakdown of output and intermediate consumption by productby product

Double deflation is not recommended when value added accounts Double deflation is not recommended when value added accounts for only a small proportion of outputfor only a small proportion of output

42

Volume Measures for Value AddedAlternative 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 AddedAlternative 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 AddedAlternative 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 AddedWork 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 addedGross 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 estimatesEmployment based estimatesTotal inputs based estimates

• Estimation of output at constant prices: some specific activities (Unique products):

ConstructionFinancial intermediation services indirectly

measuredTrade marginsNon-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 to be used when no direct price or volume information for output is available 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 PracticeSteps in Practice: When changing from 1990 to 2000 as base year:Revaluation:Revaluation: Replace With Deflation:Deflation: A change of base year by Changing the reference period from 1990 to 2000 for the deflators used at the most detailed levelVolume extrapolation:Volume extrapolation: Changing the period from which the level are being extrapolatedReplace Q90,t = V2000 * I90,t

With Q2000,t = V2000 *(I90,t / I90,2000)

qp=Q ti,0i,it, 990

qp=Q ti,0i,it, 2002000

55

Chain Indices and LinkingChain 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

t

t ttttt IIIIIII1 ,1,14,33,22,11,0,0 *****

56

Chain Indices and Linking (Contd.)

The above can easily be seen from the following formulas:

ttt

tttttt

ttt

ttt

QPVThen

QPVIf

QQQQQQ

indexVolumelinkedChain

PPPPPP

indexicelinkedChain

,0,0,0

,1,1,1

,14,33,22,11,0,0

,14,33,22,11,0,0

*,

*

*****

:

*****

:Pr

57

Thank YouThank You