gross domestic product estimates at constant prices training course material for e-library on system...
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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
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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
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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
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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”
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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)
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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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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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The Fisher Price Index
The Fisher Volume Index
Geometric average of Laspeyres and Paasche indices
PPLP=FP t0t0t0
QPLQ=FQ t0t0t0
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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 ,
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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,
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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,
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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 *****
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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
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