Constant Price Estimates
Expert Group Meeting on National Accounts
Cairo May 12-14, 2009
Presentation points
Why national accounts statistics are compiled?
Meet the needs of various users
Mainly
Government
Private analysts
Policy makers
Decision takers
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What is the major use of national accounts statistics
Assess how a country’s economy is growing over time
Study the behavior of an economy at various stages in the
economic cycle
The changes in current price estimates over time
represents combination of
Change in prices
Change in the underlying volumes
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Are national account aggregates at current price estimates enough?
Do not reveal real growth of the economy
The growth may largely reflect increase in prices of the produced
commodities
Current price estimates have two dimensions?
Price
Quantity
What is needed?
Decomposition of value in terms of prices and quantities for
various commodities
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WHY DO WE NEED PRICE AND VOLUME MEASURES ?
To properly interpret the changes in nominal figures when
relative prices and/or the general price level are changing
For goods and services this means that when the nominal
value of goods and services transacted changes
> how much is due to changes in quantity?
> how much is due to changes in the prices of the goods or services?
For nominal income this means that when such income
increases or decreases
> how much more or less of goods can be bought as a result of the
change?
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The scope of price and volume measures in the system
Price and volume measures are required
> to factor the changes in the values of goods and services into
components reflecting changes in their volumes and prices
> measure the cash flows in real terms by deflating
their values by price indices
The scope of the price and volume measures also
includes:
Taxes and subsidies
Trade margins
Balancing items (value added, GDP)
Compensation of employees
Consumption of fixed capital
Stocks of produced assets (inventories, fixed assets)
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Price and Volume measures in the System of National Accounts
main issues
What is meant by price and volume measurement for these items and
their components
What is the relationship between the current price value and the price
and the volume measures for these items?
How to aggregate them?
How to obtain price and volume measures in practice?
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Main SNA recommendation for price and volume measures
Ideal method:
Annually chained Fischer price and volume indices for GDP and its
components
Second best
Annually chained Laspeyres volume indices and Paasche price indices
OR
Annually chained Paasche volume indices and Laspeyres Price indices
Note: When chain indices are compiled for output, intermediate
consumption and value added, they are not additively consistent
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How are price and volume measurement for GD obtained?
Through 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 expenditure PLUS
for households final consumption expenditure PLUS
for NPISH’s final consumption expenditure
PLUS
for capital formation (and changes in invent.) PLUS
for exports MINUS
for imports
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What is meant by value (s) at constant prices
It is the value(s) of a product(s) for the current period using
its own price(s) from an earlier period (base year)
Values at constant prices are an aggregated volume
measure, expressed in money terms and additive
They reflect changes in quantity and/or quality
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Dose the choice of base year affect growth rates?
Yes
The underlying weights will be different in different years
Why?
The rate of price change is not the same for all goods and services
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The usefulness of constant price series depend on?
Extent of the rate of price divergence for the commodities in
the measure
Extent to which the relative price weights of the base period
differ from the price relative weights of other periods included
in the series.
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General Principles of Price and Volume Measurements
What is meant by price and volume measurements for
aggregates of goods and services
How in practice to obtain price and volume measures for these
aggregates
How to aggregate over price and volume measures for subcomponents to obtain price and volume measures for more
aggregated items
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Concept of Constant prices, price and volume indices
The current value of a single product i at time t can be
expressed as
v i ,t = p i ,t * q i ,t
Value of this product can be expressed in market price of
previous period and construct a time series where all
transactions for the product are expressed in the price of a
selected base period 0 as ( p i ,0 * q i ,t )
The current value of the same product can also be
expressed as
v i ,t = ( p i,t /p i,0 ) * p i ,0 * q i ,t
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Similar set of relationships can be established at aggregated
level between
The aggregated rate of change of the value at current
prices, and a Paasche price index and a Laspeyres volume
index,
The aggregate value at current prices, a Paasche price index
and the aggregate value measured at constant price
Vt  i Vi , t  i Pi , t  qi , t  i
 i Pi ,0  qi , t  P0, t * Q0, t
P
i
,
0

q
i
,
t
i
Pi , t  qi , t
The aggregated "price" measure - a Paasche price index
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The aggregated "price" measure - a Paasche price index
 pi , 0  pi , t * qi , t
 pi , 0 

i pi , t * qi , t

 wi , t
P 0, t 
 1 i 
 1 i 
i pi ,0 * qi , t
 pi , t  i pi , t * qi , t
 pi , t 
Paasche price index
take the ratio of the value of output in current prices in year (t) to
the value of output in year 0 measured in constant prices (prices of
year 0) (and multiply it with 100 to convert to an index form)
The ratio of any aggregate in current prices to the aggregate in
constant prices yields an implicit Paasche price deflator
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Constant price measures
Measure the monetary value of an aggregate
Where
Each individual quantity is valued at its own prices in an
earlier period
Means
Period-to-period changes in constant price estimate for
aggregated items
Reflect changes in the quantities of the different items
Aggregated Volume Measure
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Constant price estimates are
Aggregated price measure is in monetary terms
Constant price data are additive
Convenient way of constructing aggregate volume measures
The change from the base period constitutes a Laspeyres
volume index
LQ0, t 
 qi , t  pi , 0 * qi ,0
 qi , t 
Q0, t i pi , t  qi , t

wi ,0

  i
 i 
Q0,0 i pi , o * qi ,0
 qi ,0  i pi ,0 * qi ,0
 qi ,0 
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Relationship between value, price and Quantity indices can be
established at an aggregated level
Alternative index formulae for price and volume measures
The Laspeyres price index
LP 0, t
P 0, t


P 0, 0
p
p
i
i
i, t
 qi , 0
i, o
* qi , 0
Paasche output volume index
QP 0, t
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Q 0, t


Q 0, 0
p
p
i
i
i, t
 qi , t
i, t
* qi , 0
The value of base year output at prices in the current period
 Pi , t  qi ,0
i Pi , t  qi ,0 Pi ,0  qi ,0 * LP 0, t  i Pi ,0  qi ,0 * i
i Pi , t  qi ,0
The Fisher volume index
FQ
0, t

LQ
0, t
* PQ0, t
The Fisher price index
FP
0, t

Lp
0, t
* PP 0, t
Value index = Price index times volume index
Vt
 FP0, t * FQ0, t  ( LP 0, t * PQ0, t ) * ( LQ 0, t * PP 0, t )
V0
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According to the expressions in the mentioned indices
Constant price could be derived according to three
methods
Revaluation
Deflation
Volume extrapolation
With the possible exception of hyperinflation situations constant
price estimates derived through deflation can in general be
expected to produce more accurate results than extrapolation with
quantity indicators.
The justification for this is that price relatives (pt/p0) generally
display less variation than quantity relatives (qt/q0 )
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Concept of Gross value added at constant prices
Gross Value added (GVA) is a non-observable concept
It cannot be decomposed into a price and a quantity component
Concept of value added at constant prices can be defined and measured as:
P
x, i , t
i
 Xi , j , t  i Pic, i , t  ICi , j , t
Output at constant prices (minus) intermediate consumption at constant
prices
The GVA of an industry j at current and constant prices can be expressed as
P
i
0, i , 0
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 Xi ,
j, t
 i Pic, i , 0  ICi ,
j, t
Laspeyres "volume" index GVA in j-th industry can be defined as:
Ratio of GVA of j-th industry in period t at constant prices
&
GVA of j-th industry in the base year at the base year prices

i Px , i , 0  Xi , j , t  i Pic, i , 0  ICi , j , t
LQIVA j ,0, t 
i Px, i ,0  Xi , j ,0  i Pic, i ,0  ICi , j ,0
Paasche "price" index for GVA of the j-th industry can be defined as
Ratio of GVA of j-th industry in period (t) at current and constant prices

i Px , i , t  Xi , j , t  i Pic, i , t  ICi , j , t
PPVA j ,0, t 
i Px, i ,0  Xi , j , t  i Pic, i ,0  ICi , j , t
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Gross Value added at constant prices
Measure of the contribution of an individual production unit, or a
group of production units, such as an industry, to the total
output at constant prices of goods and services available for final
use in the economy (consumption, capital formation, and net
export).
A change in value added at constant prices can mean no more
than a change in value added measured at some fixed set of
prices and has no physical counterpart in the real world
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Alternative price and volume measures for GVA
Paasche "volume“ index

i Px , i , t  Xi , j , t  i Pc , i , t  Ci , j , t
PQVA j ,0, t 
i Px, i , t  Xi , j ,0  i Pc, i , t  Ci , j ,0
Laspeyres "price index

i Px , i , t  Xi , j , 0  i Pic, i , t  ICi , j , 0
LPVA j ,0, t 
i Px, i ,0  Xi , j ,0  i Pic, i ,0  ICi , j ,0
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Concept of GDP expenditure at constant prices
GDP through the expenditure approach
Can be expressed as an aggregate of actually observed transactions
Recorded independently of the accounting framework
Have a physical counterpart in the real world
Can be factored into a price and a quantity component
The corresponding price and quantity index in principle being a
weighted average of observable price and quantity relatives.
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Methods of Obtaining Constant Prices GVA estimates
Countries develope alternative methods to derive constant prices GVA
The developed methods depends on the choice of
Double or single indicator method
Use of output or input related indicator
Use of extrapolation or deflation
type of variable on which the indicators are based
All of them are variants of double indicator or single indicator
methods
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Double deflation
Since gross value added in current prices is derived indirectly as
the residual item in the production account
> It has no observable flows of goods and services as counterpart, and
> No quantity and price components. Hence,
> It may not be revalued in the prices of a base year
Gross value added at constant prices is obtained as:
> the difference between the output and intermediate inputs
at constant prices - a process called double deflation
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Double deflation
Double deflation means
output and intermediate consumption in current prices are deflated using an
appropriate (Paasche type) price index, or
extrapolated from base year values by an appropriate Laspeyres-type volume
index
Double deflation is sensitive to error especially when
> input data are not accurate, and/or
> value added is a small proportion of output
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Single Extrapolation / Deflation
As approximation of double deflation, the volume index for gross
output may be used to extrapolate the volume of gross value
added when
> an index for intermediate inputs is not available or,
> input data are not accurate
The underlying assumption is that
input-output coefficients are fixed so that price measures for intermediate
consumption are derived implicitly
Alternatively, the Paasche price deflator for output may be used to
deflate the value added data in current prices
The underlying assumption is that:
output and input prices do not diverge significantly
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Single Indicator Methods
(i) Single Output related indicator methods:
(a) Direct deflation of current price value added by a producers’
price index
(b) Direct extrapolation of base year value added using a gross
output volume index.
(c) Direct extrapolation of base year value added using indices
based on physical quantity output measures.
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(ii) Single input related indicator methods:
Deflation current price GVA by price index of (IC).
Deflation of current price GVA by wage rate index
Extrapolation of base year GVA by volume index of (IC).
Extrapolation of base year GVA by index of deflated compensation
of employees.
Extrapolation of base year GVA by index based on physical quantities
of inputs other than labor.
Extrapolation of base year GVA by index of numbers employed.
Extrapolation of base year GVA by an index of man hours worked.
Extrapolation of base year GVA by index of hours and man-hours
worked adjusted for change in labor productivity.
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Single Indicator Methods Cont….
Normally,
The volume index for output is preferred to one based on inputs,
which has greater bias because number and variety of outputs is
smaller than the number of intermediate goods and services
consumed in the production process commodity composition of
inputs is more variable over time
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Specific issues
Trade margins at constant prices :
The trade margin is calculated as the difference between the value
of the goods sold valued at current purchasers' prices and at current
producers' prices
The amount and value of the trade margin is not directly observable
Trade margins at constant prices cannot be estimated by deflating
the trade margins at current prices directly
The constant price estimates of the margin can be defined as the
difference between the value of the goods sold valued at constant
purchasers' prices and at constant producers' prices
In practice: trade margin at constant prices is obtained by many
countries by simply extrapolating total trade margins in the base
year with a volume index for trade turnover
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Specific issues ….. cont.
Taxes and subsidies on products at constant prices:
Do not have price and quantity components
Can not be estimated by deflating current estimates directly
Defined as the base year tax rate on the product multiplied by the
value of the product at constant prices
In practice: constant price estimates can be estimated by:
> Applying the implicit base year tax rates on the relevant
transactions at constant prices
> Extrapolating the base year value with volume indices for the
relevant transactions
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Constant price estimation in practice
Calculation of Passche price Indexes for all parts of the national accounts is
not always possible – data requirement
The compromised solution is to deflate current price values at the most
detailed level possible by Laspeyres deflators
The outcome of this solution is an approximation of the results which
would have been achieved by using Passche deflators
This solutions is generally satisfactory provided that the relative quantities
and/or relative prices of each item do not change significantly over time
However, it is rare for such conditions to be met in practice
What to do??
Revalue commodities causing problems separately from all other
commodities so that the price deflators have the most up-to-date weights
possible ???
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The major problems
Most of the price indices are compiled using the Laspeyres
formula
The base periods for some of the price indices differ from
the base year chosen for the national accounts
The weights used in compiling the available Laspeyres
price indices are not updated regularly
The compilation level might not be adequate to obtain an
approximation for Paasche price and Laspeyres volume
indices
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What to do??
Improve the compilation level to be at more disaggregated
level? How?
Do not use single deflators?
Improve the price statistics?
Update the weights of price indices regularly? When?
Improve the level of details in the current price estimates?
May 13, 2009