L11 - Price and Volume Measures (ENG)

7/27/2019 L11 - Price and Volume Measures (ENG)

1/18

Quarterly National Accounts Course

Joint Vienna Institute

August 5 - 16, 2013

L-11: Price and Volume Measures

Reproductions of this material or any parts of it should refer to the IMF Statistics Department as the source

Lecture Outline

I. Introduction

Scope and Main Issues

II. Main concepts and principles

A. Basic Relationship between Value, Quantity and Price

B. Laspeyres Volume Index and Paasche Price Index

C. The set of Laspeyres and Paasche Index Formulas

D. Basic Re ations ip etween Va ue, Vo ume an PriceIndices

III. GDP from the production approach

IV. GDP from the expenditure approach

IMF Statistics Department JVI/QNA/L11 : 2


2/18

Why Do we Need Price and Volume

Measures?

To ro erl inter ret the chan es in nominal fi ureswhen relative prices and/or the general price level arechanging.

1. For goods and services this means that when thenominal value of goods and services transacted

roduced consumed im orted or ex orted chan es

how much is due to changes in quantity?

how much is due to changes in the prices of the goods orservices?


To ro erl inter ret the chan es in nominal fi ures

Why Do we Need Price and Volume

Measures?

when relative prices and/or the general price level arechanging.

2. For nominal income this means that when suchincome increases or decreases

how much more or less of goods can be bought as a result ofthe change?



3/18

Scope of Price and Volume Measures in the

System

r ce an vo ume measures are requ re

1. For goods and services

to factor the changes in their values intocomponents reflecting changes in their volumesand prices

2. And to measure the cash flows in real terms by deflating their values by price indices


Scope of Price and Volume Measures in the

System

e scope o t e pr ce an vo umemeasures also includes:

3. Taxes and subsidies;

4. Trade margins;

. ,6. Compensation of employees;

7. Consumption of fixed capital;

8. Stocks of produced assets (inventories, fixed assets)



4/18

Price and Volume Measures in the 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?


Main SNA Recommendations for Price and

Volume Measures

a e o e ar

Ideal method:

Annually chained Fischer price and volume indices forGDP and its components.

Second best:

Annually chained Laspeyres volume indices andPaasche price indices; OR

Annually chained Paasche volume indices andLaspeyres price indices.



5/18

Basic Relationship between Value, Quantity

and PriceQuantity: Unit for measuring amount of a good or service. Quantities

are additive onl at the sin le roduct level

Price:Value of one unit of a good or service (of same quality)

An average of the prices of different goods or services should notbe used to measure price changes over time

Value: Price multiplied by quantity. Additive across different products

At single product level:

At an aggregated level:

where:vit,pit, and qitare the value, price and quantity of item iin period t,and

Vit is the total value at current prices in period t

ititit qxpv

i ititi itit

qxpvV


What is Meant by Value(s) at Constant Prices

It is the value(s) of a product(s) for the current period using its ownprice(s) from an earlier period.

Table 1 Car Production

Price Quantity Value Price Quantity Value Value

(000 $/un.) (No.) (000 $) (000 $/un.) (No.) (000 $) (year 0 $)

(1) (2) (3) = (1)*(2) (4) (5) (6)=(4)*(5) (7)=(1)*(5)

Model A 20 15 300 40 24 960 480

Model B 10 15 150 20 6 120 60

30 450 30 1,080 540

Year 0 Year 1

Values in column (6) are in current prices showing a 140 percentincrease over year 0 (index = 1080/450 = 240)

Values in column (7) are at constant prices of year 0, they reflectchanges in quantity and/or quality.Values at constant prices are an aggregated volume measure, expressed in moneyterms and additive



6/18

Laspeyres Volume Index Formula

The change from the base year in constant prices or the ratio of

be expressed in index form as:

LQ0t = 540 x 100 / 450 = 120.0

This is also called Laspeyres (fixed-base) volume index (LQ0t).

Mathematically:

)1(0,0,

,0,

0

,0

0,0

,00

i ii

i tiittt qp

qp

VQ

QQ

LQ

Note: the two components of the index are ADDITIVE

The Laspeyres volume index can also be written as:

where wi,o is the base period weight, i.e. the items share in the total value inthe base period

)2(0,

,0,0 i

i

tiit q

qwLQ


Relationship between Measures at Constant Prices and

Laspeyres Volume Index Formula

Accordin to this formulation 2 , L is derived asfollows using the data from the data in table 1:

Table 2

Price Quantity Value Weight Quantity

(000 $/un.) (No.) (000 $) (w0) (No.)

(1) (2) (3) = (1)*(2) (4)=(3)/

(3) (5) (6)=(5)/(2) (7)=(4)*(6)*100

Model A 20 15 300 66.7% 24 1.6 107

w0*QR

Year 0 Year 1

Quantity

relatives (QR)

Note Laspeyres (fixed-base) volume index is one of several volume index formulas Measures at constant prices are one of several alternative volume measures Others are, Paasche index formula, chain-linked indices and Fisher.

Model B 10 15 150 33.3% 6 0.4 13

30 450 30 120



7/18

Paasche Price Index FormulaTo factor the change in the value of car production from year 0 toyear 1 arising from price changes. take the ratio of the value of out ut in current rices in ear 1 to the value of

output in year 1 measured in constant prices (prices of year 0) (and multiply itwith 100 to convert to an index form):

PP0t= 1080 x 100 / 540 = 200.0

Shows 100 percent increase or doubling in prices

The above ratio is also called the Paasche price index (PP0t).Algebraically:

or

where wi,t is the current period weight, i.e. the items share in the totalvalue in the current period

)1(,0,

,,

,00

i tii

i tt

t

tt qpQ

PP

)2(1,

0,,0 i

ti

itit p

pwPP


According to the later formulation, PP0t is derived as follows from

the data in table 1:

Paasche Price Index Formula

Table 3

Year 0

Price Price Value Weight

(000 $/un.) (000 $/un.) (000 $) (w1)(1) (2) (3) (4)=(3)/

(3) (5)=(1)/(2) (6)=(4)*(5)*1 00

Model A 20 40 960 88.9% 0.5 0.44

Model B 10 20 120 11.1% 0.5 0.06

1,080 0.50

*

Price

relatives (PR)w1*PR

Year 1

The ratio of any aggregate in current prices to the aggregate inconstant prices yields an implicit Paasche price deflator

Price measures for the main national accounts aggregates are(always) derived implicitly

0

t= w 1 = . x .



8/18

The change in the current price value of car production from year 0 toyear 1 in our example can be expressed algebraically as:

Relationship between Value, Volume and Price Indexes

Multiplying and dividing by ipi,0qi,t gives:

Value index = Laspeyres Volume index * Paasche Price index / 100

i iii titit qpqpV

V0,0,,,

0

)(*)( ,0,,,0,0,,0,0

i tiii titii iii tiit qpqpqpqpV

V

The volume and price effects of value change are multiplicative When VtandV0are known and PP0t is available the Laspeyres

volume index can be derived indirectly from above formula aprocess called price deflation

200

0

120

0

240

0

ttt


Another set of volume and price indices may be obtained starting from thechange in the current price value of car production from year 0 to year 1:

Relationship between Value, Volume and Price Indexes

Multiplying and dividing by ipi,tqi,0 gives:

orValue index = Paasche Volume index * Laspeyres Price index / 100

i iii titit qpqpV

V0,0,,,

0

)(*)( 0,,,,0,0,,,0

i itii titii iii oitit qpqpqpqpV

V

PQ0tcan be obtained by inflating the base period values using the oftenavailable LP0t and then dividing the current price value by this amount.

100/100

120

0

200

0

240

0

ttt PQLPVV



9/18

Reference, Base and Weight periods

Reference period (comparison period): The period in an indexnumber time series which is taken as = 100

Base period (pricing period)

Price base period: The period whose prices are used as denominators incalculating price relatives Pt/ P0(0is the price base period)

Quantity base period: The period whose quantities are used as denominators incalculating quantity relatives Qt/ Q0(0is the price base period)

Weight period: The period from which the weights are taken

Equal to the base period for a (fixed-base) Laspeyres index (wo) and to the currentperiod for a (fixed-base) Paasche index (wt)


Fixed Base or Chain Index

When a fixed base Laspeyres is used over a long run of periods,the wei hts become ro ressivel out of date and irrelevant. Thisimplies that the base period has to be updated sooner or later andthe new index linked to the old. Chaining is simply the limitingcase in which the weights are updated each period.

Fixed base index (Laspeyres)compares between periods 0 and t.

with 1, then 1 with 2,..,then t-1 with t.

Any index number formula can be used for the links.



10/18

ChainingA chain index between periods 0 and t is path dependant- it

depends not just on the prices and quantities in 0 andt, but alsoon the rices and uantities in all the intervenin laces.

If the path is fairly smooth then the additional price and quantityinformation will tend to lead to a better measure of the overallchange. It will tend to reduce spread between Laspeyres andPaasche.

quantity information may increase the index number spread and

lead to drift, e.g. if the prices in 0 are the same as those in t, achain Laspeyres index may exceed 100 if the path is not smooth.


Change of Reference Period or Re-Referencing

Example of re-referencing:

Table 6

2000 2005 2010 2011

Index

(reference period 2000=100)

Growth rate

(percent)

New Index 83.3 91.7 100 108.3

(reference period 2010=100) (100/120) (110/120) (120/120) (130/120)

Growth rate

100 110 120 130

10.0 9.1 8.3

Note:

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

(percent)

. . .



11/18

Change of Base Year. Effect on growth rates.An example:Table 7

2000 2005 2010 2011 2000-05 2005-10 2010-11

Values in current prices

Growth rate (percent)

Price 5 10 20 22 100.0 100.0 10.0

Quantity 4 5 6 7 25.0 20.0 16.7

Value 20 50 120 154 150.0 140.0 28.3

Mutton

Price 15 10 5 4 -33.3 -50.0 -20.0

Quantity 11 10 8 7 -9.1 -20.0 -12.5

Value 165 100 40 28 -39.4 -60.0 -30.0

TOTAL

Value 185 150 160 182 -18.9 6.7 13.8

Values in constant prices of 2 000

Wool 20 25 30 35 25.0 20.0 16.7

Mutton 165 150 120 105 -9.1 -20.0 -12.5

TOTAL 185 175 150 140 -5.4 -14.3 -6.7


Wool 50 60 70 20.0 16.7 Mutton 100 80 70 - 20 .0 - 12 .5

TOTAL 150 140 140 -6.7 0.0


Wool 120 140 16.7

Mutton 40 35 -12.5

TOTAL 160 175 9.4IMF Statistics Department JVI/QNA/L11 : 21

Why Change of Base Year

Because of structural changes in:

Production

Consumption

Relative prices, and because of

appearance of new products/ disappearance of old and qualityimprovements so that goods and services are no longer comparablebetween periods that may be too far apart.

For example: Norways GDP growth rate in 1989 was 0.6 percent in 1984rices and 5 ercent in 1988 rices because

Price of crude oil jumped during 1984-1988 (Norway is an oil producer andexporter)

Oil production increased significantly (by 25 percent) during 1988-1989

Consequences:

How to derive continuous time series of index numbers from series ofindex numbers with fixed bases?



12/18

Volume Measures and Measures in Real Terms

I. Changes in the values of flows or stocks at current prices, whichhave quantity and price dimensions, can be decomposed into:

changes in their prices; and

changes in their volumes

Measured at constant prices (prices which prevailed in the past), thevalues of such flows and stocks are said to be in volumeterms.

II. Flows or stocks, which do not have quantity and pricedimensions, are measured in real terms (at constant purchasing

power) by

deflating by taking into account the change in the prices of somerelevant basket of goods and services or assets, or the change in thegeneral price level.IMF Statistics Department JVI/QNA/L11 : 23

How are Price and Volume Measures

obtained for GDP?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

or ouse o s ina consumption expen iture PLUSfor NPISHs final consumption expenditure PLUS

for capital formation (and changes in invent.) PLUS

for exports MINUS

for imports



13/18

Price and Volume Measures

for Gross Value AddedI. Double deflation double extrapolation

Gross value added is derived as the difference between the output andintermediate consumption at constant prices both obtained separately

II. Single extrapolation

Gross value added is extrapolated using output data

Gross value added is extrapolated using employment data

III. S ng e e at on

Gross value added is deflated using output deflator

Gross value added is deflated using the wage index Gross value added is deflated using a general measure of inflation like CPI

(does not result in a volume measure but one of real income)


Double Deflation

Since gross value added in current prices is derived indirectly as the residualitem in the production account

It has no observable flows of oods and services as counter art 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 - aprocess called double deflation

Double deflation means output and intermediate consumption in currentprices

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



14/18

Double Deflation

Algebraically, value added at constant prices of the base year may be written as

tt qPQP 00where P0QtandP0qt are revaluations of outputs and intermediate inputs inthe prices of the base year 0

The deflation of current price gross value added data using the followingPaasche-type price index

yields the same results as double deflation

ttttttt qPQPqPQPPPVA 000

The Laspeyres-type volume index for gross value added is given by

Note: When chain indices are compiled for output, intermediate consumption and valueadded, they are not additively consistent (Look at Handout for Double Deflation)

ttttt qPQPqPQPLQVA 00000


Single Extrapolation/Deflation

As approximation of double deflation, the volume index for gross outputmay be used to extrapolate the volume of gross value added when

input data are not accurate

The underlying assumption is that

input-output coefficients are fixed so that price measures for intermediateconsumption 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



15/18

Illustration of Single Indicator MethodsPrimary data

Output at current Intermediate Value added current

prices consump on curren prices

(1) (2) (3)=(1)-(2)

2000 3,200 2,400 800

2001 2,940 2,100 840

2001 3,680 2,700 980

Date

Output at constant

2000 prices

Paasche price deflator

for outputOutput volume index

(4) (5)=(1)/(4)*100 (6)=(4) / 3200 * 100

2000 3,200 100.0 100.0

2001 3,000 98.0 93.8

2002 3,100 118.7 96.9

Date


Illustration of Single Indicator Methods

Single extrapolation

Laspeyres volume Value added constant

index output 2000 prices

(6) (7)=800*(6) / 100

2000 800 100.0 800*1.000 = 800.0

2001 ...... 93.8 800*0.938 = 750.0

2002 ...... 96.9 800*0.969 = 775.0

Single deflation

Date

Paasche price deflatorfor output

Value added currentprices

Value added constant2000 prices

(5) (13)=(1)-(2) (14)=(13)/(5) * 100

2000 100.0 800.0 800/1.000 = 800.0

2001 98.0 840.0 840/0.980 = 857.1

2002 118.7 980.0 980/1.187 = 825.5

Date



16/18

Intermediate Inputs as an Indicator

Normally, the volume index for output is preferred to one based on inputs,which has greater bias because

num er an var e y o ou pu s s sma er an e num er o n erme a egoods and services consumed in the production process

commodity composition of inputs is more variable over time

Volume index for inputs may be used as a single indicator for value added inexceptional cases:

for example, in construction and capital goods industries where the output

for example, in construction, ship-building, etc. where production period isvery long compared with accounting year

Even in these cases, input data are usually employed in combination withemployment indicators


Employment as an Indicator

Volume index for inputs of labor services is an alternative to the volumeindex for intermediate inputs

Indices easier to compile are quantity indices of time spent at work by labor,weighted by hourly wages paid to different kinds of workers, and thus takeinto account

changes in the total number of hours worked

changes in the composition of labor force

In practice, it is common to find numbers employed (employment) as

in icators o c anges in rea va ue a e in government services (since services are labor-intensive and output is

difficult to measure - non-market services are without prices and physicalcharacteristics are difficult to quantify)

in financial, business, entertainment services (because of practicaldifficulties of quantifying their output)



17/18

Illustration of Employment plus other Inputs as IndicatorsPart 1: Construction of compound price and volume indices of inputs

Intermediate consumption and compensation of employees at constant prices

Intermediate CompensationTotal input at

Dateconsump on

constant 2000

rices

Hours workedages per our

2000

o empoyees a

constant 2000

rices

constant 2000

prices

oume n ex

total input

(1) (2) (3) (4)=(2)*6 (5)=(1)+(4) (6)=(5)/3060*100

2000 2,400.0 110.0 6.0 660.0 3,060.0 100.0

2001 2,282.6 102.0 6.2 612.0 2,894.6 94.6

2002 2,647.1 107.8 6.5 646.8 3,293.9 107.6

Total input at current prices - compound price deflator

Date

Intermediate

consumption

current prices

Compensation

of employees at

current prices

Total input at

current prices

Price deflator

total input

(7) (8)=(2)*(3) (9)=(7)+(8) (10=(9)/(5) *100

2000 2,400.0 660.0 3,060.0 100.0

2001 2,100.0 632.4 2,732.4 94.4

2002 2,700.0 700.7 3,400.7 103.2


Illustration of Employment plus other Inputs as indicatorsPart 2: Output and value added at constant prices

Input based deflation

Output at Implicit price

Dateu pu a

current pricesconstant 2000

prices

a ue a e a

constant prices

a ue a e a

current pricesdeflator value

added

(11) (12)=(11)/(10)*100 (13)=(12)-(1) (14)=(11)-(7) (14)/(13)*100

2000 3,200.0 3,200.0 800.0 800.0 100.0

2001 2,940.0 3,114.5 831.9 840.0 101.0

2002 3,680.0 3,564.4 917.3 980.0 106.8

Input based volume extrapolation

Note: Using the dataon wages per hourto deflate valueadded directly givesa different result:840/(6.2/6) = 812.9980/(6.5/6) = 904.6

DateVolume index

total input

Output at

constant 2000

prices

Value added at

constant prices

Implicit price

deflator value

added

(6) (15)=(6)*3200/100 (16)=(15)-(1) (14)/(16)

2000 100.0 3,200.0 800.0 100.0

2001 94.6 3,027.0 744.4 112.8

2002 107.6 3,444.6 797.5 122.9

Note: Using the data onemployment to extrapolatevalue added directly givesdifferent result:800 * (102/110) = 741.8800 * (107.5/110) = 781.8



18/18

Illustration of Double Deflation MethodDouble Deflation Example

2003

Current prices Constant (2000) pricesPrice indexes

GO IC GVA PPI ICI GO IC GVA

(000 $) (000 $) (000 $) (2000=100) (2000=100) (000 $) (000 $) (000 $)

(1) (2) (3)=(1)-(2) (4) (5) (6)=(1)/(4)*100 (7)/(5)*100 (8)=(6)-(7)

Mining 7,300.0 3,800.0 3,500.0 210.0 215.0 3,476.2 1,767.4 1,708.7

Manufacturing 12,800.0 6,300.0 6,500.0 185.0 206.0 6,918.9 3,058.3 3,860.7

Total 20,100.0 10,100.0 10,000.0 ---- ---- 10,395.1 4,825.7 5,569.4

2000

Current

prices

2003

GVAGVA volume

index

GVA implicit

deflator

(000 $) (2000=100) (2000=100)

(9)(10)=(8)/(9)*10

0

(11)=(3)/(8)*10

0

Mining 1,735.0 98.5 204.8

Manufacturing 3,680.0 104.9 168.4

Total 5,415.0 102.9 179.6

GO: Gross OutputIC: Intermediate ConsumptionGVA: Gross Value AddedPPI: Producer Price IndexICI: Intermediate Consumption price Index


GDP by Expenditure Categories

GDP at constant prices is derived as the sum of expenditurecomponents at constant prices

Expenditure components of GDP are aggregates of transactions thatcan be compiled by observing and recording actual transactions

Value of these transactions can be factored into their own prices andquantities

Better measures of price and volume for GDP conceptually may be

obtained from the expenditure approach (CPI for HC, export and importprices)

Commonly, the deflation of current values is used to derive the dataat constant prices for most of expenditure items, although extrapolationby volume index is also used


L11 - Price and Volume Measures (ENG)

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