Index of Industrial Production:Deflation vs. Volume

Extrapolation

13 December 2011UNSD, New York

IIP

• Main purpose to provide a measure of short term changes in value added

• However, it is difficult to collect high-frequency data to accurately measure value added

• Therefore, gross output measures are more commonly used– Value of production & turnover

• Describes the changes of the volume of goods and/or services produced over time.

2

LaspeyresAt individual product level Laspeyres volume index

Paasche volume index

3

i i

tii

iii

itii

t qq

wqp

qpL

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Kjjj

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i ti

itii

iti

ititi

t

qq

wqp

qpP

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0,,

0,,

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Kjtjtj

tititi qp

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LaspeyresAt aggregated levels, the formula uses indices

4

ci

tipg

ipg

tic IwI ,0,,

Laspeyres with DeflatorTo turn Value (price x quantity) into volume:

5

i

titi deflatorprice

valuevolume ,

,

Deflation Example

1. Preprocessing2. Value relatives (product)3. Value indices (product group)4. Value indices (class/industry)5. Deflation6. Volume indices (higher levels)

6

7Products

Product Groups

ISIC Levels

8

Products, product groups, ISIC classesISIC Class Product Group Product

1511 G1 – Leather P1 – Chamois leather

G2 – Furskins P2 – Dressed furskins

1512 G3 – Luggage P3 – Leather suitcase

1520 G4 – Leather footwear P4 – Men’s shoes with leather uppersP5 – Women’s shoes with leather uppers

G5 – Textile footwear P6 – Shoes with textile uppers

G6 – Sports footwear P7 – Ski boots

P8 – Tennis shoesP9 – Men’s running shoes

9

Products, product groups, ISIC classesISIC Class Product Group Product

1511 G1 – Leather P1 – Chamois leather

G2 – Furskins P2 – Dressed furskins

1512 G3 – Luggage P3 – Leather suitcase

1520 G4 – Leather footwear P4 – Men’s shoes with leather uppersP5 – Women’s shoes with leather uppers

G5 – Textile footwear P6 – Shoes with textile uppers

G6 – Sports footwear P7 – Ski boots

P8 – Tennis shoesP9 – Men’s running shoes

10

11

1. Preprocessing

a. Variablesb. Weights c. Deflators – PPI at industry levels

12

1. Preprocessing

Variables

Obs Prod Prd Grp ISIC Value of output

T0 T1 T2

1 P4 G4 1520 202 250 2652 P4 G4 1520 178 196 2043 P4 G4 1520 150 175 200

P4 G4 1520 530 621 669

13

1. PreprocessingWeightsObtained separately for the whole product group from other sources (e.g. structural business survey, economic census)

Product Product Group Absolute weight Relative weightP4

G4248 0.73

P5 93 0.27

Product Group ISIC class Absolute weight Relative weightG4

1520342 0.56

G5 15 0.02G6 250 0.41

Kjjj

iii qp

qpw

0,0,

0,0,0,

14

2. Value relatives at product level

0,

,,

jp

VAL

ijp

VALij

p

VV

R

Value relative of product j in period Ti

Value data of product j in period Ti (i=0,1,2)

In other words:

Value relative of a product at time t is its value at time t divided by its value at time 0

15

2. Value relatives at product level

Product [1] [2] [3]=[2]/[1] [4] [5]=[4]/[1]

P4 530 621 669

2,jpR1,j

pR 2,jp

VALV1,jp

VALV0,jp

VALV

1.17 1.26P5 1.06 1.09206 219 225

16

3. Value indices at product group level

kj

tjp

jp

tkpg

VAL RwI ,0,,

Value index of product group k in time t

Weight of product at time 0 * value relative at time t

In other words:

The product group value index is the weighted average of value relatives in that product group

17

3. Value indices at product group level

T1 T2

Prod /PrdGrp

Prod weight

Prod value

relative

Weighted prod value

relative

Prod group value index

Prod value

relative

Weighted prod value

relative

Prod group value index

[1] [2] [3]=[1]*[2] [4]=sum([3]) [5] [6]=[1]*[5] [7]=sum([6])

P4 .73 1.17 1.26P5 .27 1.06 1.09G4

0.850.29

0.920.30

1.14 1.22

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3. Value indices at product group level

Prd Group ISIC Product group value index

G4 1520 100.0 114.2 121.6G5 1520 100.0G6 1520 100.0

0,jpg

VAL I 1,jpg

VAL I 2,jpg

VAL I

110.0 115.0113.3 101.5

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4. Value indices at industry (4-digit ISIC level)

cj

tjpg

jpg

tkc

VAL IwI ,0,,

Value index of class k in time t

Weight of product group at time 0 * value relative at time t

In other words:

The industry value index is the weighted average of the value indices of the product groups in the industry

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4. Value indices at industry (4-digit ISIC level)

T1 T2

Prd Grp/ISIC

Prd Grp

weight

Prd Grp value

relative

Weighted prd grp

value rel.

ISIC value index

Prd Grp value

relative

Weighted prd grp

value rel.

ISIC value index

[1] [2] [3]=[1]*[2] [4]=sum([3]) [5] [6]=[1]*[5] [7]=sum([6])

G4 0.56 1.14 1.22G5 0.02 1.10 1.15G6 0.41 1.13 1.01

1520

0.640.030.47

1.14

0.690.030.42

1.13

21

4. Value indices at industry (4-digit ISIC level)

ISIC ISIC class value index

1511 100.01512 100.01520 100.0 113.7 113.1

0,jc

VAL I 1,jc

VAL I 2,jc

VAL I122.3 134.392.8 100.0

22

5. Deflation

Volume Index = Value index / PPI (at 4-digit level)

ijcP

ijc

VALij

cVOL I

II

,

,,

ijc

VAL I ,

ijc

VOL I ,

ijcP I ,

= volume index in period Ti for ISIC class j

= value index in period Ti for ISIC class j

= deflator (PPI) in period Ti for ISIC class j

23

5. Deflation

ISIC Producer Price Indices

1511 100.0 102.1 104.21512 100.0 102.4 103.61520 100.0 101.9 104.0

0,jcP I 1,j

cP I 2,j

cP I

Deflators (at industry level)

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5. DeflationT1 T2

Value index

PPI Volume index

Value index

PPI Volume index

ISIC [1] [2] [3]=[1]/[2] [4] [5] [6]=[4]/[5]

1511 122.3 134.31512 92.8 100.01520 113.7 113.1

102.1102.4101.9

119.890.6

111.6

104.2103.6104.0

128.896.5

108.8

25

6. Volume indices at 3 and 2 digit levels

Gross value added at basic prices is recommended to derive weights

ISIC Base period weightRelative weight

(in next higher ISIC level)

151115121520

151152

16280607

0.670.331.00

242607

0.290.72

26

6. Volume indices at 3 and 2 digit levels

Kj

tjc

VOLjc

tkK

VOL IwI ,0,,

Volume index of ISIC group k in time t

Weight of ISIC class at time 0 * value relative at time t

In other words:

The industry value index is the weighted average of the ISIC class volume indices in the ISIC group

27

6. Volume indices at 3 and 2 digit levels

T1 T2

ISIC class/

grp

Class weight

ISIC class index

Weighted ISIC class

index

ISIC group index

ISIC class index

Weighted ISIC class

index

ISIC group index

[1] [2] [3]=[1]*[2] [4]=sum([3]) [5] [6]=[1]*[5] [7]=sum([6])

1511 0.67 1.20 1.291512 0.33 0.91 0.97151

1520 1.00 1.12 1.09152

0.800.30

0.860.32

1.10 1.18

1.12 1.091.12 1.09

28

6. Volume indices at 3 and 2 digit levels

T1 T2

ISIC grp/ div

Grp weight

ISIC group index

Weighted ISIC group

index

ISIC division index

ISIC group index

Weighted ISIC group

index

ISIC division index

[1] [2] [3]=[1]*[2] [4]=sum([3]) [5] [6]=[1]*[5] [7]=sum([6])

151 0.29 1.10 0.31 1.18 0.34152 0.72 1.12 0.80 1.09 0.7815 1.11 1.11

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SummaryISIC IIP

T0 T1 T2

1511 100.0 122.3 134.31512 100.0 92.8 100.01520 100.0 113.7 113.1

151 100.0 110.1 118.2152 100.0 113.7 113.1

15 100.0 111.2 111.5

Volume Extrapolation Example

1. Preprocessing2. Volume relatives (product)3. Volume indices (product group)4. Volume indices (class/industry)5. Deflation5. Volume indices (higher levels)

30

31

Products, product groups, ISIC classesISIC Class Product Group Product

1511 G1 – Leather P1 – Chamois leather

G2 – Furskins P2 – Dressed furskins

1512 G3 – Luggage P3 – Leather suitcase, Model AP4 – Leather suitcase, Model B

P5 – Handbags, Model A

1520 G4 – Leather footwear P6 – Men’s shoes, Model A

P7 – Men’s shoes, Model B

P8 – Men’s shoes, Model C

P9 – Women’s shoes, Model A

P10 – Women’s shoes, Model B

P11 – Women’s shoes, Model C

G5 – Textile footwear P12 – Textile shoes, Model A

G6 – Sports footwear P13 – Ski boots, Model A

P14 – Tennis shoes, Model A

P15 – Men’s running shoes, Model A

32

Products, product groups, ISIC classesISIC Class Product Group Product

1511 G1 – Leather P1 – Chamois leather

G2 – Furskins P2 – Dressed furskins

1512 G3 – Luggage P3 – Leather suitcase, Model AP4 – Leather suitcase, Model B

P5 – Handbags, Model A

1520 G4 – Leather footwear P6 – Men’s shoes, Model A

P7 – Men’s shoes, Model B

P8 – Men’s shoes, Model C

P9 – Women’s shoes, Model A

P10 – Women’s shoes, Model B

P11 – Women’s shoes, Model C

G5 – Textile footwear P12 – Textile shoes, Model A

G6 – Sports footwear P13 – Ski boots, Model A

P14 – Tennis shoes, Model A

P15 – Men’s running shoes, Model A

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1. Preprocessing

a. Variablesb. Weights

35

1. Preprocessing

Variables

Obs Prod Prd Grp ISIC Unit Quantity of output

T0 T1 T2

1 P3 G3 1520 Num 32 24 292 P4 G3 1520 Num 36 36 353 P5 G3 1520 Num 103 102 113

36

1. PreprocessingWeights

Obtained separately for the whole product group from other sources (e.g. structural business survey, economic census)

Product Prod Group Absolute weight Relative weightP3

G386 0.37

P4 115 0.49P5 32 0.14

Prod Group ISIC class Absolute weight Relative weightG3 1512 284 1.00

37

2. Volume relatives at product level

0,

,,

jp

VOL

ijp

VOLij

p

VV

R

Volume relative of product j in period Ti

Volume data of product j in period Ti (i=0,1,2)

In other words:

Volume relative of a product at time t is its volume at time t divided by its volume at time 0

38

2. Volume relatives at product level

Product [1] [2] [3]=[2]/[1] [4] [5]=[4]/[1]

P3 32 24 29

2,jpR1,j

pR 2,jp

VOLV1,jp

VOLV0,jp

VOLV

0.75 0.91P4 1.00 0.9736 36 35P5 0.99 1.10103 102 113

39

3. Volume indices at product group level

Kj

tjp

jp

tkpg

VOL RwI ,0,,

Value index of product group k in time t

Weight of product at time 0 * value relative at time t

In other words:

The product group volume index is the weighted average of volume relatives in that product group

40

3. Volume indices at product group level

T1 T2

Prod/Prd Grp

Prod weight

Prod volume relative

Weighted prod vol relative

Prod group volume index

Prod volume relative

Weighted prod vol relative

Prod group volume index

[1] [2] [3]=[1]*[2] [4]=sum([3]) [5] [6]=[1]*[5] [7]=sum([6])

P3 .37 0.75 0.91P4 .49 1.00 0.97P5 .14 0.99 1.10G3

0.280.49

0.330.48

0.91 0.97

0.14 0.15

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3. Volume indices at product group level

Prd Grp ISIC Product group volume index

G1 1511 100.0G2 1511 100.0G3 1512 100.0G4 1520 100.0G5 1520 100.0G6 1520 100.0

0,jpg

VOL I 1,jpg

VOL I 2,jpg

VOL I

113.2 120.890.6 96.5

122.1 131.7

110.0 113.8116.4 115.6

108.2 103.6

42

4. Volume indices at industry (4-digit ISIC level)

T1 T2

Prd Grp/ISIC

Prd Grp

weight

Prd Grp volume relative

Weighted prd grp vol

relative

ISIC volume index

Prd Grp volume relative

Weighted prd grp vol

relative

ISIC volume index

[1] [2] [3]=[1]*[2] [4]=sum([3]) [5] [6]=[1]*[5] [7]=sum([6])

G4 0.56 1.08 1.04G5 0.02 1.10 1.14G6 0.41 1.16 1.16

1520

0.610.030.48

1.12

0.580.030.48

1.09

43

4. Volume indices at industry (4-digit ISIC level)

ISIC ISIC class volume index

1511 100.01512 100.01520 100.0 111.6 108.8

0,jc

VOL I 1,jc

VOL I 2,jc

VOL I119.8 128.990.6 96.5

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5. Volume indices at 3 and 2 digit levels

Exactly the same way as the the deflation example because they are both in volume terms at this point

Recap• Data Requirements

– Product values (deflation) or quantities (vol. ext.) at current period

– Weights at the product, product group and class level • Quantity and Price at base period

– PPI (deflation)• Reflects quality changes

• Difference in results– Deflation -> Paasche index != Laspeyres index

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RecommendationsDeflation vs. Volume Extrapolation• Deflation preferred over volume extrapolation• Deflation is recommended because:

– Better accommodates heterogeneous product mix – Makes use of the price index collection

• Quality issues already accounted for in PPI

• Volume extrapolation is easier to use for measuring industries producing homogenous goods with constant quality

Thank you.

Questions?