index of industrial production: deflation vs. volume extrapolation 13 december 2011 unsd, new york
DESCRIPTION
Laspeyres At individual product level Laspeyres volume index Paasche volume index 3TRANSCRIPT
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
0,
,0,
0,0,
,0,
Kjjj
iii qp
qpw
0,0,
0,0,0,
i ti
itii
iti
ititi
t
wqp
qpP
,
0,,
0,,
,, 1
Kjtjtj
tititi qp
qpw
,,
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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
18
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
19
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
20
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)
24
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
33
34
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
41
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
44
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
45
46
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?