Index of Industrial Production:
Deflation vs. Volume
Extrapolation
13 December 2011
UNSD, 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
Laspeyres
At individual product level
Laspeyres volume index
p

p
q
i , 0 i ,t
Lt
i
q
  wi , 0
i
i ,0 i ,0
qi ,t
wi , 0 
qi , 0
pi , 0 qi , 0
p
jK
j ,0
q j ,0
i
Paasche volume index
p
P
p
i ,t
qi ,t
i
t
i ,t
i
qi , 0

1
qi , 0
i wi,t q
i ,t
wi ,t 
pi ,t qi ,t
p
jK
j ,t
q j ,t
3
Laspeyres
At aggregated levels, the formula
uses indices
c
I i ,t   wi ,0  I i ,t
pg
pg
ic
4
Laspeyres with Deflator
To turn Value (price x quantity) into volume:
volumei ,t 
valuei ,t
price deflatori
5
Deflation Example
1.
2.
3.
4.
5.
6.
Preprocessing
Value relatives (product)
Value indices (product group)
Value indices (class/industry)
Deflation
Volume indices (higher levels)
6
ISIC Levels
Product Groups
Products
7
Products, product groups, ISIC classes
ISIC 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 uppers
P5 – Women’s shoes
with leather uppers
G5 – Textile footwear
P6 – Shoes with textile
uppers
G6 – Sports footwear
P7 – Ski boots
P8 – Tennis shoes
P9 – Men’s running
shoes
8
Products, product groups, ISIC classes
ISIC 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 uppers
P5 – Women’s shoes
with leather uppers
G5 – Textile footwear
P6 – Shoes with textile
uppers
G6 – Sports footwear
P7 – Ski boots
P8 – Tennis shoes
P9 – Men’s running
shoes
9
10
1. Preprocessing
a. Variables
b. Weights
c. Deflators – PPI at industry levels
11
1. Preprocessing
Variables
Obs
1
2
3
Prod
Prd Grp ISIC
Value of output
P4
P4
P4
G4
G4
G4
1520
1520
1520
T0
202
178
150
P4
G4
1520
530
T1
250
196
175
T2
265
204
200
621
669
12
1. Preprocessing
wi , 0 
pi , 0 qi , 0
p
jK
j ,0
q j ,0
Weights
Obtained separately for the whole product group from other sources
(e.g. structural business survey, economic census)
Product
P4
P5
Product Group
Product Group
G4
ISIC class
G4
G5
G6
1520
Absolute weight
Relative weight
248
0.73
93
0.27
Absolute weight
Relative weight
342
0.56
15
0.02
250
0.41
13
2. Value relatives at product level
p
R j ,i 
Value relative of
product j in period Ti
p
VAL j ,i
p
VAL j , 0
V
V
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
14
2. Value relatives at product level
p
VAL j , 0
[1]
p
VAL j ,1
[2]
530
206
621
219
V
Product
P4
P5
V
p
R j ,1
[3]=[2]/[1]
1.17
1.06
p
p
j ,2
VAL j , 2
[4]
[5]=[4]/[1]
V
669
225
R
1.26
1.09
15
3. Value indices at product group
level
pg
VAL k ,t
I
Value index of product
group k in time t
  w j , 0  R j ,t
p
p
jk
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
16
3. Value indices at product group
level
T1
Prod Prod
/Prd weight
Grp
[1]
T2
Prod
value
relative
Weighted
prod value
relative
Prod group
value index
Prod
value
relative
Weighted
prod value
relative
Prod group
value index
[2]
[3]=[1]*[2]
[4]=sum([3])
[5]
[6]=[1]*[5]
[7]=sum([6])
1.26
1.09
0.92
0.30
P4 .73 1.17
P5 .27 1.06
G4
0.85
0.29
1.14
1.22
17
3. Value indices at product group
level
Prd Group ISIC
Product group value index
pg
VAL
G4
G5
G6
1520
1520
1520
I j ,0
100.0
100.0
100.0
pg
VAL j ,1
pg
VAL
114.2
110.0
113.3
121.6
115.0
101.5
I
I j,2
18
4. Value indices at industry (4-digit
ISIC level)
c
VAL k ,t
I
Value index of class k
in time t

jc
pg
w j , 0  I j ,t
pg
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
19
4. Value indices at industry (4-digit ISIC
level)
T1
Prd
Grp/
ISIC
T2
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
0.64
1.22
0.69
G5
0.02
1.10
0.03
1.15
0.03
G6
0.41
1.13
0.47
1.01
0.42
1520
1.14
1.13
20
4. Value indices at industry (4-digit ISIC
level)
ISIC
ISIC class value index
c
VAL
1511
1512
1520
I j ,0
100.0
100.0
100.0
c
VAL j ,1
c
VAL
122.3
92.8
113.7
134.3
100.0
113.1
I
I j,2
21
5. Deflation
Volume Index = Value index / PPI (at 4-digit level)
c
VOL
I j ,i 
c
VAL j ,i
c
P j ,i
I
I
c
= volume index in period Ti for ISIC class j
VOL j ,i
I
c
VAL j ,i = value index in period Ti for ISIC class j
I
c
P
I j ,i = deflator (PPI) in period T for ISIC class j
i
22
5. Deflation
Deflators (at industry level)
ISIC
Producer Price Indices
c
P j ,0
I
1511
1512
1520
100.0
100.0
100.0
I j ,1
c
P j ,2
102.1
102.4
101.9
104.2
103.6
104.0
c
P
I
23
5. Deflation
T1
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
102.1
119.8
134.3
104.2
128.8
1512
92.8
102.4
90.6
100.0
103.6
96.5
1520
113.7
101.9
111.6
113.1
104.0
108.8
24
6. Volume indices at 3 and 2 digit
levels
Gross value added at basic prices is recommended to derive
weights
Relative weight
ISIC
Base period weight
(in next higher ISIC level)
1511
1512
1520
162
80
607
0.67
0.33
1.00
151
152
242
607
0.29
0.72
25
6. Volume indices at 3 and 2 digit
levels
I  w  I
K
VOL k ,t
Volume index of ISIC
group k in time t
c
jK
c
j , 0 VOL
j ,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
26
6. Volume indices at 3 and 2 digit
levels
T1
ISIC
class/
grp
T2
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
0.80
1.29
0.86
1512 0.33
0.91
0.30
0.97
0.32
151
1520 1.00
152
1.18
1.10
1.12
1.09
1.12
1.12
1.09
1.09
27
6. Volume indices at 3 and 2 digit
levels
T1
ISIC
grp/
div
T2
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
0.34
152
0.72
1.12
0.80
1.09
0.78
15
1.11
1.11
28
Summary
ISIC
1511
1512
1520
T0
100.0
100.0
100.0
IIP
T1
122.3
92.8
113.7
T2
134.3
100.0
113.1
151
152
100.0
100.0
110.1
113.7
118.2
113.1
15
100.0
111.2
111.5
29
Volume Extrapolation Example
1.
2.
3.
4.
5.
5.
Preprocessing
Volume relatives (product)
Volume indices (product group)
Volume indices (class/industry)
Deflation
Volume indices (higher levels)
30
Products, product groups, ISIC classes
ISIC Class
Product Group
Product
1511
G1 – Leather
P1 – Chamois leather
G2 – Furskins
P2 – Dressed furskins
G3 – Luggage
P3 – Leather suitcase, Model A
P4 – Leather suitcase, Model B
1512
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
31
Products, product groups, ISIC classes
ISIC Class
Product Group
Product
1511
G1 – Leather
P1 – Chamois leather
G2 – Furskins
P2 – Dressed furskins
G3 – Luggage
P3 – Leather suitcase, Model A
P4 – Leather suitcase, Model B
1512
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
33
1. Preprocessing
a. Variables
b. Weights
34
1. Preprocessing
Variables
Obs Prod Prd Grp ISIC
1
2
3
P3
P4
P5
G3
G3
G3
Unit Quantity of output
T0
1520 Num 32
1520 Num 36
1520 Num 103
T1
24
36
102
T2
29
35
113
35
1. Preprocessing
Weights
Product
Prod Group
P3
P4
G3
P5
Absolute weight
Relative weight
86
0.37
115
0.49
32
0.14
Prod Group
ISIC class
Absolute weight
Relative weight
G3
1512
284
1.00
Obtained separately for the whole product group from other sources (e.g.
structural business survey, economic census)
36
2. Volume relatives at product level
p
R j ,i 
Volume relative of
product j in period Ti
p
VOL j ,i
p
VOL j , 0
V
V
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
37
2. Volume relatives at product level
p
VOL j , 0
[1]
V
Product
P3
P4
P5
32
36
103
p
VOL j ,1
[2]
V
24
36
102
p
R j ,1
[3]=[2]/[1]
0.75
1.00
0.99
p
p
j ,2
VOL j , 2
[4]
[5]=[4]/[1]
V
R
29
35
113
0.91
0.97
1.10
38
3. Volume indices at product group
level
pg
VOL k ,t
I
Value index of product
group k in time t
  w j , 0  R j ,t
p
p
jK
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
39
3. Volume indices at product group
level
T1
Prod Prod
/Prd weight
Grp
[1]
T2
Prod
volume
relative
Weighted
prod vol
relative
Prod group
volume
index
Prod
volume
relative
Weighted
prod vol
relative
Prod group
volume
index
[2]
[3]=[1]*[2]
[4]=sum([3])
[5]
[6]=[1]*[5]
[7]=sum([6])
0.91
0.97
1.10
0.33
0.48
0.15
P3 .37 0.75
P4 .49 1.00
P5 .14 0.99
G3
0.28
0.49
0.14
0.91
0.97
40
3. Volume indices at product group
level
Prd Grp
ISIC
Product group volume index
pg
VOL
G1
G2
G3
G4
G5
G6
1511
1511
1512
1520
1520
1520
I j ,0
100.0
100.0
100.0
100.0
100.0
100.0
pg
VOL
I j ,1
122.1
113.2
90.6
108.2
110.0
116.4
pg
VOL
I j,2
131.7
120.8
96.5
103.6
113.8
115.6
41
4. Volume indices at industry (4-digit
ISIC level)
T1
Prd
Grp/
ISIC
T2
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
0.61
1.04
0.58
G5
0.02
1.10
0.03
1.14
0.03
G6
0.41
1.16
0.48
1.16
0.48
1520
1.12
1.09
42
4. Volume indices at industry (4-digit
ISIC level)
ISIC
ISIC class volume index
c
VOL j , 0
c
VOL
100.0
100.0
100.0
119.8
90.6
111.6
I
1511
1512
1520
I j ,1
c
VOL j , 2
I
128.9
96.5
108.8
43
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
44
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
Recommendations
Deflation 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
46
Thank you.
Questions?