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Chaining? User needs and
good practice!
1.
2.
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5.
Why?
Definitions
Introduction of new weights
New consumption patterns
Features
Why chaining?
t+2
t
t+1
Input
• Elementary price indices
• Weights
– remain fixed for a sequence of at least 12 months
– Change yearly?
Definitions
Weight reference period = 0, t or b
Price reference period = 0
Index reference period (year = 100)
I La
p q

p q
t 0
i i
0 0
i i
La=Laspeyres
I Pa
pq


p q
Pa=Paasche
I Lo
p q

p q
Lo=Lowe
 pit 
  s  0 
 pi 
Yo=Young
I Yo
t t
i i
0 t
i i
t b
i i
0 b
i i
b
i
Definitions
• Weight reference period
– Usually - a year (ex 2008)
• Price reference period
– Usually – a month (ex Dec 2010)
• Index reference period
– Usually – a year (ex 2005)
Do not use ”base period”
Same weights, new products
I
0:t
 w I , w 1
b 0:t
i i
b
i
If Jevons or Dutot – then;
I 0:t   wib I i0:t 1I it 1:t ,  wib  1
New weights
• Changes in relative quantities and relative prices implies
new expenditure weights. Price-updating not good enough.
– Need to reflect current expenditure pattern and consumer behaviour
• When new weights are introduced, the price reference
period for the new index can be the last period of the old
index, the old and the new indices being linked together at
this point. The old and the new indices make a chain index.
New weights – complex operation
• Provides the opportunity to introduce
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–
–
–
–
–
–
new items
new samples
new data sources
new compilation practices
new elementary aggregates
new higher-level indices
new classifications
Consumption patterns change over time
• Consumers will tend to substitute away from products of
which the prices have increased relatively
• New products are continually being introduced on the
market while others drop out
• Longer term
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Rising income
Standard of living
Demographic changes in the structure of the population
Changes in technology
Changes in preferences
Updating; Sensible and necessary practice
•
At least every five years, and more often if there is
evidence of rapid changes in consumption patterns – but
not straightforward
– It can be costly!
Important features of a chain index
• The chain index formula allows weights to be updated
• Facilitates the introduction of new items and sub-indices
and the removal of obsolete ones
• Chaining is intended to ensure that the individual indices on
all levels show the correct development through time
• Chaining leads to non-additivity
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Questions or comments?