Price-updating of weights in the CPI

1
Price-updating of weights in the CPI

• Why do we price-update expenditure weights?
• - Conceptual issues
• - Practical consequences
• What does the CPI Manual says?
• Some conclusions

2
The decision of how to calculate the
regular,ongoing monthly CPI

• Agree on the purpose(s) of the index 
• Select an ideal or target index
• Select an estimate formula for the calculation of
  the regular CPI
•  

3
The purpose(s) of the index

1. Measurement of pure price changes, or inflation 
2. Measurement of Cost of Living 

4
The ideal index

• Provides an ideal to be targeted
• Necessary to quantify bias 
• Two main types
• Basket index Cost of Living index

5

• Ideal cost of living indicesFisher, Walsh,
  Törnqvist
• Ideal basket indicesWalsh, Marshall-Edgeworth 
• Ideal indices requires weighting information
  from both the reference and the current period of
  time.
• The ongoing monthly CPI cannot be calculated as
  an ideal index.

6

• The Estimate index
• The typical situation
• b 0
  t
  T
• The problem is how to calculate the CPI when
  available weights refer to a period, usually a
  year or more, prior to the price reference
  period, and are only available at some level of
  aggregation?

Weight reference period
Price reference period
Current period
End of index link
7

• CPIs are calculated in two stages
• 1. Elementary aggregate indices
• calculated on basis of a sample of prices for
  individual products (and perhaps individual price
  weights)
• 2. Higher-level indices
• calculated as weighted averages of elementary
  aggregate indices using the expenditure shares as
  weights

8

• Typical aggregation structure of CPI

9

• What are the options for the regular CPI
  calculation?
• Calculate the CPI as the weighted aritmethic mean
  of elementary aggregate indices, using
  expenditure shares as weights
• Price-update the weights calculate a Lowe index
• Do not price-update the weights calculate a
  Young index

10
Theory Practical calculation


11

• The Lowe index
• Measures the cost of the period b basket in
  period t in relation to the cost of the same
  basket in period 0.
• Lowe gives the same rate of change as a Laspeyres
  with b as weight and price reference.
• Quantities are kept constant from b onwards.
• It will be a good estimate of an ideal basket
  index if quantities are constant, i.e. no
  substitution.

12

• The Young index
• Measures the development in consumption
  expenditure if expenditure shares are kept
  constant as from period b.
• It does not measure the changing cost of any
  actual basket.
• The unadjusted weights are estimates of the
  weights in the index link period.
• It will be a good estimate of an ideal basket
  index if expenditure shares are constant.

13

• Comparing the Lowe and the Young indices
• Lowe index Young index
• Wheter wb or wb(0) are the better estimate of
  the weights in the link period depend on the
  price elasticity of demand, s, at elementary
  aggregate level
• If s is closer to 1 than 0, Young is the better
  estimate if s is closer to 0 than 1, Lowe is the
  better estimate.
• Elasticities are difficult to estimate.

14

• Comparing the Lowe and the Young indices
• gt If there are long-term trends in the prices,
  the Lowe index will exceed the Young index.
• Examples from the HICP

1996 2005 Ann.
HICP all-items 100 117,7 1,8
Inform. processing equip. 100 19,7 -16,2
Goods 100 112,8 1,3
Services 100 125,6 2,5
15

• Comparing the Lowe and the Young indices
• Average annual rate of change 2003-04 with
• unadjusted and price-updated weights, Denmark

W99 W99(Dec02)
CPI 1,2 1,4
HICP 0,9 1,1
16

• Bias
• Calculate bias by subtracting the ideal and the
  estimate
• Example The Young and the Walsh indices
• If there are trends in prices, and
• price elasticity of demand gt 1 IY gt IW
• price elasticity of demand lt 1 IY lt IW
• price elasticity of demand 1 IY IW

17

• Conclusions
• Whether to price-update the expenditure weights
  or not is important for the interpretation of the
  CPI and for the measured rate of price changes.
• The longer the price-updating period, the larger
  the potential effect on the weights and the CPI.
• The issue can be described and analyzed in terms
  of the Lowe and Young indices, as in the CPI
  Manual.
• The ideal index does not give any clear answer on
  whether to price-update the weights or not.
• The Lowe index is conceptually clear and a good
  estimate of an ideal index if quantities are
  constant.
• The Young index is a good estimate of an ideal
  index if expenditure shares are constant.

18

• The Lowe index will exceed the Young index if
  there are long-term trends in relative prices.
• A Lowe index is most likely to exceed a Young
  index.
• The Lowe index is most likely to exceed an ideal
  index it is less clear with the Young index.
• To reduce potential bias weights should be
  updated regularly and be as representative as
  possible for the index link period.
• Different practices in different countries
  affects international comparability.
• Need for more research on theoretical and
  conceptual issues as well as the empirical
  implications.