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

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

1. Agree on the purpose(s) of the index

2. Select an ideal or target index

3. Select an estimate formula for the calculation of the regular CPI

The purpose(s) of the index

1. Measurement of pure price changes, or inflation

2. Measurement of Cost of Living

The ideal index

1. Provides an ideal to be targeted

2. Necessary to quantify bias

Two main types: Basket index Cost of Living

index

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1. Ideal cost of living indices:Fisher, Walsh, Törnqvist

2. Ideal basket indices:Walsh, 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.

The Estimate index

The typical situation

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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

CPIs are calculated in two stages:

1. Elementary aggregate indicescalculated on basis of a sample of prices for individual products (and perhaps individual price weights)

2. Higher-level indicescalculated as weighted averages of elementary aggregate indices using the expenditure shares as weights

Typical aggregation structure of CPI

CPI

Higher-level indices

Elementary Aggregate Indices

Individual Prices

Expenditure weights

What are the options for the regular CPI calculation?

1. Calculate the CPI as the weighted aritmethic mean of elementary aggregate indices, using expenditure shares as weights

2. Price-update the weights – calculate a Lowe index

3. Do not price-update the weights – calculate a Young index

Theory Practical calculation

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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.

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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.

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, σ, at elementary aggregate level

• If σ is closer to 1 than 0, Young is the better estimate; if σ is closer to 0 than 1, Lowe is the better estimate.

• Elasticities are difficult to estimate.

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Comparing the Lowe and the Young indices

=> If there are long-term trends in the prices, the Lowe index will exceed the Young index.

Examples from the HICP

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

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

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 > 1: IY > IW

• price elasticity of demand < 1: IY < IW

• price elasticity of demand = 1: IY = IW

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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.

• 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.