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Recalculations of the Danish CPI 1996-2006

Recalculations of the Danish CPI 1996-2006. Ottawa Group Meeting October 2007 Presentation by Carsten Boldsen Hansen. Overview. The data set 1996 – 2006 Calculation of ‘ideal’ indices Comparison of the regular CPI with ideal index Price-updating of weights Alternative calculations

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Recalculations of the Danish CPI 1996-2006

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  1. Recalculations of the Danish CPI 1996-2006 Ottawa Group Meeting October 2007 Presentation by Carsten Boldsen Hansen

  2. Overview • The data set 1996 – 2006 • Calculation of ‘ideal’ indices • Comparison of the regular CPI with ideal index • Price-updating of weights • Alternative calculations • Some conclusions and questions

  3. The data set 1996 – 2006 • 442 monthly elementary aggregate indices from January 1996 to December 2006 • Weights from 1994, 1996, 1999 and 2003 • Covers 98-99 % of the regular CPI • The recalculated CPI can be considered identical to the published CPI • Makes it possible to draw conclusions about the effects in practice of different calculation methods

  4. Calculation of ideal indices Fisher, Walsh, Törnqvist and Marshall-Edgeworth indices are estimated for 2 periods: • 1996 – 1999 with EA indices 1996=100 and weights from 1996 and 1999 • 1999 – 2003 with EA indices 1999=100 and weights from 1999 and 2003 The indices are not truly superlative because of different weight and price reference periods (and M-E anyway not)

  5. Calculation of ideal indices Fisher, Walsh, Törnqvist and Marshall-Edgeworth indices

  6. Calculation of ideal indices Fisher, Walsh, Törnqvist and Marshall-Edgeworth indices Conclusion: The ideal indices gives similar results under “normal” conditions

  7. CPI compared with an ideal index The Danish CPI = the expenditure share weighted arithmetic mean of the elementary price indices: • New weights are introduced every 3 years • With 2-3 years lag from the price reference period (0) to the weight reference period (b) • The weights are not price-updated from b to 0 • The index is chained when new weights are introduced

  8. CPI compared with an ideal index

  9. CPI compared with an ideal index Annual rate of change of CPI and Walsh (in %) Conclusion: The CPI exceeds Walsh by 0,05 % point on the annual rate of change, on average

  10. Price-updating of weights Most statistical offices calculate the CPI as: • Usually, the weights will refer to a period (b) prior to the price reference period (0) • It is up to the statistical office to decide whether to price-update the weights from b to 0, or not

  11. Price-updating of weights

  12. Price-updating of weights Annual rate of change, in % • Price-updating weights increases the annual rate of change by 0.1 % point, on average • The CPI with original weights is closer to Walsh being less upward biased. Annual % change 1996-2003:Walsh=2,28 CPI=2,33 PUW=2,39 • Excluding OOH gives very similar results

  13. Price-updating of weights Comparing Lowe and Young indices • Lowe and Young aims to measure different things: Lowe – CPI with price-updated weights • conceptually clear - a basket index • measures the changing cost of a fixed basket of a (past) reference period (b) in the index period 0 to t Young – CPI with original weights • the period b weights are estimates of the average weights in the index period • aims to measure average price change in the index period • consider Young as an estimate of an ideal basket index

  14. Price-updating of weights • Lowe > Young if there are long-term trends in prices - irrespective of whether substitution takes place or not • If the elasticity of substitution at EA level is closer to one, Young is the better estimate of an ideal index, if it’s closer to zero, Lowe is the better estimate • Lowe has better axiomatic properties

  15. Price-updating of weights Young doesn’t meet the timereversal test!

  16. Alternative calculations • Geometric Young index- ‘assumes’ elasticity of substitution = 1 throughout, from b to t • Geometric mean of Young and rebased Young index- meets the time reversal test - Turns out to be almost identical

  17. Alternative calculations

  18. Alternative calculations Average annual rate of change (%) Conclusion: Geometric Young and Yo** underestimate an ideal index.

  19. Alternative calculations Estimating the elasticity, σ, by the LM index • Pick the σ’s that give the better estimate of Walsh index • LM reacts only slowly to changes in σ • 1996-1999: σ=0,9 gives the better estimate • 1999-2003: σ varies from 0,2 – 0,6 • σ does not appear very stable over time, and there is not much hint about its size

  20. Some conclusions and questions • Whether weights are price-updated is likely to influence the CPI • Lowe can be expected to exceed Young • Young can be expected to provide the better, less upward biased estimate of an ideal index • Pros & cons on both Lowe and Young, but targets differ • Important to define the target of the CPI, and take the purpose(s) of the CPI into consideration … • How important are “micro” axiomatic properties at EA level? • According to the 2007 CPI Manual survey, 2/3 of NSOs price-update, 1/3 does not. International comparability? • Should the CPI Manual be more prescriptive? • More theoretical & empirical research needed

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