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Workshop on Price Index Compilation Issues February 23-27, 2015

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Presentation on theme: "Workshop on Price Index Compilation Issues February 23-27, 2015"— Presentation transcript:

1 Workshop on Price Index Compilation Issues February 23-27, 2015
Compilation of Upper-Level Indexes Gefinor Rotana Hotel, Beirut, Lebanon

2 Calculation of higher level indices
The decision on how to calculate the higher level indices Purpose(s) Ideal/target index Actual index

3 Calculation of higher level indices
The purpose(s) of the index; inflation measurement, indexation or escalation The ideal/Target index – the best estimate of what the index ideally should measure: Economic indices: Fisher, Walsh or Törnqvist Basket indices; like Laspeyres or Lowe The actual index – the formula to use for the ongoing calculation of the PPI, with constraints on data, time and resources

4 The index number problem
Problem of decomposing a change in values into a change in quantities and prices. Need to define the value aggregate. Decompose

5 Alternative formulae Mashall-Edgeworth Laspeyres Lowe Paasche Walsh
Young Törnqvist Laspeyres Paasche Fisher

6 How do we know which is best? Some approaches:
Fixed basket Divisia Axiomatic Stochastic Economic

7 The fixed basket approach and the usual suspects
Laspeyres Paasche

8 But… Laspeyres and Paasche are equally plausible and can give different answers; Need a single ‘best’ measure – a symmetric (basket) average of the two; But which average: arithmetic mean (Drobisch) or geometric mean (Fisher)? Tests: Time reversal test – an index number formula should work both ways. Laspeyres and Paasche do not, neither does Drobisch, but Fisher’s is the only homogenous symmetric mean of Laspeyres and Paasche to satisfy the time reversal test.

9 Furthermore….. The product test – the product of a price and quantity index should be a value index:

10 Symmetric averages: The Three Target Indexes if Weights were Available
Fisher Walsh index Tornqvist

11 Annual weights from previous years
In practice we do not have current period weights available. Also, it takes time to compile weights so weight reference period (base year) differs from price reference period (month). We end up with a formula that resembles a Laspeyres index but it is not exactly Laspeyres.

12 Calculation of higher level indices
What is the problem? The weights refer to an earlier period than the price reference period b t Weight ref Price ref current period A true Laspeyres index can not be calculated on monthly basis! There are two options: Price-update the weights – calculate a Lowe index Do not price-update the weights – calculate a Young index

13 The Lowe Index The quantity weights are from a previous period in the past and the price base is a more current month

14 The Young index The Lowe index is based on representative quantities, Young is based on representative revenue shares: where

15 Calculation of higher level indices
Theory Practical calculation

16 Calculation of higher level indices
Lowe is a fixed basket index – and easy to interpret Young is a fixed weight index – and perhaps not so easy to interpret The focus in Lowe and Young are different A better alternative could be the Geometric Young In practice, the difference is whether the weights are price-updated from b to 0, or not Are Wib or Wib(0) the better estimate of the average revenue shares from 0 to t?

17 Calculation of higher level indices
An example …. Assume Walsh fixed basket index is the target index Whether a Lowe or a Young index is the best estimate depends on whether Wib or Wib(0) is the best estimate of WiW

18 Calculation of higher level indices Törnqvist as the target index

19 Calculation of higher level indices
Calculation of a chain linked index Update the weights and chain link at lest every 5 years; more frequent if there are rapid changes in production patterns Introduction of new elementary aggregates and new higher level indices Partial re-weighting

20 Calculation of higher level indices
Alternatives to fixed weight indices Annual chaining Long-term and short-term links Lloyd-Moulton formula using elasticity of substitution Calculate retrospective superlative indices as weights become available

21 Thank You


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