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

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

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

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

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

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

The fixed basket approach and the usual suspects Laspeyres Paasche

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.

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

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

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.

Calculation of higher level indices What is the problem? The weights refer to an earlier period than the price reference period b 0 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

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

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

Calculation of higher level indices Theory Practical calculation

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?

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

Calculation of higher level indices Törnqvist as the target index

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

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

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