Standardized description of index numbers for
application in generic index computation software
Photis Stavropoulos1, Georges Pongas2, Spyros Liapis1, George Petrakos1, Tonia Ieromnimon1
Agilis S.A. Statistics and Informatics, e-mail: Photis.Stavropoulos@agilis-sa.gr, Spyros.Liapis@agilis-sa.gr, George.Petrakos@agilis-sa.gr,
EUROSTAT, e-mail: Georges.Pongas@ec.europa.eu
The aim of this paper is to present a scheme for the description of index numbers in a standardized manner and to show how this scheme was realized in a generic software module for the computation of index numbers. Index number theory provides statisticians with a palette of formulae and computational operations (chaining, aggregation, etc.) to build index calculation since there is no unique way of measuring an index number. The proposed scheme has been developed in such a way so as to allow the user to define the characteristics/parameters of the index: index type, base period, reference period of the weights, periodicity of input data and of the index, dissemination dimensions, mode of aggregation, etc. These characteristics may be viewed as ‘process metadata’, which can guide the computation of an index. The tool allows the different mix of index types and computational operations. It covers computational tasks common in several domains where indices are used. Moreover it can be expanded to accommodate new operations, with little extra programming, that apply to particular domains and are needed for the computational of additional indices. Further work is envisaged in making the tool even more generic to accommodate more computations and be applicable to different domains. Keywords: Index numbers, Process metadata, Building block
Index numbers are widely used in Official statistics to convey information about the relative size of a variable (price, quantity, etc.) between different points in time or between different geographical locations. Consumer price indices and purchasing power parities are examples of the former and latter type of use respectively. A large number of index number formulae are available to the Official statistician who wishes to select the most appropriate one for each application. The statistician can also choose whether or not to use a chained index. Moreover, the statistician needs to specify the periodicity of the index, which may differ from the periodicity of the raw data (e.g. monthly data may be used to produce monthly, quarterly or annual indices), the dissemination ‘dimensions’ to break the index down by (e.g. a consumer
price index may be disseminated broken down by items, regions, income classes, etc) and the particular classes of each dimension.
There are alternative ways to compute an index at different periodicities or different levels of dissemination breakdowns, in other words to aggregate the index. A quarterly index for example, may be a weighted average of the respective monthly indices or may be computed from quarterly aggregates of the monthly data that produce the monthly indices; similarly, the price index of a dissemination class may be a weighted average of the indices of the component sub-classes, may be a ratio of aggregated numerators and denominators of the component sub-indices or may be computed on aggregates of the input data that produced the sub-classes’ indices. Quite often each alternative produces a slightly different value for the aggregated index.
2. Index formulae and operations applied to index numbers
2.1 Index formulae
Several alternative kinds of mathematical formulae are in common use for the calculation of index numbers. Depending on the objective the index is calculated for, the statistician needs primarily to decide on the index type (Lowe, Laspeyres, Paasche, Fisher, etc.) and the series of weights. For instance, CPIs intend to measure either price inflation (price index) between two time...
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