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Legal links
Linked Series. Legal relationship coefficients

The implementation of any consumer price indices system means a rupture in the continuity of the series, maximal when apart from modifying the composition of the representative articles and their corresponding weightings a change in the methodology used to elaborate the indices occurs as occurs in the Consumer Price Indices System, base 2001.

From a theoretical point of view this rupture does not have a solution, however it is necessary to have available continued series at least on certain levels of breakdown, which facilitates calculating variation rates between different periods, to be applied to contractual questions such as labour agreements or the rental of housing. Moreover, making continued series available offers users the possibility of carrying out studies and predictions on the evolution of prices.

The National Institute of Statistics will calculate a link, known as a legal link, to maintain this continuity as much as possible. This link conserves the previous and subsequent variation rates at the moment of implementation of the new system, in this case January 2002.

This procedure is based on the calculation of a link coefficient that transforms the indices with base 1992 into indices with base 2001 and receives the name of legal link because the National Institute of Statistics traditionally applies it in its official certificates.

The link coefficient is obtained as a quotient among the indices in the month of December 2001 in base 1992 and base 2001:



Formula the December 2001 index in base 1992
Formula the December 2001 index in base 2001

With this procedure, at the moment of transition from one system to another (December 2001 to January 2002) the variation calculated with the new system is adopted.

The linked series are calculated by multiplying each one of the indices in base 1992 by these coefficients.

The link coefficients will be obtained independently for each one of the series of indices that have continuity in the new base which implies that any grouped index of a linked series is not the result of the weighted average of elemental indices that make it up.

Finally, it is necessary to point out that while the new system has as a base the average of the indices in base 2001 of this year the same as 100, the indices that are published for this year are indices calculated in base 1992 and linked subsequently by means of the corresponding legal link coefficients. Therefore the published series of indices in the year 2001 in base 2001 does not have to have an average of 100.

Due to the inclusion of the reduced prices in the CPI base 2001, the legal link coefficient does not solve the problem of the series rupture. Therefore, with the objective of facilitating the calculation of variation rates which include indices of two different bases a system has been implemented which facilitates it (see document relative to the effect of the reductions).