Abstract
This paper uses index number theory to disentangle changes in aggregate retail interest rates due to changes in individual component rates (“interest rate effect”) from those caused by changes in the weights of each component (“weight effect”), on the basis of the “difference” index numbers recently revisited by Diewert (2005). The paper presents the Bennet index as the optimal way to calculate of a binary index using axiomatic index number theory; on that basis, chain and direct indices are established; then, the selected decomposition and indices are applied to monthly data on euro area interest rates on loans and deposits (MIR) for the period January 2003–October 2008. It is concluded that relevant weight effects at euro area level are limited to a few indicators and periods of MIR, and that that the indices on interest rates can be a suitable tool in the analysis of variations in aggregate interest rates.
JEL classification C43 – Index numbers and aggregation, E43 – Determination of interest rates, Term structure of interest rates
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Notes
- 1.
The Eurosystem is the monetary authority of the Eurozone. It is a system of central banks consisting of the European Central Bank and the national central banks of the member states of the European Union whose currency is the euro.
- 2.
For further information on the MIR categories, definitions and compilation refer to ECB (2001) and ECB (2002).
- 3.
It is noted that “weights” in the context of interest rates has a slightly different meaning than “weights” in the context of index theory. In the latter “weight” is usually calculated as the division of transactions in one product (prices by quantities) by total transactions; in MIR it is simply the percentage of the value (in euro) of loans/deposits over total loans/deposits, therefore comparable to quantities in usual index theory but not to the usual meaning of “weight” in index number theory.
- 4.
The term “binary” is used for the comparisons between two consecutive periods as in Stuvel (1989).
- 5.
The “extended” decomposition was initially proposed by Coene (2004) on the basis of previous work by Berthier (2001).
- 6.
A particularity of MIR has been taken into account in the calculations. Whenever no operation has taken place on new business or no outstanding amounts remains for a single category in a country, no figure is reported to the ECB for that country. If this absence of interest rate figure were treated as zero it would result in a spurious impact in the interest rate component. To avoid this, whenever no interest rate was reported for a specific category and month, the latest previously reported interest rate is used to calculate the interest rate effect, resulting in no impact on the interest rate component.
- 7.
Other ways of avoiding this type of statistical break, like for example the reporting of pre-break values, are beyond the scope of this paper.
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Acknowledgments
This contribution is based on an original idea of Steven Keuning. That idea was developed and discussed in an ECB Working Paper prepared by J Huerga and L Steklacova. I am very grateful to Olivier Coene from the National Bank of Belgium, who contributed with comments and actually suggested the “extended Bennet” formulation, proposed in this paper. I would also like to thank Julia Weber for her in-depth review and suggestions on previous work, Holger Neuhaus, Ruth Magono, Roswitha Hutter and Jean-Marc Israël for their help and support, and the members of the Working Group on Monetary and Financial Statistics (WG MFS) and the participants in the International Workshop on Price Indices organised by the University of Florence on 29–30 September 2008 for their comments on previous discussions. The views expressed in this note are those of the author and do not necessarily reflect those of the ECB or the Eurosystem.
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Huerga, J. (2010). An Application of Index Numbers Theory to Interest Rates. In: Biggeri, L., Ferrari, G. (eds) Price Indexes in Time and Space. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2140-6_13
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