An Application of Index Numbers Theory to Interest Rates

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, first discusses the optimal calculation of a binary index using axiomatic index number theory; on that basis, chain and direct indices are established; finally, 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 - January 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