Computational tests as a means of assessing the inaccuracies of index numbers

Abstract

In this paper we propose using computational tests for appraising the inaccuracies of index numbers (for example, price and wage indices). This is done by programming a hypothetical situation where the true average index value is known and the variation of prices and quantities and the relation between them can be chosen. The indices are then calculated using the formulae of Laspeyres, Paasche, Fisher, the Unit index and Normalized Unit index formulae. By comparing the average values of the above formulae with the true average index value, we are able to obtain a quantitative indication of the errors in these formulae under various situations. The Normalized Unit and Fisher index formulae were found to be consistently accurate for all our tests whereas the formulae of Laspeyres and Paasche were found to have very poor accuracy in the majority of our tests. The Unit index was also consistently accurate in all our tests but its use is appropriate in the single item case thus making this formula suitable for measuring wages. In our informal discussion of stability we indicated that the Normalized unit index and the Unit index have good stability characteristics whereas the indices Laspeyres, Paasche and Fisher have poor stability characteristics. In view of the above the Normalized Unit index is the best of the formulae we have discussed for measuring prices (many item case), and the Unit index is the best of the formulae we have discussed for measuring wages (single item case).