Simulation Study of an Original Price Index Formula

Abstract

In this article, we present and discuss an original price index being a special case of a general formula for price indices. We show that the discussed formula satisfies most postulates coming from the axiomatic price index theory. We compare this index to other known and popular price indices in a simulation study.

Keywords:

• Białek index
• Fisher index
• Geary–Khamis index
• Laspeyres index
• Marhall–Edgeworth index
• Paasche index
• Price indices
• Walsh index

Mathematics Subject Classification:

• 91B82

Notes

The time moment s we consider as the basis, i.e., the reference situation, for the comparison.

The expression (14) has any sense if I_L (Q^s , Q^t , P^s , P^t ) < I_U (Q^s , Q^t , P^s , P^t ).

It is interesting that in both cases 1 and 2 we get a mean and maximum value of the Paache index greater than the same values of the Laspeyres formula (see Tables 2 and 3). The opposite relation between means of these indices is more frequent in practise. The correlation between prices and quantities seems to be possitive in our experiments.