  The Fisher and GEKS are celebrated as ideal bilateral and multilateral
indexes due to their superior axiomatic and econ-theoretic properties. The
Fisher index is the main index used for constructing CPI by statistical
agencies and the GEKS is the index used for compiling PPPs in World Bank's
International Comparison Program (ICP). Despite such a high status and the
importance attached to these indexes, the stochastic approach to these indexes
is not well-developed and no measures of reliability exist for these important
economic statistics. The main objective of this paper is to fill this gap. We
show how appropriate reliability measures for the Fisher and GEKS indexes, and
other ideal price index numbers can be derived and how they should be
interpreted and used in practice. In an application to 2017 ICP data on a
sample of 173 countries, we estimate the Fisher and GEKS indexes along with
their reliability measures, make comparisons with several other notable indexes
and discuss the implications.
