Estimating probability density functions for exact index numbers

The Konus (1924) approach to constructing price index numbers involves evaluating the expenditure function of a representative consumer at different vectors of prices. Muellbauer (1976) has shown that if consumer preferences exhibit price-independent generalised linearity (PIGL) then this representative consumer exists. This paper computes Konus price index numbers derived from expenditure functions belonging to the logarithmic PIGL class. The parameters of the expenditure functions are estimated in a Bayesian framework. Results are summarised in the form of estimated posterior probability density functions for expenditure shares and associated index numbers. Uncertainty concerning the functional form of the representative expenditure function is resolved through Bayesian model averaging. Multilateral index numbers are computed based on the EKS method applied to Fisher binary indices and to the GAIA system proposed by Neary (2004).