Extending the stochastic approach to index numbers

Abstract

The variance of the inflation rate estimator in the stochastic approach of Clements and Izan will be biased in most applications due to stringent restrictions on the variance of the OLS error term. To overcome this weakness, the stochastic methodology is reformulated and extended by deriving a variance estimator which is robust to unknown forms of heteroscedasticity. Under this new approach the exact nature of the error variance is of no concern, and can remain unidentified. A major innovation of this work is the derivation of a scalar representation for the variance estimator which has considerable intuitive appeal since it uses consumer expenditure shares to weight the relative price movements used in the calculation of the inflation rate variances.