A Robust Multivariate Weighting Technique for Computing a Measure for Inflation

Abstract

The study investigates the viability of the proposed multivariate weighting methodology for consumer price indexing when the assumption of multivariate normality fails. It also determines which of the two approaches (classical or robust) better serves as an alternative to the expenditure-based weighting method. The data generation method was purely simulation and bootstrapping. Communalities were generated by decomposing the correlation matrix obtained from the robust counterpart of the multivariate scatter estimate. Communality relativities were found and used as weights in known Consumer Price Index (CPI) formulas to measure inflation. Results obtained for the robust weighting system are similar to those of the classical approach in all situations considered in this study. It emerged that the robust technique produced smaller standard errors for higher data variables with larger sample sizes than its classical technique counterpart. It was also found that robust weights in CPI formulas resulted in smaller standard errors than the expenditure-based weights in CPI as well as accounting for 71.4% indexes within the ideal range. The robust multivariate weighting system offers an excellent alternative to generate weights (in real-time) that account for variance in price items in the composition of the consumer price index. Thus, the robust method proved more efficient for higher data variables with high KMO values. A previous study focused on adopting a classical approach that assumes multivariate normality for price data. This present research filled the gap by proposing a system not based on strong distributional assumptions.