On the Use of the First Principal Component as a Core Inflation Indicator

This paper investigates if the (OLS-scaled) first principal component (PC1), extracted from standardized yearly rates of change of basic items of the CPI, represents a reasonable option for a core inflation indicator. The evaluation is carried out by (i) confronting alternative linear transformations of the original variables; (ii) analyzing the impact of stacking lagged variables to the original database; and (iii) exploring the contents of the remaining principal components. An orthogonal factor model framework will also be introduced so as to fully reproduce any variable that can be expressed as a linear combination of the original input variables, such as, in this case, the overall inflation rate. The model incorporates the following properties: (i) the results are not conditional on the eigenvectors length; (ii) the variance of the CPI accounted for by each component is unique, and (iii) the outcome is equivalent to an OLS regression between the CPI and the PC1. Along with empirical evidence for the Portuguese case, it will be claimed that the above-mentioned (OLS-scaled) PC1 does capture the general movement of the overall inflation rate, however, no OLS regression would have to be implemented if the core indicator is fully aligned with the orthogonal factor model.