A factorial decomposition of inflation in Peru: an alternative measure of core inflation

Abstract

A dynamic factorial decomposition model of inflation is estimated using Peruvian monthly data for January 1995–July 2008. This model allows the identification of changes in three relevant inflation components: idiosyncratic relative prices, aggregate relative prices and absolute prices. Furthermore, following Reis and Watson (2007), the model allows measuring pure inflation as the common factor in the inflation rate that has a proportionate effect to all prices and that is not correlated with relative-price changes at any period of time. This pure inflation estimate relates closely to standard measures of core inflation. The results are robust to different lag structures and various stochastic assumptions on the estimated factors.

Keywords:

• factorial decomposition
• pure inflation
• core inflation
• price changes

JEL Classification:

• C32
• C43
• E31

Acknowledgements

We thank useful comments from participants to the XXVI Meeting of Economists of the Central Reserve Bank of Peru in November 2008. We are grateful to Reis and Watson for useful e-mail communications and for providing us with their estimation codes. The views expressed herein are those of the authors and do not reflect necessarily those of their institutions.

Notes

This article is a shortened and revised version of the working paper of Humala and Rodríguez (2011).

¹ Another application of the approach of Reis and Watson (2007) is Brzoza-Brzezina and Kotlowski (2009) where Polish data are used.

² For an account of inflation dynamics in Peru, see Castillo et al. (2006).

³ Another approach to estimate Equations 1(1)–2(2) is to use a restricted principal components model; see Stock and Watson (2002), Bai (2003) and Bai and Ng (2006). Using this approach, the estimates are very similar but more volatile. The results are available upon request.

⁴ The results of Reis and Watson (2007) suggest 2, 1 and 11 factors according to the information criteria of Bai and Ng (2002). In the case of Brzoza-Brzezina and Kotlowski (2009), using Polish data, the information criteria suggested 12, 9 and 12 factors, respectively. Despite these results, they conclude that the true number of factors should be equal to 2 or 3.

⁵ Reis and Watson (2007) found that over 30% of the t-statistics are above the standard 5% critical values and over 20% above the 1% critical value. Despite these large values, they accepted the restriction.