Examining the ability of core inflation to capture the overall trend of total inflation

Abstract

This article examines whether core inflation is able to predict the overall trend of total inflation using real-time data in a parametric and nonparametric framework. Specifically, two sample periods and five in-sample forecast horizons in two measures of inflation, which are the Personal Consumption Expenditure (PCE) and the Consumer Price Index (CPI), are used in the exclusions-from-core inflation persistence model. This article finds that core inflation is only able to capture the overall trend of total inflation for the 12-quarter in-sample forecast horizon using the CPI in both the parametric and nonparametric models in the longer sample period. The nonparametric model outperforms the parametric model for both data samples and for all five in-sample forecast horizons.

Acknowledgements

I would like to thank the following people for their gracious help that took various forms that ranged from guidance to comments: my anonymous referees, Richard Ashley, Yong Bao, Marcelle Chauvet, Dean Croushore, Daniel Henderson, James Morley, Peter C.B. Phillips, Zeynep Senyuz, Mark Taylor, Mark Watson, and Emre Yoldas and last but not least, the participants of the 18th Annual Meeting of the Midwest Econometrics Group (2008) and the 78th Annual Meeting of the Southern Economics Association (2008).

Notes

¹ To make it easier to determine when a particular vintage of a real-time dataset as opposed to a given observation is being discussed, the notation of ‘V_” will appear before the vintage of the real-time dataset. For instance, V_1996:Q1 refers to the vintage of the real-time dataset released in the middle of the first quarter of 1996 with the observable data ranging from 1959:Q4 to 1995:Q4 for the first sample period.

² For other time-varying models as it relates to monetary policy, see Höppner et al. (2008) and Paez-Farrell (2009).

³ In practice, the Average Residual Squares Criterion (ARSC) is used to approximate the IRSC.

⁴ It should be noted that averaging and aggregation are not used as synonyms in this article. For instance, the average estimators refer to the mean estimators, and aggregation refers to the use of all the local conditional nonparametric estimators.

⁵ In much of the existing literature, such as Rich and Steindel (2005), the F-test is used.

⁶ Regarding the estimation of the Newey–West HAC variance–covariance matrix, the procedure written by Mika Vaihekoski (2004) is used and can be obtained from the following web address: http://www2.lut.fi/~vaihekos/mv_econ.html#e3.

⁷ In estimation, as the in-sample forecast horizon increases, the level of autocorrelation in the residuals also increases, which further necessitates the need for the Newey–West (1987) HAC.

⁸ The leave-one-out form of least squares cross-validation is not used for this article due to periods of instability when estimated (Marron, 1988; Härdle, 1994; Wand and Jones, 1995; Fan and Yao, 1998; Cai et al., 2000; Fujiwara and Koga, 2004).

⁹ Another potential weakness in nonparametric methodology is the Curse of Dimensionality, which is not an issue for this article since this is a univariate model (Cleveland and Devlin, 1988; Härdle and Linton, 1999).

¹⁰ For other papers that use the residual-based window, see Fan and Yao (1998), Cai and Chen (2006), Cai (2007), Chauvet and Tierney (2009), etc.

¹¹ Creel (2008) does not use the Newey–West (1987) HAC variance–covariance matrix due to unreliability in the general dynamic latent variable model.

¹² Sometimes in nonparametric estimation, the average nonparametric regression parameters are used in an OLS framework to obtain the error terms, but this is not advisable since these error terms are not created by minimizing the residual sum of squares, and therefore, are not useful for hypothesis testing purposes.

¹³ The interpolation method for V_1999:Q4 was provided by Dean Croushore as was the information regarding V_2000:Q1.

¹⁴ For a more complete description of real-time data, see Croushore and Stark (2001), Croushore (2007), and the Federal Reserve Bank of Philadelphia.

¹⁵ As is later shown in sections ‘Parametric and global nonparametric empirical results’ and ‘Local nonparametrical empirical results’, the inclusion of a long period of time with potential structural breaks dampens the effectiveness of the regression model for both the parametric and nonparametric models.

¹⁶ For more information regarding the collection of real-time CPI, see the website of Federal Reserve Bank of Philadelphia http://www.philadelphiafed.org/econ/forecast/real-time-data/data-files/CPI/.

¹⁷ Bruce Hansen's (2001) program for testing for structural changes is used and is available from the following web address: http://www.ssc.wisc.edu/~bhansen/progs/jep_01.html.

¹⁸ Due to an attempt at limiting space, all the results are not provided in this article but are available upon request.

¹⁹ Regarding the parametric model for the second sample period, the null of unbiasedness also fails to be rejected at the 5% significance level for the following sporadic vintages not specifically mentioned in Table 9 (Panel A): h ₁: V_1999:Q4 to V_2000:Q1 and V_2001:Q4 to V_2002:Q1, h ₄: V_1999:Q4, V_2001:Q3 to V_2001:Q4, and V_2002:Q4 to V_2003:Q2, h ₅: V_1996:Q1, V_1997:Q3, V_1999:Q4, V_2003:Q3.