ARCH and structural breaks in United States inflation

Abstract

United States Phillips curves are routinely estimated without accounting for the shifts in mean inflation. As a result, we may expect the standard estimates of Phillips curves to be biased and suffer from auto-regressive conditional heteroscedasticity (ARCH). We demonstrate this is indeed the case. We also demonstrate that once the shifts in mean inflation are accounted for, the ARCH is largely eliminated in the estimated model and the model defining expected rate of inflation in the New Keynesian model plays no significant role in the dynamics of inflation.

Keywords:

• Philips curve
• ARCH
• structural breaks
• inflation
• markup

JEL Classification:

• C22
• E31

Acknowledgements

I wish to thank Genaro Sucarrat who ‘counselled’ me on the estimation of ARCH models and Tom Doan for generously making available the Bai–Perron programmes on the Estima website.

Notes

¹ The term ‘nonstationary’ in this article encompasses all statistical processes other than stationary with a constant mean. It therefore includes stationary around a shifting mean. ‘Modern’ theories include the Friedman–Phelps expectations augmented, New Keynesian and hybrid theories of the Phillips curve.

² The appendix provides details of the data used in this article.

³ Details of how the breaks are estimated are provided in the section on ‘The data’ and Table 1.

⁴ For example, see Engle (1983, 1988), Cosimano and Jansen (1988), Baillie et al. (1996), Grier and Perry (2000) and Boero et al. (2008).

⁵ For a detailed exposition of the hybrid and NK theories, see Galí (2008).

⁶ This is a generalization of Perron (1989).

⁷ See Lumsdaine and Ng (1999).

⁸ This is one conceptual interpretation of using instrumental variables for .

⁹ This is equivalent to estimating Equation 1 with a two-stage-least-squares estimator.