Issues in Estimating New Keynesian Phillips Curves in the Presence of Unknown Structural Change

Abstract

Many articles which have estimated models with forward looking expectations have reported that the magnitude of the coefficients of the expectations term is very large when compared with the effects coming from past dynamics. This has sometimes been regarded as implausible and led to the feeling that the expectations coefficient is biased upwards. A relatively general argument that has been advanced is that the bias could be due to structural changes in the means of the variables entering the structural equation. An alternative explanation is that the bias comes from weak instruments. In this article, we investigate the issue of upward bias in the estimated coefficients of the expectations variable based on a model where we can see what causes the breaks and how to control for them. We conclude that weak instruments are the most likely cause of any bias and note that structural change can affect the quality of instruments. We also look at some empirical work in Castle et al. (2014) on the new Kaynesian Phillips curve (NYPC) in the Euro Area and U.S. assessing whether the smaller coefficient on expectations that Castle et al. (2014) highlight is due to structural change. Our conclusion is that it is not. Instead it comes from their addition of variables to the NKPC. After allowing for the fact that there are weak instruments in the estimated re-specified model, it would seem that the forward coefficient estimate is actually quite high rather than low.

Keywords:

• Expectations
• IV estimation
• Phillips curves
• Regime change
• Structural change
• Weak instruments

JEL Classification:

• C13
• C32
• C63
• E52

ACKNOWLEDGEMENTS

We thank Sophocles Mavroeidis and two referees for comments on an earlier draft. Much of the work was done when the author was in the Research Department of the Reserve Bank of Australia.

Notes

¹The values to which π_t, x_t, and r_t would converge in the absence of shocks.

²Of course changes because changes.

³Of course, we need the eigenvalues of S to be less than unity.

⁴In fact, the bias can exist for very large samples, even though it disappears asymptotically.

⁵These are generally averages of the F tests for weak instruments across all replications, although when T = 1, 000 they would be close to the point estimate using just the 1,000 observations.

⁶We are grateful to Ragner Nymoen for providing the data for both the Euro Area and the U.S. and corresponding with us over its use.

⁷This is sensitive to the instruments used. They decided not to use lagged wage growth as instruments but, if one does, the coefficient becomes 0.27.

⁸We would like to thank Sophocles Mavroides for making their MATLAB program available to us to perform this computation.

⁹Magnusson and Mavroeidis (2010) look at an NKPC without Δp_t−3, Δw_t−3, and gap_t−1 over a (longer) sample period of 1984–2008. They perform inference that is robust to weak instruments and find that γ does seem to be around 0.6-0.7.