Misspecification Testing: Non-Invariance of Expectations Models of Inflation

Abstract

Many economic models (such as the new-Keynesian Phillips curve, NKPC) include expected future values, often estimated after replacing the expected value by the actual future outcome, using Instrumental Variables (IV) or Generalized Method of Moments (GMM). Although crises, breaks, and regime shifts are relatively common, the underlying theory does not allow for their occurrence. We show the consequences for such models of breaks in data processes, and propose an impulse-indicator saturation test of such specifications, applied to USA and Euro-area NKPCs.

Keywords:

• Expectations
• Impulse-indicator saturation
• New-Keynesian Phillips curve
• Structural breaks
• Testing invariance

JEL Classification:

• C5
• E3

ACKNOWLEDGMENTS

We are grateful to Guillaume Chevillon, Neil R. Ericsson, Katarina Juselius, S\o ren Johansen, Grayham E. Mizon, Bent Nielsen, Adrian Pagan, and two anonymous referees for helpful comments and suggestions. This research was supported in part by grants from the Open Society Foundations and the Oxford Martin School.

Notes

Detailed calculations are available on request.

Bårdsen et al. (2004) use GMM with results similar to the IV estimates here. Changes in the GMM estimation method affect the point estimates as much as the change to IV does. For example, there is a sign change in the estimated coefficient of the wage-share coefficient as a result of a change in the pre-whitening method.

Following Bårdsen et al. (2004), we omit the two lags of wage inflation (Δw) since their inclusion as instruments had little influence on the estimation of (30), but the estimated coefficient of s _t in (31) went even closer to zero, making the forcing variable irrelevant for inflation. Results also using Δw _t−1 and Δw _t−2 as instruments are available from the authors.

The mean of s _t is not exactly zero over the sample period, despite being described as “a deviation from steady-state” in the text.