RDP 2013-11: Issues in Estimating New-Keynesian Phillips Curves in the Presence of Unknown Structural Change 5. The Euro Area New-Keynesian Phillips Curve and Breaks

Castle et al (2010) use the euro area NKPC to illustrate the effects of breaks, arguing that the large coefficient on forward expectations is due to breaks. Our argument is that this could be true but one should always check whether it is a consequence of weak instruments. Consequently, we re-do their analysis here to look at that question.

First, we estimate the hybrid NKPC over the period 1972:Q2 to 1998:Q1:^[3]

where x_t is the labour share (s_t in their equations). Their paper states that the instruments used were , x_t−1, x_t−2, Δw_t−1, Δw_t−2, gap_t−1, gap_t−2 where Δw_t is wage inflation and gap_t−1 is the euro area output gap. The estimated hybrid curve is:

which differs from the estimates they present. To reconcile them we re-run the regression with Δw_t−1, Δw_t−2 deleted from the instrument set and then we get exactly what they report. It appears that all the results they report delete these instruments. As there is no reason to delete the lagged wage inflation variables as instruments we add them back in as we proceed.

The inclusion of dummy variables to account for breaks does not seem to have much impact upon the forward expectation coefficient.

In order to get closer to their specification we add gap_t−1 into the regression:

One interpretation of this is that gap_t−1 is a good instrument that cannot be used when the variable appears in the regression. Indeed if we regress π_t+1 against all the instruments, gap_t−1 has a t ratio of 2.6.

The results above do show a significant decline in the forward coefficient estimate when gap_t−1 is added to the regression and are compatible with what Castle, Doornik, Hendry and Nymoen (2010) report, except that they get a negative value for the forward coefficient. To get that result we had to drop Δw_t−1, Δw_t−2, from the instrument set. Doing so gave us = 0.48 and = −0.21, so a negative forward estimate seems to come from dropping some instruments, although they report = 0.51 and = −0.30.

Finally, we put the lagged wage inflation variables back into the instrument set and run the regression with gap_t−1 included, but now impose the adding up constraint α + δ = 1. Our argument is that this is often a way of dealing with weak instruments.

So the forward coefficient is largely back to what it was in Equation (5) and supports the idea that we are dealing with weak instruments. The t ratios in the instrument regression for Δw_t−1 and Δw_t−2 are 2.6 and 1.5 respectively. Because gap_t−1 is insignificant in this regression, deleting it would take us back to Equation (6), with much the same conclusion about the forward coefficient. The specification in the equation above is not particularly appealing as the marginal cost variable has a negative coefficient, although it is clearly ill determined. However, our objective is not to produce a well-defined Phillips curve but to explore the influences on the forward expectations estimated coefficient. The sequence of regressions above suggests that the changes in the forward coefficient come more from changing the instrument list than from the break dummies.

At the end of their paper Castle et al (2010) look at the NKPC estimated over a period that they think has no breaks – 1983:Q2–1998:Q1. The idea is to see if one gets a high estimate for the forward coefficient then. They report that the coefficient on E_tπ_t+1 is now 0.08 and so conclude that the high value found in the initial hybrid curve regressions was due to breaks. However to get = 0.08 one needs to delete Δw_t−1 and Δw_t−2 from the instrument set. If one does use them one gets:

which is very close to the full period regression which includes the dummies in Equation (6). Deleting gap_t−1 from this equation results in:

This is virtually the same as the long sample estimates given in Equation (5). Thus our assessment would be that the high forward coefficient does not come from breaks in the inflation process. It may reflect misspecification of the curve, which is what breaks are about; gap_t−1, which looked like it could be a possible augmenting variable, was not sustained in the shorter sample.

Footnote

We are grateful to Ragner Nymoen for providing the data and corresponding with us over its use. [3]