# RDP 2021-09: Is the Phillips Curve Still a Curve? Evidence from the Regions Appendix D: Persistence in Unemployment Fluctuations

As discussed in Section 7.2.3, Hazell et al's (2020) framework suggests that both the RBA's aggregate model and the baseline regional estimates in this paper may overstate the slope of the New Keynesian wage Phillips curve because they do not account for the persistence in unemployment fluctuations. To explore the importance of this point, we follow Hazell et al by estimating a regional panel regression that replaces the contemporaneous unemployment rate term in Equation (3) with the present discounted sum of realised unemployment rates over a five-year horizon into the future,

(D1) $Δ w it =α+κ ∑ j=0 5 β j u i,t+j + θ i + ω t + ε it$

where the discount factor $\beta$ is calibrated to be 0.99. We instrument the forward sum of the unemployment rate with the first lag of the unemployment rate $\left({u}_{i,t-1}\right).$ The forward sums in Equation (D1) mean that we lose five years of observations at the end of our sample, and the instrument means we lose one observation at the start of our sample. We estimate Equation (D1) using 2SLS.[53] We find that the lagged unemployment rate is not a weak instrument, with a first-stage F value of 59.75.

We estimate $\kappa$ to be –0.093 (p = 0.000), which is smaller than our estimate for $\delta$ of –0.227 using Equation (3) (Table 1).[54] Based on the framework of Hazell et al, the larger absolute size of the slope in Equation 3 reflects the fact that the unemployment rate is standing in for the entire future sum in Equation (D1). Since unemployment is persistent, time variation in the future sum is larger than the time variation in the unemployment rate, which leads to a smaller coefficient in Equation (D1) compared to Equation (3). Note, however, that this estimation approach is based on a theoretical model of the price Phillips curve, and we have not attempted to adapt Hazell et al's theory to the context of wage inflation. In that sense, the estimates in this appendix are only suggestive of a role for persistence.

Overall, this suggests that while our regional estimates are helpful for examining the modelling assumptions in the RBA's aggregate models (as they both identify the same parameter), we should be cautious in interpreting these estimates as the structural slope of the New Keynesian wage Phillips curve.

## Footnotes

We omit the lagged wages growth terms from the specification to increase comparability with Hazell et al's specification. Including lagged wages growth makes little difference to the conclusions in this appendix. [53]

The impact of this adjustment is far smaller than found by Hazell et al, who find that the implied slope of the Phillips curve falls from 0.112 to 0.0062 when accounting for persistence in unemployment fluctuations. [54]