# RDP 2021-09: Is the Phillips Curve Still a Curve? Evidence from the Regions 8. Robustness

## 8.1 Geographic classifications

We examine if our results are robust to the way we define ‘local labour markets’. As discussed earlier, our baseline results use our preferred classification of local labour markets derived from cluster analysis on journey to work data from the 2011 Census. Appendix C demonstrates that our results are robust to the level of geographic aggregation used in the regressions. We do this by re-estimating our preferred specification using a range of different geographic classifications as the unit of observation, including local labour markets based on the 2016 Census, SA4s, states and functional economic regions. Our estimates of the slope and curvature of the Phillips curve are remarkably insensitive to using different aggregations of the data, although precision is lower in several cases.

## 8.2 Compositional effects

Our measure of wages growth is based on annual employee income per wage earner. This measure of wages growth is potentially affected by changes in the composition of employment. This could affect our results if these compositional effects vary with the degree of labour market slack. For example, if average hours worked per employee tend to rise when demand for labour is strong (Bishop, Gustafsson and Plumb 2016), then the increase in annual earnings growth that we observe in a tight labour market may simply reflect people working more hours on average, not increases in hourly wages. That is, it may put an upward bias (in absolute value) into our estimates.

Unfortunately, measures of compositionally adjusted hourly wages growth are not available at the region level. The best available measure of ‘pure’ wages growth in Australia is the WPI, which tracks the hourly wages of a fixed basket of jobs over time and thus controls for changes in hours worked and changes in the composition of the workforce. The WPI (excluding bonuses) is available at the state and territory level from 1997 onward, but not at the sub-state level.[43]

To explore the extent of compositional bias in our estimates, we compare our state-level estimates using growth in average employee income per worker (Appendix C) to state-level estimates that replace the dependent variable with growth in the WPI. A large difference in the coefficient estimates between these two models may indicate that compositional effects are important to our results. Our estimates suggest that the Phillips curve is slightly flatter using the WPI than using average employee income (–0.20 versus –0.27).[44] This may suggest that compositional effects are biasing our estimates. However, this finding could also reflect the fact that average employee income is a broader measure of labour costs than the WPI, and that the income components excluded from the WPI – such as promotions, bonuses, travel allowances and fringe benefits – are more sensitive to slack (Leal 2019).

## 8.3 Speed limit effects

Our baseline specification relates wages growth to the level of the unemployment rate (the latter can be thought as the unemployment gap when fixed effects are included). In contrast, in the RBA's aggregate model, wages growth depends on both the level of the unemployment gap and the change in the unemployment rate (see Appendix A). The rate-of-change effect is commonly referred to as the ‘speed limit effect’ and is intended to capture the inflationary impact of rapid changes in demand.

We examine if our baseline results are robust to including the change in the unemployment rate as an additional regressor in Equation (3). The results of this robustness check are shown in the second column of Table 3, while the first column shows the baseline results for comparison. The coefficient on the change in unemployment term is close to zero and not statistically significant, and the coefficient on the unemployment rate is little changed relative to the baseline. This suggests that our results are robust to controlling for speed limit effects.[45] We arrive at a similar conclusion for our preferred specification using the restricted cubic spline; the findings are robust to adding controls for the change in the unemployment rate and the change in the spline term (column 4 of Table 3).

Table 3: Regression Results – Robustness to Controlling for Speed Limit Terms
Dependent variable = annual wages growth
Linear baseline Linear speed limit Restricted cubic spline baseline Restricted cubic spline speed limit
Unemployment rate −0.227***
(0.045)
−0.208***
(0.053)
−0.484***
(0.106)
−0.464***
(0.107)
$\text{Δ}$ Unemployment rate   0.008
(0.033)
0.016
(0.060)
Restricted cubic spline term     0.300***
(0.087)
0.305***
(0.090)
$\text{Δ}$ Restricted cubic spline term       −0.010
(0.066)
Lagged wages growth 0.247***
(0.039)
0.243***
(0.043)
0.239***
(0.039)
0.237***
(0.042)
Region fixed effects Yes Yes Yes Yes
Time fixed effects Yes Yes Yes Yes
Region-specific trends No No No No
Observations 5,639 5,639 5,352 5,352

Notes: Standard errors (in parentheses) are clustered by region; ***, **, and * denote statistical significance at the 1, 5, and 10 per cent levels, respectively; estimation is done using the Arellano-Bond estimator, and weighted by the number of employees in each region

Sources: ABS; Authors' calculations; National Skills Commission

## Footnotes

The WPI is designed to measure changes in wage rates for a given quantity and quality of labour. The index is constructed by the ABS by comparing the wage for a given job to the previous quarter; adjustments are made to exclude any changes in wages resulting from changes in the nature of the job or the quality of the work performed. It is constructed for a fixed basket of jobs, so by design it should be unaffected by changes to the composition of the labour force. [43]

The p-values for these coefficient estimates are 0.108 and 0.006, respectively. These regression estimates are based on a common sample (1999–2018) and use a model that includes time and state fixed effects. We find that the coefficient estimates (including on the spline term) are also very similar when we allow for a kink in the curve at 4 per cent. [44]

The specification with both the level and change in the unemployment rate contains exactly the same information as a specification with the current and first lag of the unemployment rate (Gordon 1997). To see this, note that Equation (3) augmented with a lag of the unemployment rate $\text{Δ}{w}_{it}=\alpha +\beta \text{Δ}{w}_{it-1}+{\delta }_{1}{u}_{it}+{\delta }_{2}{u}_{it-1}+{\theta }_{t}+{\omega }_{t}+{v}_{it}$ can be rearranged to obtain the expression with a speed limit term $\text{Δ}{w}_{it}=\alpha +\beta \text{Δ}{w}_{it-1}+\left({\delta }_{1}+{\delta }_{2}\right){u}_{it}+{\delta }_{2}\left({u}_{it}-{u}_{it-1}\right)+{\theta }_{t}+{\omega }_{t}+{v}_{it}.$ This also shows that, in a specification with the speed limit control, the coefficient on the unemployment rate is interpreted as the two-period dynamic effect of the unemployment rate on wages growth. For example, the coefficient on the unemployment rate of -0.20 (second column of Table 3) indicates that a 1 percentage point decrease in the unemployment rate in the current and previous year is associated with a 0.2 percentage point increase in wages growth. [45]