RDP 2021-09: Is the Phillips Curve Still a Curve? Evidence from the Regions 5. Benchmark Linear Model

To provide a benchmark, we first estimate a linear wage Phillips curve that ignores the nonlinearity in Figure 6. This benchmark model also aids with comparison to the international literature, which typically uses a linear specification.

5.1 Specification

We estimate the following linear wage Phillips curve model:

where $\text{Δ}{w}_{it}$ is annual wages growth in region i in year t and u_it is the region's average unemployment rate during the year. The main coefficient of interest is $\delta$, which is the slope of the wage Phillips curve in the short run.^[32] In this model, there is no nonlinearity: the slope of the Phillips curve is the same irrespective of labour market conditions. We relax this assumption in the next section.

The model also includes lagged wages growth, which helps to control for the observed persistence in wages growth. The model includes region fixed effects to control for any permanent differences in wages growth and labour market conditions across regions. The model also has time fixed effects to capture any factors that vary across time but are constant across regions - for example, a change in federal industrial relations policy that has an equal effect on all regions. Importantly, the time fixed effects address the biases discussed in Section 3.1. Due to the well-known bias in dynamic panels and the relatively short time series dimension in our sample, we estimate the model using the Arellano-Bond procedure.

A key variable that is not explicitly included in the model is inflation expectations. Unfortunately, measures of inflation expectations are not available at the region level. However, the lagged wages growth term partially controls for region-specific inflation expectations to the extent that expectations are formed adaptively. Moreover, the region fixed effects control for permanent differences in inflation expectations across regions, while the time fixed effects control for any trends in inflation expectations that are common to all regions over time. We discuss the implications of omitting direct controls for short-term inflation expectations in Section 7.2.3.

Our model also omits an explicit control for the NAIRU. Again, the region and time effects will control for permanent differences, and common changes, in the NAIRU across regions. The main sources of omitted variable bias that could affect our results are changes in the NAIRU and inflation expectations that occur within regions over time. We can partly account for these variations by also allowing for region-specific time trends, which we do as a robustness test. To the extent that the fixed effects capture most variations in region-specific NAIRUs, the $\delta$ can be interpreted as capturing the effect of a 1 percentage point change in the unemployment gap.

5.2 Results

Results for the linear model are shown in Table 1. We present results from three versions of the model, all of which include region fixed effects and lagged wages growth. Column (A) shows results from a specification without time fixed effects. In this case, we find that the Phillips curve is negatively sloped; the coefficient on the unemployment rate is negative and statistically different from zero. The point estimate suggests that a 1 percentage point decline in the unemployment rate is associated with a 0.27 percentage points increase in annual wages growth.

In column (B) we add time fixed effects, which purge our estimates of any aggregate-level variation, including changes in monetary policy, long-run inflation expectations and the aggregate NAIRU. Surprisingly, this makes little difference to our results. If anything, the Phillips curve is estimated to be flatter (at around –0.23) when time fixed effects are included, the opposite of what we would expect if identification of the Phillips curve has been blurred by endogenous monetary policy.

The robustness of our estimates to the inclusion of time fixed effects provides tentative evidence that the endogeneity issues discussed in Section 3.1 are not relevant to Phillips curve estimation in Australia, at least for the wage Phillips curve over the post-1998 period. McLeay and Tenreyro (2020) found that the slope of the post-1990 US price Phillips curve more than doubled after adding time fixed effects to their panel model of US states. This may reflect that McLeay and Tenreyro were examining price inflation rather than wages growth, with the former being more susceptible to endogeneity than the latter.^[33] It could also reflect differences in the conduct of monetary policy between the United States and Australia, or differences in the nature of the shocks that the respective central banks have faced. In any case, we proceed to use the robust version of the model – with the full set of region and time fixed effects – for the remainder of this paper.

The slope of the Phillips curve is estimated to be slightly steeper (at around –0.30) if we include region-specific linear time trends in the model (column (C)). This may suggest that region-specific NAIRUs or productivity exhibited different linear time trends over the course of our sample period.

Overall, estimates from the linear specification imply a slope of between –0.2 and –0.3, which is within the range of previously reported estimates of the slope of the wage Phillips curve. For Australia, the RBA's time series wages growth model (with a nonlinear Phillips curve specification) implies a slope of –0.29, when averaged over the 1999-2018 period. Using US state-level data, Kumar and Orrenius (2016) estimated the slope of the US wage Phillips curve to be –0.33 and Levy (2019) estimated a slope of –0.3 when using variation across regions within the euro area.^[34]

Our estimates are also in line with the (more voluminous) literature on the price Phillips curve. Using data for US metropolitan statistical areas (MSAs), Fitzgerald et al (2020) estimate the slope of the price Phillips curve to be close to –0.3 across a range of specifications and sub-periods. McLeay and Tenreyro (2020), also using MSA-level data, report a preferred point estimate of –0.379. The main exception to this pattern of findings is Hazell et al (2020), who estimate a much flatter slope of the price Phillips curve at –0.006; the main reason for this is that, in their framework, they make an adjustment for the persistence of unemployment when going from their empirical specification to their estimated slope. We discuss the implications of Hazell et al's framework in Section 7.2.3 and also Appendix D.

Column (D) in Table 1 explores the stability of the estimated Phillips curve relationship over time. We examine this by interacting the unemployment rate variable in Equation (3) with a dummy variable that equals one for the period 2012-18 and zero for the pre-2012 period. A positive coefficient on the interaction term would indicate that the wage Phillips curve flattened after 2012. We choose 2012 to divide our sample because it splits our sample into the upswing and downswing phases of the resources investment boom. The extent of the slowdown in wages growth over the post-2012 period has also been somewhat of a puzzle (Harper et al 2019). We find no evidence that the slope of the Phillips curve changed between these two periods: we do not reject the hypothesis that the coefficient on the interaction term is zero (p-value = 0.451).

Footnotes

The longer-term slope of the Phillips curve is equal to $\delta /\left(1-\beta \right)$. We use contemporaneous unemployment rather than lagged unemployment (which is used in the RBA's aggregate model) on the right-hand side because our data are annual frequency. [32]

As McLeay and Tenreyro (2020) point out, inflation-targeting central banks usually target consumer price inflation rather than wage inflation. If the central bank responds to shocks that affect price inflation but do not directly affect wage inflation, that response will not induce a correlation between the unemployment gap and the error term in the wage Phillips curve. In that case, the slope of the wage Phillips curve will be estimated consistently. Bias will only arise if the central bank leans against shocks that affect both prices and wages. [33]

Aggregate time series estimates of the slope of the wage Phillips curve for the United States range from –0.38 to –0.40 depending on the measure of hourly wages used (Hooper et al 2019). [34]