RDP 2021-09: Is the Phillips Curve Still a Curve? Evidence from the Regions 3. Is the Phillips Curve Still a Curve?

The question of whether the Australian Phillips curve is a curve rather than a straight line has not been properly revisited since Debelle and Vickery (1997). While Debelle and Vickery's models were originally run over a largely pre-inflation-targeting sample (1959–97), the RBA's current models use a post-1993 sample (or post-1998 in the case of wages growth due to the shorter history for the WPI). It is uncertain whether the nonlinearities that Debelle and Vickery explored for the earlier period still exist under the inflation-targeting regime. Moreover, as Debelle and Vickery (1997) noted, their results ‘should only be regarded as indicative of the presence of non-linearities’ because the aim of their paper was ‘not to estimate a definitive model’ of the Phillips curve. In light of this, it is important to examine whether the RBA's modelling assumptions remain appropriate.

There are several candidate approaches for examining nonlinearities in the Phillips curve. One approach would be to update Debelle and Vickery's time series analysis using more recent data. This would involve running a series of horse races between a linear model (e.g. Equation (1)) and nonlinear ones (e.g. Equation (2)) to gauge which perform best.[14] However, the time series data since the 1990s have few episodes of the unemployment rate going well below 5 per cent (the only case being the 2006–07 period; Figure 1). The lack of observations on tight labour markets echoes a broader challenge facing time series studies: those that try to estimate nonlinearities in the Phillips curve using national-level time series data usually find that variation in national data on unemployment and inflation is too limited to yield robust and statistically significant evidence of nonlinearity (Hooper, Mishkin and Sufi 2019).

Given the limitations of aggregate data for examining nonlinearities in the Phillips curve, a number of recent studies for the United States use state-level data instead (e.g. Kumar and Orrenius 2016; Babb and Detmeister 2017; Hooper et al 2019). These studies exploit the fact that some US states experience very tight labour market conditions even when aggregate US unemployment is elevated, and vice versa. States with unusually tight labour markets shed light on the slope of the Phillips curve when unemployment is very low. Similarly, states with high levels of unemployment shed light on the Phillips curve slope when there is spare capacity. These studies tend to find strong evidence of nonlinearity in US data. Levy (2019) finds similar results for the euro area.

In a similar vein, we explore nonlinearities in the Australian Phillips curve using data on wages growth and unemployment rates across local labour markets. This contrasts with most previous investigations of the Phillips curve in Australia, which use national time series data (e.g. Debelle and Vickery 1997; Gruen, Pagan and Thompson 1999; Lim, Dixon and Tsiaplias 2009; Norman and Richards 2010; Bullen et al 2014; Gillitzer and Simon 2015; Chua and Robinson 2018; Ruberl et al 2021). We focus on the wage Phillips curve rather than the price Phillips curve. Our data cover 291 local labour markets at annual frequency over a 20-year period. We focus on small regions, rather than states as in the US literature, because Australia has few states and labour market conditions often vary substantially within each state. This sub-state variation provides us with additional useful information for estimating how the slope of the Phillips curve varies with the level of labour market slack.

3.1 Identification of the Phillips curve

Another important development in the literature in recent years is the increasing awareness of the identification problems affecting estimates of the slope of the aggregate Phillips curve. There is a growing recognition that estimating the parameters of Equation (2) using OLS will yield biased estimates of the ‘true’ Phillips curve parameters. By ‘true’ Phillips curve, we mean the underlying structural (or causal) relationship between unemployment and inflation in the economy.

In particular, Phillips curve identification can be complicated due to three main endogeneity issues:

  1. the systematic response of monetary policy to economic conditions
  2. imperfect controls for inflation expectations
  3. measurement error in the unemployment gap.

Regional variation provides a way of dealing with these endogeneity issues and thus obtaining an unbiased estimate of the Phillips curve slope. This provides a second motivation for our use of regional data, in addition to the greater power it provides for detecting nonlinearities. While these issues are usually framed in the context of linear New Keynesian Phillips curve models (microfounded formulations of the Phillips curve based on rational expectations and staggered price and wage setting), the same intuition applies to nonlinear Phillips curves. In what follows, we seek only to convey the broad intuition for each issue and how it is addressed using regional data.

3.1.1 The systematic response of monetary policy

The first issue is the bias that can be introduced into Phillips curve estimates by the endogenous response of monetary policy to economic conditions. This issue is discussed in several recent papers (Fitzgerald et al 2020; McLeay and Tenreyro 2020; Hazell et al 2020), all of which were motivated by the observation that the US Phillips curve appears to have ‘flattened’ in recent decades. These papers argue that the true Phillips curve has not flattened to the extent that a simple regression of aggregate inflation on the aggregate unemployment gap would suggest. Rather, they argue that the observed inflation and unemployment data have been affected by changes in the conduct of monetary policy in a way that simply makes it appear as though the Phillips curve has become flatter. Specifically, several studies have argued that this bias is large enough to account for all of the apparent flattening of the US Phillips curve over time, and that the true Phillips curve is steeper and more stable than time series data suggest (Fitzgerald et al 2020; McLeay and Tenreyro 2020).[15]

The intuition provided by McLeay and Tenreyro (2020) is as follows.[16] A central bank with a dual mandate for achieving full employment and inflation at some target level will respond to the various shocks that hit the economy by weighing up these two objectives. Optimal stabilisation policy tries to fully offset the effects of demand shocks, because these shocks do not create a trade-off between the central bank's objectives. For example, a negative demand shock that causes inflation to fall below target and unemployment to rise above target can be addressed by expansionary policy which will help to return both variables to the desired levels. If the central bank succeeds in offsetting the effects of demand shocks, most of the remaining variation in the data for inflation and unemployment will reflect the effects of cost-push shocks.[17] Cost-push shocks move the economy away from the central bank's inflation target without necessarily moving the economy away from full employment. Because cost-push shocks induce a trade-off between the central bank's objectives, optimal policy does not attempt to fully offset them.

A central bank's response to demand shocks will make it harder to find evidence of a Phillips curve in the data, because demand-driven variations are precisely what we need to trace out the slope of the true Phillips curve (demand shocks lead to movements along a Phillips curve, while cost-push shocks lead to deviations from the Phillips curve). The central bank's reaction to cost-push shocks exacerbates this identification issue. Cost-push shocks move inflation independently of demand, and optimal policy may involve leaning against these shocks rather than ‘looking through’ them. For example, in response to a persistent negative supply shock a central bank may tighten policy to prevent inflation straying too far from target (tolerating a higher unemployment rate to achieve this).[18] In this case, the data may show a positive correlation between inflation and unemployment. If the variation used to estimate the slope of the Phillips curve is contaminated like this, a simple regression of inflation on the unemployment gap will yield a slope estimate that is biased, and could even have the ‘wrong’ sign. The extent of the bias will depend on the extent of the cost-push shocks (and whether policy responded), relative to any residual variations in demand that policy was not able to offset.

One solution to this endogeneity problem is to include controls for cost-push shocks (and other trade-off-inducing shocks) in the model. The price Phillips curve model used by the RBA controls for import prices, and also uses a measure of inflation (trimmed mean) that filters out the effects of large cost-push shocks. As such, the RBA's preferred models control for at least some of the potential bias due to endogenous monetary policy. However, there are many trade-off-inducing shocks that monetary policy could respond to that are not controlled for (e.g. changes in trend labour productivity and financial frictions), so it is possible that the model estimates are still affected by endogenous policy.

Using regional variation as we do in this paper is another solution to the identification problem. Because monetary policy only responds to aggregate shocks, region-specific variation can be used to identify the true causal relationship between inflation and unemployment (Fitzgerald et al 2020; McLeay and Tenreyro 2020). Since monetary policy does not offset region-specific demand shocks, region-level data can provide us with the variation we need to trace out the slope of the Phillips curve even when policy is fully stabilising demand at the national level. Moreover, including time fixed effects in a regional panel model will account for the endogenous response of monetary policy to aggregate trade-off-inducing shocks that would otherwise bias our estimates of the Phillips curve.[19]

3.1.2 Inflation expectations

Another issue facing national time series estimates of the Phillips curve is that direct measures of long-term inflation expectations are often poorly measured or not available. This can bias estimates of the slope of the Phillips curve if movements in long-run inflation expectations are correlated with changes in the unemployment rate. Hazell et al (2020) point to the disinflation in the United States in the early 1980s as an important example of this. The authors argue that the willingness of the Federal Reserve under Chairman Volcker to allow unemployment to rise to a high level sent a credible signal to the public about its commitment to reducing inflation. In turn, this caused a decline in long-run inflation expectations which contributed to the fall in inflation. Because long-run inflation expectations and inflation were declining at the same time that unemployment was rising, failing to control for the former in a Phillips curve model would lead one to overestimate the steepness of the Phillips curve.

Studies focusing on the flattening of the Phillips curve after the 1980s clearly need to address this issue. However, this is less of a concern for the RBA's current estimates of the Phillips curve. First, the RBA's existing suite of Phillips curve models control for long-term inflation expectations directly, which minimises the bias discussed by Hazell et al (2020).[20] Second, the estimation samples for the RBA models span a stable monetary policy regime.[21] Inflation targeting substantially reduced the variability of expectations, anchoring them at the RBA's target of 2 to 3 per cent. If true long-run inflation expectations did not vary much over the inflation-targeting period, any confounding effect of shifting long-run expectations would be small even if the measure used to proxy those expectations is not perfect.

Regional data provide a stronger approach to controlling for shifts in long-run inflation expectations (Hazell et al 2020). While short-run inflation expectations can differ across Australian regions due to differences in local economic conditions, long-run inflation expectations should evolve uniformly across regions to the extent they are determined solely by the credibility of the RBA's inflation target (which is common to all regions). When estimating the Phillips curve using a panel of regions, all changes in long-run inflation expectations will be absorbed by time fixed effects.[22] Hazell et al (2020) argue that this ability of regional models to control for long-run expectations partially explains why estimates of the slope of the US Phillips curve for the pre-1990s period are much ‘flatter’ using regional data than using aggregate data. Notwithstanding this, given that the RBA's existing models are estimated over a period with stable long-run inflation expectations, we do not expect that they are significantly affected by this issue and, as such, we do not expect this to lead to our regional estimates being significantly different to existing aggregate estimates.

3.1.3 Measurement error in the unemployment gap

Like inflation expectations, another variable we cannot directly observe is the NAIRU. There is evidence that the NAIRU has fallen over the past 20 years or so, in line with the general decline in the unemployment rate over the same period (Cusbert 2017; Cassidy et al 2019). In saying that, there are various reasons to be cautious about estimates of the NAIRU, including their wide confidence intervals and sensitivity to model specification and estimation window.[23] Any measurement error in the NAIRU will bias the estimated slope of the Phillips curve towards zero (Ball and Mazumder 2011).[24]

Again, regional data can provide a partial solution. Using regional data, it is possible to adopt a specification which uses the unemployment rate instead of the unemployment gap and relies on time fixed effects to sweep out any movements in the aggregate NAIRU over time. Region-specific time trends can also be included in the model to account for the possibility that the NAIRU has a different time trend across different regions.


One of our colleagues, Tom Cusbert, recently carried out such an exercise using time series data and considering a range of different nonlinear specifications. He finds that Debelle and Vickery's functional form provides a good fit to the post-1968 data. This analysis, in the form of an internal RBA briefing note, is available in our supplementary information <https://www.rba.gov.au/publications/rdp/2021/2021-09/supplementary-information.html>. [14]

Hazell et al (2020) provide a different explanation for the finding that regional Phillips curve slope estimates tend to be larger than aggregate ones, which we discuss in Section 7.2.3. [15]

We describe the McLeay and Tenreyro logic here because it is simple and intuitive. Fitzgerald et al (2020) arrive at a similar conclusion (that, where monetary policy is set to achieve an inflation-targeting mandate, aggregate data is uninformative as to the structural Phillips curve relationship) using a general reduced-form model that does not depend on the nature of the shock applied. [16]

This point was also made by Gillitzer and Simon (2015) as a potential explanation for the apparent flattening in the Phillips curve following the introduction of inflation targeting in Australia:
Variability of the domestic component of inflation has declined substantially [since the introduction of inflation targeting], and much of the variation in CPI inflation is now caused by imported shocks, such as commodity price and exchange rate changes. Stabilisation of the domestic component of inflation has weakened the relationship between inflation and domestic economic conditions … (p 24)

An example of something that can affect inflation at policy-relevant horizons, other than the simple pressure of demand, might be the direct impact on CPI inflation of movements in the exchange rate. [18]

The time fixed effects ‘difference out’ the effects of any variables that vary uniformly across all regions over time. [19]

The models include the ‘trend’ measure developed by Cusbert (2017), which extracts a common signal from the range of survey and financial market measures of inflation expectations available in Australia. [20]

The price and wage Phillips curves used in the RBA's forecasting process are estimated over the 1993–2019 and 1998–2019 periods respectively. The RBA's preferred measure of wages growth – the WPI – has only been compiled by the ABS since 1998. Although the preferred price and wage inflation models used by the RBA are run over the post-inflation-targeting period, some of the inputs are generated over a longer sample period. In particular, the NAIRU and trend measure of inflation expectations are themselves jointly estimated using a state-space Phillips curve framework beginning in 1968 (see Cusbert (2017)). [21]

Including region fixed effects also accounts for any permanent differences in long-run inflation expectations across regions. [22]

See Cusbert (2017) for a discussion and references to relevant literature. [23]

This will also occur if the Phillips curve model uses the unemployment rate rather than the unemployment gap. An aggregate model that includes the unemployment rate rather than the unemployment gap is likely to generate a slope estimate that is biased toward zero, given that the national unemployment rate was ‘chasing the NAIRU down’ for much of the post-2000 period. In this situation, what the regression would be picking up is shifts in the curve, rather than movements along a fixed curve. [24]