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1. Introduction
As the labour market recovers from the effects of the COVID-19 shock, a key policy question facing the
Reserve Bank of Australia (RBA) Board is at what point spare capacity in the labour market will be absorbed
and, as a result, when will there be a sustained increase in wages growth (Lowe 2021). In other words: how
strong is the relationship between unemployment and wages growth (often referred to as the wage Phillips
curve), and does the nature of that relationship change as the unemployment rate falls to lower and lower
levels?
Despite the importance of this question to the RBA (as an inflation-targeting central bank), the way in which
aggregate wages would respond at rates of unemployment below those observed in recent history remains a
key source of uncertainty, both in Australia and in other countries. In the Australian case, much of the
uncertainty stems from the lack of evidence to draw upon. In the lead up to the global financial crisis (GFC),
the unemployment rate declined steadily for a number of years (ultimately falling to a low of 4 per cent) and
wages growth rose strongly in response. However, this was the only time over the past four decades the
unemployment rate reached such a level (Figure 1).
This paper attempts to overcome this lack of historical experience by examining the relationship between the
unemployment rate and wages growth across 291 local labour markets in Australia over the past two
decades. In contrast to the national data, a panel of local labour markets provides many more observations
on what happens to wages growth when the unemployment rate falls to very low levels. For example, in our
dataset, more than one-fifth of all region–year observations have an unemployment rate below 4 per cent.
In examining whether the wage Phillips curve relationship is stronger at lower levels of unemployment, we
contribute to a well-established literature on nonlinearities in the Phillips curve. Economists have long
believed the Phillips curve to be a curve, rather than a straight line. Indeed, Phillips's (1958) original paper,
as well as many introductory textbooks, show the relationship with a steeper slope when the unemployment
rate is low and a flatter slope when the unemployment rate is high. This nonlinearity in the inflation–
unemployment trade-off has been explicitly incorporated into the RBA's wage and price inflation models since
the late 1990s, following a research discussion paper by Debelle and Vickery (1997).
The question of whether the Phillips curve is a curve rather than a straight line in Australia has not been
thoroughly revisited since Debelle and Vickery (1997). We believe that the time has come to re-examine the
shape of the Phillips curve and test whether the functional form that underpins the RBA's current suite of
Phillips curve models remains suitable. This is particularly important in light of the remarkably strong
recovery in the labour market over the past 12 months and the RBA's baseline forecast for an unemployment
rate approaching 4 per cent by end 2023 (RBA 2021b).
Using regional data also allows us to overcome the biases that can arise in identifying the slope of the
Phillips curve using national data. These biases can arise from the endogenous response of monetary policy
to economic conditions or changes in long-run inflation expectations, both of which can hinder identification
of the Phillips curve in national time series data. The literature covering the US Phillips curve has
Figure 1: Unemployment Rate
Seasonally adjusted, monthly
Source: ABS
[1]
demonstrated that it is important to account for these biases, and often exploits regional data to do so
(Fitzgerald et al 2020; Hazell et al 2020; McLeay and Tenreyro 2020). Although the recent literature largely
deals with the price Phillips curve, the same intuition applies when estimating the wage Phillips curve, which
is our focus. A key advantage of using regional data to estimate the Phillips curve is that demand-driven
variations in unemployment and wages that are specific to particular regions should be free from the biases
that can plague estimates of the Phillips curve. However, using regional data to estimate the Phillips curve
does present some challenges, most notably the task of translating regional estimates into aggregate ones.
As a benchmark, we first estimate a linear wage Phillips curve using data from 291 local labour markets over
a 20-year period. Our estimates are broadly consistent with previous linear estimates for Australia and
elsewhere; when the unemployment rate falls by 1 percentage point, annual wages growth increases by 0.2–
0.3 percentage points on average. We then allow the slope of the Phillips curve to vary with the
unemployment rate by allowing it to have a series of kinks. We strongly reject the hypothesis that the Phillips
curve is a straight line – it is a curve. When the unemployment rate exceeds 7½ per cent, we cannot reject
the hypothesis that the Phillips curve is flat. However, we find that the slope of the Phillips curve steepens
when the unemployment rate falls below 5½ per cent, and steepens further when the unemployment rate
falls below 4 per cent. Importantly, our estimates are stable over time; we find no evidence that the slope or
curvature of the wage Phillips curve has changed since 2012 despite the slowdown in wages growth that has
occurred since then.
Our estimates of the slope and curvature of the Phillips curve are remarkably similar to those inherent in the
RBA's aggregate wage Phillips curve model, suggesting that the nonlinearity assumptions adopted following
Debelle and Vickery (1997) remain broadly appropriate. The only meaningful difference emerges at
unemployment rates below 3½ per cent, where the RBA's aggregate model assumes a much sharper
increase in wages growth and inflation than our estimates based on regional variation.
These findings have important implications for policy. According to the RBA Board (RBA 2021a), the cash rate
will not be raised until inflation is sustainably within the 2 to 3 per cent target range. The relationship
between unemployment, wages growth and inflation is important for understanding how inflation will evolve.
While endogenous policy makes it difficult to extrapolate from regional evidence to draw conclusions about
outcomes at the aggregate level, our paper provides evidence as to the underlying relationship between
unemployment and wages growth. This relationship is a key component of the broader equilibrium between
unemployment, wages growth and inflation, and understanding it is crucial given the RBA's policy
objectives.
2. Background on the Phillips Curve and the
RBA's Modelling Approach
2.1 The Phillips curve
The intuition underlying the Phillips curve is that ‘[w]hen the demand for labour is high and there are very
few unemployed we should expect employers to bid wages rates up quite rapidly’ (Phillips 1958, p 283), and
firms to raise prices.
Although much of the Phillips curve literature relates to the relationship between price inflation and
unemployment, similar intuition applies to the wages growth–unemployment relationship. Notably, both the
RBA and Australian Treasury use versions of a Phillips curve as their preferred models for forecasting nominal
[2]
wages growth. In this and the following section we largely deal with wage and price Phillips curves
interchangeably. However, from Section 4 on we limit our empirical analysis to the wage Phillips curve, which
is the relationship we are most interested in.
Since Phillips (1958), a vast amount of theoretical work has built on and formalised this basic intuition. Milton
Friedman's (1968) expectations-augmented Phillips curve is:
where is inflation, is expected inflation, u is unemployment, is the non-accelerating inflation rate
of unemployment (NAIRU), and e is an error term. The difference between u and is the
‘unemployment gap’. This basic framework was also extended to include supply shocks by Gordon (1982).
Because neither expected inflation nor the NAIRU can be directly measured, they need to be estimated.
An equation like the expectations-augmented Phillips curve also appears in many New Keynesian DSGE
models, and is called the New Keynesian Phillips curve. In these macroeconomic models with sticky prices,
there is a positive relationship between the rate of inflation and the level of demand, and therefore a
negative relationship between the rate of inflation and the rate of unemployment.
2.2 Sources of nonlinearity
The Phillips curve above (Equation (1)) assumes the relationship between the unemployment gap and
inflation is linear: a 1 percentage point increase in the unemployment gap has the same effect on inflation
when the labour market is tight as it does when the labour market has plenty of spare capacity. However,
Phillips (1958) himself argued that the relationship between unemployment and wages growth is likely
‘highly non-linear’ as ‘workers are reluctant to offer their services at less than the prevailing rates when the
demand for labour is low and unemployment is high so that wage rates fall only very slowly’. This
explanation relates to the notion of downward nominal wage rigidity - that firms are either unwilling or
unable cut nominal wages. During recessions these rigidities become more binding and labour market
adjustment disproportionately occurs via higher unemployment rather than via lower wages. During
expansions, where rigidities bind less, more of the adjustment can occur via wages. This is an important
argument for a nonlinear (convex) Phillips curve, especially in a low inflation environment.
Evidence from job-level microdata up until 2018 suggests that downward nominal wage rigidity is a binding
constraint for Australian employers. A histogram of job-level annual wages growth outcomes from the wage
price index (WPI) shows clear evidence of a scarcity of wage cuts and an abundance of wage freezes,
consistent with downward nominal wage rigidity (Figure 2). In fact, only 1 per cent of all jobs experience a
wage cut in any given year, compared with around 22 per cent experiencing a wage freeze.
[3]
(1)
= + a
(
−
)
+πt πet ut u∗t et
πt πet t u∗t
t
[4],[5]
t u∗t
[6]
[7]
[8]
Another common explanation for a convex Phillips curve is the presence of capacity constraints. This
argument supposes that firms find it difficult to increase their production capacity in the short run. So, when
an economy experiences a strong rise in demand, more firms will run up against capacity constraints which
will push up wages and prices. Further, inflation becomes increasingly sensitive to demand; each additional
increase in demand leads to ever-increasing rises in inflation. Debelle and Laxton (1997), Debelle and Vickery
(1997) and Kumar and Orrenius (2016) suggest that these ‘bottlenecks’ arise when the unemployment rate
falls below the NAIRU or natural rate of unemployment.
Other explanations for a convex Phillips curve include menu costs and relative prices (Ball and Mankiw 1994)
and efficiency wages (Shapiro and Stiglitz 1984); see Dupasquier and Ricketts (1998) for a summary of these
arguments. Standard models of the labour market also imply such nonlinearity (Petrosky-Nadeau and Zhang
2017).
2.3 The RBA's modelling approach
This nonlinearity in the inflation–unemployment trade-off was explicitly incorporated into the RBA's wage and
price inflation models in the late 1990s, following a research discussion paper by Debelle and Vickery (1997).
Prior to that, the RBA's Phillips curves were estimated in a linear framework; that is, assuming that the effect
on inflation of each percentage point change in unemployment is the same regardless of the level of
unemployment.
From an empirical standpoint, Debelle and Laxton (1997) and Debelle and Vickery (1997) argued that a
nonlinear relationship between inflation and the unemployment gap provided a better fit to the national time
series data for the United Kingdom, the United States, Canada and Australia. The equation they estimated
Figure 2: Distribution of Job-level Wage Growth
Histogram, 2000:Q3–2018:Q3
Sources: ABS (job-level wage price index microdata); Authors' calculations
[9]
[10]
essentially replaced the linear unemployment gap in Equation (1), , with the unemployment gap
relative to the level of unemployment:
This specification implies a short-run slope equal to:
In this specification, a change in the unemployment rate has a different effect on inflation depending on both
the current level of the unemployment rate and the NAIRU. Since Debelle and Vickery (1997), the RBA's
workhorse wage and price Phillips curve models for policy analysis and forecasting have assumed this
nonlinear relationship between inflation and the unemployment gap (Cassidy et al 2019; Ballantyne et al
2019). In practice, the RBA's current models also control for other determinants of wage and price
inflation, including lagged inflation and controls for supply shocks. In this paper, our discussion of the RBA's
aggregate Phillips curve models focuses on the set of single-equation Phillips curve models used in
constructing the RBA's central forecasts for wage and price inflation. The specifications of these models are
set out in Appendix A (for wage inflation) and Cassidy et al (2019) (for price inflation). In practice, the RBA
also maintains a full-system economic model for risk and scenario analysis, which adopts a similar nonlinear
unemployment gap in its wages equation (Ballantyne et al 2019). Recent analysis, including the forecast
scenarios for price inflation presented in RBA (2021b), has also incorporated a nonlinear unemployment gap
in the inflation equation.