The Phillips curve: A new era of non-linearity?

The academic perspective on the Phillips curve has changed significantly in recent years. Many studies since the 1980s argued that the curve was flattening. However, later studies showed that this flattening was an unintended consequence of empirical misspecification (e.g. not including trend inflation or long-term inflation expectations, or using an inappropriate indicator of real economic activity). In the post-pandemic recovery period, evidence has emerged not only of the “steepening” of the Phillips curve but also of significant non-linearities. Among the key factors driving these changes are the effects of higher initial inflation, the size and asymmetry of price shocks, the anchoring of inflation expectations, labour market conditions, the overall state of the economy, and structural changes.

A brief historical overview

The Phillips curve is a fundamental macroeconomic concept that describes the inverse relationship between unemployment and inflation. It was introduced by the economist Bill Phillips (1958), based on observations of long-term statistical relationships in data from the United Kingdom, and described an inverse relationship between nominal wage growth and unemployment. This relationship was later confirmed using data from the United States and other countries and generalised to describe the relationship between unemployment and price inflation, with major contributions from Samuelson and Solow (1960). It is a core concept of New Keynesian macroeconomics, suggesting that lower unemployment can only be achieved through expansionary policies at the cost of higher inflation, and vice versa.

This concept, however, has been severely criticised by economists outside the New Keynesian school of thought. The criticism stems from both its theoretical shortcomings (as the original Phillips curve is not a structural relationship) and its failure in economic policy. Milton Friedman (1968) and Edmund Phelps (1967) introduced a concept in which expectations of future inflation affect current inflation. They proposed that the curve should take into account expected inflation, which replaced actual inflation in the Phillips curve relationship. This modification became widely accepted, emphasising that while a short-term relationship may exist, it depends on how inflation expectations evolve. The original long-term validity of the relationship was further undermined by the stagflation of the 1970s, when high inflation was accompanied by high unemployment. The instability of the Phillips curve over time and its sensitivity to macroeconomic policy raised a number of questions and motivated subsequent research.

The further development of macroeconomics towards the derivation of relationships from microfoundations led to the formulation of the New Keynesian Phillips curve (NKPC), which is derived from the assumptions of rational and forward-looking behaviour of firms combined with the assumption of sticky prices. The existence of nominal rigidities (modelled, for example, by menu costs, i.e. the cost of changing prices, Rotemberg, 1982, or by the assumption that only a fraction of firms can adjust prices in a given period, Calvo, 1983) implies that firms set their prices not only on the basis of current economic conditions (their marginal costs), but also on the basis of expected future prices.[1] Thus, current inflation depends not only on current real marginal costs, but also on expected future inflation. The dynamics of firms’ current and future expected marginal costs is therefore an important channel for determining inflation in New Keynesian models.

In current modelling practice, formulations of the New Keynesian Phillips curve that include not only future inflation, but also inflation from the previous period – sometimes referred to as the hybrid New Keynesian Phillips curve (HNKPC) – are widely used. The derivation of the HNKPC can be found, for example, in the model of Galí and Gertler (1999), which is an extension of the Calvo model, although the lagged inflation term can also be derived from Rotemberg’s “menu cost” model. The empirical popularity of the HNKPC lies mainly in its broader and more flexible form, which allows a better fit to the data. Modern formulations of the New Keynesian Phillips curve thus explain current inflation in terms of current marginal costs, past inflation and expected future inflation. However, real marginal costs are not directly observable in practice, so empirical studies often use the output gap or some other cyclical indicator as a proxy. The inclusion of past inflation as an explanatory variable for current inflation is consistent with the observed stickiness of inflation and the empirical evidence that firms form their expectations of future inflation by taking into account current or past inflation. If economic agents are not fully rational, past inflation can influence current inflation through the formation of expectations (Werning, 2022; Gáti, 2023). The importance of the backward-looking and forward-looking components of inflation can be assessed through a quantitative literature review – meta-regression analysis. Several such analyses, covering more than 250 empirical studies from different groups of countries, including the EU and the new Member States, have found that the relative importance of the forward-looking component in the Phillips curve is around two-thirds, while the remaining one-third is attributed to the backward-looking component (Carré, 2008; Carré, 2010; Fidrmuc and Danišková, 2020).

Flattening of the Phillips curve?

In the mid-1980s, an era known as the “Great Moderation” began, during which advanced economies experienced both low inflation and low unemployment. From the beginning of this century onwards, there was increasing discussion of a “flattening” of the Phillips curve. It appeared that changes in unemployment rates (or, more generally, the cyclical state of the real economy) were having less of an impact on inflation than in the past.

A number of studies have estimated the flattening of the Phillips curve, i.e. the reduced responsiveness of inflation to cyclical fluctuations in economic activity, and have offered various explanations for why this has happened. Factors such as globalisation, technological progress or changes in the labour market have often been identified: Del Negro et al. (2020), Ahn and Lee (2023) and Ratner and Sim (2022). Globalisation and technological progress have increased competition and efficiency, leading to more stable prices despite fluctuations in unemployment. In addition, globalisation increases the interconnectedness of price movements and, especially in small open economies, influences domestic inflation through import prices independently of the labour market situation. Among the changes in the labour market that may have led to a flattening of the Phillips curve is the decline in workers’ bargaining power that has been observed since the 1980s.

However, some studies have concluded that the flattening of the Phillips curve is the result of incorrect model specification, and that when appropriate variables and estimation methods are used, either the flattening does not occur

Bańbura and Bobeica (2023) highlight the importance of trend-adjusted inflation, while Jarociński and Lenza (2018) focus on the impact of how the output gap is measured. Both factors have a significant effect on the slope of the Phillips curve. It is also important to consider inflation expectations. Coibion and Gorodnichenko (2015) stress that when households’ inflation expectations are taken into account, there is no flattening. Including the variable of the degree of anchoring of inflation expectations in the model can achieve stability in the slope of the Phillips curve over time (Jorgensen and Lansing, 2024). In addition, the estimated slope of the Phillips curve and its statistical significance can be affected by the choice of price index (Rubbo, 2023). Using less volatile indices can provide robust estimates of the Phillips curve for the US, euro area countries and other economies (Rubbo, 2023; Ball and Mazumder, 2021; Andrle et al., 2016; Andrle et al., 2017). Hasenzagl et al. (2022) emphasise that, from a theoretical perspective, it is crucial to include trend inflation, derived from long-term expectations, in the model and to account for temporary fluctuations in energy prices in order to properly estimate the cyclical relationship between inflation and economic activity. The resulting Phillips curve is then steep and well identified. The choice of indicator of real activity also plays a key role. Gagliardone et al. (2023), using microdata from Belgian manufacturers over more than 20 years, directly construct firms’ real marginal costs and show that, when they are used, the Phillips curve is steep and shows a strong transmission of supply shocks to inflation.

…or the reported flattening is much smaller.

The empirically observed flattening of the curve can be partly explained by the fact that the model does not take into account the reduction in trend inflation, which simultaneously leads to a lower frequency of price and wage changes. This is misinterpreted as making the cyclical component of inflation less responsive to shocks (Costain et al., 2023). Moreover, the observed flattening of the curve is smaller when the model allows for time variability in long-term inflation expectations (Hazell et al., 2022). A complementary perspective is offered by non-linear models, which allow for a framework of two inflation regimes or two slopes of the Phillips curve – more on this below.

The Phillips curve “reawakens”: Non-linear relationship and sectoral heterogeneity

Discussions about the alleged flattening of the Phillips curve lasted practically until the end of the pandemic and the subsequent onset of the global energy crisis in 2021. With rising energy prices and increasing inflation, more and more studies are now concluding that the Phillips curve is back and has “reawakened”. Recently, more emphasis has been placed on non-linearity and the impact of heterogeneity across different sectors of the economy.

The latest empirical studies conclude that the Phillips curve began to steepen after the pandemic, even when using simpler specifications that had shown a “flatter” Phillips curve in the previous period. This is evident in the US and the EU, but also in 28 other OECD economies, including the Czech Republic, Hungary, Poland and Slovakia – see Inoue et al. (2024), Hobijn et al. (2023) and Baba et al. (2023). Moreover, recent studies point to an increasing importance of the backward-looking component of inflation, especially as inflation persistence increases, particularly in Central and Eastern European countries. Gudmundsson et al. (2024) show that not only has the Phillips curve become steeper in recent years, but it may also have shifted towards higher inflation at lower levels of economic activity. They attribute this development to factors such as supply chain disruptions, changes in labour market dynamics and monetary policy responses during and after the pandemic. It should be noted that empirically (and especially with shorter time series) it is difficult to distinguish shifts in the Phillips curve due to changes in demand from the effects of non-linearities or unanchored inflation expectations (Holub, 2024). Moreover, as Crump et al. (2024) point out, changes in the slope of the curve can often be attributed to a missing variable, such as the omission of time-varying inflation expectations (Hazell et al., 2022). Crump et al. (2024) suggest including expectations of the unemployment gap, which can also vary over time (see the last paragraph of Box A for more details).

The non-linearity observed in the Phillips curve, which is flat at low inflation and steeper at higher inflation, is explained by the model of Harding et al. (2022, 2023). The non-linearity is due to a kinked demand curve for goods produced by firms, meaning that when prices rise, consumers are more likely to reduce their purchases of higher-priced goods relative to lower-priced goods. This model better reflects observed economic realities and generates a stronger transmission of economic shocks (whether demand or supply shocks) during periods of higher inflation. The model suggests that central banks face a more pronounced dilemma between reducing inflation and stabilising output in a high inflation environment. Similarly, Ascari et al. (2023) present a model in which the Phillips curve is not significantly curved at inflation levels below a certain threshold (e.g. 4% in the US), but an inverse relationship between inflation and the output gap can be observed at higher inflation levels. However, unlike Harding et al. (2022, 2023), this model is based on the New Keynesian framework extended by a time-varying trend component of inflation.

The shift in the Phillips curve can be explained by fiscal policy, as shown by Hagedorn (2023). The mechanism involves the inclusion of nominal demand as a determinant of inflation alongside real marginal costs. This explains situations where inflation rises even with a small change in the unemployment rate, as changes in nominal demand can shift the Phillips curve to the right. Empirical evidence suggests that nominal demand has a significant impact on inflation, challenging traditional models based solely on real marginal costs. Furman (2022) and Hagedorn (2023) provide examples of fiscal stimuli or fiscal transfers that can shift the aggregate demand curve. In their empirical analysis, Jordà et al. (2022) include fiscal spending as a significant explanatory variable of the Phillips curve.

One type of non-linearity is related to the state of the labour market and the general economic situation. As shown by Benigno and Eggertsson (2023, 2024a,b), when unemployment is high, increased demand reduces unemployment with minimal inflation, whereas when unemployment is low, the economy is operating at full capacity and any increase in demand leads to significant inflation. This results in an inverted L-shaped Phillips curve, reflecting the different impact of economic conditions on inflation.

Cavallo et al. (2023) identify another source of non-linearity – the size of price shocks. Large shocks differ from small ones in that they propagate more quickly and prices react more flexibly. A prime example of large shocks are the energy shocks that led to double-digit inflation in Europe in 2022 and 2023. An increase in firms’ marginal costs, for example due to rising energy prices, can thus lead to a steeper Phillips curve. Expectations of a positive output gap can also contribute to a steeper Phillips curve (Atkinson and Mau, 2024). The mechanism here is that if the central bank is perceived to be pursuing a “run it hot” strategy, i.e. allowing the economy to operate above full capacity for some time, the expected output gap will also affect current inflation. Another factor that may contribute to the observed steepening of the Phillips curve is increased volatility, driven by significant shocks that cause greater fluctuations in inflation in both directions (Hall, 2023).

Another type of non-linearity is dependence on the sign and type of shocks. Asymmetry in the transmission of shocks is demonstrated by Hagedorn et al. (2024) and Blanco et al. (2024): expansionary shocks are more inflationary because the probability of price increases is higher than the probability of price decreases. L’Huillier and Phelan (2023) incorporate variable price stickiness that depends on the type of shock, such as demand versus supply shocks. In this framework, prices are sticky in response to demand shocks but flexible in response to supply shocks. The intuition is that firms can credibly justify raising prices in response to rising costs, whereas it is more difficult to do so when demand increases. As a result, supply shocks can be inflationary even with a flat Phillips curve. Studies also show that the Phillips curve is steeper during recessions, while this relationship is weaker during economic expansions (Pham and Sala, 2022; Forbes et al., 2021a,b). This implies that inflationary pressures are more sensitive to changes in unemployment during economic downturns than during expansions. Both studies also point to the increasing interconnectedness of so-called local and global (common) shocks across economies.

The impact of sectoral heterogeneity on the non-linear transmission of firm costs to the aggregate Phillips curve is demonstrated by Afrouzi et al. (2024) in a two-sector model. Using firm-level data from a small open economy (Sweden), Ahlander et al. (2023, 2024) show that the transmission of shocks to CPI inflation is almost immediate in the case of cost increases in the transport and food sectors, but slow in the automobile industry. Although different sectors are exposed to shocks to different degrees and play different roles in production chains, the subsequent changes in costs lead to non-linear changes in overall CPI inflation.

To sum up, current thinking involves extending the Phillips curve to include various types of non-linearities related to the state of the labour market and the economy in general, higher past inflation and the strength and persistence of shocks. It also emphasises the importance of accurately measuring unobservable variables, such as the output gap and the anchoring of inflation expectations, and the importance of changes in expectations over time. Another trend is the conceptualisation of the Phillips curve in the context of a multi-sector economy.

The importance of understanding non-linearities in the Phillips curve for monetary policy is highlighted by the agenda of the recent central bankers’ symposium in Jackson Hole (hosted by the Kansas City Fed)[2] and the speeches of Jerome H. Powell. Powell emphasised the anchoring of inflation expectations, the state of the labour market, the curvature of supply and demand, and unexpectedly large shocks as types of non-linearities that contributed to the recent wave of inflation. The symposium also included a presentation of the aforementioned paper by Benigno and Eggertsson (2024b).

Wage Phillips curve

Although the price-based Phillips curve dominates, the original concept of the Phillips curve, in which the main variable is wage inflation, still persists – see Box A.

Box A: The wage Phillips curve and its current use

The original wage Phillips curve, which describes the inverse relationship between the cyclical component of unemployment and nominal wage growth, remains a useful tool. One of its applications is to assess the risk of a wage-price spiral. This assessment can be made using different approaches. For example, it can be used to compare the joint dynamics of wages and prices using national or sectoral wage data and overall unemployment (Galí and Gambetti, 2019; Alvarez et al., 2022). Alternatively, a detailed regional perspective on the evolution of wages, prices and unemployment within a country can provide better insights into the causality between labour market conditions and wage inflation (Leduc and Wilson, 2017). Both approaches help to assess the joint dynamics of wage and price growth and serve to identify the onset of a wage-price spiral. National indicators (Galí and Gambetti, 2019) as well as regional data (e.g. city-level data in the US – Leduc and Wilson, 2017) suggest a flattening of the wage Phillips curve since around 2008–2009. It is worth noting that Leduc and Wilson (2017) expect the wage Phillips curve to steepen again in the coming years as the labour market recovers.

The debate about the stability of the wage Phillips curve over time essentially mirrors the discussion about the evolution of the price Phillips curve: a flattening since the beginning of this century, with signs of a steepening after the pandemic – see, for example, the empirical assessment of the wage Phillips curve in 18 advanced economies over the period 1870–2019 (Gabriel, 2023). Two main insights emerge from this analysis. First, the cyclical relationship between wage inflation and unemployment changes over time. Second, this relationship is weaker in a low-inflation environment and stronger when inflation is higher.

One of the mechanisms explaining this, presented by Blanchflower et al. (2024), focuses on the evolution of the wage Phillips curve in the US over the period 1980–2022. The authors find that the observed flattening is due to the fact that, since around 2008, the unemployment rate has lost its relevance as an indicator of labour market conditions that significantly influence wage dynamics. Instead, underemployment – defined as the share of part-time workers who would prefer to work more hours – and the inactivity rate have taken over as key factors. These factors have exerted downward pressure on US wages, particularly in recent years.

An alternative perspective is offered by Crump et al. (2024): the unemployment rate remains a useful indicator; after all, this measure has a long tradition of statistical study and allows for greater measurement precision than some newer indicators. However, it is essential to include expectations of the unemployment gap in the Phillips curve model, i.e. the difference between the actual unemployment rate and the equilibrium value that does not “accelerate inflation” – the NAIRU (non-accelerating inflation rate of unemployment). The NAIRU is unobservable and can be estimated using the wage Phillips curve. The overall conclusion is therefore that it is appropriate to assess the dynamics of prices and wages together, and that extending the model to include (changing) expectations of the unemployment gap can better explain both the rise in US inflation at the end of the pandemic and the subsequent fall in inflation in 2022 and 2023.

Conclusions

The Phillips curve remains a central pillar of economic analysis and policy and has survived in good health through periods of scepticism about its slope. Policymakers and academics are increasingly aware that the cyclical relationship between inflation and economic activity is non-linear and influenced by a wide range of factors. This concept continues to evolve and improve, with greater emphasis being placed on capturing the different types of non-linearities and factors that may affect this relationship. As such, the Phillips curve continues to play an important role as a framework for understanding the cyclical dynamics of inflation and economic activity.

What lies ahead? Directions for future research include considering inflation risks and uncertainty in the context of a new era of “high volatility”, where events such as pandemics and geopolitical and climate shocks pose new challenges for monetary policy (Schnabel, 2022). As leading monetary policymakers have pointed out, assessing the risks and costs of inflation is now an increasingly important issue (Lagarde, 2024; Powell, 2024).

The views expressed in this article are those of the authors and do not necessarily reflect the official position of the Czech National Bank. The author would like to thank Jan Brůha, Jakub Matějů and Petr Král for their valuable comments.

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[1] The intuition is as follows: unless it is certain that it will be possible to change prices in the future (Calvo’s model), or if it is costly to make large price changes (Rotemberg’s model), it is preferable to include part of the expected future price change in the current decision, i.e. in the current price increase

[2] https://www.cnb.cz/cs/o_cnb/cnblog/Zapisky-guvernera-z-konference-v-Jackson-Hole-2024, https://www.kansascityfed.org/research/jackson-hole-economic-symposium/jackson-hole-economic-policy-symposium-reassessing-the-effectiveness-and-transmission-of-monetary-policy/