In this note, we review three recent papers: Core Strength: International Evidence on the Impact of Energy Prices on Core Inflation by Gertjan Vlieghe (LSE, former BoE MPC member, and upcoming Vice Chairman at Millenium), Expectations and the Final Mile of Disinflation by Richard K. Crump (NY Fed), Stefano Eusepi (UT Austin), and Aysegul Sahin (UT Austin), and Has the Phillips Curve Flattened? by Atsushi Inoue (Vanderbilt University), Barbara Rossi (Pompeu Fabra), and Yiru Wang (Pittsburgh University).
The first paper shows that core and services inflation respond to energy price shocks and proposes to adjust these measures for the predicted effects of energy prices to obtain a more accurate measure of underlying inflation similar to pi*. The second paper studies the unemployment-inflation trade-off using a New Keynesian Phillips curve and provides model-based forecasts of U.S. inflation showing that it is expected to remain above the 2% target by the end of 2025. Finally, the third paper studies the slope of the Phillips curve using a novel econometric technique that allows for time-varying parameters while identifying the slope with an instrumental variable approach. The evidence confirms previous findings of a flattening of the Phillips curve but points to a recent steepening following the Covid shock.
Paper #1: Vlieghe (2024)
The paper Core Strength: International Evidence on the Impact of Energy Prices on Core Inflation by Gertjan Vlieghe (Vice Chairman at Millenium) studies the relation between energy price inflation and measures of underlying inflation pressures. The author shows that core and services inflation respond to energy price shocks and proposes to adjust these measures for the predicted effects of energy price increases to obtain a more accurate measure of underlying inflation.
What the paper does
What are the effects of energy prices on core inflation? The paper exploits cross-country variation in energy prices to answer this question. Country-level energy prices are measured by the energy-specific component of the consumer price index. Energy price inflation can vary across countries because of different exposures to shocks or because of different policy responses. For example, several countries implemented energy price caps after Covid. As a result, cumulative post-pandemic energy inflation in OECD countries ranges from 0% (Malta) to over 60% (Estonia).
Main results
Countries with higher energy price inflation have higher core inflation. Figure 1 shows this relation. A regression of core inflation on energy inflation has a coefficient of 0.2. Energy price inflation and pre-pandemic core inflation jointly explain half of the cross-country variation in post-pandemic core inflation. Restricting the analysis to the euro area countries confirms the results while ruling out monetary policy as a driver of cross-country differences.
Energy price increases are followed by an increase in core and services inflation. Local projection estimates show that a one percentage point increase in energy price inflation is associated with an increase in energy/services inflation of 0.2-0.3 percentage points at the peak, which occurs around 18 months after the impact.
Figure 1. Vlieghe’s (2024) comparison of energy inflation and core inflation across countries.
A critique of the paper
The paper nicely addresses the stark cross-country differences in energy price inflation and uses them to relate to differences in core inflation. While the literature has previously acknowledged that core inflation is not immune to changes in energy prices, the cross-country heterogeneity in energy price inflation after the pandemic is quite new. Because the paper uses country-specific energy price increases instead of oil prices, it can sparsely capture the effect of gas price increases as well.
The paper makes a clear point and is careful to draw the line for the interpretability of its results. A more detailed analysis could provide further useful insights. For example, the causal identification could be tightened and potentially exploit differences in country exposure to a joint energy shock to rule out other reasons for variation. A key concern is that core inflation increases because of labour market pressures or inflation expectations that have been affected by energy prices. Such variation should arguably be classed as underlying pressures. The paper also leaves open if there is cross-country heterogeneity in the sensitivity of core inflation to energy prices and which factors determine this heterogeneity. Do the monetary policy response or the structure of the production network cause differences in the pass-through?
Policy implications
Core inflation is not pi* but core net of the energy passthrough can be a useful approximation. Ideally, one would like to estimate the rate of inflation that will prevail once transitory shocks (such as energy prices) will dissipate. In other words, the true policy goal should be pi* (underlying inflation). Having said that, the estimation of pi* is not easy (indeed, we started an entire business upon this idea..). The lesson from Vlieghe (2024) is that adjusting core inflation for the predicted effect of energy shocks is a viable workaround solution.
Paper #2: Crump et al. (2024)
A recent article (Expectations and the Final Mile of Disinflation) by Richard K. Crump (NY Fed), Stefano Eusepi (UT Austin), and Aysegul Sahin (UT Austin) studies the unemployment-inflation trade-off using a New Keynesian Phillips curve. The authors provide model-based forecasts of U.S. inflation: Inflation is expected to remain above the 2% target by the end of 2025.
What the paper does
The authors employ a New Keynesian Phillips curve (NKPC). The NKPC includes a long-run trend inflation, the current unemployment gap, the expected future unemployment gap, and some supply shocks. The authors define the part of inflation not driven by supply shocks as underlying inflation, which is their object of interest.
Main results
Most of the rise in inflation is explained by supply shocks, but going forward, most of the disinflation is expected to be due to increasing unemployment. The authors first show the contribution of underlying inflation to observed inflation rates over recent years. Underlying inflation peaked at four percent, compared to a peak of over nine percent for headline inflation in the United States. The model attributes the gap to supply shocks. Since then, supply shocks have mostly abated. Out-of-sample forecasts of the model project a decline of inflation rates, see Figure 2 (black, blue and gold lines in left panel). Inflation is expected to reach 2.5% by the end of 2025 in the baseline scenario (black line; left panel). This is due to a projected increase of the unemployment rate to around 5% (black line; right panel). Depending on the path for the unemployment rate, inflation may reach its long-run trend or alternatively stay above 2.5%. The estimation uncertainty associated with these forecasts (grey shaded area) suggests that inflation could range from 1.75% to 3.25% by 2025.
Figure 2: Main result of Crump et al. (2024)
A critique of the paper
Expectations are central in modern macroeconomics, and the paper nicely uses this insight to update the traditional Phillips curve. The article offers one explanation for the failure of the traditional Phillips curve to reliably capture the inflation-unemployment tradeoff. The authors’ model estimates suggest that their Phillips curve specification reliably captures the inflation-unemployment relationship, with little variation in coefficients over time. The specification allows for a useful interpretation of the current disinflation despite tight labor markets: expected increases in future unemployment are already reflected in prices today.
However, the common criticism to the Phillips curve applies. Many papers show that the inflation-unemployment relation is unstable over time and the academic literature disagrees on the correct approach to estimate its slope. The estimation of this paper therefore needs to be viewed as one of many contributions to a crowded field.
Policy implications
Careful in declaring victory. The current labor market environment constitutes a tug of war between the prevailing labor market tightness and expectations of rising unemployment in the future. Central bankers need to evaluate carefully which force has the upper hand. In any case, the authors’ Phillips curve specification suggests that – absent favorable shocks – disinflation is not possible without an increase in the unemployment rate to above 5%. A very tricky spot for the Fed.
Paper #3: Inoue et al. (2024)
The paper Has the Phillips Curve Flattened? by Atsushi Inoue (Vanderbilt University), Barbara Rossi (Pompeu Fabra), and Yiru Wang (Pittsburgh University) studies the slope of the Phillips curve using a novel econometric technique that allows for time-varying parameters while identifying the slope with an instrumental variable approach. The evidence confirms previous findings of a flattening of the Phillips curve but points to a recent steepening following the Covid shock.
What the paper does
The authors propose a novel way to estimate the slope of the Phillips curve. A standard challenge in measuring the slope of the Phillips curve is endogeneity since inflation and unemployment are jointly determined in equilibrium. Their approach uses instrumental variables to address endogeneity concerns while allowing for time-varying parameters in the Phillips curve relation and the first-stage IV regression. The approach is also robust to weak instruments.
Main results
The Phillips curve has flattened between the 1970s and 1990s. Figure 3 shows the slope estimate for the time-varying parameter model (red solid line) and for a constant-parameter model (black line). The slope of the Phillips curve has clearly flattened over time and was not significantly different from zero in 2007. Formal tests of parameter instability reject the constant parameter model. The authors also extend the model to the Covid period and find evidence of a recent steepening of the slope to values last seen in the late 1970s.
The paper contains several additional insights. It shows that the importance of inflation expectations for current inflation has increased over time, while lagged inflation has become less relevant. The authors also estimate a time-varying Phillips multiplier, which indicates to which extent a monetary shock decreases inflation by raising unemployment. This measure provides a direct assessment of the unemployment-inflation trade-off faced by policymakers. The Phillips multiplier has decreased alongside the flattening of the Phillips curve but has remained stable at a low level since the 1990s.
Figure 3. Main result of Inoue et al. (2024). Dashed lines indicate 90% confidence intervals.
A critique of the paper
The main contribution of this paper is on the methodological front. The authors provide a new technique that jointly addresses three big issues in the literature: endogeneity, weak instruments, and parameter instability. The fact that their approach confirms previous findings is encouraging and usefully supports the interpretation of changes in the Phillips curve’s slope over time.
The instrumental variable approach relies on finding a good instrument. The authors’ methodology allows for an econometrically clean measurement of the slope of the Phillips curve, but the practical challenge is finding the right instrument. The authors argue that predetermined variables can be used but concede that this does not solve the endogeneity problem under serial correlation in the error term of the Phillips curve expression. Using aggregate demand shocks for identification indicates a much steeper Phillips curve than their main approach (average slope of -0.45 instead of -0.06) while the evidence for a flattening is still similar.
The parameters change over time following a Gaussian random walk. This specification does not allow for sudden strong changes in parameter values. This may be relevant for times of large disturbance to the economy, such as during the Covid period. Estimating the model on the whole sample period using the author’s method may falsely indicate a smooth steepening in the Phillips curve slope starting before the pandemic, while the slope change may have occurred only suddenly.
Policy implications
The paper provides two key takeaways for central bankers: 1) the secular flattening of the Phillips curve has been followed by a recent steepening, and 2) the Phillips multiplier is generally estimated to be weak. Monetary policy may need to face strong real costs in order to bring inflation back to target. The main qualification to these insights is the wide range of point estimates for the slope. While the evidence for a historical flattening is robust, the exact slope of the Phillips curve is only estimated with wide confidence intervals and can vary dramatically across different regression specifications. More generally, central banks will want to understand better which factors determine the slope of the Phillips curve. For example, if structural changes in the labor market suggest a decoupling of the unemployment rate from the output gap (e.g. due to a rise in short-term work), then the evaluation of the real cost required to achieve disinflation may need to shift to other measures.