Nonlinearities in the Phillips Curve in the Post-Pandemic Era: Threshold and Smooth-Transition Evidence from the US and Euro Area

The Phillips curve remains central to monetary policy, yet its functional form has been intensely debated following the 2021–2023 inflation surge. This paper offers novel empirical evidence by providing the first symmetric comparison of regime-dependent nonlinearities in the inflation–slack relationship between the United States and the Euro Area, using identical threshold and smooth-transition frameworks on quarterly data extending through 2025Q4, the most recent available. Core PCE inflation (US) and core HICP excluding energy, food, alcohol, and tobacco (Euro Area) are modeled as functions of unemployment and output gaps, with controls for oil shocks and inflation expectations. TAR/SETAR and LSTAR estimations uncover statistically significant steepening in tight labor-market regimes. In the US, the slope more than doubles when the unemployment gap falls below –0.61 percentage points. In the Euro Area, a comparable kink emerges near zero (–0.048 pp), with smoother transitions reflecting greater wage and price rigidities. Post-2019 subsamples exhibit amplified nonlinearity, consistent with supply-shock transmission in high-pressure conditions. Extensive robustness checks affirm these findings. The results establish a state-dependent sacrifice ratio, with sharply higher disinflation costs in tight regimes, and highlight substantial risks of monetary policy miscalibration in future high-pressure episodes.