This paper proposes a model of the divine coincidence, explaining its recent appearance in US data. The divine coincidence matters because it helps explain the behavior of inflation after the pandemic, and it guarantees that the full-employment and price-stability mandates of the Federal Reserve coincide. In the model, a Phillips curve relating unemployment to inflation arises from Moen’s (1997) directed search. The Phillips curve is nonvertical thanks to Rotemberg’s (1982) price-adjustment costs. The model’s Phillips curve guarantees that the rate of inflation is on target whenever the rate of unemployment is efficient, generating the divine coincidence. If we assume that wage decreases—which reduce workers’ morale—are more costly to producers than price increases—which upset customers—the Phillips curve also displays a kink at the point of divine coincidence.

Figure 1A: Divine coincidence in aggregate US data, 2008–2022 (Benigno, Eggertsson 2023)

Figure 1B: Divine coincidence in metropolitan US data, 2001–2022 (Gitti 2023)


Michaillat, Pascal, and Emmanuel Saez. 2024. “Moen Meets Rotemberg: An Earthly Model of the Divine Coincidence.” arXiv:2401.12475v1. https://doi.org/10.48550/arXiv.2401.12475 .

author = {Pascal Michaillat and Emmanuel Saez},
year = {2024},
title = {Moen Meets Rotemberg: An Earthly Model of the Divine Coincidence},
number = {arXiv:2401.12475v1},
url = {https://doi.org/10.48550/arXiv.2401.12475}}