This paper re‐examines the stationarity of inflation rates in 19 Organisation for Economic Cooperation and Development countries with the use of cross‐sectional information. We employ the panel unit‐root tests that allow for cross‐sectional dependency and the covariate point optimal test. These tests have high power in common due to the exploitation of cross‐sectional information, and they can assist mutually to draw a concrete conclusion on inflation dynamics for all series in the panel. Our empirical results show that allowing for cross‐sectional dependency rejects the null hypothesis that all series in the panel have a unit root, implying that there is at least one stationary series in the panel. With the help of the results of the covariate test, we can distinguish the panel into a group of stationary and a group of non‐stationary series. For robustness, the two groups of series are re‐confirmed by the panel tests. Our results reveal evidence of mean reversion in inflation for 15 of 19 countries, which is significantly stronger as compared to that obtained by the state‐of‐the‐art univariate unit‐root tests.