Inflation and unemployment rate were largely disconnected between 2000 and 2019 in advanced economies. We decompose core inflation into two parts based on the cyclical sensitivity of CPI components and document several salient facts: (i) both the cyclical and non-cyclical parts had surges across advaced economies in 2011, when unemployment rates had limited changes; (ii) the non-cyclical part had a downward trend between 2012 and 2019, which existed across countries, sectors, goods, and services; (iii) global indexes such as oil price, shipping costs, and a global supply chain pressure index do not explain the downward trend; and (iv) the cyclical part, after controlling for the impact of economic slack, also had a downward trend between 2012 and 2019. These patterns help disentangle competing explanations for the disconnect between inflation and unemployment rate. The approach has potential to help understand forces shaping price pressures during the pandemic and in the post-pandemic period ahead.