“…These two series have been shown to be useful signals of the MTT in CPI inflation. 2 For this reason, these and other similar measures have been gaining traction and are increasingly used in empirical studies, not only in the forecasting context (e.g., Smith, 2004 Schoenle and Smith 2023) but also in many other contexts as well, including: establishing and testing the robustness of stylized inflation facts (Bryan and Cecchetti, 1999;Verbrugge, 1999;Fang, Miller and Yeh, 2010); understanding inflation uncertainty (Metiu and Prieto, 2023); discriminating between models of price adjustment (Ashley and Ye, 2012); locating a stable Phillips curve (Ball and Mazumder, 2011;Stock and Watson, 2020;Ashley and Verbrugge, 2023); studying the effects of oil supply shocks (Kilian, 2008); understanding inflation expectations and their relationship to inflation (Verbrugge and Zaman, 2021); and understanding post-Great Recession and post-COVID inflation dynamics (Ball and Mazumder, 2011;Mazumder, 2018;Ball et al, 2021; Ball, Leigh, and Mishra 2022; Verbrugge and Zaman 2023b; Cotton et al, 2023). They have also been suggested as a superior measure for monetary policy targeting and communication (Cecchetti and Groshen, 2001; Dolmas and Koenig, 2019; Verbrugge, 2022).…”