Hi all,

I’m working through the paper “Inflation as a fiscal limit” by Francesco Bianchi and Leonardo Melosi (available at: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4205158). In footnote 2 on page 9, they note that \hat{x} indicates a variable which is log-linearized, while \tilde{x} indicates a variable which is in linear deviations. Linear deviations are used for variables which are normalized with respect to GDP (debt, expenditure, and taxes). It’s not clear to me how exactly to specify the observation equations for these normalized variables - is the data in log-levels or levels?

Thanks