Tomohiro Hirano and Alexis Akira Toda (2025) (henceforth HT) provide a comment paper on our article on bubbles (Miao and Wang 2018) (henceforth MW). In their paper, the authors prove the \textquotedblleft nonexistence\textquotedblright\ of \textquotedblleft rational bubbles\textquotedblright\ in the MW model based on the traditional definition of \textquotedblleft rational bubble\textquotedblright. They also aim to clarify the precise mathematical definition and the economic meaning of \textq...
