The dose-response work of Callaway, Goodman-Bacon, and Pedro Sant’Anna seems to be coming along nicely. If you haven’t had enough of the parallel trends assumption, get ready for the “strong” parallel trends assumption!
“𝘐𝘯 𝘵𝘩𝘪𝘴 𝘱𝘢𝘱𝘦𝘳, 𝘸𝘦 𝘥𝘪𝘴𝘤𝘶𝘴𝘴 𝘢𝘯 𝘢𝘭𝘵𝘦𝘳𝘯𝘢𝘵𝘪𝘷𝘦 𝘣𝘶𝘵 𝘵𝘺𝘱𝘪𝘤𝘢𝘭𝘭𝘺 𝘴𝘵𝘳𝘰𝘯𝘨𝘦𝘳 𝘢𝘴𝘴𝘶𝘮𝘱𝘵𝘪𝘰𝘯, 𝘸𝘩𝘪𝘤𝘩 𝘸𝘦 𝘤𝘢𝘭𝘭 𝘴𝘵𝘳𝘰𝘯𝘨 𝘱𝘢𝘳𝘢𝘭𝘭𝘦𝘭 𝘵𝘳𝘦𝘯𝘥𝘴. 𝘚𝘵𝘳𝘰𝘯𝘨 𝘱𝘢𝘳𝘢𝘭𝘭𝘦𝘭 𝘵𝘳𝘦𝘯𝘥𝘴 𝘰𝘧𝘵𝘦𝘯 𝘳𝘦𝘴𝘵𝘳𝘪𝘤𝘵𝘴 𝘵𝘳𝘦𝘢𝘵𝘮𝘦𝘯𝘵 𝘦𝘧𝘧𝘦𝘤𝘵 𝘩𝘦𝘵𝘦𝘳𝘰𝘨𝘦𝘯𝘦𝘪𝘵𝘺 𝘢𝘯𝘥 𝘫𝘶𝘴𝘵𝘪𝘧𝘪𝘦𝘴 𝘤𝘰𝘮𝘱𝘢𝘳𝘪𝘯𝘨 𝘥𝘰𝘴𝘦 𝘨𝘳𝘰𝘶𝘱𝘴. 𝘐𝘯𝘵𝘶𝘪𝘵𝘪𝘷𝘦𝘭𝘺, 𝘵𝘰 𝘣𝘦 𝘢 𝘨𝘰𝘰𝘥 𝘤𝘰𝘶𝘯𝘵𝘦𝘳𝘧𝘢𝘤𝘵𝘶𝘢𝘭, 𝘭𝘰𝘸𝘦𝘳-𝘥𝘰𝘴𝘦 𝘶𝘯𝘪𝘵𝘴 𝘮𝘶𝘴𝘵 𝘳𝘦𝘧𝘭𝘦𝘤𝘵 𝘩𝘰𝘸 𝘩𝘪𝘨𝘩𝘦𝘳-𝘥𝘰𝘴𝘦 𝘶𝘯𝘪𝘵𝘴’ 𝘰𝘶𝘵𝘤𝘰𝘮𝘦𝘴 𝘸𝘰𝘶𝘭𝘥 𝘩𝘢𝘷𝘦 𝘤𝘩𝘢𝘯𝘨𝘦𝘥 𝘸𝘪𝘵𝘩𝘰𝘶𝘵 𝘵𝘳𝘦𝘢𝘵𝘮𝘦𝘯𝘵 𝘢𝘯𝘥 𝘢𝘵 𝘵𝘩𝘦 𝘭𝘰𝘸𝘦𝘳 𝘭𝘦𝘷𝘦𝘭 𝘰𝘧 𝘵𝘩𝘦 𝘵𝘳𝘦𝘢𝘵𝘮𝘦𝘯𝘵. 𝘞𝘦 𝘴𝘩𝘰𝘸 𝘵𝘩𝘢𝘵 𝘸𝘩𝘦𝘯 𝘰𝘯𝘦 𝘰𝘯𝘭𝘺 𝘪𝘮𝘱𝘰𝘴𝘦𝘴 𝘵𝘩𝘦 “𝘴𝘵𝘢𝘯𝘥𝘢𝘳𝘥” 𝘱𝘢𝘳𝘢𝘭𝘭𝘦𝘭 𝘵𝘳𝘦𝘯𝘥𝘴 𝘢𝘴𝘴𝘶𝘮𝘱𝘵𝘪𝘰𝘯, 𝘤𝘰𝘮𝘱𝘢𝘳𝘪𝘴𝘰𝘯𝘴 𝘢𝘤𝘳𝘰𝘴𝘴 𝘵𝘳𝘦𝘢𝘵𝘮𝘦𝘯𝘵 𝘥𝘰𝘴𝘢𝘨𝘦𝘴 𝘢𝘳𝘦 “𝘤𝘰𝘯𝘵𝘢𝘮𝘪𝘯𝘢𝘵𝘦𝘥” 𝘸𝘪𝘵𝘩 𝘴𝘦𝘭𝘦𝘤𝘵𝘪𝘰𝘯 𝘣𝘪𝘢𝘴 𝘳𝘦𝘭𝘢𝘵𝘦𝘥 𝘵𝘰 𝘵𝘳𝘦𝘢𝘵𝘮𝘦𝘯𝘵 𝘦𝘧𝘧𝘦𝘤𝘵 𝘩𝘦𝘵𝘦𝘳𝘰𝘨𝘦𝘯𝘦𝘪𝘵𝘺. 𝘛𝘩𝘶𝘴, 𝘸𝘪𝘵𝘩𝘰𝘶𝘵 𝘢𝘥𝘥𝘪𝘵𝘪𝘰𝘯𝘢𝘭 𝘴𝘵𝘳𝘶𝘤𝘵𝘶𝘳𝘦, 𝘤𝘰𝘮𝘱𝘢𝘳𝘪𝘴𝘰𝘯 𝘢𝘤𝘳𝘰𝘴𝘴 𝘥𝘰𝘴𝘢𝘨𝘦𝘴 𝘮𝘢𝘺 𝘯𝘰𝘵 𝘪𝘥𝘦𝘯𝘵𝘪𝘧𝘺 𝘤𝘢𝘶𝘴𝘢𝘭 𝘦𝘧𝘧𝘦𝘤𝘵𝘴. 𝘛𝘩𝘦 𝘱𝘭𝘢𝘶𝘴𝘪𝘣𝘪𝘭𝘪𝘵𝘺 𝘰𝘧 𝘴𝘵𝘳𝘰𝘯𝘨 𝘱𝘢𝘳𝘢𝘭𝘭𝘦𝘭 𝘵𝘳𝘦𝘯𝘥𝘴 𝘥𝘦𝘱𝘦𝘯𝘥𝘴 𝘰𝘯 𝘵𝘩𝘦 𝘦𝘮𝘱𝘪𝘳𝘪𝘤𝘢𝘭 𝘤𝘰𝘯𝘵𝘦𝘹𝘵 𝘰𝘧 𝘵𝘩𝘦 𝘢𝘯𝘢𝘭𝘺𝘴𝘪𝘴, 𝘢𝘯𝘥 𝘸𝘦 𝘥𝘪𝘴𝘤𝘶𝘴𝘴 𝘴𝘰𝘮𝘦 𝘧𝘢𝘭𝘴𝘪𝘧𝘪𝘤𝘢𝘵𝘪𝘰𝘯 𝘴𝘵𝘳𝘢𝘵𝘦𝘨𝘪𝘦𝘴 𝘵𝘩𝘢𝘵 𝘤𝘢𝘯 𝘣𝘦 𝘶𝘴𝘦𝘥 𝘵𝘰 𝘢𝘴𝘴𝘦𝘴𝘴 𝘪𝘵.”