My first and only introduction to this class of agents was Campbell and Mankiw and Phillipe Weil’s paper. I haven’t followed the literature since then - assumption of hand-to-mouth consumption was in some ways frowned upon back when I was in graduate school since it lacked ‘microfoundations’. Likewise, habit persistence was introduced via Constantinedes in an econometrics class and then forgotten.
There was little resolution at the time what the fraction of hand-to-mouth-consumers was - Cambell and Mankiw assumed 50%. Yet the low saving rate would imply naively that most (if not all) consumers are hand to mouth. Coupled with the story on how even 1 percenters are hand-to-mouth and even the Federal Reserve Bank of St. Louis president is a hand-to-mouth consumer this proportion might even be close to the truth. This is the point made by Kaplan and Violante in their paper on the effects of the fiscal stimulus.
Habit persistence then implies that bubbles also have real effects via consumption. In particular, all agents view bubbles in a rational manner (i.e. assumes that bubbles cause a permanent rise in permanent income) and adjust their consumption accordingly by consuming entirely out of their income. If a large part of the rise in perceived permanent income is spent on durable consumption - e.g. houses, tuition for private schools, etc. then bubbles are inefficient in that consumers spend ‘too much’.