Handling large percentage of zero-valued observations in the dependent variable in a panel dataset

I am writing a paper using a panel dataset in which my depepent variable has an large percentage amount of zero values observations. Those zero values are real zeros, I mean they are not missing data or whatsoever. I have taken a look on the literature and there are many models that can be applied in this case. I am awared of the following: Tobit (Tobin, 1958), Two-Stage Model (Heckman, 1979), Two-Parts Model (Duan et al.,1984), PPML (Silva & Tenreyro, 2006) and Double-Hurdle models (Dong & Kaiser, 2008). Which one should I use and how to justify the adoption?