Panel-data models with random effects can be fit with Stata's me commands for multilevel modeling. And the metobit command can fit panel-data tobit models to censored outcomes. For instance, if y is left-censored at 10, you could type
. metobit y x1 x2, ll(10) || id:
to fit a model with random intercepts by id. In fact, you could fit this model with the existing xttobit command.
What you cannot do with xttobit is allow the slopes to vary by id. With metobit, we include random slopes for x1 in addition to the random intercepts by typing
. metobit y x1 x2, ll(10) || id: x1
You can see Multilevel tobit models for more information on metobit and for an example with both random slopes and random intercepts.
You can also fit Bayesian panel-data (multilevel) tobit models using the bayes prefix.
Learn more about Stata's panel-data features.