Panel fixed effect model with a bulk of zero in dependent variables

[Nadim Uddin]

I am now working on how migration affects the left behind family members' time allocation. My independent variable is dummy migration status while dependent variable is total time spent in off farm or farm or domestic activities. My data is panel data and I want to run a panel fixed effect model for each activity. However, a fraction of my dependent variable is zero and rest fraction is continuous. For a cross sectional data, Tobit model can fit best given the nature of data. In panel data I haven't seen any stata package which can estimate fixed effect Tobit regression. I am thinking I want to run three model for each activity---first unconditional effect where I use full sample, second: conditional effect where I drop the sample which are zero, only count the time hours which is continuous. Third, a fixed effect logit model where 0 value consider as 0 and continuous value is 1. Which one literature support? Any literature and suggestion?

[Maxence Morlet]

I would go for the user written command ppmlhdfe.

If the non-missingness in your dependent variable is non-random, then a two-step Heckman model would be appropriate.

See also Wooldridge (1995) regarding selection on fixed effects.

Is your panel balanced?

In any case, Wooldridge (2021) is also an essential read.

All the best!
Maxence

[Nadim Uddin]

My panel is unbalanced and my variable of interest is endogenous.

[Maxence Morlet]

So if it is still endogenous conditional on the fixed effects and the controls, then I recommend an IV strategy. Is the unbalancedness endogenous as well? i.e. is attrition from your sample and entry into your sample non-random and based on time-varying unobservable characteristics? You should perform a BGLW test (1986) for attrition.