Panel: Logit/Probit/Tobit + lagged dep. Var + Fixed Effects

[kbielste]

Hello,

1. LOGIT AND PROBIT MODEL

Basic Facts of my model:
- Binary dependent Variable
- Panel Data (time and sector)
- 41 Periods - 74 Companies - 3 sectors
- Unbalanced sample
- 1744 Observations
- lagged dependent Variables (2 Periods)
- 4 other independet variables (one is a Dummy)

What I did:
I created Dummies for all periods (except one) and all sectors (except one): Included fixed effects
I included a constant
I included the lagged Variables
I included the independet Variables
I estimated with the probit and the logit model. Both give simelar results.
I estimated without the fixed effects. Simelar results

I know because I use Panel Data that my estimates may be biased the way I estimated them.
That is why I would like to estimate a random effects probit model and a conditional fixed effects logit model, but both are not included.

Is there an easy way to estimate them myself?
Or can i say that T=41 Periods is big enough for both models (logit and probit) not to be biased?

Is it an additional problem that i use a lagged dependent variable aswell? What can I do to avoid additional problems?
Can I also argument that this is not a problem because T041 is large?


2. TOBIT MODEL
The dependent Variable is left censored at zero.
I have exactly the same questions conserning the Tobit model.


3. LINEAR MODEL
In a normal linear model, including fixed effects/random effects is no problem.
But with a lagged dependent Variable it may be biased.
What can I do to avoid that? Maybe use Instruments for the lagged dependent Variableß (for example the errors?)
Should I do the same in the Tobit/Probit/Logit model?
Is the Argumentation of a large T solving the bias here valid?


I hope I'm in the correct part of the forum and I apologize for my English.

I would be very thankful if you could help me.

Kind regards