Dear Statalisters,

My panel data set contains T=6 observations for N=145 different countries (balanced data set).
The dependent variable in my model, omedalshare, is a corner solution response variable, where the corner is at zero. I am interested in estimating a dynamic Tobit model. In Stata I tried the following:
Code:
tobit omedalshare olag1 lngdp lnpop polity host $yeardummies, ll(0) vce(cluster id)
Array

where olag1 is the lagged dependent variable; lngdp, lnpop, and polity are continuous covariates; host is a dummy variable; y2-y6 are year dummy variables (y1 is excluded from the model), and id identifies the 145 countries.

My concern is that the model may suffer from an endogeneity bias by a correlation between the lagged dependent variable and the error term. If I understand the theory correctly, in a linear setting we could use GMM with the instruments as proposed by, e.g., Arellano & Bond. These instruments can, however, not be used for the Tobit model since it is a non-linear model. Does there exist a way to work around this potential endogeneity problem or do 'better' estimation methods exist in Stata? Or is the estimated model as shown above OK to work with? Any help/advice is highly appreciated.