Ask help for xttobit model with fixed effect.

[Zachary Jiang]

Stata cannot execute fixed effect panel tobit model of course, but what if I doubt the result of random effect xttobit? After all, the assumption of random effect is too strong to always hold. Here is my thought to manually execute fixed effect panel tobit:
First, manually demean the dependent variable and all independent variables involved in the regression. The principle is the same as common panel fixed effect model, that is, subtracting the time-averaged x_i from x_it;
Then, run the pooled tobit regression model using tobit command.
However, it turns out that the censored limit will be changed after doing this. For example, initially the lower limit of the panel tobit model is 0 (or left censored at 0), which mean 0 is the minimum value of the dependent variable. After demeaning, however, there may be some values smaller than 0 being produced. Thought there is still a spike at 0, 0 won't be the lower limit any longer.
Under this circumstance, what model should I use to estimate? Or is it impossible to estimate panel tobit model with fixed effect because it doesnt have a sufficient statistic? Then how can we make sure the result of random effect panel tobit is stable and reliable?
Great thank to any help!

[Jeff Wooldridge]

Time demeaning followed by Tobit is not a justified strategy. You can try the correlated random effects approach instead: add the time averages of the time-varying explanatory variables. I’d use pooled Tobit and cluster the standard errors.

[Zachary Jiang]

Time demeaning followed by Tobit is not a justified strategy. You can try the correlated random effects approach instead: add the time averages of the time-varying explanatory variables. I’d use pooled Tobit and cluster the standard errors.

Just to clarify, you mean that besides the current explanatory variables, we can additionally add time averages of time varying regressors to the model then execute the pooled tobit with censored limit unchanged? This idea is interesting, and I carefully read the section of Correlated Random Effect, Chapter 14, Wooldridge, but still have a question:
why would we use pooled tobit instead of random effect panel tobit to estimate after the addition of time-averaged regressors? Since in Wooldridge Chapter 14, it always uses random effect to estimate in CRE approach (although the estimators are identical to FE).
Best luck to you professor!

[Jeff Wooldridge]

Zachary: After including the time averages -- to model the CREs -- you can use a pooled Tobit or a joint MLE. The latter is less robus because consistency requires no serial correlation in the time-varying errors. And the usual MLE standard errors are misleading because of serial correlation, too. I have a preference for the pooled method with clustered standard errors. See my 2010 MIT Press book, Chapter 17.

In the linear case, the pooled OLS and RE estimates are identical, and equal to the FE estimates on the time-varying variables. It's something I always remember about how one can think of CRE as trying to approximate a "fixed effects" approach for Tobit.

Make sure you compute the APEs to get magnitudes of effects! The details differ a bit by whether you use pooled Tobit or xttobit.

JW

[Zachary Jiang]

Zachary: After including the time averages -- to model the CREs -- you can use a pooled Tobit or a joint MLE. The latter is less robus because consistency requires no serial correlation in the time-varying errors. And the usual MLE standard errors are misleading because of serial correlation, too. I have a preference for the pooled method with clustered standard errors. See my 2010 MIT Press book, Chapter 17.

In the linear case, the pooled OLS and RE estimates are identical, and equal to the FE estimates on the time-varying variables. It's something I always remember about how one can think of CRE as trying to approximate a "fixed effects" approach for Tobit.

Make sure you compute the APEs to get magnitudes of effects! The details differ a bit by whether you use pooled Tobit or xttobit.

JW

Great thank to you! It does help a lot. Have a nice day!

[Duong Le]

Zachary: After including the time averages -- to model the CREs -- you can use a pooled Tobit or a joint MLE. The latter is less robus because consistency requires no serial correlation in the time-varying errors. And the usual MLE standard errors are misleading because of serial correlation, too. I have a preference for the pooled method with clustered standard errors. See my 2010 MIT Press book, Chapter 17.

In the linear case, the pooled OLS and RE estimates are identical, and equal to the FE estimates on the time-varying variables. It's something I always remember about how one can think of CRE as trying to approximate a "fixed effects" approach for Tobit.

Make sure you compute the APEs to get magnitudes of effects! The details differ a bit by whether you use pooled Tobit or xttobit.

JW

Dear Professor Jeff Wooldridge,

I have a question on treatment and control groups and would like to seek your suggestions. I am sorry for transferring you to a different topic but I am very happy if you have time and can take a quick look at this thread: https://www.statalist.org/forums/for...-groups-in-did

Thank you.