Tobit predict clarification

[danny klinenberg]

Hello all,

Thanks for taking my question. This is my first time posting so I apologize if my formatting is less than amazing.

I am having a technical issue with the `predict` command and Tobit.

Suppose I run the following regression with censored at 0 variable y and explanatory variable x:

tobit y x, ll(0) vce(robust)
predict y_hat, ystar(0,.)
predict y_error, stdp

y_error should be the standard error of the linear prediction (aka latent variable) based on the Tobit post-estimation document. Is it possible to get the standard error for the censored prediction? This would be line 2 in my example code

Thanks!

[Fei Wang]

Danny, I don't know the answer to your question. But if what you're interested in is the standard error of the average prediction rather than the standard error of the prediction from a single observation, the code below may help.

margins, predict(ystar(0,.))

[danny klinenberg]

Thank you for the reply Fei! I think the issue will still persist in estimating the confidence intervals for the average prediction, yes?

[Fei Wang]

Danny, the code in #2 does calculate and return the 95% CI for the average prediction.

[danny klinenberg]

Thanks Fei. I'm reading the documentation and I think it says

margins, predict(ystar(0,.)) at(x=(1(1)10))

provides the predicted average value for the censored variable when x={1,2,3,..,9,10}. Is that correct? I've only used margins for average marginal effects and such. I didn't know it was so powerful!

Thanks again for all your help!

[Fei Wang]

provides the predicted average value for the censored variable when x={1,2,3,..,9,10}. Is that correct?

Yes Danny, it's correct. Actually we may flexibly use the at() option to predict the censored outcome for individuals with particular characteristics -- similar to your goal in #1.

[danny klinenberg]

Fei Wang: This is the greatest of news! Thank you for your help.

[Jeff Wooldridge]

A bit of a non-sequitur, but I've always had a nit to pick about Stata's terminology here. Every modern (and not so modern) source that I know about uses "ystar" to denote the underlying latent variable, not the observed corner solution. Typically, ystar = x*b + u and then y = max(0,ystar). It's almost universal that y* is used as a latent variable. It's true that Tobin (1958) used y for the latent variable and w for the observed variable, but Tobin was a little unclear about how he was viewing the variable y. And he did not use y* for the observed variable.