Re: st: Using a Tobit regression with the Heckman correction

["J. Boreham" <jb648@cam.ac.uk>]

Thanks for your prompt response, and for the clarification.

I think I need to take both types of Tobit into account. The "fee" variable 
is the transfer fee paid for footballers, so is only observed when 
"transferred" is equal to 1 - so there is a Type II Tobit. However, in 
addition, "fee" is always greater than or equal to 0, so there is a Type I 
Tobit too.

Am I right in thinking that the -heckman- command will account for the Type 
II Tobit, but not the Type I Tobit? I attempted to account for both by 
using the -tobit- command (to account for the Type I), and also including 
the inverse Mills ratio ("mills_ratio" below, to account for the Type II). 
I fear, however, that this will result in invalid standard errors, as the 
Heckman correction requires non-standard errors (as "the usual formulas for 
standard errors for least squares coefficients are not appropriate" - 
Heckman, Sample Selection Bias as a Specification Error, 1979)


Thanks again for your time,

John



On Dec 17 2011, Tirthankar Chakravarty wrote:

> I think you might be mixing up a few things here. Both -heckman- and
> -tobit- fit Tobit (censored regression) models, i.e., where the
> outcome of interest is not fully observed in the sample. They differ
> in what they posit the censoring mechanism to be.
>
> 1) The model fitted by -tobit- is what is called the Type I tobit.
> Here the observability of the outcome depends on the values of the
> outcome itself - whether it crosses a non-stochastic threshold.
>
> 2) The model fitted by -heckman- is what is called the Type II tobit.
> Here the observability of the outcome (your "fee" variable) depends on
> the values of a binary indicator (probably what your "transferred"
> variable refers to), which is modelled using a probit regression.
> Conditional on the values of the binary indicator the second stage is
> a simple linear regression fitted by OLS - where the conditionality is
> taken into account using the Mills ratio.
>
> There is also the possibility of fitting the whole model in one go
> using partial maximum likelihood, but the important point is that the
> conditional model for the outcome is a linear regression, and in the
> two-step version of Heckman's estimator, the outcome is fitted using
> OLS.
>
> Lastly, note that OLS is an estimation technique and tobit is a model.
>
> T
>
> On Sat, Dec 17, 2011 at 1:16 PM, J. Boreham <jb648@cam.ac.uk> wrote:
> > Dear Statalist,
> >
> > I'm very new to Stata, so apologise if this is a silly question. I'm 
> > looking to run a Tobit regression using the Heckman correction. My 
> > Heckman code is:
> >
> > ***** heckman fee age agesq curr_app curr_goal_d curr_goal_m curr_goal_f,
> > /// select(transferred = age agesq curr_app curr_goal_d curr_goal_m
> > curr_goal_f prom) twostep *****
> >
> > But this uses OLS rather than a Tobit model. I instead attempted to 
> > create the two stage Heckman correction by first manually producing the 
> > inverse Mills ratio, and then running a Tobit regression:
> >
> > ***** probit transferred age agesq curr_app curr_goal_d curr_goal_m
> > curr_goal_f prom
> >
> > predict predicted_values, xb
> >
> > generate denominator = normal(predicted_values)
> > generate numerator = normalden(predicted_values)
> > generate mills_ratio = numerator/denominator
> >
> > tobit fee age agesq curr_app curr_goal_d curr_goal_m curr_goal_f 
> > mills_ratio *****
> >
> > However, this will not account for the non-standard errors one needs when
> > using the Heckman correction.
> >
> > So is it possible either to tell Stata to use a Tobit regression with the
> > "heckman" command, or instead to get the correct standard errors when
> > manually doing the correction by inserting the inverse Mills ratio?
> >
> >
> > Thanks for your consideration,
> >
> > John Boreham
> > *
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