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

 From Tirthankar Chakravarty To statalist@hsphsun2.harvard.edu Subject Re: st: Using a Tobit regression with the Heckman correction Date Sat, 17 Dec 2011 13:45:13 -0800

```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?
>
>
>
> John Boreham
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
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> *   http://www.ats.ucla.edu/stat/stata/

--
Tirthankar Chakravarty
tchakravarty@ucsd.edu
tirthankar.chakravarty@gmail.com

*
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```