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

[Tirthankar Chakravarty <tirthankar.chakravarty@gmail.com>]

You are looking for the truncated normal hurdle model, also called the
Craggit model.

It has been programmed up in Stata by William Burke (Stata Journal,
Volume 9, Number 4):
http://www.stata-journal.com/article.html?article=st0179

To install the command in Stata, type:
net install st0179, ///
  from(http://www.stata-journal.com/software/sj9-4)

T


On Sat, Dec 17, 2011 at 2:17 PM, J. Boreham <jb648@cam.ac.uk> wrote:
> 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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>>> *   http://www.ats.ucla.edu/stat/stata/
>>
>>
>>
>>
>>
> *
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-- 
Tirthankar Chakravarty
tchakravarty@ucsd.edu
tirthankar.chakravarty@gmail.com

*
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