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# Re: st: Dependent variable in a tobit model

 From Austin Nichols To statalist@hsphsun2.harvard.edu Subject Re: st: Dependent variable in a tobit model Date Tue, 16 Nov 2010 08:08:15 -0500

```Estrella Gomez <estrellastata@gmail.com> :

How to trick -tobit- is there in my original email, and there is much
more detail in the text referenced.  Stata's -tobit- will not include
missings, of course, which is why some people would have you replace
the log of zero (missing) with a negative number (< any observed
value).  Note that the answer you get will depend on the number you
choose, and there is in most cases no clear justification for any
particular number.  Others would have you use -heckman- where there is
a probit of y>0 on the same regressors X estimated together with OLS
of ln(y) on X, which strikes me as an even worse idea.

The one case where -tobit- is a fairly good solution is where the log
link is appropriate but there is rounding of the depvar, in which case
there is a justification for replacing the log of zero with a
particular number, namely the log of the largest number that can be
rounded to zero.  I say "fairly" good because -intreg- is the correct
solution for a rounded depvar with a homosk. normal error, so -tobit-
is still not right, but -tobit- provides a very good approximation to
-intreg-.  Neither works for the heterosk. or non-normal case.

drawnorm x e, n(100) clear seed(1)
g y=round(exp(x-5+e),.01)
g lny=ln(y)
g ly=max(lny,ln(.005))
tobit ly x, ll(`=ln(.005)')
heckman lny x, sel(x)
g y2=ln(y+.005)
g y1=ln(y-.005)
intreg y1 y2 x

On Tue, Nov 16, 2010 at 4:00 AM, Estrella Gomez <estrellastata@gmail.com> wrote:
> Dear Austin
>
> The thing is that I am comparing estimation methods to stduy the
> properties of each of these methods, that's why I am interested in
> estimating a Tobit model, as well as Poisson and others. But I am not
> sure if Stata automatically drops out the observations of the
> dependent variable that are missings (those are the observations that
> are zeros in the original variable in levels) and hence, I should
> specify instead an equation with the dependent variable in levels
> instead of logs. Is that correct?
>
> which is the command to plot the graphic in which you compare the
> estimators?
>
> Best regards,
> Estrella
>
> 2010/11/15 Austin Nichols <austinnichols@gmail.com>:
>> Estrella Gomez <estrellastata@gmail.com> :
>> Why not use -poisson- or -glm- with cluster-robust standard errors
>> (and fixed effects if you like)?  Cameron and Trivedi would have you
>> "trick" Stata's -tobit- command using a negative y in place of
>> ln(zero), but I argue in
>> http://repec.org/bost10/nichols_boston2010.pdf
>> Santos Silva and Tenreyro. 2006. "The Log of Gravity." Review of
>> Economics and Statistics, 88(4): 641-658.
>> Cameron and Trivedi. 2009. Microeconometrics Using Stata. Stata Press,
>> College Station TX.
>>
>> Note that a lot of zeros is not a problem in general, since those
>> observations may also have very low predicted values conditional on
>> observables.
>>
>> On Mon, Nov 15, 2010 at 5:19 AM, Estrella Gomez <estrellastata@gmail.com> wrote:
>>> Dear Statalist:
>>>
>>> I am estimating a gravity equation of exports and I have decided to
>>> use tobit model, since the number of zeros in the dataset is high.
>>> This model is usually estimated in its loglinear version. However, if
>>> I use the logarithm of trade as dependent variable, the zeros are
>>> dropped (since the logarithm of zero is unfeasible).
>>>
>>> This is the command I have introduced in Stata 11:
>>>
>>> xttobit lxi lGDP_i lGDP_j contig comla smctry ldist RTAboth i.exporter
>>> i.importer i.year, ll(0)
>>>
>>> where "lxi" is the logarithm of exports and the independent variables
>>> are the standard variables in a gravity equation
>>>
>>> Of course, the number of censored observations is zero, since the
>>> dependent variable is introduced in logs. I think this is not correct,
>>> but I have seen this specification in most of the gravity-related
>>> articles
>>>
>>> Could somebody help me with this?
>>>
>>> In addition, I do not know if it is correct to introduce exporter,
>>> importer and time effects in the model
>>>