Re: st: Formally comparing Tobit and Probit estimates

[Maarten Buis <maartenlbuis@gmail.com>]

The difference is that Tobit tries to do two things with one set of
coefficients: it models the probability of being censored using a
(scaled) probit and it models the (partially latent) outcome. The
coefficients of both sub-models are constrained to be equal. This is
obviously a strong constraint. For example, a Heckman model uses two
different sets of coefficients for these (but requires other strong
assumptions...).

In short the coefficients in a Tobit model, appropriately scaled using
sigma, can be compared with a probit when the dependent variable is
censored versus noncensored. I guess that might be a way of finding
potential problems with the Tobit model: If they differ substantially
then that would indicate a problem with the constraint discussed
above. I cannot think of another use for such a test though.

-- Maarten

On Wed, Jan 22, 2014 at 4:09 PM, Alfonso Sanchez-Penalver wrote:
> Hi all,
>
> My two cents in this discussion, and I leave it then to more capable and knowledgeable fellows. As Marteen says when estimating a Tobit model the likelihood of the zero observations is the probability that the latent variable is less or equal to zero. However, under the Tobit for the non-zero observations is the probability that the latent variable actually has the value we observe. The probit model has the same likelihood for the zero observations (except for the scaling, easily resolved), but the likelihood for the nonzero observations would be that they are greater than zero, and this is the point that Kit is trying to make, I believe. I have to agree with Kit that the difference in the coefficients must be then more than a question of scale, because in the Tobit estimation we have actual non-zero values for estimation.
>
> Best,
>
> Alfonso Sanchez-Penalver
>
>> On Jan 22, 2014, at 9:43 AM, Maarten Buis <maartenlbuis@gmail.com> wrote:
>>
>>> On Wed, Jan 22, 2014 at 3:02 PM, Christopher Baum <kit.baum@bc.edu> wrote:
>>> The reason why it doesn't make much sense to compare the -probit- and -tobit- coefficients is that for probit, the latent
>>> variable is unobserved for all observations, whereas for tobit, the latent variable is only latent for the censored observations.
>>> Thus the information going into the estimation differs, as  in probit, all observations are coded as 0/1.
>>
>> As I understand the Tobit, one can compute the probablity of not being
>> censored as normal(xb / sigma), where normal() is the CDF of the
>> standard normal distribution, xb is the linear predictor for the first
>> equation and sigma the constant in the second equation. This is very
>> similar to a probit, in which the probability is normal(xb). If the
>> dependent variable in the probit is 1=not censored, 0=censored and the
>> xs are the same, than the coefficients/sigma in the Tobit should be
>> the same as the coeficients in the probit.
>>
>> We usually don't look at this way, as we are usually less interested
>> in the probability of being censored, but that does not make this
>> wrong.
>>
>> -- Maarten
>>
>> ---------------------------------
>> Maarten L. Buis
>> WZB
>> Reichpietschufer 50
>> 10785 Berlin
>> Germany
>>
>> http://www.maartenbuis.nl
>> ---------------------------------
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-- 
---------------------------------
Maarten L. Buis
WZB
Reichpietschufer 50
10785 Berlin
Germany

http://www.maartenbuis.nl
---------------------------------

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