Re: Re: st: Formally comparing Tobit and Probit estimates

[Nick Cox <njcoxstata@gmail.com>]

<>

Good and fair point. My expression was very sloppy. What I had in mind
was that as the Tobit limits each go to the relevant infinity the
coefficients of the predictors go to the coefficients of the
corresponding linear regression. In any case, the units and dimensions
of the coefficients in the Tobit case are exactly the same as those in
the corresponding common or garden linear regression.

Nick
njcoxstata@gmail.com


On 22 January 2014 14:02, Christopher Baum <kit.baum@bc.edu> wrote:
> <>
> On Jan 22, 2014, at 2:33 AM, Nick wrote:
>
>> 1. The coefficients are not even in the same dimensions or units of
>> measurement.
>> (It's a pity that statistics courses and texts almost uniformly
>> neglect such matters.)
>>
>> 2. The -tobit- model is linear; the -probit- model is nonlinear.
>
> I wholeheartedly agree with Nick's point #1. However point #2 is misleading and incorrect. The -tobit- model is decidedly
> nonlinear, as its likelihood function is the additively separable sum of a Probit LLF for those observations which are censored
> and a regression LLF for those observations that are not. Although the regression terms are the same as one would write
> down for linear least squares, the probit terms are not linear in the data. That is why an iterative (maximum likelihood) technique is
> needed for its estimation.
>
> The coefficients reported by -tobit- are, like those from -probit-, estimates of the derivative of the latent index variable
> with respect to the explanatory variable, which are not themselves of interest. The estimates of the marginal effects for
> observed values of the dependent variable are the reported coefficients times the probability of being censored; that is,
> they are attenuated toward zero.
>
> 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. Of course, there is no
> correspondence between doubly-censored tobit and binomial probit.
>
> These topics are discussed in my book, An introduction to modern econometrics using Stata, chapter 10.
>
> Kit
>
> Kit Baum
> Professor of Economics and Social Work, Boston College, Chestnut Hill MA, USA
> DIW Research Professor, Department of Macroeconomics, DIW Berlin, Berlin, Germany
> baum@bc.edu  |  http://ideas.repec.org/e/pba1.html
>
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