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From |
Maarten Buis <[email protected]> |

To |
[email protected] |

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

Date |
Wed, 22 Jan 2014 16:42:26 +0100 |

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 <[email protected]> wrote: >> >>> On Wed, Jan 22, 2014 at 3:02 PM, Christopher Baum <[email protected]> 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 >> --------------------------------- >> * >> * For searches and help try: >> * http://www.stata.com/help.cgi?search >> * http://www.stata.com/support/faqs/resources/statalist-faq/ >> * http://www.ats.ucla.edu/stat/stata/ > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/faqs/resources/statalist-faq/ > * http://www.ats.ucla.edu/stat/stata/ -- --------------------------------- Maarten L. Buis WZB Reichpietschufer 50 10785 Berlin Germany http://www.maartenbuis.nl --------------------------------- * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**References**:**Re: Re: st: Formally comparing Tobit and Probit estimates***From:*Christopher Baum <[email protected]>

**Re: Re: st: Formally comparing Tobit and Probit estimates***From:*Maarten Buis <[email protected]>

**Re: st: Formally comparing Tobit and Probit estimates***From:*Alfonso Sanchez-Penalver <[email protected]>

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