Notice: On April 23, 2014, Statalist moved from an email list to a forum, based at statalist.org.

[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

From |
Christopher Baum <[email protected]> |

To |
"[email protected]" <[email protected]> |

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

Date |
Wed, 22 Jan 2014 14:02:08 +0000 |

<> 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 [email protected] | http://ideas.repec.org/e/pba1.html * * 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/

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

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

- Prev by Date:
**Re: st: Equivalent of Stata's copy command in Mata?** - Next by Date:
**Re: Re: st: Formally comparing Tobit and Probit estimates** - Previous by thread:
**Re: st: Formally comparing Tobit and Probit estimates** - Next by thread:
**Re: Re: st: Formally comparing Tobit and Probit estimates** - Index(es):