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Re: st: RE: Tobit coefficients


From   "Austin Nichols" <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: Tobit coefficients
Date   Fri, 27 Jul 2007 16:13:57 -0400

Alejandro feldman <feldman@primal.ucdavis.edu>:

It may be as much an economics question as an econometrics question,
so I hope other Statalisters will forgive this thread in advance.

The modeling choices here are sometimes matters of taste--the question
is, do you believe that the zeros represent censoring of a latent
variable that is zero or negative.  If they in fact just represent
zeros and are not "censored" then -tobit- is the wrong way to go.
Plus, -tobit- is highly parametric and sensitive to misspecification
in my experience, hence my queasiness when hearing about -tobit-
results--but a MC simulation would be the way to address that concern.

The examples given on EACSPD p.518 include "amount of life insurance
coverage chosen" where the important difference is that you can't buy
negative life insurance at anything like the same rate you can buy
positive life insurance (an annuity is like a negative life insurance,
in the sense that you have the company pay you a premium every month
and then seize assets when you die, but the private annuity market is
virtually nonexistent).  In any case, I suppose most people
considering life insurance choices don't even think there is an option
of buying negative life insurance, so there will be folks who would
like to buy negative life insurance but don't.  There you have the
latent variable that is zero or negative.

This could be the case with debt too, as I indicated with the "access
to credit" comments, but I would bet that the vast majority of those
with zero debt are not constrained to have zero debt--they actually
have negative debt, in the form of assets, which is probably a
variable sitting right there on the dataset.

Another example given on EACSPD p.518 is firm spending on R&D--hard to
see how a firm could want to spend negative amounts on R&D (hey
competitor--will you pay me to forget my past innovations?) but I'm
sure there is a very large spike at zero (seems more like a case of
-zip- than -tobit- but as always YMMV).

This discussion also pertains to the two-part model vs. alternatives
(see e.g. http://nber.org/papers/t0228) frequently modeled with
-tobit- when in fact there may be no censoring or equivalent.

I'd be interested in others' perspectives... but perhaps this
discussion belongs on a different listserv?

On 7/27/07, feldman <feldman@primal.ucdavis.edu> wrote:
> This is more an econometrics question than a Stata question
> but I hope you donīt mind.
>
> Austin Nichols said:
>
> > As I have pointed out before on this list, e.g.
> >
> http://www.stata.com/statalist/archive/2007-04/msg00549.html
> >
> http://www.stata.com/statalist/archive/2006-12/msg00466.html
> > -tobit- is inappropriate if the zeros are not censored
> > values (representing a negative y* that is observed as
> > y=0).  If the zeros are simply a point mass in the
> > distribution of a nonnegative dep var, then -poisson- or
> > -glm- are better options.
>
> ...
> > Though -poisson- is designed for count variables, it works
> > well for any model where E(y|x)=exp(xb). See Wooldridge
> > (http://www.stata.com/bookstore/cspd.html) p.651 and
> > surrounding text: "A nice property of the Poisson QMLE is
> > that it retains some efficiency for certain departures
> > from the Poisson assumption."
>
> Nevertheless, in the same book by Wooldridge (p.518 and
> other parts of chapter 16) tobit is used to model what is
> called "corner solutions outcomes", which seems to be
> exactly the case that Austin is warning against.  So my
> question is, are there any references you can recommend
> about the superiority of poisson or glm over tobit when the
> data comes from a corner solution?
>
> Thanks,
> Alejandro
>

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