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Re: st: log on the dep. Var in Tobit


From   "Austin Nichols" <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: log on the dep. Var in Tobit
Date   Tue, 12 Dec 2006 14:00:24 -0500

Pallab--
I cannot see why you are using a Tobit at all (and it's not clear you
have a proportion rather than a ratio for a dep var).  If you think
E(number of trips made/number of people) is a exp-type function of
some variables X, so you are tempted to take the log of the dep var,
then use Poisson regression like so:
g lnp=ln(number_of_people)
poisson number_of_trips_made lnp x_vars
If the variable lnp has an estimated coefficient of 1, then your
original assumption has some empirical support, but the model is more
likely to be valid in any case--to quote a previous post,
the Poisson model really only needs E(y|x)=exp(xb) to get consistent
estimates of b, which is why it is the model of choice with a
nonnegative dependent variable (esp. one that is sometimes zero, and
is theoretically unbounded above).  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,"  etc.

Note that taking the log of a nonnegative variable plus some constant
is usually a bad idea. -findit transformations- will point to several
tests and programs designed to address what the "correct"
transformation might be, and
view http://fmwww.bc.edu/RePEc/bocode/t/transint.hlp
has a discussion of several possibilities.

On 12/11/06, Pallab Mozumder <pallab74@yahoo.com> wrote:
Dear STATA Listers,
When running a Tobit model, is there any particular
reason not to take log on the dep. Var? I see some
papers that use Tobit model without taking log on the
dep. variable (even for variables with a large extent
of variability such as health expenditure). On the
other hand, what I read from the Cameron and Trivedi's
book that the underlying distributions in Tobit can be
log-normal since normality is a key assumption here.
Could any body please tell me if there is any problem
to take log in the dep. var in Tobit.

I am trying to estimate a travel demand equation and I
am taking log of the dependent variable which is a
proportion (number of trips made/number of people). I
have a lot of zero values for the proportions since in
many cases no trips have been made. I am adding one to
all zero observations and since the log of one is
zero, I am using the lower censoring limit at zero. Am
I doing it right? Thanks for your help in advance.
Pallab
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