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

 From "Austin Nichols" 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)
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

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
```*