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Re: st: Tobit interpretation and post estimation


From   "Austin Nichols" <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Tobit interpretation and post estimation
Date   Wed, 18 Apr 2007 12:29:59 -0400

Elena--
This discussion is probably better suited to Econlist (does such a
thing exist?) than Statalist, but I am compelled to argue again that
you do not have a censoring problem per se.  Censoring is, and -tobit-
is designed to handle, the situation where you do not observe the true
value of the dependent value because some other process censors it.
In the case of household debt, there is a desired level of debt for
each household (may be pos or neg) conditional on each price of debt
(interest rate bid/ask) and any rationing or discontinuities (e.g. a
home loan in the US over $417K suddenly gets more expensive). The
prices and restrictions are determined endogenously in a two-sided
market--and are themselves partly a product of choices made by
household members, and therefore reflect preferences.  And the
"censoring" here is really just "facing a very high price of borrowing
gobs of additional money," not "below the minimal detectable
concentration on my debt-o-meter, so I have no idea what the desired
level is, I just know it's less than X."

You could model this naively with a -probit- or -logit- to determine
whether folks are constrained (face rationing) and then -reg- or
-poisson- or -glm- for those who are unconstrained (one thinks of the
RAND model of health expenditures), or you could model the whole
process with -poisson- or -glm- (which often fit better, in the sense
of having higher pseudo-R2), but all of these estimates will not be
identifying some causal relationship.  You should go back to the
drawing board and ask yourself: What are the parameters of interest
here?  Where is there any exogenous variation that might identify
them?

Well, at least in your next study you should.  For now, you might just
use the -poisson- command, or -zip- where the -inflate()- option
contains the variables that predict rationing. See also the -vuong-
option (the Vuong test of zip versus poisson--this test statistic has
a standard normal distribution with large positive values favoring the
zip model and large negative values favoring the poisson model).

On 4/18/07, Elena Giarda <elena.giarda@prometeia.it> wrote:
We chose a tobit model because we have the
problem of debt rationing: some households have
zero debt not because they choose so, but
because were refused the loan by banks or
financial institutions. Also some households
might have a lower level of debt than desired
because of partial rationing. We excluded
non-rationed households (with zero debt) from
our sample (is this reasonable?) because this is
their desired level of debt. We are able to
detect rationed and non-rationed households from
a couple of questions in the Bank of Italy's
household survey. We also found reference of this
approach in the literature, but maybe is not the
most appropriate.

Anyway...we made a mistake in
our first estimates, because we set the
censoring level at zero, when instead it should
be a positive number. In case we decide to go
further with the tobit estimation how do we
choose the level of censoring?

About the "positive debt" problem pointed out by Austin:
we are using the variable "debt" (we have now
switched  to the total amount of debt=consumer
debt + mortgages) with the amount of debt
declared by the household. We are not
considering overall wealth of households,
therefore debt is either zero or positive.
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