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Re: st: log of zero

From   "Austin Nichols" <>
Subject   Re: st: log of zero
Date   Wed, 2 Jul 2008 13:06:49 -0400

If you regard the RHS zeros as true values, measured without error,
they cannot be used to estimate elasticities. Adding an arbitrary
small positive quantity guarantees arbitrary results of small
practical utility. If you regard the RHS zeros as actually positive
but measured with error, then you may be able to write down a GMM IV
model where you predict the RHS value to be some strictly positive
value using excluded instruments.  You would have to program this
yourself, with reference to -ivreg2- and -ivpois- on SSC or for a
different approach see for starters.
Alternatively you could multiply impute the zeros (see SJ 8(1):49-67
and -findit mim-) which does not require programming a new estimator,
but does require getting up to speed on multiple imputation.  A third
approach is to regress ln(Y) on X and then compute d\hat{ln(Y)}/dX * X
manually for each obs and then average across them, but note you will
still effectively be excluding obs with X=0 from the calculations
unless you modify your definition of elasticity to be not a point
elasticity but rather elasticities of discrete changes.

On the whole, you may be better off simply excluding obs with ln(0) on
the RHS, since that probably will not introduce bias (selection on X
is often OK, so if all zeros are in fact less than the smallest
observed positive value in the data, you are probably not introducing
bias by excluding those obs) and requires no additional programming.

On Wed, Jul 2, 2008 at 7:30 AM, Maarten buis <> wrote:
> --- Viktor Slavtchev <> wrote:
>> > > I want to estimate production function in logs in order to
>> > > interpret the coefficients in terms of elasticities. one of the
>> > > RHS variables has a lot of zero value.
> --- maarten Buis wrote:
>> > I think you are refering to using -glm- with the log link
> --- Nick Cox <> wrote:
>> As I understand it, -glm, link(log)-, although otherwise white magic
>> of the best Dumbledore kind, can do nothing to help with zeros in a
>> predictor that you want to log.
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