# Re: st: Grid Search in a Log Plus Constant Model

 From David Jacobs To statalist@hsphsun2.harvard.edu Subject Re: st: Grid Search in a Log Plus Constant Model Date Thu, 09 Nov 2006 15:47:07 -0500

I thought that count estimators would only handle positive integers. At least that's what the Stata reference books say. Is GLM an exception?

Dave Jacobs

At 11:26 AM 11/9/2006, you wrote:

```Paul Jacobs, Maarten Buis, Nick Cox, Le Wang, Sebastian Baumeister, et al.--

If you want to regress ln(y) on variables X, but y has some zeros that
you think are important, a natural approach is to use -poisson- since
the Poisson model really only needs E(y|x)=exp(xb) to get consistent
estimates of b, which is why it is often the model of choice for 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.

The -glm- approach mentioned by Sebastian is both similar and more
general, but -poisson- is perhaps more straightforward for a user who
wants to regress ln(y) on variables X, but keep observations where y
is zero.  The interpretation of the coefs in -poisson y x- is the same
(i.e. a _small_ one-unit change in x produces a _b[x]*100 percent
change in y) as in -reg lny x- regardless of Stata's warning about
interpretation, though the coefficients will not be identical, even if
no zeros are dropped by -reg-.  The interpretation of the coef in
-poisson y lnx- is the elasticity of y with respect to x, naturally.

webuse lowess1, clear
g lnd=ln(de)
reg d h1, r
reg lnd h1, r
poisson d h1, r
poisson d h1 if d>0, r

Note that I have reversed the y and x from -help lowess- in part as a
kind of very obscure flag to worry about endogeneity in regressing
expenditure on other observables--for a test of endogeneity in
-poisson-, see
http://www.stata.com/statalist/archive/2006-05/msg00532.html
http://www.stata.com/statalist/archive/2006-05/msg00595.html

On 11/9/06, Sebastian Baumeister <baum_statal@web.de> wrote:
```
```hi paul,
some have recommended using generalized linear models (with gamma
distribution and log link), which do not require retransformations of
the cost dependent variable after estimation (Buntin et al. 2005,
Manning et al 2005).
```
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```
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