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# Re: st: Interpretation of Interaction terms in log-lin

 From Lukas Borkowski To statalist@hsphsun2.harvard.edu Subject Re: st: Interpretation of Interaction terms in log-lin Date Tue, 22 May 2012 14:40:24 +0200

```Dear Marten,

thanks for the hint (and many previous hints on onther topics).

However, I have two concerns. First, some of my control variables are in logs as well - could I sill apply -glm- ? Second, I chose to use -xtreg- with -fe- and -re- options to control for unobserved effects. My panel has justv two time periods. How canI apply -glm- in this case, i.e. controlling for unobserved effects that are either fixed or random?

Regards

#
Lukas Borkowski

Am 22.05.2012 um 13:52 schrieb Maarten Buis:

> On Tue, May 22, 2012 at 12:24 PM, Lukas Borkowski wrote:
>> Dear all,
>>
>> my simplified model can be written as y = b0 + b1x1 + b2x2 + b3x1_x2 with the last expression being an interaction term.
>>
>> However, the dependent variable is in logs and the explanatory variables are not. I now wonder whether I have to add b2 and b3 before putting them into the e-function or to exponantiate each coeffecient seperately and then do the addition?
>
> I assume you first took the logarithm of your dependent variable and
> than used that in a linear regression model (-regress-). In most cases
> you would not do that. When you apply the exponential transformation
> to coefficients of a linear regression with a log transformed
> dependent variable you get effects in terms ratios of geometric means
> rather than ratios of arithmetic ("normal") means, see: (Newson 2003).
> In most cases you would want the latter and not the former.
>
> To get effects in terms of ratios of "normal" means you need to use
> the dependent variable in the original metric and use the log link
> function, that is, either use -glm- with the -link(log)- vce(robust)-
> options or use -poisson- with the -vce(robust)- option. See:
> <http://blog.stata.com/2011/08/22/use-poisson-rather-than-regress-tell-a-friend/>
>
> Consider the example below:
>
> *------------------ begin example ---------------------
> sysuse nlsw88, clear
> gen black = race==2 if race <= 2
> glm wage i.black##c.c_grade c.ttl_exp##c.ttl_exp , ///
> *------------------- end example ----------------------
> (For more on examples I sent to the Statalist see:
> http://www.maartenbuis.nl/example_faq )
>
> We can interpret that as follows:
> A white individual with 12 years of education (= high school) and 0
> experience (= just entering the labor market) can expect a wage of 3.5
> dollars an hour (the exponentiated constant).
>
> A black individual with 12 years of education can expect (1-.84)*100%=
> -16% less wage than white individuals with 12 years of education.
>
> A white individual can expect a 7% increase in wage for every year
> extra education.
>
> This effect of education is 4% larger for black individuals. So the
> effect of education for black individuals is 1.04*1.07=1.11, i.e. a
> year increase in education leads to an 11% increase in wage for black
> people. You can also compute this by adding the raw coefficients and
> exponentiating that sum, which you can do by typing:
>
>
> Hope this helps,
> Maarten
>
> Roger Newson (2003) Stata tip 1: The eform() option of regress. The
> Stata Journal, 3(4):445.
> <http://www.stata-journal.com/article.html?article=st0054>
>
> --------------------------
> Maarten L. Buis
> Institut fuer Soziologie
> Universitaet Tuebingen
> Wilhelmstrasse 36
> 72074 Tuebingen
> Germany
>
>
> http://www.maartenbuis.nl
> --------------------------
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```