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# Re: st: whether difference is significant

 From Maarten Buis To statalist@hsphsun2.harvard.edu Subject Re: st: whether difference is significant Date Mon, 15 Oct 2012 11:31:03 +0200

```On Mon, Oct 15, 2012 at 10:59 AM, Lynn Lee wrote:
> I have two models:
>
> Y1=beta1*x1+beta2*x2+beta3*x3+u1
> Y2=alpha1*x1+alpha2*x2+alpha3*x3+u2
> I want to interpret whether the difference between beta1 and alpha1 is
> significant. How to interpret and test this significance? How to get the
> standard error for this difference?

That depends. In most cases where people ask this question they
actually have one model instead of two, and the problem is solved by
just adding the appropriate interaction terms. For example, in the
example below Y1 would be wage for whites and Y2 would be wage for
blacks. Instead of two separate regression, you can estimate one
model(*) with the appropriate interaction terms.
Since we use a log link in this example the exponentiated coefficients
are ratios not differences, so the effect of union for blacks is 1.25
times as large as the effect of union for whites (the reference) and
this ratio is significantly different from 1(**).

*---------------- begin example ------------------
sysuse nlsw88, clear
gen black = race ==2 if race < 3
glm wage i.black##(c.grade c.ttl_exp i.union), ///
*----------------- end example -------------------
(For more on examples I sent to the Statalist see:
http://www.maartenbuis.nl/example_faq )

Hope this helps,
Maarten

(*) In this case I use -glm- to model log(E(wage)) instead of
E(log(wage)), as we are typically interested in E(wage) not
E(log(wage)). See:
<http://blog.stata.com/2011/08/22/use-poisson-rather-than-regress-tell-a-friend/>.

(**) For ratios the number 1 represents "no effect"; 1 X some number =
some number.

---------------------------------
Maarten L. Buis
WZB
Reichpietschufer 50
10785 Berlin
Germany

http://www.maartenbuis.nl
---------------------------------
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```