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# st: whether difference is significant

 From "Lynn Lee" To Subject st: whether difference is significant Date Mon, 15 Oct 2012 19:59:55 +0800

```I appreciate for your help, Maarten. Thank you.

Best Regards,
Lynn Lee

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Maarten Buis
Sent: Monday, October 15, 2012 5:31 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: whether difference is significant

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-fri
end/>.

(**) 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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```