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# AW: st: Comparing coefficients with interactions in a SUR model

 From "Pohlmann, Sara" To "statalist@hsphsun2.harvard.edu" Subject AW: st: Comparing coefficients with interactions in a SUR model Date Sun, 18 Nov 2012 15:44:09 +0100

```Thank you so much for your help, it worked perfectly!!!!

Let me add one thing I was figuring out while running the test (in case others have a similar question):

when you want to compare marginal effects accross two regression of one SUR model, the explained procedure works fine, but it is important to create two distinct variables (i.e. kstock1 & kstock2), which essentially contain the same values.
test kstock1=kstock2 then test whether the difference in marginal effects is significant.

If you do not create two variables, Sata will calculate the combined marginal effect (i.e. the sum of the marginal effect of kstock1 on invest1 and kstock1 on invest2) and its significance.

Yet another way is to substract the marginal effect of the variable in one equation from the marginal effect in the other equation:

sureg (invest1 kstock1 mvalue1) (invest2 c.kstock2##c.mvalue2)
margins, dydx(_all) post expression(predict(equation(invest1))-predict(equation(invest2)))

Then, stata will calculate the difference between the marginal effects of each variable and whether this difference is significant.
I tested it both ways and the results are identical, so substracting the marginal effects of one regression from marginal effects from the other regression works quicker since you do not have to create a new variable.

Thanks again so much for your help!

Best, Sara

________________________________________
Von: owner-statalist@hsphsun2.harvard.edu [owner-statalist@hsphsun2.harvard.edu] im Auftrag von Christopher Baum [kit.baum@bc.edu]
Gesendet: Dienstag, 13. November 2012 16:45
An: <statalist@hsphsun2.harvard.edu>
Betreff: re: st: Comparing coefficients with interactions in a SUR model

<>
Sara wrote:

I would like to compare coefficients accross models within a seemingly unrelated regression (SUR) model and with interactions.

Consider, e.g. the following SUR regression: sureg (Y x1 x2 controls) (Z x1 x2 controls).

As far as I understand, I can test whether size differences are significant with the wald test: Test [Y]x1= [Z]x1

My "problem" now is, that x1 interacts with x2 in one of the regressions:

sureg (Y x1 x2 x3 controls) (Z x1 x2 controls).  where x3 = x1*x2

If I now want to compare whether size differences are significant, i can run

Test [Y]x1 + [Y]x3= [Z] x1,  where x3 = x1*x2.

The test indicates a significant difference, however I am not sure whether the result is reliable since I created the interaction term manually.
I also tried the command Test [Y]x1 + [Y]x1#[Y]x2= [Z] x1, but it does not work. Is there another way to test whether the coefficients differ significantly  when there is an interaction or is the Wald test how I ran it appropriate?

With some excellent help from Stata tech support, here is one solution:

webuse grunfeld,clear
keep if company<3
reshape wide invest mvalue kstock, i(year) j(company)
sureg (invest1 kstock1 mvalue1) (invest2 c.kstock2##c.mvalue2)

margins, dydx(_all) post ///
expression(predict(equation(invest1))+predict(equation(invest2)))

test kstock1 = kstock2
test mvalue1 = mvalue2

Kit

Kit Baum   |   Boston College Economics & DIW Berlin   |   http://ideas.repec.org/e/pba1.html
An Introduction to Stata Programming  |   http://www.stata-press.com/books/isp.html
An Introduction to Modern Econometrics Using Stata  |   http://www.stata-press.com/books/imeus.html

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