  # Re: st: biprobit: test for difference in marginal effects

 From Wenhui Wei To statalist@hsphsun2.harvard.edu Subject Re: st: biprobit: test for difference in marginal effects Date Thu, 4 Nov 2004 15:05:41 -0500

```hi, May, thanks a lot for your quick response.

I read your response, and as far as I understand, you're testing the
difference of marginal effects for (for =0) and (for=1). However,
given that (for =0) is the base level, I'm getting marginal effects
for (for =1), and I'm interested in whether the two marginal effects
are different.

In my case, I first run the model:
biprobit y1 y2 othervar for

the following command tests whther the coeffecients for (for =1 ) are
significant different.
test [y1]for = [y2]for

However, since the probit coefficients are hard to interpret, I need
the marginal effects, by typing:
(a) mfx compute, predict(pmarg1)
(b) mfx compute, predict(pmarg2)

My question is: how to test the marginal effect of (for=1) from (a) is
significant from
that from (b).

I hope I'm not confusing you....

Thanks!

Wenhui

On 04 Nov 2004 13:38:05 -0600, May Boggess <mboggess@stata.com> wrote:
> On Thursday,  Wenhui Wei wrote:
> > I'm runing a biprobit model (two treatment modes) and get two sets
> > marginal effects by the MFX command.
> >
> >
> > My quesiton is: for a certain variable, for example, gender (with male
> > as the base), how to test whether its estimated marginal effects are
> > significant different in the 2 equations. i.e. the marginal effect of
> > female in treatment mode 1 is significantly different from that in
> > treatment mode 2?
> >
> > test command only test for the difference in the estimated
> > coefficients, not marginal effects.
> >
>
> We can do this by saving the marginal effects and their covariance
> matrix as estimation results and then use -test-. Let's begin with an
> example we can work with:
>
> clear
> sysuse auto
> set seed 12345
> gen y1=uniform()>0.5
> gen y2=uniform()>0.5
> biprobit y1 y2 mpg for
>
> I am interested in the marginal effect for for=1 and for=0.
> I am going to use a matrix to pass the numbers into the -at()-
> option of -mfx-:
>
> matrix A1=(20, 1)
> mfx, var(mpg) at(A1) tr(2)
> mat m1=e(Xmfx_dydx)
> mat D1=(.32062124, .00432451, .00432453, .11510433, -.0019256,
> -.0019256, -.00114118)
>
> When you use the -tracelvl()- option on -mfx- you get to the see
> the second derivatives that a calculated so -mfx- can use the
> delta method to get the standard error of the marginal effect.
> -mfx- doesn't save those guys in a matrix for us, so we'll have to copy
> and paste them in by hand. Same thing for the marginal effect at for=0:
>
> matrix A0=(20, 0)
> mfx, var(mpg) at(A0) tr(2)
> mat m0=e(Xmfx_dydx)
> mat D0= (.28952027, 0, .00463938, .19246524, 0, -.00111842, .00006737)
>
> mat D=D1\D0
> mat list D
>
> Now, to get the covariance matrix for these two marginal effects,
> I need the covariance matrix for the coefficients of the model:
>
> mat V=e(V)
>
> Then multiply:
>
> mat COV=D*V*D'
> mat rownames COV = m1 m0
> mat colnames COV = m1 m0
> mat list COV
>
> To be able to test if the two marginal effects are the same,
> I want to use a Wald test. This is done in Stata using the command
> -test-.
>
> I can take advantage of that by posting the marginal effects
> and the covariance matrix as estimation results. Before I do so,
> I have to make sure the rows and columns are labeled appropriately,
> which means, mathing the names on the covariance matrix COV:
>
> mat b=[m1[1,1],m0[1,1]]
> mat colnames b = m1 m0
> mat list b
> eret post b COV
> eret display
> mat list e(b)
> mat list e(V)
>
> You can see the marginal effects and the covariance matrix are now
> stored in the e() results. So now we can use test:
>
> test _b[m1]=_b[m0]
>
> --May
> mmb@stata.com
>
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