Re: Question: Testing differences of regression coefficents for significance

On Sat, 29 Mar 2008 10:49:27 -0700 (PDT), DominoTC
<sebastian.krimm@xxxxxxxxxxxxxx> wrote:

Hello ***,

first, have big fat thank you for your reply - I have been dealing
with this for a while now without getting the feeling that I am near
to a clean solution. Now I just have a few more questions left:

On 29 Mrz., 18:09, richardsta...@xxxxxxxxxxx wrote:

What you have is almost correct, but let me suggest an easier method.
For those who haven't seen the pdf, let me restate the problem more
simply. There are two equations on the same dependent variable. Both
obey the classical regression assumptions.

y = X1*b1 + e1
y = X2*b2 + e2

The simple way to test hypotheses involving both b1 and b2 is to
combine these into a single equation. (This assumes X1 is uncorrelated
with e2 and X2 is uncorrelated with e1.)

y = (X1/2)*b1 + (X2/2)*b2 + (e1+e2)

Then just use the usual procedures.

Mmh, that might be a problem since most columns of the matrices X1 and
X2 are identical.

If yu want to use separate estimation, then there is one small and one
slightly larger error in your covariance estimates in your posted pdf.

First, in estimating the covariance between the residuals across
equations don't include a constant term. The sample mean of the
residuals will be exactly zero anyhow.

Ouch, that should have been obvious to me.

Second, the covariance between the separately estimated b1 and b2 will
be
[inv(X1'*X1)*X1'e1][e2'*X2*inv(X2'*X2)]

So instead of calculating the covariance between the regression
coefficients using the covariance of the residuals I should rather use
the matrix you stated?

-*** Startz

Thanks once more,

Sebastian Krimm


Sebastian:

Having variables in common between the two equations isn't a problem.
Suppose

y = a1*x1 + a2*x2 + e1
y = b2*x2 + b3*x3 + e2

then

y = a1*(x1/2) + (a2+b2)*(x2/2) + b3*(x3/2) + (e1+e2)/2

As you suggested, use the matrix I stated to get the covariance.

You might also want to think about BOTH original equations CAN obey
the Gauss-Markov assumptions. How do you believe y is generated? My
guess is that you will need the RHS variables in one equation to be
uncorrelated with the RHS variables in the second equation (except for
those that appear in both.)
-***

PS Are you in Germany?
.