Testing equality of coefficients between separate regression

[ROSSINL]

Hi,

I would like to test whether the parameters a2 and b2 are equal in the following separate linear OLS regressions:
Y1=a1+a2X1+a3X2+a4X3+...
Y1=b1+b2X4+b3X2+b4X3+...
The models have the same dependent and control variables; only the partitioning variables X1 and X4 differ and I have to test whether X4 is significantly stronger related to Y1 compared to X1.
However, X1 and X4 exhibit a very high correlation (r > 0.85), so I would like to estimate them in separate models to avoid multicollinearity, instead of using a dummy approach (I am also required to run two separate regressions so that my results are comparable with previous research).
I know that the equality of coefficients within a single equation can be tested using the Wald test in Eviews 7, but is there a way do this for separate equations?

Thank you in advance.

[startz]

You might set up up a system and run seemingly unrelated regressions.

[ROSSINL]

Thanks for your suggestion. SUR would be helpful, but I need standard errors that are robust to heteroskedasticity and autocorrelation, and ideally adjusted for clustering at firm level. From what I've read on this forum, Eviews 7 does not currently support this..is there a way to calculate a Wald test for the difference between two coefficients of two separately estimated equations?

[startz]

There's nothing built-in. I'm sure it could be done with matrix operations, but it might not be easy.

[ROSSINL]

Well, if an Eviews expert is saying something is not easy, I'm not even going to bother trying Thanks for your swift replies.