Is there any way to test if an independent variable has a stronger impact between two models with different dependent variable?

[Dongwuk Kim]

I have a study that is trying to see which firm outcome will be more influenced by early firm activities. I'm using xtreg to test this from panel data.
So I basically have two dependent variables but the same independent variables list. One dependent variable is the number of industry awards and the other is sales.

y_1awards = beta₁ early firm activities + alpha₁ R&D + gamma1 strategy + error

y_2sales = beta₂ early firm activities+ alpha₂ R&D +gamma2 strategy + error


I've searched other communities and saw this thread here: https://www.statalist.org/forums/for...ork-with-xtreg

One of the answers in that thread said unless y1 and y2 are measured the same way comparing the beta1 and beta 2 would be meaningless. Is that true?
Is there any way to test if the firm activities can have a stronger impact on y1 awards than y2 sales?

Thank you !

[Andrew Musau]

Is there any way to test if the firm activities can have a stronger impact on y1 awards than y2 sales?

How do you define stronger? If it is the change in the coefficient of variation associated with excluding the variable, you can measure such changes separately and then compare the values. But again if you have a different set of RHS variables across the two regressions, a comparison does not make sense as you are not comparing apples to apples.

One of the answers in that thread said unless y1 and y2 are measured the same way comparing the beta1 and beta 2 would be meaningless.

That most probably refers to a test of difference in coefficients which I agree does not make sense if the outcomes are measured in different units.