How do I test against a simple null that two regressions coefficients are equal?

Hi there,

I run two regressions:

y = a1 + b1 * x + e1
y = a2 + b2 * z + e2

I want to test against the null hypothesis: b1 = b2.  How do I design the test?

I think I can add two equations together and divide both sides by 2:
y = 0.5*(a1+a2) + 0.5*b1 * x + 0.5*b2 * z + e3, where e3 = 0.5*(e1 + e2).
or just y = a3 + 0.5*b1 * x + 0.5*b2 * z + e3

If I run this new regression, I can test against the null b1 = b2 in
this regression.  Is it an equivalent test as the original one? If
yes, how do I do that in R?

Alternatively, I think I can just test against the null:
correlation(y, x) = correlation(y, z), where correlation(. , .) is the
correlation between two random variables. Is this equivalent too? If
yes, how do I do it in R?

Thanks.

Best,
Jia

Ohio State University - Finance
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