st: Aggregating subsample coefficients to get the pooled coefficient?

[Jen Zhen <jenzhen99@gmail.com>]

Dear list members,

suppose I have a relationship y=A+B*x+u and I want to estimate A and B.
Is there a way to estimate this separately for 2 subsamples and
aggregate the coefficients that will give me the same A_hat and B_hat
as estimating it on the full sample?
How about the standard errors.

On a small example dataset, I have tried obtaining B_pooled as
(N1/N)*B1+(N2/N)*B2 and that gave me a very different coefficient.
I then tried weighting by the relative size of the T stats, as a
measure of precision, rather than weighting by relative sample sizes:
(T1/(T1+T2))*B1+(T2/(T1+T2))*B2
That got me closer but still not all the way to the pooled B.
So now I'm unsure whether there is another weighting scheme that would
do the job, or whether really the only way is to do a single pooled
regression?

Thanks so much,
JZ
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