Average/median of regression coefficients? Test significance?

Hi there,

I am trying to replicate a analysis from an academic paper, in which the author conducted a regression analysis for every individual firm's stock. The stock performance was regressed on certain asset-pricing models (i.e. CAPM, Fama-French etc.). The intercept of such a regression would then be the abnormal return.

So, what this author did was conduct a regression analysis for every single firm and simply take the average and median of the regression coefficients. Furthermore, the author conducted a t-test on the average regression intercepts.

Can you do that? I mean the normal approach would be to take the average of all the stocks beforehand and conduct a regression analysis on the aggregate. But conducting firm-specific regressions and then take the average of the coefficients? ... and test this average with a t-test?

I didn't find any other publication, which does the same thing. And, believe me, there are a lot of publications out there about abnormal return analyses.

What do you think about this approach? Do you know of a paper that uses this, as well, or discusses the implications of this approach? Just seems odd to me that nobody else does it like that..

Thanks in advance!

My best, Christian

[Ilya]

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Answer 1

[Star Strider]

That doesn’t sound like a valid approach to me. I would not even average the stock data beforehand, but do a regression on the raw data. Averaging them first would require a weighted regression (possibly inverse-variance weights) to do it correctly, introducing more uncertainty in the estimated parameters than simply regressing the raw data would.

Stock analysis is not my area of expertise (analysing biomedical data is), so a caveat there.