I am still asking myself what the pricing error terms in the Fama-MacBeth regression are.
Are they the intercept I regress across all assets in each month, once? Or are they the residuals of each asset in each month?
To clarify this I attach the picture of the formula I am referring to:
Also consider this example:
I have returns of 100 stocks over 120 months.
If the alphas were the residuals, I would have a 120x100
matrix.
If the alphas were an intercept I regress (just like beta) it would be a 120
alpha values vector.
The post I am referring to:
Calculating the pricing error in Fama-Macbeth Regression for Fama/French 5 Factor model
Skoestlmeier says it is an intercept. But, from the above image (source: Cochrane) it seems to me, that alphas are the residuals for every asset i=1,...,N
over each month t
.
I would be very grateful for clarification.
Best Regards