How to do residual investigation using Fama-MacBeth regressions?

Hello, everyone!! :)

My research is in asset pricing, and I am regressing an independent variable (an anomaly to the CAPM) against a dependent variable (in this case, monthly returns for assets) using Fama-MacBeth (1973) implementation (explained below).

- My ultimate goal is to assess the effect of the anomaly on the return of the assets
- My specific problem here: how to evaluate the residuals, normality of the residual, Homoscedasticity of Residuals.

Fama and MacBeth (1973) is a two step procedure. In the first step, for each single time period a cross-sectional regression is performed. Then, in the second step, the final coefficient estimates are obtained as the average of the first step coefficient estimates.

Conceptually speaking, after doing the average of the coefficients, I believe it does not make sense to analyze the residual. (Does it?) Although, it is a necessary procedure. But, against what values would the residuals be considered residuals. (The second step average is an average of many coefficients of many cross section regression.)

Is it clear my doubt? (I hope so, I tend to have a hard time expressing myself.)

I have searched this forum and couple of others, but I have not seen any discussion about this. I have also looked into the help files of the software package (Stata), but nothing is discussed about “residual procedures” with this type of regression and the regular procedures do not work. I have also tried the original article of Fama e MacBeth (1973), but I confess my statistical background is weak, and I could not grasp exactly what they say about it (if anything).

Any help will be mostly appreciated. :D

Best regards,

*I posted here and not on the Stata forum, because I thought this could be a really conceptual question. And knowing what to do, I can search for commands within my software package manuals.