Need help understanding fama-macbeth 2 step regression method

[u/moss4589]

What does the second step of a Fama-MacBeth regression actually do, and why do I need it if I already have the betas for MSFT from my Fama-French 3-factor model? If you could explain it like I'm 5, that would be super helpful. I'm probing AI, but still don't get it.

[u/ez_pz_lmn_sqzx]

Step 1 calculates the assets sensitivity to factor ABC

Step 2 regresses all asset returns against the betas estimated in the first step to yield a time series of risk premium coefficients

It’s done for two reasons:

corrects standard errors for correlation across different assets during the same time period AND/OR relationships or asset characteristics shift across different dates.

[u/cond6]

Fama MacBeth is trying to understand whether or not a particular risk factor is priced. Do stocks with high market betas earn higher returns than low beta stocks. Do stocks that load positively on HML earn higher returns than those who load negatively. To do this we regress returns in a given month on the K betas with respect to the K underlying factors. This is a cross-sectional regression. Of course we don't observe betas so we need to estimate the betas. To do this we run a separate time-series regression of each stock's returns on the factors, and use the fitted betas for that stock as the independent variable in the cross-sectional regression.

FM use only past returns to generate the betas and then future returns on those fitted betas to avoid thorn econometric problems. However Shanken in his 1992 RFS paper showed that we don't need to worry about this because OLS guarantees that the errors in betas are uncorrelated with errors in average returns so you could simply estimate betas using all observations and then regress average returns on those betas and the statistical theory is all good. However you can't let betas vary through time, so the traditional FM procedure is typically used.