Mathematically, is there a relationship between the estimated coefficients derived from fama macbeth and the coefficients derived from a time fixed effects model?
fama macbeth regression is for each time, run cross sectional regression, then average the coefficients across time.
time fixed effects model includes a dummy for each time period: $y_{it} = \alpha_t + x_{it}\beta + \epsilon_{it}$
both account for a time effect (i.e. correlated residuals across firms for given time). The estimated $\beta$ coefficients from time FE model is derived from demeaning by the time group on both $y$ and $x$.
Maybe the $\beta$s are the same for fama macbeth and time FE model? I can't tell.
If they are different, why use FM over time FE and vice versa?
Thanks in advance.
