Finite-Sample Distributions of the OLS Estimator and T-Statistics Are Complicated $X _ { 1 } , \ldots , X _ { n }$

Short Answer

Finite-sample distributions of the OLS estimator and t-statistics are complicated, unless a. the regressors are all normally distributed.
b. the regression errors are homoskedastic and normally distributed, conditional on $X _ { 1 } , \ldots , X _ { n }$
c. the Gauss-Markov Theorem applies.
d. the regressor is also endogenous.