The typical assumption of linear regression, weak exogeneity, states, $$E(\bf{\epsilon_{i}})=0$$ when the regressors are fixed and $$E(\bf{\epsilon_{i}}|\bf{x_{i}})=0$$ when the regressors are random. I can't figure out for the life of me why you don't still need to condition upon your regressors when they are fixed. If we are going to use our model to extrapolate y values for x values other than the fixed ones we selected, won't we need to assume that the expected value of the epsilons is zero at those points as well?
Regression question - Weak exogeneity
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statistics
regression