For the given model $y = x\beta + \varepsilon$, the four assumptions would be
- The model is linear in $x$ and $\beta$, also additive in $\varepsilon$
- The conditional mean of the error terms are zero (i.e. $E[\varepsilon|x] = 0)$
- $Var[\varepsilon|x] = \sigma^2I_n$
- Exogeneity of $x$ (i.e. either $x$ is fixed or independent of $\varepsilon$)
My questions is that in the case of the following situations which assumptions have been violated.
Case 1. $E[x'\varepsilon] \neq 0$ [I am not sure whether this implies the second or fourth assumption has been violated]
Case 2. $Cov(x_i,\varepsilon_i) \neq 0$ [I suppose the third one has been violated but could it imply the violation of other assumptions?]
Any help will be greatly appreciated.