There cannot be any correlation between the explanatory variables present within a given equation and the error term. If it were the case that the error term and the explanatory variables were in fact correlated, what you would find happening is that some of the variation that occurs in the dependent or Y variable will be attributed to one or all of the explanatory variables even though this variation is as a result of the error term present with in the equation.
When ordinary least squares is performed within econometrics, it is assumed that these explanatory variables are arrived at completely independently of the error term. It is important to remember that the error term should always be entirely random i.e. it is stochastic. When there is correlation between the error term and any of the explanatory variables, the reliability of the estimates is compromised.
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