Exogeneity Vs. Endogeneity
In a stochastic model, the notion of the usual exogeneity, sequential exogeneity, strong/strict exogeneity can be defined. Exogeneity is articulated in such a way that a variable or variables is exogenous for parameter . Even if a variable is exogenous for parameter, it might be endogenous for parameter .
When the explanatory variables are not stochastic, then they are strong exogenous for all the parameters.
The problem of endogeneity occurs when the independent variable is correlated with the error term in a regression model. This implies that the regression coefficient in an Ordinary Least Squares (OLS) regression is biased, however if the correlation is not contemporaneous, then it may still be consistent. There are many methods of overcoming this, including instrumental variable regression and Heckman selection correction.
Read more about this topic: Endogeneity (economics)