What's the difference between exogenous and endogenous identifiers? What's the difference? Exogenous vs. Endogenous identifiers.

In the first step, you project all the predictors (endogenous and exogenous) onto the space of exogenous predictors only. By a property of projection operator, the projection of exogenous $X_j$ is $X_j$ again. So formally speaking, you do "replace" but in reality, nothing happens.
