Can a construct be both endogenous and exogenous at the same time? Consider the planned behavior model:



*

*Can the "intention" construct be considered endogenous and exogenous simultaneously? Why?

 A: In short, no.
Now, I am assuming that you are using the terms "exogenous" and "endogenous" as they are used in the structural equation modeling (SEM) community and not as they are used in causal analysis / econometrics. The answer would be no, either way, but the explanation would be different.
In SEM, a variable is "exogenous" if it has no predictor within the model. Otherwise, the variables is "endogenous." A variable either has a predictor in the model or it doesn't. In this model, "Intention" has three predictors, so it is "endogenous." If you removed those predictors from the model, then "Intention" would be "exogenous."
In causal analysis / econometrics, a variable is "endogenous" if it covaries with an error term. Obviously, a dependent variable is endogenous because it covaries with its own error term. "Intention" has an error term, so it is endogenous. But removing Intention's three predictors would not necessarily make Intention exogenous, because Intention might also covary with the error term for "Behavior." The model does not specify that, but the econometrician would be concerned that such a covariance may be part of the true or correct model, and would want to know if you have checked to make sure that this is not true. Thus, an econometrician will tend to regard all variables as endogenous unless there is evidence (from model design or from analysis) that they are, indeed, exogenous.
Still, using this language, a variable either is or is not correlated with an error term, so it is either endogenous or exogenous, never both.
