Exogenous Consideration and Extended Random Utility

In a consideration set model, an individual maximizes utility among the considered alternatives. I relate a consideration set additive random utility model to classic discrete choice and the extended additive random utility model, in which utility can be - for infeasible alternatives. When observable utility shifters are bounded, all three models are observationally equivalent. Moreover, they have the same counterfactual bounds and welfare formulas for changes in utility shifters like price. For attention interventions, welfare cannot change in the full consideration model but is completely unbounded in the limited consideration model. The identified set for consideration set probabilities has a minimal width for any bounded support of shifters, but with unbounded support it is a point: identification "towards" infinity does not resemble identification "at" infinity.