Before revision:  We  demonstrate how various functional form, independence, and monotonicity assumptions can be imposed as constraints in our optimization procedure to tighten the identified set, and we show how these assumptions have meaningful interpretations in terms of restrictions on latent types.
After revision:  We leverage results on hyperplane arrangements and cell enumeration from the literature on computational geometry in order to provide a tractable means of computing the identified set. We demonstrate how various functional form, independence, and monotonicity assumptions can be imposed as constraints in our optimization procedure to tighten the identified set, and we show how these assumptions have meaningful interpretations in terms of restrictions on latent types.