  This paper develops sharp testable implications for Tobit and IV-Tobit
models' identifying assumptions: linear index specification, (joint) normality
of latent errors, and treatment (instrument) exogeneity and relevance. The new
sharp testable equalities can detect all possible observable violations of the
identifying conditions. We propose a testing procedure for the model's validity
using existing inference methods for intersection bounds. Simulation results
suggests proper size for large samples and that the test is powerful to detect
large violation of the exogeneity assumption and violations in the error
structure. Finally, we review and propose new alternative paths to partially
identify the parameters of interest under less restrictive assumptions.
