Multivariate ordered discrete response models with two layers of dependence

We develop a class of multivariate ordered discrete response models featuring general rectangular structures, which allow for functionally interdependent thresholds across dimensions, extending beyond traditional (lattice) models that assume threshold independence. The new models incorporate two layers of dependence: one arising from the interdependence of decision rules (capturing broad bracketing behaviors) and another from the correlation of latent utilities conditional on observables. We provide microfoundations, explore semiparametric and parametric specifications, and establish identification conditions under logical consistency in decision-making. An empirical application to health insurance markets demonstrates the advantages of this new framework, showing how it disentangles moral hazard (captured via threshold dependence) from adverse selection (isolated in unobservable correlations), offering insights into behavioral responses obscured by lattice models.