Multivariate ordered discrete response models with two layers of dependence

TL;DR

This paper introduces a novel class of multivariate ordered discrete response models with two layers of dependence, capturing complex threshold interdependencies and latent utility correlations, and demonstrates their application in health insurance markets.

Contribution

It extends traditional lattice models by allowing functionally interdependent thresholds and two layers of dependence, with theoretical foundations and empirical validation.

Findings

Disentangles moral hazard from adverse selection in health insurance.

Shows advantages of the new models over traditional lattice models.

Provides identification conditions and microfoundations for the models.

Abstract

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.