Multivariate Ordered Discrete Response Models

Abstract

We introduce multivariate ordered discrete response models with general rectangular
structures. From the perspective of behavioral economics, these non-lattice models correspond to broad bracketing in decision making, whereas lattice models, which researchers
typically estimate in practice, correspond to narrow bracketing. In these models, we specify
latent processes as a sum of an index of covariates and an unobserved error, with unoboservables for different latent processes potentially correlated. We provide conditions that
are sufficient for identification under the independence of errors and covariates and outline
an estimation approach. We present simulations and empirical examples, with a particular
focus on probit specifications.

Keywords: ordered response, non-lattice structure, binary decision tree, identification, semiparametric models, broad bracketing, narrow bracketing

JEL Classification: C14, C31, C35, C57, D9, D12, D81