Multivariate Ordered Discrete Response Models

We introduce multivariate ordered discrete response models that exhibit non-lattice structures. From the perspective of behavioral economics, these models correspond to broad bracketing}in decision making, whereas lattice models, which researchers typically estimate in practice, correspond to narrow bracketing. There is also a class of hierarchical models, which nests lattice models and is a special case of non-lattice models. Hierarchical models correspond to sequential decision making and can be represented by binary decision trees. In each of these cases, we specify latent processes as a sum of an index of covariates and an unobserved error, with unobservables for different latent processes potentially correlated. This additional dependence further complicates the identification of model parameters in non-lattice models. We give conditions sufficient to guarantee identification under the independence of errors and covariates, compare these conditions to what is required to attain identification in lattice models and outline an estimation approach. Finally, we provide simulations and empirical examples, through which we discuss the case when unobservables follow a distribution from a known parametric family, focusing on popular probit specifications