  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 unobservables 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.
