This paper studies simultaneous equations models for two or more discrete outcomes. These models may be incoherent, delivering no values of the outcomes at certain values of the latent variables and covariates, and they may be incomplete, delivering more than one value of the outcomes at certain...

This chapter sets out the extension of the scope of the classical IV model to cases in which unobserved variables are set-valued functions of observed variables. The resulting Generalized IV (GIV) models can be used when outcomes are discrete while unobserved variables are continuous, when there...

Recent research underscores the sensitivity of conclusions drawn from the application of econometric methods devised for quantitative outcome variables to data featuring ordinal outcomes. The issue is particularly acute in the analysis of happiness data, for which no natural cardinal scale...

Models of simultaneous discrete choice may be incomplete, delivering multiple values of out- comes at certain values of the latent variables and covariates, and incoherent, delivering no val- ues. Alternative approaches to accommodating incompleteness and incoherence are considered in a unifying...

Single equation instrumental variable models for discrete outcomes are shown to be set not point identifying for the structural functions that deliver the values of the discrete outcome. Identified sets are derived for a general nonparametric model and sharp set identification is demonstrated....

We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or equivalently, the value of a linear programming problem with a potentially infinite constraint set. Our approach is...