Simultaneous equations models for discrete outcomes: coherence, completeness, and identication

This paper studies simultaneous equations models for two or more discrete outcomes. The models allow latent variables to be high dimensional and require latent variables and covariates to be independently distributed. The models may be incoherent, delivering no values of the outcomes at certain values of the latent variables and covariates. The models may be incomplete, delivering more than one value of the outcomes at certain values of the covariates and latent variates. The models partially identify the marginal distribution of the latent variables and the structural function which relates outcomes to covariates and latent variates. We characterize the identi…ed set and illustrate using the simultaneous equations model for binary outcomes studied in for example Heckman (1978) and Tamer (2003) and the triangular model with a discrete endogenous variable studied in Chesher (2005) and Jun, Pinkse, and Xu (2011). Keywords: Discrete endogenous variables, Endogeneity, Incomplete models, Incoherent models Instrumental variables, Simultaneous eqations models, Set Identi…cation, Structural econometrics. JEL Codes: C10, C14, C50, C51.