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Title:Simultaneous equations models for discrete outcomes: Coherence, completeness, and identification PDF Logo
Authors:Chesher, Andrew
Rosen, Adam M.
Issue Date:2012
Series/Report no.:cemmap working paper CWP21/12
Abstract: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 values of the covariates and latent variates. We revisit previous approaches to the problems of incompleteness and incoherence in such models, and we propose a new approach for dealing with these. For each approach, we use random set theory to characterize sharp identification regions for the marginal distribution of latent variables and the structural function relating outcomes to covariates, illustrating the relative identifying power and tradeoffs of the different approaches. We show that these identified sets are characterized by systems of conditional moment equalities and inequalities, and we provide a generically applicable algorithm for constructing these. We demonstrate these results for 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) as illustrative examples.
Subjects:Discrete endogenous variables
Endogeneity
Incomplete models
Incoherent models
Instrumental variables
Simultaneous equations models
Set Identification
Structural econometrics
JEL:C10
C14
C50
C51
Persistent Identifier of the first edition:doi:10.1920/wp.cem.2012.2112
Document Type:Working Paper
Appears in Collections:cemmap working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies (IFS)

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