Abstract :
Let y be a vector of endogenous variables and let w be a vector of covariates,
parameters, and errors or unobservables that together are assumed to determine
y. A structural model y = H(y, w) is complete and coherent if it has a
well-defined reduced form, meaning that for any value of w there exists a unique
value for y. Coherence and completeness simplifies identification and is required
for many estimators and many model applications. Incoherency or incompleteness
can arise in models with multiple decision makers, such as games, or when
the decision making of individuals is either incorrectly or incompletely specified.
This article provides necessary and sufficient conditions for the coherence and
completeness of simultaneous equation systems where one equation is a binomial
response. Examples are dummy endogenous regressor models, regime switching
regressions, treatment response models, sample selection models, endogenous
choice systems, and determining if a pair of binary choices are substitutes or
complements.
