COHERENCY AND COMPLETENESS OF STRUCTURAL MODELS CONTAINING A DUMMY ENDOGENOUS VARIABLE*
给出了一个方程是二项响应时联立方程系统连贯且完备的充要条件，适用于虚拟内生变量、制度转换、处理效应、样本选择等模型，帮助判断模型是否有良好定义的简化形式。
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.