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Coherence and Completeness of Structural Models Containing a Dummy Endogenous Variable

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  • Arthur Lewbel

    (Boston College)

Abstract

Let y be a vector 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 paper 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.

Suggested Citation

  • Arthur Lewbel, 1997. "Coherence and Completeness of Structural Models Containing a Dummy Endogenous Variable," Boston College Working Papers in Economics 456, Boston College Department of Economics, revised 04 Sep 2006.
    • Handle: RePEc:boc:bocoec:456
    Note: Previously circulated as "Coherence of Structural Models Containing a Dummy Endogenous Variable"
    as

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    References listed on IDEAS

    as
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    More about this item

    Keywords

    binary choice; binomial response; simultaneous equations; endogeneity; coherency; latent variable models;
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