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Coherence and Completeness of Structural Models Containing a Dummy Endogenous Variable

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Arthur Lewbel () (Boston College)

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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.

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Publisher Info
Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 456.

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Length: 17 pages
Date of creation: 15 Sep 1997
Date of revision: 04 Sep 2006
Handle: RePEc:boc:bocoec:456

Note: Previously circulated as "Coherence of Structural Models Containing a Dummy Endogenous Variable"
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Related research
Keywords: binary choice; binomial response; simultaneous equations; endogeneity; coherency; latent variable models;

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  1. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September. [Downloadable!] (restricted)
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  2. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," Review of Economic Studies, Blackwell Publishing, vol. 70(1), pages 147-165, January.
  3. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March. [Downloadable!] (restricted)
  4. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-59, July. [Downloadable!] (restricted)
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  5. G. S. Maddala & Lung-Fei Lee, 1976. "Recursive Models with Qualitative Endogenous Variables," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 168-188 National Bureau of Economic Research, Inc. [Downloadable!]
  6. Dagenais, M.G., 1997. "A Simultaneous Probit Model," G.R.E.Q.A.M. 97a33, Universite Aix-Marseille III.
  7. Mitali Das, 2000. "Instrumental Variables Estimation of Nonparametric Models with Discrete Endogenous Regressors," Econometric Society World Congress 2000 Contributed Papers 1008, Econometric Society. [Downloadable!]
  8. Bresnahan, Timothy F. & Reiss, Peter C., 1991. "Empirical models of discrete games," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 57-81. [Downloadable!] (restricted)
  9. Blundell, Richard & Smith, Richard J., 1994. "Coherency and estimation in simultaneous models with censored or qualitative dependent variables," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 355-373. [Downloadable!] (restricted)
  10. Gourieroux, C & Laffont, J J & Monfort, A, 1980. "Coherency Conditions in Simultaneous Linear Equation Models with Endogenous Switching Regimes," Econometrica, Econometric Society, vol. 48(3), pages 675-95, April. [Downloadable!] (restricted)
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  1. Changhui Kang & Myoung-jae Lee, 2009. "Performance of Various Estimators for Censored Response Models with Endogenous Regressors," Discussion Paper Series 0905, Institute of Economic Research, Korea University. [Downloadable!]
  2. Massacci, D., 2007. "Identification and Estimation in an Incoherent Model of Contagion," Cambridge Working Papers in Economics 0744, Faculty of Economics, University of Cambridge. [Downloadable!]
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