IDEAS home Printed from https://ideas.repec.org/a/ier/iecrev/v48y2007i4p1379-1392.html
   My bibliography  Save this article

Coherency And Completeness Of Structural Models Containing A Dummy Endogenous Variable

Author

Listed:
  • Arthur Lewbel

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. Copyright 2007 by the Economics Department Of The University Of Pennsylvania And Osaka University Institute Of Social And Economic Research Association.

Suggested Citation

  • Arthur Lewbel, 2007. "Coherency And Completeness Of Structural Models Containing A Dummy Endogenous Variable," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1379-1392, November.
    • Handle: RePEc:ier:iecrev:v:48:y:2007:i:4:p:1379-1392
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Mitali Das, 2000. "Instrumental Variables Estimation of Nonparametric Models with Discrete Endogenous Regressors," Econometric Society World Congress 2000 Contributed Papers 1008, Econometric Society.
    2. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-959, July.
    3. 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 675-695, April.
    4. 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.
    5. Dagenais, M.G., 1997. "A Simultaneous Probit Model," G.R.E.Q.A.M. 97a33, Universite Aix-Marseille III.
    6. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(1), pages 147-165.
    7. Bresnahan, Timothy F. & Reiss, Peter C., 1991. "Empirical models of discrete games," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 57-81.
    8. 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.
    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.
    10. Aradillas-Lopez, Andres, 2010. "Semiparametric estimation of a simultaneous game with incomplete information," Journal of Econometrics, Elsevier, vol. 157(2), pages 409-431, August.
    11. 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 525-545, National Bureau of Economic Research, Inc.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Arthur Lewbel, 2019. "The Identification Zoo: Meanings of Identification in Econometrics," Journal of Economic Literature, American Economic Association, vol. 57(4), pages 835-903, December.
    2. Federico Ciliberto & Elie Tamer, 2009. "Market Structure and Multiple Equilibria in Airline Markets," Econometrica, Econometric Society, vol. 77(6), pages 1791-1828, November.
    3. Francesca Molinari, 2020. "Microeconometrics with Partial Identification," Papers 2004.11751, arXiv.org.
    4. Andrew Chesher & Adam Rosen, 2012. "Simultaneous equations for discrete outcomes: coherence, completeness, and identification," CeMMAP working papers CWP21/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Hajivassiliou, Vassilis & Savignac, Frédérique, 2024. "Simultaneously Incomplete and Incoherent (SII) Dynamic LDV Models: With an Application to Financing Constraints and Firms’ Decision to Innovate," Journal of Econometrics, Elsevier, vol. 238(1).
    6. Marc HENRY & Ismael MOURIFIÉ, 2013. "Nonparametric Sharp Bounds For Payoffs In 2 × 2 Games," Working Papers tecipa-500, University of Toronto, Department of Economics.
    7. Aradillas-Lopez, Andres, 2010. "Semiparametric estimation of a simultaneous game with incomplete information," Journal of Econometrics, Elsevier, vol. 157(2), pages 409-431, August.
    8. Arthur Lewbel, 2006. "Modeling Heterogeneity," Boston College Working Papers in Economics 650, Boston College Department of Economics.
    9. Francesca Molinari, 2019. "Econometrics with Partial Identification," CeMMAP working papers CWP25/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. Aradillas-López, Andrés & Rosen, Adam M., 2022. "Inference in ordered response games with complete information," Journal of Econometrics, Elsevier, vol. 226(2), pages 451-476.
    11. Fabian Dunker & Stefan Hoderlein & Hiroaki Kaido, 2013. "Random coefficients in static games of complete information," CeMMAP working papers CWP12/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    12. Kyoo il Kim, 2006. "Semiparametric Estimation of Signaling Games," Labor Economics Working Papers 22452, East Asian Bureau of Economic Research.
    13. Paul B. Ellickson & Sanjog Misra, 2011. "Structural Workshop Paper --Estimating Discrete Games," Marketing Science, INFORMS, vol. 30(6), pages 997-1010, November.
    14. Kyoo il Kim, 2006. "Set Inference for Semiparametric Discrete Games," Labor Economics Working Papers 22454, East Asian Bureau of Economic Research.
    15. Magnac, Thierry, 2013. "Identification partielle : méthodes et conséquences pour les applications empiriques," L'Actualité Economique, Société Canadienne de Science Economique, vol. 89(4), pages 233-258, Décembre.
    16. Bryan S. Graham & Andrin Pelican, 2023. "Scenario Sampling for Large Supermodular Games," Papers 2307.11857, arXiv.org.
    17. Massacci, D., 2007. "Identification and Estimation in an Incoherent Model of Contagion," Cambridge Working Papers in Economics 0744, Faculty of Economics, University of Cambridge.
    18. Dunker, Fabian & Hoderlein, Stefan & Kaido, Hiroaki & Sherman, Robert, 2018. "Nonparametric identification of the distribution of random coefficients in binary response static games of complete information," Journal of Econometrics, Elsevier, vol. 206(1), pages 83-102.
    19. Jeremy Fox & Natalia Lazzati, 2013. "Identification of discrete choice models for bundles and binary games," CeMMAP working papers 04/13, Institute for Fiscal Studies.
    20. Wan, Yuanyuan & Xu, Haiqing, 2014. "Semiparametric identification of binary decision games of incomplete information with correlated private signals," Journal of Econometrics, Elsevier, vol. 182(2), pages 235-246.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ier:iecrev:v:48:y:2007:i:4:p:1379-1392. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley-Blackwell Digital Licensing or the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/deupaus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.