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Coherency And Completeness Of Structural Models Containing A Dummy Endogenous Variable

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  • 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.

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Bibliographic Info

Article provided by Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association in its journal International Economic Review.

Volume (Year): 48 (2007)
Issue (Month): 4 (November)
Pages: 1379-1392

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Handle: RePEc:ier:iecrev:v:48:y:2007:i:4:p:1379-1392

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  1. Dagenais, M.G., 1997. "A Simultaneous Probit Model," G.R.E.Q.A.M. 97a33, Universite Aix-Marseille III.
  2. C. Gourieroux & Jean-Jacques Laffont & A. Monfort, 1979. "Coherency Conditions In Simultaneous Linear Equation Models With Endogenous Switching Regimes," NBER Working Papers 0343, National Bureau of Economic Research, Inc.
  3. James J. Heckman, 1977. "Dummy Endogenous Variables in a Simultaneous Equation System," NBER Working Papers 0177, National Bureau of Economic Research, Inc.
  4. 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.
  5. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," Review of Economic Studies, Wiley Blackwell, vol. 70(1), pages 147-165, January.
  6. Aradillas-Lopez, Andres, 2010. "Semiparametric estimation of a simultaneous game with incomplete information," Journal of Econometrics, Elsevier, vol. 157(2), pages 409-431, August.
  7. 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.
  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. Mitali Das, 2000. "Instrumental Variables Estimation of Nonparametric Models with Discrete Endogenous Regressors," Econometric Society World Congress 2000 Contributed Papers 1008, Econometric Society.
  10. Bresnahan, Timothy F. & Reiss, Peter C., 1991. "Empirical models of discrete games," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 57-81.
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Citations

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Cited by:
  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.
  2. Yingying Dong & Arthur Lewbel, 2012. "A Simple Estimator for Binary Choice Models With Endogenous Regressors," Boston College Working Papers in Economics 807, Boston College Department of Economics.
  3. Andreas Kontoleon & Pauline Grosjean, 2007. "How Sustainable are Sustainable Development Programs? The Case of the Sloping Land Conversion Program in China," Environmental Economy and Policy Research Working Papers 26.2007, University of Cambridge, Department of Land Economics, revised 2007.
  4. Massacci, D., 2007. "Identification and Estimation in an Incoherent Model of Contagion," Cambridge Working Papers in Economics 0744, Faculty of Economics, University of Cambridge.
  5. Van Leeuwen, George & Polder, Michael, 2013. "Linking ICT related Innovation Adoption and Productivity: results from micro-aggregated data versus firm-level data," MPRA Paper 46479, University Library of Munich, Germany.
  6. Arthur Lewbel, 2006. "Modeling Heterogeneity," Boston College Working Papers in Economics 650, Boston College Department of Economics.
  7. George van Leeuwen & Pierre Mohnen, 2013. "Revisiting the Porter Hypothesis: An Empirical Analysis of Green Innovation for the Netherlands," CIRANO Working Papers 2013s-02, CIRANO.
  8. Yingying Dong & Arthur Lewbel, 2012. "Simple Estimators for Binary Choice Models with Endogenous Regressors," Working Papers 111204, University of California-Irvine, Department of Economics.
  9. Hou, Jun & Mohnen, Pierre, 2013. "Complementarity between internal knowledge creation and external knowledge sourcing in developing countries," MERIT Working Papers 010, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).

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