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Simultaneous equations for discrete outcomes:coherence, completeness, and identification

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  • Andrew Chesher

    ()
    (Institute for Fiscal Studies and University College London)

  • Adam Rosen

    ()
    (Institute for Fiscal Studies and University College London)

Abstract

This paper studies simultaneous equations models for two or more discrete outcomes. These models may be incoherent, delivering no values of the outcomes at certain values of the latent variables and covariates, and they may be incomplete, delivering more than one value of the outcomes at certain values of the covariates and latent variates. We revisit previous approaches to the problems of incompleteness and incoherence in such models, and we propose a new approach for dealing with these. For each approach, we use random set theory to characterize sharp identification regions for the marginal distribution of latent variables and the structural function relating outcomes to covariates, illustrating the relative identifying power and tradeoffs of the different approaches. We show that these identified sets are characterized by systems of conditional moment equalities and inequalities, and we provide a generically applicable algorithm for constructing these. We demonstrate these results for the simultaneous equations model for binary outcomes studied in for example Heckman (1978) and Tamer (2003) and the triangular model with a discrete endogenous variable studied in Chesher (2005) and Jun, Pinkse, and Xu (2011) as illustrative examples.

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Bibliographic Info

Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP21/12.

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Date of creation: Aug 2012
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Handle: RePEc:ifs:cemmap:21/12

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  1. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, 03.
  2. Andrew Chesher & Adam Rosen & Konrad Smolinski, 2011. "An instrumental variable model of multiple discrete choice," CeMMAP working papers CWP39/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  3. Kline, Brendan & Tamer, Elie, 2012. "Bounds for best response functions in binary games," Journal of Econometrics, Elsevier, vol. 166(1), pages 92-105.
  4. Patrick Bajari & Han Hong & Stephen Ryan, 2004. "Identification and Estimation of Discrete Games of Complete Information," NBER Technical Working Papers 0301, National Bureau of Economic Research, Inc.
  5. repec:oup:restud:v:78:y::i:4:p:1264-1298 is not listed on IDEAS
  6. Bresnahan, Timothy F. & Reiss, Peter C., 1991. "Empirical models of discrete games," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 57-81.
  7. Arie Beresteanu & Ilya Molchanov & Francesca Molinari, 2011. "Sharp Identification Regions in Models With Convex Moment Predictions," Econometrica, Econometric Society, vol. 79(6), pages 1785-1821, November.
  8. Elie Tamer & Federico Ciliberto, 2004. "Market Structure and Multiple Equilibria in Airline Markets," 2004 Meeting Papers 52, Society for Economic Dynamics.
  9. Jun, Sung Jae & Pinkse, Joris & Xu, Haiqing, 2011. "Tighter bounds in triangular systems," Journal of Econometrics, Elsevier, vol. 161(2), pages 122-128, April.
  10. Aradillas-Lopez, Andres & Tamer, Elie, 2008. "The Identification Power of Equilibrium in Simple Games," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 261-310.
  11. 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.
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Cited by:
  1. Chesher, Andrew, 2013. "Semiparametric Structural Models Of Binary Response: Shape Restrictions And Partial Identification," Econometric Theory, Cambridge University Press, vol. 29(02), pages 231-266, April.

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