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Set identified linear models

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  • Christian Bontemps
  • Thierry Magnac

    (Institute for Fiscal Studies and Toulouse)

  • Eric Maurin

Abstract

We analyze the identification and estimation of parameters β satisfying the incomplete linear moment restrictions E(z T (x β−y)) = E(z Tu(z)) where z is a set of instruments and u(z) an unknown bounded scalar function. We first provide empirically relevant examples of such a set-up. Second, we show that these conditions set identify β where the identified set B is bounded and convex. We provide a sharp characterization of the identified set not only when the number of moment conditions is equal to the number of parameters of interest but also in the case in which the number of conditions is strictly larger than the number of parameters. We derive a necessary and sufficient condition of the validity of supernumerary restrictions which generalizes the familiar Sargan condition. Third, we provide new results on the asymptotics of analog estimates constructed from the identification results. When B is a strictly convex set, we also construct a test of the null hypothesis, β 0 ε B, whose size is asymptotically correct and which relies on the minimization of the support function of the set B − { β 0 }. Results of some Monte Carlo experiments are presented.

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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 CWP13/11.

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Date of creation: Apr 2011
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Handle: RePEc:ifs:cemmap:13/11

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  1. Guido Imbens & Charles F. Manski, 2003. "Confidence intervals for partially identified parameters," CeMMAP working papers CWP09/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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Citations

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Cited by:
  1. Donald W.K. Andrews & Panle Jia, 2008. "Inference for Parameters Defined by Moment Inequalities: A Recommended Moment Selection Procedure," Cowles Foundation Discussion Papers 1676R, Cowles Foundation for Research in Economics, Yale University, revised Aug 2011.
  2. Aviv Nevo & Adam Rosen, 2008. "Identification with imperfect instruments," CeMMAP working papers CWP16/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  3. Donald W.K. Andrews & Xiaoxia Shi, 2010. "Inference Based on Conditional Moment Inequalities," Cowles Foundation Discussion Papers 1761RR, Cowles Foundation for Research in Economics, Yale University, revised May 2012.
  4. Adam Rosen, 2006. "Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities," CeMMAP working papers CWP25/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Liao, Yuan & Simoni, Anna, 2012. "Semi-parametric Bayesian Partially Identified Models based on Support Function," MPRA Paper 43262, University Library of Munich, Germany.
  6. Laura Coroneo & Valentina Corradi & Paulo Santos Monteiro, 2013. "Testing for optimal monetary policy via moment inequalities," Discussion Papers 13/07, Department of Economics, University of York.
  7. Daniel Cerquera & François Laisney & Hannes Ullrich, 2012. "Considerations on partially identified regression models," Working Papers of BETA 2012-07, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
  8. David Pacini, 2012. "Least Square Linear Prediction with Two-Sample Data," Bristol Economics Discussion Papers 12/631, Department of Economics, University of Bristol, UK.
  9. Arun Chandrasekhar & Victor Chernozhukov & Francesca Molinari & Paul Schrimpf, 2012. "Inference for best linear approximations to set identified functions," CeMMAP working papers CWP43/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  10. Hoshino, Tadao, 2013. "Partial identification in binary response models with nonignorable nonresponses," Economics Letters, Elsevier, vol. 121(1), pages 74-78.
  11. Magnac, Thierry, 2014. "Identification partielle: méthodes et conséquences pour les applications empiriques," IDEI Working Papers 814, Institut d'Économie Industrielle (IDEI), Toulouse.
  12. Karun Adusumilli & Taisuke Otsu, 2014. "Empirical Likelihood for Random Sets," STICERD - Econometrics Paper Series /2014/574, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  13. Melanie Arntz & Simon Lo & Ralf Wilke, 2014. "Bounds analysis of competing risks: a non-parametric evaluation of the effect of unemployment benefits on migration," Empirical Economics, Springer, vol. 46(1), pages 199-228, February.

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