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Identification of Mixture Models Using Support Variations

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  • Xavier d'Haultfoeuille

    (Crest)

  • Philippe Fevrier

    (Crest)

Abstract

We consider the issue of identifying nonparametrically mixture models. In thesemodels, all observed variables depend on a common and unobserved component,but are mutually independent conditional on it. Such models are important in themeasurement error, auction and matching literatures. Traditional approaches relyon parametric assumptions or strong functional restrictions. We show that thesemodels are actually identified nonparametrically if a moving support assumption issatisfied. More precisely, we suppose that the supports of the observed variables movewith the true value of the unobserved component. We show that this assumption istheoretically grounded, empirically relevant and testable. Finally, we compare ourapproach with the diagonalization technique introduced by Hu and Schennach (2008),which allows to obtain similar results.

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Bibliographic Info

Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2010-12.

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Length: 27
Date of creation: 2010
Date of revision:
Handle: RePEc:crs:wpaper:2010-12

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  1. Yingyao Hu & David McAdams & Matthew Shum, 2009. "Nonparametric Identification of Auction Models with Non-Separable Unobserved Heterogeneity," Economics Working Paper Archive 553, The Johns Hopkins University,Department of Economics.
  2. John G. Riley & William Samuelson, 1979. "Optimal Auctions," UCLA Economics Working Papers 152, UCLA Department of Economics.
  3. Robert Shimer & Lones Smith, 2000. "Assortative Matching and Search," Econometrica, Econometric Society, vol. 68(2), pages 343-370, March.
  4. John Bound & Alan B. Krueger, 1989. "The Extent of Measurement Error In Longitudinal Earnings Data: Do Two Wrongs Make A Right?," NBER Working Papers 2885, National Bureau of Economic Research, Inc.
  5. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, vol. 52(6), pages 1473-1518, November.
  6. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, 01.
  7. Yingyao Hu & Susanne Schennach, 2006. "Identification and estimation of nonclassical nonlinear errors-in-variables models with continuous distributions using instruments," CeMMAP working papers CWP17/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  8. Hu, Yingyao, 2008. "Identification and estimation of nonlinear models with misclassification error using instrumental variables: A general solution," Journal of Econometrics, Elsevier, vol. 144(1), pages 27-61, May.
  9. Whitney K. Newey, 2001. "Flexible Simulated Moment Estimation Of Nonlinear Errors-In-Variables Models," The Review of Economics and Statistics, MIT Press, vol. 83(4), pages 616-627, November.
  10. Susanne M. Schennach, 2004. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometric Society 2004 North American Summer Meetings 602, Econometric Society.
  11. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, 09.
  12. Cazals, Catherine & Florens, Jean-Pierre & Simar, Leopold, 2002. "Nonparametric frontier estimation: a robust approach," Journal of Econometrics, Elsevier, vol. 106(1), pages 1-25, January.
  13. Becker, Gary S, 1973. "A Theory of Marriage: Part I," Journal of Political Economy, University of Chicago Press, vol. 81(4), pages 813-46, July-Aug..
  14. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
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