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Sharp identified sets for discrete variable IV models

  • Andrew Chesher

    ()

    (Institute for Fiscal Studies and University College London)

  • Konrad Smolinski

    ()

    (Institute for Fiscal Studies)

Instrumental variable models for discrete outcomes are set, not point, identifying. The paper characterises identified sets of structural functions when endogenous variables are discrete. Identified sets are unions of large numbers of convex sets and may not be convex nor even connected. Each of the component sets is a projection of a convex set that resides in a much higher dimensional space onto the space in which a structural function resides. The paper develops a symbolic expression for this projection and gives a constructive demonstration that it is indeed the identified set. We provide a MathematicaTM notebook which computes the set symbolically. We derive properties of the set, suggest how the set can be used in practical econometric analysis when outcomes and endogenous variables are discrete and propose a method for estimating identified sets under parametric or shape restrictions. We develop an expression for a set of structural functions for the case in which endogenous variables are continuous or mixed discrete-continuous and show that this set contains all structural functions in the identified set in the non-discrete case.

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File URL: http://cemmap.ifs.org.uk/wps/cwp1110.pdf
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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP11/10.

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Date of creation: May 2010
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Handle: RePEc:ifs:cemmap:11/10
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  1. Andrew Chesher, 2005. "Nonparametric Identification under Discrete Variation," Econometrica, Econometric Society, vol. 73(5), pages 1525-1550, 09.
  2. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," Review of Economic Studies, Wiley Blackwell, vol. 70(1), pages 147-165, January.
  3. Andrew Chesher, 2007. "Endogeneity and discrete outcomes," CeMMAP working papers CWP05/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Andrew Chesher, 2010. "Instrumental Variable Models for Discrete Outcomes," Econometrica, Econometric Society, vol. 78(2), pages 575-601, 03.
  5. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, 03.
  6. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, 09.
  7. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, 09.
  8. Andrew Chesher & Konrad Smolinski, 2009. "IV models of ordered choice," CeMMAP working papers CWP37/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  9. Andrew Chesher, 2009. "Single equation endogenous binary reponse models," CeMMAP working papers CWP23/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  10. Das, M., 2005. "Instrumental variables estimators of nonparametric models with discrete endogenous regressors," Journal of Econometrics, Elsevier, vol. 124(2), pages 335-361, February.
  11. Jun, Sung Jae & Pinkse, Joris & Xu, Haiqing, 2011. "Tighter bounds in triangular systems," Journal of Econometrics, Elsevier, vol. 161(2), pages 122-128, April.
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