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Identification in a Class of Nonparametric Simultaneous Equations Models



We consider identification in a class of nonparametric simultaneous equations models introduced by Matzkin (2008). These models combine standard exclusion restrictions with a requirement that each structural error enter through a "residual index" function. We provide constructive proofs of identification under several sets of conditions, demonstrating tradeoffs between restrictions on the support of the instruments, shape restrictions on the joint distribution of the structural errors, and restrictions on the form of the residual index function.

Suggested Citation

  • Steven T. Berry & Philip A. Haile, 2011. "Identification in a Class of Nonparametric Simultaneous Equations Models," Cowles Foundation Discussion Papers 1787, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1787

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    References listed on IDEAS

    1. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, September.
    2. Steven Berry & Amit Gandhi & Philip Haile, 2013. "Connected Substitutes and Invertibility of Demand," Econometrica, Econometric Society, vol. 81(5), pages 2087-2111, September.
    3. Mark Bagnoli & Ted Bergstrom, 2005. "Log-concave probability and its applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 445-469, August.
    4. Guido W. Imbens & Whitney K. Newey, 2009. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," Econometrica, Econometric Society, vol. 77(5), pages 1481-1512, September.
    5. Donald J. Brown & Marten H. Wegkamp, 2002. "Weighted Minimum Mean-Square Distance from Independence Estimation," Econometrica, Econometric Society, vol. 70(5), pages 2035-2051, September.
    6. Joel L. Horowitz & Marianthi Markatou, 1996. "Semiparametric Estimation of Regression Models for Panel Data," Review of Economic Studies, Oxford University Press, vol. 63(1), pages 145-168.
    7. Roehrig, Charles S, 1988. "Conditions for Identification in Nonparametric and Parametic Models," Econometrica, Econometric Society, vol. 56(2), pages 433-447, March.
    8. C. Lanier Benkard & Steven Berry, 2006. "On the Nonparametric Identification of Nonlinear Simultaneous Equations Models: Comment on Brown (1983) and Roehrig (1988)," Econometrica, Econometric Society, vol. 74(5), pages 1429-1440, September.
    9. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    10. Donald J. Brown & Rosa L. Matzkin, 1998. "Estimation of Nonparametric Functions in Simultaneous Equations Models, with an Application to Consumer Demand," Cowles Foundation Discussion Papers 1175, Cowles Foundation for Research in Economics, Yale University.
    11. C. Lanier Benkard & Steven Berry, "undated". "On the Nonparametric Identification of Nonlinear Simultaneous Equations Models: comment on B. Brown (1983) and Roehrig (1988)," Cowles Foundation Discussion Papers 1482, Cowles Foundation for Research in Economics, Yale University.
    12. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
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    More about this item


    Simultaneous equations; Nonseparable models; Nonparametric identification;

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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