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Identification of Nonparametric Simultaneous Equations Models with a Residual Index Structure

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Abstract

We present new identification results for a class of nonseparable nonparametric simultaneous equations models introduced by Matzkin (2008). These models combine traditional exclusion restrictions with a requirement that each structural error enter through a "residual index." Our identification results are constructive and encompass a range of special cases with varying demands on the exogenous variation provided by instruments and the shape of the joint density of the structural errors. The most important of these results demonstrate identification even when instruments have limited variation. A genericity result demonstrates a formal sense in which the associated density conditions may be viewed as mild, even when instruments vary only over a small open ball.

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  • Steven T. Berry & Philip A. Haile, 2016. "Identification of Nonparametric Simultaneous Equations Models with a Residual Index Structure," Cowles Foundation Discussion Papers 2008R, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2008r
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    11. 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.
    12. Roehrig, Charles S, 1988. "Conditions for Identification in Nonparametric and Parametic Models," Econometrica, Econometric Society, vol. 56(2), pages 433-447, March.
    13. Steven T. Berry & Philip A. Haile, 2009. "Identification of a Heterogeneous Generalized Regression Model with Group Effects," Cowles Foundation Discussion Papers 1732, Cowles Foundation for Research in Economics, Yale University.
    14. Anderson Robert M. & Zame William R., 2001. "Genericity with Infinitely Many Parameters," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-64, February.
    15. Horowitz, Joel L, 1996. "Semiparametric Estimation of a Regression Model with an Unknown Transformation of the Dependent Variable," Econometrica, Econometric Society, vol. 64(1), pages 103-137, January.
    16. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, September.
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    Cited by:

    1. Wang, Ao, 2020. "Identifying the Distribution of Random Coefficients in BLP Demand Models Using One Single Variation in Product Characteristics," The Warwick Economics Research Paper Series (TWERPS) 1304, University of Warwick, Department of Economics.
    2. Allen, Roy, 2022. "Injectivity and the law of demand," Economics Letters, Elsevier, vol. 215(C).
    3. Mogens Fosgerau & Dennis Kristensen, 2021. "Identification of a class of index models: A topological approach," The Econometrics Journal, Royal Economic Society, vol. 24(1), pages 121-133.
    4. Richard Blundell & Dennis Kristensen & Rosa Matzkin, 2017. "Individual counterfactuals with multidimensional unobserved heterogeneity," CeMMAP working papers CWP60/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Wang, Ao, 2023. "Sieve BLP: A semi-nonparametric model of demand for differentiated products," Journal of Econometrics, Elsevier, vol. 235(2), pages 325-351.
    6. Dunker, Fabian & Hoderlein, Stefan & Kaido, Hiroaki & Sherman, Robert, 2018. "Nonparametric identification of the distribution of random coefficients in binary response static games of complete information," Journal of Econometrics, Elsevier, vol. 206(1), pages 83-102.

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    More about this item

    Keywords

    Simultaneous equations; Nonseparable models; Nonparametric identification;
    All these keywords.

    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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