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Identification of Nonparametric Simultaneous Equations Models with a Residual Index Structure

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Abstract

We present new results on the identifiability of a class of nonseparable nonparametric simultaneous equations models introduced by Matzkin (2008). These models combine exclusion restrictions with a requirement that each structural error enter through a "residual index." Our identification results encompass a variety of special cases allowing tradeoffs between the exogenous variation required of instruments and restrictions on the joint density of structural errors. Among these special cases are results avoiding any density restriction and results allowing instruments with arbitrarily small support.

Suggested Citation

  • Steven T. Berry & Philip A. Haile, 2015. "Identification of Nonparametric Simultaneous Equations Models with a Residual Index Structure," Cowles Foundation Discussion Papers 2008, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2008
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d20/d2008.pdf
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    Cited by:

    1. 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.
    2. 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.
    3. Suqin Ge & João Macieira, 2024. "Unobserved Worker Quality and Inter‐Industry Wage Differentials," Journal of Industrial Economics, Wiley Blackwell, vol. 72(1), pages 459-515, March.
    4. Chesher, Andrew & Rosen, Adam M., 2020. "Generalized instrumental variable models, methods, and applications," Handbook of Econometrics, in: Steven N. Durlauf & Lars Peter Hansen & James J. Heckman & Rosa L. Matzkin (ed.), Handbook of Econometrics, edition 1, volume 7, chapter 0, pages 1-110, Elsevier.
    5. Allen, Roy, 2022. "Injectivity and the law of demand," Economics Letters, Elsevier, vol. 215(C).
    6. Wang, Ao, 2023. "Sieve BLP: A semi-nonparametric model of demand for differentiated products," Journal of Econometrics, Elsevier, vol. 235(2), pages 325-351.
    7. 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.
    8. 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.

    More about this item

    Keywords

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    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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