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Generalized instrumental variable models

Author

Listed:
  • Andrew Chesher

    (Institute for Fiscal Studies and University College London)

  • Adam Rosen

    (Institute for Fiscal Studies and Duke University)

Abstract

The ability to allow for flexible forms of unobserved heterogeneity is an essential ingredient in modern microeconometrics. In this paper we extend the application of instrumental variable (IV) models to a wide class of problems in which multiple values of unobservable variables can be associated with particular combinations of observed endogenous and exogenous variables. In our Generalised Instrumental Variable (GIV) models, in contrast to traditional IV models, the mapping from unobserved heterogeneity to endogenous variables need not admit a unique inverse. The class of GIV models allows unobservables to be multivariate and to enter nonseparably into the determination of endogenous variables, thereby removing strong practical limitations on the role of unobserved heterogeneity. Important examples include models with discrete or mixed continuous/discrete outcomes and continuous unobservables, and models with excess heterogeneity where many combinations of different values of multiple unobserved variables, such as random coefficients, can deliver the same realisations of outcomes. We use tools from random set theory to study identification in such models and provide a sharp characterisation of the identified set of structures admitted. We demonstrate the application of our analysis to a continuous outcome model with an interval-censored endogenous explanatory variable.

Suggested Citation

  • Andrew Chesher & Adam Rosen, 2013. "Generalized instrumental variable models," CeMMAP working papers CWP43/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:43/13
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    File URL: http://www.cemmap.ac.uk/wps/cwp431313.pdf
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    References listed on IDEAS

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    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

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    2. Hoderlein, Stefan & Holzmann, Hajo & Meister, Alexander, 2017. "The triangular model with random coefficients," Journal of Econometrics, Elsevier, vol. 201(1), pages 144-169.
    3. Pietro Tebaldi & Alexander Torgovitsky & Hanbin Yang, 2019. "Nonparametric Estimates of Demand in the California Health Insurance Exchange," NBER Working Papers 25827, National Bureau of Economic Research, Inc.
    4. Andrew Chesher & Adam Rosen, 2017. "Incomplete English auction models with heterogeneity," CeMMAP working papers CWP27/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Andrew Chesher & Adam M. Rosen, 2017. "Generalized Instrumental Variable Models," Econometrica, Econometric Society, vol. 85, pages 959-989, May.
    6. Jiaying Gu & Thomas M. Russell, 2021. "Partial Identification in Nonseparable Binary Response Models with Endogenous Regressors," Papers 2101.01254, arXiv.org, revised Jul 2021.
    7. Magnac, Thierry, 2013. "Identification partielle : méthodes et conséquences pour les applications empiriques," L'Actualité Economique, Société Canadienne de Science Economique, vol. 89(4), pages 233-258, Décembre.
    8. Li, Chuhui & Poskitt, D.S. & Zhao, Xueyan, 2019. "The bivariate probit model, maximum likelihood estimation, pseudo true parameters and partial identification," Journal of Econometrics, Elsevier, vol. 209(1), pages 94-113.
    9. Kalouptsidi, Myrto & Scott, Paul T. & Souza-Rodrigues, Eduardo, 2021. "Linear IV regression estimators for structural dynamic discrete choice models," Journal of Econometrics, Elsevier, vol. 222(1), pages 778-804.
    10. Arthur Lewbel, 2019. "The Identification Zoo: Meanings of Identification in Econometrics," Journal of Economic Literature, American Economic Association, vol. 57(4), pages 835-903, December.
    11. Hubner, Stefan, 2016. "Topics in nonparametric identification and estimation," Other publications TiSEM 08fce56b-3193-46e0-871b-0, Tilburg University, School of Economics and Management.
    12. Iaria, Alessandro & WANG, Ao, 2020. "Identification and Estimation of Demand for Bundles," CEPR Discussion Papers 14363, C.E.P.R. Discussion Papers.
    13. Thomas M. Russell, 2020. "Policy Transforms and Learning Optimal Policies," Papers 2012.11046, arXiv.org.
    14. Bontemps, Christian & Kumar, Rohit, 2020. "A geometric approach to inference in set-identified entry games," Journal of Econometrics, Elsevier, vol. 218(2), pages 373-389.

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    More about this item

    Keywords

    instrumental variables; endogeneity; excess heterogeneity; limited information; set identification; partial identification; random sets; incomplete models;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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