IDEAS home Printed from https://ideas.repec.org/p/ifs/cemmap/43-13.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: http://www.cemmap.ac.uk/wps/cwp431313.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Andrews, Donald W.K. & Guggenberger, Patrik, 2009. "Validity Of Subsampling And “Plug-In Asymptotic” Inference For Parameters Defined By Moment Inequalities," Econometric Theory, Cambridge University Press, vol. 25(3), pages 669-709, June.
    2. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    3. 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.
    4. Federico Ciliberto & Elie Tamer, 2009. "Market Structure and Multiple Equilibria in Airline Markets," Econometrica, Econometric Society, vol. 77(6), pages 1791-1828, November.
    5. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March.
    6. Han Hong & Elie Tamer, 2003. "Inference in Censored Models with Endogenous Regressors," Econometrica, Econometric Society, vol. 71(3), pages 905-932, May.
    7. Aradillas-López, Andrés & Rosen, Adam M., 2022. "Inference in ordered response games with complete information," Journal of Econometrics, Elsevier, vol. 226(2), pages 451-476.
    8. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2013. "Testing Many Moment Inequalities," CeMMAP working papers 65/13, Institute for Fiscal Studies.
    9. Bowden, Roger J, 1973. "The Theory of Parametric Identification," Econometrica, Econometric Society, vol. 41(6), pages 1069-1074, November.
    10. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818728.
    11. Joseph P. Romano & Azeem M. Shaikh & Michael Wolf, 2014. "A Practical Two‐Step Method for Testing Moment Inequalities," Econometrica, Econometric Society, vol. 82, pages 1979-2002, September.
    12. Chesher, Andrew & Smolinski, Konrad, 2012. "IV models of ordered choice," Journal of Econometrics, Elsevier, vol. 166(1), pages 33-48.
    13. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4ao8ocg is not listed on IDEAS
    14. Andrew Chesher & Adam M. Rosen, 2013. "What Do Instrumental Variable Models Deliver with Discrete Dependent Variables?," American Economic Review, American Economic Association, vol. 103(3), pages 557-562, May.
    15. Marc Henry & Romuald Méango & Maurice Queyranne, 2012. "Combinatorial Bootstrap Inference IN in Prtially Identified Incomplete Structural Models," CIRJE F-Series CIRJE-F-837, CIRJE, Faculty of Economics, University of Tokyo.
    16. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    17. Xiaohong Chen & Victor Chernozhukov & Sokbae Lee & Whitney K. Newey, 2014. "Local Identification of Nonparametric and Semiparametric Models," Econometrica, Econometric Society, vol. 82(2), pages 785-809, March.
    18. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524131.
    19. Ivan A. Canay & Andres Santos & Azeem M. Shaikh, 2013. "On the Testability of Identification in Some Nonparametric Models With Endogeneity," Econometrica, Econometric Society, vol. 81(6), pages 2535-2559, November.
    20. Andrew Chesher & Adam M. Rosen, 2017. "Generalized Instrumental Variable Models," Econometrica, Econometric Society, vol. 85, pages 959-989, May.
    21. 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, September.
    22. Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, July.
    23. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2007. "Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves," Econometrica, Econometric Society, vol. 75(6), pages 1613-1669, November.
    24. Alfred Galichon & Marc Henry, 2011. "Set Identification in Models with Multiple Equilibria," Review of Economic Studies, Oxford University Press, vol. 78(4), pages 1264-1298.
    25. Khan, Shakeeb & Tamer, Elie, 2009. "Inference on endogenously censored regression models using conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 152(2), pages 104-119, October.
    26. Stefan Hoderlein & Enno Mammen, 2007. "Identification of Marginal Effects in Nonseparable Models Without Monotonicity," Econometrica, Econometric Society, vol. 75(5), pages 1513-1518, September.
    27. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March.
    28. Rosen, Adam M., 2008. "Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities," Journal of Econometrics, Elsevier, vol. 146(1), pages 107-117, September.
    29. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818742.
    30. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc4ao8ocg is not listed on IDEAS
    31. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," Review of Economic Studies, Oxford University Press, vol. 70(1), pages 147-165.
    32. Donald W. K. Andrews & Gustavo Soares, 2010. "Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection," Econometrica, Econometric Society, vol. 78(1), pages 119-157, January.
    33. Andrew Chesher & Adam M. Rosen & Konrad Smolinski, 2013. "An instrumental variable model of multiple discrete choice," Quantitative Economics, Econometric Society, vol. 4(2), pages 157-196, July.
    34. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524117.
    35. Joseph P. Romano & Azeem M. Shaikh, 2010. "Inference for the Identified Set in Partially Identified Econometric Models," Econometrica, Econometric Society, vol. 78(1), pages 169-211, January.
    36. Canay, Ivan A., 2010. "EL inference for partially identified models: Large deviations optimality and bootstrap validity," Journal of Econometrics, Elsevier, vol. 156(2), pages 408-425, June.
    37. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, September.
    38. D’Haultfoeuille, Xavier, 2011. "On The Completeness Condition In Nonparametric Instrumental Problems," Econometric Theory, Cambridge University Press, vol. 27(3), pages 460-471, June.
    39. Arie Beresteanu & Ilya Molchanov & Francesca Molinari, 2011. "Sharp Identification Regions in Models With Convex Moment Predictions," Econometrica, Econometric Society, vol. 79(6), pages 1785-1821, November.
    40. Andrew Chesher, 2010. "Instrumental Variable Models for Discrete Outcomes," Econometrica, Econometric Society, vol. 78(2), pages 575-601, March.
    41. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818735.
    42. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524124.
    43. Philip A. Haile & Elie Tamer, 2003. "Inference with an Incomplete Model of English Auctions," Journal of Political Economy, University of Chicago Press, vol. 111(1), pages 1-51, February.
    44. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    45. Chernozhukov, Victor & Imbens, Guido W. & Newey, Whitney K., 2007. "Instrumental variable estimation of nonseparable models," Journal of Econometrics, Elsevier, vol. 139(1), pages 4-14, July.
    46. Federico A. Bugni, 2010. "Bootstrap Inference in Partially Identified Models Defined by Moment Inequalities: Coverage of the Identified Set," Econometrica, Econometric Society, vol. 78(2), pages 735-753, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Andrew Chesher & Adam Rosen, 2018. "Generalized instrumental variable models, methods, and applications," CeMMAP working papers CWP43/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Andrew Chesher & Adam Rosen, 2015. "Characterizations of identified sets delivered by structural econometric models," CeMMAP working papers 63/15, Institute for Fiscal Studies.
    3. Ho, Kate & Rosen, Adam M., 2015. "Partial Identification in Applied Research: Benefits and Challenges," CEPR Discussion Papers 10883, C.E.P.R. Discussion Papers.
    4. 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.
    5. Francesca Molinari, 2020. "Microeconometrics with Partial Identi?cation," CeMMAP working papers CWP15/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Lee, Sokbae & Song, Kyungchul & Whang, Yoon-Jae, 2018. "Testing For A General Class Of Functional Inequalities," Econometric Theory, Cambridge University Press, vol. 34(5), pages 1018-1064, October.
    7. Francesca Molinari, 2019. "Econometrics with Partial Identification," CeMMAP working papers CWP25/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Donald W. K. Andrews & Xiaoxia Shi, 2013. "Inference Based on Conditional Moment Inequalities," Econometrica, Econometric Society, vol. 81(2), pages 609-666, March.
    9. James L. Powell, 2017. "Identification and Asymptotic Approximations: Three Examples of Progress in Econometric Theory," Journal of Economic Perspectives, American Economic Association, vol. 31(2), pages 107-124, Spring.
    10. Ivan A. Canay & Azeem M. Shaikh, 2016. "Practical and theoretical advances in inference for partially identified models," CeMMAP working papers CWP05/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2013. "Testing Many Moment Inequalities," CeMMAP working papers 65/13, Institute for Fiscal Studies.
    12. Aradillas-López, Andrés & Rosen, Adam M., 2022. "Inference in ordered response games with complete information," Journal of Econometrics, Elsevier, vol. 226(2), pages 451-476.
    13. 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.
    14. Yuan Liao & Anna Simoni, 2016. "Bayesian Inference for Partially Identified Convex Models: Is it Valid for Frequentist Inference?," Departmental Working Papers 201607, Rutgers University, Department of Economics.
    15. Brendan Kline & Elie Tamer, 2016. "Bayesian inference in a class of partially identified models," Quantitative Economics, Econometric Society, vol. 7(2), pages 329-366, July.
    16. Liao, Yuan & Simoni, Anna, 2019. "Bayesian inference for partially identified smooth convex models," Journal of Econometrics, Elsevier, vol. 211(2), pages 338-360.
    17. Christian Bontemps & Thierry Magnac & Eric Maurin, 2012. "Set Identified Linear Models," Econometrica, Econometric Society, vol. 80(3), pages 1129-1155, May.
    18. Hiroaki Kaido & Francesca Molinari & Jörg Stoye, 2019. "Confidence Intervals for Projections of Partially Identified Parameters," Econometrica, Econometric Society, vol. 87(4), pages 1397-1432, July.
    19. Yuan Liao & Anna Simoni, 2012. "Semi-parametric Bayesian Partially Identified Models based on Support Function," Papers 1212.3267, arXiv.org, revised Nov 2013.
    20. Federico A. Bugni & Ivan A. Canay & Xiaoxia Shi, 2014. "Inference for functions of partially identified parameters in moment inequality models," CeMMAP working papers 22/14, Institute for Fiscal Studies.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ifs:cemmap:43/13. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Emma Hyman (email available below). General contact details of provider: https://edirc.repec.org/data/cmifsuk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.