IDEAS home Printed from https://ideas.repec.org/p/cdl/ucsdec/qt0q43931f.html
   My bibliography  Save this paper

A Comparison of Two Quantile Models With Endogeneity

Author

Listed:
  • Wüthrich, Kaspar

Abstract

This paper analyzes estimators based on the instrumental variable quantile regression (IVQR) model (Chernozhukov and Hansen, 2004, 2005, 2006) under the local quantile treatment effects (LQTE) framework (Abadie et al., 2002). I show that the quantile treatment effect (QTE) estimators in the IVQR model are equivalent to LQTE for the compliers at transformed quantile levels. This transformation adjusts for differences between the subpopulation-specific potential outcome distributions that are identified in the LQTE model. Moreover, the IVQR estimator of the average treatment effect (ATE) corresponds to a convex combination of the local average treatment effect (LATE) and a weighted average of LQTE for the compliers. I extend the analysis to more general setups that allow for partial failures of the LQTE assumptions, non-binary instruments, and covariates. The results are illustrated with two empirical applications.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Wüthrich, Kaspar, 2020. "A Comparison of Two Quantile Models With Endogeneity," University of California at San Diego, Economics Working Paper Series qt0q43931f, Department of Economics, UC San Diego.
  • Handle: RePEc:cdl:ucsdec:qt0q43931f
    as

    Download full text from publisher

    File URL: https://www.escholarship.org/uc/item/0q43931f.pdf;origin=repeccitec
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Le‐Yu Chen & Sokbae Lee, 2018. "Exact computation of GMM estimators for instrumental variable quantile regression models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(4), pages 553-567, June.
    2. Frandsen, Brigham R. & Frölich, Markus & Melly, Blaise, 2012. "Quantile treatment effects in the regression discontinuity design," Journal of Econometrics, Elsevier, vol. 168(2), pages 382-395.
    3. Chen, Xiaohong & Pouzo, Demian, 2009. "Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals," Journal of Econometrics, Elsevier, vol. 152(1), pages 46-60, September.
    4. James J. Heckman & Vytlacil, Edward J., 2007. "Econometric Evaluation of Social Programs, Part II: Using the Marginal Treatment Effect to Organize Alternative Econometric Estimators to Evaluate Social Programs, and to Forecast their Effects in New," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 71, Elsevier.
    5. Xiaohong Chen & Demian Pouzo, 2012. "Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals," Econometrica, Econometric Society, vol. 80(1), pages 277-321, January.
    6. Sergio Firpo, 2007. "Efficient Semiparametric Estimation of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 75(1), pages 259-276, January.
    7. Heckman, James J. & Urzúa, Sergio, 2010. "Comparing IV with structural models: What simple IV can and cannot identify," Journal of Econometrics, Elsevier, vol. 156(1), pages 27-37, May.
    8. Kaplan, David M. & Sun, Yixiao, 2012. "Smoothed Estimating Equations For Instrumental Variables Quantile Regression," University of California at San Diego, Economics Working Paper Series qt888657tp, Department of Economics, UC San Diego.
    9. Victor Chernozhukov & Iv·n Fern·ndez-Val & Alfred Galichon, 2010. "Quantile and Probability Curves Without Crossing," Econometrica, Econometric Society, vol. 78(3), pages 1093-1125, May.
    10. Clément de Chaisemartin, 2017. "Tolerating defiance? Local average treatment effects without monotonicity," Quantitative Economics, Econometric Society, vol. 8(2), pages 367-396, July.
    11. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    12. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc4b6ga2g is not listed on IDEAS
    13. Alberto Abadie & Joshua Angrist & Guido Imbens, 2002. "Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings," Econometrica, Econometric Society, vol. 70(1), pages 91-117, January.
    14. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    15. Huber, Martin, 2014. "Sensitivity checks for the local average treatment effect," Economics Letters, Elsevier, vol. 123(2), pages 220-223.
    16. Gagliardini, Patrick & Scaillet, Olivier, 2012. "Tikhonov regularization for nonparametric instrumental variable estimators," Journal of Econometrics, Elsevier, vol. 167(1), pages 61-75.
    17. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107016064, November.
    18. Angrist, Joshua D, 1990. "Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records: Errata," American Economic Review, American Economic Association, vol. 80(5), pages 1284-1286, December.
    19. Markus Frölich & Blaise Melly, 2013. "Unconditional Quantile Treatment Effects Under Endogeneity," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 346-357, July.
    20. Patrick Gagliardini & Olivier Scaillet, 2012. "Nonparametric Instrumental Variable Estimation of Structural Quantile Effects," Econometrica, Econometric Society, vol. 80(4), pages 1533-1562, July.
    21. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107627314, November.
    22. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107016040, November.
    23. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    24. Angrist, Joshua D, 1990. "Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records," American Economic Review, American Economic Association, vol. 80(3), pages 313-336, June.
    25. Markus Frölich & Blaise Melly, 2013. "Identification of Treatment Effects on the Treated with One-Sided Non-Compliance," Econometric Reviews, Taylor & Francis Journals, vol. 32(3), pages 384-414, November.
    26. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    27. Su, Liangjun & Hoshino, Tadao, 2016. "Sieve instrumental variable quantile regression estimation of functional coefficient models," Journal of Econometrics, Elsevier, vol. 191(1), pages 231-254.
    28. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871532, November.
    29. James Heckman & Justin L. Tobias & Edward Vytlacil, 2001. "Four Parameters of Interest in the Evaluation of Social Programs," Southern Economic Journal, John Wiley & Sons, vol. 68(2), pages 210-223, October.
    30. V. Chernozhukov & C. Hansen, 2013. "Quantile Models with Endogeneity," Annual Review of Economics, Annual Reviews, vol. 5(1), pages 57-81, May.
    31. A. Belloni & V. Chernozhukov & I. Fernández‐Val & C. Hansen, 2017. "Program Evaluation and Causal Inference With High‐Dimensional Data," Econometrica, Econometric Society, vol. 85, pages 233-298, January.
    32. Susan Athey & Guido W. Imbens, 2006. "Identification and Inference in Nonlinear Difference-in-Differences Models," Econometrica, Econometric Society, vol. 74(2), pages 431-497, March.
    33. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107638105, November.
    34. Howard S. Bloom & Larry L. Orr & Stephen H. Bell & George Cave & Fred Doolittle & Winston Lin & Johannes M. Bos, 1997. "The Benefits and Costs of JTPA Title II-A Programs: Key Findings from the National Job Training Partnership Act Study," Journal of Human Resources, University of Wisconsin Press, vol. 32(3), pages 549-576.
    35. Joel L. Horowitz, 2007. "Asymptotic Normality Of A Nonparametric Instrumental Variables Estimator," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1329-1349, November.
    36. Matthew A. Masten & Alexandre Poirier, 2020. "Inference on breakdown frontiers," Quantitative Economics, Econometric Society, vol. 11(1), pages 41-111, January.
    37. Chernozhukov, Victor & Hansen, Christian & Jansson, Michael, 2009. "Finite sample inference for quantile regression models," Journal of Econometrics, Elsevier, vol. 152(2), pages 93-103, October.
    38. Toru Kitagawa, 2014. "A Test for Instrument Validity," CeMMAP working papers CWP34/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    39. Joshua D. Angrist, 2004. "Treatment effect heterogeneity in theory and practice," Economic Journal, Royal Economic Society, vol. 114(494), pages 52-83, March.
    40. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107016057, November.
    41. James Heckman & Justin L. Tobias & Edward Vytlacil, 2001. "Four Parameters of Interest in the Evaluation of Social Programs," Southern Economic Journal, John Wiley & Sons, vol. 68(2), pages 210-223, October.
    42. Victor Chernozhukov & Christian Hansen, 2004. "The Effects of 401(K) Participation on the Wealth Distribution: An Instrumental Quantile Regression Analysis," The Review of Economics and Statistics, MIT Press, vol. 86(3), pages 735-751, August.
    43. Eva Deuchert & Martin Huber, 2017. "A Cautionary Tale About Control Variables in IV Estimation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(3), pages 411-425, June.
    44. Blundell,Richard & Newey,Whitney & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871549, November.
    45. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4b6ga2g is not listed on IDEAS
    46. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    47. Abadie, Alberto, 2003. "Semiparametric instrumental variable estimation of treatment response models," Journal of Econometrics, Elsevier, vol. 113(2), pages 231-263, April.
    48. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107674165, November.
    49. Kaplan, David M. & Sun, Yixiao, 2017. "Smoothed Estimating Equations For Instrumental Variables Quantile Regression," Econometric Theory, Cambridge University Press, vol. 33(1), pages 105-157, February.
    50. James Heckman & Justin L. Tobias & Edward Vytlacil, 2003. "Simple Estimators for Treatment Parameters in a Latent-Variable Framework," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 748-755, August.
    51. Blundell,Richard & Newey,Whitney & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692106, November.
    52. Chernozhukov, Victor & Hansen, Christian, 2008. "Instrumental variable quantile regression: A robust inference approach," Journal of Econometrics, Elsevier, vol. 142(1), pages 379-398, January.
    53. Guido W. Imbens & Donald B. Rubin, 1997. "Estimating Outcome Distributions for Compliers in Instrumental Variables Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(4), pages 555-574.
    54. Abadie A., 2002. "Bootstrap Tests for Distributional Treatment Effects in Instrumental Variable Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 284-292, March.
    55. Yingying Dong & Shu Shen, 2018. "Testing for Rank Invariance or Similarity in Program Evaluation," The Review of Economics and Statistics, MIT Press, vol. 100(1), pages 78-85, March.
    56. Chernozhukov, Victor & Hansen, Christian & Jansson, Michael, 2007. "Inference approaches for instrumental variable quantile regression," Economics Letters, Elsevier, vol. 95(2), pages 272-277, May.
    57. Joel L. Horowitz & Sokbae Lee, 2007. "Nonparametric Instrumental Variables Estimation of a Quantile Regression Model," Econometrica, Econometric Society, vol. 75(4), pages 1191-1208, July.
    58. 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.
    59. Quang Vuong & Haiqing Xu, 2017. "Counterfactual mapping and individual treatment effects in nonseparable models with binary endogeneity," Quantitative Economics, Econometric Society, vol. 8(2), pages 589-610, July.
    60. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
    61. Chernozhukov, Victor & Hansen, Christian, 2006. "Instrumental quantile regression inference for structural and treatment effect models," Journal of Econometrics, Elsevier, vol. 132(2), pages 491-525, June.
    62. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692090, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xu, Xiu & Wang, Weining & Shin, Yongcheol, 2020. "Dynamic Spatial Network Quantile Autoregression," IRTG 1792 Discussion Papers 2020-024, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    2. Jad Beyhum & Jean-Pierre Florens & Ingrid Keilegom, 2023. "A nonparametric instrumental approach to confounding in competing risks models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(4), pages 709-734, October.
    3. Grigory Franguridi & Bulat Gafarov & Kaspar Wuthrich, 2020. "Bias correction for quantile regression estimators," Papers 2011.03073, arXiv.org, revised Jan 2024.
    4. Alecos Papadopoulos & Christopher F. Parmeter, 2022. "Quantile Methods for Stochastic Frontier Analysis," Foundations and Trends(R) in Econometrics, now publishers, vol. 12(1), pages 1-120, November.
    5. Kaspar W thrich, 2015. "Semiparametric estimation of quantile treatment effects with endogeneity," Diskussionsschriften dp1509, Universitaet Bern, Departement Volkswirtschaft.
    6. de Castro, Luciano & Cundy, Lance D. & Galvao, Antonio F. & Westenberger, Rafael, 2023. "A dynamic quantile model for distinguishing intertemporal substitution from risk aversion," European Economic Review, Elsevier, vol. 159(C).
    7. David Powell, 2020. "Quantile Treatment Effects in the Presence of Covariates," The Review of Economics and Statistics, MIT Press, vol. 102(5), pages 994-1005, December.
    8. Grigory Franguridi & Bulat Gafarov & Kaspar Wüthrich, 2021. "Conditional Quantile Estimators: A Small Sample Theory," CESifo Working Paper Series 9046, CESifo.

    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. Wüthrich, Kaspar, 2019. "A closed-form estimator for quantile treatment effects with endogeneity," University of California at San Diego, Economics Working Paper Series qt99n9197q, Department of Economics, UC San Diego.
    2. Wüthrich, Kaspar, 2019. "A closed-form estimator for quantile treatment effects with endogeneity," Journal of Econometrics, Elsevier, vol. 210(2), pages 219-235.
    3. Hiroaki Kaido & Kaspar Wüthrich, 2021. "Decentralization estimators for instrumental variable quantile regression models," Quantitative Economics, Econometric Society, vol. 12(2), pages 443-475, May.
    4. Victor Chernozhukov & Christian Hansen & Kaspar Wuthrich, 2020. "Instrumental Variable Quantile Regression," Papers 2009.00436, arXiv.org.
    5. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    6. Pereda-Fernández, Santiago, 2023. "Identification and estimation of triangular models with a binary treatment," Journal of Econometrics, Elsevier, vol. 234(2), pages 585-623.
    7. Kaspar W thrich, 2015. "Semiparametric estimation of quantile treatment effects with endogeneity," Diskussionsschriften dp1509, Universitaet Bern, Departement Volkswirtschaft.
    8. Committee, Nobel Prize, 2021. "Answering causal questions using observational data," Nobel Prize in Economics documents 2021-2, Nobel Prize Committee.
    9. Blaise Melly und Kaspar W thrich, 2016. "Local quantile treatment effects," Diskussionsschriften dp1605, Universitaet Bern, Departement Volkswirtschaft.
    10. Fusejima, Koki, 2024. "Identification of multi-valued treatment effects with unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 238(1).
    11. Huber, Martin & Wüthrich, Kaspar, 2017. "Evaluating local average and quantile treatment effects under endogeneity based on instruments: a review," FSES Working Papers 479, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    12. Huber, Martin & Wüthrich, Kaspar, 2019. "Local Average and Quantile Treatment Effects Under Endogeneity: A Review," University of California at San Diego, Economics Working Paper Series qt4j29d8sc, Department of Economics, UC San Diego.
    13. Huber Martin & Wüthrich Kaspar, 2019. "Local Average and Quantile Treatment Effects Under Endogeneity: A Review," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-27, January.
    14. Koki Fusejima, 2020. "Identification of multi-valued treatment effects with unobserved heterogeneity," Papers 2010.04385, arXiv.org, revised Apr 2023.
    15. Manuel Arellano & Stéphane Bonhomme, 2017. "Quantile Selection Models With an Application to Understanding Changes in Wage Inequality," Econometrica, Econometric Society, vol. 85, pages 1-28, January.
    16. de Castro, Luciano & Galvao, Antonio F. & Kaplan, David M. & Liu, Xin, 2019. "Smoothed GMM for quantile models," Journal of Econometrics, Elsevier, vol. 213(1), pages 121-144.
    17. Imbens, Guido W., 2014. "Instrumental Variables: An Econometrician's Perspective," IZA Discussion Papers 8048, Institute of Labor Economics (IZA).
    18. Chen, Xuan & Flores, Carlos A. & Flores-Lagunes, Alfonso, 2015. "Going Beyond LATE: Bounding Average Treatment Effects of Job Corps Training," IZA Discussion Papers 9511, Institute of Labor Economics (IZA).
    19. V. Chernozhukov & C. Hansen, 2013. "Quantile Models with Endogeneity," Annual Review of Economics, Annual Reviews, vol. 5(1), pages 57-81, May.
    20. Carneiro, Pedro & Lee, Sokbae, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," Journal of Econometrics, Elsevier, vol. 149(2), pages 191-208, April.

    More about this item

    Keywords

    Good Health and Well Being; Instrumental variables; Local quantile treatment effects; Quantile treatment effects; Rank similarity; Mathematical Sciences; Economics; Commerce; Management; Tourism and Services; Econometrics;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

    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:cdl:ucsdec:qt0q43931f. 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: Lisa Schiff (email available below). General contact details of provider: https://edirc.repec.org/data/deucsus.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.