IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2002.05253.html
   My bibliography  Save this paper

Bounds on direct and indirect effects under treatment/mediator endogeneity and outcome attrition

Author

Listed:
  • Martin Huber
  • Luk'av{s} Laff'ers

Abstract

Causal mediation analysis aims at disentangling a treatment effect into an indirect mechanism operating through an intermediate outcome or mediator, as well as the direct effect of the treatment on the outcome of interest. However, the evaluation of direct and indirect effects is frequently complicated by non-ignorable selection into the treatment and/or mediator, even after controlling for observables, as well as sample selection/outcome attrition. We propose a method for bounding direct and indirect effects in the presence of such complications using a method that is based on a sequence of linear programming problems. Considering inverse probability weighting by propensity scores, we compute the weights that would yield identification in the absence of complications and perturb them by an entropy parameter reflecting a specific amount of propensity score misspecification to set-identify the effects of interest. We apply our method to data from the National Longitudinal Survey of Youth 1979 to derive bounds on the explained and unexplained components of a gender wage gap decomposition that is likely prone to non-ignorable mediator selection and outcome attrition.

Suggested Citation

  • Martin Huber & Luk'av{s} Laff'ers, 2020. "Bounds on direct and indirect effects under treatment/mediator endogeneity and outcome attrition," Papers 2002.05253, arXiv.org, revised May 2020.
    • Handle: RePEc:arx:papers:2002.05253
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2002.05253
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. James Heckman & Rodrigo Pinto & Peter Savelyev, 2013. "Understanding the Mechanisms through Which an Influential Early Childhood Program Boosted Adult Outcomes," American Economic Review, American Economic Association, vol. 103(6), pages 2052-2086, October.
    2. Zhihong Cai & Manabu Kuroki & Judea Pearl & Jin Tian, 2008. "Bounds on Direct Effects in the Presence of Confounded Intermediate Variables," Biometrics, The International Biometric Society, vol. 64(3), pages 695-701, September.
    3. Bertrand, Marianne, 2011. "New Perspectives on Gender," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 4, chapter 17, pages 1543-1590, Elsevier.
    4. James J. Heckman, 1976. "The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 475-492, National Bureau of Economic Research, Inc.
    5. Martin Huber & Anna Solovyeva, 2020. "Direct and Indirect Effects under Sample Selection and Outcome Attrition," Econometrics, MDPI, vol. 8(4), pages 1-25, December.
    6. Demuynck, Thomas, 2015. "Bounding average treatment effects: A linear programming approach," Economics Letters, Elsevier, vol. 137(C), pages 75-77.
    7. Keele, Luke & Tingley, Dustin & Teppei Yamamoto, "undated". "Identifying Mechanisms behind Policy Interventions via Causal Mediation Analysis," Working Paper 135661, Harvard University OpenScholar.
    8. Sloczynski, Tymon, 2013. "Population Average Gender Effects," IZA Discussion Papers 7315, Institute of Labor Economics (IZA).
    9. Martin Huber, 2014. "Treatment Evaluation in the Presence of Sample Selection," Econometric Reviews, Taylor & Francis Journals, vol. 33(8), pages 869-905, November.
    10. Flores, Carlos A. & Flores-Lagunes, Alfonso, 2009. "Identification and Estimation of Causal Mechanisms and Net Effects of a Treatment under Unconfoundedness," IZA Discussion Papers 4237, Institute of Labor Economics (IZA).
    11. Molinari, Francesca, 2008. "Partial identification of probability distributions with misclassified data," Journal of Econometrics, Elsevier, vol. 144(1), pages 81-117, May.
    12. Bo E. Honoré & Elie Tamer, 2006. "Bounds on Parameters in Panel Dynamic Discrete Choice Models," Econometrica, Econometric Society, vol. 74(3), pages 611-629, May.
    13. Imai, Kosuke & Yamamoto, Teppei, 2013. "Identification and Sensitivity Analysis for Multiple Causal Mechanisms: Revisiting Evidence from Framing Experiments," Political Analysis, Cambridge University Press, vol. 21(2), pages 141-171, April.
    14. Azmat, Ghazala & Petrongolo, Barbara, 2014. "Gender and the labor market: What have we learned from field and lab experiments?," Labour Economics, Elsevier, vol. 30(C), pages 32-40.
    15. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    16. Charles F. Manski, 2007. "Partial Identification Of Counterfactual Choice Probabilities," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1393-1410, November.
    17. Carlos A. Flores & Alfonso Flores-Lagunes, 2010. "Nonparametric Partial Identification of Causal Net and Mechanism Average Treatment Effects," Working Papers 2010-25, University of Miami, Department of Economics.
    18. Thomas R. Ten Have & Marshall M. Joffe & Kevin G. Lynch & Gregory K. Brown & Stephen A. Maisto & Aaron T. Beck, 2007. "Causal Mediation Analyses with Rank Preserving Models," Biometrics, The International Biometric Society, vol. 63(3), pages 926-934, September.
    19. Luke Keele & Dustin Tingley & Teppei Yamamoto, 2015. "Identifying Mechanisms Behind Policy Interventions Via Causal Mediation Analysis," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 34(4), pages 937-963, September.
    20. Gronau, Reuben, 1974. "Wage Comparisons-A Selectivity Bias," Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1119-1143, Nov.-Dec..
    21. Joshua Angrist & Eric Bettinger & Michael Kremer, 2006. "Long-Term Educational Consequences of Secondary School Vouchers: Evidence from Administrative Records in Colombia," American Economic Review, American Economic Association, vol. 96(3), pages 847-862, June.
    22. Lafférs, Lukáš & Nedela, Roman, 2017. "Sensitivity of the bounds on the ATE in the presence of sample selection," Economics Letters, Elsevier, vol. 158(C), pages 84-87.
    23. Mitali Das & Whitney K. Newey & Francis Vella, 2003. "Nonparametric Estimation of Sample Selection Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(1), pages 33-58.
    24. Azmat, Ghazala & Petrongolo, Barbara, 2014. "Gender and the labor market: What have we learned from field and lab experiments?," Labour Economics, Elsevier, vol. 30(C), pages 32-40.
    25. Freyberger, Joachim & Horowitz, Joel L., 2015. "Identification and shape restrictions in nonparametric instrumental variables estimation," Journal of Econometrics, Elsevier, vol. 189(1), pages 41-53.
    26. Martin Huber & Michael Lechner & Giovanni Mellace, 2017. "Why Do Tougher Caseworkers Increase Employment? The Role of Program Assignment as a Causal Mechanism," The Review of Economics and Statistics, MIT Press, vol. 99(1), pages 180-183, March.
    27. 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.
    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. Daniel Kaliski, 2023. "Identifying the impact of health insurance on subgroups with changing rates of diagnosis," Health Economics, John Wiley & Sons, Ltd., vol. 32(9), pages 2098-2112, September.

    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. Martin Huber & Anna Solovyeva, 2020. "On the Sensitivity of Wage Gap Decompositions," Journal of Labor Research, Springer, vol. 41(1), pages 1-33, June.
    2. Helmut Farbmacher & Martin Huber & Lukáš Lafférs & Henrika Langen & Martin Spindler, 2022. "Causal mediation analysis with double machine learning [Mediation analysis via potential outcomes models]," The Econometrics Journal, Royal Economic Society, vol. 25(2), pages 277-300.
    3. Martin Huber & Anna Solovyeva, 2020. "Direct and Indirect Effects under Sample Selection and Outcome Attrition," Econometrics, MDPI, vol. 8(4), pages 1-25, December.
    4. Martin Huber & Mark Schelker & Anthony Strittmatter, 2022. "Direct and Indirect Effects based on Changes-in-Changes," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(1), pages 432-443, January.
    5. Lafférs, Lukáš & Nedela, Roman, 2017. "Sensitivity of the bounds on the ATE in the presence of sample selection," Economics Letters, Elsevier, vol. 158(C), pages 84-87.
    6. Viviana Celli, 2022. "Causal mediation analysis in economics: Objectives, assumptions, models," Journal of Economic Surveys, Wiley Blackwell, vol. 36(1), pages 214-234, February.
    7. Martin Huber & Giovanni Mellace, 2014. "Testing exclusion restrictions and additive separability in sample selection models," Empirical Economics, Springer, vol. 47(1), pages 75-92, August.
    8. Lukáš Lafférs, 2019. "Bounding average treatment effects using linear programming," Empirical Economics, Springer, vol. 57(3), pages 727-767, September.
    9. Martin Huber & Giovanni Mellace, 2015. "Sharp Bounds on Causal Effects under Sample Selection," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(1), pages 129-151, February.
    10. Michela Bia & Martin Huber & Lukáš Lafférs, 2024. "Double Machine Learning for Sample Selection Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(3), pages 958-969, July.
    11. Huber, Martin & Mellace, Giovanni, 2011. "Testing instrument validity in sample selection models," Economics Working Paper Series 1145, University of St. Gallen, School of Economics and Political Science.
    12. Steinmayr, Andreas, 2014. "When a random sample is not random: Bounds on the effect of migration on household members left behind," Kiel Working Papers 1975, Kiel Institute for the World Economy (IfW Kiel).
    13. Martin Huber, 2012. "Identification of Average Treatment Effects in Social Experiments Under Alternative Forms of Attrition," Journal of Educational and Behavioral Statistics, , vol. 37(3), pages 443-474, June.
    14. Martin Huber & Yu‐Chin Hsu & Ying‐Ying Lee & Layal Lettry, 2020. "Direct and indirect effects of continuous treatments based on generalized propensity score weighting," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(7), pages 814-840, November.
    15. Martin Huber & Michael Lechner & Giovanni Mellace, 2017. "Why Do Tougher Caseworkers Increase Employment? The Role of Program Assignment as a Causal Mechanism," The Review of Economics and Statistics, MIT Press, vol. 99(1), pages 180-183, March.
    16. Martin Huber & Michael Lechner & Giovanni Mellace, 2016. "The Finite Sample Performance of Estimators for Mediation Analysis Under Sequential Conditional Independence," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(1), pages 139-160, January.
    17. Kilburn, Kelly & Handa, Sudhanshu & Angeles, Gustavo & Mvula, Peter & Tsoka, Maxton, 2017. "Short-term impacts of an unconditional cash transfer program on child schooling: Experimental evidence from Malawi," Economics of Education Review, Elsevier, vol. 59(C), pages 63-80.
    18. Hamermesh, Daniel S. & Donald, Stephen G., 2008. "The effect of college curriculum on earnings: An affinity identifier for non-ignorable non-response bias," Journal of Econometrics, Elsevier, vol. 144(2), pages 479-491, June.
    19. Lukáš Lafférs, 2019. "Identification in Models with Discrete Variables," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 657-696, February.
    20. Anne‐Sophie Bruno & Nathalie Greenan & Jeremy Tanguy, 2021. "Does the Gender Mix Influence Collective Bargaining on Gender Equality? Evidence from France," Industrial Relations: A Journal of Economy and Society, Wiley Blackwell, vol. 60(4), pages 479-520, October.

    More about this item

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

    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:arx:papers:2002.05253. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.