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Direct and indirect treatment effects: causal chains and mediation analysis with instrumental variables

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  • Frölich, Markus

    () (University of Mannheim)

  • Huber, Martin

    () (University of St. Gallen)

Abstract

This paper discusses the nonparametric identification of causal direct and indirect effects of a binary treatment based on instrumental variables. We identify the indirect effect, which operates through a mediator (i.e. intermediate variable) that is situated on the causal path between the treatment and the outcome, as well as the unmediated direct effect of the treatment using distinct instruments for the endogenous treatment and the endogenous mediator. We examine different settings to obtain nonparametric identification of (natural) direct and indirect as well as controlled direct effects for continuous and discrete mediators and continuous and discrete instruments. We illustrate our approach in two applications: to disentangle the effects (i) of education on health, which may be mediated by income, and (ii) of the Job Corps training program, which may affect earnings indirectly via working longer hours and directly via higher wages per hour.

Suggested Citation

  • Frölich, Markus & Huber, Martin, 2015. "Direct and indirect treatment effects: causal chains and mediation analysis with instrumental variables," Working Paper Series 2025:12, IFAU - Institute for Evaluation of Labour Market and Education Policy.
  • Handle: RePEc:hhs:ifauwp:2025_012
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    1. 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.
    2. Alan B. Krueger, 1999. "Experimental Estimates of Education Production Functions," The Quarterly Journal of Economics, Oxford University Press, vol. 114(2), pages 497-532.
    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. 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.
    5. Maximilian Kasy, 2014. "Instrumental Variables with Unrestricted Heterogeneity and Continuous Treatment," Review of Economic Studies, Oxford University Press, vol. 81(4), pages 1614-1636.
    6. Martin Huber, 2014. "Identifying Causal Mechanisms (Primarily) Based On Inverse Probability Weighting," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(6), pages 920-943, September.
    7. Powdthavee, Nattavudh & Lekfuangfu, Warn N. & Wooden, Mark, 2013. "The Marginal Income Effect of Education on Happiness: Estimating the Direct and Indirect Effects of Compulsory Schooling on Well-Being in Australia," IZA Discussion Papers 7365, Institute of Labor Economics (IZA).
    8. Imai, Kosuke & Keele, Luke & Tingley, Dustin & Yamamoto, Teppei, 2011. "Unpacking the Black Box of Causality: Learning about Causal Mechanisms from Experimental and Observational Studies," American Political Science Review, Cambridge University Press, vol. 105(4), pages 765-789, November.
    9. 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).
    10. Markus Frölich & Martin Huber, 2014. "Treatment Evaluation With Multiple Outcome Periods Under Endogeneity and Attrition," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1697-1711, December.
    11. Kasy, Maximilian, "undated". "Instrumental variables with unrestricted heterogeneity and continuous treatment - DON'T CITE! SEE ERRATUM BELOW," Working Paper 33257, Harvard University OpenScholar.
    12. Toru Kitagawa, 2015. "A Test for Instrument Validity," Econometrica, Econometric Society, vol. 83(5), pages 2043-2063, September.
    13. Francisca M. Antman, 2011. "International Migration and Gender Discrimination among Children Left Behind," American Economic Review, American Economic Association, vol. 101(3), pages 645-649, May.
    14. Binzel, Christine & Assaad, Ragui, 2011. "Egyptian men working abroad: Labour supply responses by the women left behind," Labour Economics, Elsevier, vol. 18(S1), pages 98-114.
    15. Terza, Joseph V. & Basu, Anirban & Rathouz, Paul J., 2008. "Two-stage residual inclusion estimation: Addressing endogeneity in health econometric modeling," Journal of Health Economics, Elsevier, vol. 27(3), pages 531-543, May.
    16. Frolich, Markus, 2007. "Nonparametric IV estimation of local average treatment effects with covariates," Journal of Econometrics, Elsevier, vol. 139(1), pages 35-75, July.
    17. Gardner, Jonathan & Oswald, Andrew J., 2007. "Money and mental wellbeing: A longitudinal study of medium-sized lottery wins," Journal of Health Economics, Elsevier, vol. 26(1), pages 49-60, January.
    18. repec:mpr:mprres:6097 is not listed on IDEAS
    19. 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.
    20. Abadie, Alberto, 2003. "Semiparametric instrumental variable estimation of treatment response models," Journal of Econometrics, Elsevier, vol. 113(2), pages 231-263, April.
    21. 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.
    22. Hayfield, Tristen & Racine, Jeffrey S., 2008. "Nonparametric Econometrics: The np Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i05).
    23. Peter Z. Schochet & John Burghardt & Sheena McConnell, "undated". "Does Job Corps Work? Impact Findings from the National Job Corps Study," Mathematica Policy Research Reports 5067e4907eba4a4881f510080, Mathematica Policy Research.
    24. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    25. Giorgio Brunello & Daniele Fabbri & Margherita Fort, 2013. "The Causal Effect of Education on Body Mass: Evidence from Europe," Journal of Labor Economics, University of Chicago Press, vol. 31(1), pages 195-223.
    26. Tan, Zhiqiang, 2006. "Regression and Weighting Methods for Causal Inference Using Instrumental Variables," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1607-1618, December.
    27. Mikael Lindahl, 2005. "Estimating the Effect of Income on Health and Mortality Using Lottery Prizes as an Exogenous Source of Variation in Income," Journal of Human Resources, University of Wisconsin Press, vol. 40(1).
    28. Peter Z. Schochet & John Burghardt & Steven Glazerman, 2001. "National Job Corps Study: The Impacts of Job Corps on Participants' Employment and Related Outcomes," Mathematica Policy Research Reports db6c4204b8e1408bb0c6289ec, Mathematica Policy Research.
    29. Chen, Le-Yu & Szroeter, Jerzy, 2014. "Testing multiple inequality hypotheses: A smoothed indicator approach," Journal of Econometrics, Elsevier, vol. 178(P3), pages 678-693.
    30. Mu, Ren & van de Walle, Dominique, 2011. "Left behind to farm? Women's labor re-allocation in rural China," Labour Economics, Elsevier, vol. 18(S1), pages 83-97.
    31. 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.
    32. Philip Oreopoulos, 2006. "Estimating Average and Local Average Treatment Effects of Education when Compulsory Schooling Laws Really Matter," American Economic Review, American Economic Association, vol. 96(1), pages 152-175, March.
    33. Sara Geneletti, 2007. "Identifying direct and indirect effects in a non‐counterfactual framework," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 199-215, April.
    34. Kane, Thomas J & Rouse, Cecilia Elena, 1995. "Labor-Market Returns to Two- and Four-Year College," American Economic Review, American Economic Association, vol. 85(3), pages 600-614, June.
    35. Martin Huber & Giovanni Mellace, 2015. "Testing Instrument Validity for LATE Identification Based on Inequality Moment Constraints," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 398-411, May.
    36. Ahn, Hyungtaik & Powell, James L., 1993. "Semiparametric estimation of censored selection models with a nonparametric selection mechanism," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 3-29, July.
    37. Jeffrey M. Albert & Suchitra Nelson, 2011. "Generalized Causal Mediation Analysis," Biometrics, The International Biometric Society, vol. 67(3), pages 1028-1038, September.
    38. Joffe Marshall M & Small Dylan & Ten Have Thomas & Brunelli Steve & Feldman Harold I, 2008. "Extended Instrumental Variables Estimation for Overall Effects," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-20, April.
    39. Ruth Miquel, 2002. "Identification of Dynamic Treatment Effects by Instrumental Variables," University of St. Gallen Department of Economics working paper series 2002 2002-11, Department of Economics, University of St. Gallen.
    40. 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.
    41. Peter Z. Schochet & John Burghardt & Sheena McConnell, 2008. "Does Job Corps Work? Impact Findings from the National Job Corps Study," American Economic Review, American Economic Association, vol. 98(5), pages 1864-1886, December.
    42. Huber, Martin & Lechner, Michael & Wunsch, Conny, 2013. "The performance of estimators based on the propensity score," Journal of Econometrics, Elsevier, vol. 175(1), pages 1-21.
    43. Mealli, Fabrizia & Rubin, Donald B., 2003. "Assumptions allowing the estimation of direct causal effects," Journal of Econometrics, Elsevier, vol. 112(1), pages 79-87, January.
    44. 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.
    45. Kosuke Imai & Dustin Tingley & Teppei Yamamoto, 2013. "Experimental designs for identifying causal mechanisms," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 176(1), pages 5-51, January.
    46. Huber, Martin, 2012. "Identifying causal mechanisms in experiments (primarily) based on inverse probability weighting," Economics Working Paper Series 1213, University of St. Gallen, School of Economics and Political Science, revised May 2013.
    47. repec:mpr:mprres:2951 is not listed on IDEAS
    48. Bargain, Olivier & Boutin, Delphine, 2014. "Remittances and Child Labour in Africa: Evidence from Burkina Faso," IZA Discussion Papers 8007, Institute of Labor Economics (IZA).
    49. Lars Skipper & Marianne Simonsen, 2006. "The costs of motherhood: an analysis using matching estimators," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(7), pages 919-934.
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    Cited by:

    1. Huber, Martin & Steinmayr, Andreas, 2017. "A Framework for Separating Individual Treatment Effects From Spillover, Interaction, and General Equilibrium Effects," Rationality and Competition Discussion Paper Series 21, CRC TRR 190 Rationality and Competition.
    2. Kantorowicz, Jarosław & Köppl–Turyna, Monika, 2019. "Disentangling the fiscal effects of local constitutions," Journal of Economic Behavior & Organization, Elsevier, vol. 163(C), pages 63-87.
    3. Fabian Kosse & Thomas Deckers & Pia Pinger & Hannah Schildberg-Hörisch & Armin Falk, 2020. "The Formation of Prosociality: Causal Evidence on the Role of Social Environment," Journal of Political Economy, University of Chicago Press, vol. 128(2), pages 434-467.
    4. Denise Hörner & Adrien Bouguen & Markus Frölich & Meike Wollni, 2019. "The Effects of Decentralized and Video-based Extension on the Adoption of Integrated Soil Fertility Management – Experimental Evidence from Ethiopia," NBER Working Papers 26052, National Bureau of Economic Research, Inc.
    5. Prifti, Ervin & Daidone, Silvio & Davis, Benjamin, 2019. "Causal pathways of the productive impacts of cash transfers: Experimental evidence from Lesotho," World Development, Elsevier, vol. 115(C), pages 258-268.
    6. Christian Dippel & Robert Gold & Stephan Heblich & Rodrigo Pinto, 2017. "Instrumental Variables and Causal Mechanisms: Unpacking the Effect of Trade on Workers and Voters," CESifo Working Paper Series 6816, CESifo.
    7. Martin Huber, 2016. "Disentangling policy effects into causal channels," IZA World of Labor, Institute of Labor Economics (IZA), pages 259-259, May.
    8. Lochmann, Alexia & Rapoport, Hillel & Speciale, Biagio, 2019. "The effect of language training on immigrants’ economic integration: Empirical evidence from France," European Economic Review, Elsevier, vol. 113(C), pages 265-296.
    9. Strobl, Renate & Wunsch, Conny, 2018. "Identification of causal mechanisms based on between-subject double randomization designs," CEPR Discussion Papers 13028, C.E.P.R. Discussion Papers.
    10. Tadao Hoshino & Takahide Yanagi, 2018. "Treatment Effect Models with Strategic Interaction in Treatment Decisions," Papers 1810.08350, arXiv.org, revised Aug 2020.
    11. 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.
    12. Ohrnberger, Julius & Anselmi, Laura & Fichera, Eleonora & Sutton, Matt, 2020. "The effect of cash transfers on mental health: Opening the black box – A study from South Africa," Social Science & Medicine, Elsevier, vol. 260(C).
    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. Martin Huber & Anna Solovyeva, 2020. "Direct and Indirect Effects under Sample Selection and Outcome Attrition," Econometrics, MDPI, Open Access Journal, vol. 8(4), pages 1-25, December.
    15. Liu, Shilei & Xu, Jintao, 2019. "Livelihood mushroomed: Examining household level impacts of non-timber forest products (NTFPs) under new management regime in China's state forests," Forest Policy and Economics, Elsevier, vol. 98(C), pages 44-53.
    16. Martin Huber & Mark Schelker & Anthony Strittmatter, 2019. "Direct and Indirect Effects Based on Changes-in-Changes," CESifo Working Paper Series 7855, CESifo.
    17. Eva Deuchert & Martin Huber & Mark Schelker, 2019. "Direct and Indirect Effects Based on Difference-in-Differences With an Application to Political Preferences Following the Vietnam Draft Lottery," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(4), pages 710-720, October.
    18. 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.
    19. Muhammad Shoukat Malik & Lubna Kanwal, 2018. "Impact of Corporate Social Responsibility Disclosure on Financial Performance: Case Study of Listed Pharmaceutical Firms of Pakistan," Journal of Business Ethics, Springer, vol. 150(1), pages 69-78, June.
    20. Avdeenko, Alexandra & Frölich, Markus, 2020. "Research standards in empirical development economics: What’s well begun, is half done," World Development, Elsevier, vol. 127(C).
    21. Bijwaard, G.E.; & Jones, A.M.;, 2019. "Education and life-expectancy and how the relationship is mediated through changes in behaviour: a principal stratification approach for hazard rates," Health, Econometrics and Data Group (HEDG) Working Papers 19/05, HEDG, c/o Department of Economics, University of York.

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    More about this item

    Keywords

    Direct treatment effects; mediation analysis;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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