Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Econometric Methods

Ed. by Giacomini, Raffaella / Li, Tong

Mathematical Citation Quotient (MCQ) 2018: 0.06

See all formats and pricing
More options …

Nonparametric estimation of natural direct and indirect effects based on inverse probability weighting

Yu-Chin Hsu / Martin Huber / Tsung-Chih Lai
Published Online: 2018-06-13 | DOI: https://doi.org/10.1515/jem-2017-0016


Using a sequential conditional independence assumption, this paper discusses fully nonparametric estimation of natural direct and indirect causal effects in causal mediation analysis based on inverse probability weighting. We propose estimators of the average indirect effect of a binary treatment, which operates through intermediate variables (or mediators) on the causal path between the treatment and the outcome, as well as the unmediated direct effect. In a first step, treatment propensity scores given the mediator and observed covariates or given covariates alone are estimated by nonparametric series logit estimation. In a second step, they are used to reweigh observations in order to estimate the effects of interest. We establish root-n consistency and asymptotic normality of this approach as well as a weighted version thereof. The latter allows evaluating effects on specific subgroups like the treated, for which we derive the asymptotic properties under estimated propensity scores. We also provide a simulation study and an application to an information intervention about male circumcisions.

Keywords: causal channels; causal mechanisms; causal pathways; direct effects; indirect effects; inverse probability weighting; mediation analysis; nonparametric estimation; propensity score; series logit estimation

JEL Classification: C21


  • Abrevaya, J., Y.-C. Hsu, and R. P. Lieli. 2015. “Estimating Conditional Average Treatment Effects.” Journal of Business & Economic Statistics 33 (4): 485–505.CrossrefWeb of ScienceGoogle Scholar

  • Albert, J. M. 2008. “Mediation analysis via potential outcomes models.” Statistics in Medicine 27: 1282–1304.CrossrefWeb of ScienceGoogle Scholar

  • Albert, J. M., and S. Nelson. 2011. “Generalized causal mediation analysis.” Biometrics 67: 1028–1038.CrossrefWeb of ScienceGoogle Scholar

  • An, W., and X. Wang. 2016. “Instrumental Variable Estimation of Causal Effects through Local Average Response Functions.” Journal of Statistical Software 71: 1–13.Web of ScienceGoogle Scholar

  • Baron, R. M., and D. A. Kenny. 1986. “The Moderator-Mediator Variable Distinction in Social Psychological Research: Conceptual, Strategic, and Statistical Considerations.” Journal of Personality and Social Psychology 51: 1173–1182.CrossrefGoogle Scholar

  • Busso, M., J. DiNardo, and J .McCrary. 2014. “New Evidence on the Finite Sample Properties of Propensity Score Matching and Reweighting Estimators.” Review of Economics and Statistics 96 (5): 885–897.Web of ScienceCrossrefGoogle Scholar

  • Chinkhumba, J., S. Godlonton, and R. Thornton. 2014. “The Demand for Medical Male Circumcision.” American Economic Journal: Applied Economics 6: 152–177.Web of ScienceGoogle Scholar

  • Donald, S. G., and Y.-C. Hsu. 2014. “Estimation and Inference for Distribution Functions and Quantile Functions in Treatment Effect Models.” Journal of Econometrics 178: 383–397.Web of ScienceCrossrefGoogle Scholar

  • Donald, S. G., Y.-C. Hsu, and R. P. Lieli. 2014. “Testing the Unconfoundedness Assumption via Inverse Probability Weighted Estimators of (L)ATT.” Journal of Business & Economic Statistics 32 (3): 395–415.CrossrefWeb of ScienceGoogle Scholar

  • Donald, S. G., Y.-C. Hsu, and R. P. Lieli. 2014. “Inverse Probability Weighted Estimation of Local Average Treatment Effects: A Higher Order MSE Expansion.” Statistics and Probability Letters 95:132–138.CrossrefGoogle Scholar

  • Flores, C. A., and A. Flores-Lagunes. 2009. “Identification and Estimation of Causal Mechanisms and Net Effects of a Treatment under Unconfoundedness.” IZA Dicussion Paper No. 4237.Google Scholar

  • Gelman, A., and G. Imbens. 2013. “Why ask Why? Forward Causal Inference and Reverse Causal Questions.” NBER Working Paper No. 19614.Google Scholar

  • Hayes, A. F. 2017. An introduction to mediation, moderation, and conditional process analysis: A regression-based approach. New york, USA: Guilford Press.Google Scholar

  • Hirano, K., G. W. Imbens, and G. Ridder. 2003. “Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score.” Econometrica 71: 1161–1189.CrossrefGoogle Scholar

  • Hong, G. 2010. “Ratio of mediator probability weighting for estimating natural direct and indirect effects,” in JSM Proceedings, Biometrics Section, pp. 2401–2415. Alexandria, VA: American Statistical Association.Google Scholar

  • Hong, G. 2015. Causality in a social world: Moderation, mediation and spill-over. West Sussex, UK: John Wiley & Sons, Ltd.Google Scholar

  • Hsu, Y.-C. 2017. “Consistent Tests for Conditional Treatment Effects.” Econometrics Journal 20 (1):1–22.CrossrefWeb of ScienceGoogle Scholar

  • Huber, M. 2014. “Identifying causal mechanisms (primarily) based on inverse probability weighting.” Journal of Applied Econometrics 29: 920–943.Web of ScienceCrossrefGoogle Scholar

  • Ichimura, H., and O. Linton. 2005. “Asymptotic Expansions for Some Semiparametric Program Evaluation Estimators,” in Identification and Inference for Econometric Models: essays in honor of Thomas Rothenberg, edited by D. Andrews and J. Stock. Cambridge, England: Cambridge University Press.Google Scholar

  • Imai, K., L. Keele, and T. Yamamoto. 2010. “Identification, Inference and Sensitivity Analysis for Causal Mediation Effects.” Statistical Science 25: 51–71.CrossrefWeb of ScienceGoogle Scholar

  • Imai, K., and T. Yamamoto. 2013. “Identification and Sensitivity Analysis for Multiple Causal Mechanisms: Revisiting Evidence from Framing Experiments.” Political Analysis 21: 141–171.CrossrefWeb of ScienceGoogle Scholar

  • Imbens, G. W. 2004. “Nonparametric Estimation of Average Treatment Effects under Exogeneity: A Review.” The Review of Economics and Statistics 86: 4–29.CrossrefGoogle Scholar

  • Imbens, G. W., and J. M. Wooldridge. 2009. “Recent Developments in the Econometrics of Program Evaluation.” Journal of Economic Literature 47: 5–86.CrossrefWeb of ScienceGoogle Scholar

  • Judd, C. M., and D. A. Kenny. 1981. “Process Analysis: Estimating Mediation in Treatment Evaluations.” Evaluation Review 5: 602–619.CrossrefGoogle Scholar

  • Li, Q., and J. S. Racine. 2007. Nanparametric econometrics: theory and practice. Princeton, New Jersey: Princeton Universiry Press.Google Scholar

  • MacKinnon, D. P. 2008. Introduction to Statistical Mediation Analysis. New York: Taylor and Francis.Google Scholar

  • Pearl, J. 2001. “Direct and indirect effects,” in Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence, pp. 411–420, San Francisco. Morgan Kaufman.Google Scholar

  • Petersen, M. L., S. E. Sinisi, and M. J. van der Laan. 2006. “Estimation of Direct Causal Effects.” Epidemiology 17: 276–284.CrossrefGoogle Scholar

  • Robins, J. M. 2003. “Semantics of causal DAG models and the identification of direct and indirect effects,” in In Highly Structured Stochastic Systems, edited by P. Green, N. Hjort, and S. Richardson, pp. 70–81, Oxford: Oxford University Press.Google Scholar

  • Robins, J. M., and S. Greenland. 1992. “Identifiability and Exchangeability for Direct and Indirect Effects.” Epidemiology 3: 143–155.CrossrefGoogle Scholar

  • Rubin, D. B. 1974. “Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies.” Journal of Educational Psychology 66: 688–701.CrossrefGoogle Scholar

  • Rubin, D. B. 2004. “Direct and Indirect Causal Effects via Potential Outcomes.” Scandinavian Journal of Statistics 31: 161–170.CrossrefGoogle Scholar

  • Tchetgen Tchetgen, E. J. 2013. “Inverse Odds Ratio-Weighted Estimation for Causal Mediation Analysis.” Statistics in Medicine 32: 4567–4580.CrossrefWeb of ScienceGoogle Scholar

  • Tchetgen Tchetgen, E. J., and I. Shpitser. 2012. “Semiparametric theory for causal mediation analysis: Efficiency bounds, multiple robustness, and sensitivity analysis.” The Annals of Statistics 40: 1816–1845.CrossrefGoogle Scholar

  • Ten Have, T. R., M. M. Joffe, K. G. Lynch, G. K. Brown, S. A. Maisto, and A. T. Beck. 2007. “Causal mediation analyses with rank preserving models.” Biometrics 63: 926–934.Web of ScienceCrossrefGoogle Scholar

  • Tingley, D., T. Yamamoto, K. Hirose, K. Imai, and L. Keele. 2014. “Mediation: R package for causal mediation analysis.” Journal of Statistical Software 59: 1–38.Google Scholar

  • VanderWeele, T. J. 2009. “Marginal Structural Models for the Estimation of Direct and Indirect Effects.” Epidemiology 20: 18–26.CrossrefWeb of ScienceGoogle Scholar

  • Vansteelandt, S., M. Bekaert, and T. Lange. 2012. “Imputation Strategies for the Estimation of Natural Direct and Indirect Effects.” Epidemiologic Methods 1: 129–158.Google Scholar

About the article

Published Online: 2018-06-13

Citation Information: Journal of Econometric Methods, Volume 8, Issue 1, 20170016, ISSN (Online) 2156-6674, DOI: https://doi.org/10.1515/jem-2017-0016.

Export Citation

©2019 Walter de Gruyter GmbH, Berlin/Boston.Get Permission

Comments (0)

Please log in or register to comment.
Log in