Skip to main content

Explaining Causal Findings Without Bias: Detecting and Assessing Direct Effects


Researchers seeking to establish causal relationships frequently control for variables on the purported causal pathway, checking whether the original treatment effect then disappears. Unfortunately, this common approach may lead to biased estimates. In this article, we show that the bias can be avoided by focusing on a quantity of interest called the controlled direct effect. Under certain conditions, the controlled direct effect enables researchers to rule out competing explanations—an important objective for political scientists. To estimate the controlled direct effect without bias, we describe an easy-to-implement estimation strategy from the biostatistics literature. We extend this approach by deriving a consistent variance estimator and demonstrating how to conduct a sensitivity analysis. Two examples—one on ethnic fractionalization’s effect on civil war and one on the impact of historical plough use on contemporary female political participation—illustrate the framework and methodology.

Corresponding author
Avidit Acharya is Assistant Professor of Political Science, Stanford University (
Matthew Blackwell is Assistant Professor of Government, Harvard University (
Maya Sen is Assistant Professor of Public Policy, Harvard University (
Hide All

Thanks to Adam Cohon, Allan Dafoe, Justin Esarey, Adam Glynn, Robin Harding, Gary King, Macartan Humphreys, Kosuke Imai, Bethany Lacina, Jacob Montgomery, Judea Pearl, Dustin Tingley, Teppei Yamamoto, and conference or workshop participants at Dartmouth, Harvard, Princeton, WashU, the Midwest Political Science Association meeting, and the Society for Political Methodology summer meeting for helpful discussions and comments. Thanks to Anton Strezhnev for valuable research assistance. Any remaining errors are our own. The methods in this article are available as an open-source R package, DirectEffects, at Code and data to replicate results in this article can be found at

Hide All
Acharya Avidit, Blackwell Matthew, and Sen Maya. N.d. “The Political Legacy of American Slavery.” Journal of Politics. Forthcoming.
Alesina Alberto, Giuliano Paola, and Nunn Nathan. 2013. “On the Origins of Gender Roles: Women and the Plough.” Quarterly Journal of Economics 128 (2): 469530.
Angrist Joshua D., and Pischke Jörn-Steffen. 2008. Mostly Harmless Econometrics: An Empiricist’s Companion. Princeton: Princeton University Press.
Banerjee Abhijit, and Iyer Lakshmi. 2005. “History, Institutions, and Economic Performance: The Legacy of Colonial Land Tenure Systems in India.” American Economic Review 95 (4): 1190–213.
Blackwell Matthew. 2013. “A Framwork for Dynamic Causal Inference in Political Science.” American Journal of Political Science 57 (2): 504–20.
Blackwell Matthew. 2014. “A Selection Bias Approach to Sensitivity Analysis for Causal Effects.” Political Analysis 22 (2): 169–82.
Dell Melissa. 2010. “The Persistent Effects of Peru’s Mining Mita .” Econometrica 78 (6): 1863–903.
Fearon James D., and Laitin David D.. 2003. “Ethnicity, Insurgency, and Civil War.” American Political Science Review 97 (01): 7590.
Holland Paul W. 1986. “Statistics and Causal Inference.” Journal of the American Statistical Association 81 (396): 945–60.
Imai Kosuke, Keele Luke, Tingley Dustin, and Yamamoto Teppei. 2011. “Unpacking the Black Box of Causality: Learning about Causal Mechanisms from Experimental and Observational Studies.” American Political Science Review 105 (04): 765–89.
Imai Kosuke, Keele Luke, and Yamamoto Teppei. 2010. “Identification, Inference and Sensitivity Analysis for Causal Mediation Effects.” Statistical Science 25 (1): 5171.
Imai Kosuke, Tingley Dustin, and Yamamoto Teppei. 2013. “Experimental Designs for Identifying Causal Mechanisms.” Journal of the Royal Statistical Society. Series A (Statistics in Society) 176 (1): 551.
Imai Kosuke, and Yamamoto Teppei. 2013. “Identification and Sensitivity Analysis for Multiple Causal Mechanisms: Revisiting Evidence from Framing Experiments.” Political Analysis 21 (2): 141–71.
Imbens Guido W. 2004. “Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review.” Review of Economics and Statistics 86 (1): 429.
Joffe Marshall M., and Greene Tom. 2009. “Related Causal Frameworks for Surrogate Outcomes.” Biometrics 65 (2): 530–8.
Joffe Marshall M., Small Dylan, and Hsu Chi-Yuan. 2007. “Defining and Estimating Intervention Effects for Groups that will Develop an Auxiliary Outcome.” Statistical Science 22 (1): 7497.
Neyman Jerzy. 1923. “On the Application of Probability Theory to Agricultural Experiments. Essay on Principles. Section 9.” Statistical Science 5: 465–80. Translated in 1990, with discussion.
Nunn Nathan, and Wantchekon Leonard. 2011. “The Slave Trade and the Origins of Mistrust in Africa.” American Economic Review 101 (7): 3221–52.
Pearl Judea. 2001. “Direct and Indirect Effects.” In Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence. UAI’01 San Francisco: Morgan Kaufmann Publishers Inc., 411–20.
Robins James M. 1986. “A New Approach to Causal Inference in Mortality Studies with Sustained Exposure Periods-Application to Control of the Healthy Worker Survivor Effect.” Mathematical Modelling 7 (9-12): 1393–512.
Robins James M. 1994. “Correcting for Non-Compliance in Randomized Trials Using Structural Nested Mean Models.” Communications in Statistics 23 (8): 2379–412.
Robins James M. 1997. “Causal Inference from Complex Longitudinal Data.” In Latent Variable Modeling and Applications to Causality, ed. Berkane M.. Vol. 120 of Lecture Notes in Statistics. New York: Springer-Verlag, 69117.
Robins James M. 2003. “Semantics of Causal DAG Models and the Identification of Direct and Indirect Effects.” In Highly Structured Stochastic Systems, eds. Green P. J., Hjort N. L. and Richardson S.. Oxford: Oxford University Press, 7081.
Robins James M., and Greenland Sander. 1992. “Identifiability and Exchangeability for Direct and Indirect Effects.” Epidemiology 3 (2): 143–55.
Robins James M., Hernán Miguel A., and Brumback Babette A.. 2000. “Marginal Structural Models and Causal Inference in Epidemiology.” Epidemiology 11 (5): 550–60.
Rosenbaum Paul R. 1984. “The Consequences of Adjustment for a Concomitant Variable That Has Been Affected by the Treatment.” Journal of the Royal Statistical Society. Series A (General) 147 (5): 656–66.
Rubin Donald B. 1974. “Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies.” Journal of Educational Psychology 6: 688701.
Rubin Donald B. 2004. “Direct and Indirect Causal Effects via Potential Outcomes.” Scandinavian Journal of Statistics 31 (2): 161–70.
VanderWeele Tyler J. 2009. “Mediation and Mechanism.” European Journal of Epidemiology 24 (5): 217–24.
VanderWeele Tyler J. 2011. “Controlled Direct and Mediated Effects: Definition, Identification and Bounds.” Scandinavian Journal of Statistics 38 (3): 551–63.
VanderWeele Tyler J. 2014. “A Unification of Mediation and Interaction: A 4-Way Decomposition.” Epidemiology 25 (5): 749–61.
VanderWeele Tyler J. and Tchetgen Eric J. Tchetgen. 2014. “Attributing Effects to Interactions.” Epidemiology 25 (5): 711–22.
Vansteelandt Sijn. 2009. “Estimating Direct Effects in Cohort and Case–Control Studies.” Epidemiology 20 (6): 851–60.
Vansteelandt Sijn. 2010. “Estimation of Controlled Direct Effects on a Dichotomous Outcome Using Logistic Structural Direct Effect Models.” Biometrika 97 (4): 921–34.
Vansteelandt Sijn, and Joffe Marshall. 2014. “Structural Nested Models and G-estimation: The Partially Realized Promise.” Statistical Science 29 (4): 707–31.
Vansteelandt Sijn, and VanderWeele Tyler J.. 2009. “Conceptual Issues Concerning Mediation, Interventions and Composition.” Statistics and Its Interface 2: 457–68.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

American Political Science Review
  • ISSN: 0003-0554
  • EISSN: 1537-5943
  • URL: /core/journals/american-political-science-review
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
Type Description Title
Supplementary materials

Acharya supplementary material
Acharya supplementary material 1

 PDF (95 KB)
95 KB


Altmetric attention score

Full text views

Total number of HTML views: 74
Total number of PDF views: 1014 *
Loading metrics...

Abstract views

Total abstract views: 2261 *
Loading metrics...

* Views captured on Cambridge Core between 13th September 2016 - 24th February 2018. This data will be updated every 24 hours.