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The Product and Difference Fallacies for Indirect Effects


  • An earlier version of this article was prepared for the 25th Annual Summer Meeting of the Society for Political Methodology at the University of Michigan in 2008. The author would especially like to thank M. Steven Fish for providing the data used in this article. The author also thanks Oliver Bevan, John Bullock, Patrick Egan, Michael Hiscox, Nahomi Ichino, Kosuke Imai, Torben Iversen, Gary King, Judea Pearl, Kevin Quinn, and Tyler VanderWeele, as well as the editor and reviewers for their helpful comments and discussion. The usual caveat applies. The replication data are available at

Adam N. Glynn is Associate Professor, Department of Government, Harvard University, 1737 Cambridge Street, Cambridge, MA 02138 (


Political scientists often cite the importance of mechanism-specific causal knowledge, both for its intrinsic scientific value and as a necessity for informed policy. This article explains why two common inferential heuristics for mechanism-specific (i.e., indirect) effects can provide misleading answers, such as sign reversals and false null results, even when linear regressions provide unbiased estimates of constituent effects. Additionally, this article demonstrates that the inferential difficulties associated with indirect effects can be ameliorated with the use of stratification, interaction terms, and the restriction of inference to subpopulations (e.g., the indirect effect on the treated). However, indirect effects are inherently not identifiable—even when randomized experiments are possible. The methodological discussion is illustrated using a study on the indirect effect of Islamic religious tradition on democracy scores (due to the subordination of women).