Choosing an Identifying Set of Matching or Conditioning Variables

Political scientists estimate average causal effects with regression or matching techniques, but both techniques require the user to choose a set of matching or conditioning variables. In this paper, we show that the standard advice from both frameworks on how to choose an identifying set of variables is often insufficient and at times misleading. Furthermore, we argue that structural causal models (SCMs) provide an attractive framework to reason about this problem. SCMs provide simple rules for choosing an identifying set of variables given particular causal assumptions. This framework is equivalent to the Neyman-Rubin framework and common adjustment methods—such as those based on generalized linear models—can be analyzed within the framework. Finally, we demonstrate that SCMs allow the specification of causal modeling assumptions in a manner that is compatible with the mechanistic view of causation commonly invoked by political scientists. ∗The authors thank Thomas Richardson for introducing them to literature of graphical causal models, and also thank Neal Beck, Andy Eggers, Jim Greiner, Ben Hansen, Gary King, Judea Pearl, Anton Westveld, two anonymous referees, and the participants of 2007 Summer meetings of the Society of Political Methodology for their helpful comments and suggestions. The usual caveat applies. In addition, Quinn thanks the National Science Foundation (grants SES 03-50613 and BCS 05-27513) and the Center for Advanced Study in the Behavioral Sciences for its hospitality and support. †Department of Government and The Institute for Quantitative Social Sciences Harvard University, 1737 Cambridge Street, Cambridge, MA 02138. [email protected] ‡Department of Government and The Institute for Quantitative Social Sciences Harvard University, 1737 Cambridge Street, Cambridge, MA 02138. kevin [email protected]