Political Analysis Advance Access first published online on February 10, 2008
This version published online on February 14, 2008
Political Analysis, doi:10.1093/pan/mpm039
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Model Specification in Instrumental-Variables Regression
Department of Political Science, Yale University, PO Box 208301, New Haven, CT 06520
e-mail: thad.dunning{at}yale.edu
In many applications of instrumental-variables regression, researchers seek to defend the plausibility of a key assumption: the instrumental variable is independent of the error term in a linear regression model. Although fulfilling this exogeneity criterion is necessary for a valid application of the instrumental-variables approach, it is not sufficient. In the regression context, the identification of causal effects depends not just on the exogeneity of the instrument but also on the validity of the underlying model. In this article, I focus on one feature of such models: the assumption that variation in the endogenous regressor that is related to the instrumental variable has the same effect as variation that is unrelated to the instrument. In many applications, this assumption may be quite strong, but relaxing it can limit our ability to estimate parameters of interest. After discussing two substantive examples, I develop analytic results (simulations are reported elsewhere). I also present a specification test that may be useful for determining the relevance of these issues in a given application.
Author's note: I am grateful to David Freedman, Don Green, Nicholas Sambanis, Ken Scheve, and the anonymous reviewers, whose suggestions greatly improved this article. Bear Braumoeller, David Collier, and Jason Seawright made valuable comments on an earlier, related paper. Simulations are available on the Political Analysis Web site.