An Extended Class of Instrumental Variables for the Estimation of Causal Effects

This paper builds on the structural equations, treatment effect, and machine learning literatures to provide a causal framework that permits the identification and estimation of causal effects from observational studies. We begin by providing a causal interpretation for standard exogenous regressors and standard “valid” and “relevant” instrumental variables. We then build on this interpretation to characterize extended instrumental variables (EIV) methods, that is methods that make use of variables that need not be valid instruments in the standard sense, but that are nevertheless instrumental in the recovery of causal effects of interest. After examining special cases of single and double EIV methods, we provide necessary and sufficient conditions for the identification of causal effects by means of EIV and provide consistent and asymptotically normal estimators for the effects of interest. JEL Classification Numbers: C10, C20, C30, C51. 1 First Draft: March, 2005. The authors thank Kate Antonovics, Julian Betts, Graham Elliott, Marjorie Flavin, Clive Granger, Jinyong Hahn, Keisuke Hirano, Stephen Lauritzen, Mark Machina, Judea Pearl, Dimitris Politis, Ross Starr, Ruth Williams and the participants of the UCSD applied lunch seminar, the 4 annual Advances in Econometrics conference, the 2006 North American meeting of the Econometric Society, and the UCSD and UCLA Econometrics seminars. All errors and omissions are the authors’ responsibility. Karim Chalak, Department of Economics 0534, University of California, 9500 Gilman Drive, La Jolla, CA 92093-0534, [email protected], http://dss.ucsd.edu/~kchalak Halbert White, Department of Economics 0508, University of California, 9500 Gilman Drive, La Jolla, CA 92093-0508, [email protected], http://weber.ucsd.edu/~mbacci/white