Viewpoint: An extended class of instrumental variables for the estimation of causal effects

We examine how structural systems can yield observed variables instrumental in identifying and estimating causal effects.We provide an exhaustive characterization of potentially identifying conditional exogeneity relationships and demonstrate how structural relations determine exogeneity and exclusion restrictions that yield moment conditions supporting identification. This provides a comprehensive framework for constructing instruments and covariates. We introduce notions of conditioning and conditional extended instrumental variables (XIVs). These permit identification but need not be traditional instruments, as they may be endogenous. We distinguish between observed XIVs and proxies for unobserved XIVs. A main message is the importance of sufficiently specifying causal relations governing the unobservables. JEL classification: C10, C13, C21, C31, C51 Une classe etendue de variables instrumentales pour l’estimation des effets de causalite. Les auteurs examinent comment des systemes structurels peuvent engendrer des variables observees instrumentales dans l’identification et l’estimation d’effets de causalite. On fournit une caracterisation exhaustive des relations d’exogeneite conditionnelle potentiellement porteuses d’identification, et on demontre comment des relations structurelles determinent les restrictions d’exogeneite et d’exclusion qui engendrent les conditions de moment qui supportent l’identification. Cela fournit un cadre comprehensif pour construire instruments et covariables. On introduit des notions de variables instrumentales etendues conditionnantes et conditionnelles (XIVs). Celles-ci permettent l’identification, mais n’ont pas a etre des instruments traditionnels, parce qu’elles peuvent etre endogenes. On distingue entre les XIVs observees et les variables concomitantes avec les XIVs The authors thank Alberto Abadie, Kate Antonovics, Julian Betts, Gary Chamberlain, Graham Elliott, Marjorie Flavin, Clive Granger, Jinyong Hahn, James Heckman, Keisuke Hirano, Guido Imbens, Steffen Lauritzen, Arthur Lewbel, Mark Machina, Chuck Manski, Salvatore Modica, Judea Pearl, Dimitris Politis, Ross Starr, Elie Tamer, Ruth Williams, and the participants at the 4th annual Advances in Econometrics conference. We also thank Chuanqi Zhu for his research assistance. All errors and omissions are the authors’ responsibility. Email: chalak@bc.edu; hwhite@ucsd.edu Canadian Journal of Economics / Revue canadienne d’Economique, Vol. 44, No. 1 February / fevrier 2011. Printed in Canada / Imprime au Canada 0008-4085 / 11 / 1–51 / C © Canadian Economics Association 2 K. Chalak and H. White non-observees. Un message central est l’importance de suffisamment specifier les relations causales qui gouvernent les non-observables.