Instrumental Variables Response to Angrist and Imbens

My 1997 JHR paper neither endorsed nor condemned the use of instrumental variables (IV) to estimate the parameters of economic models. Its main goal was to remind readers of some basic points developed in a series of papers with Richard Robb (1985, 1986), We establish that when responses to "treatment" or a policy intervention vary across persons even after conditioning on observable variables (X), a variety of mean treatment effects can be defined. When responses are homogeneous (conditional on X), all mean treatment effects are the same. The "common effect," homogenous response, assumption underlies most currently used econometric methods used to evaluate social programs. When responses to treatment are homogenous, the case for social experiments and instrumental variables is the most persuasive. (Heckman, 1992; Heckman and Smith, 1992, 1993, 1998), When responses to treatment vary across persons, different mean parameters can be defined that answer different economic questions. A variety of interesting policy counterfactuals can be constructed. Social experiments are better suited for recovering some of these parameters than others. In general, identification of different parameters requires different assumptions to justify application of the method of instrumental variables in any instance, or to justify the application of any econometric method. That different parameters in general require different assumptions should not be surprising. There is no universal justification of the method of instrumental variables for identifying all economic parameters. The comment by Angrist and Imbens confuses two ideas that are fruitfully distinguished. The first idea is that every econometric estimator estimates something, provided it converges. Conditions for convergence of the IV estimator are quite weak, and involve invocation of laws of large numbers (see, for example. White, 1984), The second, and more interesting, idea is an economic one. Does the object defined by application of the estimator answer an interesting economic question? In particu-