ESTIMATING OUTCOME DISTRIBUTIONS FOR COMPLIERS IN INSTRUMENTAL VARIABLES MODELS

In Imbens and Ingrist (1994), Angrist, Imbens and Rubin (1996) and Imb ens and Rubin (1997), assumptions have been outlined under which instr umental variables estimands can be given a causal interpretation as a local average treatment effect without requiring functional form or co nstant treatment effect assumptions. We extend these results by showin g that under these assumptions one can estimate more from the data tha n the average causal effect for the subpopulation of compliers; one ca n, in principle, estimate the entire marginal distribution of the outc ome under different treatments for this subpopulation. These distribut ions might be useful for a policy maker who wishes to take into accoun t not only differences in average of earnings when contemplating the m erits of one job training programme vs. another. We also show that the standard instrumental variables estimator implicitly estimates these underlying outcome distributions without imposing the required nonnega tivity on these implicit density estimates, and that imposing nonnegat ivity can substantially alter the estimates of the local average treat ment effect. We illustrate these points by presenting an analysis of t he returns-to a high school education using quarter of birth as an ins trument. We show that the standard instrumental variables estimates im plicitly estimate the outcome distributions to be negative over a subs tantial range, and that the estimates of the local average treatment e ffect change considerably when we impose nonnegativity in any of a var iety of ways.