Estimating Outcome Distributions for Compliers in Instrumental Variables Models
证明在工具变量模型的标准假设下，可以估计依从者子群体在不同处理下的完整结果边际分布，而不仅仅是平均因果效应，并指出标准工具变量估计隐含的分布可能为负，施加非负性会显著改变局部平均处理效应的估计。
In Imbens and Ingrist (1994), Angrist, Imbens and Rubin (1996) and Imbens and Rubin (1997), assumptions have been outlined under which instrumental variables estimands can be given a causal interpretation as a local average treatment effect without requiring functional form or constant treatment effect assumptions. We extend these results by showing that under these assumptions one can estimate more from the data than the average causal effect for the subpopulation of compliers; one can, in principle, estimate the entire marginal distribution of the outcome under different treatments for this subpopulation. These distributions might be useful for a policy maker who wishes to take into account not only differences in average of earnings when contemplating the merits 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 nonnegativity on these implicit density estimates, and that imposing non-negativity can substantially alter the estimates of the local average treatment effect. We illustrate these points by presenting an analysis of the returns to a high school education using quarter of birth as an instrument. We show that the standard instrumental variables estimates implicitly estimate the outcome distributions to be negative over a substantial range, and that the estimates of the local average treatment effect change considerably when we impose nonnegativity in any of a variety of ways.