Using Instrumental Variables for Inference About Policy Relevant Treatment Parameters
中文摘要
我们提出一种运用工具变量(IV)来推断以下因果效应的方法: 即推断那些并非受当前工具变量影响的个体的因果效应。政策相关性与外部有效性取决于能否可靠地做到这一点。我们的方法利用了如下洞见: 无论是IV被估量还是许多处理参数, 都可以表示为相同的潜在边际处理效应的加权平均。由于权重是可识别的, 因此对IV被估量的了解通常会对未知的边际处理效应施加某些限制, 从而对所关注的处理参数的取值施加限制。我们展示了如何从IV被估量中提取关于所关注处理参数的信息, 并且更一般地, 从一类类IV被估量中提取此类信息, 该类被估量包括两阶段最小二乘被估量和普通最小二乘被估量等。我们的方法有若干应用。第一, 它可以用来构造假设性政策变化的平均因果效应的非参数界。第二, 我们的方法允许研究者灵活地纳入形状约束和参数假设, 从而能够将依从者的平均效应外推到不同人群或更大群体的平均效应。第三, 我们的方法可以用来检验模型设定以及关于行为的假设, 例如无选择性偏误和/或无基于收益的选择。
Abstract
We propose a method for using instrumental variables (IV) to draw inference about causal effects for individuals other than those affected by the instrument at hand. Policy relevance and external validity turn on the ability to do this reliably. Our method exploits the insight that both the IV estimand and many treatment parameters can be expressed as weighted averages of the same underlying marginal treatment effects. Since the weights are identified, knowledge of the IV estimand generally places some restrictions on the unknown marginal treatment effects, and hence on the values of the treatment parameters of interest. We show how to extract information about the treatment parameter of interest from the IV estimand and, more generally, from a class of IV‐like estimands that includes the two stage least squares and ordinary least squares estimands, among others. Our method has several applications. First, it can be used to construct nonparametric bounds on the average causal effect of a hypothetical policy change. Second, our method allows the researcher to flexibly incorporate shape restrictions and parametric assumptions, thereby enabling extrapolation of the average effects for compliers to the average effects for different or larger populations. Third, our method can be used to test model specification and hypotheses about behavior, such as no selection bias and/or no selection on gain.