In this paper we study the finite sample and asymptotic properties of various weighting estimators of the local average treatment effect (LATE), several of which are based on Abadie's (2003) kappa theorem. Our framework presumes a binary treatment and a binary instrument, which may only be valid after conditioning on additional covariates. We argue that one of the Abadie estimators, which is weight normalized, is preferable in many contexts. Several other estimators, which are unnormalized, do not generally satisfy the properties of scale invariance with respect to the natural logarithm and translation invariance, thereby exhibiting sensitivity to the units of measurement when estimating the LATE in logs and the centering of the outcome variable more generally. On the other hand, when noncompliance is one-sided, certain unnormalized estimators have the advantage of being based on a denominator that is bounded away from zero. To reconcile these findings, we demonstrate that when the instrument propensity score is estimated using an appropriate covariate balancing approach, the resulting normalized estimator also shares this advantage. We use a simulation study and three empirical applications to illustrate our findings. In two cases, the unnormalized estimates are clearly unreasonable, with "incorrect" signs, magnitudes, or both.
翻译:在本文中,我们研究了各种加权估计局部平均处理效应(LATE)的有限样本和渐近性质,其中有几个是基于Abadie(2003年)的kappa定理。我们的框架假定二进制处理和二进制工具,可能只在附加协变量的条件下有效。我们认为,其中一个Abadie估计量,也就是权重归一化的估计量,在许多情况下更可取。几个其他的估计量,它们未归一化,通常不能满足相对于自然对数的比例不变性和平移不变性的特性,在估计LATE时,它们表现出对测量单位的敏感性,以及结果变量的居中更普遍。另一方面,当不遵守一面时,某些未归一化的估计量具有基于分母限于零附近的优势。为了调和这些发现,我们证明了当使用适当的协变量平衡方法估计工具倾向得分时,所产生的归一化估计量也共享这种优势。我们使用模拟研究和三个实证应用来说明我们的发现。在两种情况下,未归一化的估计是明显不合理的,具有“错误”的符号、幅度或两者兼而有之。