In this paper we study a class of weighted estimands, which we define as parameters that can be expressed as weighted averages of the underlying heterogeneous treatment effects. The popular ordinary least squares (OLS), two-stage least squares (2SLS), and two-way fixed effects (TWFE) estimands are all special cases within our framework. Our focus is on answering two questions concerning weighted estimands. First, under what conditions can they be interpreted as the average treatment effect for some (possibly latent) subpopulation? Second, when these conditions are satisfied, what is the upper bound on the size of that subpopulation, either in absolute terms or relative to a target population of interest? We argue that this upper bound provides a valuable diagnostic for empirical research. When a given weighted estimand corresponds to the average treatment effect for a small subset of the population of interest, we say its internal validity is low. Our paper develops practical tools to quantify the internal validity of weighted estimands.

翻译：本文研究一类加权估计量，我们将这类参数定义为可表示为潜在异质性处理效应加权平均的统计量。常用的普通最小二乘估计量、两阶段最小二乘估计量和双向固定效应估计量均属于我们框架下的特例。研究聚焦于回答关于加权估计量的两个问题：第一，在何种条件下这些估计量可被解释为某个（可能为潜在的）子群体的平均处理效应？第二，当这些条件满足时，该子群体规模的绝对上限或相对于目标总体的相对上限是什么？我们认为该上限为实证研究提供了有价值的诊断指标：当给定加权估计量对应的群体平均处理效应仅来自目标总体中很小一部分子群体时，我们称其内部有效性较低。本文开发了量化加权估计量内部有效性的实用工具。