Econometrica · 2020 · Alberto Abadie、Susan Carleton Athey、Guido W. Imbens、Jeffrey M. Wooldridge
中文摘要
考虑一位研究者基于美国全部50个州的数据或某网站全部访问记录的数据来估计一个回归函数的参数。这些估计参数与标准误该如何解释？在实践中，研究者通常假定样本是从一个较大的目标总体中随机抽取的，并报告旨在捕捉抽样变动的标准误。即便在难以明确描述目标总体是什么以及它与样本有何差异的应用中，这种做法也很常见。在本文中，我们探讨了一种部分基于设计的替代性推断方法。在基于设计的设定下，某些回归元的取值可以被操纵，或许是通过政策干预。基于设计的不确定性源于对回归结果在替代性干预下会取何值缺乏了解。我们推导出的标准误考虑了基于设计的不确定性，以之取代或补充基于抽样的不确定性。我们表明，我们的标准误通常小于通常的无限总体基于抽样的标准误，并给出了二者相等的条件。
Abstract
Consider a researcher estimating the parameters of a regression function based on data for all 50 states in the United States or on data for all visits to a website. What is the interpretation of the estimated parameters and the standard errors? In practice, researchers typically assume that the sample is randomly drawn from a large population of interest and report standard errors that are designed to capture sampling variation. This is common even in applications where it is difficult to articulate what that population of interest is, and how it differs from the sample. In this article, we explore an alternative approach to inference, which is partly design‐based. In a design‐based setting, the values of some of the regressors can be manipulated, perhaps through a policy intervention. Design‐based uncertainty emanates from lack of knowledge about the values that the regression outcome would have taken under alternative interventions. We derive standard errors that account for design‐based uncertainty instead of, or in addition to, sampling‐based uncertainty. We show that our standard errors in general are smaller than the usual infinite‐population sampling‐based standard errors and provide conditions under which they coincide.