We develop a more flexible approach for identifying and estimating average counterfactual outcomes when several but not all possible outcomes are observed for each unit in a large cross section. Such settings include event studies and studies of outcomes of "matches" between agents of two types, e.g. workers and firms or people and places. When outcomes are generated by a factor model that allows for low-dimensional unobserved confounders, our method yields consistent, asymptotically normal estimates of counterfactual outcome means under asymptotics that fix the number of outcomes as the cross section grows and general outcome missingness patterns, including those not accommodated by existing methods. Our method is also computationally efficient, requiring only a single eigendecomposition of a particular aggregation of any factor estimates constructed using subsets of units with the same observed outcomes. In a semi-synthetic simulation study based on matched employer-employee data, our method performs favorably compared to a Two-Way-Fixed-Effects-model-based estimator.

翻译：我们提出了一种更灵活的方法，用于在截面数据量较大但每个单位仅观测到部分可能结果时，识别和估计平均反事实结果。这类设定包括事件分析，以及两类主体（如劳动者与企业、人与地点）之间“匹配”结果的研究。当结果由允许存在低维未观测混杂因素的因子模型生成时，我们的方法能够在增长截面规模的同时固定结果数量、并允许一般性的结果缺失模式（包括现有方法无法处理的情形）下，得到反事实结果均值的一致且渐近正态的估计量。该方法计算效率高，仅需对通过对具有相同观测结果的子集构建的任意因子估计量进行特定聚合，并执行一次特征分解。在基于匹配雇主-雇员数据的半合成模拟研究中，我们的方法相较于基于双向固定效应模型的估计量表现出更优的性能。