We develop a new, spectral approach for identifying and estimating average counterfactual outcomes under a low-rank factor model with short panel data and general outcome missingness patterns. Applications include event studies and studies of outcomes of "matches" between agents of two types, e.g. workers and firms, typically conducted under less-flexible Two-Way-Fixed-Effects (TWFE) models of outcomes. Given an infinite population of units and a finite number of outcomes, we show our approach identifies all counterfactual outcome means, including those not estimable by existing methods, if a particular graph constructed based on overlaps in observed outcomes between subpopulations is connected. Our analogous, computationally efficient estimation procedure yields consistent, asymptotically normal estimates of counterfactual outcome means under fixed-$T$ (number of outcomes), large-$N$ (sample size) asymptotics. In a semi-synthetic simulation study based on matched employer-employee data, our estimator has lower bias and only slightly higher variance than a TWFE-model-based estimator when estimating average log-wages.

翻译：本文提出一种新的谱方法，用于在低秩因子模型框架下，基于短面板数据及一般性的结果缺失模式，识别并估计平均反事实结果。应用场景包括事件研究，以及两类主体（如劳动者与企业）间“匹配”结果的研究——这类研究通常在灵活性较差的“双向固定效应”（TWFE）结果模型下进行。给定无限总体单位和有限数量的结果观测值，我们证明：如果根据子群体间观测结果重叠情况构建的特定图结构是连通的，本方法能够识别所有反事实结果均值，包括现有方法无法估计的部分。我们提出的相应计算高效估计程序，在固定T（结果数量）、大N（样本量）渐近框架下，可得到反事实结果均值的一致且渐近正态的估计量。基于匹配雇主-雇员数据的半仿真模拟研究中，我们的估计量在估计平均对数工资时，偏差低于TWFE模型估计量，而方差仅略高于后者。