Matrix Completion When Missing Is Not at Random and Its Applications in Causal Panel Data Models
本文提出一种在缺失非随机且信号较弱时仍能有效估计的矩阵补全方法，通过将缺失条目分组并采用核范数正则化，结合去偏技术实现渐近正态性，并应用于SEC的Tick Size Pilot Program数据分析，揭示处理效应的异质性和动态变化。
This paper develops an inferential framework for matrix completion when missing is not at random and without the requirement of strong signals. Our development is based on the observation that if the number of missing entries is small enough compared to the panel size, then they can be estimated well even when missing is not at random. Taking advantage of this fact, we divide the missing entries into smaller groups and estimate each group via nuclear norm regularization. In addition, we show that with appropriate debiasing, our proposed estimate is asymptotically normal even for fairly weak signals. Our work is motivated by recent research on the Tick Size Pilot Program, an experiment conducted by the Security and Exchange Commission (SEC) to evaluate the impact of widening the tick size on the market quality of stocks from 2016 to 2018. While previous studies were based on traditional regression or difference-in-difference methods by assuming that the treatment effect is invariant with respect to time and unit, our analyses suggest significant heterogeneity across units and intriguing dynamics over time during the pilot program.