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This paper develops an inferential framework for matrix completion whenmissing is not at random and without the requirement of strong signals. Ourdevelopment is based on the observation that if the number of missing entriesis small enough compared to the panel size, then they can be estimated welleven when missing is not at random. Taking advantage of this fact, we dividethe missing entries into smaller groups and estimate each group via nuclearnorm regularization. In addition, we show that with appropriate debiasing, ourproposed estimate is asymptotically normal even for fairly weak signals. Ourwork is motivated by recent research on the Tick Size Pilot Program, anexperiment conducted by the Security and Exchange Commission (SEC) to evaluatethe impact of widening the tick size on the market quality of stocks from 2016to 2018. While previous studies were based on traditional regression ordifference-in-difference methods by assuming that the treatment effect isinvariant with respect to time and unit, our analyses suggest significantheterogeneity across units and intriguing dynamics over time during the pilotprogram.

Matrix Completion When Missing Is Not at Random and Its Applications in Causal Panel Data Models