Primary Submission Category: Difference in Differences, Synthetic Control, Methods for Panel and Longitudinal Data
Mosaic inference on panel data
Authors: Asher Spector, Emmanuel Candes, Rina Foygel Barber,
Presenting Author: Asher Spector*
The analysis of panel data via linear regression is ubiquitous in applied causal inference. However, such analyses typically assume that the residuals for different observations are cluster-independent; in general, standard confidence intervals may be invalid if this assumption is violated. This paper introduces a method called the mosaic permutation test that can be used to (a) test this assumption and (b) weaken it. We elaborate on these two contributions below.
Testing: Our method allows analysts to use nearly any machine learning technique to detect violations of the cluster-independence assumption while exactly controlling the false positive rate under a mild “local exchangeability” condition. To illustrate our method, we conduct a large-scale review of the literature and survey whether cluster-independence assumptions are accurate.
Inference: Our method produces confidence intervals for linear models that are (i) finite-sample valid under a local exchangeability assumption and (ii) asymptotically valid under the conventional cluster-independence assumption. In short, our method is valid under assumptions that are strictly weaker than classical methods. In experiments on real, randomly selected datasets from the literature, we find that many existing methods produce standard errors that are up to ten times too small, whereas mosaic methods produce reliable results.