Mosaic inference on panel data

Music City Center 

The analysis of panel data via linear regression is ubiquitous across disciplines. However, standard confidence intervals typically assume that the residuals are cluster-independent. 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 contributions below.

Testing: Our method can use flexible machine learning techniques to detect violations of the cluster-independence assumption while exactly controlling false positives under a mild "local exchangeability" condition. To illustrate our method, we survey the literature and assess 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 cluster-independence assumption. In short, our method is valid under assumptions that are strictly weaker than classical methods. Experiments on real, randomly selected datasets from the literature show that many existing standard errors are up to ten times too small, whereas mosaic methods produce reliable results.

Panel data

Permutation tests

Linear regression

Semiparametric models

Hypothesis tests 

Business and Economic Statistics Section