Branching Fixed Effects: A Proposal for Communicating Uncertainty

Abstract: Economists often rely on estimates of linear fixed effects models developed by other teams of researchers. Assessing the uncertainty in these estimates can be challenging. I propose a form of sample splitting for network data that breaks two-way fixed effects estimates into statistically independent branches, each of which provides an unbiased estimate of the parameters of interest. These branches facilitate uncertainty quantification, moment estimation, and shrinkage. Algorithms are developed for efficiently extracting branches from large datasets. I illustrate these techniques using a benchmark dataset from Veneto, Italy that has been widely used to study firm wage effects.