Branching Fixed Effects: A Proposal for Communicating Uncertainty

Abstract

Economists often rely on estimates of linear fixed effects models produced by other teams of researchers. Assessing the uncertainty in these estimates can be challenging. I propose a form of sample splitting for networks that partitions the data into statistically independent branches, each of which can be used to compute an unbiased estimate of the parameters of interest in two-way fixed effects models. These branches facilitate uncertainty quantification, moment estimation, and shrinkage. Drawing on results from the graph theory literature on tree packing, I develop algorithms to efficiently extract branches from large networks. I illustrate these techniques using a benchmark dataset from Veneto, Italy that has been widely used to study firm wage effects.