ANOVA-HDFE: Fast Variance Decomposition with High-Dimensional Fixed Effects and an Application to Trade Flows

Performing an analysis of variance (ANOVA) on a large dataset spanning many dimensions becomes computationally challenging or even infeasible. We develop a new, fast procedure, ANOVA-HDFE, which uses sequential linear regressions and builds on recent advances in regression analysis with high-dimensional fixed effects (HDFE). It accommodates both balanced and unbalanced settings with many categorical and continuous covariates, while also allowing for high-dimensional fixed effects. Applying ANOVA-HDFE to bilateral trade flows, we find that 60% of the variation is at the country or country-time level. Moreover, a substantial proportion of the pair-specific variation remains unexplained by standard trade cost proxy variables.