Two Recursive Frisch-Waugh-Lovell Algorithms and Applications in Representing Bias with Multiple Omitted Variables

The Frisch-Waugh-Lovell (FWL) theorem is a foundational result in the interpretation of regression coefficients estimated by ordinary least squares, and is ubiquitous in econometrics education. In this thesis I present two recursive FWL algorithms, implement both in Python, and study their applications in representing bias with multiple omitted variables. I find that one of the algorithms, recursive FWL decompositions, can be used to obtain an expression of bias with multiple omitted variables that is equivalent to the standard result. By breaking the omitted variable bias result into smaller terms that then simplify into the standard result, the recursive decompositions approach provides a more granular perspective on the form of omitted variable bias.