(Frisch-Waugh-Lovell)': On the Estimation of Regression Models by Row

Abstract: We demonstrate that regression models can be estimated by working independently in a row-wise fashion. We document a simple procedure which allows for a wide class of econometric estimators to be implemented cumulatively, where, in the limit, estimators can be produced without ever storing more than a single line of data in a computer's memory. This result is useful in understanding the mechanics of many common regression models. These procedures can be used to speed up the computation of estimates computed via OLS, IV, Ridge regression, LASSO, Elastic Net, and Non-linear models including probit and logit, with all common modes of inference. This has implications for estimation and inference with `big data', where memory constraints may imply that working with all data at once is particularly costly. We additionally show that even with moderately sized datasets, this method can reduce computation time compared with traditional estimation routines.