Maxime Leroux

Philippe Goulet Coulombe, Maxime Leroux, Dalibor Stevanovic et al.

We move beyond "Is Machine Learning Useful for Macroeconomic Forecasting?" by adding the "how". The current forecasting literature has focused on matching specific variables and horizons with a particularly successful algorithm. In contrast, we study the usefulness of the underlying features driving ML gains over standard macroeconometric methods. We distinguish four so-called features (nonlinearities, regularization, cross-validation and alternative loss function) and study their behavior in both the data-rich and data-poor environments. To do so, we design experiments that allow to identify the "treatment" effects of interest. We conclude that (i) nonlinearity is the true game changer for macroeconomic prediction, (ii) the standard factor model remains the best regularization, (iii) K-fold cross-validation is the best practice and (iv) the $L_2$ is preferred to the $\bar ε$-insensitive in-sample loss. The forecasting gains of nonlinear techniques are associated with high macroeconomic uncertainty, financial stress and housing bubble bursts. This suggests that Machine Learning is useful for macroeconomic forecasting by mostly capturing important nonlinearities that arise in the context of uncertainty and financial frictions.

Philippe Goulet Coulombe, Maxime Leroux, Dalibor Stevanovic et al.

In a low-dimensional linear regression setup, considering linear transformations/combinations of predictors does not alter predictions. However, when the forecasting technology either uses shrinkage or is nonlinear, it does. This is precisely the fabric of the machine learning (ML) macroeconomic forecasting environment. Pre-processing of the data translates to an alteration of the regularization -- explicit or implicit -- embedded in ML algorithms. We review old transformations and propose new ones, then empirically evaluate their merits in a substantial pseudo-out-sample exercise. It is found that traditional factors should almost always be included as predictors and moving average rotations of the data can provide important gains for various forecasting targets. Also, we note that while predicting directly the average growth rate is equivalent to averaging separate horizon forecasts when using OLS-based techniques, the latter can substantially improve on the former when regularization and/or nonparametric nonlinearities are involved.