Karin Klieber

Philippe Goulet Coulombe, Mikael Frenette, Karin Klieber

We reinvigorate maximum likelihood estimation (MLE) for macroeconomic density forecasting through a novel neural network architecture with dedicated mean and variance hemispheres. Our architecture features several key ingredients making MLE work in this context. First, the hemispheres share a common core at the entrance of the network which accommodates for various forms of time variation in the error variance. Second, we introduce a volatility emphasis constraint that breaks mean/variance indeterminacy in this class of overparametrized nonlinear models. Third, we conduct a blocked out-of-bag reality check to curb overfitting in both conditional moments. Fourth, the algorithm utilizes standard deep learning software and thus handles large data sets - both computationally and statistically. Ergo, our Hemisphere Neural Network (HNN) provides proactive volatility forecasts based on leading indicators when it can, and reactive volatility based on the magnitude of previous prediction errors when it must. We evaluate point and density forecasts with an extensive out-of-sample experiment and benchmark against a suite of models ranging from classics to more modern machine learning-based offerings. In all cases, HNN fares well by consistently providing accurate mean/variance forecasts for all targets and horizons. Studying the resulting volatility paths reveals its versatility, while probabilistic forecasting evaluation metrics showcase its enviable reliability. Finally, we also demonstrate how this machinery can be merged with other structured deep learning models by revisiting Goulet Coulombe (2022)'s Neural Phillips Curve.

Philippe Goulet Coulombe, Maximilian Goebel, Karin Klieber

Machine learning predictions are typically interpreted as the sum of contributions of predictors. Yet, each out-of-sample prediction can also be expressed as a linear combination of in-sample values of the predicted variable, with weights corresponding to pairwise proximity scores between current and past economic events. While this dual route leads nowhere in some contexts (e.g., large cross-sectional datasets), it provides sparser interpretations in settings with many regressors and little training data-like macroeconomic forecasting. In this case, the sequence of contributions can be visualized as a time series, allowing analysts to explain predictions as quantifiable combinations of historical analogies. Moreover, the weights can be viewed as those of a data portfolio, inspiring new diagnostic measures such as forecast concentration, short position, and turnover. We show how weights can be retrieved seamlessly for (kernel) ridge regression, random forest, boosted trees, and neural networks. Then, we apply these tools to analyze post-pandemic forecasts of inflation, GDP growth, and recession probabilities. In all cases, the approach opens the black box from a new angle and demonstrates how machine learning models leverage history partly repeating itself.