Philippe Goulet Coulombe, Maximilian Goebel, Karin Klieber
arXiv 17 Dec 2024 · Econometrics · 4 citations (OpenAlex)
arXiv:2412.13076 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Goulet Coulombe, P (2024) A neural phillips curve and a deep output gap | 0.909 | 8 | 4 | 75% |
| 2 | Geertsema, P. and Lu, H (2023) Instance-based Explanations for Gradient Boosting Machine Predictions with AXIL Weights | 0.874 | 7 | 2 | 100% |
| 3 | Goulet Coulombe, P (2024) The macroeconomy as a random forest | 0.811 | 4 | 2 | 100% |
| 4 | Ghorbani, A. and Zou, J (2019) Data shapley: Equitable valuation of data for machine learning | 0.737 | 3 | 2 | 100% |
| 5 | Koster, N. and Krüger, F (2024) Simplifying random forests' probabilistic forecasts | 0.737 | 3 | 2 | 100% |
| 6 | McCracken, M. W. and Ng, S (2016) Fred-md: A monthly database for macroeconomic research | 0.737 | 3 | 2 | 100% |
| 7 | Buckmann, M. and Joseph, A (2023) An interpretable machine learning workflow with an application to economic forecasting | 0.644 | 2 | 2 | 100% |
| 8 | Dendramis, Y., Kapetanios, G., and Marcellino, M (2020) A similarity-based approach for macroeconomic forecasting | 0.644 | 2 | 2 | 100% |
| 9 | Foroni, C., Marcellino, M., and Stevanovic, D (2022) Forecasting the covid-19 recession and recovery: Lessons from the financial crisis | 0.644 | 2 | 2 | 100% |
| 10 | Lin, Y. and Jeon, Y (2006) Random forests and adaptive nearest neighbors | 0.644 | 2 | 2 | 100% |
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