# Bayesian Neural Networks for Macroeconomic Analysis

arXiv: https://arxiv.org/abs/2211.04752 · HTML: https://mlsanity.com/paper/2211.04752/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 91 references that are in the map.
- First posted on arXiv 9 Nov 2022.

## Builds on (most cited first, 18 of 18)

- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Financial Time Series Forecasting with Deep Learning : A Systematic Literature Review: 2005-2019](https://mlsanity.com/paper/1911.13288/) (2019)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [Learning Activation Functions to Improve Deep Neural Networks](https://mlsanity.com/paper/1412.6830/) (2014)
- [Deep Neural Networks for Estimation and Inference](https://mlsanity.com/paper/1809.09953/) (2018)
- [Model Selection in Bayesian Neural Networks via Horseshoe Priors](https://mlsanity.com/paper/1705.10388/) (2017)
- [Posterior Concentration for Sparse Deep Learning](https://mlsanity.com/paper/1803.09138/) (2018)
- [An Experimental Review on Deep Learning Architectures for Time Series Forecasting](https://mlsanity.com/paper/2103.12057/) (2021)
- [The Macroeconomy as a Random Forest](https://mlsanity.com/paper/2006.12724/) (2020)
- [Uncertainty Quantification for Sparse Deep Learning](https://mlsanity.com/paper/2002.11815/) (2020)
- [Nowcasting in a Pandemic using Non-Parametric Mixed Frequency VARs](https://mlsanity.com/paper/2008.12706/) (2020)
- [Ancillarity-Sufficiency Interweaving Strategy (ASIS) for Boosting MCMC Estimation of Stochastic Volatility Models](https://mlsanity.com/paper/1706.05280/) (2017)
- [A Statistical Recurrent Stochastic Volatility Model for Stock Markets](https://mlsanity.com/paper/1906.02884/) (2019)
- [Variable Prioritization in Nonlinear Black Box Methods: A Genetic Association Case Study](https://mlsanity.com/paper/1801.07318/) (2018)

## Built on by (most cited first, 3 of 3)

- [From Reactive to Proactive Volatility Modeling with Hemisphere Neural Networks](https://mlsanity.com/paper/2311.16333/) (2023)
- [Non-linear dimension reduction in factor-augmented vector autoregressions](https://mlsanity.com/paper/2309.04821/) (2023)
- [Macroeconomic Forecasting and Machine Learning](https://mlsanity.com/paper/2510.11008/) (2025)

## Abstract (arXiv)

Macroeconomic data is characterized by a limited number of observations (small T), many time series (big K) but also by featuring temporal dependence. Neural networks, by contrast, are designed for datasets with millions of observations and covariates. In this paper, we develop Bayesian neural networks (BNNs) that are well-suited for handling datasets commonly used for macroeconomic analysis in policy institutions. Our approach avoids extensive specification searches through a novel mixture specification for the activation function that appropriately selects the form of nonlinearities. Shrinkage priors are used to prune the network and force irrelevant neurons to zero. To cope with heteroskedasticity, the BNN is augmented with a stochastic volatility model for the error term. We illustrate how the model can be used in a policy institution by first showing that our different BNNs produce precise density forecasts, typically better than those from other machine learning methods. Finally, we showcase how our model can be used to recover nonlinearities in the reaction of macroeconomic aggregates to financial shocks.