We develop Bayesian neural networks (BNNs) that permit to model generic nonlinearities and time variation for (possibly large sets of) macroeconomic and financial variables. From a methodological point of view, we allow for a general specification of networks that can be applied to either dense or sparse datasets, and combines various activation functions, a possibly very large number of neurons, and stochastic volatility (SV) for the error term. From a computational point of view, we develop fast and efficient estimation algorithms for the general BNNs we introduce. From an empirical point of view, we show both with simulated data and with a set of common macro and financial applications that our BNNs can be of practical use, particularly so for observations in the tails of the cross-sectional or time series distributions of the target variables, which makes the method particularly informative for policy making in uncommon times.

翻译：我们开发了贝叶斯神经网络 (BNNs)，允许对宏观经济和金融变量的 (可能是大集合的) 常规非线性和时间变化进行建模。从方法论角度来看，我们允许对网络进行一般规范的规定，可以应用于密集或稀疏数据集，并结合各种激活函数、可能非常多的神经元和误差项的随机波动 (SV)。从计算角度来看，我们为我们引入的一般 BNNs 开发了快速高效的估计算法。从经验角度来看，在模拟数据和一组常见的宏观和金融应用中，我们展示了我们的 BNNs 可以实际使用，特别是对于目标变量的横截面或时间序列分布的尾部观测，这使得该方法在不寻常的时段的政策制定中特别有用。