  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.

Econometrics;Machine Learning