  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.
