Nonlinearities in macroeconomic tail risk through the lens of big data quantile regressions

Modeling and predicting extreme movements in GDP is notoriously difficult, and the selection of appropriate covariates and/or possible forms of nonlinearities are key in obtaining precise forecasts. In this paper, our focus is on using large datasets in quantile regression models to forecast the conditional distribution of US GDP growth. To capture possible nonlinearities, we include several nonlinear specifications. The resulting models will be huge dimensional, and we thus rely on a set of shrinkage priors. Since Markov chain Monte Carlo estimation becomes slow in these dimensions, we rely on fast variational Bayes approximations to the posterior distribution of the coefficients and the latent states. We find that our proposed set of models produces precise forecasts. These gains are especially pronounced in the tails. Using Gaussian processes to approximate the nonlinear component of the model further improves the good performance, in particular in the right tail.