Constructing density forecasts from quantile regressions: multimodality in macro-financial dynamics

Abstract

Quantile regression methods are increasingly used to forecast tail risks and uncertainties in macroeconomic outcomes. This paper reconsiders how to construct predictive densities from quantile regressions. We compare a popular two-step approach that fits a specific parametric density to the quantile forecasts with a nonparametric alternative that lets the "data speak." Simulation evidence and an application revisiting GDP growth uncertainties in the US demonstrate the flexibility of the nonparametric approach when constructing density forecasts from both frequentist and Bayesian quantile regressions. They identify its ability to unmask deviations from symmetrical and unimodal densities. The dominant macroeconomic narrative becomes one of the evolution, over the business cycle, of multimodalities rather than asymmetries in the predictive distribution of GDP growth when conditioned on financial conditions.

The distributional predictive content of measures of inflation expectations

“…Second, to acknowledge that there is no reason to assume that the predictive density for inflation is skewed-t, we follow Mitchell et al (2022) and construct the density forecast from the 19 quantile forecasts (τ = 0.05, 0.1, ..., 0.95) nonparametrically. To contrast the ABG densities, we label these densities "NP" (nonparametric).…”

“…Each panel the average tail-weighted CRPS. Results given for the density forecasts constructed using the QR method of ABG, the nonparametric (NP) QR method of Mitchell et al (2022), and assuming a linear Gaussian relationship (labeled "OLS/Normal"). "Combined" involves combining, by quantile, the different agents' expectations and then constructing the density forecast from the combined quantile forecasts.…”

“…Regions where the line is colored green indicate that gains (or losses), at the given quantile, are statistically significant at the 10 percent level, as judged by a Diebold and Mariano (1995) and West-type (1996) reports the average tail-weighted CRPS. Results given for the density forecasts constructed using the QR method of ABG, the nonparametric (NP) QR method of Mitchell et al (2022), and assuming a linear Gaussian relationship (labeled "OLS/Normal"). "Combined" involves combining, by quantile, the different agents' expectations and then constructing the density forecast from the combined quantile forecasts.…”