Capturing Macroeconomic Tail Risks with Bayesian Vector Autoregressions

Abstract

A rapidly growing body of research has examined tail risks in macroeconomic outcomes. Most of this work has focused on the risks of significant declines in GDP, and it has relied on quantile regression methods to estimate tail risks. Although much of this work discusses asymmetries in conditional predictive distributions, the analysis often focuses on evidence of downside risk varying more than upside risk. We note that this pattern in risk estimates over time could obtain with conditional distributions that are symmetric but subject to simultaneous shifts in conditional means (down) and variances (up). Building on that insight, we examine the ability of Bayesian VARs with stochastic volatility to capture tail risks in macroeconomic forecast distributions and outcomes. We consider both a conventional stochastic volatility specification and a specification with a common factor in volatility that enters the VAR's conditional mean. Even though the one-step-ahead conditional predictive distributions from the conventional stochastic volatility specification are symmetric, the model estimates yield more time variation in downside risk as compared to upside risk. Results from the model that includes a volatility factor in the conditional mean and thereby allows for asymmetries in conditional distributions are very similar. Our paper also extends the recent literature by formally evaluating the accuracy of tail risk forecasts and assessing the performance of Bayesian quantile regression, as well as our Bayesian VARs, in this context. Overall, the BVAR models perform comparably to quantile regression for estimating and forecasting tail risks, complementing BVARs' established performance for forecasting and structural analysis.

Constructing Density Forecasts from Quantile Regressions: Multimodality in Macro-Financial Dynamics

“…In particular, we note how the evidence for or against skewness in GDP growth varies over time. This is consistent with Carriero et al (2020a), who find, using alternative tests, weak evidence for skewness. Figure 6, in particular, shows that NP(freq) points to less negative skewness during the period of the global financial crisis.…”

“…A large literature, of course, considers the production of density forecasts using other methods; see Aastveit et al (2019) for a review. A literature has also grown up, in response to ABG, on the production of GaR and density forecasts using both parametric and nonparametric alternatives to QR; for example, see Carriero et al (2020a), Caldara et al (2021), Plagborg-Moller et al (2020), De Polis et al (2020), and Adrian et al (2021). By contrast, we deliberately stick to the QR models of ABG.…”

“…They found that deteriorating financial conditions, as captured by the Chicago Fed's National Financial Conditions Index (NFCI), have an asymmetric effect on GDP growth.8 In particular, they link GDP growth tail risks to poor financial conditions. Recessions are associated with left-skewed conditional forecast densities Carriero et al (2020a). challenge this view, noting that ABG's empirical finding that downside risk varies more than upside risk could equally well be explained by symmetric conditional forecast densities as by asymmetric unconditional forecast densities.…”

“…On the use of QR methods to produce density nowcasts and forecasts, see e.g.,Gaglianone and Lima (2012),Gaglianone and Lima (2014),Manzan and Zerom (2013),Manzan (2015),Korobilis (2017),Ferrara et al (2022),Chen et al (2021), andMitchell et al (2022). On the more specific but connected issue of the assessment of tail risks using QRs, see e.g.,Giglio et al (2016),Ghysels et al (2018),Adrian et al (2019),Carriero et al (2020a),Carriero et al (2020b),Reichlin et al (2020),Brownlees andSouza (2021), andFigueres andJarocinski (2020).…”

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

“…In an application to US GDP growth, we find that use of this nonparametric approach matches or slightly improves upon the 1 On the use of QR methods to produce density nowcasts and forecasts, see, e.g., Gaglianone and Lima (2012), Manzan and Zerom (2013), Gaglianone and Lima (2014), Manzan (2015), Korobilis (2017), Chen et al (2021), Ferrara et al (2022), and Mitchell et al (2022). On the more specific but connected issue of the assessment of tail risks using QRs, see, e.g., Giglio et al (2016), Ghysels et al (2018), Adrian et al (2019), Figueres and Jarocinski (2020), Reichlin et al (2020), Brownlees and Souza (2021), Carriero et al (2022), and Carriero et al (2023).…”