Robust Econometrics for Growth-at-Risk

Abstract

The Growth-at-Risk (GaR) framework has garnered attention in recent econometric literature, yet current approaches implicitly assume a constant Pareto exponent. We introduce novel and robust econometrics to estimate the tails of GaR based on a rigorous theoretical framework and establish validity and effectiveness. Simulations demonstrate consistent outperformance relative to existing alternatives in terms of predictive accuracy. We perform a long-term GaR analysis that provides accurate and insightful predictions, effectively capturing financial anomalies better than current methods.

Figures (11)

• Figure 1: Simulation results comparing the performance of the proposed method (in black) and the existing method (in gray) for quarter-ahead predictions of growths. The predictions are conditional on the average values of $(X_{t1},X_{t2})= x_0 :=(2.732,0.007)$. The upper panels present results for the upper tail ($\tau \in \{0.95,0.96,0.97,098,0.99\}$), while the lower panels show results for the lower tail ($\tau \in \{0.01,0.02,0.03,0.04,0.05\}$). Dots represent simulation averages, bars represent the Gaussian interquartile ranges, and triangles denote the true values. The left column illustrates results for $T=250$, and the right column illustrates results for $T=500$. The results are based on 2,500 Monte Carlo iterations.
• Figure 2: Simulation results comparing the performance of the proposed method (in black) and the existing method (in gray) for year-ahead predictions of growths. The predictions are conditional on the average values $(X_{t1},X_{t2})=x_0 :=(2.761,0.018)$. The upper panels present results for the upper tail ($\tau \in \{0.95,0.96,0.97,098,0.99\}$), while the lower panels show results for the lower tail ($\tau \in \{0.01,0.02,0.03,0.04,0.05\}$). Dots represent simulation averages, bars represent the Gaussian interquartile ranges, and triangles denote the true values. The left column illustrates results for $T=250$, and the right column illustrates results for $T=500$. The results are based on 2,500 Monte Carlo iterations.
• Figure 3: Simulation results comparing the performance of the proposed method (in black) and the existing method (in gray) for the expected shortfall $SF_{Y_{t+h}|X_t}(\pi|x_0)$ (left) and the expected longrise $LR_{Y_{t+h}|X_t}(\pi|x_0)$ (right) for $\pi=0.05$. The upper panels present results for quarter-ahead predictions, while the lower panels show results for year-ahead predictions. The predictions are conditional on the average values of $(X_{t1},X_{t2})=x_0 :=(2.732,0.007)$ for the upper panels and $(X_{t1},X_{t2})=x_0 :=(2.761,0.018)$ for the lower panels. Dots represent simulation averages, bars represent the Gaussian interquartile ranges, and the dashed horizontal lines denote the true values. The results are displayed for each of the sample sizes $T=\{250,500,750\}$. The results are based on 2,500 Monte Carlo iterations.
• Figure 4: Out-of-sample predictions of the 5th and 95th percentiles of the real GDP growth rate between 1895Q1 and 2016Q4 based on the 'Old' method (top) and the 'New' method (bottom), with the prediction ranges indicated by the shares. The black lines indicate the actual real GDP growth rates.
• Figure 5: Lower tails of the PDFs of predicted real GDP growth rates, conditional on a current-year real GDP growth rate equal to the historical median. The top panel presents the distribution under the "normal year" scenario, where the current-year Financial Conditions Index (FCI) equals its historical median. The bottom panel presents the distribution under the "crisis year" scenario, where the FCI equals its 2008Q4 level. In each panel, the dotted line corresponds to predictions from the 'Old' method, and the solid line corresponds to the 'New' method. Vertical line segments indicate the 5th percentiles of the predicted real GDP growth distributions. All predictions are based on the full time series from 1880 to 2020.

Theorems & Definitions (3)

• Proposition 1
• Proposition 2
• Theorem 3