Higher-order Moment Inequality Restrictions for SVARs 
Macroeconomic and financial fluctuations are often characterized by large shocks that have adverse macroeconomic consequences. This paper proposes to exploit this feature of the data to identify the effects of unobserved structural shocks. It introduces a new method that complements the second-order moment restrictions that are popular in the structural vector autoregression (SVAR) literature with higher-order moment properties of those shocks. More specifically, the method requires that large structural shocks occur relatively frequently so that their distribution is fat-tailed, and/or it requires that these large shocks lead more frequently to negative macroeconomic outcomes so that their distribution is skewed. The authors apply this identification method to three empirical issues: the effect of monetary policy on output and inflation, the macroeconomic impact of sovereign risk shocks in the euro area, and the impact of geopolitical risk on the US economy.
Key Findings
- An application of the method introduced in this paper illustrates how, in both large and small sample settings, higher-order moment restrictions considerably narrow the identification of the effects of monetary policy shocks compared with the results obtained using minimal sign restrictions, which are typically used in the SVAR literature.
- In particular, while the impact of monetary policy shocks on output has been found non-significant with identification methods involving minimal sign restrictions only, results show that a monetary policy tightening induces a significant output contraction when these minimal sign restrictions are combined with higher-moment inequality restrictions.
- An increase in sovereign risk leads to an immediate tightening of credit conditions as well as a contraction of output on impact and for the next two to three years. The effects on euro-area unemployment are also severe and last even longer. By contrast, the macroeconomic impact of the sovereign shocks is non-significant when the identification method relies on sign restrictions.
- An increase in geopolitical risk contracts investment, leading to a persistent tightening of US financial conditions. Importantly, an identification method that involves sign restrictions alone produces imprecise and statistically non-significant estimated macroeconomic effects of geopolitical risk shocks.
Implications
The method introduced in this paper illustrates how exploiting higher-order moment properties can be used to considerably narrow the identification of the effects structural shocks compared with the results obtained using minimal sign restrictions, which are typically used in the SVAR literature.
Abstract
We introduce a method that exploits some non-Gaussian features of structural shocks to identify structural vector autoregression (SVAR) models. More specifically, we propose combining inequality restrictions on the higher-order moments of the structural shocks of interest with other set-identifying constraints, typically sign restrictions. We illustrate how, in both large and small sample settings, higher-order moment restrictions considerably narrow the identification of monetary policy shocks compared with what is obtained with minimal sign restrictions typically used in the SVAR literature. The proposed methodology also provides new insights into the macroeconomic effects of sovereign risk in the euro area as well as the transmission of geopolitical risk to the US economy.