Identification Based on Higher Moments in Macroeconometrics

In the last two decades, identification based on higher moments has attracted increasing theoretical attention and been widely adopted in empirical practice in macroeconometrics. This article reviews two parallel strands of the literature. The first is identification strategies based on heteroskedasticity of the structural shocks, which can provide additional covariance equations. The second exploits non-Gaussianity more generally of the structural shocks for identification, generally under the assumption of independence, based on the mature independent components analysis literature. I describe in detail the seminal identification results and discuss recent extensions. For each scheme, I describe parametric and nonparametric implementations and highlight prominent empirical applications. I also discuss key issues for the adoption of such strategies, including weak identification and the interpretability of statistically identified structural shocks. I further outline key areas of ongoing research, such as the blending of multiple sources of identifying information.