  Generalized method of moments estimators based on higher-order moment
conditions derived from independent shocks can be used to identify and estimate
the simultaneous interaction in structural vector autoregressions. This study
highlights two problems that arise when using these estimators in small
samples. First, imprecise estimates of the asymptotically efficient weighting
matrix and the asymptotic variance lead to volatile estimates and inaccurate
inference. Second, many moment conditions lead to a small sample scaling bias
towards innovations with a variance smaller than the normalizing unit variance
assumption. To address the first problem, I propose utilizing the assumption of
independent structural shocks to estimate the efficient weighting matrix and
the variance of the estimator. For the second issue, I propose incorporating a
continuously updated scaling term into the weighting matrix, eliminating the
scaling bias. To demonstrate the effectiveness of these measures, I conducted a
Monte Carlo simulation which shows a significant improvement in the performance
of the estimator.
