Existing methods that assume non-Gaussian distributions to identify parameters and conduct inference in SVAR models work poorly when the deviations from Gaussianity are small. In particular, confidence bands for the impulse responses suffer from coverage distortions. We propose a robust and efficient semi-parametric approach to conduct hypothesis tests and compute confidence bands in the SVAR model. The method exploits non-Gaussianity when it is present, but yields correct coverage regardless of the distance to the Gaussian distribution. We evaluate the method in a simulation study and revisit several empirical studies to highlight the practical relevance of our methodology and the limitations of assuming non-Gaussianity for identification.

All parameters in linear simultaneous equations models can be identified (up to permutation and scale) if the underlying structural shocks are independent and if at most one of them is Gaussian. Unfortunately, existing inference methods that exploit such a non-Gaussian identifying assumption suffer from size distortions when the true shocks are close to Gaussian. To address this weak non-Gaussian problem, we develop a robust semi-parametric inference method that yields valid confidence intervals for the structural parameters of interest regardless of the distance to Gaussianity. We treat the densities of the structural shocks non-parametrically and construct identification robust tests based on the efficient score function. The approach is shown to be applicable for a broad class of linear simultaneous equations models in cross-sectional and panel data settings. A simulation study and an empirical study for production function estimation highlight the practical relevance of the methodology.