All parameters in structural vector autoregressive (SVAR) models are locally identified when the structural shocks are independent and follow non-Gaussian distributions. Unfortunately, standard inference methods that exploit such features of the data for identification fail to yield correct coverage for structural functions of the model parameters when deviations from Gaussianity are small. To this extent, we propose a robust semi-parametric approach to conduct hypothesis tests and construct confidence sets for structural functions in SVAR models. The methodology fully exploits non-Gaussianity when it is present, but yields correct size / coverage regardless of the distance to the Gaussian distribution. Empirically we revisit two macroeconomic SVAR studies where we document mixed results. For the oil price model of Kilian and Murphy (2012) we find that non-Gaussianity can robustly identify reasonable confidence sets, whereas for the labour supply-demand model of Baumeister and Hamilton (2015) this is not the case. Moreover, these exercises highlight the importance of using weak identification robust methods to assess estimation uncertainty when using 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 finite sample properties of the methodology are illustrated in a large simulation study and an empirical study for production function estimation.
This paper considers hypothesis testing problems in semiparametric models which may be non-regular for certain values of a potentially infinite dimensional nuisance parameter. I establish that, under mild regularity conditions, tests based on the efficient score function provide locally uniform size control and enjoy maximin optimality properties. This approach is applicable to situations with (i) identification failures, (ii) boundary problems and (iii) distortions induced by the use of regularised estimators. Full details are worked out for two examples: a single index model where the link function may be relatively flat and a linear simultaneous equations model that is (weakly) identified by non-Gaussian errors. In practice the tests are easy to implement and rely on χ2 critical values.