All parameters in linear simultaneous equations models can be identified (up to permutation and sign) if the underlying structural shocks are independent and at most one of them is Gaussian. Unfortunately, existing inference methods that exploit such identifying assumptions suffer from size distortions when the true distributions of the shocks are close to Gaussian. To address this weak non-Gaussian problem we develop a locally robust semi-parametric inference method which is simple to implement, improves coverage and retains good power properties. The finite sample properties of the methodology are illustrated in a large simulation study and an empirical study for the returns to schooling.
