Inference in Structural Vector Autoregressions identified with an external instrument

This paper studies Structural Vector Autoregressions in which a structural shock of interest (e.g., an oil supply shock) is identified using an external instrument. The external instrument is taken to be correlated with the target shock (the instrument is relevant) and to be uncorrelated with other shocks of the model (the instrument is exogenous). The potential weak correlation between the external instrument and the target structural shock compromises the large-sample validity of standard inference. We suggest a confidence set for impulse response coefficients that is not affected by the instrument strength (i.e., is weak-instrument robust) and asymptotically coincides with the standard confidence set when the instrument is strong.